Chemical Reaction Engineering--Houston

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Author: Vern W. Weekman | Jr. | Dan Luss

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Chemical Reaction EngineeringHouston

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.


Chemical Reaction EngineeringHouston Vern W . Weekman, Jr.,

EDITOR

Mobil Research and Development Company

Dan Luss,

EDITOR

University of Houston The Fifth International Symposium on Chemical Reaction Engineering co-sponsored by the American Chemical Society, the American Institute of Chemical Engineers, the Canadian Society for Chemical Engineering, and the European Federation of Chemical Engineering, held at the Hyatt Regency Hotel, Houston, T X , March 13-15,

1978.

65

ACS SYMPOSIUM SERIES

AMERICAN

CHEMICAL

SOCIETY

WASHINGTON, D.C. 1978


Library of Congress CIP Data International Symposium on Chemical Reaction Engineering, 5th, Houston, Tex., 1978. Chemical reaction engineering—Houston. (ACS symposium series; 65 ISSN 0097-6156) Bibliography: p. Includes index. 1. Chemical engineering—Congresses. 2. Chemical reactions—Congresses. I. Weekman, Vern W. II. Luss, Dan, 1938III. American Chemical Society. IV American Chemical Society. ACS symposiu TP5.I67 1978 ISBN 0-8412-0401-2

660.2'9'9 77-25340 ACSMC 8 65 1-619 (1978)

Copyright © 1978 American Chemical Society All Rights Reserved. T h e appearance of the code at the bottom of the first page of each article in this volume indicates the copyright owner's consent that reprographic copies of the article may be made for personal or internal use or for the personal or internal use of specific clients. T h i s consent is given o n the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U . S . Copyright Law. T h i s consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating new collective works, for resale, or for information storage and retrieval systems. T h e citation of trade names and/or names of manufacturers i n this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, repro duce, use, or sell any patented invention or copyrighted work that may i n any way be related thereto. PRINTED IN THE UNITED STATES OF AMERICA


ACS Symposium Series Robert F. Gould, Editor

Advisory Board Kenneth B. Bischoff Donald G . Crosby Jeremiah P. Freeman E. Desmond Goddard Jack Halpern Robert A . Hofstader James P. Lodge John L. Margrave Nina I. McClelland John B. Pfeiffer Joseph V . Rodricks F. Sherwood Rowland Alan C. Sartorelli Raymond B. Seymour Roy L. Whistler Aaron Wold


FOREWORD The ACS SYMPOSIU

a medium for publishing symposia quickly in book form. The format of the SERIES parallels that of the continuing ADVANCES IN CHEMISTRY SERIES except that in order to save time the papers are not typeset but are reproduced as they are submitted by the authors in camera-ready form. As a further means of saving time, the papers are not edited or reviewed except by the symposium chairman, who becomes editor of the book. Papers published in the ACS SYMPOSIUM SERIES are original contributions not published elsewhere in whole or major part and include reports of research as well as reviews since symposia may embrace both types of presentation.


PREFACE

has, as in past symposia, provided an excellent forum for reviewing recent accomplishments in theory and application. This international symposium series grew out of the earlier European Symposia on Chemical Reaction Engineering which began in 1957. In 1966, as part of the American Chemical Society Industrial and Engineering Chemistry Division's Summer Symposium series, a meeting was devoted to chemical reaction engineering and kinetics. This meeting highlighted the great interest and activity in this field in the United States, and led the organizers to join with the America European Federation of Chemical Engineers in organizing International Symposia on Chemical Reaction Engineering. The first symposium was held in Washington in 1970 and was followed by symposia in Amsterdam (1972), Chicago (1974), and Heidelberg (1976). These meetings consistently attract experts in the field who have submitted many more papers than can be accommodated. This year was no exception with more than 130 papers being submitted, only 48 of which could be accepted. Again, the international flavor was maintained with more than one-half the papers coming from Western Europe, in addition to one each from Russia, Japan, Australia, and Canada. While industrial participation was not as extensive as anticipated (30% ), it did show clearly the increasing and productive application of Reaction Engineering tools to industrial problems. The meeting format maintained three plenary review lectures each morning and three parallel, original paper sessions in the afternoon. The nine plenary review papers are being published in the American Chemical Society Symposium Series as a separate volume. We acknowledge financial support from the National Science Foundation, American Chemical Society-Petroleum Research Fund, Shell Oil Co., Mobil Oil Corp., and Exxon Co. A

V E R N W . W E E K M A N , JR.

D A N Luss

Mobile Research Corp. Princeton, NJ

University of Houston Houston, T X

October 1977 xi


Organizing Committee for the Fifth International Symposium on Chemica

Vern W . Weekman, Jr., Editor Dan Luss, Editor

Members: Chandler H . Barkelew (Shell Development Co.) K. B. Bischoff (University of Delaware) John B. Butt (Northwestern University) James M. Douglas (University of Massachusetts) Hugh M. Hulburt (Northwestern University) Donald N. Miller (Dupont Co.)

xii In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1 Design and Operation of a Novel Impinging Jet Infrared Cell-Recycle Reactor R.

LEUTE

and I. G .

DALLA

LANA

Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada

In the study of chemisorbed species on catalyst surfaces, the application of infrared spectroscopic methods has developed from the early in situ studies of Eischens and Pliskin [1] to rather detailed surface kinetics measurements [5]. The variety of techniques which have been described [1,2,3,4,5,6,7,8] increase i n their effectiveness with their a b i l i t y to discriminate between the spectra of adsorbed species which are relevant to the reaction mechanism and spectra of spurious adsorbed species. These approaches may be c l a s s i f i e d using this c r i t e r i o n as follows: (i)

I n t r i n s i c Rates/Surface Spectra Transients Measured D i r e c t l y . Under reaction conditions where adsorbed reactants, intermediates, and products display significant IR absorption band i n t e n s i t i e s , the transient intensities may be quantita t i v e l y monitored. Considerable detailed studies are required to correlate these intensities with surface concen trations.

(ii)

Global Rates/Surface Spectra Static or Transient. By carrying out studies i n an IR cell - c i r c u l a t i o n flow reactor, a cause-and-effect r e l a t i o n between reactant concentration and specific band intensities may be discerned. Such mechanistic insights may be useful i n developing more r e l i a b l e forms of rate expressions.

(iii)

Indirect Studies of Adsorption and Surface Reactions. The observation of selected spectral band intensities attributed to chemisorbed species are assumed to be related to the surface reactions involved. I f the spectra are recorded at room temperature, the presence of spurious spectra may occur. Generally, additional experimental evidence is required to demonstrate the relevance of such observations to the kinetics of the c a t a l y t i c reaction.

©

0-8412-0401-2/78/47-065-003$05.00/0


4

CHEMICAL REACTION ENGINEERING—HOUSTON

This paper d e s c r i b e s the development of an improved v e r s i o n of the IR cell-recycle r e a c t o r (type ( i i ) ) which is to be used to study the mechanism and kinetics of r e a c t i o n s of 2-propanol on v a r i o u s alumina c a t a l y s t s . While t h i s r e a c t i o n does not have direct commercial i m p l i c a t i o n s (dehydration or dehydrogenation), it e x h i b i t s many of the characteristics which make it very s u i t a b l e to demonstrate the usefulness of the IR technique. Design Factors The yin AAXU technique i n v o l v e s c a t a l y s t p e l l e t s i n the form of very t h i n wafers, about 40 mg/cm2 alumina content. The h i g h s u r f a c e area, about 4 m^/cm^- of IR beam c r o s s - s e c t i o n , enables s u f f i c i e n t adsorbed species to i n t e r a c t w i t h the IR beam even a t r e l a t i v e l y low s u r f a c e coverage that s p e c t r a w i t h good I n s t u d y i n g s o l i d - c a t a l y z e d gas-phase r e a c t i o n s , the back ground s p e c t r a r e s u l t i n g from the gas-phase are u s u a l l y e l i m i n a t e d by use of a double-beam IR spectrophotometer, i n which the sample c e l l i s matched w i t h an " i d e n t i c a l " reference c e l l without c a t a l y s t i n i t . V a r i a t i o n s i n pressure and/or temperature between sample and reference c e l l s i n c r e a s e the d i f f i c u l t y of matching the two c e l l s . When the c a t a l y s t wafer i s placed t r a n s v e r s e t o the flow of gases through the IR c e l l - r e a c t o r , the flow p a t t e r n s w i t h i n the c e l l l e a d to c o n c e n t r a t i o n gradients along the a x i s of the IR beam, and between the f r o n t and r e a r s u r f a c e concentrations on the wafer. Under r e a c t i o n c o n d i t i o n s , these aspects l i m i t the s e n s i t i v i t y of the technique because of low s u r f a c e coverages a t r e a c t i o n temperatures. The new c e l l attempts t o e l i m i n a t e many of these o b j e c t i o n a b l e f e a t u r e s . Figure l a describes a t y p i c a l geometry f o r previous c e l l designs. I t should be evident that i t i s d i f f i c u l t to o b t a i n values of the i n t r i n s i c r e a c t i o n r a t e because of the uneven c o n t a c t i n g between the gas and wafer a t v a r i o u s p o i n t s on the wafer s u r f a c e . High r e c i r c u l a t i o n r a t e s w i t h i n such a steadys t a t e r e c y c l e r e a c t o r provide d i f f e r e n t i a l values of the r e a c t i o n r a t e , but these g l o b a l values are u n l i k e l y to equal i n t r i n s i c r a t e s ( n e g l e c t i n g , f o r the moment, i n t r a p a r t i c l e d i f f u s i o n ) . C o m p a t i b i l i t y of flow p a t t e r n s between the IR c e l l and an i d e a l continuous s t i r r e d - t a n k r e a c t o r are r e q u i r e d as a minimum c o n d i t i o n . Since the mode of h e a t i n g the wafer l i k e l y i n v o l v e s IR-transparent windows being a t temperatures lower than those of the wafer, compensation f o r temperature gradients may a l s o be required. Figure l b describes the proposed geometry of the improved IR c e l l - r e a c t o r . This r e c y c l e r e a c t o r i s t o be capable of being operated i n e i t h e r open (flow) o r c l o s e d (batch) modes of o p e r a t i o n . The r e a c t o r u n i t i s maintained a t the r e a c t i o n temper ature (up t o 400°C) and the pump and sampling system are maintained at a constant u s u a l l y lower temperature (220°C) t o ensure maximum



Figure 1.

(a)

OLDER TYPE IR REACTOR CELLS

Geometrical arrangement and flow patterns in typical and improved ir cell-reactors

(b)

NEW IR REACTOR C E L L

6


l o n g e v i t y of equipment. F i g u r e 2 d e s c r i b e s the i n f o r m a t i o n flow between the IR spectrophotometer and an IBM/1800 computer system which are i n t e r f a c e d . The s p e c t r a l data are monitored at wave number i n t e r v a l s as low as 0.2 cm over the complete s p e c t r a l scan range of the spectrophotometer (about 700 to 4000 cm"" , corresponding to a maximum of about 16,000 data p o i n t s ) . The "% t r a n s m i s s i o n " versus "wave number" p o i n t s are t r a n s m i t t e d i n d i g i t i z e d form to the computer from a b s o l u t e encoders. At p r e s e n t , the complete s p e c t r a l scan may be monitored and s t o r e d i n a d i s k f i l e and r e t r i e v e d at a l a t e r time. The coupled Model 621 spectrophoto meter w i t h IBM/1800-compatible i n t e r f a c e was purchased some time ago from Perkin-Elmer. The improved c e l l u t i l i z e s axisymmetric j e t s of feed gas impinging upon both s i d e l e n t f i e l d over most of r e a c t i o n r a t e s to approximate i n t r i n s i c r e a c t i o n r a t e s at h i g h f l o w - r a t e s and i n the absence of pore d i f f u s i o n . The new c o n f i g u r a t i o n shown i n F i g u r e 1 i s housed i n an oventype enclosure c o n t r o l l e d at the temperature, T 3 , by i n t e r n a l a i r c i r c u l a t i o n . I n a d d i t i o n to the oven h e a t e r , a second heater about the i n l e t s e c t i o n , packed w i t h g l a s s beads, r a i s e s the c i r c u l a t i n g gas temperature from the reduced temperature i n the pump compart ment to T j . Because of heat l o s s e s from the IR windows, the tem perature d i f f e r e n c e , T - T , could range as h i g h as 50°C This not only changes the d e n s i t y of the f l o w i n g gas but a l s o r e s u l t s i n a c o n s i d e r a b l e d e v i a t i o n of the t r u q temperature of the c a t a l y s t wafer from the measured values T . A d d i t i o n a l heaters p l a c e d around the ends of the two c y l i n d r i c a l s e c t i o n s compensated f o r the window heat l o s s e s . In t h i s way, the temperatures, T and T 3 , could be matched w i t h i n 0.5°C, and the w a l l temperature would be expected to d i f f e r from T (or T3) only i f the c a t a l y t i c r e a c t i o n e x h i b i t e d severe thermal e f f e c t s . With g r e a t l y improved mass t r a n s f e r r a t e s normal to the wafer s u r f a c e , one would a l s o expect from s i m i l a r i t y c o n s i d e r a t i o n s enhanced heat t r a n s f e r between the wafer s u r f a c e and the impinging gas j e t . Such adjustments among the three monitored temperatures enabled the r e f e r e n c e c e l l IR beam to compensate n e a r l y e x a c t l y f o r the sample c e l l gas phase absorption spectra. By changing the c o n f i g u r a t i o n of the two c e l l s i n the sample compartment of the IR spectrophotometer t h i s enables the d e t e r mination of e i t h e r r e c i r c u l a t i n g gas composition or p l o t t i n g of the b a s e l i n e spectrum f o r the c a t a l y s t wafer. With the two c e l l s i n the double-beam mode, the c a t a l y s t b a s e l i n e and surface s p e c t r a are recorded. I f the reference c e l l was p l a c e d i n the sample beam and an a i r gap i n the r e f e r e n c e beam, q u a n t i t a t i v e absorption s p e c t r o scopy was p o s s i b l e . The IR c e l l s thus provide i n f o r m a t i o n l e a d i n g to both r e a c t i o n r a t e s and m e c h a n i s t i c i n s i g h t s concerning adsorbed species at r e a c t i o n c o n d i t i o n s . When used as a r e c i r c u l a t i n g batch r e a c t o r , the spectrophotometer-computer i n t e r f a c e can monitor but not record the "% t r a n s -1

1

3

2

2

2

2


LEAUTE AND DALLA LANA

Infrared Cell-Recycle Reactor

X = Wave Length (abscissa) Y = Transmittance (ordinate) X

I

= analog signal, Wave Length, 5 digits

Y

1

= analog signal, Transmittance, 3 digits

Linear Encoder Shaft Encoder

IR Spectra Source

Encoder Readout/ I nterf ace

Y1 I

~TT X| I

lY I

i_t

X-Y Recorder

Figure 2.

i

l X Display Y Display

Information flow between ir spectrophotometer and digital computer



8

m i s s i o n " at a f i x e d " s p e c t r a l frequency" ( u s u a l l y that of a s p e c i f i e d absorption band). At present, the drum chart on the IR recorder p l o t s the time - absorption band i n t e n s i t y r e l a t i o n c o r responding to t r a n s i e n t r e a c t i o n c o n d i t i o n s . The time constant of the spectrophotometer thermocouple sensor was s u f f i c i e n t l y s m a l l that the t r a n s i e n t r e a c t i o n r a t e s could be recorded. Experimental

Performance

1. Mass Transfer Performance t e s t s were designed to t e s t f o r micromixing or f o r mass t r a n s f e r performance and thus, to f a c i l i t a t e d e f i n i t i o n of the c e l l design s p e c i f i c a t i o n s . L i m i t e d reac t i o n data had been recorded f o r the 2-proposal r e a c t i o n over alumina. Figure 3 summarize were observed i n a protptyp wafer m a t e r i a l . A i r flows between 10 and 50 t/m±n were passed through the c e l l and the corresponding s u b l i m a t i o n r a t e s , mg/min, were recorded. Since the c e l l geometry was h e l d constant f o r a s e r i e s of flow r a t e s and the temperatures were always at room temperature, the coordinates of Figure 3 show the measured s u b l i mation r a t e s versus flow r a t e r a t h e r than Reynolds number. The exponent of the flow parameter (given by the slope of the l i n e ) i s seen to remain n e a r l y constant over a wide range of c o n d i t i o n s v e r i f y i n g that the t u r b u l e n t flow regime i s maintained. The i n f l u e n c e of changing the o r i f i c e s i z e used to create the j e t s , and of the spacing between the o r i f i c e and the wafer upon mass t r a n s f e r r a t e s are a l s o shown. In a d d i t i o n to the above t e s t s w i t h the new design, mass t r a n s f e r r a t e s were a l s o observed f o r c e l l - r e a c t o r s of the o l d type, w i t h wafers p o s i t i o n e d both p a r a l l e l and transverse to flows. These t e s t s suggest t h a t i n such geometries much of the stream bypasses the wafer surface making i t d i f f i c u l t to o b t a i n i n t r i n s i c r a t e s of r e a c t i o n . Furthermore, c o n t a c t i n g of the gas flow w i t h l o c a l i z e d p o r t i o n s of the periphery of the wafer r e s u l t e d i n abnormally h i g h l o c a l mass t r a n s f e r r a t e s . F i g u r e 3 demonstrates that o l d type c e l l designs provide mass t r a n s f e r performance i n f e r i o r to that observed w i t h the impinging j e t s . By c a l c u l a t i n g mass t r a n s f e r c o e f f i c i e n t s from the u s u a l equation f o r the r a t e of s u b l i m a t i o n , gmol/(min)(g c a t a l y s t ) . r

s

=

k

g

a

(C

. surface

-C) o

and using the bulk gas phase c o n c e n t r a t i o n , C =0, and e x t e r n a l area, a=10 cm , some experimental c o e f f i c i e n t s could be compared to values estimated from p u b l i s h e d c o r r e l a t i o n s . Table 1 shows these r e s u l t s . 2


Table 1 Comparison of Mass Transfer C o e f f i c i e n t s (cm/sec) Model Flat plate i n perpendicular flow Sphere of equal area i n a packed bed Experimental wafer, c o n v e n t i o n a l geometry Experimental wafer, new geometry

Flow = 10 l/min 1.3 cm/sec

Flow = 50 l / m i n 2.9 cm/sec

2.1

5.4

1.6

3.0

3.7

9.2

Table 1 and F i g u r e 3 both i l l u s t r a t e the marked s u p e r i o r i t y of the new IR c e l l - r e a c t o r design i n promoting mass t r a n s f e r at the wafer s u r f a c e . However, i t s t i l l remains to be demonstrated t h a t under r e a c t i o n c o n d i t i o n s , i n t r i n s i c r a t e s of r e a c t i o n may be obtained at the flow r a t e s mentioned.



10

2. Mixing W i t h i n C e l l The a n a l y s i s of performance w i t h i n a d i f f e r e n t i a l bed-recycle r e a c t o r i s u s u a l l y compared to t h a t of a continuous s t i r r e d - t a n k r e a c t o r . By operating the r e a c t o r w i t h an i n e r t wafer and by i n t r o d u c i n g a l c o h o l to the feed as a step change i n c o n c e n t r a t i o n , the mixing performance of t h i s r e a c t o r may be compared to t h a t p r e d i c t e d f o r an i d e a l CSTR of comparable volume. Figure 4 i l l u s t r a t e s such a comparison and i n d i c a t e s s u b s t a n t i a l agreement w i t h the i d e a l behaviour. I t may be expected that c h a n n e l l i n g , s t a g n a t i o n of some f l o w , e t c . are absent from the r e c y c l e r e a c t o r w i t h i n the range of performance of the pump. 3. Double-beam Compensation f o r Gas Phase A b s o r p t i o n When r e c o r d i n g IR s p e c t r a at r e a c t i o n temperature, the IR beams are attenuated by the number of molecules i n the beam path. Since the gas phase p o p u l a t i o n i s l i k e l y only one or two orders of magnitude g r e a t e r than th the wafer s u r f a c e , i t i u a t i o n i n the two c e l l s be balanced as w e l l as p o s s i b l e . For example, a pressure drop between the two c e l l s n e c e s s i t a t e s h e a t i n g the upstream c e l l to reduce i t s gas d e n s i t y to that i n the down stream c e l l . S i m i l a r l y , d i f f e r e n c e s i n temperature between the c e l l s must a l s o be compensated. Such inbalances between reference and sample c e l l gas phases r e q u i r e d c a l i b r a t i o n s ^ t o determine the values of T^ r e q u i r e d , f o r a f i x e d value of T (= T3) and given c i r c u l a t i o n r a t e at v a r i o u s i s o p r o p a n o l concentrations i n the gas-phase, to blank out gas phase absorption s p e c t r a . F i g u r e 5 shows how s p e c t r a l bands i n the 1200-1500 cm r e g i o n from gas phase i s o p r o p a n o l can be a l t e r e d be changing T j . Curve B represents n e a r - e x t i n c t i o n of the back ground whereas curves A and B represent under- and over-compensa tion, respectively. 4. Dehydration of 2-Propanol over Alumina The p r e l i m i n a r y measurements of s p e c t r a f o r adsorbed species w i l l be used to i l l u s t r a t e how the mechanism of r e a c t i o n may be c l a r i f i e d . The main f e a t u r e of the IR c e l l - f l o w r e a c t o r i s i t s c a p a b i l i t y of determining s p e c t r a at r e a c t i o n c o n d i t i o n s . Most published work on the dehydration of i s o p r o p a n o l by alumina describes Zn A^Lta s t u d i e s w i t h s p e c t r a recorded w i t h the c e l l at room temperature. Figure 6 r e v e a l s a b s o r p t i o n bands i n s e l e c t e d regions of the spectrum f o r s e v e r a l c o n c e n t r a t i o n l e v e l s of i s o p r o p a n o l vapour. Each curve, A, B, or C, represents a s p e c t r a l scan at steady-state r e a c t i o n c o n d i t i o n s w i t h a l l r e a c t i o n parameters except feed composition of i s o p r o p a n o l being kept constant. I f d i f f e r e n t curves (A, B, and C) r e s u l t , the adsorbed species a s s o c i a t e d w i t h the s p e c t r a are considered to be germane to the r e a c t i o n mechanism. In the event that the s p e c t r a l bands do not change the adsorbed species are considered to be spurious. Subsequently, the r e a c t o r may be operated i n a batch mode and the questionable band moni tored c o n t i n u o u s l y . The f a i l u r e of t h i s band to change w i t h the extent of r e a c t i o n would provide e x t r a support to the view that the band i s a s s o c i a t e d w i t h a by product species not i n v o l v e d i n the dehydration mechanism. 2

-1


LEAUTE AND DALLA LANA


Figure 4. Comparison between ideal CSTR and improved cell-reactor to step change in input concentration


12

CHEMICAL REACTION ENGINEERING—HOUSTON 1

1

1

1

110

1

1

T 2 = 2 8 7 . 8 ° C - A l c o h o l 5.5% A: T1 = 2 2 6 . 5 ° C B: T1=251.5°C C: T1 = 2 7 3 . 5 ° C

100

c | 80 (0

-4

70

60

\J

u 1

1

1500

1400

1

1300

I

I

1200

1100

Frequency, cm"

I

1000

1

Figure 5. Compensation of gas-phase adsorbance between reference and sample cells

Baseline without alcohol Alcohol Partial Pressure = 2.1 cmHg Alcohol Partial Pressure = 3.2 cmHg

Catalyst Weight = 0.151 g Temperature = 246.1°C

Free O H Groups

3800

3600

CH

3

3000

Stretching

2800

Low Frequency Region

1600

Frequency, c m "

1400 1

Figure 6. Steady-state spectral scans for dehydration of isopropanol at reaction conditions


1.

LEAUTE AND DALLA LAN A


13

The s t e a d y - s t a t e s p e c t r a l scans when recorded on the IBM/1000 may be processed. ( i ) t o s u b t r a c t the b a s e l i n e of the c a t a l y s t wafer from each s p e c t r a l scan at v a r y i n g p a r t i a l pressures of the i s o p r o panol; ( i i ) to s u b t r a c t one s p e c t r a l scan at (P - , - ) i from another s p e c t r a l scan a t of the change i n band i n t e n s i t i e s at given band f r e q u e n c i e s . A p r e l i m i n a r y i n t e r p r e t a t i o n of the s p e c t r a shown i n Figure 6 would suggest the f o l l o w i n g o b s e r v a t i o n s . The f r e e h y d r o x y l groups on the surface of alumina p r o g r e s s i v e l y disappear, A to B to C, w i t h i n c r e a s i n g reactant c o n c e n t r a t i o n , i s o p r o p a n o l . This i m p l i e s that the a l c o h o l hydrogen bonds to these hydroxyl s i t e s but i t i s not c l e a r whether the a l c o h o l 0 o r H atom i n i t s h y d r o x y l group i s i n v o l v e d The s t r e t c h i n g v i b r a t i o n panol a l s o d i s p l a y d i r e c t correspondence between t h e i r surface c o n c e n t r a t i o n and that of the i s o p r o p a n o l vapour c o n c e n t r a t i o n . This i n f o r m a t i o n suggests that isopropanol adsorption on y a l u m i n a i n v o l v e s more than one adsorption band, i . e . both hydroxyl and emthyl groups are bonded and l i k e l y to d i f f e r e n t s i t e s on the surface of alumina. In the low frequency r e g i o n , region I r e l a t e s t o carbon chain s k e l e t a l v i b r a t i o n s and r e g i o n I I to symmetrical C-H deformation v i b r a t i o n s i n the methyl group. Both of these observations are i n accord w i t h a m u l t i - s i t e a d s o r p t i o n model. Region I I I shows the s t r e t c h i n g v i b r a t i o n f o r a carboxylate species formed on the s u r f a c e . Since the band i n t e n s i t i e s i n region I I I do not change w i t h i s o p r o p a n o l vapour c o n c e n t r a t i o n , the s p e c t r a are considered i n c i d e n t a l to the r e a c t i o n mechanism. With J C Q a d d i t i o n a l experiments, i t should be p o s s i b l e to d i s t i n g u i s h which surface s i t e s on the alumina are s p e c i f i c a l l y i n v o l v e d and thus t o propose a r e a c t i o n mechanism compatible w i t h such chemical evidence. During the above s p e c t r a l measurements, steady-state r e a c t i o n r a t e s i n the r e c i r c u l a t i o n r e a c t o r were a l s o determined. These r a t e s may then be used to t e s t the k i n e t i c model r e s u l t i n g from observations o f the s p e c t r a of adsorbed s p e c i e s . Comments 1.

11

The use of a " s i n g l e - w a f e r c a t a l y t i c r e c y c l e r e a c t o r system r e q u i r e s s t r i c t a t t e n t i o n to o p e r a t i n g parameters, i f one a s p i r e s to o b t a i n i n t r i n s i c r a t e s of r e a c t i o n . By modifying the flow past the wafer to ensure h i g h l y t u r b u l e n t c o n d i t i o n s on both s i d e s of the wafer, mass t r a n s f e r r a t e s may be more than doubled over those observed i n the o l d design of c e l l s i n which flow i s transverse t o the wafer s u r f a c e . This i n d i c a t e s that the u t i l i z a t i o n of both s i d e s of the wafer i s g r e a t l y improved and that the average mass t r a n s f e r r a t e s are a l s o enhanced.


14


2.

I d e a l mixing (CSTR) i s obtained w i t h the r e c i r c u l a t i n g rates a v a i l a b l e from the bellows pump used to t h i s system. The corresponding residence time d i s t r i b u t i o n f u n c t i o n i s not of value i n the a n a l y s i s of the k i n e t i c s s i n c e i t i s a n t i c i p a t e d that n o n - l i n e a r r a t e expressions w i l l be encountered. The usefulness of a combined I R - k i n e t i c s study i n e s t a b l i s h i n g a more r e l i a b l e k i n e t i c model i s apparent. The processing of such data to a s c e r t a i n which s p e c t r a l bands are s i g n i f i c a n t i s u s u a l l y a very tedious chore. By i n t e r f a c i n g the IR spectrophotometer to a d i g i t a l computer, a number of data processing s i m p l i f i c a t i o n s are e v i d e n t . F u l l use of t h i s s i t u a t i o n has not yet been a t t a i n e d i n t h i s program. Whether or not improved r e s o l u t i o n of minor s p e c t r a l bands r e s u l t s from an o n l i n e computer f a c i l i t y s t i l l remains to be demon strated for this reactio The problem of i s o l a t i n r e a c t i o n r a t e s measured i n a single-wafer r e a c t o r appears to have been reduced but not n e c e s s a r i l y s o l v e d . If r e l a t i v e i n t e n s i t i e s of absorption bands e x h i b i t e d by reactants or r e a c t i o n intermediates can be a s c e r t a i n e d as a f u n c t i o n of time, i t may be p o s s i b l e to check r a t e expressions based upon a s i n g l e step being r a t e - c o n t r o l l i n g . Many extensions of t h i s technique (using the new r e a c t o r ) are evident i n the study of c a t a l y t i c k i n e t i c s . Some aspects worth pursuing i n c l u d e : ( i ) a study of pore d i f f u s i o n under c o n t r o l l e d c o n d i t i o n s ; v a r y i n g wafer thickness at constant p o r o s i t y should provide a d i r e c t means of c a l c u l a t i n g the e f f e c t i v e n e s s f a c t o r as a f u n c t i o n of wafer t h i c k n e s s . ( i i ) the r o l e of t r a c e amounts of c a t a l y s t promoters or i n h i b i t o r s may be examined using IR techniques and c o r r e l a t e d d i r e c t l y w i t h steady-state r e a c t i o n r a t e s .

3.

4.

5.

Acknowledgements F i n a n c i a l support of t h i s p r o j e c t by the N a t i o n a l Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8.

Eiechens, R.P., Pliskin, W.A., Advan. Cata., (1957), 9, 662. Heyne, H., Tompkins, F.G., Proc. Roy. Soc., (1966), A292, 460. Baddour, R.F., M o d e l l , M., and Goldsmith, R.L., J . Phys. Chem. (1968), 72, 3621. Dent, A.L., and Kokes, R.J., J . Phys. Chem, (1970), 74, 3653. Tamaru, K., O n i s h i , T., Fukada, K., Noto, Y., Trans. Faraday Cos., (1967), 63, 2300. Thornton, R., Ph.D. t h e s i s , U n i v e r s i t y of Delaware 1973, Shih, Stuart Shan San, Ph.D. t h e s i s , Purdue U n i v e r s i t y , 1975. London, J.W., B e l l , A.T., J . Cat., (1973), 31, 36-109.


2 Performances of Tubular and Loop Reactors in Kinetic Measurements G E R H A R D L U F T , R A I N E R R Ö M E R , and F R I T Z H Ä U S S E R Institut für Chemische Technologie der Technischen Hochschule Darmstadt, 61 Darmstadt, Petersengstrasse 15, West Germany

I n d u s t r i a l reactor terogenous c a t a l y t i s i t i v e i f the reaction conditions or the cooling rates are suddenly changed. They can be operated only i n a small range i n order to avoid damage to the apparatus or to the catalyst by super heating, also to avoid loss i n y i e l d by side reactions, favoured at high tempera tures. In a d d i t i o n , poor accuracy in the rate data, as well as i n the mass and heat transfer parameters,do not allow to calculate the exact concentration and temperature p r o f i l e s inside the reactor. This leads to incorrect p r e d i c t i o n of the reactor's dynamic behaviour. There fore these data should be determined as accurately as possible. For the measurement of reaction rates, d i f f e r e n t i a l reactors having extremely short catalyst beds or i n t e g r a l reactors with r e l a t i v e long catalyst beds are often used. In the f i r s t type of experimental reactor, the concentration and temperature gradients within the catalyst beds are n e g l i g i b l y small. Due to t h i s fact, the reaction rate point data can be measured, provided the small concentration differences can be accurately analyzed. In the i n t e g r a l reactor, the change i n con centration i s much higher. There i s i n general no d i f f i c u l t y analyzing the concentrations of the reacting species but, the reaction rates have to be determined from the concentration curves by c a l c u l a t i o n and cannot often be related to the fast changing temperature. Be cause of these obvious disadvantages, the s o - c a l l e d loop reactors are being used more and more i n k i n e t i c studies. In loop reactors, the extremely small concen t r a t i o n and temperature gradients desired within the short catalyst bed, along with s u f f i c i e n t l y high con centration difference between the reactor i n l e t and the ©

0-8412-0401-2/78/47-065-015$05.00/0


CHEMICAL REACTION ENGINEERING—HOUSTO^

Integral Tubular Reactor

Loop Reactor Figure 1.

Differential Reactor

Stirred-Tank Reactor Types of laboratory reactors


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LUFT ET AL.

Tubular and Loop Reactors

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o u t l e t , can be r e a l i z e d by r e c y c l i n g a p a r t o f t h e react i o n products. In o r d e r t o see how t h e s e advantages c o u l d be r e a l i zed i n p r a c t i c e , t h e performance o f a l o o p r e a c t o r was compared w i t h t h a t o f a c o n v e n t i o n a l l y - b u i l t i n t e g r a l r e a c t o r . I n t h i s comparison t h e c a p a b i l i t y t o handle a c t u a l i n d u s t r i a l c a t a l y s t s , t h e s e t t l i n g time o f changing experimental c o n d i t i o n s , the d i f f i c u l t y of the m a t h e m a t i c a l e v a l u a t i o n o f t h e measured d a t a were cons i d e r e d . The a c c u r a c y o f t h e d a t a s f o r s c a l e up p r o b lems was checked i n a p i l o t p l a n t . F o r t h e r e a c t i o n , the o x i d a t i o n o f o-xylene w i t h a vanadiumpentoxide c a t a l y s t , an i n d u s t r i a l l y important p r o c e s s , was chosen. Apparatus The d e s i g n o f t h changes i n t h e r e a c t i o r e , c o n c e n t r a t i o n and throughput i n a wide range. I t s core i s a d i f f e r e n t i a l r e a c t o r d i r e c t l y c o u p l e d t o t h e blower. I t sucks t h e r e a c t a n t s through t h e c a t a l y s t bed and r e c y c l e s p a r t o f i t . T h i s d e s i g n a l l o w s o n l y a s m a l l dead volume and a s m a l l p r e s s u r e drop a c r o s s t h e c a t a l y s t bed even a t h i g h f l o w r a t e s . F u r t h e r m o r e , t h e whole a p p a r a t u s i s compact and t h e r e f o r e i t can e a s i l y be m a i n t a i n e d a t c o n s t a n t temperature. The s m a l l temp e r a t u r e and c o n c e n t r a t i o n g r a d i e n t s w i t h i n t h e catalyst bed, n e c e s s a r y f o r t h e k i n e t i c measurements, can^be r e a l i z e d by r e c y c l i n g p a r t o f t h e gas about 12 m /h. I t i s v e r y l a r g e compared t o t h e feed and c o r r e s p o n d s t o r e c y c l e r a t i o s o f l o o t o 5oo, a l s o s u f f i c i e n t f o r t h e a p p r o p r i a t e study o f highly-exothermic reactions. The r e c y c l e r a t i o can be changed w i t h r e s p e c t t o t h e r e a c t i o n c o n d i t i o n s by changing t h e speed o f r o t a t i o n o f t h e blower. The blower i s d r i v e n by an asynchronousmotor whose r o t o r i s f i x e d t o t h e s h a f t o f t h e blower. I t i s separ a t e d from t h e s t a t o r by means o f a p r e s s u r e tube i n o r d e r t o e x c l u d e any l e a k a g e . The i n t e g r a l a p p a r a t u s ( F i g . 3) c o n s i s t s o f a tubul a r r e a c t o r o f 1 m-length. In o r d e r t o measure t h e conc e n t r a t i o n , about 2o sampling t a p s a r e i n s t a l l e d a l o n g the tube. Through each sampling t a p , a thermocouple i s passed t o determine t h e temperature p r o f i l e . The a i r i s f e d through d r i e r s , f l o w meters and h e a t e r s b e f o r e e n t e r i n g v a p o r i z e r , where x y l e n e i s e v a p o r a t e d . T h i s a i r - x y l e n e m i x t u r e , c o n t a i n i n g about o.9 i:ol% x y l e n e , i s f e d t o t h e t o p o f t h e t u b u l a r r e a c t o r . The p h t h a l i c a n h y d r i d e , l e a v i n g t h e r e a c t o r i s washed and condensed by water i n a s p r a y tower. The r e a c t i o n heat i s removed by an e f f i c i e n t c o o l i n g system i n which d i p h e n y l (Dow therm) i s v a p o r i z e d .


18


Figure 2.

Loop reactor


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LUFT ET AL.

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Loop Reactors

j 1 2 3 4 5 6 7

Figure 3.

Xylene storage Filter Metering pump Reactor Spray absorber Vaporizer Air pre heater

8 9 10 11 12 13

Rotameter Adsorber - Dryer Air regulater Savety switch Filter

Tubular reactor for the oxidation of xylene


20


R e s u l t s and e v a l u a t i o n The measurements i n b o t h r e a c t o r s were c a r r i e d out at steady s t a t e . The c a t a l y s t a c t i v i t y was m a i n t a i n e d at a l l times, t e s t i n g a t r e g u l a r i n t e r v a l s f o r any l o s s in activity. The r e s u l t s o f a t y p i c a l experiment a r e shown i n F i g . 4 . The c o n c e n t r a t i o n o f t h e r e a c t a n t s i s p l o t t e d v e r s u s a m o d i f i e d r e s i d e n c e time. The r e s i d e n c e time c o u l d be v a r i e d a l o n g t h e range l - l o g.h/mole by changing t h e throughput and t h e q u a n t i t i y o f c a t a l y s t . The temperature was k e p t c o n s t a n t a t 41o°C. The x y l e n e c o n c e n t r a t i o n i n t h e feed c o u l d be i n c r e a s e d up t o 1 , 3 mol %, which i s h i g h e r than the lower e x p l o s i o n l i m i t . As i t can be seen from t h e c u r v e s , t h e concent r a t i o n of the xylen increasing residenc r e a c t i o n product p h t h a l i c a n h y d r i d e (PSA) i n c r e a s e s f i r s t , then d e c r e a s e s a t h i g h r e s i d e n c e t i m e s due t o i t * o x i d a t i o n forming CO and C G . A l s o t h e c o n c e n t r a t i o n ofth intermediate products tolualdehyde (TCL) and p h t h a l i d e (PI) which a r e c o n s i d e r e d t o g e t h e r f o r s i m p l i c i t y , pass through a maximum. In t h e i n t e g r a l r e a c t o r , t h e e x p e r i m e n t s c o u l d not be c a r r i e d out i s o t h e r m a l l y ( F i g . 5 ) . The temperature ( l e f t ordinate) r i s e s s t e e p l y i n the f i r s t part of the c a t a l y s t bed, p a s s e s through a d i s t i n c t maximum and dec r e a s e s a g a i n by the c o o l i n g . The x y l e n e i s almost c o m p l e t e l y c o n v e r t e d . The concent r a t i o n o f t h e PSA i n c r e a s e s a t f i r s t s t e e p l y , then t e n d s t o l e v e l o f f i n t h e lower p a r t o f t h e r e a c t o r . Carbonmonoxide (CO) and c a r b o n d i o x i d e as w e l l as malei c a n h y d r i d e which was d e t e c t e d a t a low c o n c e n t r a t i o n , i n c r e a s e s t e a d i l y a l o n g the c a t a l y s t bed whereas t h e curve o f t o l u a l d e h y d e and p h t h a l i d e show a maximum s i m i l a r t o t h e loop r e a c t o r e x p e r i m e n t s . The e v a l u a t i o n o f t h e e x p e r i m e n t s i n both r e a c t o r s was based on t h e mechanism o f t h e o x i d a t i o n . The conc e n t r a t i o n p r o f i l e s measured i n t h e i n t e g r a l r e a c t o r , as w e l l as t h e f i n i t e s l o p e i n t h e o r i g i n o f t h e conc e n t r a t i o n - r e s i d e n c e time c u r v e s from t h e loop r e a c t o r , r e v e a l t h a t , t h e x y l e n e i s c o n v e r t e d by s i m u l t a n e o u s r e a c t i o n s t o the products p h t h a l i c a n h y d r i d e , p h t h a l i d e , t o l u y l a l d e h y d e , CO and C G . The d i s t i n c t maximum o f t h e p h t h a l i d e - and t o l u a l d e h y d e - c o n c e n t r a t i o n curve i n d i c a t e s t h a t these a r e i n t e r m e d i a t e p r o d u c t s which a r e converted mainly t o phthalicanhydride i n a consecutive s t e p . From t h e d e c r e a s e o f t h e P S A - c o n c e n t r a t i o n a t h i g h r e s i d e n c e t i m e s i t may be concluded t h a t , t h i s s p e c i e s o x i d i z e t o CO, CG , as w e l l a s water and t o a lower extend, t o MSA. F o r t h e e v a l u a t i o n o f t h e ex2

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LUFT ET AL.

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IrW/Ho Residence time Figure 4.

Results of loop-reactor experiments

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Concentration and temperature distribution in integralreactor


22


p e r i d e n t a l r e s u l t s , i t i s considered u s e f u l to s i m p l i f y the mentioned r e a c t i o n scheme; t h u s , the concent r a t i o n s of t o l u a l d e h y d e and p h t h a l i d e were i n c l u d e d t o g e t h e r . The s m a l l q u a n t i t i e s of MSA were n e g l e c t e d . At the h i g h r e c y c l i n g r a t i o s the loop r e a c t o r o p e r a t e s as an i d e a l s t i r r e d - t a n k r e a c t o r . T h e r e f o r e , the r e a c t i o n r a t e can immediately be determined from the d i f f e r e n c e i n c o n c e n t r a t i o n between the feed and the o u t l e t , the throughput and the q u a n t i t y of c a t a l y s t . T h e r a t e e q u a t i o n , d e s c r i b i n g the consumption of x y l e n e and the f o r m a t i o n of the r e a c t i o n p r o d u c t s , are c o n s i d e r e d t o be pseudo f i r s t o r d e r . The parameter of the r a t e equations, vhich are the f r e q u e n c y f a c t o r s and the a c t i v a t i o n e n e r g i e s , are determined by l e a s t square methods. In the abov 6b) measured r a t e , f i meters, w r e p r e s e n t a p p r o p r i a t e weight f a c t o r s and N i s the number of measured v a l u e s . Because the r a t e e q u a t i o n s c o u l d be d i f f e r e n t i a t e d w i t h r e s p e c t t o the unknown k i n e t i c parameters, the o b j e c t i v e f u n c t i o n was m i n i m i z e d by a s t e p w i s e r e g r e s s i o n . The s t e e p c o n c e n t r a t i o n and temperature p r o f i l e s i n the i n t e g r a l r e a c t o r d i d not a l l o w t o determine the r e a c t i o n r a t e s immediately. T h e r e f o r e , the o b j e c t i v e f u n c t i o n c o n t a i n s the measured and the c a l c u l a t e d conc e n t r a t i o n s i n s t e a d of the r e a c t i o n r a t e s , a l s o the t e m p e r a t u r e s because of the n o n i s o t h e r m a l r e a c t o r beh a v i o u r . The k i n e t i c parameters must be o b t a i n e d by d i r e c t s e a r c h t e c h n i q u e s l i k e the d e r i v a t i v e f r e e simp l e x method of N e l d e r and Mead. Comparison Comparing the two l a b o r a t o r y r e a c t o r s i t may be n o t i c e d t h a t the loop r e a c t o r i s more e x p e n s i v e . A l though the q u a n t i t y , o f c a t a l y s t and the volume of the l o o p r e a c t o r i s s m a l l , compared t o the i n t e g r a l r e a c t o r , the r e c y c l i n g of a l a r g e volume of gas r e q u i r e s a c o m p l i c a t e d blower. Hoivever, c e r t a i n advantages and d i s a d v a n t a g e s r e s u l t from the d i f f e r e n t c o n c e n t r a t i o n and temperature d i s t r i b u t i o n i n both r e a c t o r s . Because of the u n i f o r m c o n c e n t r a t i o n and temperature i n s i d e the loop r e a c t o r , the c o n c e n t r a t i o n of the r e a c t a n t s c o u l d be measured o n l y i n the r e a c t o r j n l e t and o u t l e t to determine the r e a c t i o n r a t e . The s t e e p c o n c e n t r a t i o n and temperat u r e g r a d i e n t s i n s i d e the i n t e g r a l r e a c t o r r e q u i r e measurements at many s p o t s a l o n g the tube. T h i s becomes r a t h e r e x p e n s i v e i n time i f s e v e r a l components are t o be a n a l y z e d as i n the o x i d a t i o n of x y l e n e . In the e v a l u a t i o n of the e x p e r i m e n t a l r e s u l t s the d i s t r i b u t i o n of c o n c e n t r a t i o n and temperature appear


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T

E

x

*

2

/

R

T

TOL*Pl

-

*PSA

Rate equations

N #

=

] > w

x

( r

x

- ?

w

*

x

(r

PSA PSA"'PSA

1

w

(r

• ^> TOL*PI TOL*Pl " *TOL*Pl

N •

X PSA TOL PI

w

]> CO,C0

Xylene PhthoJic anhydride Tolu—at deny de Phthalide

Figure 6b.

(r 2

C0,C0

N W ? r

?

2

" CO C0 i

) 2 2

Number of runs Appropriate weight factor Reaction rate, calculated - * - , measured

Objective function


}

24


Length

[cm]

•

Figure 7. Comparison of the loop-reactor data with pilot plant experiments


2.

LUFT ET AL.

Tubular and

25

Loop Reactors

t o be the b a s i c f a c t o r s i n t r o d u c i n g d i f f i c u l t y . The l o o p r e a c t o r can be d e s c r i b e d by simple a l g e b r a i c e q u a t i o n s of which the c o e f f i c i e n t s , p e r t a i n i n g t o the unknown f r e q u e n c y f a c t o r s and a c t i v a t i o n e n e r g i e s , can be o b t a i n e d by s t e p w i s e r e g r e s s i o n . In the case of the i n t e g r a l r e a c t o r , the e s t i m a t i o n parameters are more c o m p l i c a t e d and r e q u i r e s more computation time because of the n e c e s s i t y f o r n u m e r i c a l i n t e g r a t i o n of a s e t of d i f f e r e n t i a l e q u a t i o n s . In o r d e r t o check the a c c u r a c y of the measured data and c o l l e c t i n f o r m a t i o n f o r s c a l e - u p , a d d i t i o n a l exp e r i m e n t s were c a r r i e d out i n a p i l o t p l a n t and the r e s u l t s were compared w i t h t h e s e p r e v i o u s l y o b t a i n e d i n the l a b o r a t o r y r e a c t o r s . The p i l o t p l a n t r e a c t o r c o n s i s t e d of a tube l e n g t h t a k e n from a I t was f i l l e d w i t h about 1 kg c a t a l y s t p e l l e t s . The measured temperature- and c o n c e n t r a t i o n p r o f i l e s are p l o t t e d i n F i g . 7 v e r s u s the l e n g t h of the c a t a l y s t bed. The p o i n t s are e x p e r i m e n t a l l y determined whereas the t h i c k - l i n e c u r v e s have been c a l c u l a t e d u s i n g the k i n e t i c c o n s t a n t s o b t a i n e d i n the l o o p r e a c t o r exp e r i m e n t s . A c l o s e agreement between the e x p e r i m e n t a l r e s u l t s of the p i l o t r e a c t o r and the c a l c u l a t e d v a l u e s i s apparent. O n l y the c a l c u l a t e d CO and CG concentrat i o n s are a l i t t l e h i g h , c a u s i n g a l s o a h i g h e r temperature maximum. 2

Recommendations As the e x p e r i m e n t s i n the l o o p r e a c t o r can be carried out i s o t h e r m a l l y and at c o n s t a n t c o n c e n t r a t i o n s and the i n f l u e n c e of mass t r a n s f e r can be e x c l u d e d by a h i g h flow r a t e and s m a l l c a t a l y s t p e l l e t s , the l o o p r e a c t o r i s t o be recommendated f o r k i n e t i c s t u d i e s . F u r t h e r advantages are the f l e x i b i l i t y of the r e a c t o r w i t h r e s p e c t t o changes i n e x p e r i m e n t a l c o n d i t i o n s and l a s t but not l e a s t the u n c o m p l i c a t e d e v a l u a t i o n of the measured d a t a . The i n t e g r a l r e a c t o r shows some advantages i n the study of the p r o d u c t q u a l i t y and s e l e c t i v i t y because t e c h n i c a l c o n d i t i o n s can e a s i l y be i n c o r p o r a t e d . Furthermore, i t i s p o s s i b l e t o measure s i m u l t a n e o u s l y the heat cond u c t i v i t y i n the c a t a l y s t bed and the heat t r a n s f e r c o e f f i c i e n t through the r e a c t o r w a l l . The d i f f i c u l t i e s i n the e v a l u a t i o n of the e x p e r i m e n t s depend s t r o n g l y on the m a t h e m a t i c a l model which has t o be chosen. The e v a l u a t i o n i s c e r t a i n l y more comp l i c a t e d i f the r e a c t o r must be d e s c r i b e d by a twod i m e n s i o n a l model because o f s t e e p r a d i a l temperature g r a d i e n t s as we have observed i t i n the p h t h a l i c anhydrid reactor.


3 Kinetic Measurements of the Hydrogenation of Carbon Monoxide (Fischer-Tropsch Synthesis) Using an Internal Recycle Reactor A. ZEIN EL DEEN, J. JACOBS, and M. BAERNS Lehrstuhl für Technische Chemie, Ruhr-Universität Bochum, Postfach 102148, D-4630 Bochum, West Germany

The Fischer-Tropsch-synthesi r e s t during the l a s t years. Its goal being nowadays the formation of mainly lower o l e f i n s as chemical feed -stocks (1-5). From t h i s point of view k i n e t i c measure ments on the hydrogenation of CO have been performed in an i n t e r n a l recycle reactor with a d i f f e r e n t l y pretreated c a t a l y s t containing oxides of i r o n , manganese, zinc and potassium. Catalysts containing manganese have been described recently (4,5) as suited for producing short-chain o l e f i n s such as ethylene and propylene. The experimental r e s u l t s of t h i s investigation are discussed with respect to product d i s t r i b u t i o n and the rate determining step of the synthesis r e a c t i o n . Experimental Procedure The i n t e r n a l recycle reactor as described elsewhere (6) used for the experiments was charged with about 60 g of c a t a l y s t which was thermally pretreated and reduced with hydrogen before the synthesis r e a c t i o n . During the synthesis recycle r a t i o s (recycled volume per time and weight of c a t a l y s t divided by space v e l o c i t y under ope r a t i n g conditions) of more than 20 were used to estab lish ideal mixing as well as isothermal operation and to avoid transport l i m i t a t i o n due to f i l m resistance. The measurements were conducted i n two d i f f e r e n t regions of c a t a l y s t performance: After reduction and operation of about 5 to 10 hrs under synthesis condi tions the a c t i v i t y reached a constant l e v e l where i t remained for upto 60 to 70 hrs during which the k i n e t i c measurements were performed; thereafter the a c t i v i t y decreased continously. The analysis of the reaction mixture (H2, CO, C02, and the various C1- to C4-hydrocarbons) was c a r r i e d out by gaschromatography. © 0-8412-0401-2/78/47-065-026$05.00/0 In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

3.

ZEIN

27

Measurement of Carbon Monoxide Hydrogénation

E L DEEN

Experimental Conditions The p e l l e t i z e d c a t a l y s t (D = 3,7 nun, L = 6,2 mm) was t h e r m a l l y t r e a t e d f o r 20 h r s a t 300°C and s u b s e q u e n t l y r e d u c e d w i t h H2 f o r 50 h r s a t 3 00°C ( c a t a l y s t A) and a t 500°C ( c a t a l y s t C ) . These t r e a t m e n t s r e s u l t e d i n d i f f e r e n t s u r f a c e a r e a s S and average pore d i a m e t e r s A:

2

13,4 m /g

d

= 4,6 nm

(meso-pores)

= 3,8 nm

(meso-pores)

Ρ C:

2

10,4 m /g

d

The t o t a l pore volume amounted i n b o t h c a s e s t o 0.4 cm /g. C a t a l y s t C was used i n two d i f f e r e n t forms: F i r s t , i t was used the c a t a l y s t (C-II t i o n s s i m i l a r t o s y n t h e s i s (T = 258 t o 323°C, ρ(total) = 5 ; 10 and 15 bar) a t a l e v e l o f c o n v e r s i o n o f about 40 % r e s u l t i n g i n some d i s i n t e g r a t i o n b e f o r e k i n e t i c t e s t s were c o n d u c t e d . The k i n e t i c measurements w i t h c a t a l y s t s A, C-I and C - I I were performed under t h e f o l l o w i n g c o n d i t i o n s : 3

Catalyst

T[°C]

P

total

[

b

a

r

]

Space

veloci

x

co

[ % ]

t y (STP)[1/h] A 233-270 5 ; 1 0 ; 1 5 366-4480 8-65 C-I 323 5; 10 872-3752 8-34 C-II 309-335 10; 15 1180-5580 18-45 The f e e d gas was i n a l l i n s t a n c e s composed o f 40.1 v o l - % CO, 39.3 v o l - % H2 and 20.4 v o l - % A r . Experimental

Results

The CO was c o n v e r t e d under a l l c o n d i t i o n s t o about 45 t o 48 % C02 t h u s , r e s u l t i n g i n a n e a r l y c o n s t a n t r a t i o of CO-to H 2 - c o n v e r s i o n o f 1.4 t o 1.6. T h i s means t h a t t h e water formed d u r i n g t h e hydrogénation i s m a i n l y r e duced t o H2. The f o r m a t i o n o f c a r b o n and/or c a r b o n a c e ous m a t e r i a l i n s o l u b l e i n x y l e n e was a l m o s t n e g l i g i b l e . The remainder o f CO i . e . a p p r o x i m a t e l y 52 t o 55 % y i e l d e d hydrocarbons o f which o n l y t h e C1- t o C 4 - f r a c t i o n i s q u a n t i t a t i v e l y d e t a i l e d i n the following. Selectivity. The s e l e c t i v i t y o f t h e h y d r o c a r b o n f o r m a t i o n i s a l m o s t independent on C O - c o n v e r s i o n and p a r t i a l p r e s s u r e o f c a r b o n monoxide and hydrogen i n t h e range s t u d i e d f o r t h e c a t a l y s t s A and C-I d u r i n g t h e p e r i o d o f c o n s t a n t a c t i v i t y as e x e m p l i f i e d i n F i g u r e 1 A/B; t h e s e l e c t i v i t y i s , however, dependent upon t h e c a t a l y s t used, c a t a l y s t A p r o d u c i n g s i g n i f i c a n t l y l e s s C1- t o C4-hydrocarbons t h a n c a t a l y s t C-I and a l s o a



I "

Γ"

60

Π

Γ—-f

ο

ο

-

"*1

!

C0

20 Ί

Α

2

I

I

J

Γ

CK

4

~Ο

2

J

I

1

J

I

1

or

_J Ί

Γ

co

• •

ο

I

I

1

2

• à

ACJ° ι

(

r

1—

L· C

•gi- 2^

*4

11

Η

^2 6 î

Ο

1

1

1—

rê^b

η

η

Q

2 /νβ_ΛθΟ_Οο—«Ο

0

'

C3H °

ι

I

3

8

I—

π

1

1

Γ

1

1

1

•

A

ο-

2 0

C H 8

Ο—Ο-

.^S-g-oo-Ot9-aa> ι

ι

C4H10 I

I

LO

20 X

R N

[%]

-

C4H10" *

L

60

I

20 X

C O

[%)

CO

Figure 1. Dependence of selectivity S on CO-conversion X(CO). (A) catalyst A; Τ = 256°C; F(total) = 15 (\J), 10 (O), 5 (A) bar; (B) catalyst C-I; Τ = 322°C; F(total) = 10 (·), 5(A) bar.


3.


E L DEEN

zEiN

29

s m a l l e r p o r t i o n o f o l e f i n s . T h i s d i f f e r e n c e may be, however, due t o t h e d i f f e r e n t temperatures o f r e a c t i o n ; f o r c a t a l y s t C a h i g h e r one was n e c e s s a r y t o o b t a i n measurable c o n v e r s i o n s a t o t h e r w i s e comparable c o n d i t i o n s . The e f f e c t o f temperature i s d i s c u s s e d l a t e r i n some more d e t a i l . A change o f s e l e c t i v i t y i s , however, o b s e r v e d d u r i n g c a t a l y s t d e a c t i v a t i o n (Table I ) ; i n t h e Table I; Effect of operating time on performance of catalyst A with respect to conversion X(%) and selectivity S(C-atom%) at constant., temperature (256°C), pressure (10 bar) and space velocity (822 h" S.T.P). time [h]

2,42

26,87 31,30 29,10 27,33 28,02 27,75 27,02 25,10 23,20 18,00 1,49

X

CO H CO H

X

2

X

8,08 11,83 21,52 35,75 47,50 63,67 79,17 95,42

/X

2

s(co ) 52,33 46,52 S(CH ) 2,57 3,45 S(C H ) 0,45 0,73 S(C H ) 2,57 3,77 S(C H ) 0,78 1,12 S(C H ) 3,65 5,30 s(i-c ) 0,04 0,13 S(n-C ) 0,82 1,09 S (1-C+i-C+i-C) 3,01 4,44 S(t-2-C4n-C ) 0,67 0,86 S(c-2-C+3-M-C(1)) 0,33 0,45 2

4

2

6

2

4

3

8

3

6

4

4

4

4

4

4

Zh

5

5

4

46,67 49,69 48,07 50,81 50,52 47,77 46,59 3,92 4,46 4,71 4,65 4,51 4,98 5,04 0,82 0,99 1,11 1,15 1,11 1,27 1,34 4,19 4,72 4,75 4,54 4,18 4,50 4,27 1,13 1,28 1,28 1,30 1,22 1,27 1,29 5,77 6,37 6,53 6,20 5,96 6,29 6,12 0,07 0,11 0,11 0,11 0,11 0,12 0,13 1,13 1,28 1,25 1,22 1,18 1,27 1,25 4,78 5,16 5,25 4,94 4,77 5,06 4,87 0,86 0,95 0,96 0,94 0,96 1,00 0,99 0,48 0,51 0,53 0,50 0,52 0,52 0,47

67,21 67,86 69,83 75,52 74,55 76,36 75,05 74,06 72,37

l a t t e r case the r a t i o of o l e f i n to p a r a f f i n d i m i n i s h e s a l t h o u g h t h e a b s o l u t e amount o f t h e v a r i o u s o l e f i n i c hydrocarbons s t a y s c o n s t a n t . Activity. The a c t i v i t y o f t h e c a t a l y s t s was quant i t a t i v e l y e x p r e s s e d by t h e r a t e o f r e a c t i o n a s moles of component consumed o r formed r e s p e c t i v e l y p e r time and weight o f c a t a l y s t which c o u l d be measured d i r e c t l y by d e f i n i t i o n o f t h e r e c y c l e r e a c t o r . The a c t i v i t y was g r e a t e s t f o r c a t a l y s t A when compared w i t h C on an e q u a l temperature b a s i s ; t h e a c t i v i t y o f C - I I was h i g h e r t h a n C - I . The l a t t e r dependence i s p r o b a b l y caused by t h e s m a l l e r p a r t i c l e s i z e o f C - I I which was o b t a i n e d d u r i n g p r e t r e a t m e n t . The v a r i o u s o v e r a l l r e a c t i o n r a t e s were found t o be o n l y s l i g h t l y dependent on c a r b o n mon o x i d e p a r t i a l p r e s s u r e as i s shown i n T a b l e I I f o r t h e t h r e e c a t a l y s t s ; t h e dependence on ρ(CO) i s n o t v e r y


CHEMICAL

30

REACTION

ENGINEERING—HOUSTON

Tfrfrle I I ; C o r r e l a t i o n between reduced r e a c t i o n rate r /p ±

pressure of r

i

/ p

H

*

a

k

i

, p

CO

CO C H 2

5

n.

108

4

and

partial

rooie/fg-cat.-h'bar)

Catalyst A Component i V 1 0

H

cgrbon monoxide

Catalyst k^lO

-0.22

0.53

5

n

116

±

0.22

R 2 (

C-I PCO>

0.41

Catalyf it Jc^lG

C-II

R (P 2

223

0.04

3.64

-0.31

0.88

5.08

0.22

0.63

7.42

0.20

0.39

1.94

-0.39

0.85

2.73

0.15

0.30

4.22

0.13

0.21

C

2 6

H

0.22

+0.18

0.64

0.30

0.43

0.69

0.57

0.27

0.81

C

H

3 6

1.72

-0.40

0.65

2.38

0.14

0.28

2.85

0.32

0.47

C

3 8

H

0.20

+0.01

0.01

0.24

0.22

0.42

0.27

0.41

0.74

C

H

4 8

1.11

-0.46

C

4 10

H

0.17

-0.10

pressure range of CO Temperature

to

1.8 T

R

-

5.2

bar

1.8

e

255-1 C

T

R

to -

3.8 bar 321±1 • c

2.9

T

R

to -

C O

)

0.03

5.6 bar 322-1 C e

s i g n i f i c a n t as can be d e r i v e d from the c o r r e l a t i o n c o e f f i c i e n t R [p(CO)] which i s a l s o g i v e n i n t h i s t a b l e . T h i s r e s u l t i s i n agreement w i t h e a r l i e r p u b l i c a t i o n s (7,8) assuming t h a t t h e r a t e i s p r o p o r t i o n a l o n l y t o p(H2) and not i n any way t o ρ(CO) when the a c t i v e s u r f a c e i s a l m o s t c o m p l e t e l y c o v e r e d w i t h CO. The temperature dependency o f the o v e r a l l r e a c t i o n r a t e s was d e r i v e d from A r r h e n i u s p l o t s ( F i g u r e 2) f o r which r e a c t i o n r a t e s measured a t comparable c o n v e r s i o n s and e q u a l p a r t i a l p r e s s u r e s o f CO and H2 were used. The a p p a r e n t a c t i v a t i o n e n e r g i e s E and t h e p r e e x p o n e n t i a l r e a c t i o n r a t e s r are l i s t e d i n Table I I I f o r c a t a l y s t s A and C - I I . The a c t i v a t i o n e n e r g i e s f o r the i n d i v i d u a l compounds o b t a i n e d f o r the two c a t a l y s t s a r e a l m o s t equal c o n s i d e r i n g t h a t the accuracy of E i s approxi m a t e l y 5 t o 10 %. 2

a

0

a

Discussion Based on the a f o r e communicated e x p e r i m e n t a l r e s u l t s some s p e c i f i c a s p e c t s o f the r e a c t i o n scheme and o f the r a t e d e t e r m i n i n g s t e p s o f the F i s c h e r - T r o p s c h - s y n t h e s i s a r e d i s c u s s e d i n the f o l l o w i n g . Product d i s t r i b u t i o n . A r e l a t i o n s h i p between the r a t e o f f o r m a t i o n o f the i n d i v i d u a l hydrocarbon and i t s c h a i n l e n g t h may be f o r m u l a t e d by the f o l l o w i n g e q u a t i o n when assuming t h a t the c a r b o n s k e l e t o n i s b u i l t up by s t e p w i s e a d d i t i o n of one c a r b o n atom t o an adsorbed


ZEiN

EL

DEEN

Measurement of Carbon Monoxide

Figure 2.

Hydrogénation

Arrhenius diagram for reaction rates



32

T a b l e I I I : Apparent a c t i v a t i o n energy E f o r r a t e s ———-——— a o f CO-consumption and h y d r o c a r b o n f o r m a t i o n . a

r =

r . e x p ( -- E / R T ) , r ο Q

a

=

r

o*

Compound *a

4.0·10

CH

4

C H 2

4

C

2 6

C

3 6

C

3 8

C

C

X

8.5- 1 0

7

3.6- 1 0

6

H

2.3-10 1.7·10

r

o

5.0-10

7

26.4

2.6·10

8

32.2

25.8

8.8·10

5

26.2

26.4

1.4·10 4 3.4-10 4.3·10 4 4.7-10*

24.1 28.5

22.4

3

22.5 1.9·10 3.5 t o 3.7

H

4 10

C0

2 >

25.6

H

4 8

4

bar

25.2 26.2

5

26. 1

3.4 t o 3.6

3.6 t o 3.7

3.7 t o 3.8

12 t o 19

22 t o 28

%

°c

Τ

1

7

5.7- 1 0 4

H

c o

' CO>

4.0·10

H

P

P

2

1)

1 )

Ο

CO

H

Catalyst C-II

Catalyst A r

f ( p

309

233 t o 271

^ m o l e / ( g - c a t a l y s t χ h)

2 )

t o 335

kcal/mole

growing c h a i n and t h a t t h e p r o b a b i l i t y o f c h a i n growth W i s independent o f c h a i n l e n g t h : r

= A

V co

w

"

r i s the r a t e of formation of p a r a f f i n plus o l e f i n of c a r b o n number n. As e x e m p l i f i e d i n F i g u r e 3 t h e e x p e r i mental r a t e d a t a c a n be r e p r e s e n t e d by t h e above c o r r e l a t i o n . The c o n s t a n t s A and W have been e v a l u a t e d f o r the v a r i o u s e x p e r i m e n t a l c o n d i t i o n s and a r e l i s t e d i n T a b l e IV; A i n c r e a s e s and W d e c r e a s e s s l i g h t l y w i t h temperature. P o s t u l a t i n g t h a t t h e l i n e a r p l o t can be extended t o carbon numbers n>4 t h e t o t a l s e l e c t i v i t y f o r t h e f o r m a t i o n o f s t r a i g h t c h a i n p a r a f f i n s and a o l e f i n s 5jS [C-atom%] c a n be c a l c u l a t e d : n

n


3.

zEiN

EL


DEEN

10 6

r

co

2

1 0

1 2

3

4

C A R B O N NUMBER Figure 3. Correlation between the rate of formation of straight chain paraffins plus α-olefins (r ) and carbon number η (catalyst C - I / , F(CO) = 3.5 bar, ?(H ) = 3.7 bar) n

2


33


34

r—

S

)

=

^ n

n=°° η A W n=0

r

n

f

= 0

—

0

n

dn = A/ (lnW)'

The v a l u e s o f £ s a r e g i v e n i n T a b l e IV; t h e amounts t o about 44 %. C o n s i d e r i n g t h a t t h e l e c t i v i t y towards C02 i s a p p r o x i m a t e l y 48 % 8 % o f s e l e c t i v i t y a r e t o be c o n t r i b u t e d t o hydrocarbons and oxygenated compounds. n

average average s e the missing branched

Table IV: Parameters A and W of the product d i s t r i b u t i o n c o r r e l a t i o n and cumulative s e l e c t i v i t y ^ S

n

of s t r a i g h t

chain-hydrocarbons

Catalyst A

T

R

e

ΑΊ0

2

C a t a l y s t C II

W

T

s.*

c

R

A-10

2

W

In' c--atom %

°c

C-a torn %

233

3,13

0,776

49

309

4,88

0,697

38

245

3,76

0,776

58

316

5,17

0,704

42

254

4,34

0,755

55

322

5,44

0,687

39

263

4,20

0,732

43

329

5,53

0,679

37

270

4,57

0,724

44

335

6,00

0,655

34

S

CO

a

*

4

5

-

5

0

C-atom %

Rate d e t e r m i n i n g s t e p and a c t i v a t i o n energy. The m o d i f i e d T h i e l e - m o d u l u s (J) i s commonly used as a means f o r e v a l u a t i n g whether a r e a c t i o n i s e f f e c t e d by pore d i f f u s i o n (j)) : 2

$ =

R . r.·0 Ρ P C(H ).D 1

2

V

e f f

For the F i s c h e r - T r o p s c h - s y n t h e s i s the q u e s t i o n a r i s e s on what k i n d o f d i f f u s i o n c o e f f i c i e n t t o base t h e c a l c u l a t i o n . When a p p l y i n g a gas phase d i f f u s i o n c o e f f i c i e n t φ amounts t o about 0,001 t o 0,01; hence, pore d i f f u s i o n s h o u l d be e x c l u d e d . I t i s , however, known that the pores o f the c a t a l y s t a r e f i l l e d with high b o i l i n g l i q u i d hydrocarbons as was a l s o o b s e r v e d i n


3.

ZEIN

EL


DEEN

35

t h i s study. T h e r e f o r e i t seems a p p r o p r i a t e t o s u b s t i t u t e f o r the r e a c t a n d s the l i q u i d phase d i f f u s i o n c o e f f i c i e n t s and t h e i r s o l u b i l i t y i n the l i q u i d hydrocarbons as a measure o f c o n c e n t r a t i o n . When u s i n g e s t i mated v a l u e s f o r the m o l e c u l a r d i f f u s i o n c o e f f i c i e n t based on Π 0 ) and f o r the s o l u b i l i t y of H2 (VjJ moduli a r e o b t a i n e d i n the o r d e r o f 20 t o 50 r e s u l t i n g i n e f f e c t i v i n e s s f a c t o r s o f 0.3 t o 0.1. T h i s c l e a r l y sug g e s t s t h a t t h e r a t e o f CO-consumption i s s t r o n g l y i n f l u e n c e d by p o r e d i f f u s i o n . The magnitude o f the ap p a r e n t a c t i v a t i o n e n e r g i e s as l i s t e d i n T a b l e I I I , how ever, i s comparable t o the t r u e a c t i v a t i o n e n e r g i e s o f the s y n t h e s i s as proposed by (J^) . I t might t h e r e f o r e be assumed t h a t t h e measured v a l u e s of E a r e not e f f e c t e d by pore d i f f u s i o v a l u e s . In t h i s cas the a c t i v e s u r f a c e would have t o o c c u r by another me chanism than pore d i f f u s i o n ; s u r f a c e d i f f u s i o n has been suggested e a r l i e r (J_3) · a

Performance o f c a t a l y s t s A and C - I I . C a t a l y s t C - I I reduced a t 500°C was l e s s a c t i v e than A reduced a t 300 °C. The d i f f e r e n c e i n a c t i v i t y which i s e x e m p l i f i e d by the r e a c t i o n r a t e s of CO i n T a b l e V i s g r e a t e r than c o u l d be e x p l a i n e d by the s m a l l e r s u r f a c e a r e a of C - I I . Table V: E f f e c t o f c a t a l y s t pretreatment on a c t i v i t y c a l c u l a t e d a c c o r d i n g to the k i n e t i c d a t a o f Table I I I . Temp. 1

3

r

° - co

mole g-cat.'h

e

C Cat. A Cat.C-II

250

270

3.9 (0.6)

300

9.2 +)

(1.4)

330 +)

(29.4) (83.8) +)

5.0

+)

15.6

I t i s c o n c l u d e d t h a t t h e number o f a c t i v e s i t e s per u n i t a r e a d e c r e a s e s by t h e h i g h temperature r e d u c t i o n . There a r e minor d i f f e r e n c e s i n s e l e c t i v i t y o f the two c a t a l y s t s as i s shown i n T a b l e VI f o r e t h y l e n e and ethane. The s e l e c t i v i t y towards e t h y l e n e i s i n the temperature range i n v e s t i g a t e d s l i g h t l y h i g h e r f o r c a t a l y s t C - I I as compared w i t h A. C o n s i d e r i n g ethane i t s s e l e c t i v i t y can be l o o k e d a t as n e a r l y c o n s t a n t . Hence, the main d i f f e r e n c e o f the two c a t a l y s t s i s their activity. To e l u c i d a t e the mechanism o f the d e c r e a s e i n a c t i v i t y i n v e s t i g a t i o n s are p r e s e n t l y i n progress to determine t h e number o f a c t i v e s i t e s o f t h e c a t a l y s t s .



36

T a b l e V I : E f f e c t o f c a t a l y s t pretreatment on s e l e c t i v i t y (C-atom %) c a l c u l a t e d a c c o r d i n g t o t h e k i n e t i c data o f Table I I I . Temp.

C a t a l y s t C-II

Catalyst A S(C )

S(C )

250

3.5

0.6

5.8

(4.3)

+ )

(0.6)

+ )

(7.2) >

270

3.8

0.8

4.8

(4.2)

+ )

(0.6)

+ )

(7.0)

300

(4.1)

+ )

(4.4)

+ )

°C

2

330

S (C )/S(C2) s ( c )

+

(3.7) > +

(1.4) >

(3.1)

+ )

S(C2)/S(C )

s(c )

2

2

2

2

2

+

4.2

0.6

7.0

4.1

0.6

6.8

+ )

c a t a l y s t was n o t operate

Ac knowledgement T h i s work was s u p p o r t e d by Ruhrchemie AG, Oberhausen and t h e M i n i s t r y f o r R e s e a r c h and Technology o f t h e Fed. Rep. o f Germany. Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

(11) (12) (13)

Büssemeier B., F r o h n i n g C.D., C o r n i l s Β., Hydroc. P r o c . (1976) 11, 105. German P a t e n t A p p l i c . DAS 2.536.488 (16.8.1975). German P a t e n t A p p l i c . DOS 2.518.982 (29.4.1975). German P a t e n t A p p l i c . DOS 2.518.964 (29.4.1975). German P a t e n t A p p l i c . DOS 2.507.647 (19.2.1975). B e r t y J.M., Chem. Engng. P r o g r . (1974) 70, 78. Anderson R.B., Seligmann Β., S c h u l t z J . F . , Kelly R., Elliot M.A., I n d . Engng. Chem. (1952) 44, 391. Dry M.E., S h i n g l e s T., B o s h o f f L . J . , J. Catal. (1972) 25, 99. Satterfield C.N., "Mass T r a n s f e r in Heterogeneous Catalysis", 138, M.I.T. P r e s s , London 1970. Weast R.C. ( e d i t o r ) "Handbook o f C h e m i s t r y and P h y s i c s " F59(n-Hexane), CRC-Press, C l e v e l a n d / O h i o 1974. K ö l b e l H., Ackermann P., E n g e l h a r d t F., E r d ö l und Kohle (1965) 9 ( 3 ) , 153. Anderson R.B., H o f e r L . J . E . , J. Chem. Eng. Data (1960) 5, 511. B r ö t z W., S p e n g l e r H., Brennstoff-Chem. (1950) 31, 97.


4 Thermal and Kinetic Design Data from a Bench-Scale Heatflow Calorimeter W.

REGENASS

CIBA-GEIGY

Ltd.,

Department of Chemical Engineering, Basel, Switzerland

THERMAL AND KINETIC DESIGN DATA FROM A BENCH-SCALE HEATFLOW CALORIMETER In this paper, a heat flow calorimeter designed for the investigation of i n d u s t r i a l organic reactions i s presented. This instrument i s extensively used for the elucidation of reaction kinetics and for the assessment of thermal hazards. I t also per mits the determination of heats of reaction, specific heats and heat transfer coefficients, and due to its accurate controls, i t is an ideal "mini-pilot-reactor". Attempts to use heat evolution as an indicator for the kinetics of chemical reactions are as old as thermochemistry. Nowadays thermal methods are firmly established for the i n v e s t i gation of s o l i d / s o l i d , gas/solid and curing reactions, and they are widely used for biochemical reactions. There i s an adequate supply of instruments for this type of work. However, it i s only i n the l a s t few years that calorimeters suited to the requirements of process development have been described i n the literature [1,2,3,4], and no such instrument i s available commercially to date. Therefore, chemical engineers often are not aware of the potential of thermal methods. Thermal methods and Instrumentation As an introduction for the chemical engineer not familiar with thermal methods, a short review on instrumentation i s given here. The most important feature for classifying thermal methods is certainly the treatment of the evolved heat. In accumulation methods (adiabatic and isoperibolic calorimetry), the sample i s well insulated from its environment and its temperature change is used as a measure of the extent of conversion. In heat transfer or heat flow methods, the evolved heat flow to the environment i n ©

0-8412-0401-2/78/47-065-037$05.00/0


38


a measurable way, w h i l e the sample temperature remains near i t s s e t p o i n t j here the measured r a t e o f heat flow i s p r o p o r t i o n a l t o the r a t e o f c o n v e r s i o n . For k i n e t i c work and hazards assessment, heat flow methods are t o be p r e f e r e d . Heat f l o w c a l o r i m e t e r s may be c l a s s i f i e d f u r t h e r w i t h respect to the method o f heat t r a n s f e r c o n t r o l . I n p a s s i v e systems, heat flow i s induced by temperature changes o f the sample due t o p a r t i a l accumulation o f the evolved heat. I n a c t i v e systems, a heat t r a n s f e r c o n t r o l l e r causes heat t r a n s f e r induced by the s l i g h t e s t d e v i a t i o n o f the sample temperature from i t s s e t p o i n t . Three heat flow c o n t r o l p r i n c i p l e s are mainly used i n a c t i v e systems: 1) P e l t i e r heat t r a n s f e r 2) Compensation h e a t i n constant temperatur c o n t r o l l e d e l e c t r i c heater i s so adjusted t h a t the sample temperature i s kept a t i t s s e t p o i n t , i . e . the h e a t i n g power i s complementary t o the heat r e l e a s e of the sample) 3) adjustment o f the environment temperature Heat flow measurement i s s t r a i g h t forward w i t h the f i r s t two p r i n c i p l e s ? there a r e two methods i n connection w i t h p r i n c i p l e 3) : 31) use o f the temperature d i f f e r e n c e across the sample w a l l as a measure o f heat flow 32) heat balance on the heat t r a n s f e r f l u i d (jfj [VJ. Another c h a r a c t e r i s t i c f e a t u r e o f heat f l o w c a l o r i m e t e r s i s sample s i z e . The micro-methods ( d i f f e r e n t i a l - t h e r m a l a n a l y s i s = DTA, d i f f e r e n t i a l scanning c a l o r i m e t r y = DSC) are q u i c k and r e q u i r e l i t t l e experimental e f f o r t , b u t they p r o v i d e no means o f adding r e a c t a n t s d u r i n g measurements, and heterogeneous samples cannot be mixed. A l l micro-methods use a twin (or d i f f e r e n t i a l ) design t o e l i m i n a t e d i s t u r b i n g e f f e c t s , i . e . an i n e r t sample i s exposed to the same environment c o n d i t i o n s as the sample under i n v e s t i g a t i o n and the d i f f e r e n c e o f the two heat flows i s recorded. Laboratory (research type) heat flow c a l o r i m e t e r s (with sample s i z e s o f 20 t o 200 ml) are a v a i l a b l e from v a r i o u s suppliers. These instruments are very accurate b u t they have l i m i t e d ranges of a p p l i c a t i o n w i t h r e s p e c t t o temperature, p r e s s u r e , c o r r o s i o n r e s i s t e n c e and h a n d l i n g o f r e a c t a n t s . Two bench-scale heat f l o w c a l o r i m e t e r s (with a sample s i z e of 0.3-2.5 l i t r e s ) have been d e s c r i b e d : a design o f Hub QÛ , p a r t i c u l a r l y s u i t a b l e f o r work under r e f l u x c o n d i t i o n s , and the instrument presented i n t h i s paper, which i s a s i n g l e sample a c t i v e heat flow c a l o r i m e t e r , u s i n g the heat flow c o n t r o l method 31) . More comprehensive reviews on thermal a n a l y s i s instrumenta t i o n are found i n r e f e r e n c e s and HQ.


4. REGENASS

Thermal and Kinetic Design Data

A bench s c a l e heat flow c a l o r i m e t e r

39

ΓΣ.1.2..1Ω.Ill

For the requirements o f process development and process s a f e t y i n v e s t i g a t i o n , a bench s c a l e heat flow c a l o r i m e t e r has been developed and b u i l t . F i g u r e 1 o u t l i n e s i t s p r i n c i p l e . The s t i r r e d tank r e a c t o r (A) i s surrounded by a j a c k e t i n which a heat t r a n s f e r f l u i d i s c i r c u l a t e d a t a very h i g h r a t e . A cascaded c o n t r o l l e r (B) a d j u s t s the temperature o f the c i r c u l a t i o n loop (C) so t h a t heat t r a n s f e r through the r e a c t o r w a l l e q u i l i b r a t e s the heat e v o l u t i o n i n the r e a c t o r . I n j e c t i o n o f thermostated hot or c o l d f l u i d i s used t o a d j u s t the temperature i n the loop. The r a t e o f heat t r a n s f e r q (which equals the r a t e o f heat e v o l u t i o n ) i s r e l a t e d t o the observed temperature d i f f e r e n c e Δτ between the j a c k e t f l u i d and the r e a c t i o n mixture by the r e l a t i o n q = U · A · ΔΤ = f c where the c a l i b r a t i o n f a c t o r f i s the product o f U, the o v e r a l l heat t r a n s f e r c o e f f i c i e n t , and A the a c t i v e (= wetted) heat t r a n s f e r a r e a . Because both A and U depend on the r e a c t o r contents and on the s t i r r i n g c o n d i t i o n s , s p e c i f i c c a l i b r a t i o n i s r e q u i r e d . T h i s i s done by producing a known heat i n p u t r a t e t o the r e a c t i o n mixture by means o f an e l e c t r i c heater (D). The need o f frequent c a l i b r a t i o n i s o f some inconvenience as compared w i t h heat balance c a l o r i m e t e r s . On the o t h e r hand, t h e method chosen permits the use o f an u n i n s u l a t e d g l a s s r e a c t o r and thus a l l o w s v i s u a l o b s e r v a t i o n o f phase changes, c o l o u r changes and m i x i n g c o n d i t i o n s . T h i s i s a d i s t i n c t advantage f o r process development work. Our standard instrument, which i s shown i n f i g . 2 , i s equipped w i t h a r e f r i g e r a t i o n u n i t , e l e c t r o n i c c o n t r o l s f o r temperature programming; automatic c a l i b r a t i o n and w i t h f e e d i n g systems (not shown) f o r gases, s o l i d s and l i q u i d s . Thus, a l l standards operations c a r r i e d out w i t h i n d u s t r i a l s t i r r e d tank r e a c t o r s can be performed. The s p e c i f i c a t i o n s are as f o l l o w s : r e a c t o r temperature : -20 t o 200°C temperature programm : i 1 t o 200°/hour pressure (glass r e a c t o r ) : - 1 t o 2 bar volume o f r e a c t o r : 0.5/2.5 l i t r e s (exchangeable) volumen o f r e a c t a n t : 0.3-2.5 l i t r e s s e n s i t i v i t y : 0.5 Watts f o r low v i s c o s i t y r e a c t i o n mixtures heat removal c a p a c i t y : 500 Watts ( f o r temp. >· 30°C) response time (to a step change o f the heat r e l e a s e r a t e ) : 20 seconds f o r 50%, 200 seconds f o r 99% o f the f u l l s i g n a l . c

S p e c i a l u n i t s f o r h i g h temperature (250°C), low temperature (-60°C, f l l ] ) and moderate pressure (50 bar) are a l s o i n use.



40

D

Figure 1. Bench scale heat flow calorimeter

Figure 2. Bench scale heat flow calorimeter


4.

REGENASS


41

F i g . 3 presents a t y p i c a l heatflow r e c o r d o f an i s o t h e r m a l run. I n the example a c e t i c anhydride was hydrolyzed a t 25°. The f o l l o w i n g events are i n d i c a t e d : (A) I n i t i a t i o n o f the r e a c t i o n by instantaneous a d d i t i o n o f 0.88 moles o f a c e t i c anhydride t o a l a r g e amount o f 0.1 η aqueous HCl (B) dynamic l a g (heat flow t o the j a c k e t has t o e q u i l i b r a t e w i t h heat r e l e a s e i n the r e a c t o r ) (C) heat e v o l u t i o n decreasing e x p o n e n t i a l l y ( f i r s t order r e a c t i o n ) (D) c a l i b r a t i o n (superimposed on r e a c t i o n ) Thermal data The r a t e o f heat e v o l u t i o n which i s o f primary i n t e r e s t f o r s a f e t y and design c o n s i d e r a t i o n s observed temperature d i f f e r e n c The t o t a l heat o f r e a c t i o n f o l l o w s by i n t e g r a t i n g the surface under the heat flow curve. Heat c a p a c i t i e s and s p e c i f i c heats are obtained from tempera ture programmed runs. When t h e r a t e o f imposed temperature change Τ i s a l t e r e d , there i s a step change i n heat flow (s i n f i g . 4 ) : Aq = Δ(Τ)

· (w + m C , ) r ρ r In t h i s r e l a t i o n w denotes the p r o p o r t i o n a t e heat c a p a c i t y o f the c a l o r i m e t e r (a q u a n t i t y which depends on temperature and on the volume o f the c a l o r i m e t e r contents and has t o be c a l i b r a t e d f o r a s p e c i f i c r e a c t o r ) , m and Cp, are the mass and the s p e c i f i c heat o f the mixture under i n v e s t i g a t i o n . r

r

The e v a l u a t i o n o f heat flow data obtained from the bench s c a l e c a l o r i m e t e r has been t r e a t e d by M a r t i n [T]and Gautschi QJO]. Kinetics For s i n g l e r e a c t i o n s , the r a t e o f r e a c t i o n i s d i r e c t l y propor t i o n a l t o the r a t e o f heat e v o l u t i o n observed. The most common o b j e c t i o n s t o the use o f thermal methods a r e r e l a t e d t o the f a c t s t h a t most r e a c t i o n s a r e n o t s i n g l e and t h a t heat i s a very uns p e c i f i c i n f o r m a t i o n . Therefore the c o n c l u s i o n could be drawn t h a t thermal methods a r e o f l i t t l e value f o r k i n e t i c work. However, i n the authors experience on s e v e r a l hundred r e a c t i o n s o f w i d e l y d i f f e r e n t k i n d s , t h i s i s not the case.In a s u r p r i s i n g l y l a r g e number o f cases, the main r e a c t i o n i s dominating t h e r m a l l y t o such an e x t e n t , t h a t the i n f l u e n c e o f concentrations and o f temperature on the r e a c t i o n r a t e can be obtained by heat flow experiments alone. I n most other cases, thermal data provide v a l u a b l e informa t i o n a d d i t i o n a l t o the data obtained by c l a s s i c a l means, a f a c t which d r a s t i c a l l y speeds up k i n e t i c work. Of course, thermal methods are not appropriate f o r s e l e c t i v i t y determinations.


CHEMICAL REACTION


Figure 3. Isothermal run of the hydrolyse of acetic anhydride

Figure 4. Temperature programmed run of a diazo-decomposition


4.


REGENASS

43

In order to u t i l i z e c a l o r i m e t r y t o i t s f u l l e x t e n t , i t i s important to have d i f f e r e n t means o f r e a c t i o n i n i t i a t i o n a t ones d i s p o s a l . The bench-scale c a l o r i m e t e r described permits the f o l l o w i n g i n i t i a t i o n s of reaction: 1) instantaneous a d d i t i o n o f a r e a c t a n t ( f i g . 3) o r a c a t a l y s t ( f i g . 5 and 6) 2) gradual (continuous) a d d i t i o n o f l i q u i d , gaseous o r s o l i d r e a c t a n t s ( f i g . 7) 3) gradual r i s e o f temperature (as shown i n f i g . 4 f o r the f o r mation o f a p h e n o l i c compound by the decomposition o f the corresponding d i a z o - s a l t : ArN^HSO^ + H 0—»-ArOH + N +H S0 ) 2

2

2

4

By temperature programmed o p e r a t i o n , heat of r e a c t i o n , s p e c i f i c heat, frequency f a c t o r and a c t i v a t i o n energy may be ob t a i n e d from one s i n g l e run the f o l l o w i n g parameter constant k (433 K) : 1.0-10~ s ? a c t i v a t i o n energy E: 2.1-10^ Joule/mole? heat o f r e a c t i o n ΔΗ: 2.29·10^ Joule/mole, w i t h estimated v a r i a t i o n c o e f f i c i e n t s o f 7%, 6% and 4% r e s p e c t i v e l y . 2

_1

F i g . 5 and 6 are taken from an i n v e s t i g a t i o n by M a r t i n on the i s o m e r i s a t i o n o f t r i m e t h y l p h o s p h i t e (TMP): P(0CH ) 3

3

•

CH -PO(OCH ) 3

3

2

This r e a c t i o n i s c a t a l y s e d by CH J and i n h i b i t e d by N(C H _) . F i g . 5 demonstrates the ease o f i n v e s t i g a t i n g i n f l u e n c e s on r e a c t i o n r a t e by means o f the c a l o r i m e t e r . A f t e r c a t a l y s t a d d i t i o n (marked C), there i s an immediate increase i n r e a c t i o n rate? a f t e r the a d d i t i o n o f i n h i b i t o r (marked I) there i s a f a s t exothermic r e a c t i o n between the c a t a l y s t and the i n h i b i t o r and then a decrease o f the r a t e o f i s o m e r i s a t i o n . F i g . 6 i l l u s t r a t e s the value o f d i r e c t i n f o r m a t i o n on r e a c t i o n r a t e . A f t e r c a t a l y s t a d d i t i o n there i s a t f i r s t a marked increase o f r e a c t i o n r a t e a t constant temperature, where one would expect a f i r s t order decrease. This i s due to a considerable i n crease i n p o l a r i t y o f the r e a c t i o n mixture as a consequence o f conversion. The heat flow record demonstrates t h i s f a c t more e v i d e n t l y than a c l a s s i c a l conversion versus time diagram . 3

2

C

3

A comprehensive review on the k i n e t i c e v a l u a t i o n o f thermal data has been given by Wendtland and coworkers / the evaluation procedures s p e c i f i c to heat flow c a l o r i m e t r y have been t r e a t e d by Becker \Î2} , M a r t i n OQ and Gautschi [ÏQj · Assessment o f thermal hazards Thermal explosions do occur, when the heat e v o l u t i o n r a t e o f a r e a c t i o n (with a high l a t e n t a d i a b a t i c temperature r i s e ) exceeds the heat t r a n s f e r c a p a c i t y o f the r e a c t o r . Events o f t h i s type which have happened i n i n d u s t r y , may be d i v i d e d i n t o two c l a s s e s :



NOT INITIATED

INITIATED Watt

Κ 433 -heat flow

50

393

0 100

/

cni /-—RCL a d d e d - ν 5 0 1 / / / u

Figure 7.

Formation of Grignard compound

h 413

/! I j

/

'

temperature^ .5

1.

0

.5

j

373 353 333

1. hours


4.

REGENASS

45


1) exothermal decomposition o r p o l y m e r i s a t i o n o f t h e r m a l l y i n s t a b l e mixtures (e.g. n i t r o compounds, b e n z y l - h a l i d e s , 2) "run away" o f an intended r e a c t i o n .

etc.)

Type 1 hazards a r e e a s i l y assessed u s i n g w e l l e s t a b l i s h e d t e s t methods [^4,15] , e.g. the t h e r m o a n a l y t i c a l micro-methods DTA or DSC? a t e s t e s t a b l i s h e d by L u t o l f \ ΐ β ] . which i s now standard i n Swiss firms? o r the "Sikarex" . However, the e l a b o r a t i o n o f safe r e a c t i o n c o n d i t i o n s (which avoid type 2 hazards) i s s t i l l a problem. Whenever p o s s i b l e , h i g h l y exothermal r e a c t i o n s are performed i n such a way, t h a t the r e a c t a n t s disappear by r e a c t i o n as they enter the r e a c t o r (semibatch o r continuous o p e r a t i o n ) . Under these c o n d i t i o n s , any accumulation o f r e a c t a n t s i n the r e a c t o r i s hazardous. I t may have 21) too low temperatur 22) i n s u f f i c i e n t mixing 23) wrong k i n e t i c assumptions (a case o f t e n encountered i n process development: the r e a c t i o n i s assumed t o be f a s t and the heat evolved a f t e r the a d d i t i o n o f the r e a c t a n t s i s n o t n o t i c e d on l a b o r a t o r y scale? then a t the p i l o t stage, there i s a run away). 24) i n c o r r e c t i n i t i a t i o n F i g . 7 demonstrates the i n v e s t i g a t i o n o f a type-24)-hazard d u r i n g formation o f a Grignard-reagent. A h a l i d e i s added gradually to magnesium suspended i n a s o l v e n t (RC1 + Mg • RMgCl). A f t e r c o r r e c t i n i t i a t i o n ( l e f t ) , the r e a c t i o n proceeds almost l i k e a n e u t r a l i s a t i o n ? w i t h o u t i n i t i a t i o n ( r i g h t ) , the r e a c t i o n does n o t s t a r t u n t i l f a r too much h a l i d e has been added, and then gets o u t of c o n t r o l . Even s l i g h t l y exothermal r e a c t i o n s may become dangerous, when a t a higher temperature an exothermal decomposition i s t r i g g e r e d o f f . For t h i s reason,the p o t e n t i a l a d i a b a t i c temperature r i s e o f i n d u s t r i a l r e a c t i o n s i s o f general i n t e r e s t . When s y n t h e t i c work i s done i n the b e n c h - s c a l e - c a l o r i m e t e r , the r e q u i r e d data are ob t a i n e d without a d d i t i o n a l e f f o r t . Heat t r a n s f e r c o e f f i c i e n t s F i l m heat t r a n s f e r c o e f f i c i e n t s may be estimated from flow c o n d i t i o n s and from p h y s i c a l p r o p e r t i e s . For f o r c e d convection and t u r b u l e n t flow ( i . e . c o n d i t i o n s p r e v a i l i n g i n s i d e s t i r r e d tank r e a c t o r s ) , the r e l a t i o n f \ _ ,„ %ι

(3a) i s v a l i d , where a i s a geometric f a c t o r and d i s the v e s s e l d i a meter. N e g l e c t i n g the r a t i o o f the v i s c o s i t i e s i n the bulk and a t the w a l l , a rearrangement y i e l d s


46


r

2 2 λ ρ ·ο Ρ Λ

h =

1/3 2/3

(3b)

•r.

w i t h s denoting the s t i r r e r , r being the r a t i o of the a c t u a l s t i r r e r frequency f to a standard frequency f , s p e c i f i c f o r a given s t i r r e r type and v e s s e l s i z e , and g (the g r a v i t a t y a c c e l e r a t i o n ) introduced to make Ζ dimensionless. In the r i g h t hand r e p r e s e n t a t i o n of (3b), f i r s t proposed by J e h l e and Oeschger [Xj], Ζ i s a property of the r e a c t o r (which can be t a b u l a t e d f o r standardized r e a c t o r s ) and γ i s a property of the l i q u i d . For v i s c o u s r e a c t i o n mixtures where we have a p a r t i c u l a r i n t e r e s t i n knowing h, th mine y, are not e a s i l y culate γ from the o v e r a l l heat t r a n s f e r c o e f f i c i e n t U i n the heat flow c a l o r i m e t e r , which i s obtained by the c a l i b r a t i o n procedure : Δ (Δτ) àq A

d

, 1 1 w 1 ' A = — = -— + τ— + -— U h. λ h D w r

= Β +

1 —— „ 2/3 Ζ -r -y c f

(4)

Here the i n d i c e s denote j a c k e t , w a l l , r e a c t i o n mixture and o a l o r i m e t e r v e s s e l , and Β i s the sum of the r e s i s t a n c e s of the w a l l and of the f i l m i n the j a c k e t . Β i s i n f l u e n c e d by the heat t r a n s f e r f l u i d , by the c i r c u l a t i o n c o n d i t i o n i n the j a c k e t and by the r e a c t i o n v e s s e l chosen. For a given s e t of equipment, Β de pends only on temperature and can be c a l i b r a t e d once and f o r a l l . This c a l i b r a t i o n has to be done c a r e f u l l y s i n c e Β i s the domina t i n g term of (4), due to the l a r g e r e s i s t a n c e of the g l a s s used as r e a c t o r w a l l . Therefore, the procedure o u t l i n e d here i s suggested f o r t y p i c a l r e a c t i o n mixtures (with v i s c o s i t i e s s i m i l a r to s u l f u r i c a c i d or higher) and not f o r l i q u i d s l i k e methanol or water. For very v i s c o u s f l u i d s , where (3) becomes i n v a l i d , Z l o k a r n i k [18] has proposed a more general r e l a t i o n . Experimental work i n t h i s flow r e g i o n i s i n progress. F i g . 8 compares a few y-values obtained experimentally i n the heat flow c a l o r i m e t e r w i t h the values c a l c u l a t e d from p h y s i c a l p r o p e r t i e s Q.9]. Table I i l l u s t r a t e s the s c a l i n g up procedure. One may conclude from t h i s t a b l e , t h a t r e l i a b l e estimates of heat t r a n s f e r c o e f f i c i e n t s are not only u s e f u l f o r design purposes, but are a l s o a v a l u a b l e c l u e f o r improving heat t r a n s f e r i n e x i s t i n g equipment. We have o f t e n found, p a r t i c u l a r l y i n g l a s s l i n e d v e s s e l s , t h a t poor c i r c u l a t i o n i n the j a c k e t c o n t r i b u t e s more to the o v e r a l l heat t r a n s f e r r e s i s t a n c e than the f i l m of the r e a c t i o n mixture.


4.


REGENASS

47

'TUT (Watt/m K) 3

2

- calcexp — • • H S0 96 % — A A Glycerol 100% 2

4

• Figure 8. Temperature depend 273

323

373

y

423

Table 1 L i q u i d mixture

τ [κ]

(1) Ύ

Reactor-type

' Z

(2)

( 1 )

r

h

r

( 1 )

cale

υ found

organic i n H S0

400

6100 .6 m ,(3)(5) .183 1040 350 150 (7) ±370 ί 40 320 (8) ±2000

nitrobenzene/

380

7100 ±3000

2

AICI

4

3

3

4 m , (3) (6) .153 1090 370 320 ±450 ± 50 3

naphta, aqu.ZnCl^ 330 s o l i d organic

80 (7) 3600 10 m , (3) (5) .134 480 270 ±140 ΐ 30 220 (8) ±1000

caustic fusion

500 ± 200

470

3

4 m , (4) (5) .153 3

77 70 + 30± 30

85

Remarks : (1) S i - U n i t s : watt/nr Κ (2) anchor a t s t a n d a r d i z e d frequency (3) g l a s s l i n e d s t e e l w i t h j a c k e t (4) N i - c l a d s t e e l , outside c o i l s (5) c o o l i n g by c i r c u l a t e d water (6) steam heating (7) before improving c i r c u l a t i o n (8) a f t e r improving c i r c u l a t i o n i n jacket.

American Chemical Society Library "55 16th St., N.W.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS SymposiumWashington, Series; AmericanD.C. Chemical Society: Washington, DC, 1978. 20036

48


Conclusions There i s an obvious need f o r thermal a n a l y s i s instruments which are s u i t e d t o the s p e c i f i c requirements of process develop ment. The bench-scale c a l o r i m e t e r presented i n t h i s paper i s de signed t o f i l l t h i s gap by p r o v i d i n g thermal and k i n e t i c informa t i o n i n conjunction with conventional synthetic i n v e s t i g a t i o n s . The r e a c t i o n models obtained from thermal data are as a r u l e v a l i d over a wide range of experimental c o n d i t i o n s and i n g e n e r a l p e r m i t the e l u c i d a t i o n o f the thermal s a f e t y aspects of a reaction. Used as a m i n i - p i l o t - r e a c t o r , the b e n c h - s c a l e - c a l o r i m e t e r i n many cases p r o v i d e s data which permits a d i r e c t scale-up t o p l a n t s c a l e , when c o n v e n t i o n a l means would n e c c e s s i t e a p i l o t stage. Thus, i t i s a powerful reducing c o s t and time Acknowledgment The author i s indebted t o many collègues f o r h e l p , i n p a r t i c u l a r to A. Runser, H.P. Gfrôrer, A. Mauerhofer, Dr. H. M a r t i n , Dr. W. G a u t s c h i , Dr. H. Randegger, Dr. P. F i n c k and Dr. W. Kanert f o r t h e i r c o n t r i b u t i o n t o the design of the c a l o r i m e t e r and t o Dr. H.U. M e i s t e r f o r f r u i t f u l s t i m u l a t i o n and generous support. He i s a l s o o b l i g e d t o P r o f . M. Brenner and t o P r o f . D.W.T. R i p p i n f o r t h e i r support of fundamental work on the method presented.

Nomenclature A p d g h f m Pr q r Re Δτ c

Τ U w Ζ y λ

e f f e c t i v e heat t r a n s f e r area s p e c i f i c heat J kg K diameter (or t h i c k n e s s ) dimensional constant 9.81 ms f i l m heat t r a n s f e r c o e f f i c i e n t Wm -2K -1 frequency (of s t i r r i n g ) s mass (of c a l o r i m e t e r contents) kg P r a n d t l number heat f l o w r a t i o (of frequencies) Reynolds number temperature d i f f e r e n c e (between c a l o r i m e t e r contents and j a c k e t ) r a t e of temperature change o v e r a l l heat t r a n s f e r c o e f f i c i e n t Wm" K e f f e c t i v e heat c a p a c i t y of c a l o r i m e t e r v e s s e l J K " "heat t r a n s f e r p r o p e r t y " of a s t i r r e d tank Wm" K "heat t r a n s f e r p r o p e r t y " of l i q u i d heat c o n d u c t i v i t y Wm V 1 X

Z

±

_ 1

1

2


1

1

4. y p

REGENASS

49


dynamic v i s c o s i t y density

kg m s kg m

subscripts : b : b u l k , j : j a c k e t , r : r e a c t o r contents, s: s t i r r e r , w: w a l l Literature cited 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Köhler, W. e tal.,Chem.Ing.Techn. 45 (1973), 1289 M a r t i n , H., Ph. D.Thesis, B a s e l , 1973 Regenass, W., G a u t s c h i , W., M a r t i n , H. and Brenner, Μ., Proc. 4th Int.Conf.Thermal A n a l . 3, 834, Budapest 1974 Hub, L., Ph.D.Thesis, ΕΤΗ, Z u r i c h , 1975 Becker, F. and W a l i s c h , W., Z.Phys.Chem. NF 46 (1965), 279 Swiss Patent 455 32 Regenass, W., Thermochim Wendtland, W.W., "Thermal Methods o f A n a l y s i s " , Wiley, 1974 US-Patent 3 994 164 G a u t s c h i , W., Ph.D.Thesis, ΕΤΗ, Zürich, 1975 Kanert, W., Ph.D.Thesis, B a s e l , 1977 Sestak, J. e tal.,Thermochim. Acta 7 (1973), 335 Becker, F., Chem.Ing.Techn. 40 (1968), 933 C o f f e e , R.D., AIChE-64th-Natl.Meeting (1969), P r e p r i n t 25C Eigenmann, Κ., 2nd Int.Symp. on Loss P r e v e n t i o n (1977) Lütolf, J., Staub, Reinh. L u f t 31/3 (1971), 94 J e h l e , E. and Oeschger, V., Ciba-Geigy, presented a t Dechema Jahrestagung 1968, but never p r i n t e d S l o k a r n i k , Μ., Chem.Ing.Techn. 41 (1969), 1195 G a u t s c h i , W., Ciba-Geigy, unpublished


5 Adsorption Studies at Reaction Conditions—Reactor Development and Evaluation for Transient Studies at Millisecond Rates R I C H A R D D. S T O L K *

and A L D R I C H

SYVERSON

Department of Chemical Engineering, Ohio State University, Columbus, OH

43210 The role of adsorptio i heterogeneou catalysi i t easily evaluated becaus sorption and reaction and the difficulty of measuring surface con centrations of reacting species on the catalyst at these conditions. Exploratory research directed toward devising a method for studying adsorption in gas-solid systems by means of a batch adsorber-reactor has been underway in this laboratory for several years. This technique provides an opportunity to examine the "adsorption" and "reaction" steps sequentially at reaction temperatures and pressures. How sharply the individual steps can be separated depends largely upon the magnitude of the differences in rates and upon the data resolution capability of the experimental apparatus. Interpretation of the transient rapid response measurements in terms of steady state operation is needed if these results are to be most useful. Recent studies in this laboratory indicate that this approach holds some promise and it is the purpose of this paper to describe the adsorber-reactor system and its performance capabilities. The most recent design provides rapid gas-solid contact in a constant volume cell with transient rates for temperature and pressure measurements in the millisecond region. Few adsorber-re actors have been devised to measure adsorption at reaction conditions. Winfield (1) described a high speed apparatus for adsorption studies at low pressure. Macarus (2) reported results on a high speed adsorption-reaction apparatus; his data were correlated with fixed bed catalyst studies of Sashihara (3) with encouraging results. The second generation high speed adsorption apparatus was built by Edwards (4) and Keller (5) and improved by Haering (6) in the early 1960's. They overcame many of the previous limitations by first treating and sealing the catalyst sample in a glass capsule which was then placed in the adsorber-reactor containing gaseous reactants at the desired temperature and *Present Address: Monsanto Enviro-Chem Systems, Inc. 800 N. Lindbergh Blvd., St. Louis, Missouri 63166 ©

0-8412-0401-2/78/47-065-050$05.00/0


5.

STOLK A N D SYVERSON

Adsorption Studies at Reaction Conditions

51

p r e s s u r e . The r e a c t i o n w a s i n i t i a t e d by c r u s h i n g the c a p s u l e b y remote c o n t r o l u s i n g a feedthrough d e v i c e . T h i s procedure a l l o w e d a pretreatment o f the c a t a l y s t w i t h r e a c t a n t s or products before s e a l i n g the c a p s u l e . For a binary s y s t e m either of the g a s e o u s r e a c t a n t s may be a d s o r b e d by the c a t a l y s t prior to the r e a c t i o n . Pretreating the c a t a l y s t p r o v i d e s some i n s i g h t i n t o the e f f e c t s of m u l t i - c o m p o n e n t a d s o r p t i o n at r e a c t i o n c o n d i t i o n s . The reactor d e s c r i b e d h e r e i n may be c o n s i d e r e d third g e n e r a t i o n . D a t a c o l l e c t i o n w a s f i r s t a c c o m p l i s h e d by r e c o r d i n g the a n a l o g s i g n a l s o n a tape r e c o r d e r . Later a m o d i f i e d P D P - 1 5 d u a l p r o c e s s o r d i g i t a l computer w a s d i r e c t l y c o u p l e d to the reactor i t s e l f . The equipment w a s c o m p l e t e d i n 1971 (7). S i n c e that time others i n c l u d i n g Becher (8), W o l f e (9), and N a s h (10) have u s e d the system for h i g h spee

Reactor D e s i g n Features The primary d e s i g n c o n s i d e r a t i o n w a s the arrangement of r e actor components to i n s u r e r a p i d g a s - s o l i d c o n t a c t . T h e m e a s u r ing d e v i c e s had to be c a p a b l e of operating at high temperature and have m i l l i s e c o n d time c o n s t a n t s . The parameters of i n t e r n a l and c a t a l y s t volume and their ratio are k e y elements i n a constant volume s y s t e m . The i n t e r n a l reactor volume must be m i n i m i z e d . C a t a l y s t volume w a s c h o s e n to c a u s e a d e t e c t a b l e p r e s s u r e change i n the s y s t e m d u r i n g the e x p e r i m e n t . After e v a l u a t i n g s e v e r a l d e s i g n c o n c e p t s to a c h i e v e r a p i d g a s - s o l i d c o n t a c t f o l l o w e d by e f f e c t i v e m i x i n g , a c o m b i n a t i o n " f l y w h e e l / f a n " w a s d e s i g n e d to c r u s h the g l a s s c a p s u l e and to provide gas c i r c u l a t i o n . A n i n c l i n e d grid and s c r e e n were added to separate the c a t a l y s t p a r t i c l e s from the c a p s u l e before c o n t a c t with the f l y w h e e l to reduce a t t r i t i o n . C l e a r p l a s t i c prototypes were b u i l t for e v a l u a t i o n at ambient c o n d i t i o n s . H i g h s p e e d (4000 fps) motion p i c t u r e s permitted o b s e r v a t i o n of a c a p s u l e b e i n g broken i n s i d e the r e a c t o r . E x a m i n a t i o n of the p i c t u r e s showed that g a s - s o l i d m i x i n g was e f f e c t i v e i n the m i l l i s e c o n d range and that v e r y l i t t l e d i s i n t e g r a t i o n of the c a t a l y s t o c c u r r e d . The reactor components and the a s s e m b l e d reactor are shown i n Figure 1 . Components of the reactor i n c l u d e : (1) c a p s u l e h o l d e r , (2) f l y w h e e l , (3) rotary f e e d t h r o u g h , (4) grid and s c r e e n , (5) p r e s s u r e t r a n s d u c e r , and (6) t h e r m o c o u p l e . The i n t e r n a l volume was 415 c c and h e l d a 24 c c c a p s u l e . The reactor w a s made of 304 s t a i n l e s s s t e e l and w e i g h e d about 35 p o u n d s . S p e c i f i c a t i o n s are p r e s e n t e d i n T a b l e 1 d e s c r i b i n g the upper l i m i t s of temperature and pressure for the major c o m p o n e n t s .


52


Figure 1. Adsorber-reactor


5.

A.

B.



53

T a b l e 1 . S p e c i f i c a t i o n s for the A d s o r b e r - R e a c t o r (1) Rotary Feedthrough 450 C 6Ô"psia (2) Pressure T r a n s d u c e r 485°C 68 p s i a (3) Thermocouple 485 C (4) M a n u a l Feedthrough B e l l o w s 30 p s i a Response Time to a Step C h a n g e (Time Constant) (1) Pressure T r a n s d u c e r 2-3 m i l l i s e c o n d s (2) Thermocouple 2-10 m i l l i s e c o n d s U

The capsule h o l d e r c o n t a i n e d the a c t i v a t e d catalyst i n a s e a l e d g l a s s c a p s u l e at the start of the t e s t . The r e a c t i o n w a s i n i t i a t e d b y m a n u a l l y rotating the holder 180 d e g r e e s r e l e a s i n g the c a p s u l e into the f l y w h e e l . H i g h Speed Pressure T r a n s d u c e r . The c h a r a c t e r i s t i c s of the D a t a m e t r i c s T y p e 531 B a r o c e l p r e s s u r e transducer are shown i n T a b l e g[. It c a n be operated a s a d i f f e r e n t i a l or a b s o l u t e type up to 450 C without c o o l i n g .

A. B. C. D. E.

T a b l e II. C h a r a c t e r i s t i c s of P r e s s u r e Transducer S e n s i n g Element: c a p a c i t i v e potentiometer R i s e T i m e : 2-3 m i l l i s e c o n d s H y s t e r e s i s : L e s s than 0.2% Temperature C o e f f i c i e n t of S e n s i t i v i t y : 0.01% C A c c u r a c y at 7 5 ° C : 0.2% of Reading p l u s 0 . 0 1 % F . S .

H i g h Speed T h e r m o c o u p l e , M i c r o - m i n i a t u r e c h r o m e l - a l u m e l t h e r m o c o u p l e s h a v i n g 0 . 0 0 2 - 0 . 0 1 0 s e c o n d time c o n s t a n t s were p u r c h a s e d from B L H E l e c t r o n i c s / I n c . The thermocouple w i r e i s 0 . 0 0 1 i n c h i n d i a m e t e r . A n a m p l i f i e r w i t h a g a i n up to 1000 w a s u s e d to produce a 10 v o l t s i g n a l . D a t a C o l l e c t i o n and Reduction In the b e g i n n i n g a tape recorder w a s u s e d to record the h i g h s p e e d t r a n s d u c e r d a t a . H o w e v e r , b e c a u s e of h i g h n o i s e l e v e l i n the s y s t e m , the data c o l l e c t i o n w a s i n t e r f a c e d w i t h a m o d i f i e d P D P - 1 5 d u a l p r o c e s s o r d i g i t a l computer. C o m p a r i n g the s i g n a l - t o n o i s e r a t i o for both s c h e m e s , the former h a d a 14:1 ratio w h i l e the latter h a d a 250:1 r a t i o . The p r e c i s i o n h a s been improved from about 10 torr for the tape recorder scheme to 0 . 3 torr for the c o m puter scheme without time a v e r a g i n g the d a t a . The e l e c t r i c a l s i g n a l s from the m e a s u r i n g d e v i c e s were t r a n s mitted v i a s h i e l d e d c a b l e d i r e c t l y into the computer. Internal to


54


the computer, the a n a l o g data were d i g i t i z e d to binary d e c i m a l and f i n a l l y recorded on D E C t a p e . The quantity of gas adsorbed w a s determined from the p r e s s u r e and temperature changes i n the constant volume c e l l . A f a s t r e s p o n s e pressure transducer and thermocouple monitored c o n t i n u o u s l y at a m i l l i s e c o n d f r e q u e n c y p r o v i d e d the b a s i c t r a n s i e n t d a t a . M e a s u r e m e n t of gas c o m p o s i t i o n i n s u c h a r a p i d l y changing s y s t e m i s d i f f i c u l t b e c a u s e of the n e e d to sample at high rates for a n a l y s i s . H o w e v e r , both i n i t i a l and f i n a l c o m p o s i t i o n s may be s a m p l e d when the s y s t e m i s at e q u i l i b r i u m . A p r o v i s i o n w a s made to i n s t a l l a p a i r of f i l a m e n t s for c o n t i n u o u s measurement of the gas thermal c o n d u c t i v i t y but they were not u s e d i n this s t u d y . Computer Program D e s c r i p t i o n ten i n both Fortran IV and M a c r o - 1 5 a s s e m b l e r l a n g u a g e . The p r o gram u s e d to c o l l e c t and store the data was written i n M a c r o - 1 5 language to a l l o w a 1000 c y c l e per s e c o n d s a m p l i n g r a t e . The program c a n sample three data c h a n n e l s , perform time a v e r a g e s , and make other c a l c u l a t i o n s a l l w i t h i n one m i l l i s e c o n d . It "waits" u n t i l the next m i l l i s e c o n d before r e p e a t i n g the c a l c u l a t i o n s and storage of d a t a . F i v e data sets were c o l l e c t e d during the e x p e r i m e n t . Two were at steady state prior to b r e a k i n g the c a p s u l e to evaluate the reactor c o n d i t i o n s . Thirty s e c o n d s of steady state data were c o l l e c t e d at a one s e c o n d f r e q u e n c y . One hundred data p o i n t s w i t h a one m i l l i s e c o n d s e p a r a t i o n were recorded to evaluate the n o i s e l e v e l o n the n o n - t i m e averaged d a t a . The three r e m a i n i n g data sets were a v e r a g e s b a s e d on 16 m i l l i s e c o n d v a l u e s . After the f i r s t s e c o n d of time had b e e n r e c o r d e d with m i l l i s e c o n d data p o i n t s , the s a m p l i n g rate was r e d u c e d to ten p o i n t s per s e c o n d for a ten s e c o n d p e r i o d . It w a s further r e d u c e d to one point per s e c o n d for the r e m a i n i n g p e r i o d . A t o t a l of 6390 data p o i n t s were c o l l e c t e d during the experiment l a s t i n g 15 m i n u t e s . Other computer programs were u s e d to reduce the data to p r e s sure and temperature v a l u e s . The data i n the two steady state data sets were reordered w i t h r e s p e c t to time s i n c e e a c h w a s c o l l e c t e d i n a l o o p w h i c h w a s c o n t i n u o u s l y b e i n g rewritten before the c a p s u l e b r o k e . A time b a s e w a s added to the data before b e i n g transferred to t a p e . Experimental Results In order to i l l u s t r a t e the c a p a b i l i t y of t h i s d e v i c e and p o s s i b l e areas of a p p l i c a t i o n to r e s e a r c h i n c a t a l y s i s , examples of


5.


Adsorption Studies at Reaction Conditions 55

r e s u l t s are reported i n the f o l l o w i n g c a t e g o r i e s : (a) d y n a m i c r e s p o n s e of the s y s t e m to a step p r e s s u r e c h a n g e , (b) a d s o r p t i o n rate s t u d i e s of water o n an a l u m i n a c a t a l y s t , and (c) t y p i c a l a d s o r p t i o n - r e a c t i o n r e s u l t s for c a t a l y t i c dehydration of tertiary butanol on alumina. Pressure R e s p o n s e C h a r a c t e r i s t i c s . A m e c h a n i c a l d e v i c e w a s not u s e d to i n i t i a t e the data c o l l e c t i o n b e c a u s e a f i n i t e time e l a p s e d after the c a p s u l e w a s r e l e a s e d from the holder u n t i l i t c o n t a c t e d the f l y w h e e l ; i n s t e a d a v o l t a g e change o n the t r a n s ducer s i g n a l e q u i v a l e n t to 15 torr w i t h i n 10 m i l l i s e c o n d s w a s found to be the b e s t w a y to start data c o l l e c t i o n . The s y s t e m r e s p o n s e to a step change c a u s e d by b r e a k i n g an empty c a p s u l e under v a c u u m surrounde stants were c a l c u l a t e d for 63.2% r e s p o n s e to the pressure change. T h e v a l u e s of 0 . 9 and 0 . 8 m i l l i s e c o n d s were r e c o r d e d at 13 and 196 C r e s p e c t i v e l y . The r e s p o n s e time of the pressure t r a n s d u c e r w a s adequate for t h i s m e c h a n i c a l s y s t e m and for the water and t - b u t a n o l s t u d i e s o n a l u m i n a . (Prior work showed that a 100 torr p r e s s u r e change o c c u r r e d i n 20-30 m i l l i s e c o n d s after the alumina w a s e x p o s e d to the a d s o r b a t e ) . 0

Transient Adsorption Studies: Water on Alumina. One e i g h t h i n c h a l u m i n a p e l l e t s (Type 100S) s u p p l i e d b y A i r Products C o r p . , Houdry D i v i s i o n were c r u s h e d i n t o s m a l l e r p a r t i c l e s and separated i n t o v a r i o u s f r a c t i o n s from - 1 0 to +200 m e s h . The alumina w a s a c t i v a t e d at 300 C at l e s s than 100 microns pressure for three h o u r s . A l l c a l c u l a t i o n s were b a s e d o n sample weight after activation. A s e r i e s of samples w a s t e s t e d u s i n g the s i z e f r a c t i o n s p r e sented i n Table III. Ad s o r p t i o n - t i m e c u r v e s of t h e s e samples are shown i n Figure 3 .

- M e s h Size 12/20 C a t . W e i g h t (g) 5 . 7 7 5 Initial Conditions Pressure (torr) 787 Temperature ( C)193

20/35 7.421

770 111

20/35 7.936

35/65 7.476

65/100 6.382

784 203

782 196

783 195

F i n a l C o n d i t i o n s After 15 minutes Pressure (torr)

579

357

525

523

545

Temperature ( C) 191 Max-temp. Ob s.( C.)223

114 136

199 227

194 215

193 220

$$ϊ£λ%

( g /g)*0-52 . 1.06 . 0.47 0.51 , 0.54 * m g m / g - m i l l i g r a m m o l e s adsorbed per gram o f c a t a l y s t m

T

m

u



56

Figure 2.

System response to pressure change

Figure 3.

Adsorption of water on 100S alumina


5.



57

The c u r v e s i n Figure 3 i n t e r s e c t the time corrdinate at 1 to 2 m i l l i s e c o n d s . T h i s time l a g a r i s e s b e c a u s e of the w a y the c o m puter c o r r e c t s for the c a p s u l e v o l u m e and sets time zero w h i l e the c a p s u l e i s b r e a k i n g i n the f i r s t two m i l l i s e c o n d s . S i n c e p a r t i c l e s i z e and shape are s i g n i f i c a n t factors i n m a s s transfer c o n s i d e r a t i o n s and the s i z e and shape d i s t r i b u t i o n s w i t h i n a g i v e n mesh s i z e for t h e s e experiments are not known , q u a n t i t a t i v e e v a l u a t i o n o f transport properties may not be m e a n i n g f u l . C e r t a i n l y the p o t e n t i a l for s u c h quantitative measurements seems p o s s i b l e . In a q u a l i t a t i v e s e n s e , the c u r v e s of Figure 3 are i n the order e x p e c t e d i f m a s s transfer were a dominant f a c t o r . A d s o r p t i o n R e a c t i o n S t u d i e s : D e h y d r a t i o n of t - b u t a n o l on A l u m i n a . Previous wor r e s u l t s i n a r r i v i n g at L a n g m u i r - H i n s c h e l w o o d or H o u g e n and W a t s o n type k i n e t i c models ( 2 , 6 , 8 , 1 0 ) w h e n the amount of a d s o r p t i o n at r e a c t i o n c o n d i t i o n s has b e e n d e t e r m i n e d . The t y p i c a l r e s u l t s p r e s e n t e d here repeat some e a r l i e r experiments w i t h , h o w e v e r , a much superior a p p a r a t u s . The b a s i s for t h i s procedure for e v a l u a t i n g the c o n c e n t r a t i o n o f a b s o r b e d s p e c i e s at r e a c t i o n c o n d i t i o n s r e s t s upon b e i n g able to measure a d s o r p t i o n w h i l e a much s l o w e r r e a c t i o n step t a k e s p l a c e . If the study i s to go b e y o n d the a d s o r p t i o n s t e p , the r e a c t i o n must be of the type that p r o d u c e s a change i n p r e s s u r e at c o n s t a n t v o l u m e and temperature. Figure 4 shows portions of a t y p i c a l a d s o r p t i o n r e a c t i o n h i s t o r y for the c a t a l y t i c d e h y d r a t i o n o f t - b u t a n o l on A l u m i n a 100S w h i c h has been treated or " c o n d i t i o n e d " w i t h water (6). The r e a c t i o n w h i c h i s endothermic p r o d u c e s one mole of i s o b u t y l e n e and a mole of water for e a c h mole of t - b u t a n o L The steep d e c r e a s e i n p r e s s u r e during the f i r s t s e c o n d (approximately) w a s c a u s e d by a d s o r p t i o n , then the s l o w r i s e r e s u l t e d from the r e a c t i o n . The ratio of a d s o r p t i o n rate to r e a c t i o n rate for t h i s c a s e w a s about 1700. The temperature r o s e during the f i r s t three s e c o n d s as a r e s u l t of the heat of adsorption then f e l l b e c a u s e of the endothermic r e a c t i o n and heat l o s s to the r e a c t o r . The temperature l a g may be due i n part to the s l o w e r r e s p o n s e of the t h e r m o c o u p l e . The amount of t - b u t a n o l w h i c h w a s measured b y the drop i n p r e s s u r e from the i n i t i a l v a l u e to the minimum i s c o n s i d e r e d to be the a d s o r p t i o n at r e a c t i o n c o n d i t i o n s . The t e c h n i q u e of c o n f i n i n g the c a t a l y s t i n a c a p s u l e permits v a r i o u s treatment or a c t i v a t i o n procedures as w e l l as e x a m i n a t i o n of m u l t i - c o m p o n e n t a d s o r p t i o n e f f e c t s . For a s i n g l e reactant s y s t e m r e a c t i o n products c a n be p r e a d s o r b e d at a known quantity to a s c e r t a i n the e f f e c t t h e s e might have on reactant a d s o r p t i o n and


58


700 h

Figure 4. Adsorption-reaction pressure transient for catalytic dehydration of tert-butanol

ί 0

I

I

I

I

L

0.2

0.4

0.6

0.8

1.0

Time-seconds

Figure 5.

Effect of water on tert-butanol adsorption


5.



59

r e a c t i o n r a t e . To a v o i d transport or d e s o r p t i o n the i n i t i a l p a r t i a l p r e s s u r e of the products i n s i d e and o u t s i d e the c a p s u l e c a n be made e q u a l . For r e a c t i o n s w i t h more than one r e a c t a n t , the b i n a r y a d s o r p t i o n e f f e c t s c a n a l s o be m e a s u r e d . Figure 5 shows the e f f e c t o f water o n the adsorption of t - b u t a n o l on 100S a l u m i n a . A i l r u n s i n v o l v i n g t - b u t a n o l (TBA) had about the same i n i t i a l p a r t i a l p r e s s u r e . M o s t adsorption-reaction experiments r e a c h the minimum pressure i n one s e c o n d , hence the time s c a l e for Figure 5 . The top curve r e p r e s e n t s the a d s o r p t i o n of 2:1 mixture of TBA and w a t e r . T h i s curve i s o n l y s l i g h t l y above the TBA c u r v e , w h e r e a s , were the a d s o r p t i o n of the two c o m p o n ents i n d e p e n d e n t , the total a d s o r p t i o n w o u l d be 60-100% higher as c a n be s e e n by adding the two s i n g l e component c u r v e s . The lower curve r e p r e s e n t s th a b s o r b e d water e q u i v a l e n t to a pressure of 208 t o r r . The s u p p r e s s i o n of the a d s o r p t i o n of TBA by preadsorbed water i s i n d e e d substantial. A d s o r p t i o n measurements at r e a c t i o n c o n d i t i o n s have b e e n c o u p l e d w i t h f i x e d b e d k i n e t i c data to arrive at s i m p l e k i n e t i c models w i t h one or two a d j u s t a b l e parameters (2 and 6). In r e c e n t work (10) the a d s o r b e r - r e actor has b e e n u s e d as a b a t c h reactor far o b t a i n i n g k i n e t i c data up to h i g h c o n v e r s i o n s i n a d d i t i o n to i t s u s e as an a d s o r b e r . Conclusions The d e s i g n and experimental r e s u l t s for some t y p i c a l a p p l i c a t i o n s of a h i g h temperature, h i g h speed constant volume a d s o r b e r reactor have b e e n p r e s e n t e d . Preliminary experiments i n d i c a t e that a d s o r p t i o n s t u d i e s c a n p r o v i d e a better i n s i g h t i n t o transport m e c h a n i s m s and the role of a d s o r p t i o n i n heterogeneous c a t a l y s i s thereby a s s i s t i n g the development of i m p r o v e d k i n e t i c models for these complex reactions. Acknowledgement The authors thank P r o f e s s o r E . R . H a e r i n g for h i s h e l p f u l a d v i c e on the t - b u t a n o l k i n e t i c s , Professor J . T . H e i b e l for h i s a s s i s t a n c e o n the computer data a c q u i s i t i o n f a c i l i t i e s and programming and M i c h a e l Kukla for h i s h e l p o n e l e c t r o n i c s . Financial support for f e l l o w s h i p s and g r a n t s - i n - a i d from The A m e r i c a n O i l C o m p a n y , Exxon C o m p a n y , E . I . duPont C o m p a n y , M o n s a n t o C o m p a n y , H e n r y D r e y f u s T e a c h i n g F e l l o w s h i p Program and the C h e m i c a l E n g i n e e r i n g D e v e l o p m e n t Fund are gratefully acknowledged.


60

CHEMICAL REACTION


Literature Cited 1. W i n f i e l d , M.E., Aust. J. of C h e m . , (1953),6, 221. 2. Macarus, D.P., Syverson,A. I&EC Proc. Design Dev, (1966), 5, 397. 3. Sashihara, T.F., Syverson, Α . , I&EC Proc. Design D e v . , (1966),5, 392. 4. Edwards, D.C., M.Sc. Thesis (1961), The Ohio State University, Department of Chemical Engineering. 5. Keller, R.M., M.Sc. Thesis (1962), The Ohio State University, Department of Chemical Engineering. 6. Haering, E.R., Syverson, Α . , (1974). J . of C a t a l y s i s , 3 2 , (3), 396-414. 7. Stolk, R.D., PhD Dissertation (1971) Th Ohi University, Departmen 8. Becher, J.H., PhD. Dissertation, (1972), The Ohio State University, Department of Chemical Engineering. 9. Wolfe, D.B., PhD. Dissertation, (1974), The Ohio State University, Department of Chemical Engineering. 10. Nash, G.L., M.S. Thesis, (1976), The Ohio State University, Department of Chemical Engineering.


6 Methanation in a Parallel Passage Reactor E . W . DE B R U I J N , W . A . DE JONG, and C . J. VAN DER S P I E G E L Laboratory of Chemical Technology, Delft University of Technology, Delft, The Netherlands

One of the steps i n the process of making SNG via coal g a s i f i cation, the methanation o attention i n recent years of the reaction, the temperature control of methanation reactors is difficult. Among the solutions proposed are the application of p a r a l l e l plate (1) and coated tube (2) reactors. I t i s also possi ble to apply recirculation of cold product gas, but when this i s done with conventional fixed-bed reactors the resulting high pres sure drop i s a disadvantage. The parallel passage reactor (PPR) recently described i n connection with S h e l l ' s Flue Gas Desulphurization Process (3) does not have this drawback because it contains shallow beds of solid reactant separated from narrow channels by wire screens, the gaseous reactants flowing through the channels with a r e l a t i v e l y low pressure drop. Such reactors could, i n p r i n c i p l e , be applied i n any process i n which large volumes of gas must be treated at minimum pressure drop, provided that sufficient capacity for absorption of the heat of reaction i s available. Ex amples of such processes are oxidation reactions, Fischer Tropsch synthesis and, as outlined above, carbon oxide methanation. This paper describes preliminary results of a study on this reactor using the methanation of carbon dioxide i n hydrogen at atmospheric pressure as the test reaction. Moreover, a mathematical model was formulated and used to compare computed conversions with experimental data. The objective of the first phase of this work is to obtain a rough estimate of the a p p l i c a b i l i t y of the PPR for methanation purposes. Experimental The test reaction^ C0 + 4 H CH, + 2 H 0 (ΔΗ° = -164.7 kJ/mole C0 ) 2 2 4 2 r,s 2 has been studied extensively and r e l i a b l e k i n e t i c data are a v a i l able (4_) . Work on the use of this reaction i n studying the tran sient behaviour of an adiabatic methanator indicates that i t can be applied as a test reaction between 200 ° and 280 °C, with good o

0

o

© 0-8412-0401-2/78/47-065-063$05.00/0


0

64


r e s u l t s (5). The k i n e t i c equation used i n the present work i s given i n t a b l e 1, along w i t h the experimental c o n d i t i o n s of the i n i t i a l phase of the work. The set of c o n d i t i o n s being covered i n current work i s a l s o given i n the t a b l e , as w e l l as i n f o r m a t i o n on the i n d u s t r i a l methanation c a t a l y s t a p p l i e d . Table I The r e a c t i o n r a t e i s given by: K exp.(-E /RT)p œ

r

a

^

C02

=

C Q

mol.h

2

1

+

K

C0 pC0 2

.g

2

Experimental c o n d i t i o n s

f i r s t phase

current work

Temperature Concentration Flow T o t a l pressure Reactant

208 0,1 0,0

190 -

°C vol% Nm /h atm. 3

H, 2

224

242

1 C0

H,

2

2

C a t a l y s t : G i r d l e r G-65 Ni/AUO.; NiO/AUO. = 3 : 3 s i z e = 0,35 - 0,42 mm; S = 42,4 m /g; 2

B E T

240

1 - 1 2 CO, C0 ,

w/w;

2

H0 2

particle = 6,6 m /g 2

The equipment used i s s i m i l a r to that of r e f . 4 , except f o r the p a r a l l e l passage r e a c t o r and the gas throug>ut, which i s between 0,1 and 0,5 Nm^/h. I t c o n s i s t s of a feed p r e p a r a t i o n s e c t i o n f o r metering and c o n t r o l l i n g the reactant mixture, the PPR immersed i n a f l u i d i z e d bed thermostat and a s e c t i o n f o r o n - l i n e a n a l y s i s of feed and product gases by gas chromatography. Figure 1 shows a b l o c k diagram. The dimensions of the r e a c t o r are shown i n f i g u r e 2. The two c a t a l y s t beds are f i l l e d w i t h p a r t i c l e s of 0.35-0.42 mm; the bottom and top p a r t s of the beds c o n t a i n i n e r t m a t e r i a l of the same dimensions to ensure that the flow regime i n the channel i s completely e s t a b l i s h e d when the gas reaches the c a t a l y s t beds. Reactor Model Let ζ be the coordinate i n l o n g i t u d i n a l d i r e c t i o n and y i n l a t e r a l d i r e c t i o n and assume that the c o n c e n t r a t i o n changes caused by r e a c t i o n and mass t r a n s p o r t to the c a t a l y s t bed are s i m i l a r to that of f i g u r e 3. I f the flow regime i n the channel i s laminar and the r e a c t o r i s o t h e r m a l , and supposing that mass t r a n s p o r t i n channel screen and c a t a l y s t bed are e n t i r e l y due to d i f f u s i o n , the mass balance f o r the channel reads: ν JC y 9z d 2 y The equation contains the assumption that the d i f f u s i o n can be represented by F i c k ' s law, i n other words that flow due to the volume change by chemical r e a c t i o n can be neglected. Furthermore, a x i a l d i f f u s i o n i s not taken i n t o account. A l s o , the channel i s taken to be wide enough to consider i t as being bounded by two = ] D


( 1 )

6.

BRuijN E T A L .

Methanation in a Parallel Passage Reactor

65

vent COo

reactor gas conditioning

H * I GC I gas chromatograph carrier gas p

2

digital integration Figure 1.

6

5

6

Block diagram of a parallel passage reactor

mm lateral cross section

wire screen

gas channel

inert longitudinal cross section catalyst

inert Figure 2.

Dimensions of a parallel passage reactor


66

CHEMICAL REACTION


i n f i n i t e l y wide p a r a l l e l p l a t e s . The boundary c o n d i t i o n s

are:

f| = 0 a t y = 0 ( 2 ) ; C = C a t ζ = 0 ( 3 ) ; D-|f - » - | f ^ q

B

=

f

(

a t

y

=

y

( 5 )

a n d

y-ia (4);

8c

V

=

1

a

6

e f f ^ V k y " (y^ > The d i f f u s i o n c o e f f i c i e n t i n the w i r e screen QD i n eq.4) i s taken to be equal t o the product of the screen p o r o s i l y and the d i f f u s i o n c o e f f i c i e n t i n the gas channel. Boundary c o n d i t i o n (5) must be found by i n t e g r a t i n g the mass balance over the c a t a l y s t bed, which f o r a volume w i t h thickness dy i n the x-z plane reads: eff· f £ - C < V b e d 3y 2 In t h i s equation, r ^ represents the r a t e equation of t a b l e I The e f f e c t i v e d i f f u s i o to the d i f f u s i o n c o e f f i c i e n bed p o r o s i t y and a f a c t o r f o r the t o r t u o s i t y of the d i f f u s i o n path. Both f a c t o r s are assumed t o be 3 according t o r e f . 6^. Assumptions made i n formulating the mass balance over the c a t a l y s t bed are that pore d i f f u s i o n l i m i t a t i o n i n the c a t a l y s t p a r t i c l e s can be neglected over the e n t i r e c o n c e n t r a t i o n range of e x i s t i n g i n the bed ( 5 ) , that the bed i s isothermal and homoge neous, and that mass t r a n s p o r t i n the bed i s e n t i r e l y due t o d i f f u s i o n . The boundary c o n d i t i o n s are: B

C = C

at y = y

k

r

k

p

(8) and | | = 0 at y = y

( 7 )

w

(9)

Numerical s o l u t i o n o f the mass balance i n the c a t a l y s t l a y e r i s r e l a t i v e l y simple. However, a complete s o l u t i o n i s superfluous since we are p r i m a r i l y i n t e r e s t e d i n mass transport at Ύ Ύ^Ι t h i s transport can be c a l c u l a t e d i f the f i r s t d e r i v a t i v e of the con c e n t r a t i o n i n the y - d i r e c t i o n i s known. I t i s p o s s i b l e t o o b t a i n t h i s d e r i v a t i v e a n a l y t i c a l l y from equation ( 8 ) ; i f t h i s i s done the r e s u l t i s : 3C 2A — = (—Ô(BC - I n (1 + B C ) ) + i n t e g r a t i o n constant ay 2 The i n t e g r a t i o n constant can be determined w i t h boundary c o n d i t i o n (9); i f C i s the c o n c e n t r a t i o n of reactant at the r e a c t o r w a l l one f i n d s : ~ = (^y(BC - I n (1 + BC) - BC + I n (1 + BC ) ) * (10) 0 : | ^ = ν = ω = 0 , Ψ = | dr 0 < r < 1, z = 0

(8)

: ω = 0 , Ψ = \ (1-r ) 2

(9)

2 r = 1, ζ > 0:ϋ = ν = Ψ = | ^ = 0 , ω = ^-4 dr

(10)

In the numerical a n a l y s i s the r a d i a l and a x i a l d e r i v a t i v e s of the p a r a b o l i c equations are replaced by the c e n t r a l d i f f e r e n c e ap proximations and the backward d i f f e r e n c e approximations, r e s p e c t i v e l y . Thus N-l s e t s of f i n i t e p a r a b o l i c d i f f e r e n c e equations are ob t a i n e d , Ν being the number of r a d i a l steps. The number* of e q u i d i s tant g r i d p o i n t s i n r a d i a l d i r e c t i o n amounted to 40, w h i l e f o r the f i n i t e d i f f e r e n c e increment of ζ(= 2z/Re) a value of 1.25 10"^ was used. D e t a i l s of the numerical s o l u t i o n procedure are given elswhere (J_2). F i g u r e 1 i s a g r a p h i c a l r e p r e s e n t a t i o n of the development of the a x i a l v e l o c i t y obtained by the numerical s o l u t i o n procedure. This r e s u l t agrees q u i t e w e l l w i t h that obtained by Vrentas e t . a l . (11). The Tube Wall Catalyzed Reaction Assuming incompressible flow of a Newtonian f l u i d and no c o n t r i b u t i o n s i n the azimuthal d i r e c t i o n a mass balance f o r a d i f f e r e n t i a l element i n the en trance r e g i o n of the tube y i e l d s the f o l l o w i n g steady s t a t e d i mensionless d i f f e r e n t i a l equation: 1^2 + !kp' poison d e p o s i t i o n r a t e constants, d e f i n e d i n eqns. ( 2 ) , (6) and (5) r e s p e c t i v e l y L l e n g t h of m o n o l i t h , 8.1 cm L t o t a l c a t a l y t i c a l l y a c t i v e s i t e s , gmole/cm Leo t o t a l amount t h a t c o u l d be adsorbed at s a t u r a t i o n , gmole/cm t t h i c k n e s s of c a t a l y t i c l a y e r , 0.0025 cm P,P fluid-phase Pecle respectively, P P f l u i d - p h a s e P e c l e t number f o r heat, P r R e [ ( a / 2 ) / L ] , 0.4 Q dimensionless parameter of s o l i d phase c o n d u c t i v i t y , [(2naLkf)/(k S )]«[L/a], 2500 Re Reynolds number, 150 r r a t e of r e a c t i o n gmole/cm sec, a l s o r a d i a l c o o r d i n a t e , cm S e f f e c t i v e s u r f a c e area of c a t a l y t i c l a y e r per volume of c a t a l y t i c l a y e r , cm /cm S c r o s s - s e c t i o n area f o r s o l i d phase, c a t a l y t i c l a y e r p l u s the ceramic r e g i o n , cm t time, sec t» time t o s a t u r a t e a v a i l a b l e s i t e , i f the poison deposited immediately, sec, 2 π a L £ S L » / π a ν c Τ temperature, °K u dimensionless c o n c e n t r a t i o n f o r CO, c o / C 0 0 ν dimensionless temperature, T/T ' w dimensionless c o n c e n t r a t i o n f o r poison p r e c u r s o r , Cp/cç-Q w = 0.0002 ζ a x i a l c o o r d i n a t e , cm

(-AH)CQ

4

2

r

3

λ

2

2

!I

f

s

c

3

v

2

3

c

2

2

v

p f

c

c

0

0

Greek Symbols t h e r m i c i t y parameter f o r CO, [k^Q o ( " ^ ) c O C O o ^ ^ t o l > 0.16 t h e r m i c i t y parameter f o r p o i s o n p r e c u r s o r , [kp,o(-AH) c a>L]/[kT ], 0 a / i , 25 A r r h e n i u s numbers f o r CO o x i d a t i o n and s e l e c t i v e poison d e p o s i t i o n r e s p e c t i v e l y , E / R T , E"/RT d i f f u s i v i t y ratio, D /D dimensionless a x i a l c o o r d i n a t e , z / L unpoisoned f r a c t i o n of a d s o r p t i o n s i t e s , ( l - c / L ) , and (1 - c^/L) r e s p e c t i v e l y f o r n o n - s e l e c t i v e and s e l e c t i v e poisoning dimensionless r a d i a l coordinate f o r f l u i d phase, r/a dimensionless r a d i a l c o o r d i n a t e f o r s o l i d phase, (r-a)/£ dimensionless Jtime, t(Dp C0 0 ^ ( v ^ ^ ) l t and [ (D c )/(LcoS 't )ft f o r s e l e c t i v e and n o n - s e l e c t i v e H

β β"

p

γ e,e

M

C 0

0

|_ § τ

a

if

o

0

ie

w

c

L S

e

2

p e

C 0 > 0

k T

o

C0

Δ ζ θ

c

v


œ

10.

Poisoning in Monolithic Catalysts

L E E A N D ARIS

0,0p

poisoning r e s p e c t i v e l y , approx. 0.2t/too T h i e l e moduli f o r CO and poison p r e c u r s o r , i*/kco 0^ ( ^\/kp /D respectively dimensionless a d s o r p t i o n c o e f f i c i e n t , 65.5 y , 0 e x p ( 9 6 1 / T v ) , y o , 0 - > s> ° D

y

0

to

pe

= 0

C 0

CO f ο ρ ps s w 11

121

o

s

04

T

K

C

Subscripts carbon monoxide fluid-phase value reference value, i . e . i n l e t value poison precursor poison p r e c u r s o r a t t h e s o l i d s u r f a c e solid-phase value poison deposited Superscripts poison p r e c u r s o r v a l u e a p p r o p r i a t e t o the c a t a l y t i c cup-mixing v a l u e

surface

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Butt, J . B . , Adv. Chem. Ser., (1972), 109, 259. Hegedus, L . L . and Petersen, Ε. E.; Chem. Engng. Sci., (1974), 28, 345. Hegedus, L . L., Ind. Eng. Chem. Fundls., (1974), 13, 3, 190. Becker, E. R. and Wei, J., 4th ISCRE, Heidelberg(April 1976). Froment, G. F . and Bischoff, Κ. Β . , Chem. Engng. Sci., (1961), 16, 189. Luss, D. and Erwin, Μ. Α., AIChE J1., (1970), 16, 979. Olson, J . H . , Ind. Eng. Chem. Fundls., (1968), 7, 185. Wei, J., Adv. in Catalysis, (1975), 24, 57. Heck, R. H . , Wei, J., and Katzer, J . R., AIChE J1., (1976), 22, 477. Finlayson, B. A. and Young, L . C., AIChE J1., (1976), 22, 331. Hegedus, L . L., Baron, Κ., J1., Catalysis, (1975), 37, 127. A r i s , R. and Lee, S.-T., Chem. Engng. Sci., i n press. Smith, J . M . , "Models i n Ecology," Cambridge University Press, Cambridge, 1974.


11 Micromixing Phenomena in Continuous Stirred Reactors Using a Michaelis-Menten Reaction in the Liquid Phase E D U A R D P L A S A R I , R E N É D A V I D , and J A C Q U E S V I L L E R M A U X Laboratoire des Sciences du Génie Chimique, C N R S - E N S I C 1, rue Grandville, 54042 Nancy Cedex, France

Micromixing phenomen work i n recent years. Their importance i s now recognized from both p r a t i c a l and fundamental points of view. In practice, micro mixing plays an important role when two streams of reacting fluids are put into contact and react rapidly before achieving perfect mixing on the molecular scale (e.g. combustion and precipitation reactions), or when complex reactions are carried out i n viscous media (e.g. continuous polymerization reactions). On the fundamen tal side, the study of coupling between reaction and mixing may y i e l d valuable information on the mechanism of turbulent mixing. In spite of the publication of many papers on the subject, micro mixing processes are far from being c l e a r l y understood. In one category of models, micromixing i s described i n the age space. These models are often abstract and they obviously lack a clear physical meaning. In a second category, interaction i s supposed to take place i n the physical space between neighbouring f l u i d aggregates. Three mechanisms have been invoked : 1) Random coalescence processes (1_) characterized by the i n teraction frequency ω±, or the interaction time t j = Ι/ωχ. 2) mass-transfer between one particular aggregate and a bulk made up of a l l other aggregates that are s t a t i s t i c a l l y interacting with i t (2) (3_) (4_) . The parameter i s here a f i c t i t i o u s mass trans fer coefficient or i t s reciprocal, the micromixing time t (I.E.M. model). 3) molecular diffusion of species into the aggregates (5_) (, X 3 are mole f r a c t i o n s of ethylene, propylene, and l> 2 hexadiene r e s p e c t i v e l y i s vanadium i o n c o n c e n t r a t i o n ( m i l l i m o l e / l i t e r ) τ i s shear s t r e s s i s volumetric flow Q a, h, Κ and g are d e f i n e d i n the t e x t ±

x

x

Acknowledgement : The author i s g r a t e f u l t o R. L. Turner f o r d i s c u s s i o n s of h i s work on laminar v e l o c i t y d i s t r i b u t i o n s and f o r p o i n t i n g out the method of L. H. Thomas.


152


REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Husain, A. and A. E. Hamielec, CEP Symposium Series (1976) 160 112 Sala, R., F. Valz-Griz and L. Zanderighi, Chemical Eng. S c i . (1974) 29 2205 Wyman, C. E. and L. F. Carter, CEP Symposium Series (1976) 160 1 Ghosh,M., D. W. Foster, J. P. Lenczyk and T. H. Forsyth, CEP Symposium Series (1976) 160 102 Shih, Chi-Kai, Unpublished von Rosenberg, D. V, "Methods for the Numerical Solution of P a r t i a l D i f f e r e n t i a l Equations," P-8, American Elsevier, New York, 1969 Petersen,R. E. A. an Lynn, S. and J. E Lynn, S. AIChE Journal (1977) 23 389


13 Comparison of the Performances of Various Fermentors and Selection Criteria J. P. E U Z E N , P. T R A M B O U Z E , and H .

VAN

LANDEGHEM

Institut Francais du Petrole, C . E . D . I . , B.P. 3, 69390,Vernaison, France

For several decade i n d u s t r i a l operation. Systemati bega y years ago, chiefly at the time of the development of processes whose main objective was the production of biomass. Our own research was carried out i n this context, and accompanied the development of fermentation processes using as substrate either hydrocarbons or methanol. Our pre-occupation was to improve the economics of the process : it was therefore necessary to find appliances which could operate with a minimum fermentor volume and low energy consumption. Our criteria of choice were therefore essentially based on biomass productivity (weight of biomass/unit of volume and time) and energy consumption per kg of dry material produced. The acquisition of comparative values for different a p p l i ances i s very difficult. In fact it became apparent that the nature of the s t r a i n and fermentation conditions noticeably affected the conditions of mass transfer and consequently the overall kinetics of the cell growth. A priori oxygen and hydrocarbons are i n the same s i t u a t i o n , that means that mass transfer phenomena between two f l u i d phases will l i m i t free c e l l growth, but we shall see that hydrocarbons have a special behaviour. In fact since 1967, several authors (1_, 2_) have confirmed that the transfer of paraffins was far too rapid to be explained l i k e O2 transfer by a transfer v i a the aqueous phase : diffusion and s o l u b i l i t y coefficients are far too low. In the same way a direct transfer between the c e l l s and the hydrocarbon drops seems highly u n l i k e l y . I t was A.AIBA who i n 1969 ( 2 ) introduced the idea of pseudo-solubility or "accomodation" of the hydrocarbon i n sub-micronic drops. The v a l i d i t y of this idea has been demonstra ted on several occasions (3, 4_, _5, 6) which now allows to treat hydrocarbons as a soluble substrate with, however, this p a r t i c u l a r i t y that the value of the saturation constant depends not only on the nature of the s t r a i n but also on the previous history of ©

0-8412-0401-2/78/47-065-153$05.00/0


154

CHEMICAL

REACTION


the c u l t u r e . I t has i n f a c t appeared t h a t t h i s accomodation occurs only thanks to the presence i n the c u l t u r e medium of a c e r t a i n number of s t i l l not c l e a r l y i d e n t i f i e d s u r f a c t a n t s . Consequently a l i m i t a t i o n by hydrocarbons i s not more l i k e l y to occur than t h a t of other s o l u b l e s u b s t r a t s , so that i n a w e l l conducted fermentation, oxygen has every chance of being the only growth l i m i t i n g s u b s t r a t e . We know moreover that s u r f a c t a n t substances i n f l u e n c e mass t r a n s f e r s , even g a s - l i q u i d t r a n s f e r s , as a r e s u l t of m o d i f i c a t i o n s of the i n t e r f a c i a l area and of the t r a n s f e r c o e f f i c i e n t (among others ( 7 ) ) . Conclusions which might be drawn on the t r a n s f e r k i n e t i c s from chemical or physico-chemical measurements are t h e r e f o r e suspect, and only d i r e c t compariso f fermentatio r e s u l t g i v e r i s e to v a l i d c o n c l u s i o n s well-known and c o n t r o l l e d however to some experimental r e s u l t s obtained by the o x i d a t i o n of sodium s u l p h i t e method. Experimental Methods. a

) " Oxydation of sodium s u l p h i t e . The method and the physico-chemical c o n s t a n t s , were borrowed from REITH ( 8 ) . b) - Fermentations. The fermentations were c a r r i e d out i n an aqueous n u t r i t i v e medium w i t h o p t i m i z a t i o n f o r the e s s e n t i a l c o n s t i t u e n t s (Ν, Κ, P, o l i g o - e l e m e n t s , v i t a m i n s ) t a k i n g care to a v o i d any d e f i c i e n c y of s o l u b l e s u b s t r a t e s . The carbon source was a η-paraffin commercial cut w i t h 12-20 carbon atoms. The s t r a i n used was a Candida T r o p i c a l i s ; a i r provided the oxygen w h i l e the n i t r o g e n supply and pH c o n t r o l (pH « 3,5) was made by ammonia i n j e c t i o n . Some e v o l u t i o n of the s t r a i n c h a r a c t e r i s t i c s allowed a s m a l l i n c r e a s e of the fermentation temperature i n the l a s t experiments (30 to 35 °C). Experimental R e s u l t s and I n t e r p r e t a t i o n . We were i n t e r e s t e d i n 3 types of fermentors d u r i n g t h i s study : - m e c h a n i c a l l y s t i r r e d fermentors - a i r - l i f t fermentors - loop fermentors. The l a s t - o n e , s t i l l undergoing experimentation w i l l thus only be r e f e r r e d to b r i e f l y . Concerning i n t e r p r e t a t i o n of the r e s u l t s we have adopted the following simplifications : - the oxygen consumption i s of 2 kg/kg of c e l l s - i n our s t i r r i n g c o n d i t i o n s the t r a n s f e r c o e f f i c i e n t k^ w i l l be taken as a constant equal to 1,80 m/h; t h i s approximation has f r e q u e n t l y been confirmed (7^ 8).


13.

EUZEN

ET AL.

Fermentor Performance and Selection Criteria

155

a) - M e c h a n i c a l l y s t i r r e d fermentors. F i g u r e 1 shows diagrams of 3 fermentors s t u d i e d . The f l a t - b l a d e t u r b i n e may be surrounded by a c y l i n d e r p i e r c e d w i t h openings between the t u r b i n e s and w i t h s m a l l holes at the l e v e l o f the t u r b i n e s . I t was the v e r s i o n without a c y l i n der which was p r e f e r a b l y used i n the fermentation t e s t s , w h i l e d i f f e r e n t geometries were s t u d i e d more s y s t e m a t i c a l l y by the oxydation of sodium s u l p h i t e . R e s u l t s obtained are summarized i n f i g u r e 2 i n the form suggested by REITH ( 9 ) . The powers and i n t e r f a c i a l areas are thus expressed per u n i t volume of non-expanded l i q u i d phase. The power Ρ i s the sum of the one r e s u l t i n g from the i s o t h e r m i c expansion of the i n j e c t e d gas and the mechanical power absorbed by the l i q u i d phase. The i n t e r f a c i a l area method, o r e l s e c a l c u l a t e d from fermentation r e s u l t s . The f o l l o w i n g comments might be made : - the c y l i n d r i c a l b a f f l e s f i t t e d to provoke a strong shearing a c t i o n at t u r b i n e l e v e l have a negative e f f e c t f o r oxygen t r a n s f e r , and serve no purpose f o r the t r a n s f e r of hydrocarbons,which w i t h a good s t r a i n are p s e u d o - s o l u b i l i z e d by the s u r f a c t a n t s ; - the energy supply i s more e f f i c i e n t l y used i f i t i s provided by a i r , r a t h e r than by s t i r r e r s ; - f o r a g i v e n energy source and f o r a g i v e n s t r a i n the r e s u l t s can be expressed a p p r o x i m a t i v e l y as f o l l o w s : Ζ = P/V L ΚΖ (1) with 0,6 < α < 0,7 100 < Κ < 200 f o r the systems used T

α

A good choice of fermentor should t h e r e f o r e be able to g i v e a Κ v a l u e of a t l e a s t 200 (a = 0,65), which i m p l i e s a kÂ v a l u e c a l c u l a t e d as f o l l o w s :

\k = 1,8 * 200 Z

a

= 360 Z

a

1

(h" )

(l

f

)

b) - A i r l i f t fermentors. Two types o f fermentors were used ( f i g . 3 ) . F i v e dimensions, from 60 to 1 900 l i t e r s , were t e s t e d f o r type A. The experimental data ( t a b l e I and f i g u r e s 4 & 6 ) were, once more, c o r r e l a t e d by a law of the form suggested by WANG (J2) A = K Z with 0,6 < α < 0,7 The Κ f a c t o r i s i n f l u e n c e d by the geometry of the system, by operating c o n d i t i o n s , and by the nature of the s t r a i n . Moreover successive s e l e c t i o n s m o d i f i e d the nature o f the s t r a i n between c e r t a i n t e s t s e r i e s on a i r l i f t s . This e x p l a i n s why d i f f e r e n t performances may have been noted on s i m i l a r fermentors. Thus the s t r a i n used i n the type A 850 1 a i r l i f t r e a c t o r i s probably l e s s oxygen demanding, which would b r i n g the value of A down to a l e v e l approwimately 40 % lower (arrows on f i g u r e 4 ) . The outputs being non-ambiguous magnitudes, t a k i n g energy consumption per kg a


156


Figure 2. Mechanically-stirred fermentors


EUZEN ET

foam

AL.


breaker

coolant

TYPE

Β

Figure 3. Two types of airlift fermentors

Figure 4. Air lift fermentors



cm/s

S

V

3

26

3,5

2,75 -

780

4,20

0,5

0,65

0,58

0,13

0,47

-

3,20

1,5

590

19

0,29

0,33 4,30

800

-

1,40

12,5

0,28

3,2

2,00

370

-

1 ,50

18 590

0,75

1 ,50

278

-

1 ,15 -

-

0,56 0,77

1 ,35

250

-

0,75

9

13,5

0,89

0,17

0,74

333

-

8

0,09

0,65

1 ,55 1 ,80

287

-

1

1 ,33

-

0,41

15

1 ,70

315

-

0,7

8

_

0,26

12

1,55

287

C - LOOP FERMENTOR -

3 300

Type_R

1 900

850

235

160

60

Tyge_A

• 0,4

0,87

3,0

280

55

2,60

2,90

450

5

-

1,42

2,4

79

Β - AIR LIFT

-

1 ,38

2,6

236 220

86

3,60

1 - ε

3,40

Ε kWh/kg02

Energy Consumption

1 ,45

YoV! kg 02/nrh

Product!vi ty XF

1,95

A m2/m3

Interfacial area

450

kW/m3

Mechanical energy fraction (%)

450

(1 000 rev/mi η)

A - MECHANIC AL STIRRING -

1

V

L

Volume

Performances of some fermentors

TABLE I

Symbol s

©

v

Δ

8

8

X X 0 0 0

• •

• • •

of fig. 4, 5

00

13.

EUZEN ET AL.


159

of oxygen consumed against Ζ = P / V ^ seems more s u i t a b l e . This r e p r e s e n t a t i o n avoids the ambiguity on the 0~ concentra t i o n i n the bulk o f the l i q u i d . Indeed, the presence o f hydrocar bons i n the medium provokes an important d r i f t on the 0£ measurements w i t h d i s s o l v e d O 2 probes. I f , as a f i r s t approximation, the oxygen p r o d u c t i v i t y π i s p r o p o r t i o n a l t o the i n t e r f a c i a l area π - A = Κ Z (2) we can s t a t e as s p e c i f i c energy consumption a

Ε = Ζ/π = Kj Ζ

1

α

"

(3)

This relationship i s respected ( f i g . 6 ) , and Kj depends on the s t r a i n and on the fermentation system. A l l our previous c o n c l u sions a r e , o f course, confirmed by t h i s r e p r e s e n t a t i o n . I t does c l e a r l y appear t h a t , a Ζ = P / V L i s more worth bulky. The compromise between these two c o n t r a d i c t o r y f a c t o r s which, i n the absence o f other requirements, w i l l go to make up the c r i t e r i a f o r fermentor choice. c) - Loop fermentors. F i g u r e 5 shows the b a s i c designs o f a loop fermentor (10, 11). The important r e c i r c u l a t i o n ensures a good b r o t h homogeneity and permits i n t e r e s t i n g heat and mass t r a n s f e r s . The s o l e o p e r a t i o n a l p o i n t a v a i l a b l e f o r an i n d u s t r i a l p l a n t , i s l o c a t e d c l o s e t o the r e s u l t s observed f o r the other fermentors (fig. 6 ) . Conclusions. Apart from a c e r t a i n number o f requirements, the r e l a t i o n s h i p developed so f a r enable us t o draw some u s e f u l c o n c l u s i o n s r e g a r ding the choice o f the fermentation system and i t s o p e r a t i n g c o n d i t i o n s . I t i s thus that mechanical systems, showing up badly i n f i g u r e s 2 and 6 , are not t o be r e t a i n e d , and t h a t , among a i r l i f t type equipment, a compromise should be sought between r e a c t i o n a l volume and energy consumption. The f a c t o r s on which t h i s compromise might be based are i n f a c t a v a i l a b l e . The h o u r l y cost o f o p e r a t i o n fermentation equipment producing X kg/h o f yeasts might be s t a t e d : c o s t = a X+ aj + a EXY + P Q

2

Q

R

+ P

Where : a^ nutrient price a^ f i x e d expenditure a^ cost o f a i r compression energy ( t a k i n g i n t o account y i e l d ) P cost o f r e a c t o r ( a m o r t i z a t i o n ) Pç cost o f compressor idem R

c

(F/h)

(4)

F/kg o f yeast F/h o f o p e r a t i o n F/kWh F/h of o p e r a t i o n

These two l a t t e r terms could be w r i t t e n as f o l l o w s :


CHEMICAL

160

REACTION


air out Γ Γ Τ ~ medium in i I | |

j

coolant

® medium in

coolant

k air out

m

medium out

air out

medium out

•βdesaprating pump

Figure 5.

Loop fermentors

Ε kwh/kgO?

Symbols see table I

K,= VL

0.65

(P

^ K,=

_1,0

0,30

V

1

I

,

1 0

Ψ kw Vj. m

3

Figure 6. Final comparison of the various studied fer mentors


13.

EUZEN

P

R


ETAL.

=

(

V L

)

161

supposing the p r i c e o f the r e a c t o r depends on i t s l i q u i d volume

a

a^ a^

C 4 * s p e c i f i c operating cost o f fermentor s p e c i f i c o p e r a t i n g cost o f compressor . Thus the p r i c e o f the yeast i n F/kg would come t o :

p r i c e = a + aj/X + a E Y Q

2

Q

+ a (V )^/X + 3

L

Ύ

Ρ /Χ (F/kg) (5)

For b i g compressors γ i s i n the range of 0.8 t o 1 (13). I f f o r the sake o f s i m p l i c i t y we take γ = 1, we o b t a i n : p r i c e = a + α /Χ + Κ , Υ ^ + α^Ζ^Κα^ χ

Q

owing t o

V

L

= Ρ/Ζ,

Ρ/Χ = E Y

Q

and

X ^.Y^-Z^F/kg^)

Ε = KjZ

.

Then the optimal Ζ v a l u e i s obtained when : Ζ

. opt

Il-a

a

(K-XY a

2 4

1

0

) J

1 +αβ-α

(7)

As we have seen α i s c l o s e to 2/3, w h i l e β i s somewhere between 0,6 and 1. I t can be pointed out that a b i g s i z e fermentor has to be operated w i t h a lower P / V ^ value than a s m a l l s i z e one. We can a l s o see that the optimum P/Vt f o r l a r g e appliances which, i n 1969, was i n the r e g i o n of 1.5 kW/m^, i s tending t o evolve as a r e s u l t o f changes i n r e l a t i v e energy/investment c o s t s , towards l e s s productive u n i t s w i t h a lower s p e c i f i c ener gy consumption. An ambiguity does however p e r s i s t f o r a i r l i f t fermentors: the volume which we c a l c u l a t e d above i s a l i q u i d volume. However there i s no means by which, i n these a p p l i a n c e s , we can p r e d i c t and c o n t r o l the expansions. As a r e s u l t , i n i n d u s t r i a l p r a c t i c e , a very high "expansion volume" i s to be expected, w h i l e adapting the gas v e l o c i t y to the foaming p r o p e n s i t i e s o f the c u l t u r e i s an i n s i t u o p e r a t i o n . I t i s t h i s absence o f p r e c i s i o n i n the design stage, i n v o l v i n g as i t does the danger o f a c e r t a i n l a c k of homo g e n e i t y , which i s the weak p o i n t o f these a p p l i a n c e s . Loop fermen t o r s , e a s i e r to c o n t r o l from t h i s p o i n t of view, could thus represent a step foreward on c o n d i t i o n however that t h e i r u n i t volume and t h e i r energy consumption prove to be c o m p e t i t i v e . I n any case they w i l l always have an advantage i n terms o f the heat t r a n s f e r c o e f f i c i e n t s i n the r e - c i r c u l a t i o n loop. I t should a l s o be noted t h a t the c r i t e r i a of p r o d u c t i v i t y and energy consumption alone are i n s u f f i c i e n t c r i t e r i a on which to base a choice o f fermentor. The importance of m a i n t a i n i n g a homogeneous " b r o t h " c o u l d , i n f a c t , be d e c i s i v e i f , f o r example, the f u n c t i o n i n g were to be d i s t u r b e d by excessive sedimentation or foaming. On the other hand, w h i l e s u b s t r a t e y i e l d depends on



162

the fermentor p r o d u c t i v i t y , some o v e r s i m p l i f i c a t i o n has been made i n t h i s study and more experimental work i s needed t o f i n d out the t r u e o v e r a l l optimum f o r the process. In t h i s respect i t must never be f o r g o t t e n t h a t , w h i l e a fermentor i s c e r t a i n l y a chemical r e a c t o r , i t i s a l s o one i n which the presence o f l i v i n g substances d i s t u r b s the t r a d i t i o n a l working of the equipment, i n p a r t i c u l a r as f a r as t r a n s f e r and expansion f a c t o r s are concerned. I t i s t h e r e f o r e o n l y by comparing equipments, i n the presen ce o f the s t r a i n whose i n d u s t r i a l use i s being considered, that i t would be p o s s i b l e t o o b t a i n t r u l y r e p r e s e n t a t i v e c o n c l u s i o n s . L i s t o f Symbols A Ε k-^ Ρ Vg X YQ Ζ ε φΜ ΤΓ

i n t e r f a c i a l area nrVnr s p e c i f i c energy consumptio g mass t r a n s f e r c o e f f i c i e n t m/h t o t a l power kW l i q u i d volume i n fermentor m^ s u p e r f i c i a l gas v e l o c i t y cm/s pondéral b r o t h f l o w r a t e kg/h weight oxygen consumed/weight c e l l s produced t o t a l power per u n i t o f l i q u i d volume kW/m l i q u i d volume f r a c t i o n i n fermentor mechanical energy f r a c t i o n % p r o d u c t i v i t y expressed as kg C^/m o f l i q u i d . h

Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

B. ERDSIECK, Thesis, Eindhoven (The Netherlands) (1967) A. AIBA et alii, J. Ferment. Technol, 47, 211 (1969) F. YOSHIDA and alii, Bioeng.& Biotechn, X I I I , 215(1971); i b i d XV, 257 (1973) ; i b i d XVI, 635 (1974) M. CHAKRAVARTY et alii,ibid, XIV, 61 (1972) ; i b i d XVII, 399, (1975) D.A. WHITWORTH et alii,ibid, XV, 649 (1973) G. GOMA et alii, J . Ferment. Technol., 51, 616 (1973) A. BENEDECK et alii, Bioeng.& Biotechn., X I I I , 663 (1971) T. REITH, Thesis, Delft (1968) T. REITH, Brit. Chem. Eng. 15, 1562 (1970) H. ZIEGLER et alii, Bioeng. & Biotechn., XIX, 507 (1977) K. SCHEIER, Chem. Rundschau, 38, 18 (1976) D.I.C. WANG et alii,8e World Petroleum Congress, Panel discussion "Petroleum and Microbiology" P.152(1971) P. LEPRINCE et alii, Manuel d'Evaluation économique de procédés. Ed. Technip. Paris (1976)


14 Kinetic Analysis of Unbalanced Bacterial Growth in Temperature Shift T A T S U R O S A W A D A and T E T S U J I C H O H J I Department of Chemical Engineering, Faculty of Technology, Kanazawa University, Kanazawa 920, Japan SIGERU K U N O Department of Biochemistry, School of Medicine, Kanazawa University, Kanazawa 920, Japan

Attempts to assess quantitatively the bacterial growth and their physiological state have long been pursued by many i n v e s t i gators. Bacteria can be cultivated i n a virtually unchanging environment for long periods during which they simply repeat the same cycle of mass increase and d i v i s i o n . Depending on culture conditions, however, a large number of physiological states ex ists, each of which is characterized by a particular size and chemical composition of the c e l l s (1, 2). In balanced growth with a sufficient amount of substrate, a simple relationship ex i s t s between the growth rate and the average mass or macromolecu le content of the cells, and thus the state of the balanced growth can be characterized by either the growth rate or the average mass or macromolecular content. In utilization of microorganisms for sanitary and i n d u s t r i a l purposes, it is d i f f i c u l t to maintain a constant environment for microbial growth. Since a change i n environment results usually i n a change i n the growth rate as well as the size and the chemi cal composition of the cells, a plausible conjecture as to the mode of growth i s difficult. We have studied a method to evalu ate quantitatively the unbalanced growth i n response to shifts i n environmental condition. For p r a c t i c a l reasons we chose growth temperature for environmental change. Although the cell size and composition were almost independent of the growth temperature i n a given medium containing a sufficient amount of substrate (1), it was found that a shift i n the growth temperature brought changes i n the physiological state i n a medium containing a lower concentration of substrate. In the present communication, we will present the behavior and formular expression of the bacteri a l growth i n t h i s unbalanced state. Materials and Methods Organism and Growth Medium. ©

The strain used throughout the

0-8412-0401-2/78/47-065-163$05.00/0



164

experiments was Escherichia coli BB. A b a s a l medium contained 0.25 % (NHi ) HP0i , 0.15 % NaCl, and 0.01 % MgSOi^îÔ. To t h i s b a s a l medium, v a r i o u s c o n c e n t r a t i o n s o f glucose (maximum 0.5 %) were added. The pH o f t h e media was maintained a t 7.0 throughout the experiment. t

2

+

Experiment i n Batch C u l t u r e . I n a b a t c h c u l t u r e , t h e c e l l c o n c e n t r a t i o n was l e s s than 1 0 c e l l s / m l so t h a t a change i n g l u cose c o n c e n t r a t i o n was n e g l i g i b l e d u r i n g t h e experiments. A t i n t e r v a l s , samples were withdrawn and v i a b l e c e l l s were measured by the double agar l a y e r method. 4

Experiment i n Continuous C u l t u r e . An a l i q u o t o f o v e r n i g h t c u l t u r e was added i n a T-shaped tube (working volume = 100 ml) c o n t a i n i n g 90 ml o f t h the o p t i c a l d e n s i t y at c u l t u r e was poured i n t o a fermentor (working volume = 500 ml) con t a i n i n g i*00 ml o f t h e f r e s h medium. A f t e r 5 t o 6 h r s c u l t i v a t i o n , a supply o f t h e medium which contained 0.5 mg/ml glucose and had been s t o r e d i n a r e s e r v o i r was i n i t i a t e d t o s t a r t a continuous run. The schematic diagram o f t h e fermentor i s shownΛη F i g u r e 1. A g i t a t i o n was p r o v i d e d by means o f a magnetic s t i r r e r and a remov able b a f f l e . A i r f l o w r a t e was 2 wm. The a i r from t h e compres sor was s a t u r a t e d w i t h water vapor by p a s s i n g i t through a humidi f i e r t o p r o t e c t e v a p o r a t i o n o f t h e medium. When t h e e f f e c t o f a temperature was s t u d i e d , t h e fermentor was immersed i n a v e s s e l c o n t a i n i n g i s o p r o p y l a l c o h o l and d r y i c e . When t h e temperature o f t h e medium reached t h e d e s i r e d v a l u e , t h e fermentator was q u i c k l y t r a n s f e r r e d i n t o a new water-bath which had been a d j u s t e d t o t h e d e s i r e d temperature. T h i s method made i t p o s s i b l e t o change t h e c u l t u r e temperature w i t h i n one minute. The c o n c e n t r a t i o n o f glucose i n t h e c u l t u r e was determined a c c o r d i n g t o t h e method o f Park and Johnson (3) after centrifugat i o n (3,500 rpm, 5 min) t o remove c e l l s . 9

R e a c t i o n Model The Monod's equation (^_, , which was obtained on t h e b a s i s o f M i c h a e l i s - M e n t e n s equation f o r enzymatic r e a c t i o n , has been one o f t h e most w i d e l y accepted models, f o r a q u a n t i t a t i v e a s s e s s ment o f m i c r o b i a l growth. I f b a c t e r i a are grown i n media i n which excess i n o r g a n i c n u t r i e n t s but a l i m i t i n g amount o f glucose ( c a r bon source) are p r e s e n t , a s p e c i f i c growth r a t e , μ, o f t h e b a c t e r i a i s s p e c i f i e d as a f u n c t i o n o f t h e c o n c e n t r a t i o n , y, o f glucose i n t h e medium, and can be expressed by the f o l l o w i n g Monod s equation: 1

f

y = y where y

m

m

y/(Ks + y )

d)

and K3 are t h e maximum v a l u e o f μ and a s a t u r a t i o n con-


14.

SAWADA ET AL.

Bacterial Growth in Temperature Shift

165

stant ( n u m e r i c a l l y equal t o t h e glucose c o n c e n t r a t i o n a t 1/2 y ) , r e s p e c t i v e l y . I t i s w e l l known t h a t y i s a f u n c t i o n o f tempera t u r e . Since Kg i s apparently e q u i v a l e n t t o t h e d i s s o c i a t i o n con stant i n t h e Michaelis-Menten s equation, l/Kg appears t o show degree o f u t i l i z a b i l i t y o f s u b s t r a t e by c e l l s and t o be a l s o a f u n c t i o n o f growth temperature. Thus, y and l/Kg may be given by f o l l o w i n g A r r h e n i u s equations. m

m

1

m

1

(2), l/K

Pm = A i exp(-Ei/RT)

s

=A

2

(3)

exp(-E /RT) 2

In our previous study (l), i t was demonstrated t h a t a content of macromolecule, such as DNA, RNA and p r o t e i n , per c e l l was ex pressed by an e x p o n e n t i a l f u n c t i o n o f s p e c i f i c growth r a t e : Ci = C

i 0

exp

where C^ i s a content o f macromolecule, i , per c e l l , C±Q i s a con t e n t o f macromolecule per c e l l a t t h e zero growth r a t e , and oti i s a f u n c t i o n o f temperature and a gradient i n t h e p l o t s o f l o g a r i t h mic values o f C i against y. The value o f C i o was shown t o be con stant and independent o f temperature. From equations ( l ) and (h), Ci/Cio - ( C / C ) i m

i 0

y / ( K

S

+

y

(5)

)

where C ^ i s t h e macromolecular content per c e l l a t t h e maximum growth r a t e , y . Since t h e maximum growth r a t e i s obtained i n t h e presence o f a s u f f i c i e n t amount o f glucose (thus y >> Kg), C i i s a constant r e g a r d l e s s o f growth temperature. However, C i a t a l i m i t i n g c o n c e n t r a t i o n o f glucose may be v a r i e d by growth tempera t u r e , unless E value i n equation (3) i s zero. T h i s r e l a t i o n s h i p i s i l l u s t r a t e d i n F i g u r e 2. The s o l i d l i n e s i n t h e f i g u r e r e p r e sent a r e l a t i o n s h i p between y and DNA content per c e l l a t a given temperature c a l c u l a t e d from equation (h). The broken l i n e s i n d i cate a r e l a t i o n s h i p between y and DNA content p e r c e l l a t a given c o n c e n t r a t i o n o f g l u c o s e , and a r e obtained by c a l c u l a t i o n o f equa t i o n s ( 1 ) , (3) and ( 5 ) . m

m

2

R e s u l t s and D i s c u s s i o n E f f e c t o f Temperature on \i and Kg» F i g u r e 3 shows t h e r e l a t i o n s h i p between t h e s p e c i f i c growth r a t e and s u b s t r a t e (glucose) c o n c e n t r a t i o n . I n t h e f i g u r e , 1/y has been p l o t t e d against a r e c i p r o c a l o f glucose c o n c e n t r a t i o n s i n media f o r seven d i f f e r e n t growth temperatures. I t i s c l e a r from the equation ( l ) t h a t t h e i n t e r c e p t s on t h e v e r t i c a l a x i s and t h e base l i n e g i v e l / y and - l / K g , r e s p e c t i v e l y , and t h a t both y and Kg are f u n c t i o n s o f temperature. I n F i g u r e k t h e logarithms o f y and Kg are p l o t t e d a g a i n s t l / T . These Arrhenius p l o t s give s t r a i g h t l i n e s , and t h e a c t i v a t i o n energies f o r y and Kg were c a l c u l a t e d from the slopes as 8.51 and 1 5 . 7 kcal/g-mole, r e s p e c t i v e l y . I t i s obvious t h a t m

m

m

9

m

m


CHEMICAL REACTION ENGINEERING—HOUSTOIN

166

Feed-

1 2 3 4 5 6

• Effluent

Water-bath Ja Baffle Magneti spi Magnetic stirrer Thermometer

Figure 1.

7

Humidifier

10 Control heater 11 Oriftce

Apparatus for continuous culture

TB

Μβ2 μ%\

TA

MA2

μ

MAI 1

Chr"]

Figure 2. DNA contents per cell as a function of specific growth rate at temperatures Ύ and T . The broken lines represent the relationship at a glucose concentration of y or y,. Α

B

m


SAWADA

ET AL.

Bacterial Growth' in Temperature Shift



168 the 10

5

e x t r a p o l a t e d p o i n t s o f the l i n e s t o l / T = 0 g i v e Αχ = 7.31 h r " and A = 1.99 10 ml/mg o f equations (2) and ( 3 ) . 1

x

*

1 5

2

R e l a t i o n s h i p between Average DNA Content and μ. I n F i g u r e 5> the DNA content per c e l l was p l o t t e d a g a i n s t μ. The s o l i d l i n e s i n the f i g u r e were c a l c u l a t e d from equations ( l ) , ( 2 ) , (3) and ( 5 ) , u s i n g C D O = ^.1 * 1 0 " m g / c e l l and C = 8.5 * Η Γ mg/cell obtained i n our p r e v i o u s r e p o r t ( l _ ) . The broken l i n e s i n the f i g ure were obtained by c a l c u l a t i o n o f equations ( l ) , (2) and (5). The experimental data were i n agreement w i t h the c a l c u l a t e d v a l u e . As expected from F i g . 2, i t was shown t h a t the DNA content per c e l l was independent o f growth temperature at h i g h e r glucose con c e n t r a t i o n s , w h i l e the DNA content decreased w i t h a l o w e r i n g o f the growth temperature a suboptimal c o n c e n t r a t i o n f glucose 1 2

1

2

D m

E f f e c t s o f Temperature S h i f t on Growth i n Batch C u l t u r e . As r e p o r t e d p r e v i o u s l y ( l ) , when the b a c t e r i a are grown i n a s u f f i c i ent amount o f s u b s t r a t e , the b a c t e r i a are capable o f adapting without any l a g t o a sudden change i n growth temperature because the p h y s i o l o g i c a l s t a t e o f the b a c t e r i a i s independent o f growth temperature under t h i s c o n d i t i o n . However, i n an i n s u f f i c i e n t supply o f g l u c o s e , the sudden upward or downward s h i f t i n tempera t u r e w i l l cause the b a c t e r i a t o l a g i n adapting t o a new c o n d i t i o n , because the p h y s i o l o g i c a l s t a t e o f the c e l l d i f f e r s by grow t h temperature i n t h i s case. When the medium contains a l i m i t i n g amount o f g l u c o s e , y i , p h y s i o l o g i c a l s t a t e s o f t h e b a c t e r i a are B s t a t e at temperature T , and Αχ s t a t e at T^ ( F i g . 2 ) . When the growth temperature o f the steady s t a t e c u l t u r e i s suddenly s h i f t e d from Tg t o T&, the p h y s i o l o g i c a l s t a t e o f t h e c e l l s w i l l move from B t o A and t o A\. S i m i l a r l y a temperature s h i f t from T^ t o T w i l l cause a change i n the p h y s i o l o g i c a l s t a t e from A\ t o Βχ and to B . T h e r e f o r e , a change i n growth r a t e (as measured by c e l l number, N) may occur a f t e r some time l a g i n temperature s h i f t - u p , and an i n i t i a l overshot growth may be observed i n temperature a shift-down. These s i t u a t i o n s are probably s i m i l a r t o those obser ved i n s h i f t - u p t o an enriched medium or a shift-down t o a poorer medium (6^). These conjectures were v e r i f i e d i n the s h i f t - u p and shift-down experiment w i t h the batch c u l t u r e , as shown i n F i g u r e 6. Although the temperature s h i f t i n the batch c u l t u r e brought q u a l i t a t i v e l y expected r e s u l t s , i t was d i f f i c u l t t o measure c e l l mass and macromolecule c o n t e n t , because the c e l l d e n s i t y i n the c u l t u r e had t o be kept v e r y low t o m a i n t a i n the c u l t u r e at the f i x e d and much lower c o n c e n t r a t i o n o f glucose. T h e r e f o r e , a con tinuous c u l t u r e was c a r r i e d out t o f o l l o w changes i n the p h y s i o l o g i c a l s t a t e o f c e l l s at the temperature s h i f t . 2

B

2

2

B

2

E f f e c t s o f Temperature S h i f t on Growth i n Continuous C u l t u r e . At the steady s t a t e i n the continuous c u l t u r e , the c u l t u r e p o p u l a t i o n d e n s i t y i s maintained c o n s t a n t , and the s p e c i f i c growth r a t e i s equal t o the d i l u t i o n r a t e , D (the i n f l u e n t volume per hr


SAW ADA ET AL.


Figure 5. Rehtionship between DNA contents per cell and the specific growth rate at various glucose concentrations and temperatures. Solid and broken lines represent the cal culated curves at isothermal conditions and those at the same glucose concentrations, respectively.

10.0

274* 37 °C ·'

5.0

!

5.0

2.0^ ο 1.02

% 2.0

H0.5

^ V

(α)

!

> 1 -10

1_,

1

1 2 t Chr]

3

Figure 6. Increment in cell number after a shift in temperature. Filled cir cles and open circles show increments in cell number with 0.5 rag/mL and 2 X 10~ mg/mL glucose, respectively, (a) Growth temperature was shifted up from 27°-37°C at t = 0. (b) Growth temperature was shifted down from 37°-27°C att = 0. 4



170

per t h e t o t a l volume o f medium i n t h e growth v e s s e l ) . The concen t r a t i o n o f glucose (y) i n t h e growth v e s s e l i s a l s o maintained constant i n t h e balance between t h e input and t h e output p l u s con sumption by b a c t e r i a . Thus, i t i s p o s s i b l e t o measure c e l l mass and chemical components o f c e l l s i n t h e steady s t a t e c u l t u r e under extremely low glucose c o n c e n t r a t i o n . However, t h e upward o r down ward s h i f t i n growth temperature under t h e c o n d i t i o n causes i n e v i t a b l y a change i n t h e consumption r a t e o f glucose by b a c t e r i a as w e l l as a change i n growth r a t e , and t h e r e f o r e i t i s d i f f i c u l t t o maintain the f i x e d c o n c e n t r a t i o n o f glucose i n t h e medium before and a f t e r t h e temperature s h i f t . I f t h e temperature o f t h e steady s t a t e c u l t u r e i s suddenly lowered without changing t h e d i l u t i o n r a t e , the glucose c o n c e n t r a t i o n w i l l i n c r e a s e . And i f t h e s p e c i f i c growth r a t e i s much dilutio concentration w i l l diminis from t h e v e s s e l , and t h e p h y s i o l o g i c a l s t a t e o f b a c t e r i a w i l l f i n a l l y reach t o t h e s t a t e w i t h maximal supply o f glucose at t h a t temperature (e.g. % s t a t e i n F i g . 2 ) . Therefore t h e temperature s h i f t i n the continuous c u l t u r e w i l l cause an unbalanced growth which i s more complicate than t h a t i n t h e batch c u l t u r e . During t h i s unbalanced growth, the net change i n c o n c e n t r a t i o n o f organ isms (x) and i n glucose c o n c e n t r a t i o n (y) can be expressed on t h e b a s i s o f Monod s model as f o l l o w s : f

dx/dt = y

m

(6)

χ y / ( K + y) - D χ s

dy/dt = - ( l / n ) y

m

(7)

χ y / ( K + y ) + D ( y - y) s

0

where t i s the time a f t e r t h e s h i f t , η i s a y i e l d c o n v e r s i o n , and y i s a i n f l u e n t s u b s t r a t e c o n c e n t r a t i o n . However, these equa t i o n s do not i n v o l v e a proper c o n s i d e r a t i o n o f t h e d i f f e r e n c e s i n the p h y s i o l o g i c a l s t a t e o f c e l l s before and a f t e r t h e temperature s h i f t . F i g . 7 i l l u s t r a t e s t h e experiment i n which t h e steady s t a t e c u l t u r e s w i t h the d i l u t i o n r a t e o f 0.500 h r " (a) and 0.529 hr" (b) were s h i f t e d from 37 t o 27 °C. The f i l l e d and open c i r c l e s i n d i c a t e c e l l mass (measured by o p t i c a l d e n s i t y ) , x, and g l u cose c o n c e n t r a t i o n , y, r e s p e c t i v e l y . The broken curves show t h e time course o f χ and y obtained by c a l c u l a t i o n o f equations (6) and ( 7 ) . I t i s apparent t h a t t h e c a l c u l a t e d curves d e v i a t e enor mously from t h e experimental data. These d e v i a t i o n s can probably be a t t r i b u t e d t o time l a g f o r a t t a i n i n g t o t h e new p h y s i o l o g i c a l s t a t e . From t h i s v i e w p o i n t , equations (6) and (7) were m o d i f i e d as f o l l o w s , though the m o d i f i c a t i o n i s e n t i r e l y o u t s i d e t h e scope of p h y s i o l o g i c a l i m p l i c a t i o n . 0

1

1

dx/dt = { t / ( K

L

+ t ) } y χ y / ( K + y) - D χ

dy/dt = - ( l / n ) { t / ( K where

m

L

(8)

s

+ t ) } y χ y / ( K + y) + D ( y - y) m

s

0

(9)

i s a constant. The s o l i d l i n e s i n t h e f i g u r e were ob-


14.

SAWADA ET AL.

î


ChrJ

171

t Chrl

Figure 7. Time course of cell mass and glucose concentrations after the growth temperature was shifted down from 37 -27°C in the continuous culture at dilution rate = 0.500 hr (a), and 0.529 hr (b). Filled circles and open circles show cell mass and glucose concentrations, respectively. Triangles show the yield to be almost constant after and before the shift. Broken and solid lines represent calculated lines from Equations 6 and 7 and from Equations 8 and 9, respectively. 1

1

Figure 8. Relationship between a difference in DNA content per cell and K L



172

t a i n e d by c a l c u l a t i o n o f equations ( 8 ) and (9) as K = 0 . 3 8 h r (a) and 0 . 2 3 h r ( b ) , and show s a t i s f a c t o r y agreement w i t h the data. K L shows a time constant o f delay and should be dependent on a d i f f e r e n c e i n the s t a t e s before and a f t e r the temperature s h i f t . F i g u r e 8 i l l u s t r a t e s the r e l a t i o n s h i p between a d i f f e r e n c e i n DNA content per c e l l and K ^ . ACj) r e p r e s e n t s a d i f f e r e n c e i n DNA content per c e l l b e f o r e and a f t e r the temperature s h i f t . In a steady s t a t e o f b a c t e r i a l growth, the p h y s i o l o g i c a l s t a t e o f c e l l s , such as c e l l mass,, and macromolecular content per c e l l , i s p r i m a r i l y defined by the c u l t u r e medium and i s an expo n e n t i a l f u n c t i o n o f the growth r a t e a t a f i x e d temperature. When an environment o f b a c t e r i a l growth i s changed t o another s t a t e , the b a c t e r i a can adapt immediately t o the new environment, p r o v i d ed t h a t the p h y s i o l o g i c a l s t a t e s i n two environmental c o n d i t i o n s are i d e n t i c a l , such as s u f f i c i e n t amount o f n u t r i e n t s t r a n s f e r r e d t o a new c o n d i t i o n i n which a d i f f e r e n t p h y s i o l o g i c a l s t a t e i s g i v e n , they r e q u i r e some time l a g t o accommodate t o t h e new c o n d i t i o n . I n the present i n v e s t i g a t i o n , i t has been shown t h a t a q u a n t i t a t i v e e x p r e s s i o n o f growth was p o s s i b l e w i t h temperature s h i f t s i n a suboptimal n u t r i e n t s u p p l y , by u s i n g t h e parameter K ^ , t h e f u n c t i o n o f the d i f f e r e n c e i n p h y s i o l o g i c a l states. L

Nomenclature Αχ, A = frequency f a c t o r s Cj) = DNA content per c e l l D = d i l u t i o n rate Ε = a c t i v a t i o n energy L» S constants Ν = c e l l number R = gas constant Τ = temperature t = time x, y = c e l l mass and glucose c o n c e n t r a t i o n s α = constant η - yield μ = s p e c i f i c growth r a t e 2

K

K

=

1

[ h r " ] , [ml/mg] [mg/cell] [hr- ] [cal/g-mole] [ h r ] , [mg/ml] [cells/ml] [cal/°K-g-mole] [°K] [hr] [mg/ml] [hr] 1

[ 1

[hr- ]

Literature Cited (1) Chohji, T . , Sawada, T . , and Kuno, S . , Appl. Environ. Microbi ol., (1976), 3 1 , 8 6 4 . (2) Schaechter, Μ., Maaløe, O., and Kjeldgaard, N . O., J. gen. M i c r o b i o l . , (1958), 19, 529. (3) Park, J. T . , and Johnson, M. G . , J. Biol. Chem., (1949), 181. 149. (4) Monod, J.; Ann. Rev. M i c r o b i o l . , (1949), 3, 371. (5) Monod, J.; Ann. Inst. Pasteur, (1950), 79, 390. (6) Kjeldgaard, N . O., Maaløe, O., and Schaechter, Μ., J. gen. M i c r o b i o l . , (1958), 19, 607.


15 Nonisothermal Behavior and Thermal Runaway Phenomena in Chain Addition Copolymerization D O N A L D H . S E B A S T I A N and J O S E P H A. B I E S E N B E R G E R Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030

The condition of therma actors has been characterize tures (dT/dt » 0) and an upward concavity in the temperature profile (d T/dt > 0 ) . When runaway additionally exhibits para metric s e n s i t i v i t y i t is termed thermal ignition (IG). Beyond the obvious consequence of large temperature rises and possible i n s t a b i l i t y , RA could cause a sharp reduction in polymer molecu lar weight and an increased spread in molecular weight d i s t r i b u tion. 2

2

Runaway Analysis of Polymerizations and Copolymerizations A study of RA in chain polymerizations was undertaken in our laboratories with the aim of developing quantitative c r i t e r i a for predicting the onset of both RA and IG. A modification of Semenov-type dimensional analysis, together with computer simula tion and experimentation, have shown (1,2) that 5 independent parameter groupings characterize the thermal behavior of chain homopolymerizations: a,Β,b,ε,εΕ' . The approach of Semenov deals with the thermal energy balance. Putting temperature and concen tration in dimensionless form the thermal energy balance for homopolymerization appears as (1) : ι mm 1/2 . = expÎEV/l+T'ï-iiT'-T;) (0 d

The f i r s t term of the RHS of Eq. 1 can be interpreted as the rate of heat generation function while the second term as heat removal. The Semenov technique locates the c r i t i c a l temperature for RA at the point where heat generation and removal are not only equal, but their change with temperature ( i . e . , derivative with respect to Τ ) is also equal. Applying these steps to the generation and removal terms of Eq.l eliminates T',with resulting c r î t e r i a formed as functions of ' a and ε. The effect of the remaining para meters was investigated through numerical simulation. The impor tant c r i t e r i a for RA is a < 2, and for parametrically sensitive RA, Β > 20 and b > 100. Parameters Β and b are dimensionless 1

©

0-8412-0401-2/78/47-065-173$05.00/0



174

groupings appearing i n the monomer and i n i t i a t o r component b a l ances r e s p e c t i v e l y . The a n a l y t i c a l methods employed i n the R A a n a l y s i s o f homop o l y m e r i z a t i o n a r e not immediately a p p l i c a b l e to chain a d d i t i o n c o p o l y m e r i z a t i o n . The e q u i v a l e n t expression to Eq. 1 i s λ 6

+

ηΠ»] exp Ε ^ τ ' / l + Τ

XQ22

M

2

Β

Χ

Ρ

Ε

2 2

Τ

,

/

1

+

T

'

J

1

+

m

o

/ 2

( Q|2 X

H

'

"

+ X

X

G21 ^

R

1

(

T

m

l

'

M

"

2

T

E

X

R

P

1 2

E

]

T

'

(

+

2

T

'

)

The b a s i c k i n e t i c equations f o r chain a d d i t i o n copolymeriza t i o n are given i n Table I f o r three t e r m i n a t i o n models: geometric mean (GM), phi f a c t o r (PF) and penultimate e f f e c t (PE). I t i s important to note the symmetr e f f e c t o f choice o f t e r m i n a t i o f u n c t i o n H. A Semenov-type a n a l y s i s cannot be a p p l i e d to Eq. 2 . The presence of four exponential terms w i t h d i f f e r e n t a c t i v a t i o n en e r g i e s , and the complicated f u n c t i o n a l form o f H = H/H preclude e x p l i c i t s o l u t i o n f o r a c r i t i c a l T . A more general technique based upon p h y s i c a l i n t e r p r e t a t i o n o f R A parameters has led to c o p o l y m e r i z a t i o n analogs f o r the groupings a,B,b,e and εΕ^. Each such parameter can be expressed as the r a t i o o f a p p r o p r i a t e time constants. While appearing as c o e f f i c i e n t s i n the balances, time constants serve a l s o as i n i t i a l values f o r the balance. For ex ample i n E q . l , note that the r e c i p r o c a l of XG» the c h a r a c t e r i s t i c time f o r heat g e n e r a t i o n , i s a l s o the value o f the heat genera t i o n f u n c t i o n when dimensionless c o n c e n t r a t i o n s and temperature take on t h e i r i n i t i a l values o f one. The second i n t e r p r e t a t i o n , when a p p l i e d to the generation p o r t i o n o f Eq. 2 , d e f i n e s an over a l l AQ f o r c o p o l y m e r i z a t i o n . S i m i l a r a t t a c k on the t o t a l monomer balance y i e l d s an expression f o r A , the c h a r a c t e r i s t i c time f o r monomer decay. In homopolymerization a n a l y s i s ( J j the time constant X j = ελβ i s c r u c i a l to the f o r m u l a t i o n o f runaway parameters a, B,b, ε and εΕ^. I t does not appear e x p l i c i t y i n any o f the d i mensionless balances, but rather i s a consequence of a Semenovtype a n a l y s i s . In the process of t a k i n g the temperature d e r i v a t i v e o f the heat generation f u n c t i o n of Eq. 1 the product E'/XQ 1/eXG a r i s e s . Because t h i s a n a l y s i s could not be a p p l i e c to c o p o l y m e r i z a t i o n , an a l t e r n a t e means was r e q u i r e d . The R A parameter 'a' i s more than a mere by-product o f a Semenov ap proach. I t i s the r a t i o of i n i t i a l values o f the temperature de r i v a t i v e o f the heat removal and generation f u n c t i o n s o f Eq. 1 . Expressed i n terms o f time constants t h i s r a t i o i s X j/XR, and thus the i n t e r p r e t a t i o n o f X | as the i n i t i a l temperature d e r i v a t i v e o f the heat generation f u n c t i o n serves t o d e f i n e an analog, âd f o r copolymer i z a t ion. By making use o f A j i n combination w i t h other o v e r a l l time c o n s t a n t s , a s e t o f R A parameters f o r c o p o l y m e r i z a t i o n corresponding to i t s homopolymerization 1

Q

1

M

ac

=

ac

ac

a c


15.

SEBASTIAN AND

BiESENBERGER

Chain Addition Copolymerization

175

counterpart ( 0 , was d e f i n e d . The parameters are given i n Table I I . I t i s important t o note that the homopolymerization c r i t e r i a evolved from combined s e n i - a n a l y t i c a l and numerical s o l u t i o n s t o s p e c i f i c k i n e t i c equations. In t h i s work, p h y s i c a l s i g n i f i c a n c e has been attached t o each parameter i n a manner that permits ex tension o f the RA a n a l y s i s , independently o f the k i n e t i c form. The u t i l i t y o f the runaway and s e n s i t i v i t y parameters a,B, and b has been demonstrated through both numerical s i m u l a t i o n and experimentation (3,^0· Numerical s i m u l a t i o n s employed l i t e r a t u r e values f o r the k i n e t i c constants f o r the monomer p a i r s o f StyreneMethyl Methacrylate (SMMA), S t y r e n e - A c r y l o n i t r i l e (SAN) and, Acrylonîtrile-Methyl Methacrylate (ANMMA). P h i - f a c t o r k i n e t i c s were g e n e r a l l y used, however both geometric mean and r e c e n t l y advanced penultimate e f f e c t k i n e t i c (6) tested well Ex periments were confine system, however, the f u l rang composition e x t e n s i v e i n i t i a l r a t e study was performed on t h i s system to de velop the k i n e t i c constants needed t o evaluate the runaway para meters ( 4 , 5 ) . A convenient way t o i l l u s t r a t e the e f f e c t o f the RA para meters i s through the use o f RA boundaries. K i n e t i c constants as s o c i a t e d w i t h real polymer systems l i m i t the values o f Β t o a narrow range ( g e n e r a l l y 30 - 60) and t h i s i s above the region where monomer s e n s i t i v i t y e f f e c t s become important. Furthermore, i n i t i a t o r consumption w i t h i t s stronger temperature dependence plays a f a r greater r o l e i n reducing s e n s i t i v i t y than monomer con sumption does. T o t a l l y u n r e a l i s t i c values o f i n i t i a t o r concentra t i o n (on the order o f 100 m/1) are needed i f monomer s e n s i t i v i t y l i m i t a t i o n s are t o be e x h i b i t e d in the absence o f i n i t i a t o r l i m i t a t i o n s . Thus the most meaningful way t o represent runaway bound a r i e s i s t o show acr vs b w i t h other dimensionless groups as con stant parameters. D e t a i l e d s t u d i e s o f homopolymerization have i l l u s t r a t e d t h i s dependence (2). What i s noteworthy i s that the copolymer systems f o l l o w the same q u a n t i t a t i v e behavior. Figure 1 shows dimensionless runaway boundaries f o r several copolymer sys tems shown along w i t h the a s s o c i a t e d homopolymerization boundary. A l l boundaries are not p e r f e c t l y c o i n c i d e n t due t o the e f f e c t s o f composition d r i f t in the c o p o l y m e r i z a t i o n s . The d e v i a t i o n s are rather small although the d r i f t a s s o c i a t e d w i t h SAN and ANMMA sys tems f o r Β = 41 i s s i g n i f i c a n t . In Table III values f o r RA parameters a t the t r a n s i t i o n p o i n t are presented f o r v a r i o u s comonomer-initiator systems. Note that RA parameter 'a c o n s i s t e n t l y takes on values near the expected value o f two when RA occurs. As i n homopolymerizations, the c r i t i c a l value o f 'a' becomes depressed as 'b decreases. This e f f e c t i s a by-product o f the decreasing s e n s i t i v i t y o f the cop o l y m e r i z a t i o n c o r r e c t l y c h a r a c t e r i z e d by the d e c l i n i n g value o f 'b'. Figures 2 and 3 i l l u s t r a t e i n i t i a t o r - l i m i t e d s e n s i t i v i t y more c l e a r l y . At a value o f b = 195 there i s a s h a r p l y defined t r a n s i t i o n from non-runaway t o runaway behavior, and t h i s i s 1

1


CHEMICAL REACTION

176

TABLE

ENGINEERING—HOUSTO

I

RATE FUNCTIONS AND BALANCES FOR COPOLYMER IZATI ON

Balance Ini

equations

tiator

dim ] 7^

=

dt

Κ >L

d

ο

J

Co-monorners

dim J —dt

-

R

dt

p

pl2

d

d M dt

Thermal

P

C

m

i

]

d

[

m

2 dt

dt

]

energy

P£

= Σ Σ

(

i

j

"

[ -

"

where

C

p22

I

a

H

Û H

n

k

-

Δ

p n

k

k

22 p22

( u / t ) ( T

ν ν ι -

l

p Z l h

k

2

"

(

H

' .2

+

4

2

p l

-

ν

H

21

t

2t'"2l ]

m

)

k

k

p 2 p21

[

I

o

]

'»" /2

m

,

H

m

2

)

(U/t)(T

"V

= y/A w

Rate

functions for

propagation 1/2

Rp-11 ii =

R

pl2

"

k

ii

k

pll

o» U ^

p21 \

k

t

2

k

n

t

2

I K ] [ m J°

^ 1 2 ^ 2 l / r ^ til

1 / 2

1

2 /

[m^tm^tmj

H

1

/

2

H

-

R

p 2 1

t22^ 1/2

V 2

-

%n^2k-T-) ^ tl! k

WV » 2

k

t22j

and H is :


SÉBASTIAN

for

Copolymerization

g e o m e t r i c mean (GM) model

k

[ m

p21 l

(k for

Chain Addition

BiESENBERGER

AND

phi f a c t o r

t22

3

p!2

)T72

l

J

2 ΓΪ72

~tir

(PF) model

_,2 (k )

2\-1/2 k

2φ

Ï72

p2^Pl2

penultimate

(k

effect

k

[

p21 "l

(k

(22

m

l

]

[

m

2

k

] +

172

t M

for

[

k

t22 tl1

[m

p12 2

]

(kt l T J / 2

]

(PE) model

]

) 1/2

J

k

[m

r

3

pl2 2 T72

1/2

2 U [m

fei « [m

+

r [m J 2

2

]

+ [m^

TABLE II

E

(E

Bi

i l T l l 12T12 Y

+

E

*J_ ad A

VT21 * 2 2 W ~ i f j

E

+

E

-1 -1 -1 -1 3H -1 îl GU + 12G12 * 12621 + 22622* * W G -1 < mll ml2 m21 m22 > X

E

j -1 r il Gll E

X

X

+

E

+

X

+

X

E

X

+

X

A

X

-1 -1 -1 12G12 * 12G21 22G22

E

X

E

X

+

E

X

)

3H +

-1 -1 * h 6U * J2G12 * 12G21 * 22G22 H -1 -1 -1 -1 G11 G12 G21 G22 E

"ad

+

Y

X

bi

-1

DIMENSIONLESS RUNAWAY PARAMETERS

ad

X

E

A

X

E

X

X

E

A

X

X

~

Λ

-1 ) Gj1 X

m

3Τ·



178

Δ "

Δ 5

ο

ο

ο Br 41 e=0.025 Δ .26 S A N

10

2

10

3

10

4

10

5

b Figure 1.

Simulated RA boundary for two copolymer systems

TABLE

πι

SIMULATION RESULTS Τ

System

ο

Β

u/t

Wo

Ε'

b

a

RA

c a l / c e s e c °K

mol/1

°K 1.57 x Ι Ο " 1.55

5

45

28.6

300

2.025 1.998

No Yes

1.61 χ Ι Ο " 1.60

2

45

23.5

300

1.998 1.985

No Yes

8.99 χ Ι Ο " 8.88

6

45

31.3

300

2.075 2.05

No Yes

ϊ.54 χ ΙΟ" 1.52

6

45

33.5

300

2.05 2.026

No Yes

.05

1.04 χ ί ο " 1.03

2

36

30

400

1.985 1.975

No Yes

.025

4.86 χ Ι Ο " 4.82

3

136

1.915 1.90

No Yes

.01

3.01 χ Ι Ο 2.97

86

1.875 1.85

No Yes

.10

3.55 χ ί ο " 3.49

2

42

1.77 1.74

No Yes

.05

2.37 χ Ι Ο " 2.34

2

30

1.67 1.65

No Yes

1

.2

322

.8

378

.2

318

1.21 χ 10"

.8

306

7.44 χ ίο"**

S/AN/DTBP

.7

403

S/AN/BP

.7

373

AN/MMA/BP

S/MMA/BP

S/AN/AIBN

.7

373

1.33 x ίο" »

• 119

3

1

3

36.0

28.0


SÉBASTIAN A N D

1

BiESENBERGER

3

Figure 2.


5 •Med

7

9

RA transition, b = 195


180


c a u s e d by a 0 . 3 % change i n ' a . When b i s d e c r e a s e d t o 30 t h e RA p o i n t i s not c l e a r l y d e f i n e d . A continuous spectrum of p r o f i l e s f i l l s the t r a n s i t i o n r e g i o n . Changes i n p a r a m e t e r ' a a r e an o r d e r o f magnitude g r e a t e r than i n the p r e v i o u s case t o b r i n g a b o u t s i m i l a r changes i n t h e t h e r m a l h i s t o r i e s . In a d d i t i o n , t h e v a l u e o f 'a' i n t h e r e g i o n o f t r a n s i t i o n has been s i g n i f i c a n t l y d e c r e a s e d f r o m t h e n o m i n a l v a l u e o f two. 1

1

The

Copolymer

Approximate

Form

(CPAF)

The f a c t t h a t c o p o l y m e r and homopolymer runaway e n v e l o p s a g r e e d b o t h q u a l i t a t i v e l y and q u a n t i t a t i v e l y s u g g e s t s t h a t perhaps c o m p l e x c o p o l y m e r i z a t i o n k i n e t i c s m i g h t be s u c c e s s f u l l y a p p r o x i mated by s i m p l e r k i n e t i c s , s i m i l a r t o t h e homopolymer f o r m . I t is p r o p o s e d t h a t be r e p l a c i n parameter i t h homopolyme balance by t h e i r c o p o l y m e r a n a l o g s AQ, and ε = A J / A Q r e s p e c t i v e l y them we w i l l o b t a i n c o n v e r s i o n and t h e r m a l h i s t o r i e s t h a t match the h i s t o r i e s o f t h e e x a c t k i n e t i c f o r m . I n d e e d , t h i s was t h e case. Thus Eq. 2 w o u l d be a p p r o x i m a t e d by t h e f a r s i m p l e r f o r m : 3C

dT« ^

-1 = A

G

Ε'

1/2

Λ

mm

o

Τ'

exp

1 -

^

, , (Τ τ

τ

,ν

T ) R

(3)

I n d e e d , i t c a n be shown t h a t i f c o n c e n t r a t i o n changes a r e n o t con s i d e r e d , the r e m a i n i n g t e m p e r a t u r e dependent p o r t i o n o f Eqs. 2 and 3 a r e n u m e r i c a l l y e q u i v a l e n t . Under i s o t h e r m a l c o n d i t i o n s th< c o n v e r s i o n h i s t o r i e s match p r o v i d e d t h a t one o f t h e comonomers i s not exhausted p r i o r t o the c o m p l e t i o n o f the r e a c t i o n . Under noni s o t h e r m a l c o n d i t i o n s , c o m p o s i t i o n d r i f t i n f l u e n c e s the agreement between t h e two f o r m s . When d r i f t i s t o w a r d s t h e more r e a c t i v e comonomer, t h e a p p r o x i m a t e f o r m u n d e r e s t i m a t e s t h e t h e r m a l t r a j e c t o r y (See F i g . 4 ) . C o n v e r s e l y , when d r i f t i s t o w a r d s t h e l e s s re a c t i v e o f the p a i r , the approximate form o v e r e s t i m a t e s the t r a j e c tory. S i m i l a r b e h a v i o r i s n o t e d i n t h e RA b o u n d a r i e s o f F i g . 1. P o i n t s f o r t h e SAN s y s t e m l i e a b o v e t h e homopolymer b o u n d a r y , and d r i f t i s t o w a r d s h i g h AN c o n t e n t c o m p o s i t i o n s . P o i n t s f o r t h e ANMMA b o u n d a r y l i e b e l o w t h e homopolymer b o u n d a r y , and d r i f t i s t o w a r d s t h e l e s s r e a c t i v e o f t h e p a i r , MMA. As c o n d i t i o n s become e i t h e r more a d i a b a t i c o r more i s o t h e r m , s p r e a d between t h e forms narrows. The p o o r e s t a g r e e m e n t o f t h e forms o c c u r s a t t h e p a r a m e t r i c a l l y s e n s i t i v e p o i n t o f t h e RA t r a n s i t i o n . E x p e r i m e n t a l T e s t s o f t h e Runaway

Parameters

The SAN c o p o l y m e r s y s t e m was c h o s e n f o r e x p e r i m e n t a l s t u d y due t o i t s g r o w i n g i n d u s t r i a l i m p o r t a n c e . T h e r e i s a l a c k o f pub l i s h e d r a t e d a t a f o r t h i s s y s t e m , as w e l l as b r o a d d i s a g r e e m e n t among t h e d a t a r e p o r t e d f o r h o m o p o l y m e r i z a t i o n o f AN. Without k i n e t i c d a t a t h e r e w o u l d be no way t o e v a l u a t e t h e d i m e n s i o n l e s s parameters a s s o c i a t e d w i t h experimental runs. T h e r e f o r e c o p o l y m e r i z a t i o n k i n e t i c s t u d i e s were conducted v i a the t e c h n i q u e o f D i f f e r e n t i a l S c a n n i n g C a l o r i m e t r y , w h i c h had p r e v i o u s l y been used


15.

SEBASTIAN A N D

BiESENBERGER


181

by o t h e r s f o r homopolymerîzation s t u d i e s . The c o p o l y m e r a p p r o x i mate k i n e t i c f o r m (CPAF) p r o v i d e d t h e means f o r s e p a r a t i n g r e a c t i o n r a t e f r o m h e a t o f r e a c t i o n r e q u i r e d by t h e u s e o f t h i s technique. I t s h o u l d be n o t e d t h a t under i n i t i a l c o n d i t i o n s t h e e x a c t and a p p r o x i m a t e k i n e t i c forms a r e n u m e r i c a l l y e q u i v a l e n t , t h u s t h e r e i s no e r r o r i n v o l v e d i n a p p l y i n g t h e a p p r o x i m a t e f o r m to i n i t i a l r a t e s t u d i e s . The i n i t i a l r a t e s f o r SAN s y s t e m s w i t h s t y r e n e c o n t e n t o f t e n to n i n e t y mole p e r c e n t were d e t e r m i n e d w i t h b o t h b e n z o y l p e r o x i d e and azo-bîs-îsobutyronîtrîle i n i t i a t o r s . T h e s e r a t e s were used t o c a l c u l a t e t h e t e r m i n a t i o n p a r a m e t e r s f o r b o t h PF and PE models o f c o p o l y m e r t e r m i n a t i o n . No s i n g l e , c o m p o s i t i o n - i n d e p e n d e n t value of t h e PF a d e q u a t e l y f i t t h e i n i t i a l r a t e d a t a . The PE model p r o v i d e d f a i r a g r e e m e n t . H i g h s t y r e n e c o n t e n t c o p o l y m e r s showed t h e widest scatter i n the average value o f the P q u a l i t a t i v e l y h i g h e r r a t e s t h a n t h e PE m o d e l . E x p e r i m e n t a l s t u d i e s o f t h e r m a l runaway i n t h e homopolymerîz a t i o n o f s t y r e n e have been c o n d u c t e d i n t h e s e l a b o r a t o r i e s . The Thermal I g n i t i o n P o i n t A p p a r a t u s (TIPA) d e v e l o p e d f o r t h i s work (7) was u s e d f o r t h e e x p e r i m e n t a l s t u d y o f runaway i n SAN c o p o l y merization. The c o m p o s i t i o n s o f 90, 80, 70, 60, 40, and 20% s t y r e n e were p r o v o k e d f r o m non-runaway t o runaway c o n d i t i o n s a t t h e f e e d t e m p e r a t u r e o f 373°K by m a n i p u l a t i n g t h e i n i t i a l c o n c e n t r a t i o n o f i n i t i a t o r a z o - b i s . The 90, 80, and 70% c o m p o s i t i o n s were a l s o t e s t e d a t 363°K and t h e 70% c o m p o s i t i o n was t e s t e d w i t h benzoyl peroxide as i n i t i a t o r . ( F u r t h e r m o r e , an i g n i t i o n e n v e b p e o f T v s [ l ] was c o n s t r u c t e d f o r t h e 70% SAN s y s t e m i n i t i a t e d by b e n z o y l p e r o x i d e ) (k). V a l u e s o f t h e runaway p a r a m e t e r s a,B, and b f o r t h e e x p e r i m e n t a l RA t r a n s i t i o n s u s i n g e a c h o f t h e t h r e e p o p u l a r t e r m i n a t i o n mechanisms, a r e p r e s e n t e d i n T a b l e IV. They r e f l e c t t h e t r e n d s ob s e r v e d i n t h e b e h a v i o r o f t h e e x p e r i m e n t a l r u n s . A l l RA's were o f t h e t y p e c l a s s i f i e d a s n o n - s e n s i t i v e . The v a l u e s o f p a r a m e t e r b c l e a r l y a r e i n agreement w i t h t h i s o b s e r v a t i o n . L o w e r i n g f e e d t e m p e r a t u r e r e s u l t e d i n h e i g h t e n e d s e n s i t i v i t y , and a g a i n an i n c r e a s e d v a l u e o f b i s i n agreement w i t h t h i s o b s e r v a t i o n . Figjres 5 and 6 i l l u s t r a t e t h i s b e h a v i o r f o r 80% SAN a t 363°K and 373°K respectively. They a r e c o m p u t e r g r a p h s o f e x p e r i m e n t a l d a t a w h i c h are not c u r v e - f i t t e d , but r a t h e r a r e p o i n t - t o - p o i n t connect ions o f t h e d a t a . The c u r v e s i n b o t h f i g u r e s a p p e a r v e r y s i m i l a r t o t h e n o n - s e n s i t i v e t r a n s i t i o n i n F i g . 3 o b t a i n e d from n u m e r i c a l s i m u lation. The p a r a m e t e r s i n T a b l e IV r e f l e c t t h e d e c r e a s e i n s e n s i t i v i t y c a u s e d by i n c r e a s e d t e m p e r a t u r e . As c h a r a c t e r i z e d by *b' t h e e f f e c t o f t e m p e r a t u r e on t h e r a t e o f i n i t i a t i o n îs r e s p o n s i b l e f o r t h e d e c r e a s e d s e n s i t i v i t y a s i n i t i a l t e m p e r a t u r e r i s e s (4). A t a c o n s t a n t i n i t i a t o r l e v e l , runaway c a n be c a u s e d by m a n i p u l a t i n g t h e i n i t i a l s t y r e n e c o n t e n t . With i n i t i a l i n i t i a t o r con c e n t r a t i o n f i x e d a t 0.03 m/1 and i n i t i a l t e m p e r a t u r e T = 373°K, r u n n i n g t h e r a n g e o f c o m p o s i t i o n s from 90 t o 20% c a u s e s t h e o n s e t 0

0

Q


182

CHEMICAL

REACTION


S A N BP (*,)o

[ilç τ .0734 383 β* 35.6 26.7 β

0.60 b

195

exact —

1

5

3

Figure 4.

7

TABLE

IV

PARAMETERS FOR EXPERIMENTAL RUNS

GM Τ ο .9

SAN/AIBN

363 373

.8

SAN/AIBN

363 373

.7

SAN/AIBN

363 373

.6 .4 .2

SAN/AIBN

SAN/A IBN

SAN/AIBN

373 373 373

9

Exact and Cpaf nonisothermal histories, 60% SAN

DIMENSI0NLESS

System

approx

PF

PE

a

Β

b

a

B

b

a

B

b

Typ

0.87 0.79

35 35

34

0.94 0.86

36 36

31 32

0 98 0 89

34 34

30

N R

0.71 0,58

33 33

16

.05

0.75 0.62

34 34

15 16

0 79 0 65

32 32

.05 .06

0.80 0.76

36 36

30 34

0.94

38 38

26 29

0 99 0 94

34 34

24

0.89

27

N R

.015 .02

0.80 0.64

35 35

12

0.91 0.73

36 36

10 11

1 00 0 80

33 33

9 10

N R

.0425 .05

1.03 0.87

39 39

44

1.37 1.Ί4

42 42

33 35

1 41

N

1 19

36 36

32

45

33

R

.015 .0175

0.95 0.57

36 36

11 16

0.85 0.71

38 38

12

33 33

10 11

N

13

0 95 0 78

.0075 .01

0.72

12 14

0.98

42 42

9 11

1 .12 0 .97

34 34

8

0.63

39 39

N R

.0035 .005

0.71 0.69

44 44

12 16

1.19 1.18

49

7 9

1 .44 1 .39

34 34

6 8

N

49

.0035 .005

0.55 0.39

51 51

17 19

1.32 0.92

57 57

7 8

1 .99 1 .44

27 27

4

N

5

R

Mo .09

.04

35 17

13

0.85


31 14 15

9

N R

R

R

SÉBASTIAN A N D

BiESENBERGER



184


o f RA a t t h e 80% l e v e l . I t s h o u l d be n o t e d t h a t t h e v a l u e s o f 'a' a s s o c i a t e d w i t h e x p e r i m e n t a l RA t r a n s i t i o n s a r e somewhat l o w . The e x t r e m e l y i n s e n s i t i v e n a t u r e o f t h e r e a c t i o n s would depress t h e v a l u e o f a consîderably. S c a t t e r i n t h e d a t a used t o d e t e r m i n e t h e p a r a m e t e r s f o r t e r m i n a t i o n was s u f f i c i e n t t h a t i n o r d e r t o f i t t h e e n t i r e r a n g e o f c o m p o s i t i o n s w i t h a s i n g l e m o d e l , e r r o r was i n troduced i n the r a t e s . The c r i t i c a l v a l u e s o f ' a ' s h o u l d l i e more i n t h e v i c i n i t y o f 1.4 t h a n 1.0. A l t h o u g h t h e r e i s an o f f s e t i t i s important t o note t h a t t h e e x p e r i m e n t a l systems respond i n t h e same manner as t h e p a r a m e t e r s p r e d i c t . When e x p e r i m e n t s i n d i c a t e d e c r e a s i n g s e n s i t i v i t y t h e p a r a m e t e r s change i n t h e same direction. When t h e e x p e r i m e n t s show t h e r m a l t r a j e c t o r i e s be coming i n c r e a s i n g l y more non-îsothermal t h e parameter 'a' de creases accordingly. The p a r a m e t e r s see i s o b s e r v e d , and t h u s RA t r a n s i t i o n w o u l d be p r e d i c t e d a t l o w e r values of T f o r a given [ l ] . C e r t a i n l y , the results using the k i n e t i c constants developed s a t i s f y t h e engineering accuracy ex p e c t e d o f them. The s t r o n g q u a l i t a t i v e agreement s u g g e s t s t h a t more p r e c i s e d e t e r m i n a t i o n s w o u l d c a u s e p r e d i c t i o n s and e x p e r i m e n t a t i o n t o merge. F u r t h e r m o r e , t h e c r i t e r i a w e r e f o r m u l a t e d i n such a way t h a t s h o u l d a more a p p r o p r i a t e t e r m i n a t i o n mechanism be d e t e r m i n e d o r s h o u l d t h e h e t e r o g e n e o u s k i n e t i c mechanism o f a c r y l o n i t r i l e p o l y m e r i z a t i o n and acrylonitrîle - r i c h c o p o l y m e r i z a t i o n be s u c c e s s f u l l y m o d e l l e d , t h e r e s u l t i n g p a r a m e t e r s c o u l d be e a s i l y adapted. c

Q

r

Q

Symbol s a

=

b,B

=

Cp Ε E

= = =

ε jk

= =

f H AHjk

= = =

I k I

= = =

1

E

m. J

=

R-A p a r a m e t e r d e f i n e d i n r e f e r e n c e 1 f o r h o m o p o l y m e r i z a t i o n s and T a b l e M l f o r c o p o l y m e r î z a t i o n s IG p a r a m e t e r s d e f i n e d i n r e f e r e n c e 1 f o r h o m o p o l y m e r i z a t i o n s and T a b l e M l f o r copolymerîzatîons s p e c i f i c heat a c t i v a t i o n energy (with a p p r o p r i a t e s u b s c r i p t ) E/RgT = d i m e n s i o n l e s s a c t i v a t i o n e n e r g y ( w i t h a p p r o priate subscript) Ι/Ε' ( p j k ' Epiu) 1/2 ( E " E - j - E ) = Ekj f o r copoly mer ιzation initiator efficiency factor a f u n c t i o n defined i n Table I h e a t o f r e a c t i o n between f r e e r a d i c a l w i t h end u n i t j and monomer k free-radical initiator reaction rate constant heat t r a n s f e r l e n g t h = V/A , r e a c t o r volume/wetted heat t r a n s f e r area comonomer j o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f comonomer j , [mj]/[mj] Q

E

+

d

tJ

TN

w

0


15.

SEBASTIAN A N D

m

=


BiESENBERGER

185

I n i t i a t i n g species or dimensionless concentration of i n i t i a t i n g s p e c i e s , [ m ] / [ m ] ; for i n i t i a t o r s used i n t h i s s t u d y , I -*· 2m r e a c t i o n r a t e p o i n t f u n c t i o n w i t h u n i t s moles/volume/time (and w i t h a p p r o p r i a t e s u b s c r i p t s ) u n i v e r s a l gas c o n s t a n t t e m p e r a t u r e (K) ( Τ - To)/To time o v e r a l l heat t r a n s f e r c o e f f i c i e n t mole f r a c t i o n o f comonomer j time c o n s t a n t s o r c h a r a c t e r i s t i c times ( w i t h a p p r o p r i a t e subscr i pts) 2 2 ^ ^ Εj / X 0

0

0

Q

R

=

Rg Τ Τ* t U xj λ,Λ

= = = = = =

=

ad

k

j = l k=l λ

1II pC Τ /(-ΔΗ)(k ) [m] [m ] f o r homopolymerization p o a p o o o o pC Τ / ( - A H . , ) ( R .. ) f o r c o p o l y m e r i z a t i o n ρ ο jk pjk ο

=

0

G λ... Gjk

=

2

^G

=

^2 ^2 ^ ^ G j k ^ j = l k=l

λ. J X

l/(k

mjk

ρ [ Y

-1

2

=

Κ

]

=

o r

c

°P°Wmer izat ion 1 / 2

..) [ f ( k . ) / ( k , . . ) pjj ο d o / t j jο ο /

(

Κ

1

[m ] ο ο

/

2

ρ ] ^ ο

j = l k=l density molar c o n c e n t r a t i o n

= ] =

Tyk

^

X

A

Gjk R

Subscr i pts ap d G i j,k

= = = = =

£

=

m ο ρ R t

= = = = =

a p p a r e n t o r lumped decomposition o f i n i t i a t o r g e n e r a t i o n o f heat initiator depletion or initiation comonomer o r r e p e a t u n i t o f t y p e j o r k, where j = 1 , 2 and k = 1,2 i n d e x w h i c h t a k e s on v a l u e s I = 1,2 b u t a l w a y s such that £ = j monomer d e p l e t i o n feed c o n d i t i o n s (except i n m ) propagation r e s e r v o i r ( t h e r m a l ) o r removal o f h e a t termination Q



186 Acknowledgment

T h i s work was s u p p o r t e d i n p a r t by a G r a n t f r o m t h e N a t i o n a l S c i e n c e F o u n d a t i o n (ENG-7605053). The a u t h o r s a l s o w i s h t o t h a n k U n i o n C a r b i d e f o r s u p p l y i n g t h e s t y r e n e monomer a t no c o s t .

Literature Cited 1. 2. 3. 4. 5. 6. 7.

Biesenberger, J . Α., Capinpin, R . , and Sebastian, D . , Appl. Polymer Symp. (1975), 26, 211. Biesenberger, J. Α., Capinpin, R., and Yang, J., Polymer Eng. Sci., (1976), 16, 101. Sebastian, D. H. and Biesenberger, J. Α., submitted to J. Appl. Polym. Sci. Sebastian, D. H., Ph.D. Thesis, Stevens Institute of Tech nology (1977). Sebastian, D. H. an Polymer S c i . Russo, S., Munari, S., J. Macromol. Sci-Chem., (1967), A-1,5, 2159. Sebastian, D. H. and Biesenberger, J. Α., Polymer Eng. Sci., (1976), 16, 117.


16 Comparison of Different Determination Methods for Effective Thermal Conductivity of Porous Catalysts U . H O F F M A N N , G . E M I G , and H. H O F M A N N Institut fur Technische Chemie I, University of Erlangen—Nuremberg, 8520 Erlangen, West Germany

For the design and analysis of fixed-bed c a t a l y t i c reactors as well as the determination of c a t a l y s t ef f i c i e n c y under nonisothermal conditions, the e f f e c t i v e thermal conductivity of the porous p e l l e t must be known. A c o l l e c t i o n of thermal conductivity data of s o l i d s pub l i s h e d by the Thermophysical Properties Research Centre at Purdue University [1] shows "a d i s p a r i t y i n data probably greater than that of any other p h y s i c a l prop erty". Some of these differences n a t u r a l l y can be ex plained, as no two samples of s o l i d s , e s p e c i a l l y porous c a t a l y s t s , can be made completely i d e n t i c a l . However, the main reason i s that the assumed boundary conditions for the Fourier heat conduction equation

never can be met experimentally exactly. On the other hand, the magnitude of values predicted by pore s t r u c ture models d i f f e r up to 40 % [2] and there i s there fore a need for experimental measurement. In order to come as close as possible to the required boundary con d i t i o n s , d i f f e r e n t authors have developed d i f f e r e n t s t a t i c and dynamic methods for the experimental deter mination of the thermal conductivity of s o l i d s . A r e view of these methods has been given recently by J.E. Parrot and A . D . Stuckes [2]. For porous p a r t i c l e s i n p a r t i c u l a r much less information i s a v a i l a b l e [ 3 , 4 , 5 , 6 , 7,8,9,10,11]. The aim of t h i s paper i s to compare r e s u l t s from d i f f e r e n t experimental methods for several types of c a t a l y s t s i n order to explore t h e i r advantages and d i s advantages . ©

0-8412-0401-2/78/47-065-189$05.00/0


190

CHEMICAL

REACTION


E x p e r i m e n t a l Methods Among t h e s t a t i c methods t h e l i n e a r heat f l u x me thods seem t o be most commonly used f o r porous p a r t i c l e s . In t h i s case, i t i s assumed t h a t the t r a n s p o r t o f h e a t t h r o u g h t h e specimen i s m a i n l y i n one d i r e c t i o n thus t h e F o u r i e r law g i v e n by Eqn. (1) becomes one d i m e n s i o n a l and can be c a l c u l a t e d a c c o r d i n g t o \

L ^ _L » A(T--T ) A R 12 ρ To g e t c o r r e c t v a l u e s o f X from t h i s e q u a t i o n , t h e heat l o s s e s from th n e g l i g i b l e . This conditio e x t e n t i n t h e so c a l l e d conductometer, o r i g i n a l l y de v e l o p e d by J . Schroder [12] and now c o m m e r c i a l l y a v a i l a b l e t h r o u g h C o l o r a MeBtechnik GmbH. The p r i n c i p l e o f t h e q u i c k and s i m p l e , y e t e l e g a n t and a c c u r a t e method ( l a i n T a b l e 3) c o n s i s t s i n c o n t a c t i n g a c y l i n d r i c a l sample w i t h two b o i l i n g l i q u i d s L- and L o f d i f f e r e n t boiling points and T (ΔΤ=10 t o 20 K ) . F i g u r e 1 shows t h a t t h e l i q u i d or h i g h e r b o i l i n g p o i n t i s con t a i n e d i n t h e lower v e s s e l Β , t h e o t h e r i n the upper one B . The c o n t a c t between t h e sample Ρ and t h e v e s sels i s p r o v i d e d by two s i l v e r s t o p p e r s a t t h e t o p o f t h e lower S- and t h e bottom o f t h e upper v e s s e l S to a v o i d r a d i a l temperature g r a d i e n t s . The heat f l o w from t h e lower v e s s e l t h r o u g h t h e sample causes the l i q u i d i n B t o b o i l a t a c o n s t a n t r a t e under s t a t i o n a r y con d i t i o n s . A c o n s t a n t temperature d i f f e r e n c e T ^ - T i s r e a c h e d between t h e two s i l v e r p l a t e s . The vapor from the upper v e s s e l i s condensed i n a condenser C and t h e condensate i s c o l l e c t e d i n a measuring b u r e t t e B. The time t needed f o r t h e e v a p o r a t i o n of a c e r t a i n amount o f l i q u i d i s measured. The e f f e c t i v e t h e r m a l c o n d u c t i v i t y o f t h e sample t h e n can be c a l c u l a t e d a c c o r d i n g t o Eqn. (2) w i t h t h e known s p e c i f i c heat o f v a p o r i s a t i o n ( - A H ) by s e t t i n g A

=

=

(:

K Z }

p

0

2

2

2

2

2

2

v

f

=

V

2

£

2

2

(3)

To a v o i d s y s t e m a t i c e r r o r s , e.g. caused by r a d i a l h e a t l o s s e s , a r e l a t i v e measurement i n s t e a d o f an ab s o l u t e d e t e r m i n a t i o n i s recommended i n which t h e t h e r mal c o n d u c t i v i t y o f t h e sample i s compared w i t h t h a t o f a r e f e r e n c e m a t e r i a l . In a d d i t i o n , t h i s e l i m i n a t e s


16.

HOFFMANN ET AL.

Thermal

Conductivity

Determination

Methods

191

the n e c e s s i t y o f knowing the e x a c t v a l u e o f (-ΔΗ )~ and the b o i l i n g temperature o f the lower b o i l i n g l i q u i a . High p u r i t y copper, Armco i r o n , n i c k e l a l l o y s and p a r t i c u l a r g l a s s e s are commonly used as r e f e r e n c e m a t e r i a l . The method i s g e n e r a l l y s u i t a b l e f o r ( i ) the whole tem p e r a t u r e range f o r which one can f i n d s t a b l e l i q u i d s w i t h w e l l d e f i n e d b o i l i n g p o i n t s , and ( i i ) n e a r l y a l l s o l i d s w i t h the e x c e p t i o n o f t h o s e w i t h v e r y h i g h t h e r mal c o n d u c t i v i t y l i k e copper and s i l v e r , because i n t h i s case heat l o s s e s («xl/L) a r e too g r e a t or measuring times (o % ^ (f) . (9) a ζ On the b a s i s o f e x p e r i m e n t a l r e s u l t s i t has been demonstrated f u r t h e r m o r e [16] t h a t w i t h c y l i n d r i c a l par t i c l e s , h a v i n g a l e n g t h t o d i a m e t e r r a t i o o f 1, t h e lim i t i n g temperature d i f f e r e n c e r e a c h e d i s 1.203 times l a r g e r than t h a t f o r s p h e r i c a l p a r t i c l e s , which means that A m A

T

lim

=

1.203 — 6 i

C

,cL 2>

2

(

χ ( l o )

The a d d i t i o n a l i n f o r m a t i o n ( d e n s i t y and heat c a p a c i t y of t h e p e l l e t ) , needed i n o r d e r t o c a l c u l a t e the t h e r mal c o n d u c t i v i t y from a, can be g a i n e d by s t a n d a r d r o u t i n e methods. Experimental Results T a b l e 1 shows the p r o p e r t i e s o f t h e c a t a l y s t s used i n t h i s study. V a l u e s o f t h e t h e r m a l c o n d u c t i v i t y i n W/m,K of d i f f e r e n t nonporous r e f e r e n c e and embedding m a t e r i a l s are g i v e n i n T a b l e 2. Values of the e f f e c t i v e thermal c o n d u c t i v i t y i n W/m,K, d e t e r m i n e d a c c o r d i n g t o t h e d e s c r i b e d methods a r e g i v e n i n T a b l e 3. 1

^Methods w i t h a p e r i o d i c v a r i a t i o n of temperature a r e not d i s c u s s e d h e r e . In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

[JL4]

196

CHEMICAL

REACTION


thermostat bath with programmed heating rate catalyst particle with central and periphered thermocouple thermocouple line recorder indicating linear increasing bath temperature and Δ Τ between center and periphery e programmer for heating rate f circulation pump

Figure 5.

Principle of the apparatus for the dynamic method


16.

HOFFMANN ET

AL.

Thermal Conductivity Determination Methods

197

D i s c u s s i o n and C o n c l u s i o n The d a t a g i v e n i n T a b l e 1 show t h a t i n t h i s s t u d y a b r o a d spectrum o f c a t a l y s t p r o p e r t i e s has been cove r e d . A l l o f t h e c a t a l y s t s a r e o f t e c h n i c a l importance. The r e s u l t s g i v e n i n T a b l e 3 and t h e e x p e r i e n c e g a i n e d d u r i n g the i n v e s t i g a t i o n p e r m i t t h e f o l l o w i n g s t a t e ments : 1) For the d e t e r m i n a t i o n o f t h e e f f e c t i v e t h e r m a l c o n d u c t i v i t y o f porous c a t a l y s t p e l l e t s no s t a n d a r d i z e d method e x i s t s and p r o b a b l y w i l l never be d e v e l o p e d . On the c o n t r a r y , t h e most s u i t a b l e method depends s t r o n g l y on the p r o p e r t i e s o f the c a t a l y s t . In t h i s c o n n e c t i o n s i z e and form o f th ture, i t s s o l u b i l i t y t i v i t y o f t h e s o l i d m a t e r i a l and r e a c t i o n m i x t u r e a r e most i m p o r t a n t . As a g e n e r a l r u l e , t h a t method s h o u l d be p r e f e r e d i n which the c a t a l y s t can be a p p l i e d as used i n t h e r e a c t o r . T h i s i s not always p o s s i b l e . O f t e n the c a t a l y s t must be s p e c i a l l y p r e p a r e d f o r t h e measurement by g r i n d i n g and r e p e l l e t i z i n g , c o a t i n g , embedd i n g , e t c . , i n o r d e r t o produce a more o r l e s s s u i t a b l e sample. The i n f l u e n c e o f t h e c a t a l y s t p r e p a r a t i o n i s seen most c l e a r l y from the v a l u e s f o r c a t a l y s t A i n T a b l e 3. The c a t a l y s t was used i n i t s o r i g i n a l form o n l y i n methods l b and I I I . 2) Among t h e c o m m e r c i a l l y a v a i l a b l e u n i t s , the Col o r a conductometer seems t e c h n i c a l l y f u l l y d e v e l o p e d and can be r e a d i l y adapted f o r c o n d u c t i v i t y measurements on c a t a l y s t p e l l e t s . The d e s i g n m i n i m i z e s t h e unc o n t r o l l a b l e heat l o s s and a s s u r e s n e a r l y c o n s t a n t temp e r a t u r e i n any h o r i z o n t a l p l a n e t h r o u g h the sample. The time n e c e s s a r y f o r one measurement i s about 3 h o u r s . I f the r e f e r e n c e method i s used, no a d d i t i o n a l i n f o r m a t i o n i s needed f o r the d e t e r m i n a t i o n o f the e f f e c t i v e thermal c o n d u c t i v i t y . Other c o m m e r c i a l l y a v a i l a b l e u n i t s , m a i n l y des i g n e d f o r d e t e r m i n a t i o n o f the t h e r m a l c o n d u c t i v i t y o f b u i l d i n g m a t e r i a l s i n t h e form o f p l a t e s , l i k e t h e L i n s e i s L91 u n i t , s u f f e r from the s h o r t c o m i n g t h a t i n o r d e r t o minimize heat l o s s e s , the sample d i a m e t e r i s 80 t o 120mm. T h i s l a r g e d i a m e t e r makes i t d i f f i c u l t t o o b t a i n good c o n t a c t between the h e a t e r s and the c a t a l y s t sample. Furthermore, w i t h e l e c t r i c h e a t e r s i t i s d i f f i c u l t t o r e a l i z e a c o n s t a n t temperature a c r o s s the e n t i r e c r o s s s e c t i o n o f t h e probe. F i n a l l y t h e sample s i z e demands a r a t h e r l a r g e amount o f c a t a l y s t . The dynamic method ( I I I ) used i n t h i s study has the advantage o f a s h o r t measuring time (0.5 h o u r s ) ,


198

CHEMICAL

Table 1

Sample

catalyst

REACTION ENGINEERING—HOUSTOÎ

1

Properties

specific density s p e c i f i c pellet s u r f a c e a r e a (kg/m ) h e a t porosity (mVka) (kJ/kg,K) 56900 1950 1.07 0.468 3

A.

25%Ni on A1 0 2

3

Β

Ca/Niphosphate

C

Fe/Mo-oxid

D

Zeolite

Ε

6%Zn-acet a t e on ac t i v e carbon

145000

1350

1.98

0.570

7500

2260

0.66

0.448

253000

1040

2.15

0.490

3310

Table 2 P r o p e r t i e s meth od la Ha lie III

o f R e f e r e n c e and Embedding M a t e r i a l s

a c r y l i c Hostaform T e c h n o v i t Re1opal glass C 9021 GK 4071 0.21 0.24 0.15 0.18 — 0.42 0.20

T a b l e 3 E f f e c t i v e Thermal C o n d u c t i v i t i e s o f Porous C a t a l y s t s , Determined by D i f f e r e n t Methods meth mean meas od u r i n g tem p e r a t u r e (K)

367

Ic

III

D

C

0.18

0.30

0.22

0.67 0.52

1.60

0.19

0.63

D.82

0.26

0.68

0.40

-

333-353

1.19

Ε

Β

0.37

313

lib lie

A 0.57

la lb

catalysts

-

0.51 0.24

3 ]

0.29

l)ground a . r e p e l l e t i z e d , 2) broken p e l l e t s , i z e d under h i g h p r e s s u r e

0.22

0.63

3) p e l l e t -


16.

HOFFMANN

ET

AL.

Thermal Conductivity Determination Methods

199

p r o v i d e d a p r o p e r b a l a n c e between p e l l e t diameter, h e a t i n g r a t e and t h e r m a l d i f f u s i t y o f t h e p e l l e t can be reached.. In t h i s study p e l l e t d i a m e t e r s o f 6 t o 20mm and h e a t i n g r a t e s between 100 and 300 K/h had been found s u i t a b l e . The a p p a r a t u s f o r t h i s method i s easy t o b u i l d u s i n g s t a n d a r d l a b o r a t o r y equipment. I f a v a i l a b l e , a DTA u n i t c o u l d a l s o be used f o r t h i s s p e c i a l purpose. 3) The embedding o f c a t a l y s t p a r t i c l e s i n q u i c k h a r d e n i n g p l a s t i c T e c h n o v i t 4071 ( K o l z e r ) causes no problems, p r o v i d e d t h e p e l l e t s have a c o n s t a n t c r o s s s e c t i o n a l a r e a a c r o s s t h e sample h e i g h t L. With i r r e g u l a r shaped p a r t i c l e s t h e d e t e r m i n a t i o n o f t h e d e n s i t i e s needed i n E q u a t i o n 5 sample l e a d t o u n c e r t a i l a r g e sample d i a m e t e r (method l i a ) i t i s d i f f i c u l t t o obtain a p e r f e c t l y plane contact s u r f a c e . C o a t i n g o f r e g u l a r shaped p e l l e t s w i t h a s u i t a b l e two component p o l y u r e t h e n e v a r n i s h (Fliigger u. Boecking K.G.) caused no problems i f a methanol-water o r g l y c e r i n e - w a t e r m i x t u r e i s used as i n method l i e . I f carbon t e t r a c h l o r i d e must be used t o r e a c h a low enough v a l u e f o r the t h e r m a l c o n d u c t i v i t y , a n o t h e r c o a t i n g system has t o be found. I r r e g u l a r shaped p a r t i c l e s c o u l d n o t be c o a t ed s a t i s f a c t o r i l l y i n t h i s study as no way was found t o make t h e v a r n i s h f i l m t h i n enough. To suppress t h e t h e r m a l c o n v e c t i o n o f t h e l i q u i d m i x t u r e i n t h e v o i d s between t h e p e l l e t s (as another s o u r c e o f e r r o r ) t h e c o a t e d p a r t i c l e s s h o u l d be as s m a l l as p o s s i b l e and f i l l up t h e measuring chamber com pletely. 4) The s t a n d a r d d e v i a t i o n o f t h e measurement de t e r m i n e d f o r c a t a l y s t C w i t h method l a was 0.013 f o r a mean v a l u e o f 0.30 which i s v e r y s a t i s f a c t o r y as t h i s value i n c l u d e s both the v a r i a t i o n i n the c a t a l y s t pre p a r a t i o n as w e l l as t h e e x p e r i m e n t a l e r r o r s . Symbols 2 A c r o s s - s e c t i o n a l area (m ) a=X/$ c thermal d i f f u s i v i t y o f the c a t a l y s t p e l l e t (m /s) C Ρ Bemperature gradient i n the ambient f l u i d (K/s) c s p e c i f i c heat (kJ/kg K) D probe diameter (m) d p e l l e t diameter (m) f f r a c t i o n a l area (m /m t o t a l ) (-ΔίΟ heat o f evaporation (kJ/kg) L d i s t a n c e (m) R thermal r e s i s t a n c e (K/W) R e l e c t r i c a l r e s i s t a n c e (V/A) P


200


Τ temperature (K) ^ • l i m l i m i t i n g temperature d i f f e r e n c e (K) t time ( s ) U v o l t a g e (v) V volume o f L condensed (m^) w weight f r a c t i o n (kg/kg t o t a l ) λ thermal c o n d u c t i v i t y (W/mK) S d e n s i t y (kg/m ) φ heat flow r a t e (W) Indices f fm ρ m t

fluid l i q u i d mixture pellet p l a s t i c matrix total

Literature

[1] Touloukian,Y.S. (Ed.), 1970, Thermophysical Properties of Ma ter. The Thermophysical Properties Research Centre Data Se r i e s , Volumes 1 und 2 (IFI/Plenum Press, New York) [2] P a r r o t , J . E . and Stuckes,A.D., Thermal Conductivity of Solids Pion Limited, 207 Brondsbury Park, London NW2 5JN [3] Sharma,C.S. and Hughes,R., Can.J.Chem.Engng. 54 (1976)538-36 [4] Sehr,R.A., Chem.Engng.Sci 9 (1958) 145 [5] S a t t e r f i e l d , C . N . , Mass Transfer i n Heterogeneous Catalysis, M.I.T. Press, Cambridge, Mass./USA, 1970 [6] Butt, J.B., Α . I . C h . E . J . 11 (1965) 106 [7] Masamune,S. and Smith,J.M., J.Chem.Engng.Data 8 (1963) 54 [8] Cunningham, R . S . , Carberry, J.J. and Smith,J.Μ., Α . I . C h . E . J . 11 (1965) 636 [9] H a r r i o t t , P . , Chem.Engng.J., 10 (1975) 65-71 [10] Sharma,C.S., H a r r i o t t , P . and Hughes,R., ibid., 10 (1975) 7380 [11] Saegusa,T., Kamata,K., Iida,Y. and Wakao,N., Int.Chem.Engng. 14 (1974) 169-173 [12] S c h r ö d e r , J . , Review of S c i e n t i f i c Instruments, 34 (1963) 615-621 [13] Ritter,J., Helm,Ε. and F ü r s t , H . , Chem.Techn. 28 (1976) 232-621 [14] Gunn,D.J. and De Souza,J.F.C., CES 29 (1974) 1363-1371 [15] Carslaw,H.S. and Jaeger,J.C., Conduction of Heat i n Solids, Oxford, Clarendon Press, 1959 [16] Jirátová,K. and Horák,J., Chem.Techn. 28 (1976) 550-553


17 Interpretation of Catalyst Deactivation by Fouling from Interactions of Pore Structure and Foulant Deposit Geometries C. C. H U G H E S and R E G I N A L D

MANN

Department of Chemical Engineering, University of Manchester Institute of Science and Technology, Manchester, England

Deactivation is a encompasses several d i s t i n c t processes, that give r i s e to a lowering of catalyst a c t i v i t y . Poisoning, ageing, sintering and fouling are particular examples of deactivation and these terms ought in principle to clearly indicate and discriminate the mechanisms involved. In practice, probably due to the potential complexity if these processes take place simultaneously, there is often some overlap and confusion i n their use. Levenspiel 1 has referred to fouling as being primarily rapid, accompanied by deposition and a physical blocking of surface. He then defines poisoning as a slow modification of a c t i v i t y by chemisorption on the active s i t e s , the poison being characterised by difficulty of removal. It i s our view that rate of loss of a c t i v i t y is not a sufficiently meaningful discriminant. Instead, we propose that poisoning should refer to active site deactivation by monolayer type adsorption at the site, and thereafter no further poison adsorption takes place at that location. In this way, a very great loss of a c t i v i t y can take place with the adsorption of very small amounts of poison. I f , however, successive adsorption on the surface can take place, such that significant amounts of material accumulate, then t h i s represents fouling of the catalyst. The c l a s s i c a l treatments of a c t i v i t y loss by poisoning by Thiele 2 and Wheeler 3t support the above d i s t i n c t i o n s , since the poison was not considered to have any influence upon the pore geometry or effective d i f f u s i v i t y . Uniform, non-uniform and anti-selective poisoning do give r i s e to a wide spectrum of deactivation behaviour, but the non-comprehensive capability of a theory of poisoning to explain deactivation when significant accumulation takes place, requires that new approaches be made. This is confirmed by several more recent observations. Thus, Butt's 4 measurements of a very non-uniform coke p r o f i l e , indicate that ultimate penetration of a coke type foulant into a catalyst p a r t i c l e i s very quickly attained, and sybsequent deposition occurs entirely within an outer s h e l l . ©

0-8412-0401-2/78/47-065-201$05.00/0


202

CHEMICAL

REACTION

ENGINEERING—HOUSTOI

There remains an uncoked c e n t r a l c o r e , apparently never contactée by r e a c t a n t . The work o f Rostrup-Nielsen 5 and L e v i n t n e r 6 a l s o suggests t h a t pore mouth c l o s u r e by coke plugs may be t h e o r e t i c a l l y r e q u i r e d , and a s i m p l i f i e d theory has been r e c e n t l y proposed by Newson 7· There i s t h e r e f o r e a good d e a l o f evidence t o support t h e i d e a t h a t the e f f e c t o f f o u l a n t d e p o s i t s on a c t i v i t y , s e l e c t i v i t y and p e l l e t macroscopic p r o p e r t i e s i s s e n s i t i v e t o both the pore s t r u c t u r e and the f o u l a n t deposit s t r u c t u r e . Such an approach should improve upon the more e m p i r i c a l l y based methods used by Voorhies 8 and Wojciechowski 9» which have t r a d i t i o n a l l y attemptedTto describe d e a c t i v a t i o n when f o u l i n g occurs. O u t l i n e o f the Theory The nature o f the i n t e r a c t i o n o f the pore s t r u c t u r e and f o u l a n t deposit geometries i s determined from two b a s i c assumptions. F i r s t l y , t h a t t h e pore s t r u c t u r e may be represente( by a set o f i d e a l i s e d p a r a l l e l s i d e d non i n t e r s e c t i n g pores o f v a r i a b l e r a d i u s , but each o f a c e r t a i n l e n g t h L. This i s the so c a l l e d ' p a r a l l e l bundle' model. Secondly, t h a t the f o u l a n t accumulates by simultaneous p e n e t r a t i o n and t h i c k e n i n g , g i v i n g r i s e t o successive l a y i n g down o f f o u l a n t . We c a l l t h i s t h e 'wedge l a y e r i n g ' model o f f o u l a n t d e p o s i t i o n . The q u a l i t a t i v e f e a t u r e s o f the subsequent i n t e r a c t i o n are depicted i n F i g . 1. The s m a l l e s t pore A b l o c k s f i r s t as t h i c k e n i n g proceeds and t h e r e a f t e r the remaining surface w i t h i n pore A i s rendered i n a c c e s s i b l e and thus c a t a l y t i c a l l y i n a c t i v e . I f the d e s i r e d n o n - f o u l i n g r e a c t i o n i s t a k i n g place without d i f f u s i o n i n f l u e n c e , the l o s s i n a c t i v i t y i s equal t o t h i s l o s s o f area i n pore A. T h i s i s shown i n F i g . 2 . As p e n e t r a t i o n and t h i c k e n i n g continue a t the same r e l a t i v e r a t e , a d d i t i o n a l l o s s e s i n a c t i v i t y take p l a c e , as the remaining l a r g e r pores become plugged. I t i s c l e a r t h a t i n the absence o f a theory o f p l u g g i n g , the a c t i v i t y l o s s would be erroneously i n t e r p r e t e d as being caused by p o i s o n i n g w i t h d i f f u s i o n a l r e s i s t a n c e . T o t a l f o u l a n t content as a f u n c t i o n o f p e l l e t a c t i v i t y i s perhaps the most important c h a r a c t e r i s t i c i n a n a l y s i n g f o u l i n g behaviour, s i n c e i t i s f a i r l y simply observed by experiment. F i g . 3 shows some q u a l i t a t i v e aspects. I t i s c l e a r t h a t a t any given f o u l a n t content two p o s s i b i l i t i e s e x i s t f o r t h e d i s t r i b u t i o n o f f o u l a n t t h a t g i v e r i s e t o the same a c t i v i t y . Thj i s i l l u s t r a t e d i n F i g s . 3 ( a ) , ( c ) . I f the f o u l a n t has a s m a l l t h i c k n e s s and l a r g e p e n e t r a t i o n as i n ( a ) , t h i s can be viewed as a p o i s o n i n g mode o f d e a c t i v a t i o n . On the other hand, the same amount o f f o u l a n t could be present as a l a r g e t h i c k n e s s s m a l l p e n e t r a t i o n wedge as i n F i g . 3 ( c ) , and t h i s would be a pore mouth plugging mode o f d e a c t i v a t i o n . A f u r t h e r o b s e r v a t i o n i s t h a t a t a c e r t a i n l e v e l o f the parameter β defined by β = rate o f foulant thickening/rate o f foulant penetration


17.

HUGHES

AND M A N N

Catalyst Deactivation by Fouling

Figure 1. Fouling by "wedge layering" in a parallel bundle pore structure model

0-6 h

PORE Ap*

FOULANT PENETRATION

Figure 2. Activity hsses as foulant penetrates and accumulates


203

204

CHEMICAL

Figure 3.

REACTION


Illustration of differing modes of deactivation


17.

HUGHES

Catalyst Deactivation by Fouling

AND MANN

205

which i s here assumed t o be a constant i r r e s p e c t i v e o f degree o f p e n e t r a t i o n o r t h i c k e n i n g , a pore o f a g i v e n s i z e reaches a maximum f o u l a n t content as β i n c r e a s e s from zero (pure poisoning) to i n f i n i t y (pure pore mouth p l u g g i n g ) . T h i s i s i n d i c a t e d i n F i g s . Ma) and ( b ) . T h i s c h a r a c t e r i s t i c o f maximum f o u l a n t accumulation a t some c r i t i c a l value β has been deduced w i t h respect t o pores o f a s i n g l e s i z e . lS order f o r the theory t o f i n d general a p p l i c a b i l i t y , i t requires extension t o p e l l e t s with d i s t r i b u t e d pore s i z e s . For a u n i t mass o f c a t a l y s t , i f f ( r ) d r i s the surface area contained i n pores o f s i z e between* r and r+dr, then r

00

ίο

f (r)dr 8

(1)

a S *

where S i s the s p e c i f i pore moith p o i s o n i n g were t o take p l a c e under n o n - d i f f u s i o n i n f l u e n c e d c o n d i t i o n s , the reduced a c t i v i t y a t a g i v e n p e n e t r a t i o n χ i s g i v e n by (-co

(1 - τ)

Ι f (r)dr/S = 1 - f (2) Jo where L i s the l e n g t h dimension o f the p a r a l l e l pore bundle. Now, i f f o u l i n g takes p l a c e by wedge l a y e r i n g such t h a t β = h/x, pores w i l l remain unplugged, and t h e i r i n t e r i o r surface w i l l be a c c e s s i b l e and c a t a l y t i c a l l y a c t i v e , provided t h a t r>h. Therefore the reduced a c t i v i t y a t a g i v e n p e n e t r a t i o n χ w i l l be g i v e n by w

S

δ

L

-00

(1 - £) Γ Jh

(3)

f (r)dr/S 6

The dimensionless a c t i v i t y i s t h e r e f o r e i d e n t i f i e d w i t h nonf o u l e d pore surface t h a t succeeds i n remaining a c c e s s i b l e . As mentioned p r e v i o u s l y , t h i s e f f e c t due t o mouth p l u g g i n g can be s p u r i o u s l y i d e n t i f i e d as pore d i f f u s i o n a l r e s i s t a n c e accompanying p o i s o n i n g . In c a l c u l a t i n g the corresponding volume o r mass o f accumulated f o u l a n t , those pores which have a l r e a d y become sealed have t o be d i s t i n g u i s h e d from those t h a t y e t remain t o be plugged. For unplugged pores, i f f ( r ) d r i s the number f r a c t i o n o f pores s i z e d between r and r+dr, the f o u l a n t volume i n t h i s category o f pores at a p o t e n t i a l mouth t h i c k n e s s h i s g i v e n by -co V£(h) = J

£ττ(

2 Γ

2

2

- β χ )χΝί (Γ)ά Ν

Γ

W

where Ν i s the t o t a l number o f pores c o n s t i t u t i n g the p a r a l l e l bundle w i t h i n a u n i t mass o f c a t a l y s t . For the category o f plugged pores, a pore becomes plugged and t h e r e a f t e r remains plugged a t the i n s t a n t when h = βχ = r , and hence a l l the pores between 0 and h are blocked o f f f o r a


206


FOULANT CONTENT (a) FOR 04) i s l a r g e r than t h e molar volume o f t h e r e a c t a n t s o l i d (e.g., CaO), a t t e n t i o n i s f o c u s e d on a s i m p l e case o f a c y l i n d r i c a l pore o f i n i t i a l r a d i u s and l e n g t h L ( F i g u r e l a ) . As gaseous r e a c t a n t (e.g., SO2) i s absorbed t o form a p r o d u c t l a y e r o f C a S Û 4 , t h e geometry o f t h e pore changes w i t h time ( F i g u r e l b ) . A f t e r some time t h e pore mouth w i l l p l u g and r e a c t i o n w i l l cease. Assuming i s o t h e r m a l c o n d i t i o n s and n e g l e c t i n g b u l k f l o w , r a d i a l c o n c e n t r a t i o n g r a d i e n t s i n t h e pore and e x t e r n a l mass t r a n s f e r r e s i s t a n c e , t h e f o l l o w i n g d i m e n s i o n l e s s form o f t h e pore p l u g g i n g model i s d e r i v e d (13 ). a. Pore D i f f u s i o n

6

ft

(

g

l

c

)

=

fe

1 < 3

1 ^1 ^ D

)

]

+

2 σ α

χ

< '^

(D

where G(x,t)

= g

±

υ

(g

l f

t)

(2)

and w i t h t h e f o l l o w i n g i n i t i a l c(x,0) b.

= 0; c ( l , t )

Product

σ 3t

r 3r

Layer

1

and boundary c o n d i t i o n s

= 1; c ( 0 , t ) = 0

(3)

x

Diffusion (4)

}

dr

with the f o l l o w i n g i n i t i a l

and boundary c o n d i t i o n s

Ô(x,0)=0; c ( g t ) = c ( x , t ) ; - 6 ( g , t ) = K c ( g , t ) 1

r

2

2


(5)

CHROSTOwsKi A N D GEORGAKis

Pore Plugging Model

CAO

Ό

CAO

-so

2

h a)

Initial Pore Geometry

b)

Pore Geometry after tome reaction has occured (t>0)

Figure 1. Geometric changes of cylindrical pore because of the large molar volume of solid product



228 c.

R e a c t i o n F r o n t Change

3g I

= I

6

(g ,t)

with g (x,0) = 1

2

(6)

2

and the f o l l o w i n g e q u a t i o n r e l a t i n g the i n t e r f a c e t o the s o l i d - s o l i d i n t e r f a c e g\ = α +

(l-a)g

gas-solid

(7)

2

D e f i n i t i o n o f a l l symbols i s g i v e n i n the N o t a t i o n section. S i n c e the v a l u e o f β i s u s u a l l y q u i t e s m a l l , the pseudo-steady-state hypothesis i s j u s t i f i e d with r e s pect to t h e ^ d i f f u s i o n a solved f o r c(r,x,t 1 + Kg ln(g /r) c(r,x,t) = c(x,t) χ Kg ln(g / ) 2

2

( 8 )

+

2

Then the o v e r a l l model reduces 3 9x

2 3c ^ l ^ l * ^

2

g i

to g

=

2

σ

Κ

2^ Kg ln(g /

1 +

2

2

w i t h boundary c o n d i t i o n s g i v e n by eq.

3t~ " 2

1 + Kg ln(g / 2

2

g i

)

9

( χ 2

g i

(9)

)

( 3 ) , and

'

0 )

"

1

(10)

Here the d i m e n s i o n l e s s d i f f u s i o n c o e f f i c i e n t D(g^) assumed t o depend on g^ i n the f o l l o w i n g way D(g ) x

= Vg^d

is

(11)

+ Vg ) ±

s i n c e Knudsen d i f f u s i o n i s t a k e n t o be e q u a l l y impor t a n t as m o l e c u l a r d i f f u s i o n . Ramachandran and Smith (7_) r e c e n t l y p r e s e n t e d a s i m i l a r model, but assumed t h a t the d i f f u s i o n c o e f f i c i e n t i s not changing as the geometry o f the pore changes. 2.

A n a l y t i c a l E v a l u a t i o n o f the P l u g g i n g Time

I f a t t e n t i o n i s f o c u s e d on the changes t a k i n g p l a c e a t the mouth o f the pore (x = 1) where the d i m e n s i o n l e s s c o n c e n t r a t i o n i s u n i t y , eq. (10) l e a d s t o dg (l,t) £ dt 2

=

, ± 2 1+

± Kg ln(g / 2

2

(12) g i

)


v ±

;

19. CHROSTowsKi A N D GEORGAKis Eq.

(12)

can be

Pore Plugging Model

integrated to

229

yield 2

g

(g

- i) + f

2

{g

l n

g

2

+

l

n

g

2

l

}

=

t

/

2

( 1 3 )

where g and g imply g , ( l , t ) and g ( l , t ) . A t the t i m e , t p , t n a t the pore mouth w i l l p l u g , g-^ becomes z e r o . L e t t i n g the c o r r e s p o n d i n g v a l u e o f g be denoted by w from eq. (7) i t f o l l o w s t h a t 1

2

2

2

g?

= w

2

( 1 4 )

= -2^.

^2

α - 1

Then eq. (13) t = 2(w

can be - 1)

r e a r r a n g e d so

that

which g i v e s the d i m e n s i o n l e s s time r e q u i r e d t o p l u g the p o r e as a f u n c t i o n o f the d i m e n s i o n l e s s parameter K. 3.

Perturbation

S o l u t i o n f o r S m a l l Times

In o r d e r t o o b t a i n a n a l y t i c a l s o l u t i o n s f o r the n o n l i n e a r model g i v e n i n s e c t i o n 1, v a l i d f o r s m a l l t i m e s , a T a y l o r s e r i e s e x p a n s i o n i s assumed f o r g (x,t): 2

2

g ( x , t ) = 1 + t h ( x ) + t h ( x ) + ... 2

x

I t then f o l l o w s

(16)

2

that

g^Xjt) = 1 +

(1 - o O t h ^ x ) + ...

(17)

and 1 + Kg ln(g / 2

provided

2

g i

t h a t aKt

)

= 1 - aKth.(x) " " " l

)

A special case which has received much attention (1-2, 4-6) is the plug flow model, resulting from Eqn (7) in the limit Pe ~*»: a

09

Λ"*

5.

B i

2

-4a z

Data Analysis The models were subjected to two stages of analysis:

(A) Overall.Analysis A stringent test of the models i s provided by f i t t i n g them simultaneously to data measured at several bed depths. In the axial dispersion model, the parameters Pe , Pe and Bi were est ated by minimising the sum of squares of residuals on the 32 be exit temperatures: a

Ν F

=;

32 ;

r

9

(texp.0 - W o )

o°

where Ν is the number of bed depths; t ] p is calculated from either Eqn. (7) or (8), depending upon which boundary condition is adopted at the bed exit, at the appropriate radial measuring points for z=L. c a

Ç j

(B) Depth_bY_Degth_AnalYsis The a b i l i t y of the models to f i t the data at individual bed depths (N=l) was next examined in order to detect any trend in t parameters with bed depth. The non-linear function minimisations of Eqn.(10) and i t s simpler cases were carried out by the Marquardt search algorithm


20.

DIXON

ETAL.

Heat Transfer in Packed Beds

243

(Fortran sub-routine E04 FBF NAG library, NAG Ltd., Oxford). A preliminary grid search was made to check for irregularities in the sum of squares surface and provide a starting point for the search. Previous analysis of experimental errors (8) substantiated the validity of the unweighted least squares criterion (]0) for estimation of the model parameters. 6.

Evaluation of Models Results of Depth by Depth Analysis

Neither model showed significant lack of f i t to the data at the 95% confidence level th plu flo model were found to decrease systematicall Fig. (3) shows this effect quite clearly in the case of the effect ive radial conductivity. No such effect was observed with the axial dispersion model, as i s apparent from Fig. (4). DeWasch and Froment (6) also noted the dependence of the plug flow model parameters with bed depth. They therefore only correlated their data obtained on the longest beds hoping to minimize axial dispersion effects. However, i f Figs. (3) and (4) are superimposed, the estimates of k obtained from the axial dispersion model are significantly greater than those obtained on the longest bed using the plug flow model, even at the quite large Reynolds numbers of industrial practice. The two sets of estimates ultimately merge at large Reynolds numbers. No doubt the differences would have been even greater had a larger bed been used. r

This behaviour of the plug flow model may be a significant factor in explaining some of the scatter in literature correlations obtained on beds of different length. Results of Overall Analysis When a l l the bed depths were analysed simultaneously, the plug flow model was clearly rejected for a]J[ the different particles and Reynolds numbers considered. The ratio Fcalc/Fo.05 found to be between 1.5 and 8, where F ] is the estimated F ratio from analysis of variance and FQ.05 is the appropriate s t a t i s t i c at the 5% significance level. w

c a

a

s

c

For a l l the beads the axial dispersion model (Eqn. 7) showed no significant lack of f i t at any Reynolds number, F Ç ^ C / F Q lying between 0.4 and 0.9. Fig. (5) shows a typical t i t of this model. Fig. (5), however, i s unusual in that the calculated and experimental entrance profiles (z=0) agree well. In the majority of cases this was not so, which we attribute in part to unsatisfactory measurements at the entrance.


244

CHEMICAL

SL5mmcERAMic

à

too

Figure 3.

ENGINEERING—HOUSTON*

SPHERES

—ièo Ν

REACTION

RE

ώο -

Correlation of k with bed depth for the plug flow model r


1

20.

DIXON

ET AL.



245

Figure 5. Fit of axial dispersion model to angular smoothed radial temperature profiles


DIXON E T

20.


AL.

247

Incorporation of the f i n i t e bed boundary condition into the model (Eqn. 8) generally led to a poorer f i t , in many cases leading to a significant lack of f i t . Its main effect was to increase estimates of Pe by some 10-20%, the other parameters Pe and Bi remaining virtually unaffected. a

r

It was observed that, in general, the model f i t is worst at low Reynolds number and improves progressively as the Reynolds number increases. This is probably due to the d i f f i c u l t y of measuring the development of the radial temperature profile, since at low Reynolds number the bed attains the wall temperature within a few particle diameters of the entrance (z=0). A typical cross-section of the parameter cross correlations is shown in Table 2. Table 2:

Typical Parameter Cross-Correlations: Ceramic Beads: Bed Depth 17.5 cms.

'Re

Vw -0.72 -0.77 -0.82 -0.91

535 430 290 140

r* a

Vw

-0.10 -0.05 +0.06 +0.34

-0.11 -0.07 -0.07 -0.26

k

h

12.7 ntn

h

k

Estimates of (k ,k ) and (k »h ) are virtually uncorrected except possibly at low Reynolds number; those for (k hw) strongly correlated at a l l Reynolds numbers. While k i s not a conductivity in the true sense, i t nevertheless has a sound theoretical basis, as proposed by Argo and Smith (9_); h on the other hand is perhaps no more than an empirical parameter needed in the model to account for a decreasing k near the wall. r

a

a

w

a r e

rJ

r

w

r

7.

Correlation of Heat Transfer Data

Analysis of the data revealed that the radial conductivity (k ) is of particular importance. It would be desirable, therefore, to develop a model which gives a priori prediction of this parameter in terms of flow rate, particle diameter and conductivity and compare the predictions with our experimental data. r

7.1

A Model for Prediction of the Radial Conductivities

Starting along the lines of Argo and Smith (9J, the radial conductivity is given by k

r

= k

q

+ k, , + k . td series American Chemical Society Library

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; 1155 16th St.» M.W. ACS Symposium Series; American Chemical Society: Washington, DC, 1978. Washington, O.C. 20036

(11)


248

where k , k j and k · represent the molecular conductivity of the f l u i d , the turbulent conductivity and the effective conductivi ty of the solid, a l l based on unit of void + non-void area. g

tc

$

s

The turbulent conductivity k^d i s given in terms of the Rey nolds, Prandtl and Peel et numbers by td m = Re Pr rm < ) where k is the molecular conductivity of the f l u i d . From turbuleni mixing data (10), Pe = 10 for N R > 4 0 , and for a i r Np =0.72. Thus, Eqn. (12) simplifies to / k

k

N

N

/ P e

12

m

rm

td'

k

k

=

m

g

°-

0 7 2

N

f

N

Re

( Re

> 4

13

°)

Heat transfer betwee occur by a static proces gas f i l l e t s at the point of contact, and a dynamic process involv ing a series mechanism of solid conduction, film convection and turbulent mixing,as in Fig. (6). The static and dynamic processes occur in p a r a l l e l , thus k

series

=

k

st

+

k

( 1 4 )

dyn

The static contribution can be measured experimentally (Y\J or estimated from the model of Kunii and Smith ( 1 2 ) . The dynamic term is obtained by f i r s t integrating the heat flux over the hemispher ical surface between e=0 and θ=90° in Fig. (6). After some algebra, the total heat flow is given by 0 Q

P td - φ )

2 π

-

T

"

R

k

β

{

_J_ Vl

1 η β

.

/dL ' dH

1 }

1 Π β

, }

(

Π5) f l u i d

( , b )

where B=hk / k V j (h+k /R ) and (dT/dr) -j 4 is the temperature gradient in tne f l u i d in the direction of heat flow (assumed linear). Eqn. (15) enables an effective conductivity k^yn to be defined, based on solid projected area i T R p , f

U

d

2

'dyn

•

k

T^frtFr"*-"

(,6

»

For a packed bed, Eqn. (16) must be modified to account for the bed voidage and for the number of contacts (n) a pellet makes with i t s neighbours, corrected for the cross-sectional areas norma to the direction of heat flow and for the frequency of the orient ations. Assuming an actual bed is a composite of loose and close packings then, according to Kunii and Smith (12), n-2 for beds of voidage ε=0.44 to 0.46, as measured in our studies. Thus,

dyn = ^ t d T F i j i F T ^ -

k

1

1

}


( 1 7 )

20.

DIXON E T A L .

Heat

Transfer

in

Packed

249

Beds

Eqns. (11), (13), (14) and (17) permit a priori prediction of k in terms of the underlying heat transfer processes. No adjustable parameters are involved. A comparison of this model with our data is shown in Fig. (7). Static conductivities were measured separate ly using Sehr's electrical heating method (Vl_) and the correlation of DeAcetis and Thodos (13J was used to estimate h. r

The results show an encouraging agreement over a wide range of flow rate,particle size and conductivity. In particular, i t is found that (a) k increases linearly with N for N >40 but does not extra polate linearly to the static results. (b) k is virtually independent of pellet diameter. (c) k„ is only weakly dependen 100-fold increase i r

Re

Re

r

Also shown in Fig. (7), for comparison, is the contribution to k due to turbulent conduction (k^d). It is apparent that heat transfer through the solid forms a significant, i f not dominant, fraction of the total radial heat transfer within the Reynolds number range of interest. r

7.2

The_Wall_Biot_Number

If the data are plotted as (Bi) χ (d /dL)^vs. N then the results for different particle sizes and conductivity are brought together on a single curve, at least to within the scatter of the data. The results show that the Biot number decreases with Reynolds number, according to (see Fig. 8). ι r Q κι -0.262 ,„ (Bi) (dp/d )J = · * (18) Re

ΛΧ

5

3

t

R e

which correlates the data to within 15% in the range 100 θ

θ

Q Figure 5a. Relationship between relative catalyst activity for desulfurization and relative catalyst age. Runs at various space velocities.

b Figure 5b. Relationship between relative catalyst activity for desulfurization and relative catalyst age. Runs at different pres sures.



266

CATALYST: Co/Mo/A 1^3 (N« S) FEED: CARIBBEAN LONG RESIDUE (FEED I) • STANDARD TEMPERATURE Δ ST. - 2 5 ° C Ο ST. - 4 5 ° C

Figure 5c. Relationship between rehtive catalyst activity for desulfurization and relative catalyst age. Runs at various tempera tures.

CATALYST: C o / M e / A ^ O g (Ne R) FEED: Ο CARIBBEAN L0M6 RESIDUE ( FEEO I ) Δ MIDOLE EAST LONG RESIDUE ( FEED S )

Figure 5d. Relationship between rehtive catalyst activity for desulfurization and relative catalyst age. Runs with different feed stocks.


21.

DAUTZENBERG E T A L .

Deactivation through Pore Mouth Plugging

267

= pseudo 1 . 5 t h - o r d e r r e a c t i o n r a t e constant f o r s u l f u r removal at r e l a t i v e c a t a l y s t age Θ kg.kg- .h-1(?wS)-§ t = run time h Θ = r e l a t i v e c a t a l y s t age Tmin minimum l i f e t i m e o f c a t a l y s t h SAD c a t a l y s t age at the s t a r t o f a c c e l e r a t e d d e c l i n e h SV = space v e l o c i t y kg.kg" .h-1 Vf = vanadium content o f t h e feed ppm(w) Vp = vanadium content of t h e product at c a t a l y s t age Θ ppm(w) Sf = s u l f u r content o f the feed %w Sp = s u l f u r content o f t h e product a t c a t a l y s t age Θ %w n = c a t a l y s t e f f e c t i v i t y f o r metal removal n = relative catalys

k

s

1

=

T

=

1

m

f

s

Literature Cited (1) Van Ginneken, A.J.J., van Kessel, M.M., Pronk, K.M.A., and Renstrom, G . , O i l and Gas Journal, A p r i l 28, 1975, p. 59-63. (2) Yamamoto, M.D., Oil and Gas Journal, May 16, 1977 p. 146-165. (3) Hoog, H., K l i n k e r t , H . G . , and Schaafsma, Α., P e t r o l . R e f i n . , (1953) 32 (No. 5), 137. (4) Le Nobel, J.W., and Choufoer, J.H., 1st World Petroleum Congress (1959), Section III, p. 233 paper 18. (5) Van Zoonen, D . , and Douwes, C.Th., J. Inst. of P e t r . , (1963) 49 383. (6) Van Deemter, J.J., Proc. 3rd Eur. Synro. Chem. Reaction Eng., (1964) 215. (7) Larson, O.A., and Beuther, Η., Div. Petr. Chem. ACS Preprints, Pittsburg, (1966) B-95. (8) Newson, E. J., Div. Petr. Chem. ACS Preprints, Chicago, (1970) A141. (9) Moritz, K.H. et. al., Japan Petr. Inst. Fuel Oil Desulfurization Symposium Tokyo, Japan, March (1970).


22 Simulation of Thermal Cracking Furnaces H. A .

J.

VERCAMMEN

and

G.

F.

FROMENT

L a b o r a t o r i u m voor Petroehemische T e c h n i e k Rijksuniversiteit, K r i j g s l a a n 271, G e n t , B e l g i u m

Until now the simulation of a thermal cracking coil has g e n e r a l l y bee box by i m p o s i n g either a tube w a l l temperature profile or a heat f l u x profile. I t i s then checked a p o s t e riori whether or not the fire box p e r m i t s such p r o files to be attained. The fire box calculations gene rally proceed a l o n g the Lobo & Evans approach ( 1 ) , a l t h o u g h more recently zone methods have been applied, thus p e r m i t t i n g a temperature distribution in the fire box to be calculated ( 2 , 3, 4, 5 ) . In the work r e p o r t e d here the coil and the fire box were s i m u l a t e d s i m u l t a n e o u s l y by means of an o p t i m i z e d computer package in which the d e s i g n of the r a d i a n t s e c t i o n of the furnace i s an e x t e n s i o n and r e f i n e m e n t of Hottel's zone method ( 3 ) . In this paper the approach i s a p p l i e d to the s i m u l a t i o n of an i n d u s trial ethane c r a c k i n g f u r n a c e . The o n l y a d a p t a b l e parameter left i n the s i m u l a t i o n model is a burner d e s i g n factor, namely the fraction of the heat gene r a t e d i n the burner t h a t i s t r a n s f e r r e d to the burner cup. The parameter i s determined by matching the e x i t conversion. 1. C r a c k i n g c o i l d e s i g n

equations

The c o n t i n u i t y - , e n e r g y - and p r e s s u r e drop equa t i o n s f o r the t u b u l a r c r a c k i n g r e a c t o r are w e l l known : L dz

(1.1) 1=1

© 0-8412-0401-2/78/47-065-271$05.00/0


CHEMICAL

272

1 IF. c

dt dz

k

dp

P

t

k

]_ dv_ V dz 1

t

dz

P

with

ïïd Q(z)-

inlet

at

z=o

In

(1.1)

+

i

k

l

A

H

(1.2)

l

+

t "

=

r

ENGINEERING—HOUSTOÎ

J_ d t ζ t dz Ω β GA

i

(1.3)

F.=(F,) k k o

conditions

r

L Ω Σ 1=1

REACTION

T=T

o

and P = ( P ) t

parameters

A s e t o f r e a c t i o n s h a s t o be c o n s i d e r e d d i c t t h e p r o d u c t d i s t r i b u t i o n . The f o l l o w i n g m o l e c u l a r r e a c t i o n s was a d o p t e d : Order

C

2 6^ 2 4

H

C

H

6 ^ Î

H

C

2

C

H

2

+

H

4

+

4

•C H H 2 4" C H + 2 H , 0 >2C0+3H 2 ( H 0)

C

2

H

2

o

C

H

H

2

H

+ H

' 3 6 2 •C H CH

3 8 2C H ^C 2 C

2

2

SV C

2 +

2

2 4-

> C

2

4 +

Frequency Factor

4

4

(Kcal/Kmol).10 82

8. i o

1 2

67

7 .i o

1 3

76

1 .i o

1 3

104.6

5 .i o

1 3

1

-3

63 .3

3. 2 . 1 0

1 3

63

3 .2 . 1 0

1 1

45

4. i o

4

to pre s e t of

6

8 .i o

2 C H

0

T

Table I r e a c t i o n scheme a n d k i n e t i c

Molecular

t

60

1 3

S i n c e t h e f e e d c o n t a i n e d some p r o p a n e t h e a b o v e scheme a l s o c o n t a i n s d e c o m p o s i t i o n r e a c t i o n s f o r t h i s com ponent . In (1.3) t h e symbol ζ stands f o r 0.0227R, +0.0847d . (1.4) 0.092 _R -0.2 + . D t t

A

e

R;

In (1.4) t h e a d d i t i o n a l bends of t h e h o r i z o n t a l ed f o r .

p r e s s u r e drop i n t h e r e t u r n c r a c k i n g c o i l a r e a l s o account


22. 2.

V E R C A M M E N AND

Fire

Thermal Cracking Furnace Simuhtion

FROMENT

box heat

273

transfer

2.1 Non r a d i a t i v e h e a t f l u x e s . The f u r n a c e c o n s i d e r e d i n t h i s work, s c h e m a t i c a l l y r e p r e s e n t e d i n F i g . 1, i s f i r e d by 60 r a d i a n t b u r n e r s , p l a c e d i n t h e s i d e w a l l s . A s m a l l f r a c t i o n only of t h e heat o f combustion i s t r a n s f e r r e d t o t h e r a d i a n t b u r n e r c u p i t s e l f . The major f r a c t i o n of t h e r e l e a s e d heat e n t e r s t h e f i r e box w i t h t h e c o m b u s t i o n gases t h r o u g h r a d i a t i o n and c o n v e c t i o n . The e x a c t v a l u e o f t h i s s p l i t , r e p r e s e n t e d by y , i s n o t g i v e n i n t h e t e c h n i c a l l i t e r a t u r e , however. I t w i l l , t h e r e f o r e , be t h e o n l y a d a p t a b l e p a r a m e t e r l e f t i n t h e d e s i g n model o u t l i n e d here. The s i m u l a t i o s e c t i o n . The c o n v e c t i v to t h e r e f r a c t o r y w a l l s i n t h a t s e c t i o n was c a l c u l a t e d by means o f t h e u s u a l c o r r e l a t i o n s ( 6 , 7, 8 ) . H e a t l o s s by c o n d u c t i o n t h r o u g h t h e r e f r a c t o r y w a l l s a n d b y n a t u r a l convection a t the outside of the furnace w a l l s was a l s o a c c o u n t e d f o r . 2.2 R a d i a t i v e h e a t t r a n s f e r . To o b t a i n a r e p r e s e n t a t i v e temperature d i s t r i b u t i o n i n the r a d i a n t sec t i o n o f t h e f u r n a c e t h e f i r e box and t h e o u t s i d e w a l l o f t h e c o i l w e r e d i v i d e d i n t o a number o f i s o t h e r m a l z o n e s a s shown i n F i g . 2. The s e t o f h e a t b a l a n c e s o n t h e z o n e s c a n be w r i t t e n c o n c i s e l y i n m a t r i x n o t a t i o n a s shown i n ( 2 . 1 ) . I n e a c h z o n e Z. ( v o l u m e o r s u r f a c e ) t h e n e t r a d i a t i o n captured i s equated to the n e t n o n - r a d i a t i v e f l u x l e a v i n g t h e z o n e Q!. The r a d i a t i v e f l u x f r o m Z. t o Z. i s g i v e n by. Ζ. Ζ . Ε . I w h e r e E.= 0 T . a n d w h e r e Z.i. i s t h e t o t a l excàaneâ a r e a b e t w e e n i . a n d Ζ., i n er . i ι . w o r d s t h e f r a c t i o n o f t h e h e a t r a d i a t i o n e m i t t e d b y Z. t h a t i s a b s o r b e d by Ζ. : ^ 1 .Ζ,Ζ z,z . . i -Σ z . z , 1 1 η 1 z z - Σ τ 7 .Ζ Ζη 2 1 ι 2' (2.1) z

z

2

¥. V l

2

Z

Ε

2

Z

n 2

2

Ζ Ζ -Σ η η i

Ζ .Ζ ι η

Ε

Ε η

The s o l u t i o n o f t h i s s e t o f e q u a t i o n s y i e l d s t h e t e m p e r a t u r e s i n t h e volume and s u r f a c e z o n e s . S i n c e t h e s e t i s n o n l i n e a r i t h a s t o be s o l v e d by i t e r a t i o n . A N e w t o n - R a p h s o n p r o c e d u r e was f o u n d t o be v e r y e f f i c i e n t for this. The t o t a l e x c h a n g e a r e a s a r e o b t a i n e d i n s e v e r a l


274

CHEMICAL

REACTION

ENGINEERING—HOUST(

Figure 1. Representation of thermal cracking furnace


22.

V E R C A M M E N AND

Thermal Cracking Furnace Simulation

FROMENT

275

s t e p s . The f i r s t s t e p i s t h e c a l c u l a t i o n o f t h e v i e w f a c t o r s i . e . t h e f r a c t i o n o f t h e r a d i a t i o n l e a v i n g an e m i t t o r t h a t i s e m i t t e d i n the d i r e c t i o n of a r e c e p t o r The m u l t i p l e i n t e g r a l s i n v o l v e d i n t h i s w e r e o b t a i n e d by M o n t e - C a r l o s i m u l a t i o n , b a s e d u p o n a s a m p l e o f 2 0 0 0 0 e m i t t e d beams. To p e r m i t t h e c a l c u l a t i o n o f v i e v f a c t o r s using other viewfactors obtained i n d i f f e r e n t M o n t e C a r l o i n t e g r a t i o n s and s t i l l a s c e r t a i n t h a t t h e sum o f t h e v i e w f a c t o r s f o r e a c h e m i t t o r e q u a l s o n e , Vercammen & F r o m e n t (9^) d e v e l o p e d a r e g r e s s i o n t e c h n i q u e e l i m i n a t i n g the i n h e r e n t s t a t i s tical errors. The v i e w f a c t o r s f ^ o b t a i n e d i n t h i s way are v a l i d f o r a d i a t h e r m i c medium o n l y The v i e w f a c t o r f between s u r f a c e zone f o l l o w s from : f = f X (2.2) J

* where by :

χ

.

d

.

.

i s t h e mean t r a n s m i s s i o n

.

.

coefficient,

given

S Γ

X

= j

max (2.3) X(S)

DDF(y)

dS

I n (2.3) τ(S) mm i s t h e t r a n s m i s s i o n f o r a beam h a v i n g a l e n g h t S and D D F ( y ) i s t h e d i m e n s i o n l e s s beam l e n g h t d i s t r i b u t i o n f u n c t i o n , w i t h y =(S-S . ) (S -S . )· mm max mm Vercammen and F r o m e n t (SO p r o p o s e d t h e f o l l o w i n g f o r m f o r DDF(y) : DDF (y ) = V y ( l - \ / y ) ( - l n y ) (a+by + c y + . . . )/n ! ( 2 . 4 ) T h i s f o r m has b e e n f o u n d t o be q u i t e c o n v e n i e n t f o r w i d e l y v a r y i n g c o n f i g u r a t i o n s of the s u r f a c e z o n e s . The t e m p e r a t u r e d e p e n d e n t t r a n s m i s s i o n c o e f f i c i e n t X (S) i s r e l a t e d t o t h e a b s o r p t i o n f a c t o r k* by : 9

n

z

(

-kS

2

·

5

)

R b

X(S) = e A c c o r d i n g t o E c h i g o e . a . (J_0) t h e mean a b s o r p t i o n t o r k* i s c a l c u l a t e d f r o m : -kS C_Au)(l-e

) =

r /

fac

- k ( ω )S (1-e

)d(0

(2.6)

When t h e v i e w f a c t o r i s m u l t i p l i e d by t h e s u r f a c e of the e m i t t o r the s o - c a l l e d d i r e c t exchange a r e a i s o b t a i n e d . The d i r e c t e x c h a n g e a r e a s b e t w e e n s u r f a c e z o n e s and v o l u m e z o n e s a r e c a l c u l a t e d f r o m t h o s e r e l a ted to a l l the s u r f a c e zones b o u d i n g the volume z o n e s , f i c t i t i o u s zones i n c l u d e d .


CHEMICAL

276

REACTION


The t o t a l e x c h a n g e a r e a t a k e s i n t o a c c o u n t t h e d i r e c t r a d i a t i o n , t h e a b s o r b e d r a d i a t i o n and i n a d d i t i o n m u l t i p l e r e f l e c t i o n on t h e s u r f a c e z o n e s ; M a t r i c e s o f t o t a l e x c h a n g e a r e a s w e r e s e t up f o r CO^ and H«0 a b s o r p t i o n b a n d s and a n o t h e r one f o r t h e d o m a i n i n t h e a b s o r p t i o n s p e c t r u m i n w h i c h no r a d i a t i o n was a b s o r b e d . The m a t r i c e s w e r e w e i g h t e d w i t h r e s p e c t t o the e m i t t e d energy a s s o c i a t e d w i t h the domain of the f r e q u e n c y s p e c t r u m b e i n g c o n s i d e r e d and summed up, y i e l d i n g t h e t o t a l e x c h a n g e a r e a m a t r i x shown i n ( 2 . 1 ) . 3.

Simulation

procedure

The s i m u l a t i o d i s c u s s e d h e r i limited th r a d i a n t s e c t i o n of th t a k i n g p l a c e . The s i m u l a t i o the f u r n a c e i s s t r a i g h t f o r w a r d . The s u b d i v i s i o n shown i n F i g . 2 y i e l d e d 110 i n d e p e n d e n t non z e r o v i e w f a c t o r s . F i f t y f o u r r e a l s u r f a c e zones were c o n s i d e r e d , t o g e t h e r w i t h 3 f i c t i t i o u s , h o r i z o n t a l s u r f a c e z o n e s and 4 v o l u m e z o n e s . O p p o s i t e p a r t s o f t h e s i d e w a l l s ( e . g . A. and C j ) a r e considérée t o be one z o n e o n l y . S e c t i o n s o r t h e two p a r a l l e l c o i l s l o c a t e d a t an e q u a l d i s t a n c e o f t h e i n l e t ( R j e.g.) are a l s o l u m p e d i n t o one z o n e . F i n a l l y , a 5 8 x 5 8 m a t r i x f o r t h e c a l c u l a t i o n o f t h e t o t a l e x c h a n g e a r e a s was ob tained . I t s h o u l d be a d d e d t h a t f o r t h e h e a t t r a n s f e r a s p e c t s t h e c o i l s w e r e s t r a i g h t e n e d t o i n c l u d e on e a c h s i d e h a l f o f t h e b e n d . The f u r n a c e l e n g h t was c o r r e s pondingly adapted. To i l l u s t r a t e t h e c a l c u l a t i o n p r o c e d u r e t h e com p l e t e m a t h e m a t i c a l m o d e l i s s u m m a r i z e d as f o l l o w s : φ

(

η *>

- Q =

φ γ

η

ν

(T

(3-D

n

Q

m ,h*,t±) = Q η' η' η ^n dF

ip(t,F,Q)

= If

true ( ) s

s

NOTES:

3.47

DATA "OBSERVED" RATES ( c ) 4. 07 8. 70 2. 29 5. 69 1. 58 10. 58 1 40

4. 34 0. 62 1. 65 1. 15 3. 66 0. 63 1. 44 2. 92 3. 16 2. 72 1. 66 3. 57 1. 96 4. 11 1. 15 4. 70 4. 12 0. 91 2. 95 3. 16

4. 60 0. 74 2. 36 1. 10 3. 50 0. 56 1. 80 2. 77 2. 77 2. 77 1. 35 5. 49 1. 95 3. 26 1. 11 4. 10 3. 79 1. 06 2. 77 2. 77

4. 43 0. 88 2. 35 1. 19 3. 26 0. 59 1. 77 2. 93 2. 93 2. 93 1. 43 5. 81 1. 80 3. 62 1. 13 4. 29 5. 89 1. 32 2. 93 2. 93

4.54 0.80 2.29 1.25 3.34 0.55 1.74 2.93 2.93 2.93 1.43 5.81 1.85 3.58 0.95 4.48 6.03 1.31 2.93 2.93

3.13

3.08 0.07 °· ° ·

3.24 0.01 °·

3.25 0.02 °°'

b

2 2

b

(a) (b)

(c)

MODEL PREDICTIONS EXPOHEURISTIC NENTIAL #1 #2 4.24 4. 13 3. 34 10. 28 10.54 10. 68 2. 05 1.85 1. 71 5.31 5. 45 5. 48 2. 76 2. 54 2.91 7. 58 8. 14 7.76 1 37 1.27 1 31

1

2 6

4

0

Λ

2

2 7

0 8

E r r o r i s d e f i n e d as ( D a t a - P r e d . ) / D a t a . S k and S ^ are standard deviations of the e r r o r as d e f i n e d above, based on t h e " o b s e r v e d " and " t r u e " d a t a , r e s p e c t i v e l y . "Observed" r a t e s were d e r i v e d from " t r u e " r a t e s by imposing a 20 p e r c e n t random normal e r r o r . Models a r e based on "Observed" R a t e s . Q

s

r u e


24.

CROPLEY

Heuristic Approach to Complex Kinetics

297

t o t h e c a t a l y s t bed may be z e r o . We w i l l use some o f the i n f o r m a t i o n i n t h i s model i n t h e development o f t h e h y p e r b o l i c model. I f temperature and t h e c o n c e n t r a t i o n s o f a l l t h e c h e m i c a l s p e c i e s i n t h e study were important i n both the numerator and denominator o f t h e h y p e r b o l i c model, t h e r e would be, f o r η s p e c i e s , ( 4 n + 2 ) unknown p a r a meters i n t h e model. In t h e example study, t h e r e would be 18 parameters. In t h e " t r u e " expression, t h e r e are 10 parameters, because not a l l s p e c i e s a r e impor t a n t i n both numerator and denominator. Even i f t h e " t r u e " mechanism were known, t h e r e would be t o o many parameters t o e s t i m a t e s i m p l y by t o s s i n g t h e d a t a i n t o a n o n - l i n e a r e s t i m a t i o n program The heuristi lem down t o a s i z e t h a the form o f t h e e q u a t i o n a b i t t o permit good v a l u e s of t h e parameters t o be c a l c u l a t e d . The problem o f f i n d i n g i n i t i a l estimates i s completely e l i m i n a t e d . Rule 2: E l i m i n a t e from c o n s i d e r a t i o n any v a r i a b l e t h a t was not s i g n i f i c a n t i n t h e e x p o n e n t i a l model. In t h e example, t h e p a r t i a l p r e s s u r e o f carbon d i o x i d e i s thus e l i m i n a t e d . Rule 3: E l i m i n a t e t h e temperature terms i n t h e denomina tor. I f they a r e i n d e e d n e c e s s a r y , they can be added later. U s u a l l y a change o f t h r e e o r f o u r k i l o c a l o r i e s i n t h e apparent a c t i v a t i o n energy compensates ade q u a t e l y f o r t h e i r absence. Rule 4: Develop t h e h y p e r b o l i c e q u a t i o n i n terms o f t h e d i m e n s i o n l e s s v a r i a b l e s o f Rule 1. By d o i n g so one b r e a k s t h e i n t e r d e p e n d e n c e o f e x p o n e n t i a l and p r e e x p o n e n t i a l terms, and one o f t h e b i g problems o f non l i n e a r estimation i s minimized. (See Rule 7.) Rule 5: A r b i t r a r i l y a s s i g n exponents t o t h e terms i n t h e denominator. Here one u t i l i z e s h i s knowledge o f t h e c h e m i s t r y and t h e s t o i c h i o m e t r y o f t h e assumed ad sorption e q u i l i b r i a . These may be changed l a t e r , but f o r now use v a l u e s o f 1/2, 1.0, o r 2.0. (The 1/2 i s



298

c h a r a c t e r i s t i c f o r c h e m i s o r p t i o n o f d i a t o m i c gases l i k e oxygen, the 2.0 f o r m o l e c u l e s t h a t adsorb as d i m e r s . ) Rule

was

6: Use the v a l u e f o r E, the a c t i v a t i o n energy, t h a t o b t a i n e d i n the e x p o n e n t i a l model.

Rule

7:

Determine the p r e - e x p o n e n t i a l term i n the numer a t o r by o b s e r v i n g t h a t the c o n c e n t r a t i o n and tempera t u r e terms are a l l u n i t y at the c e n t e r - p o i n t l e v e l s . Hence, the h y p e r b o l i age r a t e at the c e n t e r?

A

=

C P

1

+ΣΚ.

or, A

=

r

c

p

(l

+EK ) 1

where A i s the p r e - e x p o n e n t i a l f a c t o r and the are the adsorption e q u i l i b r i u m constants. At t h i s p o i n t , the h y p e r b o l i c model i s ready f o r n o n - l i n e a r e s t i m a t i o n and l o o k s l i k e t h i s f o r our example :

-23295/1

V r

i + K

o2 vy +

e

R

1\

a

b

^ ^(!og) (V) 37

-

T h e r e are f i v e parameters t o e s t i m a t e : a, b, K Q 2 , K ^ , and K . V a l u a l d e h y d e was e l i m i n a t e d from the numerator because i t s exponent i n the e x p o n e n t i a l e q u a t i o n was s t r o n g l y n e g a t i v e , which a l s o suggested the denominator exponent of 2.0. y

Rule

8:

Set the n o n - l i n e a r s e a r c h ranges f o r the numerator exponents between 0 and 2.0. They w i l l seldom be found o u t s i d e t h a t range. Set the s e a r c h ranges f o r the denominator


K's

24.

CROPLEY


299

between 0 and 5. The l o g i c f o r t h i s r u l e i s q u i t e s i m p l e . At t h e c e n t e r - p o i n t c o n d i t i o n s , t h e v a l u e s f o r a l l t h e d i m e n s i o n l e s s v a r i a b l e terms w i l l be u n i t y , and the denominator w i l l be, as noted b e f o r e i n Rule 7: 1

+ΣΚ

£

f

In o r d e r t o have i n f l u e n c e on t h e r a t e , each o f t h e K s must be s i g n i f i c a n t w i t h r e s p e c t t o t h e 1.0, and, a t the same time, not overwhelm i t . Most K s w i l l be found i n t h e 1.0 t o 3.0 range. f

Rule 9: U t i l i z e computerize numerator exponents and t h e denominato f i n a l r e s u l t i n o u r example i s : •23295/1

1 \

s

s

K-values.

e

ftl

20.18e r =

The p r e d i c t e d v a l u e s u s i n g t h i s model a r e shown i n T a b l e I I under H e u r i s t i c Model #1. The s t a n d a r d d e v i a t i o n s o f t h e e r r o r f o r t h e " o b s e r v e d " and " t r u e " d a t a a r e about 26 and 12 p e r c e n t , r e s p e c t i v e l y . Thus the h e u r i s t i c model p r e d i c t s t h e " t r u e " d a t a s l i g h t l y b e t t e r than t h e e x p o n e n t i a l model does, but doesn't f i t t h e "observed" d a t a as w e l l . I t i sactually the b e t t e r model, a l t h o u g h t h e comparison seems t o pose a paradox. A c t u a l l y , t h e h e u r i s t i c model i s t h e more c o n s t r a i n e d o f t h e two, because i t has been s t r u c t u r e d to r e f l e c t a p a r t i c u l a r chemistry. It i sless likely t o be i n f l u e n c e d by t h e e r r o r s t r u c t u r e o f t h e d a t a than i s t h e e x p o n e n t i a l model, which i s more g e n e r a l . Rule 10: Examine t h e h e u r i s t i c model f o r any c l u e s o r s u g g e s t i o n s t h a t may improve t h e form o f t h e model. Two p o s s i b i l i t i e s a r e immediately apparent. The numer a t o r exponent f o r t h e oxygen i s v e r y c l o s e t o 0.5, and i t i s t h e r e f o r e a good i d e a t o s i m p l y s e t i t t o 0.5 t o agree w i t h t h e exponent i n t h e denominator. Likewise, the exponent f o r dammitol i n t h e numerator i s n o t f a r removed from 1.0 ( i t s exponent i n t h e denominator) and so we w i l l s e t i t t o 1.0. The s e a r c h v a r i a b l e s have


300

CHEMICAL

REACTION


been narrowed t o t h r e e : the e q u i l i b r i u m constants i n the denominator. A f t e r r e - f i t t i n g , the r e s u l t i s

21.lie r

2.0

1+1.83 The r e s u l t s o f t h e p r e d i c t i o n s o f t h i s model a r e shown i n T a b l e I I as H e u r i s t i c Model #2. The s t a n d a r d d e v i a t i o n o f t h e e r r o r w i t h r e s p e c t t o t h e "observed" d a t a i s not q u i t e a d eithe f th othe models, but i t p r e d i c t ter — the standard o n l y about 8 p e r c e n t . Once a g a i n we see t h e paradox. The b e s t model o f t h e t h r e e f o r p r e d i c t i o n and d e s i g n purposes a c t u a l l y f i t s t h e d a t a from which i t was developed t h e p o o r e s t . I t i s , t h e r e f o r e , the l e a s t l i k e l y t o be used i n p r a c t i c e . T h i s happens q u i t e f r e q u e n t l y w i t h e r r o r - c o n t a i n i n g d a t a , and i s , i n t h e a u t h o r ' s judgment, a f r e q u e n t cause f o r t h e f a i l u r e o f models t o p r e d i c t d e s i g n e d performance a d e q u a t e l y . The o b v i o u s q u e s t i o n i s how t o t e l l when a model i s adequate f o r d e s i g n and when i t i s not — o r which i s t h e b e s t o f s e v e r a l . One o b v i o u s l y cannot use a model merely because i t conforms t o a mechanism o f some s o r t and doesn't f i t t h e d a t a v e r y w e l l . But j u s t f i t t i n g t h e d a t a w e l l i s o b v i o u s l y not enough. There a r e t h r e e answers t o t h e above q u e s t i o n . The f i r s t i s t o improve t h e a c c u r a c y o f t h e d a t a t o the extent p r a c t i c a b l e . Ten p e r c e n t d a t a i s d i f f i c u l t t o produce, but t h e problems c i t e d here a r e u s u a l l y not s e r i o u s with data of that q u a l i t y . The second answer i s t o t e s t t h e model e x t e n s i v e l y a g a i n s t d a t a t h a t were not used i n i t s development, and p r e f e r a b l y i n a r e a c t o r o f d i f f e r e n t geometry. If a f i x e d - b e d c a t a l y t i c r e a c t o r i s t o be used, then t h e model s h o u l d be t e s t e d i n a t e s t r e a c t o r o f s i m i l a r d e s i g n — a s i n g l e p l a n t - s c a l e tube makes an e x c e l l e n t test reactor. The t h i r d answer i s t o u t i l i z e n o n - k i n e t i c means to d i s c e r n t h e t r u e mechanism o f the r e a c t i o n . I t i s p o s s i b l e t o determine, f o r example, whether a s p e c i e s l i k e dammitol chemisorbs t o an a p p r e c i a b l e e x t e n t on a catalyst. Had such i n f o r m a t i o n been a v a i l a b l e i n the study o f t h e example, dammitol would have been e l i m i n a t e d from t h e denominator and t h e s t a n d a r d d e v i a t i o n o f t h e e r r o r f o r t h e " t r u e " d a t a would have been


24.

CROPLEY


301

o n l y about two p e r c e n t . But the paradox would s t i l l remain — the s t a n d a r d d e v i a t i o n f o r the " o b s e r v e d " d a t a would have been about the same as f o r the o t h e r h e u r i s t i c models, and not as good as t h a t f o r the e x p o n e n t i a l model. But the a b i l i t y o f the h e u r i s t i c models t o p r e d i c t " t r u e " v a l u e s i s t y p i c a l l y b e t t e r than t h a t of the more f l e x i b l e p o w e r - s e r i e s model f o r complex r e a c t i o n s . A Comparison With Modern S t a t i s t i c a l

Methods

There has been s u b s t a n t i a l p r o g r e s s o v e r the past twenty y e a r s i n the use o f modern s t a t i s t i c a l methods to develop non-linea t h e s e approaches emphasiz t o narrow the c o n f i d e n c e i n t e r v a l s of the e s t i m a t e d parameters and t e c h n i q u e s t o d i s c r i m i n a t e between r i v a l mechanisms. There i s an e x t e n s i v e l i t e r a t u r e on the s u b j e c t , and the r e a d e r i s r e f e r r e d t o one or two e x c e l l e n t r e v i e w a r t i c l e s as s t a r t i n g p o i n t s ( 4 ) , ( 5 ) . In g e n e r a l , t h e s e approaches have not met w i t h w i d e - s p r e a d s u c c e s s i n i n d u s t r y because they are v i r t u a l l y l i m i t e d t o n o n - l i n e a r models o f fewer than f o u r o r f i v e unknown p a r a m e t e r s . As the number o f p a r a meters i s i n c r e a s e d t o d e s c r i b e complex c h e m i s t r y more a d e q u a t e l y , the ranges of the r e a c t i o n c o n d i t i o n s r e q u i r e d f o r the e s t i m a t i o n of unique parameter v a l u e s c o r r e s p o n d i n g l y widen. I t o f t e n happens t h a t the r e q u i r e d ranges are u n r e a l i s t i c because the r a t e l i m i t i n g mechanisms change b e f o r e such ranges can be reached. The h e u r i s t i c approach was d e v e l o p e d t o b l e n d mathematics w i t h a knowledge o f c h e m i s t r y t o accomp l i s h f o r complex systems what n e i t h e r i s a b l e t o alone. Conclusions In t h i s paper I have attempted t o demonstrate a method f o r the development of h y p e r b o l i c r a t e models t h a t are adequate f o r the d e s i g n o f c h e m i c a l r e a c t o r s . The method i s r a p i d and overcomes most of the problems t h a t h i s t o r i c a l l y have hampered the development o f such models f o r complex r e a c t i o n s . I have shown t h a t the q u a l i t y o f f i t o f a model t o e r r o r - c o n t a i n i n g d a t a i s a poor c r i t e r i o n f o r model d i s c r i m i n a t i o n , and t h a t s e v e r a l models may p r e d i c t almost e q u a l l y w e l l . This, of c o u r s e , has been known f o r a l o n g time, but i t has not been w i d e l y r e c o g n i z e d t h a t the model t h a t f i t s the d a t a l e a s t w e l l may be the b e s t model, and t h a t the c o n v e r s e a l s o may be t r u e . In the f i n a l a n a l y s i s


CHEMICAL REACTION

302


a model must be t e s t e d t h o r o u g h l y b e f o r e r e a c t o r design i s f i x e d . Because o f i t s r a p i d i t y and s i m p l i c i t y , t h e h e u r i s t i c approach p e r m i t s t h e i n v e s t i g a t o r more time f o r c r i t i c a l t e s t i n g and m o d i f i c a t i o n . Literature (1) (2) (3)

(4) (5)

Cited

B e r t y , J., Chem. Eng. P r o g . , (1974), 7 0 ( 5 ) . Box, G.E.P., B i o m e t r i c s , (1954), 10, 16-60. D a v i e s , O.L., "Design and A n a l y s i s o f I n d u s t r i a l Experiments", 534-5, Hafner P u b l i s h i n g Company, New York, 1960. Reilly, P.M., and B l a u , G.E., Can. J . Chem. Eng., (1974) 52, 289-299 Kittrell, J.R., and Chemical R e a c t i o E n g i n e e r i n g " , 119-32, American C h e m i c a l S o c i e t y P u b l i c a t i o n s , Washington, D.C., 1967.


25 Kinetics of Catalytic Liquefaction of Big Horn Coal Y. T. S H A H , D . C. C R O N A U E R , H . G . M c I L V R I E D , and Gulf Research and

Development Co.,

J. A.

PARASK0S

Pittsburgh, PA 15230

A number o f coal l i q u e f a c t i o n processes, i n c l u d i n g Gulf CCL, are being developed to help counter the coming l i q u i d f u e l shortages. In most coal l i q u e f a c t i o n processes, coal i s l i q u e f i e d i n the presence o f a solvent. In a d d i t i o n , the c o a l - o i l s l u r r y may be contacted by a hydrogen-rich gas, and a c a t a l y s t may also be present. The process of l i q u e f a c t i o n produces a wide b o i l i n g range l i q u i d , as well as l i g h t gases (C -C ) and by-products, such as water, ammonia, hydrogen s u l f i d e , e t c . Data f o r the k i n e t i c s of coal l i q u e f a c t i o n have been p u b l i s h ed i n the l i t e r a t u r e (1-11). A review o f the reported studies has r e c e n t l y been given by Oblad (12). The reported data were mostly obtained i n bench-scale r e a c t o r s . Guin et al. (7) studied the mechanism of coal p a r t i c l e d i s s o l u t i o n , whereas Neavel (7), Kang et al. (8), and Gleim (10) examined the r o l e of solvent on coal l i q u e f a c t i o n . T a r r e r et al. (9) examined the e f f e c t s of coal minerals on r e a c t i o n rates during coal l i q u e f a c t i o n , whereas Whitehurst and M i t c h e l l (11) studied the short contact time coal l i q u e f a c t i o n process. It i s b e l i e v e d that hydrogen donor solvent plays an important r o l e i n the coal l i q u e f a c t i o n process. The r e a c t i o n paths i n a donor solvent coal l i q u e f a c t i o n process have been reviewed by Squires (6). The reported studies examined both thermal and c a t a l y t i c l i q u e f a c t i o n processes. So f a r , however, very little e f f o r t has been made to present a d e t a i l e d k i n e t i c model f o r the intrinsic k i n e t i c s of coal l i q u e f a c t i o n . The primary purpose of t h i s paper i s to describe the k i n e t i c s of c o a l l i q u e f a c t i o n derived from a p i l o t - s c a l e u n i t . The s p e c i f i c coal studied was Big Horn subbituminous c o a l . The experimental data were obtained i n a p i l o t - s c a l e Gulf patented (13) r e a c t o r . The data i l l u s t r a t e the e f f e c t s of r e a c t o r space time and temperature on the product d i s t r i b u t i o n . Since the r e a c t o r behaves as a bubble column, the i n t r i n s i c k i n e t i c s of the l i q u e f a c t i o n process can be extracted by means of a kinematic model o f the r e a c t o r . The experimental data were found to be 1

©

4

0-8412-0401-2/78/47-065-303$05.00/0


304

CHEMICAL

REACTION


adequately c o r r e l a t e d by a simple r e a c t i o n mechanism. Experimental A schematic o f the experimental u n i t i s shown i n Figure 1. This u n i t p r i m a r i l y c o n s i s t e d o f a feed tank, charge pump, p r e heater, r e a c t o r and product r e c e i v e r s . A separate hydroclone u n i t was used t o prepare r e c y c l e s o l v e n t . The r e a c t o r was 6 cm I.D. by 122 cm long. The u n i t was operated w i t h a cocurrent upflow c o a l s l u r r y r a t e o f 1.8 kg/hr, the feed s l u r r y c o n s i s t e d of mixture o f 40% c o a l and 60% hydroclone overflow. Big Horn (WY) subbituminous c o a l was used f o r t h e experiments. I t was p u l v e r i z e d and screened t o minus 20 mesh, but was not p r e d r i e d ; t h e r e f o r e , t h e moisture l e v e l o f t h e feed c o a l was t y p i c a l l y 22 wt%. The ash conten carbon, hydrogen and oxyge and 19.9 wt%, r e s p e c t i v e l y . A l l runs were made a t 24.1 MPa pressure and a gas r a t e o f 2575 dm /hr. A G u l f developed c a t a l y s t was used. S u f f i c i e n t analyses were made t o o b t a i n d e t a i l e d m a t e r i a l balances over the l i q u e f a c t i o n r e a c t o r . S o l v a t i o n o f the c o a l organic matter on a moisture and ash-free (maf) b a s i s was c a l c u l a t e d u s i n g t h e f o l l o w i n g equation: 3

ο ο , ^. maf c o a l feed - maf u n d i s s o l v e d c o a l % Solvation = τ—ζ—ι x 100 maf c o a l feed Ί Λ η

Έ

Reactor. The r e a c t o r used i n t h i s study was a p i l o t p l a n t v e r s i o n o f the G u l f patented (13) segmented bed r e a c t o r . The c a t a l y s t was h e l d i n tubes o f 17 mm I.D. by 114 cm length con s t r u c t e d o f 10-mesh (U.S.) s t a i n l e s s s t e e l screen. In many o f the runs, the c a t a l y s t charge was placed i n f o u r o f the above tubes which t y p i c a l l y h e l d 750 g o f the c a t a l y s t . Some runs were made u s i n g only one o r two c a t a l y s t tubes by b l o c k i n g o f f a p o r t i o n o f the r e a c t o r cross s e c t i o n . Glass model s t u d i e s (14) w i t h an upflow a i r - w a t e r system have shown t h a t gas flow p l a y s a s i g n i f i c a n t r o l e i n a c h i e v i n g a x i a l mixing i n t h e open spaces between the c a t a l y s t tubes and r a d i a l mixing w i t h i n t h e c a t a l y s t tubes; both a x i a l and r a d i a l mixing i n c r e a s e d w i t h an i n c r e a s e i n the hydrogen flow r a t e . I t i s b e l i e v e d t h a t the r e a c t i o n process i n v o l v e s depolymeri z a t i o n and s o l v a t i o n o f t h e c o a l , w i t h these r e a c t i o n s o c c u r r i n g p r i m a r i l y i n t h e open spaces between the c a t a l y s t tubes. Once the c o a l fragments a r e l i b e r a t e d , they a r e e i t h e r s t a b i l i z e d by hydrogen o r repolymerized. Thus, the molecular weight o f the l i q u e f a c t i o n products i s determined by a combination o f c o a l p r o p e r t i e s and hydrogénation a c t i v i t y w i t h i n the r e a c t o r . The process o f s o l v a t i o n i s improved as t h e hydrogen donor c a p a c i t y of the l i q u i d phase i s increased. I n order t o improve the a v a i l a b i l i t y o f the c a t a l y s t surface t o the r e a c t a n t s , entrapment


SHAH

ET AL.

Catalytic Liquefaction of Coal

Simplified Flow Unit Bench Scale Liquefaction Unit SOLVENT HYDROGEN COAL

VENT

GAS METER COLD SEPARATOR

LIGHT E N D S RECEIVER

CATALYST TUBES.114cm

LONG

SLURRY RECEIVER

Hvdrocyclone Unit (Batch Operation) NITROGEN

VENT

Figure I.

Experimental set-up


CHEMICAL

306

REACTION


of c o a l p a r t i c l e s w i t h i n the c a t a l y s t tube must be minimized, and a high degree o f r a d i a l mixing w i t h i n the c a t a l y s t tubes must be achieved. Both o f these can be improved by increased hydrogen and o i l flow r a t e s . Upgrading o f the product o i l occurs p r i m a r i l y w i t h i n the c a t a l y s t tubes. The d i s s o l v e d hydrogen r e q u i r e d f o r both s o l v a t i o n and upgrading i s continuously s u p p l i e d from the gas phase. Both the l i t e r a t u r e and a v a i l a b l e experimental data on hydrogen s o l u b i l i t y i n c o a l l i q u i d s at r e a c t i o n temperature and pressure i n d i c a t e that mass t r a n s f e r of hydrogen from the gas i n t o the l i q u i d phase i s not a l i m i t i n g f a c t o r i n the r e a c t i o n process. Reactor Model. The i n t r i n s i c k i n e t i c i n f o r m a t i o n f o r the l i q u e f a c t i o n process can be evaluated from the data by accounting f o r mass t r a n s f e r e f f e c t s system was modeled by makin and l i q u i d flow as a uniform s l u r r y w i t h i n the r e a c t o r . Based on the study o f Kato et al», (15) i t i s reasonable to assume that the backmixing c h a r a c t e r i s t i c s of c o a l and o i l are about the same. (2) There are no r a d i a l c o n c e n t r a t i o n or temperature gradients w i t h i n the r e a c t o r . (3) The c o n c e n t r a t i o n of hydrogen i n the s l u r r y i s always i n excess o f that r e q u i r e d f o r r e a c t i o n , and (4) The a x i a l d i s p e r s i o n e f f e c t w i t h i n the r e a c t o r i s s i g n i f i c a n t . In the present study, we have assumed a simple r e a c t i o n mechanism f o r c o a l s o l v a t i o n i l l u s t r a t e d by Equation (1). Gaseous Products (H 0, 9

k Coal

1->

l i g h t gases, N H

Oils (

V

H S, ?

naphtha, furnace and heavy f u e l o i l s , e t c .

etc.)

CD

This mechanism i s c o n s i s t e n t w i t h our understanding of the low s e v e r i t y c a t a l y t i c l i q u e f a c t i o n process. More complex r e a c t i o n mechanisms which i n c l u d e hydrocracking ( i . e . , degeneration of high er b o i l i n g hydrocarbons i n t o lower b o i l i n g components) and hydroger donor r e a c t i o n s may be important under high s e v e r i t y thermal process. Gas and s l u r r y flow c o c u r r e n t l y upwards through the open spaces between the c a t a l y s t tubes. The gas flow i s the primary cause o f backmixing i n the s l u r r y phase. L i t e r a t u r e on hydroprocessing operations i n d i c a t e s t h a t the mass t r a n s f e r r e s i s t a n c e f o r the t r a n s f e r o f hydrogen from the gas to the l i q u i d phase can be neglected. Furthermore, very high s o l u b i l i t y of hydrogen i n c o a l l i q u i d s d i c t a t e s t h a t , f o r a l l p r a c t i c a l purposes, the mass t r a n s f e r r e s i s t a n c e of hydrogen at the g a s - l i q u i d i n t e r f a c e can be neglected. This does not mean, however, that the r a t e of d i f f u s i o n o f hydrogen through the l i q u i d i s n e g l i g i b l e compared with the r a t e at which hydrogen i s consumed at the c a t a l y s t surface. However, because of the reasons mentioned l a t e r , i t i s


25.


SHAH E T A L .

307

assumed t h a t the hydrogen c o n c e n t r a t i o n i s i n excess and constant for a l l pertinent reactions. The c o a l depolymerizes, d i s s o l v e s i n the l i q u i d , and forms v a r i o u s gaseous and l i q u i d products. The s i m p l i f i e d mechanism assumes t h a t both gaseous and l i q u i d products are d i r e c t l y formed from c o a l . The c a t a l y s t w i t h i n the c a t a l y s t tubes con t i n u o u s l y s u p p l i e s hydrogen-rich solvent f o r hydrogen t r a n s f e r r e a c t i o n s . The s o l v a t i o n o f c o a l i s undoubtedly accompanied by some hydrocracking r e a c t i o n s (degeneration o f higher b o i l i n g hydrocarbons i n t o lower b o i l i n g components), but these appear t o be r e l a t i v e l y unimportant, and i n the present study, they were not i n c l u d e d i n the mechanism. The r e a c t o r feed i n c l u d e s a moisture- and ash-free coal component designated "C." d c a r r i e solvent d hydroge and f l u s h o i l are incluàe The product stream i s composed o f a p f r a c t i o n ( l i g h t gases H 0 , CO, C 0 , H S, NH ), a "C" f r a c t i o n (unconverted moisture- and ash-free c o a l ) , and an f r a c t i o n (coal l i q u i d s p l u s s o l v e n t , i . e . , C^+). The concentrations o f the above-defined feed and product components are expressed i n terms o f dimensionless weight f r a c t i o n s ; m a t e r i a l balance feed and product q u a n t i t i e s have been normalized w i t h respect t o feed moisture- and ash-free c o a l ; i . e . , ρ = Ρ / C , c = C /C. , and £ = L /C. , where Ρ , e t c . , * o ο 1* O 0 1* Ο 0 1* ο . ' are the c o n c e n t r a t i o n s by weight o f components p, e t c . , i n the product, and C. i s the c o n c e n t r a t i o n o f the maf c o a l a t the reactor i n l e t . D i f f e r e n t i a l mass balances based on the standard a x i a l d i s p e r s i o n model can be expressed a s : 2

2

( R dx

• R )

2

3

r

- ± Pe dx

_i_£i-dR Pe dx dx

Pe dx

+

R

2

C =

0

c = 0

dx

The independent v a r i a b l e "x" i s the dimensionless r e a c t o r l e n g t h , i . e . , χ = ζ/ξ, where ζ i s the d i s t a n c e from the r e a c t o r i n l e t and ξ i s the t o t a l r e a c t o r l e n g t h . and R2 are the dimensionless r a t e constants. They can be expressed as: R^

—

k^f,

(3) R2 — ^2^*



308

where k and k a r e i n t r i n s i c r a t e constants which i n c l u d e c a t a l y s t v o i d t r a c t i o n and d i l u t i o n e f f e c t s . The q u a n t i t y Γ i s defined as the r e c i p r o c a l o f s l u r r y space v e l o c i t y (g s l u r r y / g c a t / h r ) , i . e . , s l u r r y space time. Pe i s the P e c l e t number d e f i n e d as ϋξ/ϋ , where U i s the s u p e r f i c i a l v e l o c i t y o f l i q u i d s l u r r y and D the a x i a l d i s p e r s i o n c o e f f i c i e n t measured i n a g l a s s model under the present r e a c t o r c o n f i g u r a t i o n (14). Equation (2) assumes t h a t the P e c l e t numbers f o r a l l species are equal. The magnitude o f the P e c l e t number c h a r a c t e r i z e s the extent o f backmixing w i t h i n the r e a c t o r . At the l i m i t i n g condi t i o n s , an i n f i n i t e P e c l e t number means plug flow, while a P e c l e t number o f zero means completely backmixed flow, i . e . , the r e a c t o r operates j u s t l i k e a continuous s t i r r e d tank r e a c t o r . Equation (2) i s subjecte tions: ?

α

C

1 dc " P e dx -±J&

0 = ρ . P

Pe dx

ι

(4)

Pe dx

and dc dp dil dx = dx = c E =

^

Λ 0

ι χ = 1-

, (5) r c

Equation (2) assumes that t h e feed contains only c o a l and s o l v e n t . An a n a l y t i c a l s o l u t i o n t o Equations (2)-(5) can be obtained i n a s t r a i g h t f o r w a r d manner. The s o l u t i o n f o r the coal concen tration i s

c =

V

T-

^

x

- ae

Ψ

2

^

x

6

where

q = / 4 (R R ) / 1 + k: — Pe +

α

' α

2

= +

U q)

- (1-q) e

F e q

ilÎ -Peq (i+q) ι e

2

S i m i l a r s o l u t i o n s f o r "p" and

can be obtained.


(7)

25.

SHAH E T A L .


309

Results and D i s c u s s i o n The best values o f the r a t e constants were obtained by non l i n e a r l e a s t square f i t t i n g o f the data t o the a n a l y t i c a l equations (16). Experimental c o a l s o l v a t i o n s and the y i e l d s o f gases and o i l s are compared w i t h model p r e d i c t i o n s i n Figure 2. As shown by t h i s f i g u r e , the model c o r r e l a t e s the experimental data q u i t e w e l l . From the experimental data, r a t e constants f o r two r e a c t i o n s were obtained a t three temperature l e v e l s . The Arrehenius p l o t s f o r the r a t e constants are shown i n Figure 3. I n t e r e s t i n g l y , the a c t i v a t i o n energies f o r a l l the r e a c t i o n s were found t o be c o n s i d e r a b l y higher than normally encountered i n f i r s t order c a t a l y t i c r e a c t i o n s This o f f e r s f u r t h e r evidence that the c a t a l y s t i s no reaction. The major d i f f e r e n c e between the k i n e t i c model presented i n t h i s study and those presented i n the l i t e r a t u r e i s t h a t , here, c o a l l i q u e f a c t i o n i s assumed t o occur i n a p a r a l l e l r e a c t i o n mechanism. A l l the products, l i g h t o r heavy, are assumed t o be formed d i r e c t l y from c o a l . The models proposed i n the l i t e r a t u r e assume a s e r i e s r e a c t i o n mechanism, wherein only heavy components ( i . e . , high b o i l i n g o i l f r a c t i o n s ) are formed d i r e c t l y from c o a l , and the l i g h t e r components ( i . e . , low b o i l i n g o i l f r a c t i o n s ) and the gases are produced by the c r a c k i n g o f the heavy compon ents. The present model a l s o assumes that the c a t a l y s t provides an excess o f hydrogen donor solvent r e q u i r e d f o r the c o a l l i q u e f a c t i o n . A more r i g o r o u s model (which would a l s o take c a t a l y s t aging e f f e c t s i n t o account) should i n c l u d e the r o l e o f hydrogen donor s o l v e n t . Separate measurements o f water, l i g h t gases (C^-C^) and by products as f u n c t i o n s o f space time and temperature were a l s o carried out. These data were c o r r e l a t e d by a k i n e t i c model which assumes t h a t water, l i g h t gas and by-products a l l are produced d i r e c t l y from c o a l by f i r s t - o r d e r i r r e v e r s i b l e r e a c t i o n s . This type of'shooting star" mechanism c o r r e l a t e d the separate data f o r water, l i g h t gases and by-products as f u n c t i o n s o f space time as w e l l as the data f o r the t o t a l gas shown i n Figure 2. Further more, the a c t i v a t i o n energies f o r the r e a c t i o n s c o a l --> water, c o a l --> by-product and c o a l --> l i g h t gases were found to be 53,500, 63,500 and 85,200 c a l / g mole. In a backmixed r e a c t o r , the gas flow r a t e should have a s i g n i f i c a n t e f f e c t on the product d i s t r i b u t i o n . High gas flow i s important f o r e l i m i n a t i n g p o s s i b l e r e s i s t a n c e s t o the t r a n s f e r o f hydrogen from the gas phase t o the c a t a l y s t surface. Two important r e s i s t a n c e s i n the present case are the g a s - l i q u i d i n t e r f a c e r e s i s t a n c e and the i n t e r - p a r t i c l e d i f f u s i o n a l r e s i s t a n c e w i t h i n the c a t a l y s t tube. A l a r g e gas flow would, however, a l s o give s i g n i f i c a n t backmixing i n the open p o r t i o n o f the r e a c t o r , 1



310

1.0 α

CD

Ζ

ional

«-* Φ

duct/

>

0.8

4>-CH-CH

3

+

CH

4>-CH-CH3

->

4>-CH=CH2

+

Η

->

-CH-CH3

+

H

->

Φ"ΟΗ

2

(4)

H

+ 4>-CH -CH

(5)

H

+

3

+

(6) (7)

CH

2

3

4>-CH2 CH

2φ-ΟΗ

3

->

C

2

H

4

2

3

6

φ—CH CH 2

2

-Φ

E t h y l b e n z e n e i s d i s i n t e g r a t e d i n t h e well-known i n i t i a t i o n r e a c t i o n (1). Methyl i n i t i a t e s the r e a c t i o n c h a i n i n which s t y r e n e and hydrogen a r e formed. T o l uene i s formed i n t h e t r a n s f e r r e a c t i o n ( 5 ) , w h i l e i n t h e two r e a c t i o n s (6) and (7) r e c o m b i n a t i o n o f r a d i c a l s occurs. K i n e t i c p a r a m e t e r s ( p r e e x p o n e n t i a l f a c t o r s and a c t i v a t i o n e n e r g i e s ) have been a l l o c a t e d t o t h e p a r t i c u l a r r e a c t i o n s t e p s . F o r r e a c t i o n (1),(2) and (6) the v a l u e s were t a k e n from t h e l i t e r a t u r e , f o r t h e o t h e r r e a c t i o n s v a l u e s have been e s t i m a t e d from ana l o g o u s a p p r o x i m a t i o n s (2)-(£). These a r e l i s t e d i n T a b l e I . C a l c u l a t i o n s o F t h e r e a c t i o n based on t h e scheme were made and t h e r e s u l t s compared w i t h t h e e x p e r i m e n t a l r e s u l t s o b t a i n e d from t h e r u n s c a r r i e d o u t i n t h e NPA. Good agreement was o b t a i n e d f o r t h e d e c r e a s e i n e t h y l b e n z e n e and t h e i n c r e a s e i n s t y r e n e and hydrogen c o n c e n t r a t i o n s . I n t h e NPA e x p e r i m e n t s r e l a t i v e l y l a r g e amounts o f e t h y l e n e and benzene were formed a t temperatures below 760°C. To t a k e


26.

EBERT E T A L .

Models for Complex

Gas Phase

Reactions

317

Figure 1. Low pressure apparatus. (1) inlet, (2) vacuum pump, (3) manometer, (4) ion source of mass spectrometer.

Figure 2. Normal pres sure apparatus. (1) inlet argon carrier, (2) inlet ethylbenzene, (3) inlet ar gon quench, (4) silit heater housing, (5) mixing cham ber, (6) sampling line to GC, (7) outlet, (8) ther mocouple, (9) reaction zone.

601

I

92$ 777

I

1091

1118

I 1122 I

1031

1209

1177

1254

I 1231 I

1288

1321

1273

Ι

I

.

;

13M

„

K

1349

1 ι 1ι 1 ι 1 ι 1ι I ι 1 ι ι ι Γ V

1 5 - METHYL

»

1 6 - METHANE

-

·

26-

ACETYLENE

28-

ETHYLENE

3 9 - C3H3

.

.

.

.

.

.

*

.

·

»

»

»

·

·

.

·

•

•

•

•

•

·

•

·

·

·

»

t

a

t

t

•

•·· ·

»

•

• •

·

•

·

·

·

>

»

*

·

•

•

·

·

» •

M -

PROPANE

50-

DιACETYLENE

78-

BENZENE

65- C5H5

89- C7H5

79- C H 6

90-

9 1 - BENZYL 9 2 - TOLUENE 1 0 2 - PHENYLACETYLENE 1 0 4 - STYRENE 105-

•

•

•

•

•

a

t

7

PHENYLCARBEN

ETHYLBENZYL

1 0 6 - ETHYLBENZENE 1 2 8 - NAPHTHALENE

.

.

1 8 2 - DIBENZYL

Figure 3. Survey pattern of LP A experiments. Abun dances of various species at different temperatures.


318


t h e s e two s p e c i e s i n t o account t h e f o l l o w i n g s t e p s were s e t up and have been added t o t h e r e a c t i o n scheme : (3a) (3b)

-CH-CH

-> ->

3

C H 6

(4a)

5

+

-CH -CH

H

+

φ—CH2 "*CH 3

2

(4b)

C

(4c)

3

H

+

6

C H 6

5

+

C H

+

φ-CH

+

C2H4

+

C2H4

2

6

4

C Hn 8

8H11

C H 6

7

>

C H

(4d)

C H

4 3

D i s i n t e g r a t i o n of the e t h y l b e n z y l leads t o the f o r mation o f p h e n y l and e t h y l e n e , t h e former s t r i p p i n g a hydrogen atom from e t h y l b e n z e n e t o form benzene and e t h y l b e n z y l . S i n c e , as t h e temperature g e t s h i g h e r , t h e p r o d u c t i o n o f e t h y l e n e by f a r exceeds t h a t o f benzene r e a c t i o n s (4a-4d) a r e p r o p o s e d , i n which t h e a r o m a t i c r i n g i s d e s t r o y e d and two m o l e c u l e s o f e t h y l e n e a r e produced. B i a c e t y l e n e as w e l l as t h e t h r e e r a d i c a l s 8 n / CeH , ^ 4 3 have been d e t e c t e d i n t h e low p r e s s u r e e x p e r i m e n t s . A g a i n , k i n e t i c parameters have been e s t i m a t e d and a l l o c a t e d t o t h e v a r i o u s r e a c t i o n steps (Table I ) . F o r v e r i f i c a t i o n o f t h e c a l c u l a t i o n s o f t h e exc

a n c

H

C

H

7

ER

NO

(1) da) (2) (2a) (3) (3a) (3b) (4)

1 0

log A

Ε

ER No

lolog A

Ε

15.3 16.0 7.82 13.0 14.85 14.85 11 .0 10.5

305.4 347.3 29 .3 125.5 125.5 182 31 .4 21 .0

(4a) (4b) (4c) (4d) (5) (6) (7)

11 .0 13.0 13.0 13.0 11 .0 10.34 11 .9

46 105 105 105 0 0 0

T a b l e I . K i n e t i c ( A r r h e n i u s ) parameters f o r a l l r e a c t i o n s t e p s ER o f t h e comprehensive r e a c t i o n mechanism. P r e e x p o n e n t i a l F a c t o r A i n s e c . " o r (1/mol-sec) r e s p . , A c t i v a t i o n Energy i n ( k J / m o l ) . 1


26.

EBERT ET

AL.

Models for Complex Gas Phase Reactions

319

tended r e a c t i o n scheme a r a t h e r l a r g e v a r i e t y of exp e r i m e n t a l d a t a were a v a i l a b l e from the NPA r u n s . Two s e t s o f experiments were performed, one up t o temperat u r e s o f 720°C and c o n v e r s i o n s o f e t h y l b e n z e n e t o 13% and t h e second up t o temperatures as h i g h as 830°C a c c o r d i n g t o c o n v e r s i o n s o f approx. 75%.The f l o w o f the r e a c t i o n gas was c o n s t a n t i n a l l t h e s e experiments the r e a c t i o n time v a r i e d , due t o d i f f e r e n t temperat u r e s , between 2 and 3 msec. Good agreement was obt a i n e d w i t h the e x p e r i m e n t a l d a t a f o r the experiments c o v e r i n g the temperatures up t o 750°C. T h i s i s shown i n F i g u r e s 4-7, i n which f o r e t h y l b e n z e n e , s t y r e n e , benzene and e t h y l e n e c o n v e r s i o n s a t s p e c i f i c r e a c t i o n times a r e p l o t t e d a g a i n s t the r e a c t i o n temperature The d o t t e d l i n e s r e p r e s e n extended r e a c t i o n scheme t a i n e d f o r the p r o d u c t i o n of methane and t o l u e n e where l a r g e r amounts were o b t a i n e d i n the experiments than r e s u l t e d from the c a l c u l a t i o n s . However i t s h o u l d be noted t h a t the a b s o l u t e amounts o f b o t h s u b s t a n c e s were r e l a t i v e l y low i n t h i s temperature range. For f u r t h e r t e s t i n g o f the r e a c t i o n scheme we c a l c u l a t e d c e r t a i n q u o t i e n t s of molar q u a n t i t i e s o f s p e c i e s and compared them w i t h the e x p e r i m e n t a l d a t a . Some o f them are shown i n F i g u r e s 8-10. The hydrogen-styrene r a t i o s h o u l d be u n i t y as b o t h s p e c i e s are produced i n the same r e a c t i o n c h a i n e x c l u s i v e l y , which i s conf i r m e d by the e x p e r i m e n t a l r e s u l t s o v e r the whole temperature range, as shown i n F i g u r e 8. F i g u r e 9 shows the b r a n c h i n g o f r e a c t i o n s (3) and ( 3 a ) . A g a i n good agreement i s o b t a i n e d between the c a l c u l a t i o n s and the e x p e r i m e n t s . As the tempera t u r e i n c r e a s e s , the c h a i n r e a c t i o n s (3) and (4) d e c r e a s e i n terms o f r e l a t i v e c o n v e r s i o n s . The second b r a n c h i n g w i t h i n the r e a c t i o n scheme i s the c o n c u r r i n g r e a c t i o n s (4) and (4a), which can be e x p r e s s e d by the e t h y l e n e s t y r e n e r a t i o . In F i g u r e 10 the e x p e r i m e n t a l v a l u e s a r e compared w i t h t h e c a l c u l a t i o n s . The a g r e e ment i s a g a i n v e r y s a t i s f a c t o r y which means t h a t the a r o m a t i c r i n g i s d e s t r o y e d even a t r e l a t i v e l y low temperatures. F o r t h e methane and t o l u e n e f o r m a t i o n s the c a l c u l a t e d v a l u e s were t o o s m a l l compared w i t h the c a l c u l a t i o n s , and i t seems t h a t t h i s has t o be taken i n t o account by the a d d i t i o n of f u r t h e r r e a c t i o n s t e p s . P r o b a b l y the two s u b s t a n c e s a r e formed i n a c a t a l y t i c p r o c e s s on the r e a c t o r w a l l s , which needs a more c o m p l i c a t e d mechanism. As shown i n F i g u r e 4 the c a l c u l a t i o n o f the o v e r a l l r e a c t i o n r a t e s w i t h the extended scheme agrees


320

CHEMICAL

1.00

REACTION


0.50

t

\

t c

t/

r

0.80 h

t\ 0.60

•

030

t

-

t •

0 40

-

/ .-r

- 1

600

800 °C

700

600

800 °C

700

Figure 5. Styrene

Figure 4. Ethylbenzene

1

0.50

•

tr

1

1

020

·/ mi I I

1 1 1

c

•

1

/

/

0.30

/

! /·/·

!

010

1

•i

•

/* **

010

•

/ 0.00

/ ' -»''

600

700

Figure 6. Benzene

800 °C

600

!

.

700

800 °C

Figure 7. Ethylene

Figures 4-7. Comparison of the decomposition of ethylbenzene and yields of different products or ratios of them in relative molar concentrations at various temperatures in the NPA ( · A experiments at different runs) with calcuhtions of the extended (· · -) and comprehensive ( ) reaction schemes


EBERT E T


AL.

10.00 r

4.00

aoo 3.00

600

2.00 4.00 h

1.00

Ι ι ·

A

k

A

ι I·• a

I

600

Figure 8.

I

800 °C

600

Hydrogen/styrene

Figure 9.

700

700

800 °C

Styrene/benzene

1 50

1

oo Ι

ο 50 h

îi

1

800 °C

Figure 10.

Ethylene/styrene

Figures 8-10. Comparison of the decomposition of ethylbenzene and yields of different products or ratios of them in relative molar concentrations at various temperatures in the NPA ( · A experiments at different runs) with calculations of the extended (· · · ) and comprehensive ( ) reaction schemes


322

CHEMICAL

REACTION


w e l l w i t h the experiments c o v e r i n g temperatures up t o 750°C. Above t h i s temperature the e x p e r i m e n t a l r a t e s a r e a p p r e c i a b l y h i g h e r and accompanied by an i n c r e a s e i n benzene and e t h y l e n e c o n c e n t r a t i o n s . To account f o r t h i s we i n t r o d u c e d a second i n i t i a t i o n r e a c t i o n : (1a)

-CH CH 2

3

+

C H 6

5

+

C H 2

5

i n which e t h y l b e n z e n e i s s p l i t i n the a - p o s i t i o n . P h e n y l undergoes r e a c t i o n (3a) and e t h y l d i s i n t e g r a t e s as f o l l o w s : (2a)

C H 2

5

+

C H 2

4

+

H

Both r e a c t i o n s hav (see T a b l e I) and adde scheme. As shown i n F i g u r e s 4 and 5 c a l c u l a t i o n s now f i t t e d i n much b e t t e r w i t h the e x p e r i m e n t a l d a t a up t o temperatures o f 825°C. Benzene and e t h y l e n e p r o d u c t i o n g i v e s v e r y good agreement w i t h the c a l c u l a t i o n as can be seen from F i g u r e s 6 and 7. In a s e r i e s o f p r e l i m i n a r y experiments i n the NPA c o n v e r s i o n - t i m e runs have been performed a t 675°C s i m p l y by changing t h e f l o w r a t e . S p e c i a l c a r e has been t a k e t o keep the temperature c o n s t a n t . D e v i a t i o n s c o u l d not be p r e v e n t e d a t low f l o w r a t e s , i . e . h i g h c o n v e r s i o n s . The r e s u l t s are shown i n F i g u r e s 11-13. D e v i a t i o n s a t h i g h e r c o n v e r s i o n s may be due t o a d e c r e a s e i n temperature o r i n h i b i t i o n r e a c t i o n s . The agreement a t s h o r t r e a c t i o n times i s remarkably good, and i n d u c t i o n p e r i o d s were i n a l l c a s e s o f t h e same shape i n b o t h the c a l c u l a t i o n s and the e x p e r i ments . Summarising and C o n c l u d i n g

Remarks

For the p y r o l y s i s of ethylbenzene a r e a c t i o n scheme c o u l d be s e t up by f i r s t l y s e l e c t i n g the most s i m p l e r e a c t i o n scheme, t a k i n g i n t o account t h e main p r o d u c t s o f the r e a c t i o n a t low t e m p e r a t u r e s . Secondl y , on r a i s i n g the temperature and the c o n v e r s i o n the number o f s p e c i e s i n the r e a c t i o n m i x t u r e g e t s more abundant, t h e r e a c t i o n scheme was improved by a d d i n g new r e a c t i o n s f o r which e x p e r i m e n t a l e v i d e n c e c o u l d be o b t a i n e d from the LPA e x p e r i m e n t s . Then a l l r e a c t i o n s t e p s were a l l o c a t e d k i n e t i c c o n s t a n t s , which e i t h e r were t a k e n from the l i t e r a t u r e o r e s t i m a t e d from analogous r e a c t i o n s . Minor a l t e r a t i o n s o f some of the k i n e t i c c o n s t a n t s were made f o r b e t t e r a g r e e ment w i t h the e x p e r i m e n t a l d a t a . In t h i s way, g r a d -


EBERT


ET AL.

015

0.10 h

0.05 Κ

β

m» 8

Figure 11. Ethylbenzene

t_J

Ο

1

l 2

1 3

l 4

L_J 5 6

Figure 13. Benzene

3

4

5

6

7ms 8

Figure 12. Styrene

ί7ms 8

7 ms 8

Figure 14. Ethylene

Figures 11-14. Comparison of relative molar concentrations against time of different species at 675°C with calculations of the comprehensive mechanism


324

CHEMICAL

REACTION


u a l l y , the r e a c t i o n mechanism, which f i n a l l y c o n s i s t s o f 15 r e a c t i o n s t e p s , has been d e v e l o p e d up t o r e a c t i o n temperatures of 825°C and c o n v e r s i o n s o f n e a r l y 80%. Care was taken t o ensure t h a t each r a d i c a l c o u l d r e a c t w i t h i n a t e r m i n a t i o n r e a c t i o n . T h e r e f o r e some more t e r m i n a t i o n r e a c t i o n s than those f o r m u l a t e d above were o r i g i n a l l y i n t r o d u c e d i n t o the c a l c u l a t i o n s . Some o f them c o u l d l a t e r be dropped, when i t was found t h a t they were o f o n l y minor importance t o the calculation. For the r e a c t i o n chosen the agreement o f the c a l c u l a t i o n s and e x p e r i m e n t a l r e s u l t s was good. The d i s t r i b u t i o n of a l l main p r o d u c t s c o u l d be c a l c u l a t e d within a r e l a t i v e l The method o u t l i n e a p p l i c a b l e t o c o m p l i c a t e d r e a c t i o n s and p r o v i d e s k i n e t i c r e s u l t s o f good q u a l i t y , i n v o l v i n g an e f f o r t which i s j u s t i f i a b l e i n many c a s e s . A l s o i t g i v e s an i n s i g h t i n t o the c o u r s e o f a r e a c t i o n , showing how the i n d i v i d u a l elementary r e a c t i o n s c o n t r i b u t e t o the p r o c e s s . Furthermore the r e a c t i o n mechanism can be compressed by d r o p p i n g c e r t a i n r e a c t i o n s t e p s which a r e o f minor i n t e r e s t , o r by combining s e v e r a l s t e p s i n t o one e q u a t i o n w i t h a p p r o p i a t e c o n s t a n t s , which may be h e l p save computer time. I n t h i s way i t seems p o s s i b l e t o modify a r e a c t i o n mechanism t o s u i t a s p e c i a l problem w i t h o u t s a c r i f i c i n g a c c u r a c y o f the r e s u l t s obtained. Literature

Cited

(1) Gear W.C., "Numerical Initial V a l u e Problems i n Ordinary Differential Equations" P r e n t i c e - H a l l I n c . , New York, 1972. (2) Benson S.W., "Thermochemical Kinetics", John W i l e y , New York, 1968 (3) Benson S.W., O'Neal H.E., " K i n e t i c Data on Gas Phase M i n i m o l e c u l a r R e a c t i o n s " NSRDS-Nat.Bur.of S t a n d a r d s 21, Washington, 1970 (4) K e r r J.Α., Parsonage M.J., " E v a l u a t e d K i n e t i c Data on Gas Phase Hydrogen T r a n s f e r R e a c t i o n s o f M e t h y l R a d i c a l s " B u t t e r w o r t h , London, 1976 (5) K e r r J.Α., Parsonage M.J., " R e a c t i o n s o f Atoms and R a d i c a l s w i t h A l k e n e s , A l k y n e s and A r o m a t i c Compounds" B u t t e r w o r t h , London, 1972 (6) K o n d r a t i e v V.N., "Rate C o n s t a n t s o f Gas Phase R e a c t i o n s " NSRDS-Nat.Bur.of S t a n d a r d s , Washington, 1972


27 Aromatic Sulfonation in a Cyclone Reactor, a Stirred Cell, and a Cocurrent Tube Reactor; Influence of Mass Transfer on Selectivity A N T O N I E A. C. M . B E E N A C K E R S Department of Chemical Engineering, Twente University of Technology, Enschede, P.O. Box 217, The Netherlands For mass transfer, followed by a

Van de Vusse [1] pointed out that selectivity with respect to I increases with an increase of the mass transfer coefficient (k ). In light of this observation, we have developed a new reactor of cyclonic type in which, due to strong centripetal forces on the gas bubbles, a very high k is realized [2]. This paper deals with the selectivities obtained in sulfonation of benzene with sulfur trioxide. Both neat benzene and benzene diluted with 1,2-dichloroethane were used. This re action was selected as a model reaction for industrially important aromatic sulfation (e.g. deter gents). We studied the reaction in three reactor types that greatly differ in mass transfer charac teristics, i.e. in a stirred cell reactor (low k ), a co-current gas-liquid tube reactor (intermediate k ) and in the cyclone reactor(highk ). L

L

L

L

L

Reaction Kinetics; Regime of Mass Transfer with Chemical Reaction We have discussed reaction mechanism and kinetics of sulfonation of benzene (B) with SO (A) in aprotic media [3] and have concluded that the reaction proceeds according to Van de Vusse kinetics (1-3), with k (25°C) >9.4 m /kmol s and z = / . Pyrosuifonic acid (I) and Ar S O H (I') are both unstable and react with benzene to give the desired product benzenesulfonic acid (P) and the unwanted product diphenyl sulfone (X), respectively 3

3

1

x

2

3

9

Reaction (4) is slow with respect to mass transfer and thus of negligible influence on absorption rate. Reaction (5) consumes only minor amounts of benzene (all experimentally observed selec tivities are (often much) above 70%based on benzene). Therefore this reaction also does not influence absorption rate appreciably. For reaction sequence (1-3), the relation between mass transfer parameters and conversion rate is — in general — complex. However, as long as observed selectivity η is high, the influence of reaction (3) on SO absorption rate is an effect that may be neglected in the first, rough estimation of the regime of absorption with reaction [4] which characterizes the system. Which regime occurs, mainly depends on the numerical values of the dimensionless groups Ha, Eând mk E/k . Due to uncertainties in the kinetic rate constant, in local liquid viscosity in the interface diffusion zone (to be discussed later), and in S0 -solubility, a prediction of the regime characterizing sulfonation of benzene, solved in 1,2-dichloroethane, is not free of speculation. In case of no liquid viscosity increase at the interface during reaction, Table I gives numerical estimations of the relevant parameters for atmospheric sulfonation at 3

L

Q

3

©

0-8412-0401-2/78/47-065-327$05.00/0



328

2 0 ° C with a mixture of S 0 % benzene

k

by

Ha

G

1 + zD m(c )

volume

A

A

mk

G

L

taining 10 mol % S 0

3

3

and nitrogen con

(typical for our experi

ments in cyclone and tube reactor) in a conven tional bubble c o l u m n . In our stirred cell sulfona

> 4

5.6

0.7

30

> 2.2

2.4

0.7

tion experiments, k

10

> 1.3

1.4

0.7

10 lower than the value 1.2 10"

5

> 0.9

1.2

0.7

calculating Table I. Therefore Ha »

100

/zD m(c ) A

T a b l e I.

Estimated mass transfer parameters for

sulfonation of

benzene, solved in

1,2-dichloroet

hane with gaseous sulfur trioxide (10 m o l

A

Q

L

was found to be a factor of 4

[m/s] used in 1 +

D c B

B

in the stirred cell. This means that

the reaction is instantaneous with respect to mass transfer in that reactor.

% in ni

r

trogen) at 2 0 C and 1 0 Pa in a conventional bub0.7 10

ble c o n t a c t o r with μ

s Pa and k i t h e m i -

Influence of Mass Transfer on Selectivity

n i m u m value of 9.4 m ^ / k m o l s. F o r h y d r o d y n a m i cal

and physical constants applied, see reference

No

[3].

plies Ha > 0.5 and not much smaller than

A s first pointed out by V a n de Vusse [1 ] the ob

[5]. Some experimental results are available for

chlorination [1,6-9]. A numerical analysis [10], an analog simulation [1 ] and trial and error pro cedures [6,8,10] by which approximate solutions can be obtained, have been presented. A s in our sulfonation experiments, there is often much doubt about the exact values of the relevant parameters (c, m, ρ, μ , D, T) at the interface, mainly because local interface conditions differ from bulk conditions. Because of this difficulty, explicit rough approximate relations for 1? are sophisticated enough to discuss experimental results and are therefore very useful. Harriott [5] derived such a simple model for the intermediate regime between fast and instantaneous re action. Our experiments are mainly in the instantaneous regime. Based on film theory, we deriv ed for this regime [3]

k D 2

(1

[D c /D, +

A

B

c,]

(6) 2z

for (1

B

-η')=k

L

2 E

~

2

- τ ? ' ) « 1 .

Equation (6) shows the manner in which the selectivity is favoured in the instantaneous regime by a high value of k , provided that the selectivity is not much smaller than one. T h e latter con L

dition is always fulfilled in our experiments.

Experimental The stirred cell reactor was of the Danckwerts type [4, page 180]. The reactor was filled with de gassed (diluted) benzene and kept under its own vapour pressure. T h e experiment was then start ed by connecting the space above the liquid to a thermostrated ( 3 0 ° C ) container, filled with de gassed stabilized liquid sulfurtrioxide, which was also under its own vapour pressure. Due to the difference in partial pressure of reaction mixture and liquid S 0 , the latter evaporated and flow 3

ed via a flow controller and a rotameter to the cell reactor where it absorbed into the liquid. Figure 1 is a sketch of the cyclone reactor. The liquid is fed tangentially into it (A). A gas mixture of S 0 The

3

and N

2

is introduced into the reactor via a porous section of the cylindrical wall.

liquid phase is the continuous phase in the reactor, except near the cyclone-axis. Here, a

gaseous core is f o u n d , due to a strong centripetal field, generated by the rotating liquid. This field causes gas bubbles to spiral from the wall to the cyclone-axis. Gas leaves the reactor via the upper outlet which is known as the vortex. Liquid leaves the reactor via the bottom outlet which


27.

329

Aromatic Sulfonation and Mass Transfer

BEENACKERS

is referred t o as the apex. Cone Ε prevents gas entrainment with the liquid. Liquid entrainment through the vortex varied between 12 and 2 0 % depending o n gas and liquid velocities. L i q u i d conversion per pass through the reactor was small. Therefore the system was operated batch wise with respect to the liquid, b y recycling reaction mixture over the reactor. Absorption efficiency of S 0

was ^ 100%.

3

3

The diameter o f the cocurrent gas-liquid tube reactor was 8 1 C T m . Gas and liquid were in troduced via a T-piece of the same diameter.

Results and Discussion Mass Transfer in Absorption without Reaction. We measured k 0

2

- H

0 system (figure 2). Forced convection k

2

L

in the stirred cell with an

L

in the reaction mixtures was calculated from

this result according t o [11] n

Sh~

Re Sc

l / 3

(7

with η = 1.1. Reaction effects wer ments, as will be explained in a later section, a local increase of viscosity at the interface caused by pyrosulfonic acid accumulation, produced a lower k We measured k

L

L

than calculated this way.

in a cyclone reactor with simultaneous absorption of C 0

droxide solution [2]. Figure 3 gives results. T h e figure shows that k

L

2

and 0

2

in a hy

reaches extremely high

4

values in this reactor ( k is o n the order of 10" m/s in conventional reactors as the stirred tank L

[13], the bubble column [14], the bubble cap plate [15] and the packed column [ 1 6 , 1 7 ] . Slugflow is obtained in the tube reactor in the range of gas and liquid velocities, we applied in sulfonation [18, Figure 10.3]. k

L

values realized in this flow regime have been reported b y

Gregory and Scott [19]. F r o m this reference we calculated [3] k

L

in our tube reactor (see Figure

3). Mass Transfer in Stirred Cell Reactor during Sulfonation. T h e actual k

L

during sulfonation

follows experimentally from

k

(8)

L=C

Ai

E

As derived earlier, sulfonation of benzene is instantaneous in a stirred cell reactor. Therefore [4]: 2D c B

c

E

A i

a

s

° A i

+

B

- S —

Because o f uncertainties in c

(

A

j

, only an approximate k

L

9

)

during sulfonation can be obtained this

way. Experiments were carried out with both neat and diluted benzene (5.3 and 3 0 vol% benzene initial

Τ

reaction

J

(1 -n)

[ ° C ] [10 " k m o l / m ^ 3

mixture

k

L

c

Ii

-0.5

=1

= 4.1

= 1.5

= 3.75

0 187

= 2.2

0 25

= 1.5

0.15

0 031

=2

30 vol%

25

0.092

0 107

35

0.13

0 137

45

0.23

28

0.35

T

i

t°c]

= 3.6

35

T a b l e II.

x

3

_5

5.3 vol%

100% Β

Ii"5I

C10 m/s] [kmol/m J

2

k 2DA 5 2 [m /kmol s ]

51

3.0 Ι Ο "

= 0.7

44

0.67 Ι Ο "

= 0 .6

53

1.9 1 0 " 1 1

= 4.25

= 0.8

67

4.2 1 0 " 1 1

= 8.75

= 1

78

14 1 0 " 1 1

1 1

1 1

E s t i m a t e d values f o r gas-liquid interface p y r o s u l f o n i c acid c o n c e n t r a t i o n rise ( C j j - C j ) , s u r f a c e tempera

ture rise (Tj-T) a n d reaction rate constant ^ D / ^ ) '

ns t

i

r r e

d

c

e

" reactor sulfonation experiments.


CHEMICAL REACTION

330


26

33

Figure 1. Cyclone reactor. Unit of length: J 0 " m. ( A) liquid inlet (4 J O " m), (B) gas outlet (vortex) (3 JO" m), (C) liquid outlet (apex) (8.66 J O " m ), (D) gas inlet, (E) cone (120°C), (PI) pressure indicator, (a)8°C. 3

3

3

6

2

Figure 2. k in stirred cell reactor. (O), ( ) our measurements (O in H 0at25°C);( ) Jhaveri and Sharma [12]; (- · -) SOs in both 1,2dichloroethane and benzene, with Equation 7. L

s

2


27.

Aromatic Sulfonation and Mass Transfer

B E E NA C K E R S

in 1,2-dichloroethane

331

respectively). Stirrer speed (N) varied between 0 and 2 r e v / s . k ^ showed

to be independent of Ν and t o be appreciably lower than without reaction. T h e average values of k

L

are summarized in Table II. Table II also shows that both the interface pyrosulfonic acid

concentration ( c ) and the interface temperature M

(T.) are much higher than in the bulk of the

liquid. T h e first quantity (c .) has been approximated with (

1

c .-c = / r?J/k |

j

2

T h e second quantity

(10)

L

(T.) has been estimated from the simple film model according to Danck-

werts [4]

Τ. —Τ = J D ι

R

Β

(ΔΗ

a

+ ΔΗ ) / r

ΧΛ.

(11)

S L

T h e influence o f pyrosulfonic acid concentratio because o f the

instability

viscosit

i

neithe

know

measurabl

o f thi

mixture at 2 3 . 5 ° C as a function o is:

Ιη(μ(χ )/μ(ο))=8.85χ ρ

Without

(12)

ρ

measurements, our best possible assumption is that pyrosylfonic acid has the same

influence on viscosity as sulfonic acid. Recalling from eqn. (7) that

k ~(D/M)

2 / 3

L

and applying the Stokes-Einstein equation results in

k

It

L

~M"

4

/

3

(13)

follows from x

( j

(Table

II) and eqns (12,13) that k

L

is appreciably lowered by viscosity

effects that occur during reaction. In practice this tendency is counteracted by both the inter face temperature

rise and free convection, driven by density and/or surface tension gradients.

Both effects lower the extent of interface viscosity increase. T h u s , a k

L

is obtained which is

independent of stirrer speed and lower than that for forced convection in the absence of inter face viscosity effects as given in Figure 2. Selectivity in Stirred Cell Reactor.

Observed 1 -

η is always «

1. Therefore eqn. (6)

is expected t o be applicable though its accuracy is probably low due to the discussed interface viscosity increase. F r o m eqn. (6)

1-T?~1/k

2

(14)

L

Figure 4 shows (1— η)

t o be nearly independent o f N . Even the abcense o f stirring does not

lower selectivity significantly. This fact is in agreement with, and additional argument for, our preceding conclusion that k

L

is independent of stirrer speed.

Figure 4 shows that by-product formation Taking as a first approximation D

Q

= D , c, « (

increases with initial benzene concentration. δ

β

and 1 - η = 1 - i? (allowed for f «

1)

we obtain from eqn. (6) with ζ = % :

1-T?^k D 2

A

c

B

/(k EJ

2

L


(15)


332

Figure 3. k as f(U ) for C0 in 2.07M NaOH solution in a cyclone reactor with Vi = 5.97 m/s (1) and 9.15 m/s (2) and in tube reactor for U = I m/s (3) and 1.75 m/s (4) L

s

2

L

30-

1-η[·/.] *

t

; 20-

υ-, 0

, 066

,

,

,

1

133

2

•

N[s-1]

Figure 4. By-product formation in sulfonation of benzene with gaseous sulfur trioxide in a stirred-cell reactor in rehtion to initial benzene concentration and stirrer speed. (A) 5.3 vol % benzene in dichloroethane, T ss 35°C, ζ = 0.8; (Ο) 30 vol % benzene in dichloroethane, T ss 25°C, ζ 0.09; (Ο) 30 vol % benzene in dichlo roethane, Τ ss 35°C, ζ Ξ* 0.1; (A) 100 vol % benzene in dichloroethane, Τ as 28°C, ζ ss 0.005.


27.

333

Aromatic Sulfomtion and Mass Transfer

BEENACKERS

Combining with equation (8) gives k D = * ( 1 - T?) J / ( c c 2

2

A

B

2 A j

)

(16)

ι/Vith this equation, the value of k D 2

II). Figure 5 shows log k D 2

k D 2

A

=k

0

0

D

A

e-

A

E

/

R

T

A

has been estimated from the experimental results (Table

as a function of 1/T.. Fitting the experimental data to

A

i

(17)

esults in

k

and

oo

D

5

=4.5 m /kmol s

A

2

6

Δ Ε = 3 0 . 7 10 J/kmol

The obtained value for Δ Ε is likel approximate same value for Δ Ε in a chemically, very similar reaction in sulfonation of chloroberizene. Assuming at the interface: D 2

l 0

A

2

s 1 0 " m / s , it follows from eqn. (17) that k

2

(25°C) =

3

1.7 10" m / k m o l s. Reaction rate constant for the first reaction (eqn. (2)) has been shown to be 3]: 3

k ( 2 5 ° C ) > 9 . 4 m /kmols 1

Hence, in homogeneous sulfonation, no diphenyl sulfone will be obtained. Selectivity in the Cyclone and in the Tube Reactor. Differential selectivity (τ?') was measued as a function o f f . A b o u t 25 experimental runs were carried o u t . Table III shows the range between τ

Initial

vol %

f

A

ς

benzene i n liquid

40

ved η

on

[m/s]

20

the operation

depended mainly o n ini

tial benzene concentration and

phase

[°cl

which

parameters were varied. Obser

10

0 02 - 0.04

3.5 - 6.8 0 09 - 0 1 1 0 1 3 - 0 46

30

0 01 - 0.38

3.3 - 7.9 0 06 - 0 13

0 07 - 0 42

100

0 01 - 0.21

2.8 - 6.6 0 08 - 0 13

0 01 - 0 05

30

0 01 - 0.08

2.7 - 7.9 0 09 - 0 12

0 04 - 0 51

100

0 01 - 0.02

2.4 - 7.6 0 11 - 0 12

0 01 - 0 05

are

s

summarized

Figure

6

in Figure 6.

also

shows

results

from tube reactor experiments (1 < U
1. For t h i s case a zero-order d e s c r i p t i o n i n Ο i s v a l i d . 2 When F Q < 1, a l l 0 -consuming r e a c t i o n s were m u l t i p l i e d by the f a c t o r F Q 2 . This means that i n t h i s case a f i r s t - o r d e r r e a c t i o n i n 0^ 2 i s assumed. The example shown i n F i g . 2 serves to i l l u s t r a t e to what extent the l a b o r a t o r y experiments are covered by the model. 2

3. MODEL OF THE GAS-LIQUID REACTOR With regard t o the g a s - l i q u i d r e a c t o r the f o l l o w i n g assumptions have been made : - the l i q u i d phase and the gas phase are p e r f e c t l y mixed, - the i s s u i n g gas stream i s i n p h y s i c a l e q u i l i b r i u m w i t h the i s s u i n g l i q u i d stream, - the r e a c t o r operates a d i a b a t i c a l l y , - the compositions, f l o w r a t e s , temperatures and pressures o f the feed streams are known. In c a l c u l a t i n g the p h y s i c a l e q u i l i b r i u m , we made use o f gasl i q u i d e q u i l i b r i u m constants, which are defined as (z) (P_Ô(z)x-p ).

L

,

T

(11) I n e q n s (10) t i t i e s were o b t

and (11) t h e introduced: Y

t

K

G

P>(z)

6

L

d

L

G

-

GO

S

(1 +

OC)

—

(1-x

)

Ο

=

L ^L

=

k

quan

( Π )

H

{ l Z )

(13)

L

(14) 6

St.

0

l+0t(l-z)

= U

Pe

^

following dimensionless

£

Γ

L

—2-

(15) S L Here p r e s e n t s t h e l i q u i d s i d e mass t r a n s f e r c o e f f i c i e n t , L t h e e n t i r e c o l u m n l e n g t h , R t h e gas constant, Τ t h e t e m p e r a t u r e , and u the s u p e r f i c i a l l i q u i d v e l o city . The i n i t i a l c o n d i t i o n f o r eqn (10) i s T

U

χ(Ο) The b o u n d a r y of c o c u r r e n t

= χ

(16)

ο

c o n d i t i o n s f o r eqn f l o w (a = -1) :

(11)

are

f o r the


case

30.

DECKWER

ET

r

L dz

365

CO Inter phase Mass Transfer

AL.

+

Va Pe,

dp

(Ο)

T

L

dz

(17)

( 1 )

=

(18)

Ο

for countercurrent

flow

(a

= +1) :

dp (0) L

(19)

~"dz

P (1) L

dz

Pe,

Li

The i n d e x i r e f e r s t o i n l e t c o n d i t i o n s . The d i f f e r e n t i a l e q n s (10) and (11) w e r e s o l v e d n u m e r i c a l l y by t h e m e t h o d o f Lee (_14_) w h i c h i s w e l l s u i t e d t o s o l v e n o n - l i n e a r boundary v a l u e problems w i t h non-con s t a n t c o e f f i c i e n t s . H o w e v e r , as w i l l be d i s c u s s e d l a t e r i t was n o t p o s s i b l e t o o b t a i n c o n v e r g e n c e f o r c e r t a i n parameter combinations, p a r t i c u l a r l y at high values of k . I t i s a s s u m e d t h a t t h i s h a s t o be a t t r i b u t e d t o s t i f f n e s s of the system of d i f f e r e n t i a l e q u a t i o n s . Since d e p e n d s on g a s v e l o c i t y ( s e e eqn ( 7 ) ) and t h i s v a r i e s c o n s i d e r a b l y a l o n g the column p r e l i m i n a r y computations were c a r r i e d o u t w i t h d i f f e r e n t v a l u e s o f calculated from u and u ^ (gas v e l o c i t y a t o u t l e t ) / r e s p e c t i v e l y . These c a l c u l a t i o n s r e v e a l e d t h a t computed gas p h a s e p r o f i l e s a r e p r a c t i c a l l y n o t e f f e c t e d by f o r the p o s s i b l e range of v a r i a t i o n . T h e r e f o r e D was calcula t e d f r o m eqn (7) w i t h t h e mean gas v e l o c i t y w h i c h i s def i n e d by G o

1

u

G

( ζ ) dz

(21)

w h e r e t h e l o c a l v a l u e s o f u ( z ) a r e o b t a i n e d f r o m eqn (9) by c o n s i d e r a t i o n o f eqn (6) and t h e m e a s u r e d g a s p h a s e p r o f i l e . The l i q u i d s i d e mass t r a n s f e r c o e f f i c i e n t i s now t h e o n l y q u a n t i t y w h i c h i s u n k n o w n . I t was t h o u g h t t h a t t h e s e k - v a l u e s c a n s i m p l y be determined by f i t t i n g m o d e l p r e d i c t i o n s t o e x p e r i m e n t a l g a s p h a s e p r o f i l e s . No s p e c i a l o p t i m i z a t i o n p r o c e d u r e was a p p l i e d . S i n c e o n l y one p a r a m e t e r h a d t o be d e t e r m i n e d and t h e c o m p u t a t i o n s were f a s t enough a t r i a l - a n d - e r r o r method was sufficient. G


CHEMICAL

366 Description

of Measured

REACTION


Profiles

When u s i n g c o n s t a n t v a l u e s o f k the model equa t i o n s c o u l d not d e s c r i b e r e a s o n a b l y the e x p e r i m e n t a l p r o f i l e s . T h i s i s shown i n f i g . 2 f o r d e s o r p t i o n mea s u r e m e n t s . The c u r v e s f o r f = 1 r e f e r to k -values w h i c h a r e c o n s t a n t o v e r t h e e n t i r e c o l u m n . T h o u g h ex p e r i m e n t a l and t h e o r e t i c a l r e s u l t s c a n be b r o u g h t i n agreement nearby the top of the column, the c a l c u l a t e d mole f r a c t i o n s a r e a l w a y s c o n s i d e r a b l y t o o low c l o s e t o the bottom. F u r t h e r i n c r e a s e of k d i d not improve the agreement but l e d u s u a l l y to s t i f f n e s s s i n c e convergence c o u l d n o t be o b t a i n e d any m o r e . As t h e t h e o r e t i c a l p r o f i l e s indicate that transfe i to small merel n e a r t h e gas d i s t r i b u t o applied there. Favorabl r u n s c o u l d be o b t a i n e d i f t h e c o n s t a n t mass t r a n s f e r c o e f f i c i e n t was r e p l a c e d by a p r o f i l e w h i c h i s shown i n f i g . 3. F o r r e a s o n s o f s i m p l i f i c a t i o n i n t e g e r v a l u e s of f were t a k e n o n l y : 2 ^ f < 4 ( s e e t a b l e 1 ) . Thus a s t r i k i n g a g r e e m e n t b e t w e e n t h e m e a s u r e d d a t a and t h e m o d e l p r e d i c t i o n s ( f u l l d r a w n c u r v e s ) i s o b t a i n e d as c a n be s e e n f r o m f i g . 1. F i g . 4 and 5 p r e s e n t C 0 pro f i l e s o f t h e g a s and l i q u i d p h a s e , r e s p e c t i v e l y , f o r the case of a b s o r p t i o n runs at c o u n t e r c u r r e n t f l o w . Once a g a i n a s u f f i c i e n t a g r e e m e n t i s o b s e r v e d . I t i s i n t e r e s t i n g t o n o t e t h a t t h e gas p h a s e c o n c e n t r a t i o n c a n r u n t h r o u g h a minimum v a l u e . T h o u g h t h i s minimum i s v e r y f l a t i t i s r e p r o d u c i b l e and was a l s o f o u n d f o r o t h e r r u n s . S u c h e x t r e m e v a l u e s i n gas c o n c e n t r a t i o n were not o b s e r v e d e x p e r i m e n t a l l y b e f o r e , however, t h e y were a l r e a d y p r e d i c t e d t h e o r e t i c a l l y from n u m e r i c a l s t u d i e s f o r t h e c a s e o f c o c u r r e n t f l o w (4_) . For the c o u n t e r c u r r e n t a b s o r p t i o n run presented i n f i g . 4 t h e minimum r e s u l t s f r o m t h e r a t h e r h i g h i n l e t c o n c e n t r a t i o n o f CO^ i n t h e l i q u i d p h a s e , s e e f i g . 5. Due to the h y d r o s t a t i c head the c o n c e n t r a t i o n of C 0 i n the g a s p h a s e d e c r e a s e s t o a l o w e r v a l u e t h a n t h a t one w h i c h corresponds to the i n l e t p a r t i a l p r e s s u r e i n the l i q u i d p h a s e . T h e r e f o r e a t column t o p s m a l l amounts o f C 0 desorb from the l i q u i d phase which i s s u p e r s a t u r a t e d a g a i n s t gas p h a s e . T h o u g h t h e o b s e r v e d m i n i m a a r e i r r e l e v a n t f o r any t e c h n i c a l a p p l i c a t i o n t h e y p r e s e n t a j u s t i f i c a t i o n of the a p p l i e d model s i n c e s i m p l e r models are not a b l e to d e s c r i b e the measured p r o f i l e s . I f c o n s t a n t v a l u e s o f t h e h o l d - u p and t h e i n t e r f a c i a l a r e a (^ (z) = 1) w e r e a p p l i e d i n t h e c a l c u l a t i o n s a r e a s o n a b l e f i t t i n g of the measured p r o f i l e s c o u l d not be o b t a i n e d . T h i s i s shown i n f i g . 6 w h e r e t h e d o t t e d l i n e s i n d i c a t e t h e o r e t i c a l p r o f i l e s w i t h the s m a l l e s t B

2

2

2


30.

DECKWER

ET AL.

χ

367

CO ^-Interphase Mass Transfer

0,6

0

OA

0,2

0,6

0.8

1.0

—

2

Figure 2. Measured and calculated gas phase mole fraction of C0 for different values ofi 2

B

Figure 3. Applied profile of liquid phase mass transfer coefficient


CHEMICAL

368

χ

REACTION


0.8

0 Figure 4.

0.2

0,4

0.6

0.8

1,0

Measured and calculated gas profiles at countercurrent absorption


30.

DECKWER

ET AL.

CO -Interphase Mass Transfer 2


369

370

CHEMICAL

REACTION


a t t a i n a b l e d e v i a t i o n ( k = 0.0235 cm/s and f = 2 for r u n 12, = 0.0133 and f = 3 f o r run 14). This obser v a t i o n l e a d s t o the c o n c l u s i o n t h a t the proposed model i s a b l e to d e s c r i b e the measured p r o f i l e s o n l y because *f (z) i s known w i t h s u f f i c i e n t a c c u r a c y t o o . The k - and f - v a l u e s d e t e r m i n e d f r o m m a t c h i n g t h e o r e t i c a l p r e d i c t i o n s to experimental r e s u l t s are g i v e n i n t a b l e 1. S i n c e t h e i m p o r t a n t h y d r o d y n a m i c p r o p e r t i e s are l o c a l l y dependent i t i s understood t h a t the mass t r a n s f e r c o e f f i c i e n t i s a l s o a f u n c t i o n o f z. The o b t a i n e d k ~ d a t a are i n the r e a s o n a b l e range. However, c o n t r a r y t o p r e v i o u s f i n d i n g s a t l o w i n t e r p h a s e mass t r a n s f e r (6_) t h e y d i f f e r l a r g e l y f o r a b s o r p t i o n and desorption runs. Furthermor t desorptio yield s u r p r i s i n g l y higher value The d e p e n d e n c y o f k operating p a r t i c u l a r l y on t h e f r e q u e n c y f a c t o r s o f b u b b l e c o a l e s c e n c e and b r e a k up (8_) w i l l be d i s c u s s e d t o g e t h e r w i t h f u r t h e r m e a s u r e m e n t s i n a f o l l o w i n g p a p e r (_1_5) · L

L

Conclusion The f i n d i n g s o f t h i s s t u d y on a b u b b l e c o l u m n o f i n d u s t r i a l l e n g t h and a d i a m e t e r s u f f i c i e n t l y l a r g e n o t to i n v o l v e w a l l e f f e c t s c o n f i r m s the s i g n i f i c a n c e of the a p p l i e d model which a c c o u n t s f o r the h y d r o s t a t i c h e a d and gas f l o w v a r i a t i o n s . H o w e v e r , t h e e x c e l l e n t a g r e e m e n t b e t w e e n e x p e r i m e n t a l and t h e o r e t i c a l r e s u l t s c o u l d o n l y be o b t a i n e d w i t h c o n s i d e r a t i o n o f d e t a i l e d i n f o r m a t i o n on t h e h y d r o d y n a m i c p a r a m e t e r s . Unfortunate l y s u c h e x a c t k n o w l e d g e on h y d r o d y n a m i c p r o p e r t i e s i s seldom a v a i l a b l e . T h i s f a c t w i l l c e r t a i n l y not p e r m i t the w i d e s p r e a d a p p l i c a t i o n o f the proposed model i n i n d u s t r y at the p r e s e n t t i m e . T h e r e f o r e f u r t h e r s t u d i e s at o p e r a t i n g c o n d i t i o n s p r e v a i l i n g i n i n d u s t r y a r e nee ded w h i c h a r e f o c u s e d on m e a s u r e m e n t s i n s i d e t h e e q u i p ment and w h i c h a r e e v a l u a t e d on t h e b a s e o f r e a l i s t i c m o d e l s . I t c a n be e x p e c t e d t h a t o n l y f r o m s u c h s t u d i e s r e a s o n a b l e g u i d e l i n e s may be d e v e l o p e d w h i c h p r o v i d e for a r e l i a b l e d e s i g n of bubble columns. Acknowledgement The a u t h o r s g r a t e f u l l y a c k n o w l e d g e s u p p o r t f r o m Deutsche Forschungsgemeinschaft and S t i f t u n g V o l k s w a g e n we r k .


30.

DECKWER

ET

AL.

CO -lnterphase Mass Transfer

371

2

Literature Cited (1)

Pavlica,

R.T.,

Olson,J.H.,

I n d . E n g . C h e m . (1970)

62 45

(2) (3)

M h a s k a r , R . D . , C h e m . E n g n g . S c i . ( 1 9 7 4 ) 2 9 897 Szeri,A., Shah,Y.T., Madgavkar,A., Chem.Engng.Sci.

(4) (5) (6)

Deckwer,W.-D., C h e m . E n g n g . S c i . (1976) 31 309 Deckwer,W.-D., C h e m . E n g n g . S c i . (1977) 32 51 D e c k w e r , W.-D., Burckhart,R., Zoll,G., Chem.Engng.

(1976) 31 225

Sci.

(7) (8)

(9)

(1974)

29

2177

D e c k w e r , W.-D., Zaidi,A., Adler,I., Chem.-Ing.T e c h n . (1976) 48 1075 Deckwer,W.-D., Zaidi,A., Adler,I., Preprints Eur Congr.: Transfer Nuremberg,Germany, , y lerus B a i r d , H . M . I . , R i c e , R . G . , Chem.Engng.J. (1975) 9 171

(10) S u b r a m a n i a n , G . ,

Tien,C.,

Can.J.Chem.Engng.

(1975)

53 611

(11) T o w e l l , G . D . , A c k e r m a n , G . H . , P r o c . ISCRE 2, B 3 - 1 , A m s t e r d a m 1972 (12) S e r p e m e n , Y . , Deckwer,W.-D., I n d . E n g . C h e m . F u n d a m . (1974) 13 399

(13) Göhler,P., D r . - I n g . thesis, TU Berlin, 1973 (14) L e e , E . S . : "Quasilinearisation a n d Invariant Im bedding" A c a d e m i c Press, New York, 1968 (15) Deckwer,W.-D., Zaidi,A., Adler,I., Chem.Engng.J., in preparation


31 Determination of Fluid Dynamic Parameters in Bubble Column Design T H . P I L H O F E R , H . F . B A C H , and K. H. M A N G A R T Z Lehrstuhl A für Verfahrenstechnik, Technische Universität München, West Germany

Bubble columns are applied employed in the sam also in waste water cleaning (2). Quite recently, their use for microbial processes has become increas ingly important (3). In spite of the variety of these applications and the number of known experimental studies, the design and scale-up of a bubble column is still a difficult task. In this paper, results of ex periments are presented, which are concerned with the determination of fluiddynamic parameters for column design. The description of a process, taking place in a bubble column, requires the selection of a suitable model. In most cases the application of the one-dimen sional dispersion model has proven satisfactory. When a differential mass balance is made around a differen tial segment of the column, disregarding radial depen dencies, the following equations result for the case of counter-current:

The l i n e a r velocities o f the c o n t i n o u s and d i s p e r s e phase, u and u , can be a d j u s t e d arbitrarily, whereas the mass t r a n s f e r coefficient k depends first o f all on the system's p h y s i c a l p r o p e r t i e s . On the o t h e r hand the f l u i d d y n a m i c parameters like interfacial a r e a a, gas holdup ε and the d i s p e r s i o n coefficients and are i n f l u e n c e d s t r o n g l y by the phases throughputs. I t is t h e r e f o r e n e c e s s a r y to p r e p a r e a p p r o p r i a t e correlC

D

L

©

0-8412-0401-2/78/47-065-372$05.00/0


31.

PILHOFER

Parameters in Bubble Column Design

ET AL.

373

ations f o r the c a l c u l a t i o n o f these parameters i n o r der to solve equation ( l ) a n d ( 2 ) . The f o l l o w i n g state ments a r e concerned w i t h t h i s problem. F i r s t of a l l , the l a y - o u t of the gas d i s t r i b u t o r l l be treated. I t s t a s k i s t o g e n e r a t e swarms o f bbles. I f a sieve t r a y i s used, one should be aware the fact, that a l l the holes must be i n o p e r a t i o n . h e r w i s e , u n d e s i r e d c i r c u l a t i o n s come i n t o existence. rthermore, weeping must be a v o i d e d when u s i n g large enings. This i s most i m p o r t a n t , i f the l i q u i d tends incrustate o r s o l i d i f y . These phenomena a r e caused b y t h e mechanism o f t h e p a r t i c l e formation on the sieve t r a y . The openings work i n the j e t t i n g r e g i o n and n o t i n the b u b b l i n g r e g i o n (k). Therefore, to o b t a i so much a g a s t h r o u g h p u t h a s t o b e p r e s e n t e d , that a l l openings work at least at the beginning o f the j e t t i n g region. The minimum gas l o a d r e l a t i v e tqjeach h o l e c a n be d e t e r m i n e d b y t h e f o l l o w i n g e q u a t i o n s (k): Small hole diameters:

w i bu of Ot Fu op to

We.

=

w

L

Large

hole

,

d

L ' P p

=

2

(3)

a

L

diameters:

Fr^

= _ ί ί _ . ( _ 2 _ ) d -g ΔΡ

(4)

=0,37

T

The v a l i d i t y o f f o l l o w i n g value

d These

Q

=

Li both equations i s separated o f the hole diameter:

2,32 · ( a / p -

equations

D

a r e v a l i d

5

g

)°' · ( ρ / Δ ρ )

5

by the

/

(5)

8

0

f o r g a s / l i q u i d

systems

w e l l

as

as f o r l i q u i d / l i q u i d systems (k)· The swarms o f b u b b l e s p r o d u c e d b y t h e d i s t r i b u t o r moves upward t h r o u g h t h e l i q u i d . Now, the nature o f the bubble motion i s most important f o r t h e develop ment o f t h e p r o c e s s i n the column. A t l o w gas v e l o c i t i e s the bubble h a r d l y hinder each other and the swarm r i s e s u p w a r d i n a r e g u l a t e d manner. This i s c a l l ed t h e "bubbly f l o w regime (5.). P r e s u m i n g a constant bubble s i z e , there i s a maximum v a l u e o f gas t h r o u g h put w i t h i n t h i s bubbly f l o w regime, that can be deter mined by f l o o d i n g p o i n t c a l c u l a t i o n s (6). I f the throughputs a r e increased beyond t h i s p o i n t , a f l o w a l t e r a t i o n takes place. I n order to reach higher buoy ancy forces f o r gas transport, bubble c l u s t e r s o r plugs a r e formed. This i s c a l l e d the "churn turbulent regime" ( 5 ) · 1 1


374

CHEMICAL

REACTION


F o r t h e s e two f l o w r e g i m e s f i g u r e 1 shows s c h e m a t i c a l l y t y p i c a l c u r v e s f o r the dependency o f the gas h o l d u p on t h e gas v e l o c i t y . D u r i n g b u b b l y f l o w t h e gas h o l d u p i n c r e a s e s s u p e r p r o p o r t i o n a l l y w i t h t h e gas throughput. With the b e g i n n i n g f o r m a t i o n of bubble c l u s t e r s , these curves are s h i f t e d to the r i g h t because of the c o n t i n u o u s l y i n c r e a s i n g bubble s i z e . This r e s u l t s i n a s u b p r o p o r t i o n a l r i s e o f t h e gas h o l d u p w i t h gas t h r o u g h p u t . I t i s t h e r e f o r e n e c e s s a r y t o d i s t i n g u i s h b e t w e e n t h e s e two f l o w r e g i o n s . A t t h e moment i t i s n o t p o s s i b l e t o s p e c i f y t h e l i m i t s of both regimes. For a rough approximation the f o l l o w i n g c a l c u l a t i o n may be c a r r i e d o u t : W a l l i s recommends t h e f o l l o w i n equatio f o th motio f swarm o f b u b b l e s i n (6 )

= ( ι - ε ) Using a batch-type l i q u i d , f o r the r e l a t i v e the f o l l o w i n g h o l d s : w = u / R

The

flooding

D

velocity

ε

(7)

condition i s : du

D

/ άε

=

0

F r o m e q u a t i o n (6) a n d (7) we g e t a t t h e f l o o d i n g a g a s h o l d u p o f 0,5 and the r e l a t i o n s h i p : u

D

=

0,25-Woo

(8) point (9)

F o r a u s u a l r i s e v e l o c i t y o f a s i n g l e b u b b l e o f 23 cm/s, f r o m e q u a t i o n (9) a maximum l i n e a r g a s v e l o c i t y o f 5i7 cm/s a r i s e s . A t h i g h e r g a s v e l o c i t i e s o n l y t h e c h u r n t u r b u l e n t r e g i m e e x i s t s . Y e t , e x p e r i m e n t s show, t h a t f l o w a l t e r a t i o n may a l r e a d y o c c u r a t l o w e r g a s t h r o u g h p u t s. A t hi^te moment e q u a t i o n (6) may be r e c o m m e n d e d f o r t h e c a l c u l a t i o n o f t h e gas h o l d u p i n t h e b u b b l y f l o w r e g i m e . A b e t t e r c o r r e l a t i o n can be o b t a i n e d , i f equations f o r the motion of s o l i d s are m o d i f i e d i n a c o n v e n i e n t way. T h i s h a s a l r e a d y b e e n a c h i e v e d f o r t h e m o t i o n o f d r o p l e t swarms ( 7 ) · T h o u g h t h e c h u r n t u r b u l e n t r e g i m e i s t h e more s i g n i f i c a n t r e g i o n , t h e r e a r e no e q u a t i o n s g e n e r a l l y a p p l i c a b l e t o d e t e r m i n e the gas h o l d u p . Beyond t h i s , most e x p e r i m e n t s have been c a r r i e d out w i t h a i r / w a t e r s y s t e m s . I n o u r e x p e r i m e n t s p r e f e r e n c e was t h e r e f o r e given to the v a r i a t i o n of the system's p h y s i c a l pro p e r t i e s . F o u r l i q u i d s w e r e u s e d u n d e r d i f f e r e n t tem p e r a t u r e s ; experiments under pressure are s t i l l going on b u t n o t y e t e v a l u a t e d . F o r e x a m p l e , i n f i g u r e 2 measurements o f t h e gas h o l d u p a t d i f f e r e n t l i n e a r gas


PILHOFER


ET AL.

bubbly

flow

Figure 1. Dependency of the gas holdup on the linear gas velocity for different flow regions

0.3-

C O O C ο ο c

»

Q ο

α

α · ο

ο·

δ

ο

t%

*

• Ί ° * *

°· „

·

ο ° . \ ο

°. ν

η α

• 0 ι °· ο

»*

•

8

ο

3

liquid

ndo

butane diol

29.5 6,8

ethylene glycol octanol

11.7

•

3.2

tetrabromo eth 0

5

10

1.7

15 cm/s

gas phase linear velocity u

20

0

Figure 2. Measured gas holdup values for four different liquids as a function of gas linear velocity


376

CHEMICAL

REACTION


v e l o c i t i e s w i t h d i f f e r e n t l i q u i d s are p l o t t e d . E v a l u a t i n g o u r own m e a s u r e m e n t s a n d c o n s i d e r i n g t h e r e s u l t s o f K u s t e r s (£0 a n d Hammer/Rahse (9.) , u s i n g c o l u m n s w i t h t h e same d i m e n s i o n s , t h e f o l l o w i n g e q u a t i o n f o r the dependency o f the gas h o l d u p f r o m the l i n e a r gas v e l o c i t y and t h e p h y s i c a l p r o p e r t i e s h o l d s : ——

= 0,115

( u

3

/

( v . g - A p /p c

))

c

0 , 2 3

do)

E q u a t i o n (10) i s v a l i d f o r a c o l u m n w i t h a n i n n e r d i a m e t e r o f 100 mm a n d a c l e a r l i q u i d h e i g h t g r e a t e r t h a n 1200 mm. I n a f u r t h e r s t e p we t h e r e f o r e e x a m i n e d , wèther g a s h o l d u p i s i n f l u e n c e d b y t h e c o l u m n d i m e n sions. In f i g u r e 3 S holdup measurements are p l o t t e d v e r s u s gas l i n e a r v e l o c i t y ed o u t i n c o l u m n s w i t 150 mm a n d c l e a r l i q u i d h e i g h t s h i g h e r t h a n 1000 mm. F u r t h e r m o r e , t h e e m p l o y e d gas d i s t r i b u t o r s c a u s e d a c h u r n t u r b u l e n t f l o w a l r e a d y a t l o w gas throughputs. I t c a n be s e e n , t h a t a l l t h e v a l u e s a r e d e s c r i b e d b y one r e g r e s s i o n l i n e j w i t h s a t i s f a c t o r y a c c u r a c y . C o n s e q u e n t l y , t h e r e i s no d e p e n d e n c y o f g a s h o l d u p f r o m column d i m e n s i o n s . Because of the agreement of the e x p o n e n t o f t h e gas l i n e a r v e l o c i t y i n e q u a t i o n (10) w i t h t h e r e s u l t s o f f i g u r e 3, e q u a t i o n (10) c a n be r e commended f o r g a s h o l d u p c a l c u l a t i o n s . I t i s p o s s i b l e , t h a t t h e c o n s t a n t v a l u e o f 0,115 m u s t be c o r r e c t e d i n s i g n i f i c a n t l y , a s e q u a t i o n (10) has been d e r i v e d f o r a column o f 100 mm i n n e r d i a m e t e r w h e r e a s f i g u r e 3 f e r s to columns w i t h a d i a m e t e r equal or g r e a t e r than 150 mm. The m e n t i o n e d d e p e n d e n c i e s c o m p l y w e l l w i t h t h e r e s u l t s o f R i q u a r t s ' s c o n s i d e r a t i o n s ( 10 ) f o r . f l u i d i z e d beds. An a d d i t i o n a l f l u i d d y n a m i c p a r a m e t e r t o be d e t e r m i n e d i s t h e i n t e r f a c i a l a r e a a: a s

r e

a

=

6·ε

/ d

3 2

(11)

I n e q u a t i o n (11) t h e g a s h o l d u p c a n be d e t e r m i n e d by e q u a t i o n (10) o r r e s p . (6). Further informations are n e e d e d w i t h r e g a r d t o t h e medium b u b b l e s i z e d . U n f o r t u n a t e l y t h e r e i s n o t much e x p e r i m e n t a l data on b u b b l e s i z e s r e s p . b u b b l e s i z e d i s t r i b u t i o n s due t o the c o m p l i c a t e d m e a s u r i n g methods. For our measurements a new e l e c t r i c m e a s u r i n g d e v i c e (11 ) ,(12 ) was u s e d . A p a r t i a l stream of the d i s p e r s e f l u i d two-phase system i s s u c k e d o f f by a v e r t i c a l f u n n e l c o n n e c t e d w i t h a g l a s s c a p i l l a r y . The c a p i l l a r y d i a m e t e r i s c h o s e n s o , t h a t most o f t h e b u b b l e s a r e d e f o r m e d t o p l u g s . These a r e d e t e c t e d t w i c e b y a s u i t a b l e l i g h t s e n s i n g means t h a t i n f o r m s on t h e l e n g t h o f t h e p l u g s . I f t h e p l u g


31.

PILHOFER

ET AL.


377

c r o s s - s e c t i o n i s determined by a d d i t i o n a l c a l i b r a t i o n p r o c e d u r e s , the volume o f each p a r t i c l e c a n be c a l c u l a t e d ^ i t i s a n advatage o f t h i s m e a s u r i n g method t o enable high measuring f r e q u e n c i e s . I n f i g u r e 4 m e a s u r e d mean b u b b l e s i z e s a r e shown f o r the a e r a t i o n o f x y l e n e and propanol by n i t r o g e n . The m e a s u r e m e n t s t o o k p l a c e i n a c o l u m n o f 225 mm d i a m e t e r . The m e a s u r i n g h e i g h t w a s 850 mm a b o v e t h e g a s d i s t r i b u t o r , w h i c h was f o r m e d a s a s i e v e t r a y w i t h d i f f e r e n t h o l e d i a m e t e r s . I t can be seen, t h a t t h e s a u t e r mean d i a m e t e r d i s almost independent o f t h e g a s t h r o u g h p u t . K u s t e r s (8^) g o t s i m i l a r r e s u l t s . More d e t a i l e d i n f o r m a t i o n r e s u l t s f r o m a n a n a l y s i s of bubble s i z e d i s t r i b u t i o n s Thes hav bee approxi mated by a l o g a r i t h m i value o f thesauter b e f o r e . The c e n t r a l v a l u e s d and the standard d e v i a t i o n s 0£, c a l c u l a t e d i n t h e way m e n t i o n e d b e f o r e , a r e p l o t t e d i n f i g u r e 5- The d e p e n d e n c y o f t h e c e n t r a l v a l u e s o f t h e g a s t h r o u g h p u t i s b a s i c a l l y t h e same a s on s i n g l e h o l e s . A f t e r t h e t r a n s i t i o n o f a l l h o l e s i n t h e j e t t i n g r e g i o n ( u » l cm/s ) a s t r o n g d e c r e a s e o f d_ appears, which f l a t t e n s w i t h higher gas through p u t s . Y e t , i t must be c o n s i d e r e d , t h a t t h e s t a n d a r d d e v i a t i o n s a t f i r s t i n c r e a s e stroPgly w i t h gas holdup, before reaching a constant value. With respect t o t h e p a r a l l e l s t o s i n g l e o r i f i c e s , a f u r t h e r a s p e c t must be n o t e d : t h e b u b b l e s , e m e r g i n g f r o m t h e s i e v e p l a t e , s h o u l d b e n o t l a r g e r t h a n a c e r t a i n maximum v a l u e ; o t h e r w i s e t h e y a r e no l o n g e r s t a b l e a n d d e v i d e i n t o s m a l l e r p a r t i c l e s . A c c o r d i n g t o M e r s m a n n (13)> t h e maximum s t a b l e p a r t i c l e d i a m e t e r r e s u l t s f r o m t h e r e lation : n

Q

d

(12)

P · g

max Taking a l l experiments i n t o account, i f p a r t i c l e s c o l l a p s e , a churn t u r b u l e n t f l o w r e g i o n a l r e a d y appears at lower gas throughputs. I n sieve p l a t e design, t h i s a s p e c t h a s t o be checked a d d i t i o n a l l y . F o r the d e t e r m i n a t i o n o f t h e s i z e o f t h eemerging bubbles, w e l l - known methods l i k e t h a t o f R u f f ( l4) c a n be u s e d . I n d e t e r m i n i n g mean b u b b l e s i z e s i n c o l u m n s , t h e r e i s s t i l l a l a c k o f s u i t a b l e c o r r e l a t i o n s . Even o u r r e s u l t s do n o t e n a b l e m o r e p r e c i s e s t a t e m e n t s . T h e r e f o r e we r e c o m m e n d t o d e t e r m i n e mean b u b b l e s i z e s f r o m e q u a t i o n (12). A c c o r d i n g t o o u r c a l c u l a t i o n s t h e r e i s a n a c c u r a c y o f +_ JO % w i t h r e s p e c t t o m e a s u r e d v a l u e s , i f t h e l i q u i d v i s c o s i t y i s l o w e r t h a n 10 c P . F i n a l l y , the d e t e r m i n a t i o n o f the d i s p e r s i o n c o e f f i c i e n t s i n b o t h p h a s e s i s t o b e t r e a t e d . The

Π0 3

°- 3

atr/water nitrogen /n-proponol atr/glycol 30

40

50

60

relative velocity wR

70 cm/s

Figure 7. Gas phase dispersion coefficient as a function of the relative velocity be tween gas and liquid


CHEMICAL

382 N o m e n c l a2 t u r3e : a m /m c kmol/kmol c* / m d_p m dg m d Q m Fr g-" D m /g g m/s HQ m m/s t s u m/s w m/s We χ m ε m /m η |g/ms V m / s ρ kg/m^ Δρ »/" Cf N/m 11

lf

1

subscripts : C D F G L co

REACTION ENGINEERING—HOUSTON

i n t e r f a c i a l area concentration equilibrium concentration hole diameter s a u t e r mean d i a m e t e r column diameter central value d i m e n s i o n l e s s mod, F r o u d e - n u m b e r dispersion coefficient gravitational acceleration clear l i q u i d height mass t r a n s f e r c o e f f i c i e n t tim linea velocity d i m e n s i o n l e s s Weber-number length gas holdup dynamic v i s c o s i t y kinematic v i s c o s i t y density density difference surface tension standard d e v i a t i o n

continuous phase d i s p e r s e phase liquid gas hole referring to single

bubbles

Literature cited: (1) Mashelkar R.A., Brit. Chem. Eng, (1970),15,1297 (2) Ploos v. Amstel J.J.Α., Rietema Κ . , Chem.Ing. Techn.,(1970),42,981 (3) Todt J., Lücke J., Schügerl Κ., Renken A., Chem. Engng.Sci.,(1977),32,369 (4)RuffΚ., Pilhofer T h . , Mersmann Α., Chem.Ing. Techn.,(1976),48,759 (5) Wallis G . B . , ASME Int.Dev.Heat Trans.,(1962),319 (6) Lapidus L., Elgin J.C., AIChE J.,(1957),3,63 (7) Pilhofer T h . , Chem.Ing.Techn.,(1976),48,273 (8) K ü s t e r s W., Ph.D.Diss. TH Aachen Germany 1976 (9) Hammer H., Rähse W.,Chem.Ing.Techn.,(1973),45,968 (10) Riquarts H . P . , Verfahrenstechnik,(1977),11,164 (11) Pilhofer T h . , Jekat Η . , Miller H . D . , M ü l l e r J.H., Chem.Ing.Techn.,(1974),46,913


31. piLHOFER ET AL. (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26)


US Pat. 3.818.200 Mersmann Α . , Verfahrenstechnik,(1976),10,641 Ruff Κ . , Chem.Ing.Techn.,(1972),44,1360 Ohki Υ . , Inoue Η . , Chem.Engng,Sci.,(1970),25,1 Badura R . , Deckwer W.D., Warnecke H.J., Lange mann Η . , Chem.Ing.Techn.,(1974),46,399 Hikita Η . , Kikukawa Η., Chem.Eng.J.,(1974),8,191 Towell G.D., Ackermann G.H., 2.Int.Symp.Chem. React.Eng., Amsterdam 1972, Preprints B3 Kastanek F., Nyvlt V., Rylek Μ., Coll.Czech.Chem. Comm.,(1974),39,528 Deckwer W.D., Burckhart R . , Zoll G., Chem.Engng. Sci.,(1974),29,2177 Freedman W., Davidso J.F., Trans.Instn.Chem Engrs.,(1969),47,25 Akita Κ . , Yoshida F., Ind.Eng.Chem.Proc.Des.Dev. (1973),12,76 Reith T., Chem.Engng.Sci.,(1968),23,619 Towell G.D., Strand C.P., Ackermann G.H., AIChE - I.Chem.E.Symp.Ser.,(1965),10,97 F a i r J.R., Ind.Eng.Chem.Proc.Des.Dev.,(1962),1,33 Jekat Η . , Ph.D.Diss. TU München Germany 1976


383

32 Catalyst Effectiveness Factor in Trickle-Bed Reactors M . P.

DUDUKOVIĆ

and P. L . M I L L S

Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington University, St. Louis, MO 63130

Observed rates in a in hydrodesulfurization cate that they operate in the regime free of major gas-liquid mass transfer limitations (1,2,3,4,5). Due to the fact that often the liquid reactants are nonvolatile or dilute at the operating condi tions used the reaction is frequently liquid reactant limited and confined to the catalyst effectively wetted by liquid. Since po rous packing, typically 1/32" to 1/8" (0.08 cm to 0.318 cm) extru dates is most often employed it is clear that reaction rates may be affected both by internal pore fill-up with liquid and by inter nal diffusional limitations. Catalyst effectiveness factors from 0.5 to 0.85 have been generally reported (1,3,5,6,7,8,). In order to interpret or predict trickle-bed performance at tempts have been made to account for liquid maldistribution, devia tion from plug flow and for incomplete wetting of catalyst parti cles (4,9,10,11,12). It has been shown that liquid phase d e v i a t i o n from plug flow does not have significant e f f e c t s on conver s i o n in commercial and pilot s c a l e t r i c k l e - b e d r e a c t o r s (13). A p p l i c a t i o n of Mears' (14) criterion confirms the i n s i g n i f i c a n c e of d i s p e r s i o n e f f e c t s . Incomplete c a t a l y s t w e t t i n g ( i . e . con t a c t i n g e f f i c i e n c y , c a t a l y s t u t i l i z a t i o n ) as a f f e c t e d by the hydrodynamic regime i n the bed was s i n g l e d out as the most important parameter which determines r e a c t o r performance (12). One may d i s t i n g u i s h between r e a c t o r s c a l e incomplete contacting caused p r i m a r i l y by flow m a l d i s t r i b u t i o n and g l o b a l hydrodynamic e f f e c t s , and p a r t i c l e s c a l e incomplete c o n t a c t i n g which i s determined by l o c a l v i s c o u s , i n e r t i a and surface f o r c e s . When transport e f f e c t s c o n t r o l the o v e r a l l r e a c t i o n r a t e r e a c t o r hydrodynamics has a dom inant e f f e c t on r e a c t o r performance. When k i n e t i c s masked by i n t e r n a l d i f f u s i o n c o n t r o l s the r a t e s i n g l e p a r t i c l e phenomena deter mine r e a c t o r performance to a great degree. The purpose of t h i s paper i s t o summarize previous i n t e r p r e t a t i o n s of the e f f e c t of incomplete c a t a l y s t w e t t i n g on t r i c k l e - b e d performance and to develop a model f o r the e f f e c t i v e n e s s f a c t o r f o r p a r t i a l l y wetted c a t a l y s t p e l l e t s . I n the case of a r e a c t i o n ©

0-8412-0401-2/78/47-065-387$05.00/0


CHEMICAL

388

REACTION

ENGINEERING-HOUSTON

confined to the wetted p o r t i o n of the c a t a l y s t only the wetted volume of the p e l l e t c o n t r i b u t e s to r e a c t i o n and the supply of l i q u i d r e a c t a n t occurs only across the wetted, e x t e r n a l surface of the p e l l e t . Under these c o n d i t i o n s the c a t a l y s t e f f e c t i v e n e s s f a c t o r i s a f u n c t i o n of the r a t i o of the maximal k i n e t i c r a t e and maximal r a t e of i n t e r n a l d i f f u s i o n , of the e x t e r n a l c o n t a c t i n g e f f i c i e n c y and of i n t e r n a l pore f i l l - u p . An approximate equation d e s c r i b i n g t h i s r e l a t i o n s h i p and based on the work of A r i s (15) can be incorporated i n the t r i c k l e - b e d r e a c t o r performance equa t i o n . S o l u t i o n s to more r i g o r o u s models r e p r e s e n t i n g the e f f e c t i v e n e s s of p a r t i a l l y wetted p e l l e t s were sought a l s o i n order to assess the v a l i d i t y of the approximate models. Review of Previous Models Most of the p r e v i o u s l y expression p l e t e c a t a l y s t w e t t i n g i n t r i c k l e - b e d s are summarized i n Table I . A l l of these, w i t h the exception of the l a s t one, are based on the assumptions of a) plug flow of l i q u i d , b) no e x t e r n a l mass t r a n s f e r l i m i t a t i o n s , c) i s o t h e r m a l c o n d i t i o n s , d) f i r s t order i r r e v e r s i b l e r e a c t i o n w i t h respect to the l i q u i d r e a c t a n t , e) n o n v o l a t i l e l i q u i d r e a c t a n t , f ) no n o n c a t a l y t i c homogeneous l i q u i d phase reac tion. S a t t e r f i e l d (5) suggested comparing the apparent r a t e constant. k , obtained from t r i c k l e bed data to the r a t e constant, k , de termined i n p e r f e c t l y mixed s l u r r y r e a c t o r s , as a measure of t r i c k l e bed e f f e c t i v e n e s s . The r a t i o k / k t c l e s s than u n i t y was i n t e r preted on the b a s i s of l i q u i d d e v i a t i o n s from p l u g flow (10) and of incomplete c a t a l y s t w e t t i n g (8,16). Ross (12) i n t r e a t i n g the data from commercial and p i l o t p l a n t h y d r o d e s u l f u r i z a t i o n r e a c t o r s assumed that l i q u i d space time i s the b a s i c parameter i n r e a c t o r performance. This a s s e r t s that performance and the apparent r a t e constant are p r o p o r t i o n a l to l i q u i d holdup as shown i n equation (1). Bondi (17) developed an e m p i r i c a l expression (2a) i n i n t e r p r e t i n g data f o r the h y d r o d e s u l f u r i z a t i o n of heavy gas o i l . This expres s i o n r e l a t e s the space time r e q u i r e d to achieve 50% conversion, τ^, to the analogous space time at complete w e t t i n g , τ^°, and to l i q u i d s u p e r f i c i a l v e l o c i t y , U L « This can a l s o be w r i t t e n as equation (2b) i n terms of p r e v i o u s l y defined constants. Henry and G i l b e r t (11) extended Ross (12) formula by i n c o r p o r a t i n g i n t o i t an a v a i l able c o r r e l a t i o n f o r l i q u i d holdup which r e s u l t e d i n expression (3). F i n a l l y , Mears (4) hypothesized that the apparent r a t e constant, k , i s p r o p o r t i o n a l to the true r a t e constant on completely wetted c a t a l y s t , k^ to the c a t a l y s t e f f e c t i v e n e s s f a c t o r , η^, and to the c o n t a c t i n g e f f i c i e n c y , riçE> i . e . to the f r a c t i o n of the e x t e r n a l c a t a l y s t area contacted by l i q u i d . By i n c o r p o r a t i n g the c o r r e l a t i o n of Puranik and Vogelpohl (18), which was developed f o r i n complete c o n t a c t i n g i n absorbers packed w i t h d i f f e r e n t packing s i z e and shape, Mears (4) a r r i v e d to expression (4). S y l v e s t e r and P i t a y a g u l s a r n (19) reproduced the model of Suzuki and Smith v

t c

v

1

v

C9


32.

DUDUKovic A N D

Catalyst Effectiveness in Trickle-Bed Reactors 389

MILLS

Table I Suggested Performance Equations f o r T r i c k l e - B e d Reactors -

k

1

H

tc TL

-

7"^ν

= T-^-

(2a)

5

+

ν

^

+

; 0.5 < b < 0.7

tc

,

n

(2b)

U L

1 in

krs.. L 1/3 tt cc m m /o (LHSV)2/ _ 0.32, L (LHSV) m AJ

Œ

:-

1-X 1 In -r-rr 1-X

œ

—

TtlotrN

/o\

d

ρ

(

c

τ

Τ

in J L = Λ ω

(5)

3

where

χτ

Λ

Β = -f-

3

[1 + 4 Λ / Ν 2

- 1]

β

(5a)

Ο Λ

( 5 b )

2 = 1/Α + 1/Ν , 1 st Ί

Λ

ι

=

Ί

[

V

o

t

h

φ

τ ~

1 1

( 5 c )

(20) f o r gas s o l i d c a t a l y t i c r e a c t i o n s and a p p l i e d i t t o three phase systems i n t r i c k l e beds. Incomplete w e t t i n g was accounted f o r by assuming only a p o r t i o n of the r e a c t o r , i . e . an e f f e c t i v e l y smaller volume, to be c o n t r i b u t i n g t o r e a c t a n t conversion. This i s again e q u i v a l e n t t o assuming t h a t a primary parameter i s l i q u i d space time. When the e x t e r n a l mass t r a n s f e r l i m i t a t i o n s and a x i a l d i s p e r s i o n e f f e c t s are neglected the model expressed by equations (5) i s reduced to Ross (12) expression (1) m u l t i p l i e d w i t h c a t a l y s t effectiveness factor. Recently (21) another approximate model f o r the c a t a l y s t s e f f e c t i v e n e s s f a c t o r i n t r i c k l e bed r e a c t o r has been proposed. I n t h i s model the e f f e c t i v e n e s s f a c t o r f o r a p a r t i a l l y wetted c a t a l y s t p e l l e t i n a t r i c k l e - b e d r e a c t o r f o r a r e a c t i o n o c c u r r i n g only i n the l i q u i d f i l l e d pore r e g i o n of the p e l l e t i s defined by: 1

η TB

= ( a c t u a l r a t e on a p a r t i a l l y wetted p e l l e t ) / i d e a l maximum r a t e a t bulk c o n d i t i o n s \ Ion a completely wetted p e l l e t J

=


CHEMICAL REACTION ENGINEERING-HOUSTON

390

= ( a c t u a l r a t e per u n i t volume of p a r t i a l l y wetted p e l l e t ) i d e a l maximum r a t e per u n i t volume of completely \ wetted p e l l e t )

χ

(

( f r a c t i o n of p e l l e t a c t u a l l y i n t e r n a l l y wetted) f

Using A r i s (15) d e f i n i t i o n f o r the modulus of i r r e g u l a r the f o l l o w i n g modified modulus was obtained: n Φ

particles

i

=

ΤΒ

(6)

( 7 )

*T

which r e s u l t s i n the expression f o r the e f f e c t i v e n e s s f a c t o r given below: . , , tanh ( — η

=

\B

n

(8)

CE

Expression (8) reduces t o the product of η^ η , as used by Mears (4) under two c o n d i t i o n s . Ε

n Φ

Τ

>

>

1 ;

η

ΤΒ

~

CE 0Ε Τ

=

η

η

τ

( 9 a )

In t h i s case the i n t e r n a l pore d i f f u s i o n a l l i m i t a t i o n s a r e severe and thus r e a c t i o n occurs only i n a narrow zone ( s h e l l ) c l o s e t o the e x t e r i o r s u r f a c e . The u t i l i z a t i o n of the p e l l e t i s d i r e c t l y p r o p o r t i o n a l t o the s i z e of t h i s zone which i n t u r n i s d i r e c t l y r e l a t e d t o the f r a c t i o n of e x t e r n a l area wetted.

n./n

CE

= l;

= n

(9b)

CE

The second case i m p l i e s t h a t the pores i n the c a t a l y s t p e l l e t s a r e not interconnected and that the f r a c t i o n of i n t e r n a l w e t t i n g c o r responds d i r e c t l y t o e x t e r n a l w e t t i n g . This i n general i s not the case when d e a l i n g w i t h r e a l c a t a l y s i s and hydrocarbon feeds which r e a d i l y wet i n t e r n a l pore s t r u c t u r e s (22). For s m a l l m o d u l i i i . e . very slow r e a c t i o n s such as t y p i c a l of h y d r o d e s u l f u r i z e r s expression (12) reduces t o : ^TB

*\

t

1

" i

2s

ls+

A

o

- • 2A.+3s

+ A

2s+

3+

s

(7) s'+A. Is

f

-> 2A +3s

surface oxidation and reduction

3

•s +A

?

Intrinsic Rate Expressions Model 2

Model 1

Equil: θ (χ ,χ ) = K x ( l - x ) / ( l + K x )

(1) Equil: θ ^ , χ ^ =

R

(2) Equil: θ (χ χ ) = K 'C (l-x )/(l+K

1

=

2 k C 2

R

=k

2/F

C

1

2

1

1

2

1

1

[(l-x )/(l+K x )] 2

x

x

£

1

M

x

1

2

(3) R = k c

)

3 3 l F l 2 3( ' 2 R = k 9 (x ,x )x f (u,x )

3

3

ρ

ljF

(l-x )/(1+K^) 2

2

x e 1

2

2 F

2

(χ ,χ )

2

1

2

>

4

4

1

1

2

2

4

(4) R

2

R = 0 5

(

R = 0

5) R

4

= k e (x x )9 (x ,x ) 4

p

χ

θ

2

χ

1

2

χ

5 = ^Ρ 1 2( 1» 2)

(6) R = k 9 ( x , x ) 6 ( x , x )

6

6

R = 0

(7) R

?

where χ = C /0 χ

x

1

2

2

=

θ

6

1

1

2

2

1

= k [9 (x ,x )] x

2

v

?

7

1

1

2

2

where x^ = C^/C^ ρ

χp

2 Equations Model 1

Model 2 Balance on total CO:

Balance on total CO: dx-i

2τ

dx-,

C

ST • i " * !

1,F Balance on chemisorbed 0 dx ax ?

l

c -d

• c^

3 model l a where m = { 4 model lb

err

- V

: 2

Balance on oxidized sites: dx τι. 2

1,F where m = {3 4 5 6

model 2a model 2b model 2a model 2b


]L

490


(This model i s a s p e c i a l v e r s i o n of a more general model described i n Table k of reference 1.) The main r e s u l t o f our a n a l y s i s o f model 1 i s that i f the functions f ^ and f ^ (see r a t e expressions R3 and R^ f o r model 1 i n Table l ) i n models l a and l b r e s p e c t i v e l y are assumed to be u n i t y , then n e i t h e r case can y i e l d o s c i l l a t o r y s t a t e s according to the c r i t e r i o n s t a t e d e a r l i e r . This i s some what s u r p r i s i n g at f i r s t glance because model l b , which i n c l u d e s r e a c t i o n U, gives a p o s i t i v e feedback e f f e c t due to CO i n h i b i t i o n by chemisorption on a c t i v e s i t e s . However, t h i s p o s i t i v e e f f e c t i s o f f s e t by the negative feedback e f f e c t of the chemisorption o f oxygen. We found f u r t h e r that i f a k i n e t i c model i s formulated so as to account f o r a p o s i t i v e feedback e f f e c t of chemisorbed oxygen by t a k i n g and f ^ t o be the quantity ( l - x ) , then the value of μ must be at l e a s t 2 f o r o s c i l l a t o r y s t a t e s t o be p o s s i ble. An i n h i b i t i o n e f f e c p l a u s i b l e unless i t i s (-μχ2), wherein the chemisorbed oxygen has the e f f e c t of i n c r e a s i n g the a c t i v a t i o n energy f o r the r a t e o f formation of CO2. Such dependencies of a c t i v a t i o n energies on surface coverage are sup ported from t h e o r e t i c a l c o n s i d e r a t i o n s and have been observed experimentally. I f t h i s a c t i v a t i o n energy dependence on X2 i s incorporated i n t o the k i n e t i c model i n e i t h e r of the two subcases, the c o n d i t i o n that aF /3x2 > 0 r e q u i r e s that the f o l l o w i n g i n e q u a l i t y be s a t i s f i e d : y

2

2

-

(k - m)

- (1 - x ) / x 2

2

+ μ (1 - x ) 2

> 0

(2)

where m has the value 3 i n model l a and k i n model l b . As i n e q u a l i t y (2) i n d i c a t e s , o s c i l l a t i o n s are p o s s i b l e f o r model 1 i f μ i s greater than some c r i t i c a l value. We c a l c u l a t e d the c r i t i c a l values to be k and 1 f o r models l a and l b r e s p e c t i v e ly. Thus r e a c t i o n h i s more l i k e l y t o l e a d t o o s c i l l a t o r y s t a t e s than i s r e a c t i o n 3, according to t h i s model The magnitudes o f the c r i t i c a l values appear t o be quite reasonable. The a n a l y s i s of other v a r i a t i o n s o f t h i s model are described i n reference 1 and some computer simulations of o s c i l l a t o r y s t a t e s are presented l a t e r i n t h i s paper. Important items o f information obtainable through a more extensive a n a l y s i s are t h a t ( l ) the model admits m u l t i p l e steady s t a t e s (2) the added i n c l u s i o n o f a surface cov erage-dependent chemisorption e q u i l i b r i u m constant for CO, to account f o r a decrease i n the enthalpy o f CO adsorption with oxygen coverage, enhances the p o s s i b i l i t y o f o s c i l l a t o r y s t a t e s and (3) the assumption o f a d i s s o c i a t e d form o f chemisorbed oxygen decreases the l i k e l i h o o d o f s a t i s f y i n g i n e q u a l i t y (2). I t should be noted here that although t h i s model with the a c t i v a t i o n energy dependence on oxygen surface ocverage permits o s c i l l a t o r y s t a t e s , i t i s not capable o f d e s c r i b i n g a l l o f the experimentally observed features of o s c i l l a t o r y behavior ( 1_). Therefore, no c l a i m i s made that t h i s model i s g e n e r a l l y s a t i s f a c t o r y . The main c o n c l u s i o n t o be drawn i s that i f one i s t o base a mathematical d e s c r i p t i o n of


40.

SHEiNTucH AND SCHMITZ

Oscillatory

Catalytic

Reactors

491

CO o x i d a t i o n on the r e a c t i o n steps and r a t e expressions underlying t h i s model, as i s t h e c u r r e n t l y popular approach, then t h e i n c o r p o r a t i o n o f an a c t i v a t i o n energy dependence on surface coverage seems reasonable as does t h e assumption o f more than one r a t e determining step — a t l e a s t over c e r t a i n ranges o f c o n d i t i o n s . In model 2 the o x i d a t i o n and r e d u c t i o n o f surface s i t e s , as represented by r e a c t i o n s 5, 6 and 7 i n Table I , are taken i n t o account. I n order t o r e t a i n a second-order d i f f e r e n t i a l model, •we invoke the assumption t h a t both chemisorption steps ( r e a c t i o n s 1 and 2) are i n e q u i l i b r i u m . We f u r t h e r assume t h a t t h e i n h i b i t i o n e f f e c t o f chemisorbed oxygen i s n e g l i g i b l e . The r a t e - d e t e r mining s t e p s , t h e r e f o r e , are r e a c t i o n s 3 through 7 t h e r a t e expression f o r which are l i s t e d i n Table I . Here x-^ i s t h e reduced gas-phase c o n c e n t r a t i o n o f CO as i n the previous model and X2 i s t h e f r a c t i o n assumed t o be i n a c t i v e expressions Rcj and Rg are assumed t o be p r o p o r t i o n a l t o t h e 0 0 formation r a t e s i n expressions R 3 and R^ r e s p e c t i v e l y . This assumption was prompted by the r e s u l t s o f o x i d a t i o n s t u d i e s reported by Ostermaier e t a l . (k). Notice a l s o t h a t t h e r e a c t i o n order ν i n the expression f o r Rj i s u n s p e c i f i e d . I n the a n a l y s i s o f t h i s model, we are i n t e r e s t e d i n the c r i t i c a l value o f ν beyond which o s c i l l a t o r y s t a t e s are p o s s i b l e . Again we consider two subcases. I n the f i r s t o f t h e s e , model 2a, r e a c t i o n s k and 6 do not occur, and i n the second, model 2b, r e a c t i o n s 3 and 5 do not take p l a c e . Both subcases l e a d t o mathematical d e s c r i p t i o n s o f the form given i n equation ( l ) , and the c r i t e r i o n f o r o s c i l l a t i o n s s t a t e d e a r l i e r i s r e a d i l y a p p l i e d . Our a n a l y s i s by t h i s approach l e d t o c r i t i c a l values o f ν o f 2 and 3 f o r models 2a and 2b r e s p e c t i v e l y . That i s t o say t h a t ν must have values g r e a t e r than these i n order f o r o s c i l l a t o r y s t a t e s t o be p o s s i b l e . From a fun damental viewpoint, t h e r e q u i r e d high order o f the surface r e duction step i s bothersome. The important p o i n t , however, i s that t h e o x i d a t i o n and r e d u c t i o n o f c a t a l y t i c s i t e s during reac t i o n can indeed l e a d t o o s c i l l a t i o n s . A l t e r n a t e r a t e expressions or r e a c t i o n s t e p s , perhaps more r e a l i s t i c ones which account f o r the m i g r a t i o n o f o x i d i z e d s i t e s i n t o the b u l k o f the m e t a l , would l e a d t o more p l a u s i b l e explanations o f o s c i l l a t i o n s . We are con d u c t i n g f u r t h e r i n v e s t i g a t i o n s i n t o the e f f e c t s o f v a r i a t i o n s o f t h i s model. 5

2

A c o n c l u s i o n t o be drawn from the r e s u l t s o f a n a l y s i s o f t h e two models described here i s t h a t some accounting f o r i n s i d i o u s mechanistic d e t a i l s i n c a t a l y t i c r e a c t i o n s , more than i s u s u a l l y necessary f o r r e a c t i o n engineering purposes, i s apparently neces sary i n order t o describe o s c i l l a t o r y behavior. The models each possessed mechanisms o f p o s i t i v e feedback r e s u l t i n g from the r o l e of a surface species — as was shown t o be necessary from the d i r e c t a p p l i c a t i o n o f well-known theorems.


4b>Z


Some Experimental

Observations

and Computed R e s u l t s

Due to space l i m i t a t i o n s , we do not present an extensive a r r a y o f computed and experimental r e s u l t s , but i n s t e a d show a s u f f i c i e n t sample t o give an a p p r e c i a t i o n o f key f e a t u r e s . F i g u r e 1 shows l i m i t c y c l e s computed from model l a w i t h ί3(μ,Χ2) = exp ( - μ χ 2 ) . (Our computations f o r model l a are f a r more e x t e n s i v e than f o r other models, but r e s u l t s f o r the others do not seem t o be s i g n i f i c a n t l y d i f f e r e n t from those o f model l a . ) N o t i c e t h a t the axes o f the phase plane are CO c o n c e n t r a t i o n and the r a t e of CO conversion. We used t h i s r a t e on the v e r t i c a l a x i s because i t s instantaneous values could be computed i n exper iments d i r e c t l y from s t r i p chart data o f CO2 c o n c e n t r a t i o n versus time. As the value o f τ proach a r e l a x a t i o n c y c l e bottom p o r t i o n o f the c y c l e f o r τ = 20 sec. c l o s e l y f o l l o w the branches of the steady r a t e curve (dashed curve i n F i g u r e l ) f o r CO conversion. (Notice t h a t the steady r a t e curve, computed from the s t e a d y - s t a t e equation f o r t h i s model i s m u l t i v a l u e d at lower CO c o n c e n t r a t i o n s and t h a t the upper branch shows a decreasing r a t e w i t h i n c r e a s i n g CO c o n c e n t r a t i o n . The decreasing r a t e has been w e l l e s t a b l i s h e d through recent y e a r s , but the mul t i v a l u e d geometric n a t u r e , caused by the form of ^^{\i,X2) employed, has not been s u b s t a n t i a t e d . Steady s t a t e s o l u t i o n s , according t o the steady species balance f o r CO, would be the p o i n t s o f i n t e r s e c t i o n o f the r a t e curve w i t h s t r a i g h t l i n e s of negative slope — the supply l i n e s . ) Decreasing the capacitance f a c t o r , £ has the same q u a l i t a t i v e e f f e c t on model p r e d i c t i o n s o f l i m i t c y c l e s as i n c r e a s i n g τ. Experimental l i m i t s c y c l e s i n the r a t e - c o n c e n t r a t i o n plane are shown i n F i g u r e 2 . The important p o i n t s r e g a r d i n g t h i s f i g u r e are: ( l ) the amplitude of the o s c i l l a t o r y s t a t e s were found t o i n c r e a s e as τ i s decreased — i n c o n f l i c t w i t h the t h e o r e t i c a l curves o f F i g u r e 1 ; ( 2 ) s t a b l e n o n o s c i l l a t o r y s t a t e s were obtained at residence times below ^9 sec. and above 130 s e c ; (3) multipeak c y c l e s were observed at lower residence times as the b i f u r c a t i o n to s t a b l e s t a t e s was approached. (See the i n s e r t i n F i g u r e 2 and the time t r a c e i n F i g u r e 3 . ) Multipeak c y c l e s r e q u i r e a higher dimensional space f o r t h e i r r e p r e s e n t a t i o n and are i n d i c a t i v e t h a t more than two r a t e - d e t e r m i n i n g r e a c t i o n steps are i n v o l v e d under some c o n d i t i o n s . c

F i g u r e k presents an example o f another experimental obser v a t i o n — t h a t o f a m u l t i p l i c i t y of l i m i t c y c l e s — which has not p r e v i o u s l y been r e p o r t e d and i s not p r e d i c t e d by the models d e s c r i b e d e a r l i e r . When such m u l t i p l i c i t y was encountered, we were able t o reach e i t h e r o f the two p e r i o d i c r e a c t o r s t a t e s by means of a p p r o p r i a t e feed c o n c e n t r a t i o n changes. I t i s i n t e r e s t i n g t o note t h a t the p e r i o d of the single-peak c y c l e (curve b i n F i g u r e k) i s very n e a r l y h a l f t h a t o f the complex c y c l e , curve


40.

SHEiNTucH AND scHMiTz

Oscillatory

Catalytic

Reactors

Figure 1. Simulated limit cycles for model la with ΐ (μ>^2) = exp (—μχ ). Parameter values: μ = 8; l = 0.08; K = 10; a^k-j = 0,01 sec' , aJksCjg,*' = 0.12 sec' . 3

2

2

c

1

1

CO Concentration in Reactor,vol % Figure 2. Experimental limit cycles for reactor temperature of 217°C; feed composition: 1.95% CO, 19% 0 ,and 79% N (by vol). Insert shows a magnification of multipeak cycle at the high concen tration extreme for τ = 58 sec. 2

2


493


494

Ο

95Γ

Figure 3. One period of a three-peak cycle for τ = 49 sec with experimental conditions given in Fig ure 2

T i m e , min

T i m e , min

Figure 4. Multiplicity of periodic states—(a) multipeak cycle and (b) simple cycle—at reactor tem perature of 217°C, residence time of 82.6 sec and feed state: 2.15% CO, 12.9% 0 ,85% N 2

2


40. SHEiNTucH AND scHMiTz

Oscillatory Catalytic Reactors

495

( a ) , -which contains two l a r g e peaks. Even a more i n t r i g u i n g type of behavior was observed i n one s i n g l e run at a r e a c t o r temperature o f 2T1°C and a feed composi t i o n o f 1.9935 CO, 19.3% 0 , and 19.1% Ν · In t h i s run our data gave strong evidence t h a t " c h a o t i c " s t a t e s e x i s t e d at residence times below 29 sec. Such s t a t e s are c h a r a c t e r i z e d by s u s t a i n e d time-dependent but nonperiodic behavior. P r i o r t h e o r e t i c a l work suggests t h a t such behavior may be i n t r i n s i c i n d i f f e r e n t i a l systems o f order three and h i g h e r (5.) and might g e n e r a l l y be accompanied by such phenomena as multipeak c y c l e s and m u l t i p l e p e r i o d i c s t a t e s (6.). There a r e , o f course, competing explanations f o r c h a o t i c outputs, i n c l u d i n g the simple one t h a t the r e a c t o r s t a t e under c e r t a i n c o n d i t i o n s i s very s e n s i t i v e t o s m a l l e x t r i n s i c d i s t u r b a n c e s . We are s t r o n g l y i n c l i n e d toward a c c e p t i n g the existence o f i n t r i n s i c chaoti matter r e q u i r e s c o n s i d e r a b l imentation than we have given i t thus f a r . In c o n c l u s i o n we should comment f u r t h e r on two p o i n t s . ( l ) T h e o r e t i c a l and experimental r e s u l t s are not i n agreement. Models which we have examined here serve mainly t o exclude c e r t a i n mechanisms and r a t e expressions. S t i l l the p r i n c i p a l f e a t u r e s i n c o r p o r a t e d s e p a r a t e l y t o account f o r o s c i l l a t o r y behavior, namely an a c t i v a t i o n energy dependence on surface coverage and metal o x i d a t i o n and r e d u c t i o n c e r t a i n l y are r e a l i s t i c f e a t u r e s . We f e e l t h a t some a l t e r n a t e method o f d e s c r i b i n g them or o f i n c l u d i n g both e f f e c t s simultaneously (or perhaps i n c l u d i n g other r a t e processes) t o o b t a i n q u a l i t a t i v e agreement w i t h experimental i n f o r m a t i o n w i l l l i k e l y shed new l i g h t on the k i n e t i c s o f CO o x i d a t i o n and perhaps on c a t a l y t i c o x i d a t i o n r e a c t i o n s i n general. (2) As i s n e a r l y always the case w i t h c a t a l y t i c r e a c t i o n e x p e r i ments, we f a c e d , i n our l a b o r a t o r y work, the problem o f a chang i n g and nonreproducible c a t a l y t i c a c t i v i t y . The i n f o r m a t i o n shown i n Figures 2 and 3 was obtained during a r e l a t i v e l y s t a b l e a c t i v i t y p e r i o d and could be reproduced q u i t e a c c u r a t e l y over a p e r i o d of a few days. A f t e r regeneration o f the c a t a l y s t , the q u a l i t a t i v e features shown and d e s c r i b e d f o r those f i g u r e s were u s u a l l y preserved, but a l l q u a n t i t a t i v e i n f o r m a t i o n was a l t e r e d . The changing a c t i v i t y makes i t p a r t i c u l a r l y d i f f i c u l t t o s t a t e c o n c l u s i v e l y t h a t such phenomena as the m u l t i p l e l i m i t c y c l e s shown i n Figure 3 and the c h a o t i c behavior (which i n c i d e n t a l l y was observed on only one occassion — on the t h i r d day f o l l o w i n g c a t a l y s t r e generation) d e s c r i b e d above are t r u l y b e h a v i o r a l t r a i t s and not simply the e f f e c t o f t r a n s i e n t a c t i v i t y l e v e l s . Unfortunately t h e o r e t i c a l and experimental s t u d i e s and the understanding o f the causes and e f f e c t s o f i n s i d i o u s a c t i v i t y changes have not yet reached t o the p o i n t a t which questions r e l a t i n g t o such matters can be answered w i t h assurance. 2

2



496 Nomenclature Α^,Α^,Α^

chemical components CO, the gas phase

^ls'A"2s

chemisorbed

0^, and CO^

respectively, in

components CO and 0^ r e s p e c t i v e l y

c a t a l y s t area per u n i t v o i d volume gas phase c o n c e n t r a t i o n o f CO i n the r e a c t o r C

C

l

F' 2

F^jF^

concentrations o f CO and 0^ i n the feed stream functions o f μ and χ used i n r a t e expressions R^ f o r model 1 elements i n the v e c t o r F

Ε J

vector of function Jacobian matri

Κ

F

dimensionless chemisorption e q u i l i b r i u m constant, K

Κ

and 5

?

Κ

*1 ' ·2

Ι

V 1,F C

chemisorption e q u i l i b r i u m constants f o r CO and

0^

k. _J Ε

r e a c t i o n v e l o c i t y constant f o r the j t h r e a c t i o n matrix o f capacitance f a c t o r s

&

surface chemisorption c a p a c i t y f a c t o r f o r CO, JVâ^/C^ ^

c

m M

index d e f i n e d where used concentration of active s i t e s

s

η q R. J s s t V χ χ-^,χ^ f

(moles/area)

index d e f i n e d where used volumetric flow r a t e at r e a c t o r temperature r a t e expression f o r the j t h r e a c t i o n i n Table I a c t i v e surface s i t e oxidized (inactive) surface s i t e dimensionless time, time/τ v o i d r e a c t o r volume general v e c t o r o f s t a t e v a r i a b l e s dimensionless s t a t e v a r i a b l e s d e f i n e d i n Table I f o r s p e c i f i c models

Greek L e t t e r s θ

^1' 2 θ . s μ ν τ

f r a c t i o n o f s i t e s occupied by chemisorbed respectively f r a c t i o n o f s i t e s i n the o x i d i z e d s t a t e

CO and

0^

parameter used as r e a c t i o n order or as c o e f f i c i e n t i n exponent i n r e a c t i o n s 3 and k o f model 1 order o f r e a c t i o n 7 with respect o f CO coverage i n model 2 residence time, V/q


40. SHEiNTucH AND scHMiTz

Oscilhtory Catalytic Reactors

497

Ac knowle dgment This work was supported by grants from the N a t i o n a l Science Foundation and the G u l f O i l Corporation.

Literature Cited 1. 2. 3. 4. 5. 6.

Sheintuch, M. and Schmitz, R. Α . , Cat. Rev.-Sci. & Eng. (1977) 15, 107. Plichta, R. T. and Schmitz, R. A. (in press). Sheintuch, Μ., Ph.D. Thesis, Univ. of Ill., Urbana (1977). Ostermaier, J . J.; Katzer, J. R. and Manogue, W. H . , J. Cat. (1976) 41, 277. Rössler, O. Ε . , Z. Naturforsch. (1976) 3la 259 May, R. M., J. Theor


41 Theoretical and Experimental Study of Self-Sustained Oscillations in a Stirred Tank Reactor P. H U G O and H.-P. W I R G E S * Institut für Technische Chemie, Technische Universität Berlin Strasse des 17. Juni 135, 1000 Berlin 12, West Germany

1. Mathematical model The dynamics of temperatur continuous-flow stirre the material and energy balances. For a simple first order chemical reaction they are in a dimensionless form dudө=- u

+ Da (l-u)exp

(la)

0

1 b d v d ө = - µ * v + Da (l-u)exp

[v1

0

+

εV]

(lb)

where u, ν , Θ are the dimensionless conversion, temperature difference and time, respectively, defined by 2 (T - T ) a

u = 1 - cc ; v = ERT E

0

0

nd ө = tT

T is the stationary temperature of the cooled reactor in the absence of a chemical reaction 0

T = T +µTk1+µ (3) with µ = k FMC 0

E

W

p

as a dimensionless heat transfer coefficient. The type of reaction and the reaction conditions are re presented by four dimensionless parameters B = E(-ΔH) c R E

p

c T p

p

2

*

; ε = RT E ; µ = 1+µB ;Da = 0

0

* Present address: Bayer AG, Werk Urdingen, 4150 Krefeld.

©

0-8412-0401-2/78/47-065-498$05.00/0


41.

HUGO AND wraGEs

Oscillations in Stirred Tank Reactor

499

This choice of the dimensionless parameters is useful for a mathematical description of stability. 2. Steady state and stability At a steady state the solutions of Eq. (1) are: Da u

s

=

TT1£Ç

u

v

6a

s = ** s

< >'
ο; i n s t a b i l i t i e s of the type 3 < ο correspond to multiplicity phenomena [1]. For 3 > ο and α > ο oscillatory i n s t a b i l i t i e s can be observed i f +

( 1 + ;

1

—lu—

6

>-

75

) 2 J

9

μ Such sustained oscillations (limit cycles) of the temperature and the conversion are mostly due to a unique steady state solution of Eq. (1) which is unstable to small perturbations. The region of parameter space for which i n s t a b i l i t i e s occur can be plotted into a so-called s t a b i l i t y diagram. Fig. 1 gives μ* versus u^ with Da as a fixed parameter. The curves α = ο and 3 = o calculated from Eqs. (7) and (8) are drawn into this diagram. It will be used here to present the results for a l o t of numerical calculations concerning limit cycles in the region α > o, 3 > o. 0

3. Numerical calculations Several attempts have been made [ 3 , 5 - 8 ] to describe limit cycles by approximate solutions of the balance equations (1).


500

CHEMICAL REACTION


However the range of v a l i d i t y of such approximate solutions is small. The application i s either limited to comparatively small B-values or to the neighbourhood of the borderline α = o. To find out a better description of limit cycles, extensive numerical calculations were carried out for B-values from 10 to 30 and ε = ο to 0.02075. Details of these calculations are pre sented in [9]. As an example Fig.2 shows a temperature oscillation computed under rather extreme conditions. Typical for the temperature oscillations i s the asymmetry of the oscillation due to the law of Arrhenius. From the numerical calculations the computed frequency is obtained by ω com

=

(10)

ΔΟ i s the dimensionless time difference between two succeeding maxima of temperature. From the maxima and minima of the temperature oscillations a modified amplitude A can be calculated A

'

1

ν max 7 1 + v , max e

m

v

ν · min 1 + ev . min

(11)

m

Further a time averaged conversion u was calculated: 2π/ω / Ο

ÏÏ = £

u d 0

(12)

In the subsequent sections these results will be compared with approximate solutions and empirical correlations. 4. Frequency of limit cycle For fixed values Β, ε and by varying μ* and Da several frequen cies were computed. From these data pairs of parameters μ*, Da were selected which gave the same frequency. Fig. 3 and 4 show the result for ε = 0.02075 and Β = 15 and 30. The values a)omp were compared with approximate solutions. The linearized theory [1] gives 0

C

u>

L

=

/β - α

(13)

ζ

This approximation i s useful for small α-values but f a i l s in the center of the region α > o. We found empirically that the simple e q U a t i 0

"

ω

1 ο

=

ΓΓ

gives in most cases a sufficient approximation. A better f i t of the data of the computer simulation was obtained by the regression equation


(14)

41.

HUGO AND WIRGES


501

Figure 1. Stability diagram (B = 20,£ = 0) 12

w . 10 10

|l

10 50

1090

1 'I 1130

11,70

!

1210

1

12,50

i

12,90

13,30

Θ • Figure 2. Typical temperature oscillation from computer simuhtion (B = 30, e = 0 02075, * = 0,44505, u = 0,65) μ

8


502


Figure 3. Stability diagram with curves of equal frequency (B = 15, c = 0,02075)


HUGO AND WIRGES

41.


u> = 9 . 6 - 3 5 . 7 u

+ 23.9 u

D

s

K

< 0.95

$

K

5.

J

x

s

+ 10.6 u e

(15)

s

and

ο ο < u

+ 2 0 . 5 y V - 0 . 2 By*

2

s + 0.23

0.40

c

503

10

< Β < 30

0.2

< μ*
)/ a ) , was + 1 0 % . comp R " comp D

A m n

Comparison of some r e p r e s e n t a t i v e f r e q u e n c i e s .

Amplitude of temperature o s c i l l a t i o n s

A l o t of more severe d i f f i c u l t i e temperature i s to be p r e d i c t e d . Several proposed approximations [ 3 ] , [ 5 ] [ 6 ] , Γ 7 ] are only useful i n a small range, namely in the neighbourhood of the b o r d e r l i n e α = ο and f o r comparatively small B-values. The asymmetric behavior of the temperature o s c i l l a t i o n s can approximately be accounted f o r by s e t t i n g 5

Δν a

ν - v

=

$

=

-

In ( 1 - a cos ω Θ) where

(16) (17)

= tanh (A)

F i g . 5 and 6 show curves of equal a-values f o r ε = 0 . 0 2 0 7 5 and Β = 1 5 and Β = 3 0 . These diagrams i l l u s t r a t e that small tempera ture amplitudes are r e s t r i c t e d to a very small zone near the b o r d e r l i n e α = o. A l l a n a l y t i c a l approximations must f a i l in the main part of the region α > ο , β > ο where the a-values are very near to 1 . A r e g r e s s i o n method was a p p l i e d s e l e c t i n g about 5 0 0 r e p r e s e n t a t i v e data from the computer s i m u l a t i o n . The best f i t t i n g was found by A

*

= - 1 1 . 5 - 5 4 . 4 μ* + 5 7 . 2 u. + 0 . 7 6 Β - 5 7 . 2 ε

D

"»|^ -

-

1i ·J

-

-

56.5 u

Jt.t μ

$

2

Τ

- 0.012Β

\JI.L·

2

+ 5 1 . 1 *u P

$

(18)

which i s v a l i d i n the same range of the parameters as E q . ( 1 5 ) . As f a r as A < 5 the maximum percentage e r r o r (A - A R ) / A was about + 3 0 % . To our own s u r p r i s e a comparatively simple semi-empirical approximation works q u i t e well in the range of high temperature amplitudes. From Eq. ( 1 ) a c o u p l i n g equation can be obtained by e l i m i n a t i o n the dimensionless r e a c t i o n r a t e

£ 0

+ 0

* =

ν

;

Υ = Β υ _ ^ By* - 1


(

1

9

)


504

Table I: Comparison of some representative frequencies ω comp Eq.dO)

parameters

ω

Eq.(13)

Ι_ο Eq.(14)

Eq.(15)

B=10 ε=0

u =0 80 μ*=0 280

2,406

2,449

2,451

2,210

B=10 ε=0

u =0 80 μ*=0 2509

1,917

2,118

2,132

1,800

B=10 ε=0

u =0 60 μ*=0 261

0,938

0,561

0,717

0,868

B=30 ε=0 02075

u =0 80 μ*=0 311

B=30 ε=0,02075

u =0,75 μ*=0 310

4,325

2,060

4,100

4,511

B=30 ε=0 02075

u =0 60 μ*=0 3038

3,159

imagin.

2,485

2,981

B=30 ε=0,02075

u =0 55 μ*=0 2716

2,394

imagin.

1,705

2,580

s

9

9

s

9

9

s

9

9

9

9

s

9

9

s

9

s

9

9

s

9

9


41. HUGO AND WIRGES


505

From several numerical calculations we found that the oscillations of y are considerably smaller than those of v. This effect i s demonstrated for a typical limit cycle with a high temperature amplitude in Fig. 7. So we tested the approximation Y ( v ) = v where the e x t r

$

corresponding conversion u i s obtained from Eq. (lb) by setting %

= o. One gets (Bu* - l ) v - Β - v s

D a

D a

extr = o

e x

-

e x t r

·v

(20)

e x t r

extr 1 +

P

(21)

The f i r s t and the third intersection of the curve f ( v , ) with the line Ψ = v (see Fig. 7) yield approximate values for v - j and v which are used to calculate A from Eq. (11). e J

t r

s

m

n

m a x

Table II: Comparison of some representative amplitudes of temperature 6. Time averaged conversion A short comment should be made to the time-averaged conversion. By an approximate solution [ 9 J we obtained

and

II

> u

$

for

v" < 2

U

< u

s

for "v > 2

From our numerical calculations we found that this rule i s valid even at high B-values.__From the practical point of view the i n crease of conversion (u - u ) in the range ν < 2 is comparatively small. The severe problems of a reactor with self-sustained oscillation makes i t unrealistic to use this way for increase of conversion. s

7. Experimental results In the experimental part of this study the catalytic decomposition of hydrogen peroxide by Fe(No3)3 * ^ 2 ° ' t r i c acid solution was used as a model reaction. This reaction has the advantage ob being f i r s t order [10, 11]. The concentrations of Fe^ and H remain constant during the reaction. The following rate expression was obtained by kinetic experiments: H

i n

a

m

+

1 8

C

3

* - ι 6.in Fe * " ^ 'c + 0,01 r

1

0

H +

. 14620, H 0 ' P(- - T - >

n c

ex

2

2

g-mole l i t r e - sec


+

. < )

/ 9 9

22


506

μ* οβ

Γ

Figure 6. Stability diagram with curves of equal temperature amplitude (B = 30, c = 0,02075)

ψ(ν)

26

'

1

ι

·

ι

·

1

'

1

B»30 C «002075 u *Qf5 μ* > OUSI s

22 ....

-

ψ|ν) ^) φ ( ν

20

-

\/ I

Figure 7.

.

I

.

I

.

I

.

I

.

ι

Limit cycle φ(ν) for Β = 30, e — 0, 02075, μ* = 0, 445pnd u = 0,65 s


41.

HUGO AND WIRGES


507

The values of the activation energy (E = 121,5 kJ/g-mole) and of the reaction enthalpy (-ΔΗ = 94,8 kJ/g-mole) are high enough to f u l f i l Eq.(9) so that the oscillatory behaviour of temperature and conversion in the CSTR can be observed for a wide range of operating conditions (see Table III). The acid/hydrogen peroxide solution and the catalyst were pumped in two feed streams via rotameters into the reactor. The liquid phase volume (V = 500 ml) was kept constant with an outlet valve. The extent of the reaction was followed by titration of hydrogen peroxide and by sensing the temperature with a thermo couple. Table III Range of experimental conditions 800 ml/h

< v

1. A t β = 0.902 l a r g e r d e v i a t i o n s a r e o b s e r v e d . T h i s may be due t o a g r o w i n g d i s c r e p a n c y between model a s s u m p t i o n s and e x p e r i m e n t a l r e a l i t y i f s m a l l e r v a l u e s o f B a r e a p p r o a c h e d . T h i s was done by k e e p i n g mg c o n s t a n t and l o w e r i n g t h e gas v e l o c i t y t o 5.5 cm/s NTP a t B = 0.902. I n the range o f low gas v e l o c i t i e s e f f e c t s o f h e a t l o s s e s u s u a l l y become more pronounced, a f a c t t h a t i s a l s o o b s e r v e d i n f i x e d bed e x p e r i m e n t s . I n o r d e r t o t e s t t h i s p o i n t o f view we have r e p l a c e d i n be i ) t h e e x i t t e m p e r a t u r e g r a d i e n t (dT /dx) = 0 by a n e g a t i v g r a d i e n t e s t i m a t e d fro measurements. The d o t t e gradient of (dTg/dx) uppe l i m i t i n g c u r v e ϊο h i g h e r gas i n l e t t e m p e r a t u r e s i s o b s e r v e d which g i v e s a b e t t e r f i t t o t h e d a t a . T h i s shows t h a t i n d e e d heat l o s s e s may be r e s p o n s i b l e f o r t h e o b s e r v e d d i f f e r e n c e s between t h e o r y and e x p e r i m e n t a t B = 0.902. s

L

Conclusions The two-phase model o f a moving bed c h e m i c a l r e a c t o r w i t h c o u n t e r c u r r e n t o p e r a t i o n was s o l v e d n u m e r i c a l l y . Due t o t h e i n c r e a s e d f e e d b a c k by t h e c o u n t e r c u r r e n t movement a b r o a d range o f m u l t i p l i c i t y was o b t a i n e d . E x p e r i m e n t s c o n f i r m e d the p r e d i c t e d r e s u l t s . T h i s work was s p o n s o r e d by t h e Deutsche F o r s c h u n g s g e m e i n s c h a f t (SFB 153). Nomenclature

J

tot

ΔΗ d h L m mg Pi r P

F

f S

l i n e a r p a r t o f t h e system o f d i f f . e q u a t i o n s i n matrix form s p e c i f i c heat o f gas ( c o n s t , p r e s s . ) J/kg/K s p e c i f i c heat o f s o l i d , J/kg/H c o n c e n t r a t i o n o f t h e gas m i x t u r e ( a t s t a n d a r d c o n d i t i o n s ) , kmole/m^. reaction enthalpy, J/kmole diameter of c a t a l y s t p a r t i c l e , m h e a t t r a n s f e r c o e f f i c i e n t , J/m^/hr/H length of the reaction section,m mass v e l o c i t y o f gas, kg/m /hr mass v e l o c i t y o f s o l i d , kg/m^/hr Legendre p o l y n o m i a l ^ r e a c t i o n r a t e , kmole/m / h r n o n l i n e a r p a r t o f t h e d i f f . equ. i n v e c t o r form s u r f a c e a r e a p e r u n i t bed volume, 1/m t e m p e r a t u r e o f t h e gas, H 2


44. THOMA AND VORTMEYER

Tp Tg Tg Ty χ y y *o

D

Q

Steady States of Moving Bed Reactor

549

i n l e t temperature o f the gas, H temperature o f the s o l i d , H i n l e t temperature o f the s o l i d , Κ ujall temperature, Η a x i a l distance, m mole f r a c t i o n o f ethane mole f r a c t i o n o f ethane a t t h e e n t r a n c e

Greek l e t t e r s a,,

c o e f f i c i e n t d e s c r i b i n g heat l o s s e s t o t h e u j a l l J/m /hr/K 3

α

2 ε XS^f ρF PS ξ

void fractio e f f e c t i v e therma J/m/hr/K d e n s i t y o f t h e g a s , kg/m d e n s i t y o f t h e s o l i d , kg/m s o l u t i o n v e c t o r , c o n t a i n i n g the expansion c o e f f . 3

Literature cited (1) Weekman, V.W., Nace, D.M., AIChE J.,(1970),16,397. (2) Van Heerden, C., Chem.Eng.Sci., (1958),8,133. (3) Amundson, N.R., Canad.J.Chem.Engng.,(1965), 43, 49. (4) Wicke, E., Padberg, G . , Arens, H., Proc.Europ. Symp. Chem.Reaction Eng., 4th, Brussels (1968). (5) Schaefer, R.J., Vortmeyer, D., Watson, C.C., Chem. Eng.Sci.,(1974),29,119. (6) Luss, D.L., Amundson, N.R., I&EC Fund.,(1967),6,437. (7) Yoshida, S., Tamura, S., Kunii, D., Int.J.Heat Mass Transfer (1966), 9,865. (8) Simon, B., thesis, T e c h n . U n i v e r s i t ä t München (1976). (9) Simon, B., Vortmeyer, D., Chem.Eng.Sci., in Press. (10) Szekely, J., Poveromo, J.J., AIChE J.,(1975),21,769. (11) Finlayson, B.A., "The method of weighted residuals a. variational principles", Acad. Press (1972). (12) Reilley, M.J., Schmitz, R.A., AIChE J., (1966),12,153.


45 Cell Model Studies of Radial Flow, Fixed Bed Reactors J. M .

CALO

Department of Chemical Engineering, Princeton University, Princeton, NJ 08540

The radial flow, fixed bed reacto (RFBR) originall de veloped to handle larg of ammonia. Since then, RFBRs have been used, or considered for, catalytic reforming, desulfurization, nitric oxide conversion, catalytic mufflers, and other processes in which fluids must be contacted with solid particles at high space velocities. The prin cipal advantages of the RFBR over the more conventional tubular, axial flow, fixed bed reactor (AFBR) have been outlined elsewhere (1,2). Although usually cylindrical in geometry, spherical RFBRs have also been considered (3). Perhaps the first published analysis of an RFBR was by Raskin, et al. (4), who developed a quasicontinuum distributed parameter model for a radial ammonia synthesis reactor. General conclusions were limited, however, since the model was specifically concerned with ammonia synthesis and later carbon monoxide conversion (5), where both processes are second order and reversible. However, these authors did note that "radial reactors are anisotropic", i.e., they observed higher ammonia yields for centripetal radial flow (CPRF -- periphery to the center) than for centrifugal r a d i a l flow (CFRF -- center to periphery) (4) . In the present work, a packed bed c e l l model i s used to calcu late temperature and concentration profiles i n the adiabatic RFBR for exothermic c a t a l y t i c reactions with interphase resistance to mass and heat transfer. In p a r t i c u l a r , differences between the RFBR and the AFBR, operated at the same space v e l o c i t y , are explor ed with respect to uniqueness, m u l t i p l i c i t y , and s t a b i l i t y of the steady state, p r o f i l e location, s e l e c t i v i t y i n p a r a l l e l and series reactions, and transient behavior. RFBR C e l l Model Following Vanderveen, et a l . (6), the mass and energy conser vation equations for the f l u i d and the p a r t i c l e i n the j t h c e l l for a f i r s t order, i r r e v e r s i b l e , exothermic reaction are M.(v. . - v.) - (v. - v.) =a fdv./dt) D 3-1 Ύ 3 Τ 1 1 J

© 0-8412-0401-2/78/47-065-550$05.00/0


[1]

45. CALO

Radial Flow, Fixed Bed Reactors

551

( V J - v.) - k.v. = a ( d v . / d t )

C3]

3

(y. - y . l + 3k .v. = a.fdy./dt) [4] 3 3' 3 3 4 3 s u b j e c t t o the i n l e t c o n d i t i o n s VQ = VQ(t) = 1.0 and yo = y o ( t ) = 1.0 and a p p r o p r i a t e i n i t i a l c o n d i t i o n s (see N o t a t i o n and Vanderveen, e t a l . (β) f o r parameter d e f i n i t i o n s ) . In r a d i a l f l o w , the f l u i d i n t e r s t i t i a l v e l o c i t y , u j , i s a f u n c t i o n o f p o s i t i o n i n the bed, and hence, c e l l number, j . The interphase mass and heat t r a n s f e r c o e f f i c i e n t s vary approximately as R e (£, 1_) , and thus Mj and Hj are f u n c t i o n s o f Re® ·** which increase i n CPRF and decrease i n CFRF w i t h bed depth, k j i s a l s o a f u n c t i o n o f U j due t With the assumptio the bed (_5) , the c o n t i n u i t y equation f o r c y l i n d r i c a l geometry i n t e grates t o ur = U^Ri = U2R2; w h i l e f o r s p h e r i c a l geometry, u r = 1 1 = U2 2 I n t e g r a t i o n o f the v e l o c i t y , u = ±dr/dt (+ f o r CFRF and - f o r CPRF), from the bed entrance t o the bed e x i t y i e l d s the space time d i s t r i b u t i o n along the bed l e n g t h . R e s u l t s o f t h i s c a l c u l a t i o n r e v e a l t h a t i n r a d i a l flow the l o c a l residence time near the o u t e r p e r i p h e r y o f the bed i s increased a t the expense o f residence time near the i n n e r core o f the bed as compared to a x i a l flow a t the same t o t a l space time. The steady s t a t e temperature p r o f i l e s presented i n F i g u r e 1 were determined by an i n i t i a l value c e l l - b y - c e l l c a l c u l a t i o n f o r the same feed c o n d i t i o n s , average space v e l o c i t y , and bed depth. A l l the parameter v a l u e s are those o f Vanderveen, e t a l . (6) ex cept as otherwise noted. As can be seen, the CPRF p r o f i l e appears e a r l i e r , and the CFRF p r o f i l e appears l a t e r i n the bed than the ax i a l flow p r o f i l e as a r e s u l t o f residence time reapportionment. This " e a r l y - l a t e " phenomenon i s accentuated by d e c r e a s i n g aspect r a t i o and by s p h e r i c a l over c y l i n d r i c a l geometry a t the same aspect ratio. Uniqueness, M u l t i p l i c i t y , and S t a b i l i t y V

0 , 6

U

R

2

R

2

A l g e b r a i c m a n i p u l a t i o n o f the steady s t a t e forms o f the con s e r v a t i o n equations [104] i n the same manner as E r v i n and Luss (8) yields y. * y- -, = (M.+l)k.(y . - y.)/M. = G. (y.) 3 3-1 3 3 m3 3 3 3 3 Κ

J

,

[5]

Κ

f

where y j i s the maximum p a r t i c l e temperature i n the j t h c e l l (8}. Equation [5] can be r e w r i t t e n as m #

1 = G.CyJ/ly. - y.^)

Ξ F. (y.)

[6]

and the steady s t a t e s o f the system are determined by the i n t e r s e c t i o n o f t h e h o r i z o n t a l l i n e a t u n i t y and the f u n c t i o n F j ( y j ) . For s m a l l y j , d F j ( y j ) / d y j i s n e g a t i v e , and i f A


552


0

10

20

30

40

50

60

70

80

90

100

C e l l Number, j

Figure 1. Unique steady state temperature profiles for CPRF and CFRF ( and axialflow(P = 9kP , T — 667 K , T = 667 Κ,β = 5, M/H = 1.67) 0

a

0

0


P

=

0.25)

45.

CALO


dF. (y.)/dy. < 0 3 3

,

j

J

J

2

y.e(y

3

m,3

KJ

553 ., y. _)

3~1

[7]

J

then t h i s i s a s u f f i c i e n t c o n d i t i o n f o r uniqueness of the steady s t a t e . I f c o n d i t i o n [7] i s v i o l a t e d , then F j ( y j ) w i l l e x h i b i t extremum a t y-j

= ΙΎΙΥ_ ^

1

j [ ^'ί

where

Q

=

Ύ2

y4_J

+

+Y

j-1

±

) 2 +

ôJ/ [y^ + Ύ - y^_J 2

4Yy

j-l m,ji j-l 5

y

"Y

w

" Vj)]*

In order t o i n s u r e c o n d i t i o n [ 7 ] , the argument of Qj must be nega tive , or Inf 4 l<j 1, CPRF i n c r e a s e s the range of parameter space f o r which m u l t i p l i c i t y can occur, and CFRF decreases the range, as compared to a x i a l flow a t the same t o t a l space time. The opposite i s t r u e f o r M/H < 1. Again, t h i s e f f e c t becomes more pronounced f o r de c r e a s i n g aspect r a t i o and f o r s p h e r i c a l over c y l i n d r i c a l geometry at the same aspect r a t i o . C o n d i t i o n [9] i s s u f f i c i e n t but not necessary t o i n s u r e uniqueness of the steady s t a t e . I f i t i s v i o l a t e d , m u l t i p l e steady s t a t e s w i l l e x i s t i n c e l l s f o r which F j ( y j + ) > 1 > F j ( y j - ) . T y p i c a l behavior o f the F j ( y j ) curves w i t h c e l l number i s i l l u s t r a t e d i n Figure 2, which shows t h a t f o r M/H > 1, y j - l i n c r e a s e s w i t h bed depth, and y j i n c r e a s e s , but l e s s r a p i d l y , t o ym. Simultaneously, the F j ( y j ) curve r i s e s , y j - approaches yj+,ând a t some p o i n t i n the bed, yj+ = y j - Ξ y j and Fj(yj+) = F j ( y j - ) = F j ( y j , t ) ~ the t r i f u r c a t i o n p o i n t . I f j ( Y j , t ) 1* m u l t i p l e steady s t a t e s e x i s t for^some c a t a l y s t p a r t i c l e s i n the bed i n the r e g i o n where j*yj ) j(yj~)' However, i f F j ( y j ) < 1, then a l l c a t a l y s t p a r t i c l e s have a unique steady s t a t e , and the r e a c t o r p r o f i l e i s unique. F j ( y j ^ ) < 1 i s both a necessary and s u f f i c i e n t c o n d i t i o n f o r uniqueness of the steady s t a t e . In r a d i a l f l o w , j ( Y j , t ) cannot be c a l c u l a t e d a p r i o r i as i n F

m #

f t F

F

+

>

1

>

> F

/ t

t

F


r

554


a x i a l flow because the values o f Aj and k ( i n k j ) a t the t r i f u r c a t i o n p o i n t are not known. Nevertheless, i t can be shown t h a t the lowest i n t e r s t i t i a l v e l o c i t y i n the bed, i . e . , a t the outer p e r i p h e r y , y i e l d s an upper bound i n e v a l u a t i n g j ( y j , t ) - Thus, i f j ^ j # t ) u . b . I* then t h i s i s a s u f f i c i e n t , but not necessary con d i t i o n f o r uniqueness o f the steady s t a t e . The d i f f e r e n c e i n behavior between the F j ( y j ) curves f o r CPRF and CFRF i n F i g u r e 2 i s due t o the s c a l e f a c t o r e f f e c t o f (Mj+1)/ Mj and kg ( i n k j ) . These velocity-dependent terms are l a r g e r f o r CPRF and s m a l l e r f o r CFRF i n the i n i t i a l p o r t i o n o f the bed, and they cause the F j ( y j ) curves t o r i s e f a s t e r from c e l l t o c e l l i n CPRF. Therefore, i f m u l t i p l e steady s t a t e s e x i s t , the region o f m u l t i p l i c i t y w i l l be s h i f t e d toward the bed entrance i n CPRF and toward the bed e x i t i n CFRF. This e f f e c t can be b e t t e r appreciated i n F i g u r e 3, which i s a of j f o r the same c o n d i t i o n and F j ( y j - ) branches cross u n i t y and coalesce a t the t r i f u r c a t i o n p o i n t f i r s t f o r CPRF, next f o r a x i a l f l o w , and l a s t f o r CFRF. The open i n t e r v a l [ F j ( y j + ) , j ( y j ~ ) 3 i s measure o f the pa rameter space f o r which m u l t i p l i c i t y can occur. CPRF presents a l a r g e r i n t e r v a l and CFRF a s m a l l e r i n t e r v a l than a x i a l flow a t the same average space v e l o c i t y . Thus, i n g e n e r a l , CFRF suppresses m u l t i p l i c i t y and CPRF promotes m u l t i p l i c i t y as compared t o a x i a l flow a t the same average space v e l o c i t y . I n a l l the c a l c u l a t i o n s performed, however, CPRF never induced m u l t i p l i c i t y nor d i d CFRF completely suppress m u l t i p l i c i t y when compared t o the " e q u i v a l e n t " a x i a l flow case. On the other hand, the p o s s i b i l i t y t h a t condi t i o n s may e x i s t under which t h i s could occur has not been e l i m i nated. I t should be noted t h a t Hlavacek and Kubicek (1) concluded t h a t CPRF, and not CFRF, tends t o suppress m u l t i p l e s o l u t i o n s f o r the quasicontinuum a x i a l d i s p e r s i o n model without interphase t r a n s port resistance. A s t a b i l i t y a n a l y s i s o f the t r a n s i e n t equations [1-4] y i e l d s the same necessary and s u f f i c i e n t s e t o f c o n d i t i o n s f o r asymptotic s t a b i l i t y as obtained by Vanderveen, e t a l . {6), v i z . g

F

F

Ul

0

;b

D2

>

0

a

2

2

; b. b H > b _b. . + b _ ; b > D l J2 33 3I J4 33 34

0

,

[11]

except, o f course, t h a t f o r r a d i a l f l o w , M and H are f u n c t i o n s o f j . The f o u r t h c o n d i t i o n , b j 4 > 0 , i s simply c o n d i t i o n [ 7 ] , i . e . , d F j ( y j ) / d y j < 0 . Thus a l l steady s t a t e s on the p o s i t i v e slope branch o f F j ( y j ) are unstable w i t h respect t o s m a l l p e r t u r b a t i o n s . Steady s t a t e s on the h i g h and low temperature branches w i t h nega t i v e slope have a chance o f being s t a b l e i f i n a d d i t i o n they s a t i s fy the f i r s t three c o n d i t i o n s i n [ 1 1 ] . For g a s - s o l i d systems w i t h a i 4 / a 3 » 1, the f i r s t two c o n d i t i o n s i n [11] imply the slope c o n d i t i o n (§_ §_,9) . C o n d i t i o n [7] i s stronger than the slope c o n d i t i o n i f f

(l V

+ H . ) M . / ( H . ( M . + δ.)) 3 3 3 3 3 '

> 1

,


[12]

CALO


Figure 2. Fffîj) curves as a function of cell number for CPRF and CFRF ( = 0.5). (P = 9kP , T = 667°K, T = 667% β = 7.5, M/H = 1.1183). The curves are labeled with cell numbers. P

0

a

0

0



C e 1 1 Numbe r ,

j

Figure 3. F/$+) and F/5,—) as a function of cell number for CPRF, CFRF, and axial flow for the same conditions as in Figure 3. The CPRF and CFRF curves are dashed to F/5i,t)„.. since the Fj(yjj) are not known. &


45.

CALO

557


which i s always s a t i s f i e d f o r M/H > l,and thus c o n d i t i o n [7] im p l i e s the f i r s t , second, and f o u r t h c o n d i t i o n s i n [11]. For M/H < 1 and 6 j - 1, i n e q u a l i t y [12] i s not s a t i s f i e d , and the slope c o n d i t i o n w i l l be s t r o n g e r . In any case, f o r a steady s t a t e on the negative slope branches o f F j ( y j ) t o be stable., the t h i r d con d i t i o n i n [11] must a l s o be s a t i s f i e d , and as has been p o i n t e d out (§_r§) ι t h i s c o n d i t i o n i s a complex expression w i t h no obvious p h y s i c a l meaning. A comparison o f r e l a t i v e magnitudes o f c o n d i t i o n [12] f o r M/H > 1 r e v e a l s t h a t r a d i a l flow tends t o d e s t a b i l i z e the bed a t the outer p e r i p h e r y and s t a b i l i z e the bed a t the i n n e r core t o a g r e a t e r extent than a x i a l flow a t the same t o t a l space v e l o c i t y . Selectivity Effects The reapportionmen gous t o v a r i a b l e volume would be expected t o a f f e c t product s e l e c t i v i t y i n s e r i e s and para l l e l r e a c t i o n s . For two p a r a l l e l f i r s t o r d e r , exothermic r e a c t i o n s , the p a r t i c l e equations [3, 4] become (v. - v.) - (k . + k .)v. = 0 3 3 ID 23 3 K

J

K

[13]

j

[14]

(Yj " Y j ) + ( 3 ^ 1 . + 3 k ) v . = 0 2

2 j

The r e s u l t s o f a t y p i c a l c a l c u l a t i o n are presented i n Figure 4. For the parameters chosen (see f i g u r e c a p t i o n ) , CPRF i n c r e a s e d the y i e l d o f R and decreased the y i e l d o f S, w h i l e CFRF acted i n the opposite sense. Thus, i n t h i s case, the y i e l d o f R v a r i e d 6.2% and t h a t o f S 6.7% simply according t o whether the r e a c t o r was operated i n CPRF o r CFRF. For two s e r i e s f i r s t order, exothermic r e a c t i o n s , the p a r t i c l e mass balance i s the same as Equation [ 3 ] , but the p a r t i c l e energy balance (Eq. [4]) becomes y

j "h

+

'ΛΛ

+

2 2?j -

&

k

0

-

[15]

where Wj i s the f r a c t i o n o f i n t e r m e d i a t e . A l s o , a d d i t i o n a l p a r t i c l e and f l u i d mass balances are r e q u i r e d f o r the i n t e r m e d i a t e . The r e s u l t s o f a t y p i c a l c a l c u l a t i o n f o r t h i s case are presented i n F i g u r e 5. As compared t o a x i a l f l o w , and f o r the parameter values chosen (see f i g u r e c a p t i o n ) , CPRF i n c r e a s e d the y i e l d o f product S and decreased the y i e l d o f intermediate R, w h i l e CFRF again acted i n the opposite sense. The y i e l d o f S v a r i e d 9.5% and t h a t o f R 77.3% simply a c c o r d i n g t o flow d i r e c t i o n i n c y l i n d r i c a l r a d i a l flow. A l s o , when the crossover p o i n t f o r R and S i s near the r e a c t o r e x i t i n a x i a l f l o w , CPRF can y i e l d a product w i t h S > R, w h i l e CFRF y i e l d s a product w i t h R > S. This occurs when the crossover p o i n t moves toward the bed entrance i n CPRF, i n c r e a s i n g S over R, and moves out o f the r e a c t o r e x i t i n CFRF, thereby i n c r e a s i n g R over S. Of course, d i f f e r e n c e s i n s e l e c t i v i t y due t o flow d i r e c t i o n i n an RFBR are extremely s e n s i t i v e t o the s p e c i f i c k i n e t i c parameters.


558



45. CALO


559

However, i t i s c o n c e i v a b l e , depending on the r e a c t i o n system, t h a t s e l e c t i v i t y e f f e c t s i n r a d i a l flow could be s i g n i f i c a n t . T r a n s i e n t Behavior When m u l t i p l e steady s t a t e s e x i s t , steady s t a t e p r o f i l e s can be determined o n l y by a t r a n s i e n t a n a l y s i s . T y p i c a l r e s u l t s o f the numerical s o l u t i o n o f the t r a n s i e n t simple c e l l equations [1-4] are presented i n F i g u r e 6. Here f l u i d temperature p r o f i l e s are presented f o r CPRF and CFRF f o r c y l i n d r i c a l geometry (p = 0.25), and a x i a l flow f o r the same average space v e l o c i t y a t 5, 15, and 30 minutes a f t e r s t a r t up. The feed and i n i t i a l c o n d i t i o n s are noted i n the f i g u r e c a p t i o n . S e v e r a l i n t e r e s t i n g features are apparent. The i n c i p i e n t p r o f i l e s a t 5 minutes are much c l o s e r t o gether than a t 30 minutes. I n each case the r e a c t i o n zone i s f o r med w i t h i n 15 minutes, an the bed e x i t . I t i s q u i t the most, and the CPRF p r o f i l e the l e a s t . I t i s a l s o i n t e r e s t i n g to note t h a t a l l the CFRF and a x i a l flow p r o f i l e s s i g n i f i c a n t l y overshoot the maximum a d i a b a t i c f l u i d temperature, y , w h i l e the CPRF p r o f i l e a l s o does but t o an almost i m p e r c e p t i b l e e x t e n t . The creep behavior i s d i r e c t l y r e l a t e d t o the degree o f temperature overshoot, s i n c e i t i s caused by c o o l i n g o f the over-temperature c e l l s t o l e s s than o r equal t o y , which, o f course, cannot be ex ceeded a t steady s t a t e . Thus i n F i g u r e 6, the a x i a l flow and CFRF p r o f i l e s continue t o creep u n t i l the c e l l s near the bed e x i t c o o l . The degree o f overshoot, and hence, p r o f i l e creep, i s a func t i o n o f the i n i t i a l bed temperature, y-jo- study was conducted i n which the i n i t i a l bed temçerature was v a r i e d keeping a l l the other parameters constant. As yjQ was increased from 1.0 t o 1.17, t h e p r o f i l e s f o r a l l three flow modes i g n i t e d c l o s e r t o the bed en t r a n c e . A l l the p r o f i l e s were s t a t i o n a r y a t 30 minutes from s t a r t up except f o r the CFRF p r o f i l e f o r yjQ = 1.17, which overshot the maximum a d i a b a t i c f l u i d temperature and was s t i l l c r e e p i n g . A l s o , for yjQ = 1.17 the CPRF and a x i a l f l o w p r o f i l e s were the c l o s e s t together, w h i l e the CFRF was f a r t h e s t from the other two and mov ing away. Thus, f o r i n i t i a l bed temperatures exceeding the feed temperature, steady s t a t e m u l t i p l i c i t y tends t o accentuate the " e a r l y - l a t e " r e a c t i o n zone phenomenon observed f o r the unique steady s t a t e p r o f i l e s . m

m

A

Conclusions In g e n e r a l , CPRF i s the b e t t e r mode o f o p e r a t i o n f o r the RFBR when m u l t i p l e steady s t a t e s are p o s s i b l e . I n a d d i t i o n t o e x p e d i t ing the approach t o steady s t a t e , the establishment o f the CPRF p r o f i l e e a r l y i n the bed i s an advantage i n cases where the r e a c t i o n zone g r a d u a l l y creeps toward the bed e x i t due t o c a t a l y s t de a c t i v a t i o n . When o n l y unique steady s t a t e s are p o s s i b l e and/or f o i p a r a l l e l and s e r i e s r e a c t i o n s , the p r e f e r r e d flow mode may depend on other c o n s i d e r a t i o n s .



Figure 6. Transient behavior of temperature profiles in ÇPRF, CFRF (p = 0.25), and axial flow ( = 0.25, P = HkP , T = 667°K, T = 883°K, β = 5 M/H = 1.67) P

0

a

G

0


45.

CALO


561

Notation [see a l s o Vanderveen, e t a l . (6)] Aj Fj Gj Hj

= = = =

defined i n t e x t Oj d e f i n e d by Eq. [6] R r d e f i n e d by Eq. [5] U,u dimensionless HTU f o r heat t r a n s f e r v,w k j = dimensionless r a t e constant y Mj = dimensionless HTU f o r mass transfer f

3 = (-AH)k /hfT γ = (-ΔΕ)/RgT g

0

0

= defined i n text = radius = i n t e r s t i t i a l f l u i d ve locity = r e a c t a n t mole f r a c t i o n •» T / T Q (dimensionless temperature)

oj = k j / ( l + k j ) ρ = Ri/R

2

S u b s c r i p t s and S u p e r s c r i p t j m η 0

= c e l l number = maximum = last cell = feed c o n d i t i o n s

= p a r t i c l e phase 1 = inner radius 2 = outer r a d i u s

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.

Hlavacek, V . , and Kubicek, M . , Chem. Eng. S c i . (1972), 27, 177. Dudukovic, M. P . , and Lamba, H. S., 80th AIChE National Meet ing, Boston (1975), paper #576. Cimbalnik, Z . , et al., 2nd CHISA Cong., Czechoslovakia (1965). Raskin, A. Y a . , et al., Theor. Found. Chem. Tech. (1968), 2, 220. Raskin, A. Y a . , and S o k o l i n s k i i , Yu. Α., Khim Prom. (1969), 45, 520. Vanderveen, J . W., Luss, D . , and Amundson, N. R., AIChE J . (1968), 14, 636. Wicke, E., Chem. Ing. Tech. (1965), 37, 892. Ervin, Μ. Α., and Luss, D . , AIChE J. (1970), 16, 979. L i u , S.-L., and Amundson, N. R., IEC Fund. (1962), 3, 200.


46 Flow Control Operation of a Plug-Flow Tubular Reactor with High Heat Diffusivity Y U . P. G U P A L O , V . A . N O V I K O V , and Y U . S. R Y A Z A N T S E V The Institute for Problems in Mechanics, USSR Academy of Sciences, Moscow, USSR

1. Formulation of the problem I t i s known that c o n t r o l l e actors at n a t u r a l l y unstable conditions should be of i n t e r e s t i n the design of some commercial reactors because the unstable or s o - c a l l e d intermediate s t a t e s may o f f e r a d e s i r a b l e compromise between a s t a t e of very low a c t i v i t y or conversion on the one hand and a s t a t e of poor s e l e c t i v i t y on the other [1]. In the present paper the model of a t u b u l a r r e a c t o r with n e g l i g i b l e mass diffusivity and high diffusivity of heat i s considered. The dimensionless equations with the boundary and initial conditions governing the unsteady mass and heat t r a n s f e r i n the one-dimensional plug flow t u b u l a r r e a c t o r with high heat d i f f u s i v i t y can be w r i t t e n i n the form


46.

GUPALO ET AL.

Flow Control of Plug Flow Tubular Reactor

563

where X i s a s p a t i a l coordinate ( 0 ≤ X ≤ L), L i s a reactor length, t i s a time, c i s a concentra t i o n of r e a c t i v e species i n r e a c t o r volume, c is a feed concentration of r e a c t i v e s p e c i e s , ξ i s an ex tent, u i s flow v e l o c i t y , ε i s the r a t i o of a bulk fluid volume to a t o t a l one, Τ i s a temperatu re; V , S are a r e a c t o r volume and a surface of r e a c tor w a l l s , * g density and a heat capacity o

c

of f l u i d ;

j* , c s

Q

a

r

e

a

are a density and a heat capacity

of c a t a l y s t , T i s a feed flow temperature, h i s a heat of r e a c t i o n for reaction rate, Ε i s a gas constant, u* i s c h a r a c t e r i s t i c reactant flow v e l o c i t y * In obtaining Eqs (1.1) and (1.2) mass d i f f u s i v i t y has been neglected; high d i f f u s i v i t y of heat and f i r s t order Arrhenius k i n e t i c s f o r one step exother mic chemical r e a c t i o n has been assumed. These assump t i o n s can serve as a f a i r approximation f o r some kinds of f l u i d i z e d - b e d r e a c t o r [g] . The Eq. (1.2) can be derived f o r m a l l y by i n t e g r a t i o n over the t o t a l length of the r e a c t o r . The s o l u t i o n s of the steady-state forms of Eqs (1.1) and (1.2) can be w r i t t e n as Q

The dependence of the steady-state temperature Θ on parameter ν f o r f i x e d values of θ£ , and g obtained from Eq. (1.6) are presented i n F i g . 1, which shows that the m u l t i p l i c i t y of the steady s t a tes i n p o s s i b l e . F o r example three steady-state tem peratures correspond to the value ν = v » I t i s known that the upper and lower steady s t a t e s 0 , 0"" are s t a b l e , meanwhile the intermediate steady s t a t e i s unstable [ 3 ] · 0

e

+

2. The method of c o n t r o l Consider the p o s s i b i l i t y of s t a b i l i z a t i o n of the un^ s t a b l e intermediate steady s t a t e by the method of p r o p o r t i o n a l c o n t r o l (see, f o r example [ 4 ] ). Up t o now the theory of chemical r e a c t o r c o n t r o l was f o c u -



564

sed primerely upon the c o n t r o l of a s t i r r e d r e a c t o r 1^2 · The f i r s t example of the a n a l y s i s of the un stable steady s t a t e s t a b i l i z a t i o n f o r d i s t r i b u t e d pa rameter r e a c t o r was given r e c e n t l y by Oh and Schmitz

[1]· In the case under consideration the c o n t r o l l e d v a r i a b l e i s the temperature θ and the manipulated v a r i a b l e i s the flow v e l o c i t y ν . The feed back r e l a t i o n s h i p i s as f o l l o w s v ( t ) = v { l + ά [ θ ( ΐ - ΐ ) - θ|]} 0

(2.1)

4

where θ| i s intermediate steady-state temperature, f j i s a time l a g , d i s t a b i l i z a t i o In view of (2.1 tively, -g exp (- β/θ°) - θ° + 1 - exp — = : a.= 0 (2.2) v [ l + d(9°- 9|)J The r e l a t i o n s h i p (2.2) shows that i n the pre sence of c o n t r o l the upper and lower steady-state temperatures depend on parameter d and can be de termined as the i n t e r s e c t i o n points of curve 1, with l i n e s θ° = θ| + d ( v - v ) . corresponding to d i f f e r e n t values of d ( l i n e s 2-7) i n F i g . 1; The dependence of θ° on d r e s u l t i n g from Eq. (2.2) are pointed out i n F i g . 2. I t can be seen that f o r d > d the i n termediate steady s t a t e turns to be the lower one and f o r d > d± i t becomes the s i n g l e steady s t a t e . The value of d can be obtained from the c o n d i t i o n that 0

c

c

the l i n e θ° = 9Î + d ( v - v ) i s tangent to the curve 1. 0

β d

= —

?

v

0

Γβ g exp(- β/θ|) exp L E . +

I f the i n e q u a l i t y dy s t a t e condition considered as d>d_.

d >d

Ί (

2

>

3

)

takes place the s t e a -

θ° = θ| should s a t i s f y the s o - c a l l e d slope f o r s t a b i l i t y . Therefore one can expect the system of r e a c t o r c o n t r o l to be e f f e c t i v e This q u a l i t a t i v e conclusion requires r i g o -

rous approaches. In order to analyse the s t a b i l i t y of steady state under c o n t r o l , ire use the small ^pertur bation method. By s u b s t i t u t i n g Θ ( Ό = 9 ° + e ' W and ξ(χ,-ε) = ?/(x) + ξ ' ( χ , Ό i n t o Eqs (1.1)-(1.4) and (2.1) one can obtain by the Laplace transform the so l u t i o n f o r θ'(C) and ξ ' ί χ , Ό . I t can be found that a l l the s i n g u l a r i t i e s of t h i s s o l u t i o n s are poles and


46. GUPALO ET AL.

Flow Control of Plug Flow Tubular Reactor

565

are determined by the roots of c h a r a c t e r i s t i c equation. Y(s)

= s

2

0

0

+ a^s exp (- sv £

«—h-

-

-

b

exp(- | ) ] 0

C

1 + exp (- | ) ]

θ " -

0

, bχ exp ( - -o)

( p - i s the Laplace transform v a r i a b l e ) . The neces sary and s u f f i c i e n t c o n d i t i o n f o r s t a b i l i t y of the c o n t r o l l e d r e a c t o r to small perturbations i s that the r e a l parts of the roots of Eq. (2.4) are negative. Therefore the c o n t r o l l e d r e a c t o r are s t a b l e i f a l l the roots of the Eq. (2.4) l i e i n the r i g h t h a l f - p l a ne of the complex plane s = χ + i y . We chose the countor Γ » Γ + Q where fj i s the r i g h t h a l f - c i r c l e of large radius R with the centre l o c a t e d i n Zero point and Γ i s the part of the imaginary axis l y U R . I t can be shown that the increament of argument V(s) on Π| at R oo i s equal t o 2^r f o r any value of a · Λ

ζ

3· The i d e a l c o n t r o l i n Eq.

In the s p e c i a l case of i d e a l c o n t r o l by putting (2.4) f j , = 0 one can obtain

Y ( s ) = s 2 + fljs -

+ £ 2 ( 1 - e~ )/s s

(3.1) £,=

- a3 " 4» a

&z=

a

5

- a 6f

^3= i a

+

a

2

The f u n c t i o n ( 3 · Ό depends on s as w e l l as on three parameters & , Ω,χ . To analyse the s t a b i l i t y of c o n t r o l l e d r e a c t o r we have to f i n d thedomain i n three-dimensional space ( Çl^ Ω > ^3 ) ^ k& k η

9

2

n

w


c


566

there are no roots of V ( s ) with p o s i t i v e r e a l p a r t s . To do t h i s we consider the behaviour of the f u n c t i o n Y ( s ) on Γ , I t can be seen that the r e a l p a r t s of roots of Y ( s ) vanish f o r those values of , Ώ-ζ* Ώ which belong to the surface defined by the f o l l o wing equations 2

3

= -y

ο

2

sm y

+ a y

Ί

,

o

=

Q

3

1 - cos y

—z—

(3.2)

1 - cos y

04 y < 0 0 The a n a l y s i s of Eq ( 3 · 2 ) reveals that f o r the domain bounde

and plane Sl - - f l the increament of argument V (s) on i s equal to -2X . Therefore the t o t a l i n c r e a ment on Γ -+ i s nought and i s the s t a b i l i t y 1

ή

domain because i t contains no roots of V (s) with po s i t i v e r e a l parts. The r e s u l t s obtained permit to analyse the i n fluence of the c o n t r o l on the intermediate steady s t a t e s t a b i l i t y . The s e c t i o n of the s t a b i l i t y domains and the point A corresponding to intermediate steady temperature θ° = θ| f o r d i f f e r e n t values of parame ter d are shown i n F i g . 3 . The s e c t i o n of s t a b i l i t y domain corresponding to d = 0 i s dashed i n F i g . 3 · I t i s seen that the intermediate steady s t a t e becomes s t a b l e when d > d . I f d = d the point A achieves the boundary of the s t a b i l i t y domain. The value d can be obtained from the equation Sl^—fï^, which i s i d e n t i c a l to Eq. (2.4). Thus the intermediate steady s t a t e becomes s t a b l e when i t turns to be the lower steady-state. The numerical a n a l y s i s shows that i n the n o n l i n e a r case the value of d depends on the pert u r b a t i o n amplitude. F o r example i f d = d the i n t e r mediate steady s t a t e i s s t a b l e as the temperature perturbations are l e s s than Δ θ (see F i g . 2). 2

4. The influence of time l a g I t has been shown that i f d > d and f = 0 the c o n t r o l l e d steady s t a t e i s s t a b l e . To study the e f f e c t of time l a g on s t a b i l i t y we consider the i n crease of argument of f u n c t i o n (2.4) on f f o r d i f f e r e n t values of t] t o propose (5) d i d not have a s u f f i c i e n t l y l a r g e v a r i a t i o n o f p^Q t o d i s c r i m i n a t e between (5) and (6) w h i l e a t h o r o u g h e x a m i n a t i o n o f a l l a v a i l a b l e ε - d a t a i n [1] i n c l u d i n g some w i t h a 30-fold v a r i a t i o n o f p^Q p o i n t s t o (6) as the most l i k e l y e q u i l i b r i u m s t e p ? Th s t a t i s t i c a l a n a l y s i f -dat show t h a t n=m=2 i s t i o n o f i n t e g e r exponent model 2. Both (5) and (6) are based on d i f f u s i o n f r e e d a t a o b t a i n e d w i t h e i t h e r an e q u i l i b r a t e d gas phase (no o v e r a l l r e a c t i o n t a k e s p l a c e ) o r w i t h l i q u i d s d i s p e r s e d w e l l enough t o a v o i d d i f f u s i o n e f f e c t s . The v a r i a t i o n o f ε w i t h l i q u i d l o a d i n g i s shown i n F i g . 1 which i s based on [5J . L i n e C i s d e s c r i b e d by ( 6 ) . A s o l u b i l i t y o f 4-6$ i n K S 0 a t 400-600^0 i s found i n [7] and B o r e s k o v [8] i d e n t i f i e d by ESR two v(4) s p e c i e s below 480°C. The e x i s t e n c e o f c r y s t a l s o f a p r e c i p i t a t e d v(^) compound i s mentioned i n [5>6.»7.1 · 2

Y

liq

Z

Y

2

7

( 7 )

solid

P r e c i s e measurement o f the s o l u b i l i t y o f Y i s d i f f i c u l t but q u a l i t a t i v e l y we know t h a t [Y_ i n c r e a s e s below SΟ

HQ

450°C when the c a t a l y s t i s reduced by SO2, p r o b a b l y d i r e c t l y c o n n e c t e d w i t h the i n c r e a s e o f ε by (5) o r (6). A r r h e n i u s p l o t s o f the a p p a r e n t r a t e c o n s t a n t f o r S 0 - o x i d a t i o n i n v a r i a b l y show a break a t ^450*0 and t h e apparent a c t i v a t i o n energy i s o f t e n v e r y h i g h a t l o w t e m p e r a t u r e [_8,_4]. T h i s phenomenon i s c l e a r l y c o n n e c t ed w i t h the l o w e r o x i d a t i o n l e v e l o f V a t low tempera t u r e , p r o b a b l y enhanced by l i q u i d d i f f u s i o n r e s i s t a n c e and accompanied by i n a c t i v a t i o n o f v' '. To improve the low t e m p e r a t u r e a c t i v i t y o f vanadium c a t a l y s t , a p r i m a r y g o a l i f the cumbersome i n t e r a b s o r p t i o n c o n v e r t e r d e s i g n i s t o be a v o i d e d , our u n d e r s t a n d i n g o f t h e s e complex phenomena must be advanced. 2

Experimental 190 S 0 - o x i d a t i o n r a t e measurements were o b t a i n e d i n a r e c i r c u l a t i o n r e a c t o r d e s c r i b e d i n [2] . The experimen t a l s t r a t e g y i s summarized i n Table I . 2



584

I:

ournmary

data points

1)

of

rate

measurements

1)

Vanadium cent et it

2)

1

24

2.85

Orthogonal

d e s i g n a t 480 C. 0. : V.h-V>i, :Τ^:

·?

16

2.85

Orthogonal

d e s i g n a t 480 C.

Oy

22-48%, S 0 :

9-20%, S O ^

3

19

2.85

Orthogonal


0:

7-16%, SO-,:

2.9-6.5%, SOy

4

16

2.85

y'40-550 C,

10 ·" t e m p e r a t u r e

.Uep.-;. and

s t a n d a r d gas

composition

5

lb

2.85

'400-480 C,

10 C t e m p e r a t u r e

s t e p s and

s t a n d a r d gas

composition

1?

1.37

3δΟ-46θ 0,


s t e p s and

s t a n d a r d gas

composition

*430-570 C,

10

C temperature

s t e p s and

s t a n d a r d gas

composition

s t e p s and

s t a n d a r d gas

composition

?

?

7

20

8

12

9

8

14.2

10

8

24.2

380-450 C,


11

20

21.1

Orthogonal


Oy.

6-16%, SO.,:

12

17

21.1

Orthogonal

d e s i g n a t 530 0.

Oy.

7.2-16*, S 0 :

21.1 7.87

2.1-ό.5%, 3 0 ^ :

2.5-6?

7-17% 2.2-6%

400-48 400-48

3-6.8%, S O ^ 2

3-7%,

SOy.

1.9-5.4% 2-5.2%

The s u p p o r t i s c o n t r o l i e d - p o r e g l a s s (CPC, E l e c t r o - N u c l e o n i c s , I n c . F a i r f i e l d , N.J.) w i t h p u r e v o l u m e 1.02 c m / g , p o r o s i t y 69%, p o r e r a d i u s 1530 A, p a r t i c l e s i z e 2 0 / 3 0 ";θ then εε =S p r o v i d e s an e x t r a e q u a t i o n which combinea w i t h the p r e v i o u s equa t i o n s g i v e s Ν, ε and ε f o r ε 100

ς

Model

6

?a c o n f i d e n c e

y kcal/mole

Standard error

SSQ£

SSQN

0.^8*0.05

7.2±2

11

0.6

O.b

0.35±0.03

i4.0±3

13

0.6

l.u

k,, α,, a

?

becomes i n d e t e r m i n a t e

since the f i r s t

]

1

step i s close t o equilibrium.



590

The e q u i l i b r i u m c o n s t a n t s and Kp o f Table I I a r e n o t d i r e c t l y c o m p a r a b l e w i t h t h o s e i n 15) a n d ( 6 ) , s i n c e t h e l a t t e r p a i r i s based on measured e and i n c l u d e p r e c i p i t a t e d V"(^'. A t h i g h Τ w h e r e no v ' ^ ' i s p r e c i p i t a t e d t h e agreement i s v e r y good f o r K]_. F o r ε SO^

η

2

ΊΠ

p

Ν,Ν^,Ν^,Ν^^

T u r n o v e r f r e q u e n c y , moles/(gatomV)/sec

p,p^

Pressure, p a r t i a l pressure,

Rg

Gas

S ,S y

SSQ,SSQ ,SSQ £

Τ V"

atm

constant

Solubility

y Q

N

Sum

of

defined i n

1

1 ε ε C

9

1

d.

1

Eq.13

o f squares d e f i n e d i n E q . l 6

Temperature T o t a l c o n c e n t r a t i o n o f vanadium (gatomV) /cm* α ,α ,β ,3 Power law exponents T

e q u ·i lτi bκr i u· m

in liquid,

0

d

Degree of reduction i n the liquid phase [V ' L . /V, T o t a l f r a c t i o n o f vanadium r e d u c e d t o ' The The ff rr aa cc tt ii oo nn ooff tt oo tt aa ll vanac vanadium c o n t e n t which i s d i s s o l v e d i n the l i q u i d v

ο Q


48. GRYDGAARD ET AL.

S0

2

Oxidation on Molten V 0-K S 0 2

2

2

7

Catalyst

595

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.

V i l l a d s e n , J. and L i v b j e r g , H., "Supported Liquid phase c a t a l y s t s " , C a t a l . Reviews, Chem.Eng. (1978) L i v b j e r g , H., Jensen, K . P . , and V i l l a d s e n , J., J. Catalysis (1976) 45 216 Mars, P. and Maessen, J.G.H., J. Catalysis 10 1 (1968) Boreskov, G . K . , Polyakova, G . M . , Ivanov, Α.Α., Mastikhin, V . M . , Dokl.Akad.Nauk. (USSR) 210(3) 626 (1973) (Engl. t r a n s i , p. 423) Mastikhin, V . M . , Polyakova, G . M . , Z y u l k o v s k i i , Y., Boreskov, G . K . , Kinetics and Catalysis (USSR) 14 1219 (Engl. t r a n s l . ) (1970) H ä h l e , S. and (USSR) 12(5) 127 Holroyd, F . P . B . and Kenney, C . N . , Chem.Eng.Sci. 26 1971 (1971) Boreskov, G . K . , Davydova, L.P., Mastikhin, V.M., Polyakova, G . M . , Dokl. Akad. Nauk. (USSR) 171(3) 648 (1966) (Engl. transl. p. 760) Jensen-Holm, H . , Ph.D. Thesis, Technical U n i v e r s i ty of Denmark, Lyngby, To appear 1978.


INDEX A Absorbance sample cells, gas-phase .. 12 Absorbed radiation 276 Absorption 10,57 without reaction, mass transfer in .. 329 Acetic acid 574 Acetic anhydride hydrolyse, isothermal run of 42 Acetylene 527, 535 conversion 531 hydrogénation of 526 Acid, acetic 574 Acrylonitrile-methyl methacrylat (ANMMA) 17 Activation energy 34,490 of CO-consumption 32 of hydrocarbon formation 32 rate equation parameters 22 values of the 507 Active monlith, entrance effect in 80 Adiabatic calorimetry, accumulaton method .. 37 methanator 63,70 pilot plant data 290 reactor multiplicities 473 run 90,91 Adsorbed species, spectra 3 Adsorber-reactor 50, 52 specifications 53 use of 59 Adsorption effects binary 59 of multicomponent 51,57 of water on ieri-butanol 58 in heterogeneous catalysis 50 mechanism, Langmuir-Hinchelwood 283 reaction studies 57 studies, transient 55 types of reaction heat 63 of water on alumina 56 Advantage of parallel passage reactor 70 Agitation rate on performance, effect of 452 Agitation tests 451 Air-lift fermentors 154-157 Algorithm, Gears 103 Algorithm, Newton-Raphson 88

Alumina adsorption of water on 55, 56 cobalt-molybdenum on 448 dehydration of feri-butanol on 57 dehydration of 2-propanol over 10 Ammonia, catalytic synthesis of 550 Amplitude, stability diagram 504 Amplitudes of temperatures 505 Analysis equipment, cyclic feed makeup apparatus, effluent 529 Analysis, Semenov-type dimensional.. 173 Analytical evaluation of the plugging time 228

continuous culture 166 effluent analysis equipment, cyclic feed makeup 529 Arab Light naphtha 287, 288 Argon 314,477 feed mixture 482 Aromatic sulfonation 327 Aromatics 288 Arrhenius diagrams for reaction rates 31 equations 165 expressions 588 kinetics 563 law of 500 parameters, kinetic 318 plot ( s ) 30, 77,310,583, 586,587 Ash-free coal 307 Asynchronousmotor 17 Autoclave, back-mixed catalyst 293 Auto-oxidation system 350 Autothermal operation 86 Axial conduction 101,249 dispersion 426-428 coefficient 308 model 242-246,307,359 distributions 115-118 flow 554-557 in packed beds 541 steady state temperature profiles 552 mixing 304,338-340,343 effect of diameter on 342 gas flow rate on 342 packings on 345 plates on 345

599


600


mixing (continued) of liquid in packed bubble col umns of large diameter 337 of liquid in perforated plate col umns of large diameter 337 Peclet numbers 242,249 profiles 360 temperature for different thermal conductivities 102 thermocouple 412 velocity field development 76 Axisymmetric jets 6

Β Back-mixed catalyst autoclave 293 Backmixing model, countercurrent .... 400 Bacterial growth, kinetical analysi of unbalanced 16 Bacterial growth, steady state of 172 Bacterial time lag 172 Balance equation, mass 430 mass 64,66 on transport cell, force 419 Barocel pressure transducer, datametrics type 53, 531 Base metal catalyst, oxidation of carbon monoxide over a 83 Basket reactor, multiphase kinetic studies with a spinning 447 Basket stainless steel reactor, continuous flow spinning 527 Batch culture 164 Batch operation 431-433 Batch reactor, recirculating 6 Beam, reference cell ir 6 Bed(s) axial flow in packed 541 catalytic reactor, fixed 513 catalytic reactor, isothermal heterogeneous 512 freely bubbling 400 gas in a bubbling fluidized 436 height 441 variations of composition with 442-445 volumetric gas flow and 439 parameters 412 reactor(s) catalyst effectiveness factor in trickle387 cell model studies of radial flow, fixed 550 design of a moving 540 fixed 539 fluidized563 Gulf-patented segmented 304 modeling the slugging fluidized .. 400

reactor(s) (continued) moving 543 performance equations for trickle389 trickling fixed 447 round-nosed slugging 401 slugging fluidized 404 Behavior of the reactor for finite perturbations, transient 568 Bench-scale heat flow calorimeter 37-40,43 Bench-scale reactors 303 Bendixon theorems 487 Benzene 288,315-322, 327,334 composition profiles, paraffin and .. 288 to maleic anhydride, oxidation of .. 440 molar concentrations of 323 production of maleic anhydride from 215 with S 0 , sulfonation of 327 /styrene, molar concentrations of .. 321 sulfonation of 328-334 Benzenesulfonic acid 327 Big Horn coal, kinetics of catalytic liquefaction of 303 Binary adsorption effects 59 Binder-Schmidt method 67 Biomass, production of 153 Biot number 393,396 Biphenyl 451 Boric acid 348 Boundaries, R A 175 Boundary condition(s) 66,88,104,541 finite bed 247 infinite bed 241 Bubble column (s) 337,341-343,360 C0 -interphase mass transfer in a 359 design, determination of fluid dynamic parameters in 372 gas 401 phase 440 size 380 Bubbling fluidized bed, gas in a 436 Bubbly flow regime 373, 374 Butadiene 524 hydrogénation of 515 Butane 524 oxidation of 574 terf-Butanol dehydration 57, 58 Butanol, hydrogénation of 2-butanone into 2414 Butanone 411-414 1-Butene oxidation 479, 482 Byproducts, diversity of 350 3

2


601

INDEX

C CH-oxidation process, improvement of the 349 Calcium sulfate 225 Calorimeter, bench-scale heat flow 37-40,43 Calorimetry adiabatic accumulation methods .... 37 differential scanning 181 isoperibolic accumulation method .. 37

Candida tropicalis

154

Capillarity 417 Caprolactam, preparation of 348 Carbon dioxide formation of 488 gas phase mole fraction of 367 interphase mass transfer in a bubble column 35 liquid phase partial pressure of 369 Carbon monoxide 30, 482 and 1-butene oxidation, limit cycles during simultaneous 479 concentration s ) ....117,118,463,468,492 consumption 32, 35 conversion 27 dependence of selectivity on 28 rate of 492 hydrogénation 26 inhibition by chemisorption 490 multiple steady states for 2% 480 oxidation 83, 465,466,476, 491 in an integral reactor 461 over platinum 475 steady state multiplicity during .. 477 Carbon oxides, methanation of 63 Caribbean residues 255-262 Carrier solvent 307 Catalysis adsorption in heterogeneous 50 of P ( O C H ) isomerization 44 Ziegler 140,149 Catalyst(s) activity 29,255 coked 210 HDS 208 age, relative 258,260 autoclave, back-mixed 293 basket, annular 449 basket, reactor development— 450 bed concentration changes 68 concentration profile in the 67 diffusion coefficient in the 66 temperature 414 catalytic oxidation reactions over supported platinum 476 cobalt-molybdate ( C O M O X 1661) 207,210 3

3

Catalyst ( s ) ( continued ) copper chrome "aero ban" 84 deactivation 29 by fouling 201 mechanism of 255 through pore mouth plugging .... 254 dynamic studies of acetylene hydrogénation on nickel 526 effectiveness 387,393,394 hydrogénation of 2-butanone on a ruthenium 411 industrial 585 Kieselguhr 513 life in a stirred-tank reactor 260 limit cycle phenomena 475 manganese-containing 26 oxidation of carbon monoxide over

molten V 0 - K S 0 582 particles 417 deactivation of a single 255 pellets 389,391,462 performance 29,35 poisoning in monolithic 110 pretreatment 35 properties 195,462 Pt-alumina 463,466 reaction rate on the 217 thermal conductivity of porous 189 utilization, selection of system to determine maximum 428,429 wetting 387,388,427 zeolite cracking 288 Catalytic cracking 440 decomposition of hydrogen peroxide, nitric acid 505 hydrogénation of acetylene, ethylene, ethane, vapor phase .. 526 liquefaction processes 303, 306 mufflers 550 oxidation reactions over supported platinum catalyst 475, 476 partial oxidation reactions 215 reactions effect of periodic operation on the selectivity of 512 kinetic modeling for oscillatory .. 487 vapor-phase 293 reactor, fixed bed 513 reactor, isothermal heterogeneous fixed-bed 512 recycle reactor, single-wafer 13 reformer, fixed bed 283 synthesis of ammonia 550 Catalyzed reaction, tube wall 74 Catalyzed reactors 98 2

5

2

2

7


602


Column(s) Cell(s) bubble 337,341-343,360 aromatic sulfonation in a stirred .... 327 C0 -interphase mass transfer in model studies of radial flow, a bubble 359 fixed-bed reactors 550 design 372 number 555,556 of large diameter 337 after a shift in temperature 169 liquid/liquid spray 539 fractional yield as function of 558 Comparison with experimental data Centripetal radial flow, ammonia for sulfation of fully calcined yields for 550 limestone 231 Channels, effect of multiple 103-107 Complex gas phase reactions, develChemisorption, C O inhibition by 490 opment of reaction models for .... 313 Chemisorption of oxygen 488 Composition(s) Chlorination of saturated Arrhenius plot of reaction rate hydrocarbons 440 with gas 587 Chromatograph with bed height, variations 442-445 flame ionization type gas 528 effluent 530 gas 315, 513 gas-liquid 20 Chromatographic method, gas paraffin and toluene 288 Chromatography 514 profiles 288 Churn turbulent regime 373,374,379 paraffin and benzene 288 Closed (batch) modes of operation .... 4 steady state 528 Coal Computer ash-free 307 -aided development of the cyclokinetics of catalytic liquefaction hexane oxidation process 348 of big Horn 303 digital 7 moisture-free 307 IBM/1800 6 particle dissolution, mechanism of . 303 interface, spectrophotometer6 solvation 304, 310 program description 54 Cobalt-molybdate catalyst simulation 569 ( C O M O X 1661) 207 typical temperature oscillation Cobalt-molybdenum on alumina 448 from 501 Cocurrent cooled reactors 218 Concentration s ) anol 349 -countercurrent movement 539 anone 348-349 flow 216,364 axial distribution 117 gas-liquid tube reactor 329 balance 540 operation 86 benzene 323 reactors 220, 222 carbon monoxide 463, 468, 492 runs 90,93 against D a number, residual iodine 128 system 215 ethylbenzene 323 tube reactor, aromatic sulfonation ethylene 323,531 in a 327 ethylene/styrene 321 Coefficient gas phase 366 axial dispersion 308 glucose 165-171 diffusion 66, 77 hydrogen feed 531 gas-liquid mass transfer 311 hydrogen/styrene 321 gas phase dispersion 379,381 integral reactor 21 heat transfer 8, 9, 45, 89, 241,249,498 oscillation of 568 liquid phase dispersion 379,380 perturbation, single inlet 461 mass transfer 365-367 polymer 143 temperature 53 profile(s) 67,72,230,235,261 Coil design equations, cracking 271 ethylene 535 Coke 201,258 pulses in the regime of isothermal catalyst activities 210 multiplicities, transient deposition 207,209 response to 461 Collocation method 542 of a rectant species 441 orthogonal 67, 103 -residence time curves 20 of solution, perturbation/ 232 2


603

INDEX Concentration ( s ) ( continued ) of styrene/benzene 321 styrène 323 sulfur 255 valualdehyde 295 vanadium 255-259,588 Conductivity 101,102 axial 249 model for prediction of the r a d i a l . . . 247 molecular 248 of a pellet, thermal 191 of porous catalysts, thermal 189 radial 250 static 249 thermal 190,194,195,315 turbulent 248,249 Conductometer 192 Configurations, mixed flow Constant matrix, selectivity rat Constant, realtime activity rate 283 Consumption, C O 32,35 Contacting efficiency 395,397 Continuity equation 271 steady state 73 Continuous culture 164 Continuous flow stirred tank reactor 125,337,498 Continuum heat transfer models, homogeneous 239 Controlled reactor, stability of 565 Convection 273 flow model, diffusion/ 577 Convective transport of vorticity 74 Conversion 515, 517 acetylene 531 enhancement, effects of pulse on 469-472 of ethane 544,546 measured oscillations of temperature and conversion 508 nitric oxide 550 plot of selectivity vs 520 plot of yield vs 520 rate of C O 492 selectivity, yield 514 vs. space velocity 68, 69 time-averaged 505 Convertor, concentration and velocity profiles in the entrance region of a monolithic 72 Coolant, flowrate of 220 Coolant pass reactors 221 Copolymer approximate kinetic form ( C P A F ) 181,182 Copolymer systems, simulated R A boundary for 178 Copolymerization 149,173 Copper ...^ ^ 191 chrome "aero ban" catalyst 84 Corrsin's expression 130

Countercurrent backmixing model cooled reactors flow movement, cocurrent operation reactor reactor-heat exchanger run system trickle-bed reactor Cracking furnace, thermal Crossflow monoliths Curve, hysteresis Cycle(s) experimental limit limit multipeak

372 400 218 216,363 539 86 215,220 90,92 222 414 274 83-85 477 493 500,506 494

simple 494 simulated limit 493 during simultaneous C O and 1-butene oxidation 479 three-peak 494 Cyclic feed makeup apparatus effluent analysis equipment 529, 533 form, new model mechanistic 403 runs 517 Cyclohexane conversion 349,352 Cyclohexane oxidation 354-356 process, computer-aided development of the 348 Cyclohexanol 348 Cyclohexanone 348 Cyclohexylhydroperoxide intermediate, decomposition of the 349 Cyclohexyl radicals 350 Cyclone reactor 328-334 aromatic sulfonation in a 327, 333 selectivity in the 333 D Damkohler ( D a ) number 75-79,128 Dammitol, oxidation of 292, 294 Danckwert conditions 541 Data, fixed bed kinetic 59 Data, kinetic 586 Datametrics type 531 barocel pressure transducer 53 Davidson, model of Hovmand and 408,409 de Acetic—Thodos correlation 466 Deactivation 204,206 by fouling, catalyst 201 mechanism of catalyst 255 poisoning mode of 202 pore mouth plugging mode of ... 202, 254 of a single catalyst particle 255



604

Diffusion (continued) Decomposition of hydrogen peroxide, pore 226 nitric acid, catalytic 505 process 420 Decomopsition reactions of hydro regime, kinetics of the liquid 590 carbons, thermal 313 resistance 225 Dehydration liquid 592 of ieri-butanol on alumina 57, 58 zone, interface 327 of 2-propanol over alumina 10 7 Dense-phase gas 401 Digital computer 17 Dense phase voidage 438 Diphenyl (Dow Therm) Diphenyl sulfone 327 Density 307,308,426-428 function, residence time 572 Dispersion, axial Dissolution, mechanism of coal parameters 167 particle 303 residence time 576 Distribution(s) Deposits correlation of straight-chain coke 207 hydrocarbons, product 34 on the desulfurization activity, of emission breakthrough and inter effect of metal 262 geometries 201,20 metal sulfide 25 integral reactor 21 Derivative-free simplex method of oxygen 118 (Nelder and Mead) 22 of poison deposition 115 Design product 30 data from a bench-scale heatflow residence time 576-580 calorimeter 37 theory, residence time 571 factors 4 D N A contents 166-171 model, validity of a 359 Dolomite, absorption of S 0 by 225 of a moving bed reactor 540 Dufort and Frankel method 67 of multitubular reactors 214 Dynamic orthogonal 584 lag 41 central-composite 293 methods 195,196 factorial 585, 586 process 248 Desulfurization 255, 262-266, 550 catalyst deactivation through pore mouth plugging 254 Ε dibenzothiophene 451 Early late reaction zone phenomenon 559 effect of metal deposition on 262 Effective conductivity 248 and H uptake 433 Effectiveness factor 114,395,397 kinetics 447 411 Development, axial velocity field 76 Efficiency, wetting 113 Diameter on axial mixing, effect of . . . 342 Eigenfunction expansion Elliptic differential equations 74 Diameter ratio, heat transfer in packed beds 238 Emission breakthrough at different axial positions 117 Diazo-decompositions temperatureEnergy programmed run 42 activation 34,490 Dibenzothiophene 448 balances 173,540 desulfurization 451 of CO-consumption, activation 32 in white oil 447, 452 consumption 153,159 Differential equation 271 equations, elliptic 74 of hydrocarbon formation, equations, stiff 315 activation 32 reactors 10,15 values of the activation 507 scanning calorimetry ( D S C ) 38,181 thermal analysis ( R T A ) 38 Equation(s) Arrhenius 165 Diffusion continuity 271 coefficient 66 cracking coil design 271 of ethylene in air 77 with the Damkohler number 76 —convection flow model 577 elliptic differential 74 influence, liquid 582 energy 271 limitation region 77, 80 2

2


605

INDEX

Equation ( s ) ( continued ) intrinsic rate mass balance mass transport Michaelis-Menten Monod of motion, Navier-Stokes for oxidation of ethylene pressure drop radical reaction reaction rate with the Schmidt number steady-state continuity Stokes-Einstein for trickle-bed reactors, performance tubeside reactor Wilsons Equilibrator, external hydrogen Equilibrium constant Equilibrium flash Equipment, experimental Escape probability for a particle

416 430 73 164 164 72, 73 80 271 350 414 76 492 73 331 389 21 35 428 585 430 238 572

Experiments, results of loop reactor .... 21 Exponential model 297 Expression, Corrsin 130 Expression, Lennard-Jones 77 Extinction temperature 98,101

F Factorial design, orthogonal Factorial design for reactor gas composition Fan, flywheel/ Feed concentration, hydrogen makeup apparatus effluent analysis equipment, cyclic mixture, argon

586 585 51 531 529 482

teristics or 431 Feedstocks 255 Fermentation 153,154 Fermentors air-lift 154-157 comparison of various 160 Escherichia coli 164 loop 154,159,160 Ethane 535 mechanically stirred 154-156 conversion of 544 performances of various 153 cracking furnace 271 Fick's law 64 gas inlet temperature, measured 439 conversion of 546 "Fines" content 247 Ethane yields 531 Finite bed boundary condition Ethyl acetate 574 Finite perturbations, transient behavior of the reactor for 568 Ethylbenzene 315-322 273 decomposition 320,321 Fire box heat transfer 26, 63 molar concentrations of 323 Fischer-Tropsch synthesis pyrolysis of 313-316 Fixed-bed adiabatic methanator 70 Ethylbenzyl 316 catalytic reactor 513 disintegration of the 318 catalytic reformer 283 Ethylene 207,316-322 kinetic data 59 concentration 531 reactor(s) 539 profile 535 cell model studies of radial flow .. 550 ethane, vapor phase catalytic trickling 447 hydrogénation of acetylene 526 reforming pilot plant, isothermal .... 287 hydrogénation of 512 155 molar concentrations of 323 Flat-blade turbine 220 oxidation of 77,80,440 Flexibility consideration in the design of styrene, molar concentrations of .... 321 multitubular reactors 214 Evaluation of the plugging time, analytical 228 Flow ammonia yields for centripetal Exchanger radial 550 heat 353 axial 554-557 monolithic reactor-heat 83, 89 behavior, fluid 571 systems, simple heat 215 cocurrent 216 Exit profile 144 control operation 562 Expansion, gas 438 countercurrent 216,363 Experimental methods 190 diagram, process 454 Experimental study of velocity and fixed bed reactors, cell model concentration profiles 72 studies of radial 550 Experiments, L P A 317


606


Flow (continued) increases with gas velocity and "fines" content, interstitial 439 laminar 72 methods, heat 37 model, diffusion/convection 577 modes, M R H E 87 modes of operation, open 4 in packed beds, axial 541 patterns in typical ir-cell reactors .... 5 plug 72 polymerization of E P D M polymer, laminar 140 radial 553,554 inlet 541 rate of coolant 220 rate, heat 38 reactor(s) catalyst utilization in a trickl for hydrotreating heavy oil, trickle 425 isothermal continuous 526 plug 428 trickle 431 recycle 584 steady state temperature profiles, axial 552 velocity profile analytic solution for nonuniform viscous 149 Fluid(s) field 216 flow behavior 571 interstitial velocity 551 mixing behavior 571 Newtonian 73, 74 nonNewtonian 149 Fluid dynamic parameters in bubble column design, determination of 372 Fluid dynamic properties 362 Fluidized-bed reactor 563 model(s) 436,438 modeling the slugging 400 Fluxes, heat 273, 277 Force balance on transport cell 419 Formation of C 0 488 Formation rate, straight chain paraffins 33 Foulant deposit geometries 201, 202 Fouling from interactions of pore structure and foulant deposit geometries 201 Fourier law 190 Frankel, Dufort and, methods 67 Frequency factors, rate equation parameters .... 22 spectral 8 stability diagram with curves of equal 502 2

G Gas (es) 63,310 analysis system 513 bubble 401 in a bubbling fluidized bed 436 chromatograph 315,513 flame ionization type 528 method 531 composition, Arrhenius plot of reaction rate with 587 composition, orthogonal factorial design for reactor 585 dense-phase 401 exchange 401,402 rate 441 expansion 438, 440 flow

rate, molar 360 inlet temperature, measured conversion of ethane 546 linear velocity 375-380 -liquid chromatograph 207 interface 428 mass transfer 387 coefficients 311 reactor(s) 351-353 systems 373 tube reactor, cocurrent 329 phase absorbance sample cells 12 absorption, double-beam compensation for 10 concentration 366 dispersion coefficient 379,381 equilibrated 583 intrapellet 463 mole fraction of C 0 367 profile 365 reactions 4, 447 development of reaction models for complex 313 temperature variations 479 profiles 368,369 -solid mixing 51 noncatalytic reactions 226 reactions, pore plugging model for 225 systems 554 solubilities 593 temperature, inlet gas 544 velocity and "fines" content 439 Gears algorithm 103 Geometries, nature of the interaction of the pore structure and foulant deposit 201,202 2


INDEX

607

Glass tubular reactor 207 Global rates 3 Glucose concentration 165-171 Glucose consumption rate 170 Graetz problem 89 Grain models 225 Grain size, variation of 225 Grignard-reagent, formation 44, 45 Growth in batch and continuous culture 168 kinetical analysis of unbalanced bacterial 163 rate 163 reciprocal plots between the specific 167

specific

165,169

at varying temperatures, specific Gulf-patented segmented bed reactor

166

transfer (continued) property, temperature dependence of radiative Henry's law 362, Heptanes Heterogeneous catalysis, adsorption in Heuristic approach to complex kinetics Hexanes Hinschelwood equation, Langmuir— .. Hinschelwood, kinetic models, Langmuir— Homogeneous continuum heat transfer models

47 273 588 288 50 292 288 209 57 239

Homopolymerization

Hougen and Watson kinetic models .. Hovmand and Davidson, model of 408, 409 32,34 Hatta numbers 125 Hydrocarbon(s) chlorination of saturated 440 Hazards, assessment of thermal 43, 45 distribution, steady state, and Heat periodic effluent 529 of adsorption 57 thermal decomposition reactions of 313 types of reaction 63 trace 479 balances in matrix notation 273 306 capacities 41 Hydrocracking reactions 307 diffusivity, flow control operation Hydrodesulfurization 254-261,387 of a plug-flow tubular reactor of residual oils 255 with high 562 of thiophene 207 evolution, rate of 41 exchanger 353 Hydrodynamic entrance effect 89 monolithic reactor— 83, 89 Hydrofluorination of U 0 440 run Hydrogen 288,307, 448 cocurrent reactor93 cycling, feed 533 countercurrent reactor92 donor reactions 306 for the pellet-filled reactor90 equilibrator, external 428 systems, simple 215 feed concentration 531 flow mole fractions of 517, 532 calorimeters 37-40 peroxide, nitric acid, catalytic control principles 38 decomposition of 505 methods 37 reduction of ores 440 rate 38 styrene, molar concentrations of 321 flux (es) 277 -styrene ratio 319 methods, linear 190 sulfide 448 nonradiative 273 uptake, desulfurization and 433 profile 271 Hydrogénation of reaction 41 of acetylene, ethylene, ethane, transfer vapor phase catalytic 526 coefficient 45, 89, 241, 249,498 of butadiene 515 control, method of 38 of 2-butanone 411,414 data 247 carbon monoxide 26 fire box 273 of ethylene 512 mechanism 218, 250 of α-methylstyrene 414 models, homogeneous continuum 239 on nickel catalysts, dynamic in packed beds of low studies of acetylene 526 tube/particle diameter ratio 238 solvent 311 parameters 15 in trickle-bed reactor, butanone 413 H

2



608

Hydrolyse, isothermal run of acetic anhydride 42 Hydrotreating heavy oil, trickle flow reactors for 425 Hyperbolic model 295-298 Hysteresis 53,101 in the conversion-inlet temperature domain 467 curves 99-101,477 in wall-catalyzed reactors 98 I I B M model, equivalence between the SA model and the 133 Ideal mixing ( C S T R ) 14 Ignition point apparatus ( Ή Ρ Α ) , therma temperatures 98,10 zone 101 Industrial reactors, performance of .... 571 Infinite bed boundary condition 241 Information System, (TIS) Technological 352 Infrared beam, reference cell 6 cell-reactors 3-5,10 spectrometer 7 spectrophotometer 4-6 Initiator limitations 175 Instrumentation, thermal 37 Integral reactor 15,17, 462 advantages of 22 carbon monoxide oxidation in an .... 461 concentration 21 experiments 20 temperature distribution 21 Integration constant determination 66 routine, Rung-Kutta variable step size 103 rule, Simpson's 286 Intensity function 576-580 representation of residence time variability 571 Interface axial distribution of fractional active sites at fluid-solid 115 gas/liquid 428 liquid/solid 428 spectrophotometer-computer 6 Interstitial flow increases with gas velocity and "fines" content 439 Iodine concentration against D a number 128 Iodine consumption 126 Ionization chamber, electron impact .. 314 Ionization type gas chromatograph, flame 528

Iron 191 Isobutene 359 Isomerization, of P ( O C H ) 44 Isoperibolic calorimetry, aceumullation method 37 Isotherm, Langmuir 464, 465 Isothermal conditions 388 continuous flow reactor 526 fixed-bed reforming pilot plant 287 heterogeneous fixed-bed catalytic reactor 512 multiplicities 461 reactor 72 reforming reactor profiles 289 run 42-44 Isotropic transport 420 3

3

J Jet stirring Jones expression, Lennard-

136 77

Κ Ketone aqueous solution 412 methyl ethyl 574 vapor pressure 421 Kieselguhr catalyst 513 Kinetic(s) 41 activity 282 effect of catalyst pretreatment on 35 Arrhenius 563 parameters 318 of catalytic liquefaction of Big Horn coal 303 data 586 fixed-bed 59 desulfurization 447 determination of the realtime activity 287 design data from a bench-scale heatflow calorimeter 37 form ( C P A F ) , copolymer approximate 182 heuristic approach to complex 292 of the liquid diffusion regime 590 measurements 3,15, 26 modeling for oscillatory catalytic reactions 487 models 57-59,453,488-490 nonlinear 301 parameters 22 penultimate effect 175 phi-factor 175 reforming model 282 resistance 225,230 selectivity 282


609

INDEX Kinetic(s) (continued) studies with a spinning basket reactor, multiphase S 0 oxidation Kummer's hyper geometric function .. Kutta variable step size integration routine, Runge2

447 582 113 103

L L91 L I N S E I S equipment 191 L P A experiments 317 LP91 L I N S E I S conductometer 192 Lag dynamic 41 influence of time 566 temperature 57 time 568 Laminar flow 7 polymerization of E P D M polymer .. 140 Langmuir -Hinschelwood adsorption mechanism 283 equation 209 kinetic models 57 isotherm 464, 465 monolayer theory 516 LaPlace-transformation 340 Late reaction zone phenomenon, early559 Law of Arrhenius 500 Law, Fick's 64 Law, Fourier 190 Law, Henry's 362,588 Law, Michaelis-Menten 126 Layer diffusion, product 226 Least square, nonlinear 309 Legendre polynomials 542 Lennard-Jones expression 77 Limestone, absorption of S 0 by calcined 225 Limestone, comparison with experimental data for sulfation of fully calcined 231 Limit cycle(s) 506 experimental 493 frequency of 500 phenomena during catalytic oxidation reactions over a supported platinum catalyst 475 simulated 493 Limtiation region, diffusion 77, 80 Linear heat flux methods 190 regression methods 295 statistical methods 292 velocity, gas 375-380 Liquefaction of Big Horn coal, kinetics of catalytic 303 process (es) 303-306 2

Liquid diffusion influence 582 regime, kinetics of the 590 resistance 592 distribution in a trickle-bed 417 full upflow reactor 428 -gas chromatograph 207 -gas systems 373 interface, gas/ 428 - l i q u i d spray column 539 - l i q u i d systems 373 phase deviation from plug flow 387 dispersion coefficient 379,380 mass transfer coefficient 367

geneous 388 -solid interface 428 -solid transport 393 velocity dependence of reaction rates 415-418 Loop fermentors 154-160 Loop reactor 15-18 advantages of 22-25 data with pilot plant experiments, comparison of 24 design of 17 experiments, results of 21

M Macromixing 126 Macromolecular content 163—165 Magnetic deflection mass spectrometer 477 Maleic anhydride from benzene, production of 215 Maleic anhydride, oxidation of benzene to 440 Manganese-containing catalysts 26 Mass balance 64-66 equation 430 spectrometer, magnetic deflection .. 477 spectrometer, time of flight 314 transfer 8,153,154 in absorption without reaction .... 329 in a bubble column, C0 -interphase 359 with chemical reaction, regime of 327 coefficient 8,9,365-367 effects 306 factors 57 interphase 428 limitations 428 parameters 15 performance 8 rates 13 representation of reactants 418 2


610


transfer (continued) on selectivity, influence of 327, 328 in stirred cell reactor during sulfonation 329 in a trickle-bed reactor, mathe matical model of 420 transport to the catalyst bed, con centration changes caused by .. 68 transport equation 73 Material balances 405,406 Matrix eigenvalues of the selectivity 284 eigenvectors of the selectivity 284 notation 283 heat balances in 273 selectivity rate constant 285 truncation on catalyst effectiveness effect of 39 Measurement(s) heat flow 38 kinetic 1,15,26 transient rapid response 50 Mechanical stirring, relative efficiency of 134 Mechanically stirred fermentors ...154-156 Mechanism(s) heat transfer 218, 250 of interaction 125 reaction 488 Mechanistic model 404, 408,409 Melt 585 Menten's equation, Michaelis126,164 Metal catalyst, oxidation of carbon monoxide over 83 deposition on the desulfurization activity, effect of 262 removal in a stirred-tank reactor .... 260 sulfide deposits 258 Methanation 63,70 Methane 316 Method(s) ASTM 193 collocation 542 dynamic 195,196 experimental 190 linear heat flux 190 regression 295 statistical 292 perturbation 564 collocation 232-235 Rung-Kutta 315 static 190,195 steady state 339 thermal 37 Thomas 143 two-plate 191 unsteady state 339 water displacement 513

Methyl ethyl ketone 574 Methylstyrene, hydrogénation of α- .. 414 Michaelis-Menten's equation .125,126,164 Micro-methods 38 Micromixing 8 effects 126 experimental parameters for 127 phenomena in continuous stirred reactors 125 time(s) 129-131,134 Mid-Continent naphtha 287, 288 Middle East residues 255,261, 262 Mini-pilot reactor 37 Minimum lifetime 259-262 Mixed flow profiles 220 Mixed flow reactor 219 axial 304,337-345 behavior, fluid 571 gas-solid 51 radial 304-306 (STR), ideal 14 Model(s) axial dispersion 242, 307, 359 axially dispersed plug flow 239 for complex gas-phase reactions, development of reaction 313 countercurrent backmixing 400 diffusion/convection flow 577 dual site 455 evaluation of 243 exponential 297 fluidized bed reactor 436, 438 for gas-solid reactions, pore plugging 225 homogeneous continuum heat transfer 239 Hougen and Watson kinetic 57 of Hovmand and Davidson 408, 409 hyperbolic 295-298 kinetic 59,453,488, 490 Langmuir—Hinschelwood kinetic .... 57 of the liquid distribution in a trickle-bed 417 of mass transfers in a trickle-bed reactor 42C mechanistic 403, 404, 408, 40S Monod's 17C nonlinear kinetic 301 one-dimensional dispersion 372 "parallel bundle" 202 plug flow 242-244 pore plugging 226,231, 233, 23S pore structure 20c for prediction of the radial conductivities 241 pseudomonomolecular kinetic reforming 282


INDEX

611

Monad's (continued) for reaction in partly wetted catalyst pellets 391 "shrinking aggregate" 130 slugging fluidized bed reactor 400 621 spectrophotometer 6 studies of radial flow, fixed bed reactors, cell 550 time-averaged 408, 409 trickle-bed reactor 411 two-phase 400-403,539 dispersion 359 "wedge layering" 202 Modeling for oscillatory catalytic reactions, kinetic 487 Modulus, Thiele 34, 99,125 Moisture-free coal 307 Molar concentrations 321-32 Molar gas flow rate 360 Mole fraction 515 of C 0 , gas phase 367 feed hydrogen 532 of H 517 profiles for different thermal conductivities 102 Molecular conductivity 248 Molten V 0 - K S 0 catalyst, oxida tion of S 0 on supported 582 Monod's equation 164 Monod's model 170 Monolith(s) channels 72,103 entrance effect in active 80 catalysts, poisoning in 110 convertor, concentration, and velocity profiles 72 pellet-filled 83-85 physical dimensions of crossflow .... 84 reactor (active wall) 72 reactor-heat exchanger 83, 89 Monomer disappearance 143 Monomer sensitivity limitations 175 Monte Carlo integrations 275 Movement, cocurrent-countercurrent 539 Moving bed reactor, design of a 540 Multi-component adsorption, effects of 51, 57 Multiphase kinetic studies with a spinning basket reactor 447-449 Multiplicity 551 during C O oxidation, steady state .. 477 measured and calculated, ranges of 547 phenomena 499 steady state 98 and uniqueness, regions of 545 upper and lower temperature profiles region or 546 in wall-catalyzed reactors 98 Multitubular reactor(s) 215 Mutta technique, Runge90 2

2

2

5

2

2

2

7

Ν Naphtha 306 Arab light 287,288 Mid-Continent 287,288 Nigerian 287 Naphthalene 8 sublimation rate of 9 Navier-Stokes equation of motion ...72,73 Nelder and Mead, derivative-free simplex method 22 Newton-Raphson algorithm 88 iteration 114 method 103 procedure 273 Newtonian fluid 73,74

catalysis, dynamic studies of acetylene hydrogénation on .... 526 content 531 Nigerian naphtha 287 Nitric acid, catalytic decomposition of hydrogen peroxide 505 Nitric oxide conversion 550 Nitrogen 425 Noncatalytic homogeneous liquid phase reaction 388 Noncatalytic reactions, gas-solid 226 Nonisothermal behavior in chain addition copolymerization 173 Nonisothermal histories 180 Nonlinear kinetic models 301 Nonlinear least square 309 Non-Newtonian fluids 149 Nonradiative heat fluxes 273 Nonselective poisoning 110-111,115 cell 555,556 fractional yield as function of cell .. 558 Nusselt 99 Peclet 248, 249,308, 338-344,578-580 Prandtl 248 Reynolds 243-249, 465 wall biot 249, 251 Nylon-6 348 Nyquist plane 566-569

Oil(s) dibenzothiophene in white flush furnace heavy fuel trickle flow reactors for hydrotreating heavy vaporized white One-dimensional dispersion model ....


310 447 307 306 306 425 448 448 372


612

Packed bed ( s ) ( continued ) Operating time on catalyst perform axial flow in 541 ance, effect of 29 of low tube/particle diameter Operation on the selectivity of ratio, heat transfer in 238 catalytic reactions, effect of periodic 512 Packed bubble columns of large diameter, axial mixing of Ores, hydrogen reduction of 440 liquid in 337 Organism and growth medium 163 Packing efficiency 346 Orthogonal central-composite 345 design 293 Packing on axial mixing, effect of 339,344 Orthogonal collocation 67,103 Pall rings 288 Orthogonal design 584-586 Paraffin composition profiles Paraffin formation rate, straight chain 33 Oscillation ( s ) 202 amplitude of temperature 503 "Parallel bundle" model Parallel passage reactor asymmetric behavior of the advantage of 70 temperature 503 dimensions of 65 of concentration 568 methanation in a 63 at different temperatures 480-483 experimental period in compariso with computed period 50 Parallel reaction mechanism 309 from computer simulation, typical temperature 501 Parameter(s) cross-correlations 247 in a stirred tank reactor, theoretical and experimental study of heat transfer 15 mass transfer 15 self-sustained 498 of a pseudomonomolecular kinetic of temperature and conversion .508,568 reforming model, realtime Oscillatory catalytic reactions, activity 282 kinetic modeling for 487 RA . 175 Oscillatory phenomena 482 search technique, Rosenbrock's 287 Oxidation 99,173 of anol to anone 348 Parametric sensitivity 30 of benzene 217, 440 Partial pressure of carbon monoxide .. of butane 574 Particle(s) catalyst 417 1-butene 482 diameter ratio, heat transfer in carbon monoxide ...83,465,466,476,491 packed beds of low tube/ 238 cyclohexane 354, 356 diffusional resistance through the of dammitol 292, 294 pores of the 225 efficiency 352 escape probability for a 572 of ethylene 77,80, 440 size 584 in an integral reactor, carbon monoxide 461 Particulate phase, piston-flow region of 405 kinetics, S 0 582 Peclet Pe number 242,248,249, 308, limit cycles during simultaneous 338-344,578-580 C O and 479 over platinum, carbon monoxide .... 475 Pellet(s) catalyst 462 process, computer-aided develop -filled crossflow monolith 83-85 ment of the cyclohexane 348 mathematical model for reaction in process, improvement of the C H - .. 349 partly wetted catalyst 391 reactions 63 partially wetted catalyst 389 catalytic partial 215 thermal conductivity of a 191 section by means of T I S F L O , Penultimate effect kinetics 175 simulation of a plant 352 420 of sodium sulfite 154 Percolation theory of S 0 512,582 Perforated plate columns of large diameter, axial mixing of liquid steady state multiplicity during C O 477 in 337 tubular reactor for xylene 19 Oxygen 477, 488 Performance of industrial reactions .... 571 Periodic effluent concentrations 534 Ρ Periodic effluent hydrocarbon distri P ( O C H ) isomerization 44 butions, steady state and 529 Packed bed(s) 248,250 Periodic operation 520-523 2

2

3

3


INDEX

613

Permeability 437 Perturbation(s) collocation method 232-235 of the initial steady state, deliberate 468 method 564 single inlet concentration 461 solution for small times 229 transient behavior of the reactor for finite 568 Phase deviation from plug flow, liquid 387 Phase, equilibrated gas 583 Phenomenon, early-late reaction zone 559 Phi-factor kinetics 175 Physical component, azimuthal 73 Physical dimensions of crossflow monoliths 84 Pilot plant, adiabatic data 29 Pilot plant, isothermal fixed-bed reforming 287 Pilot-reactor, mini37 Pilot unit scale reactor 577 Piston-flow region 404-406 Plane, Nyquist 566-569 Plant experiments, comparison of loop reactor data with pilot 24 Plant oxidation section by means of T I S F L O 352 Plant reactor 25, 574, 575 Plant scale reactor 574 Plastic powders, nonporous 193 Plate(s) on axial mixing, effect of 345 efficiency 346 method, modified 194 Platinum 477 -alumina catalyst 463, 466 carbon monoxide oxidation over .... 475 catalyst, catalytic oxidation reactions over supported 475, 476 Plot(s) Arrhenius 310,583,586 of conversion vs. space velocity 69 for oxidation of ethylene, Arrhenius 77 of reaction rate with gas composition, Arrhenius 587 of selectivity vs. conversion 520 between the specific growth rate, reciprocal 167 of yield vs. conversion 520 plug flow 72, 425 of liquid 387, 388 model 242-244 axially dispersed 239 reactor 254,337,428 tubular reactor with high heat diffusivity 562 Plugging, pure pore mouth 202-205, 254 Plugging time, analytical evaluation of the 228

Poincaré theorems Poiseuille profile, laminar Poison (ing) deposition mode of deactivation in monolithic catalysts nonselective pure selective Polymer concentration Polymer molecular weight Polymerization Polynomials, legendre Pore blockage diffusion

487 72 115 202 110 110-111,115 205 111-115 143 173 140,173 542 232 226

desulfurization 254 mouth plugging, pure 202, 205 plugging model 225,226,231-235 for gas-solid reactions 225 size 584 structure and foulant deposit geometries 201, 202 internal 391 model 203 of the particle, diffusional resistance through the 225 Porosity changes 225 Powders, nonporous plastic 193 Prandtl's number, (Pr) 45,248 Precipitation 591 Pressure apparatus 314 of C 0 , liquid phase partial 369 of carbon monoxide, partial 30 change, system response to 56 drop equation 271 ketone vapor 421 response characteristics 55 transducer 53 transient for ferf-butanol catalytic dehydration, adsorption-reaction 58 Probability for a particle, escape 572 Problems, stability 539 Product, diffusional resistance through the solid 225 Product gas, recirculation cold 63 Profile(s) analytic solution for nonuniform viscous flow, velocity 149 axial 360 flow, steady state temperature .... 552 in the catalyst bed, concentration .. 67 composition 288 concentration 230,261 description of measured 366 2


614


Profile(s) (continued) for different thermal conductivities, mole fraction 102 in the entrance region of a monolithic convertor 72 ethylene concentration 535 exit 144 gas 368,369 gas phase 365 heat flux 271 initial velocity 144 inlet velocity 144 isothermal reforming reactor 289 laminar Poiseuille 72 mixed flow 220 in multiple channels, radial temperature 107 paraffin and benzene compositio region of multiplicity, upper lower temperature 546 solid temperature 116 steady state 559 temperature 144, 239,240, 246,514, 540 transient behavior of temperature .. 560 tubeside temperature 220 tube wall temperature 271 Program description, computer 54 2-Propanol 4 Propanol, aeration of 377, 378 over alumina, dehydration of 10 Properties of catalysts 195,462 Properties, fluid dynamic 362 Proportional control 563 Pseudomonomolecular kinetic reforming model, realtime activity parameters of a 282 Pseudosolubility 153 Pulse amplitudes 468-471 Pulse duration on conversion enhancement, effects of 468-472 Pulsing at various temperatures 469 Pump, metal bellows recycle 476 Pyrolysis of ethylbenzene 313-316 Pyrosulfonic acid 327-329

Q Qualitative trends of the hysteresis curve Quartz

99 314

R Radial conductivity 247-250 dispersion effects 363 distribution of fractional sites 116 distribution of poison deposition .... 115 flow 550-554 inlet 541 mixing 304-306

Radial (continued) Peclet numbers 242 temperature profiles in multiple channels 107 Radiation 273,276 Radiative heat transfer 273 Radical reaction equations 350 Raphson algorithm, Newton88 iteration, Newton114 method, Newton103 Rasching rings 339 Rate(s) . on axial mixing, effect of gas flow .. 342 of C O conversion 492 constant(s) effect of coke deposition on

reaction 310 realtime activity 283 of conversion 38 determination of, reaction 22 equation(s) 23 intrinsic 416 parameters, activation energies and frequency factors 22 reaction 414 as a function of product sulfur, reaction 454 with gas composition, Arrhenius plot of reaction 587 gas-exchange 401,441 glucose consumption 170 growth 163 intrinsic 3 mass transfer 13 molar gas flow 360 of oxidation of S 0 over vanadium oxide 512 on performance, effect of agitation 452 reaction 457 shear 149 static global 3 of sublimation 8, 9 superficial liquid velocity dependence of reaction 415,418 transient global 3 Ratio, recycle 17 Reactant(s) feed system 513 mass transfers, representation of ... 418 nonvolatile liquid 388 species, concentration of a 441 system reaction, single 57 Reaction(s) adsorption 3 to the catalyst bed, concentration changes caused by 68 2


INDEX

615

Reaction(s) (continued) catalytic partial oxidation 215 conditions, adsorption at 57 development of reaction models for complex gas phase 313 effect of periodic operation on the selectivity of catalytic 512 equation(s) with the Damkohlen number 76 radical 350 with the Schmidt number 76 first-order irreversible 388 first-order steady-state chemical .... 402 gas-phase 4,447 gas-solid noncatalytic 226 heat adsorption, types of 63 of hydrocarbons, thermal decomposition 31 hydrocracking 306,30 kinetic modeling for oscillatory catalytic 487 in the liquid phase, micromixing phenomena in continuous stirred reactors 125 mass transfer in absorption without 329 mechanisms 309,488 models for complex gas phase reactions, development of 313 noncatalyst homogeneous liquid phase 388 oxidation 63 in partly wetted catalyst pellets 391 pore plugging model for gas-solid 225 rate(s) 457 Arrhenius diagrams for 31 of carbon monoxide, reduced 30 on the catalyst 217 constants 310 determination of 22 equation 414 as a function of product sulfur ... 454 with gas composition, Arrhenius plot of 587 superficial liquid velocity dependence of 415, 418 temperature dependency 30 regime of mass transfer with chemical 327 selectivity 574 studies, adsorption 57 over supported platinum catalyst 475, 476 tube wall catalyzed 74 vapor-phase catalytic 293 zone phenomenon, early-late 559 Reactor(s) adsorber50-53,59 backmixed 309 bench-scale 303 coated tube 63

Reactor(s) (continued) cocurrent 218-222 gas-liquid tube 329 components 51 conditions during comparisons of trickle and batch operations .... 432 configurations, comparison of 217 continuous flow spinning basket stainless steel 527 continuous flow stirred tank 337,430,498 coolant pass 221 countercurrent 218-220,414 cyclone 328-334 design features 17, 51, 540 development 50,450 differential 10,15 evaluation 50 fixed bed 513,539 fluidized-bed 563 gas-liquid 352,353 glass tubular 207 Gulf-patented segmented bed 304 -heat exchanger 83,89-93 honeycomb 77 impinging jet infrared cell-recycle .. 3 ir cell 4, 5,10,11 inlet temperature 282,288 integral 15-17,22, 462 internal recycle 26 isothermal 72,512,526 laboratory 16 liquid full upflow 428 loop 15-25 mini-pilot 37 mixed flow 219 model(s) fluidized 436-438 gas-liquid 351 multitubular 215 slugging fluidized bed 400 trickle-bed 411 monolithic (active wall) 72 moving bed 543 multiphase spinning basket 449 multiplicity wall-catalyzed 98 multitubular 215 parallel passage 63-70 performance of industrial 571 pilot unit scale 577 plant 474,575 plug flow 254,337,428 prototypes, cell 9 recirculating batch 6 recirculation 583 selectivity in 331-333 single-wafer catalytic recycle 13 spinning basket 448 stirred cell 328-334



616

Reactor(s) (continued) trickle-bed 414-416,447 trickle flow 431 tube 15-17,219,334,512 Realtime activity kinetics 287, 288 Realtime activity parameters 282,283 Recirculation reactor 583 Recycle flow 584 pump, metal bellows 476 ratio 17 reactor impinging jet infrared cell3 internal 26 single-wafer catalytic 13 Reduction of ores, hydrogen 440 Reduction, vanadium 585, 591 Regime, kinetics of the liquid diffusion 59 Residence time 337, 516, 527 analysis 571 curves, concentration20 data 573-579 density 572-579 distribution 339-341,571, 576-580 Residue, Caribbean 255-262 Residues, Middle East 255-262 Resistance, kinetic 225,230 Resistance, liquid diffusion 592 Reynolds number 8, 45, 89, 243-249, 465 Rings, Pall 339,344 Rings, Rasching 339 Rosenbrock's parameter search technique 287 Rotameters 507 Run(s) 90-93 cyclic 517 Runaway analysis ( R A ) 175-183 Runge-Kutta methods 315 technique 90 variable step size integration routine 103 Ruthenium catalyst 411 S Scanning calorimetry, differential 181 Scans, steady-state spectral 12,13 Schmidt method, Binder— 67 Schmidt number 75, 76 Selective poisoning 111-115 Selectivity of catalytic reactions, operation on the 512 on C O conversion, dependence of .. 28 vs. conversion, plot of 520 conversion, yield 514 in the cyclone reactor 333

Selectivity (continued) effects 557 of catalyst pretreatment of 35 ethane 531 influence of mass transfer on 327,328 matrix 284 under periodic operation 521-523 rate constant matrix 285 reaction 574 steady state 519 in stirred cell reactor 331 of straight chain hydrocarbons 34 in the tube reactor 333 Semenov-type dimensional analysis ... 173 Sensitivity analysis 353 limitations, monomer 175

Shear rate 149 Sherwood numbers 99 Shrinking aggregate model 130 Simplex method (Nelder and Mead), derivative-free 22 Simpson's integration rule 286 Single reactant system reaction 57 Single-wafer catalytic recycle reactor 13 Sliding thermocouple 412 Slugging fluidized bed reactor 400, 404 Sodium hydroxide 339 Sodium sulfite, oxidation of 154 Solid contact and mixing gas51 interface, fluid— 115 interface, l i q u i d 428 reactions, pore plugging model for gas225 systems, gas— 554 thermal conductivity 101 transport, l i q u i d 393 Solvation, coal 304-310 Space velocity conversion vs 68, 69 Spectra, surface 3, 6 Spectral scans, steady-state 12,13 Spectrometer ir 3-7 magnetic-deflection mass 477 time of flight mass 314 Spinning basket reactor 447-449 stainless steel, continuous flow 527 Spray column, liquid/liquid 539 Stability 551 of controlled reactor 565 diagrams 501-504 domain 567-569 parameter 564 problems 539 steady state 499, 566


617

INDEX Stainless steel reactor, continuous flow spinning basket 527 Start-of-cycle reactor inlet temperatures 282 Static conductivities 249 global rates 3 methods 190,195 process 248 surface spectra 3 Steady state for 2% C O , multiple 480 compositions 528 continuity equation 73 conversion of C H 6 518 conversion performance with puls ing at various temperatures .... 469 diagrams 56 equation 492 gas analyses 513 hysteresis in the conversion-inlet temperature domain 467 methods 339 multiplicity 98, 466, 477 profiles 559 runs 517 selectivity 519 spectral scans 12,13 stability 499,566 temperature 532, 563-567 yield of C M 519 Stirred cell reactor 328-334 aromatic sulfonation in a 327-329 selectivity in 331 Stirred tank experiments 262 reactor 4, 430 catalyst life in a 260 continuous flow 125, 337, 498 metal removal in a 260 self-sustained oscillations in a . . . 498 Solubilities, gas 593 Stokes-Einstein equation 331 Stokes equation of motion, Navier- ...72, 73 Styrene 315-323 -acrylonitrile ( S A N ) 175 -methyl methacrylate ( S M M A ) .... 175 Sulfite, oxidation of sodium 154 Sulfide deposits, metal258 Sulfonation aromatic 327 of benzene 327,334 experiments 329-333 mass transfer 329 Sulfovanadate complexes 582 Sulfur 425 concentration 255 dioxide absorption of 225 4

4

8

dioxide (continued) oxidation kinetics over vanadium oxide, rate of oxidation of reaction rate as a function of product trioxide Sulfuric acid Synthesis of ammonia, catalytic Synthesis, Fischer-Tropsch

Technological Information System (TIS) Temperature(s) amplitude, stability diagram of

582 512 454 327-332 359 550 26,63

352 504

distribution of Ο 118 cell number after a shift in 169 coefficient of sensitivity 53 comparison of some representative amplitudes of 505 control of methanation reactors 63 conversion of ethane gas inlet 546 and conversion, measured oscilla tions of 508 dependence of "heat transfer property" γ 47 dependency, reaction rate 30 for different wall thermal conductivities 101,102 distribution, integral reactor 21 domain, steady state hysteresis in the conversion-inlet 467 extinction 98 ignition 98 inlet gas 544 lag 57 in multiple channels, wall 105-106 oscillation of 480-483, 501-503, 568 profile( s ) 144, 219-221, 240, 246, 514, 540 axial flow 552 in multiple channels, radial 107 radial 239 region of multiplicity, upper and lower 546 transient behavior 560 tube wall 271 solid 116 tubeside 220 programmed run, diazo-decomposition's 42 reactor inlet 282, 288 shift on growth, effects of 168 specific growth rate at varying 166 steady-state 469, 463-567 transient behavior of reactor 569 variations, gas phase 479



618

Termination models 174 Theorems, Bendixon 487 Theorems, Poincaré 487 Theory Langmuir monolayer 516 percolation 420 residence time distribution 571 true volume ideal two-phase 438 two-phase 436 Thermal conductivity 190-195,315 mole fraction profiles for different 102 of a pellet 191 of porous catalysts 189 solid 101 temperatures for different wall 101,102 cracking furnace 271-274 data 4 decomposition reactions of hydrocarbons 313 design data from a bench-scale heatflow calorimeter 37 energy balance 173 hazard(s) 43-45 ignition 173 ignition point apparatus 182 instrumentation 37 liquefaction processes 303 methods 37 phenomena in chain addition copolymerization 173 runaway ( R A ) 173,182 Thermocouple ( s ) 17, 53, 57 axial 412 Cr/Al 238 sliding 412 Thiele modulus 34,99, 125 Thiophene 207 Thodos correlation, de Acetis466 Thomas method 143 Time analysis, residence 571 -averaged conversion 505 -averaged model 408,409 curves, concentration-residence 20 data, abstract residence 573 density function, residence 572 distribtuions, residence 339 of flight mass spectrometer 314 lag 568,569 bacterial 172 influence of 566 residence 337,527 testing of the plant reactors, residence 574 Toluene 288,315,316 Transfer, mass 8,13-15,153,154, 388 in absorption without reaction 329 in a bubble column, C0 -interphase 359 2

Transfer, mass (continued) with chemical reaction, regime of .... 327 coefficient 311,365-367 effects 306 gas-liquid 387 representation of reactants' 418 on selectivity, influence of 327,328 in stirred cell reactor during sulfonation 329 in a trickle-bed reactor 420 Transformation, LaPlace340 Transient analysis 559 Transient behavior of reactor temperature 568-560 Transition, R A 179,183 Transport to the catalyst bed, concentration

equation, mass 73 isotropic 420 liquid-solid 393 of vorticity, convective 74 Trickle-bed reactor 416 butanone hydrogénation in 413 catalyst effectiveness factor in 387 countercurrent 414 model 411 of the liquid distribution in a 417 of mass transfers in a 420 performance equations for 389 Trickle flow and batch operation, comparison of 432, 433 reactor 431 catalyst utilization in a 425 Tropsch synthesis, Fischer63 Truncation on catalyst effectiveness, effect of matrix 393 Tube -particle diameter ratio 238 reactor 334 aromatic sulfonation in a cocurrent 327 cocurrent gas—liquid 329 selectivity in the 333 wall-catalyzed reaction 74 wall temperature profile 271 Tubeside temperature profiles 220 Tubular reactor(s) 15-19,63,512 glass 207 with high heat diffusivity, flow control operation of a plug-flow .... 562 limitations 149 polymerization in a 140 Turbulant conduction 248,249 Two-phase model 359,400-403, 539 Two-phase theory, true volume ideal.. 438 Two plate method 191


619

INDEX

U U 0 , hydrofluorination of Upflow reactor, liquid full Utilization, experimental system for determining maximum catalyst.... 2

440 428 429

V2O5-K2S2O7 catalyst, oxidation of S 0 on supported molten 582 Valualdehyde 294-298 Vanadium 255-259, 588, 592 oxide, rate of oxidation of S 0 over 512 removal 261-263 reduction 585, 591 Vapor phase catalytic hydrogénation 526 Vapor phase catalytic reaction Vapor pressure, ketone 42 Variability, intensity function representation of residence time 571 Vector, vorticity 73 Velocity conversion vs. space 68,69 dependence of reaction rates, superficial liquid 415-418 in the entrance region of a monolithic convertor 72 field development, axial 76 and "fines" content, interstitial flow increases with gas 439 fluid interstitial 551 gas linear 375-380 profiles 75,144,149 Viscous flow, velocity profile analytic solution for nonuniform 149 2

2

Wall biot number 242,249-251 -catalyzed reaction 74 -catalyzed reactors 72,98 thermal conductivities 101 Water displacement method 513 Water on ierf-butanol adsorption, effect of 58 Watson kinetic models, Hougen and 57 "Wedge layering" model 202,211 Wetted catalyst pellets 391 Wetted slab 394 Wetting efficiency 411 external 390,391 incomplete catalyst 427 internal 390

X Xylene, aeration of 377,378 Xylene oxidation, tubular reactor for 19

Y Yield vs. conversion, plot of conversion, selectivity ethane as function of cell number, fractional under periodic operation, mean and selectivity under periodic operation

517 520 514 532 558 521 523

Ζ

W Wafer catalytic recycle reactor, single-

13

Zeolite cracking catalysts Ziegler catalysis Zone, ignition


288 140,149 101

Chemical Reaction Engineering--Houston

Chemical Reaction

Chemical Reaction Engineering