Reinhard Billet
Packed Towers
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Reinhard Billet
Packed Towers
VCH Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
© VCH Verlagsgesellschaft mbH, D69451 Weinheim, (Federal Republic of Germany), 1995 Distribution: VCH, P.O. Box 1011 61, D69451 Weinheim (Federal Republic of Germany) Switzerland: VCH, P.O. Box, CH4020 Basel (Switzerland) United Kingdom and Ireland: VCH, 8 Wellington Court, Cambridge CBl 1HZ (United Kingdom) USA and Canada: VCH, 220 East 23rd Street, New York, NY 100104606 (USA) Japan: VCH, Eikow Building, 109 Hongo 1chome, Bunkyoku, Tokyo 113 (Japan) ISBN 3527286160
Reinhard Billet
Packed Towers in Processing and Environmental Technology
Translated by James W. FuUarton
VCH
Weinheim • New York • Basel • Cambridge • Tokyo
Professor Dr.Ing. Reinhard Billet Institut fur Thermo und Fluiddynamik Fakultat fiir Maschinenbau RuhrUniversitat Bochum UniversitatsstraBe 150 D44801 Bochum
This book was carefully produced. Nevertheless, the author, translator and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Published jointly by VCH Verlagsgesellschaft mbH, Weinheim (Federal Republic of Germany) VCH Publishers, Inc., New York, NY (USA)
Editorial Directors: Louise Elsam, Karin Sora Production Manager: Peter Biel
Library of Congress Card No. applied for. British Library CataloguinginPublication Data: A catalogue record for this book is available from the British Library. Die Deutsche Bibliothek  CIPEinheitsaufnahme Billet, Reinhard: Packed towers in processing and environmental technology/ Reinhard Billet. Transl. by James W. Fullarton.  1. ed. Weinheim ; New York ; Basel; Cambridge ; Tokyo : VCH, 1995 ISBN 3527286160
© VCH Verlagsgesellschaft mbH, D69451 Weinheim (Federal Republic of Germany), 1995 Printed on acidfree and lowchlorine paper All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form  by photoprinting, microfilm, or any other means  nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition: Hagedornsatz GmbH, D68519 Viernheim Printing: Betzdruck GmbH, D64219 Darmstadt Bookbinding: Industrie und Verlagsbuchbinderei Heppenheim GmbH, D64646 Heppenheim Printed in the Federal Republic of Germany
Preface In the chemical and allied industries, there is a continuously rising trend towards separation processes that are operated in packed columns with systematically stacked or randomly dumped beds. It was initiated by the 1973 oil crisis and the associated demand for saving fuel by optimum design and operation of the processes. Another factor that has contributed towards the widespread adoption of packed beds in industry has been the increasing severity of ecological legislation. Since they can be operated under more moderate conditions, packed columns are superior to plate columns in coping with the demands of saving energy and protecting the environment. Thus packed columns can offer the following advantages:  They allow lower energy consumption in separation processes that entail a large number of theoretical stages.  They can more readily satisfy the requirements for the economic use of heat pumps.  They permit thermally instable mixtures to be separated at lower temperatures at the foot of the column and can thus minimize or even completely avoid products of decomposition or polymerization reactions that may be responsible for pollution.  In absorbers, particularly those for offgas scrubbing, they require compressors of lower power ratings than those installed in plate columns. Beds of packing are also being used to an increasing extent for direct heat transfer between liquids and gases (or vapours) and for liquidliquid extraction. The trend runs parallel to striking improvements in the design of traditional packing and has also led to the development of completely new packing geometries. However, the results obtained in process engineering studies did not always agree satisfactorily with the traditional relationships given in the literature. Consequently, research work had to be directed at devising new correlations and models for the efficiency and operating characteristics of packed columns with the aim of developing physically wellfounded design methods that are applicable to all types of packing used in industry. The book "Packed Towers in Processing and Environmental Technology" is intended as a contribution towards this aim. The reliability of the methods presented here has been demonstrated by results gained in comprehensive experiments that embraced more than sixty types of metallic, ceramic, and plastics packing of various geometries and dimensions and were performed on systems that covered a wide range of physical properties in the liquid and the gas or vapour phases. These pilotplant experiments were carried out over a period of more than 20 years in the course of the author's activities in research and industry. The results thus obtained provided a sound basis upon which a theoretical model could be developed to describe the hydrodynamics and mass transfer in packed columns. The experiments also served to verify the scientific accuracy of the models and thus to ensure close agreement between theory and practice. The author has presented papers on the subject at meetings held by various engineering institutions, including the VDI, EFCE and AIChE, and at the ACHEMA, CHISA and ACHEMASIA fairs. He has also held seminars on packed columns, e.g. in the Conicet Institute, Santa Fe and Bahia Blanca, Argentina; at the Glitsch Symposium in Dallas, Texas, USA; the Korean Institute of Energy Research in Taejon, South Korea; the Petrobras in Rio
VI
Preface
de Janeiro; the Belo Horizonte University in Brazil, and the Tientsin University in China. The book has been written in response to many requests for a review of the engineering aspects in packed columns. The author wishes to take this opportunity of expressing his most sincere thanks to all those who assisted him in the experimental work, to Dr. M. Schultes for his valuable cooperation in evaluating the examples, to M. Ernst for her commitment in typing the German manuscript, to Th. Cipa for his assistance in proofreading, and  in particular  to J. W. Fullarton for translating the work into English. Bochum, January 1994
R. Billet
Biography Reinhard BILLET gained his Dipl.Ing. (in 1953) and Dr.Ing. (in 1957) degrees in Process and Chemical Engineering at the Technical University of Karlsruhe. From 19541960, he was a Scientific Assistant under Professor E. Kirschbaum at the Plant and Process Engineering Institute of Karlsruhe University. In 1960, he joined the staff of the BASF Chemical Engineering Research Department and was subsequently involved in plastics production, plant design, environmental protection, and industrial safety. In 1975, he was appointed Professor of Process Engineering and called to the Chair for Thermal Separation Processes; and 1992, to the Chair for Process and Environmental Engineering at the RuhrUniversity of Bochum. During the period 1983/1984, he acted as the Dean of the Faculty of Mechanical Engineering. Professor Billet was awarded the Ring of Honour of the German Institute of Engineers (VDI) in 1964; and, in 1986, the Medal for Outstanding Merit, by the Technical University of Wroclaw. Most of his research work has been in the fields of evaporation, distillation, absorption, liquidliquid extraction, and environmental engineering. He has written over 200 scientific articles, four university booklets, and three monographs in German. His book ,,Industrielle Destination" has been translated into English, Czechoslovakian, and Chinese; ,,Verdampfung und ihre technischen Anwendungen", into English and Chinese; and ,,Energieeinsparung bei thermischen Stofftrennverfahren", into Polish. The "Proceedings of the Packed Column Analysis and Design Seminar" is also available in Korean and Chinese. The results of his research work have been presented at national and international congresses and meetings. Professor Billet is a member of the VDI Panel of Experts on the thermal separation of gases and liquids and the European Federation of Chemical Engineering (EFCE) Working Party on Distillation, Absorption and Extraction. He is also a member of the New York Academy of Sciences.
Contents 1
Introduction
1
1.1 1.2 1.3 1.4
Fundamental operating characteristics of packed columns for gasliquid systems Theoretical column efficiency 11 Energy consumption and number of theoretical stages 17 Height of bed determined from the HTUNTU model 20
2
Types of packing
2.1 2.2 2.3
Packing dumped at random 24 Packing stacked in geometric patterns Geometric packing parameters 27
3
Experimental determination of packing performance
3.1 3.2 3.3 3.4
Pilot plants for testing gasliquid systems Evaluation of measurements 31 Test systems 37 Experimental results 41
4
Fluid dynamics in countercurrent packed columns 73
4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10
Fluiddynamics model 73 Resistance to flow 76 Loading conditions 82 Flooding conditions 84 Relationship between boundary loads 87 Pressure drop in packed columns 88 Liquid holdup in packed beds 96 Liquid entrainment at high loads 100 Phase inversion in packed beds 102 Relationship between loading and flood points
5
Mass transfer in countercurrent packed columns
5.1 5.2 5.3 5.4 5.5 5.6
Mass transfer in the liquid phase 119 Mass transfer in the vapour phase 121 Vapourliquid phase boundary 124 Relationship between mass transfer and fluid dynamics 130 Mass transfer at high liquid loads 139 Mass transfer in absorbers accompanied by chemical reaction in the liquid phase
23 25
31
31
112
119
141
X
Contents
6
End effects in packed columns
147
6.1 6.2 6.3 6.4 6.5
Phenomenological description 147 Correlation of end effects 150 Experimental results 154 Column design and scaleup 157 Examples of scaleup 167
7
Liquid distribution at the inlets of packed columns
7.1 7.2 7.3 7.4 7.5 7.6
Theoretical considerations 171 Effect of inlet liquid distribution on the efficiency of packed columns Maximum packing efficiency in inlet zones 176 Effect of phase ratio on relative efficiency 183 Effect of height of packing on relative efficiency 185 Estimation of relative efficiency 185
8
Scaleup for end effects and phase distribution
8.1 8.2 8.3 8.4 8.5 8.6 8.7
Scaleup model 194 Inlet and end effects in industrialscale plants identical to those in pilot plants 197 Inlet and end effects in industrialscale plants different to those in pilot plants 198 Determination of the limiting number of liquid distributor outlets 199 Effect of phase maldistribution 206 Gas or vapour distribution 210 Effect of mass transfer coefficient on scaleup 212
9
Phase redistribution in columns
9.1 9.2 9.3
Estimation of optimum number of phase redistributors Costs relationships 219 Examples 225
10
Design of distributors
10.1 10.2
Fundamental design aspects and relationships Types of phase distributors 233
11
Overall evaluation of packing
11.1 11.2 11.3 11.4
Materials of construction 239 Capital investment 241 Evaluation for the separation of thermally unstable mixtures Evaluation in terms of minimum column volume 247
171 173
191
213 213
230 230
239
244
Contents
XI
11.5 11.6 11.7 11.8
Theoretical considerations in the design of column internals State of the art in the development of packing 255 Optimum area per unit volume in beds of packing 262 Limits to the further development of packing 270
12
Retrofitting columns by the installation of packing
12.1 12.2 12.3 12.4
Advantages of retrofitting 291 Potential for retrofitting with lowpressuredrop packing 296 Advantages of packing in steam rectification 302 Improvement in product purity caused by restricting the pressure drop in beds of packing 310
13
Applications for packing in liquidliquid systems
13.1 13.2 13.3 13.4 13.5 13.6 13.7
General aspects 313 Experimental 314 Fluid dynamics of dispersed and continuous phases 318 Dispersedphase holdup 318 Phase throughput 322 Mass transfer in the dispersed and continuous phases 324 Extraction efficiency, test results and derivation of model 327
14
Examples for the design of packed columns
14.1
Determination of the diameter of an offgas absorption column with various types of packing 342 Design of a packed column for the rectification of an isobutane/nbutane mixture 344 Scaling up measurements performed in pilot plants 348 Design of an absorber for removing acetone from process air 350 Design of a desorber for removing carbon dioxide from process effluents 355 Determination of the difference between the theoretical and the real liquid holdup 360 Additional column height required to compensate maldistribution 361 Retrofitting a plate column with packing for steam distillation of crude oil 362 Reduction in height effected by redistributors 363 Advantages of geometrically arranged packing in fractionating fatty acids 364 Recovery of acetone from production effluents by liquidliquid extraction 365
14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11
250
291
313
337
XII
Contents
15
Recent trends in packing technology
15.1 15.2 15.3
Fluidized beds of packing 369 Hydrodynamics of fluidized packed beds 370 Mass transfer in fluidized packed beds 370
References
Index
379
373
369
Key to symbols a a'
[m2/m3] [s/m]
ah aPh as
[m2/m3] [m2/m3] [m/s]
A Ah
[s/m] [m2] [m2] [m2] [s] [kmol/h];[kg/h] [kmol/m3] [DM/m3] [DM/m] [DM] [DM/m2] [DM]; [DM/m 3 [DM]
As B B c Cp CPs
Cr Cs
c Cc
ch cL CP
Cs Cv d dh dP ds D D D e E Ec Ev
fs fv fw
[m] [m] [m] [m] [DM/m] [m2/s] [kmol/h];[kg/h] [DM/m2]
[1/s]
total surface area per unit packed volume packing area per unit efficiency and per unit volumetric vapour flow rate hydraulic area of packing per unit volume of packed bed effective interfacial area per unit packed volume column shell area per unit efficiency and per unit volumetric vapour flow rate constant, specific for the packing crosssectional area of an individual channel total area of packing free crosssectional area constant, specific for the packing flow rate of bottom product concentration costs per unit volume of packing costs per unit height of column costs for one redistributor in a column of diameter ds costs per unit area of column shell costs; costs per unit volume of the packed column capital investment costs for a packed column packing constant to allow for liquid holdup packing constant to allow for mass transfer in liquid packing constant to allow for pressure drop costs of the packing to be evaluated in relation to those of a random bed of 50mm Pall rings packing constant to allow for mass transfer in gas size of an element of packing hydraulic diameter particle diameter column diameter costs factor, specific for the material and method of production of the packing diffusion coefficient of transferring component flow rate of distillate (overhead product) relative efficiency, or energy parameter costs factor, specific for the material and method of construction of column shell column efficiency volumetric packing efficiency wall factor vapour load factor wetting factor
XIV
Key to symbols
[DM/m3]
costs factor, specific for the material and method of construction of column shell F [kmol/h];[kg/h] flow rate of feed [kg^m^V1] vapour capacity factor related to the free column crosssection Fv [m/s2] acceleration due to gravity g h [kJ/kmol] molar enthalpy Ah [kJ/kmol] molar condensation; evaporation enthalpy [m3/m3] liquid holdup hL H [m] effective height of fill of column packing [m] height of inlet zone in a bed of packing Ht [m] HTU height of a mass transfer unit [m] overall height of a mass transfer unit HTUO k [m/s] overall mass transfer coefficient K [DM s/m3] total costs, i.e. for the bed of packing and the column shell, per unit efficiency and per unit volumetric vapour flow rate Kp; Ks [DM s/m3] packing costs per unit efficiency and per unit volumetric vapour flow rate length of flow path for phase contact [m] L [kmol/h] flow rate of carrier liquid L [kmol/h] ;[kg/h] flow rate of liquid slope of equilibrium line myx;mYX  [kmol/kmol] M maldistribution nh number of flow channels number of theoretical stages corresponding a bed height H nt N number of separation units N packing density K3] NTU number of transfer units in a phase number of overall transfer units NTUO [bar];[mbar] pressure P Ap [mbar];[mmWG] pressure drop P [bar];[mbar] boiling pressure of a component liquid distribution coefficient [kJ/h] energy consumption Q film thickness s [m] s [m] thickness of the basic material, i.e. sheet, foil or fibre, of the packing elements S [kmol/h] flow rate of carrier steam t time [s] liquid phase residence time tL [s] T temperature [K] [m3m~2s~1] uL liquid load (also related to hour) uL [m/s] local liquid velocity Uy [m/s] superficial gas or vapour velocity Uy [m/s] average effective gas or vapour velocity v' volume of packing material per unit efficiency and volumetric gas [s] or vapour load
u
Key to symbols Vy
V V w w' X
X y Y Z
zh
[m3/(m3/s)] [kmol/h] [kmol/h];[kg/h] [kg/m3]
[kg nrV 1 ] [kmol/kmol] [kmol/kmol] [kmol/kmol] [kmol/kmol] [m~2]
[m2]
specific column volume flow rate of carrier gas flow rate of gas or vapour specific gravity of packing packing weight per unit volumetric flow rate of gas or vapour and unit efficiency mole fraction in liquid phase molar load fraction of transfer component in liquid mole fraction in gas or vapour phase molar load fraction of transfer component in gas or vapour number of liquid distributor outlets number of flow channels per unit area of column crosssection
Greek symbols a CO.
8
[m/s] [m3/m3]
ri
[kg
V
Q
a T
Xy
[kg;kmol] [m2/s] [kg/m3] [kg/s2] [s] [N/m2]
relative volatility mass transfer coefficient void fraction of packing efficiency dynamic viscosity column efficiency stripping factor molecular mass; molar mass kinematic viscosity coefficient of resistance mass density surface tension duration of contact between the phases shear stress in gas flow diameter ratio flow parameter
Subscripts B C D e
F Fl L o P Ph
XV
bottom product continuous phase distillate (overhead product) effective feed flood point liquid surface pilot plant interface
ML
s S T V W
Key to symbols
film thickness; column shell loading point technical or industrial scale vapour or gas wetting
Dimensionless numbers Fo Fr Ma Re Sc We
Fourier number Froude number Marangoni number Reynolds number Schmidt number Weber number
1 Introduction The clamour for energysaving techniques in almost all branches of industry has acted as a spur in the development of thermal separation equipment. The design and process engineering improvements that have ensued entail that feedstocks are subjected to less severe treatment and can thus be optimally exploited. They also entail production under ecologically favourable conditions (cf. Fig. 1.1). A typical example is provided by lowpressuredrop packing in the vacuum rectification of mixtures that are unstable to heat and that necessitate a large number of theoretical stages for their thermal separation. The attendant decrease in the total pressure drop and operation under vacuum ensure that the temperature at the bottom of the column is comparatively low. Hence, decomposition products that are detrimental to the environment can be largely avoided, i.e. atmospheric pollution is reduced and less residues have to be disposed of. Another advantage is that the reduction in the average column pressure brought about by vacuum operation increases the average relative volatility of the components in the mixture and thus reduces energy consumption. Lowpressuredrop, highperformance packing is an essential requirement in the economic design of an integrated separation plant, because it permits heat pumps to be installed and a number of columns to be linked together.
Fig. 1.1. Relationships established by separation techniques between energy consumption, processing and environmental protection Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
2
1
Introduction
From this point of view, it is not surprising that packing designed to conserve energy has been the subject of many new developments on the part of equipment manufacturers. However, before any one particular type of packing can be selected for a given separation task, adequate knowledge must be available on the performance characteristics, e. g. the separation efficiency, the pressure drop, the liquid holdup, the capacity, and the costs. A physical model is required to describe the hydraulics and the mass transfer efficiency in a given separation column and thus to allow the main dimensions to be calculated and the process engineering performance to be predicted. The parameters that affect the design, the capacity, and the specific properties of the product and inlet streams must be known in order to devise the model, and the only means of acquiring these data is by experiment. Consequently, the aim of this book is to supplement the theoretical considerations by the results of relevant studies that were performed in the author's laboratories and pilot plants and were scaled up to meet practical requirements. It is known that packed columns, whether random or stacked, allow lower pressure drops per theoretical stage than plate columns and are thus better suited to meet demands on optimum energy consumption in thermal separation plants. The main applications for packed columns are the separation of vapourliquid or gasliquid systems, e.g. in rectification, absorption, and desorption. In many cases, they have also proved to be superior to conventional plate columns for liquidliquid extraction processes. Greatest significance from the aspect of saving energy is attached to their use in rectification, a subject to which particular attention has been devoted in the course of this book. In future, these separation processes will not be confined to petroleum refineries and the chemical and allied industries. They will also be adopted on a wider scale in ecological engineering for purifying offgas streams and for water treatment, and the demand for the necessary equipment, including packing, will grow accordingly. Rectification, absorption, desorption, and liquidliquid extraction processes consist essentially of passing two countercurrent phases through a packed column (cf. Fig. 1.2). In rectification, the vapour produced in the distillation section of the column flows countercurrent to the liquid formed in a condenser. Contact between the two phases is thus established, with the result that the lowboiling component flows upwards and the high boiler accumulates at the bottom of the column. Physical absorption processes consist of mass transfer from the gas into the liquid phase, i. e. into a solvent that selectively absorbs the desired component from the gas stream. In desorption  often referred to as stripping  mass transfer proceeds in the opposite direction, i.e. from the liquid into the gas phase. In the extraction of a component from a mixture of liquids by means of a selective solvent, mass transfer takes place between two liquid phases. It is taken for granted here that the reader is already acquainted with these separation processes and their thermodynamic fundamentals together with the literature on the subject and the standard terminology. The scope of this book has therefore been restricted to a comprehensive treatment of packedbed technology and its application to separation processes.
/. 1
Fundamental operating characteristics of packed columns for gasliquid systems
Packed towers for continuous Rectification
Absorption Solvent I A (absorbent)J { b a s
Feed
Liquid = A Loaded feed :  gas
Extraction Feed j f Extract
*
Bottom product
Loaded solvent
 Feed Fig. 1.2.
Desorption
y
DesorbedTTcarrier liquid t t / 5 ™
gas
— Auxiliary product
f Raff mate ^ I Solvent
End product
Applications for packed columns in thermal separation processes
1.1 Fundamental operating characteristics of packed columns for gasliquid systems The optimum choice of a packed column for a given separation task would be impossible without a sound knowledge of the characteristic parameters and physical quantities that permit process engineering evaluation and comparison. The gas or vapour load in a packed column is usually expressed by the capacity factor, which is given by Fy = Uy
(11)
where uv is the superficial velocity, o v is the density of the gas or vapour, and QL is the density of the liquid. At low or moderate pressures, QV is small compared to QL and can thus be neglected. Hence, the vapour capacity factor, which is often resorted to in practice as a measure of the dynamic load on the column, is the product of the superficial velocity uv and the square root of the vapour density, i.e. Fy = Uy \J~Qy~
(12)
1
Introduction
The maximum permissible value for the capacity factor also depends on a dimensionless flow parameter that allows for the ratio of the liquid to the vapour flow rate LIV and is given by (13) In practice, the capacity of packed columns is frequently described by the following function, which has to be determined by experiment: Fy
(14)
yfoL
A crucial factor in evaluating packed columns, especially those intended for vacuum rectification, is the resistance offered by the bed of packing to the flow of vapour. A major criterion in selecting packing for absorption processes in which gas is forced through the column by a compressor is the pressure drop Ap in the bed, because it largely governs the compressor rating. The pressure drop per unit height of bed Ap/H depends on the gas uv and liquid uL loads (cf. Fig. 1.3). It is usually expressed as a function of the capacity factor F v for a given liquid load uL or a given liquidgas ratio, i.e. (15) Another factor of great importance in evaluating packed columns is the pressure drop per unit of separation efficiency, which is defined by the number of theoretical stages nt in rectification or by the number of transfer units NTU in absorption and desorption. A general term, i.e. the number of separation units N required for a given process, may be taken to cover both cases. Thus,
Gas or vapour
Liquid PT
Ap
Gas or vapour I
H=N T
? Liquid
Fig. 1.3.
Flowchart for a packed column
1.1
Fundamental operating characteristics of packed columns for gasliquid systems
N = nt or N = NTU
5
(16)
The total pressure drop in the gas or vapour is given by
&P=PBPT
where
(17)
pB is the pressure at the lower column inlet and pT is the pressure at the upper column outlet.
In analogy to Eqn (15), the total pressure drop per separation unit can be expressed as a function of the capacity factor for a given ratio LIV of the liquid to the vapour flow rate, i.e.
~  = HFy)
(18)
The following relationship thus applies: ^
(19)
If the vapour pressure at the top of the column is kept constant during rectification, that at the bottom of the column  and thus the boiling point  become less as the pressure drop per unit efficiency for the specific bed of packing decreases. Low boiling points are an absolute necessity in the vacuum rectification of thermally instable mixtures. They also entail larger differences between the temperature of the heating medium and that of the mixture, i.e. more effective heat transfer. Moreover, if a large number of theoretical stages is required in a given vacuum rectification, a low pressure drop allows entire installations to be designed from the aspect of optimum energy consumption. The number of theoretical stages nt required to separate a binary feed with a molar flow rate F can be determined diagrammatically by the McCabeThiele method, which is based on the concept of an equilibrium stage, i.e. a stage in which the ascending vapour is in phase equilibrium with the descending liquid. An example of the corresponding diagram is shown in Fig. 1.4, in which x¥ is the mole fraction in the feed of the more volatile component that has to be concentrated to a mole fraction xD in the overhead product (distillate) with a molar flow rate D; and xB is the mole fraction of this volatile fraction that remains in the bottom product (molar flow rate B). The equilibrium curve is the locus of the points x, y. The two operating lines derived from material balance equations  BI for the stripping zone and DI for the enrichment zone  intersect at the point / on the gline, which is the locus of all points of intersection of the two operating lines for any given feed stream. The number of theoretical stages nt is represented by the steps that link the equilibrium curve with the two operating lines between the points x B and xD. It is the sum of the number of stages in the enrichment zone ntez and the number in the stripping zone ntsz, i. e. nt = nt,ez + nt,sz
(110)
1
Introduction
Reflux condenser^
Number of theoretical stages n t Equilibrium curve Operating *i V
0
xB
xF xD Liquid mole fraction x
Fig. 1.4. Determination of the the number of theoretical stages in a continuous rectification column, taking a binary mixture as an example
If xF, xD and xB are given, nt depends on the phase equilibrium in the mixture, i. e. on the shape of the equilibrium curve for the binary system, and on the position of the two operating lines BI and DI. The position of the intersect / can be obtained from the material balance at the inlet crosssection of the column, i.e.
The factor / in this equation is a measure for the thermal state of the feed and is given by /=!"
h'FhF Ahv
(112)
where hF is the molar enthalpy of the feed at the inlet temperature, h'F is the molar enthalpy at the operating temperature in the inlet crosssection of the column, and Ahv is the molar condensation enthalpy of the vapour stream in the inlet crosssection. If the individual components of the mixture have roughly the same molar evaporation enthalpy, the molar flow rates of both the vapour and liquid will remain practically constant along the respective flow paths both above and below the inlet, i.e. in both the enrichment and stripping zones. In this case, the relationship between the vapour y and the liquid x mole fractions of the more volatile component in the enrichment zone is given by the following linear equation:
y = r + 1• x
+
r+ 1
(113)
1.1
Fundamental operating characteristics of packed columns for gasliquid systems
7
where r is the ratio of the reflux flow rate L to the overhead product flow rate D, i.e. r=
d14)
The corresponding equation for the stripping zone is
where b is the ratio of the flow rate of liquid L in the stripping zone to that of the bottom product B, i. e. b = j
(116)
If the values for xF and / are given and those for xD and xB are specified, the operating lines for the enrichment and stripping zones in Fig. 1.4 can be easily plotted. Inserting x = 0 in Eqn (113) yields the value for y0 at the intercept with the axis of ordinates, i.e.
d17) where xD is the mole fraction of the more volatile component in the overhead product. The reflux ratio r at the head of the column is a factor that greatly affects the economics of rectification. If the molar evaporation enthalpies for the lowboiling A/z, and the highboiling Ahh components differ significantly, a linear relationship no longer exists between the mole fractions v and x of the more volatile component in the vapour and in the liquid respectively. In this case, allowance for the difference between Aht and Ahh is made by the expression K —^— Ahh  Ahi
(118)
The equation for the enrichment zone is thus no longer linear, i.e.
r+1 y= r+1
^
r+1
#
The intercept >;0 with the axis of ordinates in this case is given by —
(120)
8
1
Introduction
Whether its position is higher or lower than the corresponding intercept formed by the linear relationship {cf. Eqn (117)} depends on which of the two components  the highboiler or the lowboiler  has the greater molar evaporation enthalpy. Likewise, the relationship for the stripping zone in the column is also nonlinear if the molar evaporation enthalpies of the components differ. In this case, the following equation applies: /
yA
*—r
(1 21)
"
where the parameter mI is given by xFxB m, =
^
r,+f
^
(122)
the reflux ratio r7 at the inlet crosssection, by
=
and yt and xt are the coordinates of the intersect / (cf. Fig. 1.4). An alternative concept to the number of theoretical stages nt for the evaluation of separation efficiency is the number of transfer units NTU. If the molar flow rates for the liquid L and the vapour V are kept constant and there is no mixing in the axial direction, the NTU for steadystate operation can be expressed as follows in the terms of the concentration difference y*  y in the vapour (cf. Fig. 1.5): —£
(1.24)
where y* is the phase equilibrium concentration of the more volatile component in the vapour in contact with the liquid of concentration x* at the phase boundary in any given horizontal crosssection of the column; and x and y are the fractions that correspond to the concentrations of the more volatile component in the bulk of the vapour and in the liquid respectively. It may often be assumed that the resistance to mass transfer in rectification is predominantly in the vapour phase, i. e. x —» x*. In this case, the surface mass transfer coefficient in the liquid phase is 3L —» °o and that in the vapour phase fV is identical to the overall mass transfer coefficient on the vapour side kov. Accordingly, NTUV = NTUOV. The height of a transfer unit is then defined by
1.1
Fundamental operating characteristics of packed columns for gasliquid systems
HTUOV =
H NTUn
H
(125)
dy yey
If it is assumed that kov is constant over the height of the column in mass transfer controlled by the vapour phase, a mass balance yields HTUOV =
(126) ds kov aph
where aph is the phase contact area per unit column volume, ds is the column diameter, V is the molar flow rate of the vapour, and HTUOV is usually determined by experiment. Hence the following relationship exists between the number of theoretical stages per unit height nt/H and the height of a transfer unit HTUOV: V H
HTUn
(127)
\n[myxy
(p v ) x * = x =k o v
"it y*dy x+dx
0&Z7/Z2 y
Liquid mole fraction x ^o
x0
J
a=
Fig. 1.5. Determination of the number of transfer units by the twofilm theory
10
1 Introduction
In other words, the number of transfer units in systems with a low relative volatility is given by (NTUov)a
= smal,
= n,
(128)
Likewise, the height of a transfer unit can be equated to the height equivalent of a theoretical stage, i.e. {HTUOy)
a
,
small
= HETS = —
(129)
The stripping factor X for a given section of the column is defined as the product of the mean slope myx of the equilibrium curve and the molar vapour/liquid ratio VIL, i. e. \ = myxj
(130)
Once the height of a transfer unit HTUOV and the number of transfer units NTUOV are known, the height of the column required for the relevant separation process can be obtained from their product. Hence, cy
H = HTUQV
' NTUOV = HTUOV
^—
(131)
The figure thus derived is identical to that obtained from the number of theoretical stages nt and the separation efficiency ntIH for the packing concerned {cf. Eqn (127)}, i. e. H
=
An analogous analysis applies for mass transfer in the liquid phase. This procedure for the determination of column height is referred to in the literature as the HTUNTU concept. It is applied in Chapters 3, 5 and 14. The efficiency, expressed as the number of separation units per unit height NIH, can be assessed graphically from its relationship to the column load or capacity factor, which can be written as NIH = i{Fv)
(133)
A knowledge of this function is essential in determining the load relationships for the pressure drop per unit height AplH {Eqn (15)} and the pressure drop per separation unit Ap/TV {Eqn (18)}. These relationships allow the column volume vv per unit of vapour flow rate and unit of separation efficiency to be determined in terms of the capacity factor /v{Eqn (134)} or the pressure drop per unit of separation efficiency ApIN {Eqn (135)}, i. e.
1.2
Theoretical column efficiency
11
vv=i(Fv)
(134)
vv=f(Ap/N)
(135)
The specific column volume vv is an important factor in determining the capital investment costs and is defined by
where H is the effective height of the column, N is the number of theoretical separation units, and uv is the superficial vapour velocity.
1.2 Theoretical column efficiency The relative volatility a, a term that was introduced in Eqns (128) and (129), is a measure for the ease with which a mixture can be separated. It expresses the relationship between the molar fraction y of the more volatile component in the vapour and that of the liquid x with which it is in phase equilibrium; and it is defined by
Its magnitude governs the shape of the equilibrium curve (cf. Fig. 1.4), which is defined by the following equation:
y =f
w
= i
a + (
/i)x
^38)
If a is constant, the curve assumes the form of an equilateral hyperbola. The greater the value of a, the greater the value of y for a given value of x. As a rule, the relative volatility a of the two components of a mixture, and thus the ease with which they can be separated, decreases with a rise in pressure. Thus, if the value of a for a given mixture is comparatively small, the number of theoretical stages nt required for separation increases with the specific pressure drop Ap/nt within the packing, particularly during vacuum operation. If the pressure at the head of the column pT is kept constant, the pressure drop Ap governs the rise in pressure up to the value at the bottom of the column pB, i.e.
[^y
(139)
It follows that the reflux ratio required for separation in the enrichment zone of a rectification column rises. In other words, the energy consumption must increase. In view of the following relationship, the liquidvapour ratio also increases:
12
1
Introduction
L_ V
(140)
r+ 1
Hence, the number of theoretical stages required for a given separation task, as defined by Eqn (141), is greater in beds of packing with high values of Ap/n, than in those with low values (cf. Fig. 1.6): Ap
Ap V\ n,
(141)
If this aspect is taken into consideration in the planning stages of a separation plant, it will be seen that the maximum feasible load entails not only the smallest column diameter but also the largest number of theoretical stages, and thus the greatest height. Hence, if separation is under vacuum with a large number of theoretical stages, the optimum load will be less than the maximum to an extent that depends on the pressure drop characteristic for the packing selected. Accordingly, the design load in separation tasks of this nature depends on the optimum pressure drop per separation stage and is associated with the minimum total costs. Particular attention must therefore be devoted to the pressure drop per theoretical stage Ap/nt in selecting packing for rectification processes involving a large number of theoretical stages. As Ap/nt increases, the relative volatility a of the mixture decreases in the direction from the top to the bottom of the column. Consequently, the theoretical number of separation
0
Liquid/Vapour ratio L/V
Reflux ratio r Fig. 1.6. Qualitative effect of the pressure drop per theoretical stage on the relationship between the number of theoretical stages and the reflux ratio
1.2
13
Theoretical column efficiency
stages nt ought to be higher than that in an isobaric column (ntiso), i.e. a column in which there is theoretically no pressure drop, and the ratio ntisolnt {Eqn (142)} can be regarded as the theoretical column efficiency r\c {Eqn (143)}: (nt)
Ap/nt = 0
(nt)
Ap/m > 0
=
nttiso
(142)
n
t
f [pT, a r Ap/nt> nt(L/V,
(143)
In other words, the theoretical column efficiency depends on the operating pressure pT and relative volatility aT at the top of the column, the pressure drop per separation stage Ap/nt, and the number of theoretical stages nt. The value of r\c thus varies from the one separation task to another. It is comparatively difficult to calculate x\c accurately from phase equilibrium relationships, and a graphicalmathematical method based on the qualitative method shown in Fig. 1.7 would therefore be more expedient for the evaluation of Eqn (141). This plot is analogous to that proposed by Gilliland for isobaric (theoretically Ap/nt = 0) columns. The ordinates in the diagram are referred to as stagenumber parameters and are defined by Eqn (144) for isobaric and by Eqn (145) for nonisobaric columns, i. e. _ ft t, iso n
^t,min,iso , 1L
t,iso ~
ll

(144)
ll
t
S
_ 
t,min,iso
„
Fig. 1.7. Determination of the theoretical column efficiency
. 1

S
Wnt
(145)
> 0
o(vD v rrmm,iso •
e=
v
g rmin,iso+
Energy parameter
The abscissae are referred to as energy parameters and are defined by Eqn (146) for isobaric and Eqn (147) for nonisobaric columns, i. e.
14
1
Introduction risormin.iso
(vl)rminjso
=
e
^
=
o
( 1
j
^+1
.46)
7
vg rw/n^/50 + 1
According to Eqn (146), the reflux ratio riso in the isobaric column exceeds the minimum rminJso by a factor v, i. e.
Similarly, according to Eqn (147), the reflux ratio r in the real column exceeds the minimum in the isobaric column rminiso by a factor vg, i.e. f
=
V
g rmin,iso
(! 49 )
If the factor v by which the actual reflux ratio exceeds the minimum rmin in the real column is the same as that for the isobaric column, as determined by Eqn (147), the following equation would apply: r = v rmin
(150)
In this case, the factor vg for the real column is given by Eqn (151), which is obtained by combining Eqns (149) and (150); and the reflux ratio r for the real column, by Eqn (152), which is obtained by combining Eqns (148) and (150), i. e.
(151)
r =ris0^shL
(152)
'min, iso
This method allows the number of theoretical stages nt and the reflux ratio r for a real column to be determined from the corresponding values ntminiso and rminiso for an isobaric column. The theoretical column efficiency, as defined by Eqn (142), can then be obtained quite easily in the light of the qualitative diagram in Fig. 1.7. The following relationships apply and can be evaluated by alternative means: t, min. iso
iso
si co\
r] c = — —^—J v\c = nt,iso
(153) 1  5
n
t,min,iso
=
d54) ' ^
_Lz±_ numinAso + siso *
^iso
n
t,min,iso
'
3
1.2
15
Theoretical column efficiency
An example of a diagram that can thus be obtained is shown in Fig. 1.8. It allows the actual values for the reflux ratio and the number of theoretical stages to be obtained in both isobaric and real columns, i.e. for both Ap/nt = 0 and Aplnt > 0, from the corresponding minimum values for an isobaric column, i.e. a column with no pressure drop. In this case, the theoretical column efficiency r\c will also be known. It is evident from Fig. 1.9 that a low theoretical column efficiency, corresponding to a large number of theoretical stages, can be expected if the energy requirements are high in rectification columns with a moderate to comparatively high pressure drop per theoretical stage Ap/nt. This applies in this case particularly to columns that are operated with a lower reflux ratio, as defined by 1
(156)
Hence, an urgent requirement in separation processes of this nature is packing with a very small pressure drop per theoretical stage, e.g. 0 < Ap/nt < 3 mbar. The advantages of packing with small values of Ap/nt are demonstrated in Fig. 1.10. They apply particularly to operation under vacuum with a large number of theoretical stages nt.
0.7 0.6 0.5
V\ \ A V V\ \ \A \ \
\s s \
0.4
N
\
n s
tntmin.iso 1
r
s
s
0.3
X
2
0.2 nnin.iso 'Vg ~ ' ) Vg ^m i n. i s o "*"'
0.1
0.1
0.2
0.3
0.4
\ ^\
\
0.5
0.6
0.7
0.8
0.9
1.1
Energy parameter e Fig. 1.8. Diagram for the determination of the number of theoretical stages in nonisobaric vacuum rectification. Plotted for vacuum systems with relative volatilities between 1.1 and 3.6 and overhead pressures between 20 and 250 mbar
16
Introductior
eon column effi cien
1.0
Ap/n t = 6.5 fnbar
\
f
0.8
^. —' l , "C — ^—
0.6
T" 7 r~~ k7
i—•
"120 f)pm = 0 1 53 ] = 0.947 f =1
Ap/nt = 13mbar
I
0.2
• •
PT =15C mb(Jl
/
0.4
x B = 2 0 0 ppm »» —
•
90
100
110 120 Reflux ratio r
130
140
150
Fig. 1.9. Theoretical column efficiency as a function of the reflux ratio in the rectification of a mixture of thionyl chloride and ethylene chloride
too
=
,
=
=
:?
•
/
0.96 \
0.92 0.88 0.84
/ /
0.80 g  0.76
/ / /
0.72 0.68 10
7
/
A
I / /
\
V
j
/
/
/ *
7 /
/I
J
A 'J7 / / 20
1/ /
40 60
x D =0.9995, a T = \M ^tmin.Jso
100
=
^L
200
400 600 1000
Pressure at head of column pT [mbar] Fig. 1.10.
Theoretical column efficiency as a function of the overhead pressure
1.3
Energy consumption and number of theoretical stages
17
1.3 Energy consumption and number of theoretical stages One of the most important tasks in planning rectification plants is the exact determination of the relationship expressed by Eqn (141), i. e. between the number of theoretical stages nt and the reflux ratio r that corresponds to a constant pressure pT at the top of the column and that is required to separate a mixture with lowboiling mole fractions of xF, xD and xB in the feed, distillate and bottoms. This relationship forms the basis for all optimization calculations by fixing the mutual dependence of capital expenditure and the costs of utilities. This is demonstrated qualitatively in Fig. 1.11. The number of theoretical stages under otherwise identical conditions is theoretically higher in the separation of systems with a low relative volatility a than of systems with a high one. This relationship can be expressed in thermodynamic terms and, as has been demonstrated in Section 1.2, is of particular importance in planning rectification processes with a large number of theoretical stages designed to separate mixtures whose relative volatilities are comparatively small and, furthermore, become even less at higher pressures. The economics in cases of this nature dictate the use of packing with a low pressure drop per theoretical stage Ap/nt. This requirement is illustrated qualitatively in Fig. 1.6, which shows the number of theoretical stages nt as a function of the reflux ratio r for columns with low and high values of Ap/nt. A diagram of this nature is characteristic for the vacuum rectification of a mixture whose relative volatility a is comparatively small at a column overhead pressure pT and becomes progressively smaller as a result of the rise in pressure that occurs as the mixture descends through the column. Economic limits are imposed on the pressure drop per theoretical stage Ap/nt in separation tasks of this nature, because the minimum total costs CT>min, i.e. the sum of the capital investment C7 and the operating costs Co, shifts towards high reflux ratios r and towards large numbers of theoretical stages. The relationship is shown qualitatively in Fig. 1.12. The consequence of the shift is a pronounced rise in the minimum total costs CT>min, as is evident from the qualitative diagram presented in Fig. 1.13. The only economic solution for vacuum rectification in this case is to install lowpressuredrop, highly efficient packing, because it allows considerable savings in costs.
\ CO CD CO
x F , x D , xB = const
)
•
CO
1D3I
\
\
man! o
I ZD
Fig. 1.11. Qualitative relationship between the number of theoretical stages and the reflux ratio with the relative volatility as parameter
rmini
^ ^ " ^ ^
Reflux ratio r
18
1 Introduction
Theoretically, the curve that joins the minima M7, M2, in the set of total costs curves presented in Fig. 1.13 passes through a minimum itself. This case would arise in vacuum rectification with a large number of theoretical stages when the progressive increase in the pressure drop per theoretical stage Ap/nt is initially associated with a drop in capital investment costs; and subsequently, with a rise. The drop could be caused by the reduction in column diameter; and the rise, by the cumulative effect of the growing number of theoretical stages. Hence packing of this nature has an optimum value for the pressure drop per theoretical stage (Ap/nt)opt, at which the total costs CT pass through a minimum. The parameters that are given by the definition of the task are the molar flow rate F of the mixture fed with a molar fraction of xF of lowboiling components and the specified purities of the distillate and bottoms, which flow at rates of D and B and with molar fractions of xD and xB, respectively, of the lowboiling component. The rate of heat flow Q in a rectification plant operated along the lines of the flow chart shown in Fig. 1.4 is governed by the reflux ratio r, the characteristic molar liquid enthalpies hD' and hB of the distillate and bottoms at their respective boiling points, the molar liquid enthalpies hF and hF of the feed at its boiling point and its inlet temperature, respectively, and the molar evaporation enthalpy Ahvof the overhead product vapour, i.e. _ xD  xB
h
The parameter that decisively affects the rate of heat consumption is thus the reflux ratio r. It must always be higher than the minimum value rmin that is associated with an infinitely large number of theoretical stages and would therefore raise the costs to an infinite extent (cf. Fig. 1.11). In binary systems the minimum reflux ratio rmin is comparatively easy to determine (cf. Fig. 1.14). Thus, if flow is equimolar, min
~
x ° ymin
1
x
° ~yi ylx]
n ^sn (1 58) "
If the molar vaporization enthalpy A/i, of the lowboiling component differs from that of the high boiler Ahh, r r
"""
=
K yi
~
KxD
XD X
~ '
 1
yix,
(159)
(159)
where K is the factor given by Eqn (118) in Section 1.1. In Fig. 1.14, ymin is the point where the enrichment line, which passes through the common intersect / of the gline and the equilibrium curve, intersects the axis of ordinates. The boundary case, in which hardly any overhead product is withdrawn arises if the reflux ratio r is infinitely large. The curves for the rectification and stripping zones then coincide with the diagonals in the ylx diagram. This case corresponds to a minimum number of theoretical stages ntmin, which can be calculated from the values of xD and xB for the lowboiling fractions in the overhead product and the bottoms by means of the Fenske equation, if it is assumed that the relative volatility is constant, i.e.
1.3
Energy consumption and number of theoretical stages
00
1  — as
20
60
100
140
180
220
260
300
340
380
420
460
500
Area per unit volume a [ m 2 /m 3 ] Fig. 2.3. The relationship between the relative void fraction, the area per unit volume, and the average wall thickness of packing
2.3
Geometric packing parameters
29
In principle, Eqns (21) to (24) are valid for all beds of packing, but the information that they yield on the efficiency, capacity, and pressure drop is purely qualitative. Other parameters are required to evaluate the performance, and they must allow for the geometry and texture of the packing. Together with 8 and a, they govern the phase distribution and the area of contact between phases. Eqn (24) reveals the limits within which the effective void fraction 8 for a desired surface area per unit volume a can be altered by appropriate selection of the practically realizable thickness s of the material. It can be seen from the nomogram presented in Fig. 2.3 that the effective void fraction increases as the thickness of the material decreases. The packing density TV and thus the area a per unit volume in random beds may be somewhat greater in largediameter columns (subscript T) than in pilot columns (subscript P)
Fig. 2.4. Flue gas desulfurization plant in one of BASF AG's power stations. It consists of two absorption columns of 9.4 m diameter and 35 m total height. The beds of 50mm plastic Hiflow rings are packed to an effective height of c. 8 m
30
2
Types of packing
of comparatively small diameter. The differences in the area per unit volume and the relative void fraction can be obtained from the following equations: (25) ET = 1  (1  EP) ^~
(26)
J\p
A photograph of a twinline absorption plant is shown in Fig. 2.4. This example clearly demonstrates that columns with random beds of modern packing can also give good results in plants of large capacity.
3 Experimental determination of packing performance Accurate knowledge of the performance characteristics is a fundamental requirement for the optimum design of absorption, desorption and rectification columns from the aspects of fluid dynamics and mass transfer. Systematic experiments have led to new fundamental concepts and fresh knowledge in modern packing technology. They have allowed mathematical models to be derived from comprehensive physical relationships between the packing performance, the fluid dynamics, the loading conditions, the geometry of the packing, and the properties of the system to be separated. The results of the experiments have been evaluated in terms of the interrelationships between the separation efficiency, pressure drop, liquid and gas loads, liquid holdup, residence time, and pressure drop. Particular attention is attached to the load at which the liquid commences to hold up in the column and that at which flooding occurs. The studies have also yielded information on the operating zone of a packing, a knowledge of which is required for safe design and operation.
3.1 Pilot plants for testing gasliquid systems The experimental results reported here were gained in a number of benchscale and pilot plants. The flow chart for one of the pilot plants used for absorption/desorption experiments and hydraulic studies is reproduced in Fig. 3.1; and that of the layout for the rectification experiments, in Fig. 3.2. Various distributors with different numbers of perforations, five of which are shown in Figs. 3.33.7, were taken to determine the effect exerted by the number of liquid streams per unit of crosssectional area. In the main tests, the number of liquid distribution points was varied between 15 and 2400 per square metre.
3.2 Evaluation of measurements The rectification efficiency, as expressed by the number of theoretical stages per unit height of packing nt/H, is a function of the vapour capacity factor Fv at a constant liquidvapour ratio LIV, i.e. nJH = f(Fv)
(if LIV = const.)
(31)
The same applies to the pressure drop per unit height, i.e. Ap/H = f(Fv)
(if LIV = const.)
(32)
The absorption efficiency, i.e. the height of a transfer unit HTUOV in the bed of packing, can also be expressed as a function of the capacity factor Fv if the liquid load uL is kept constant, i.e. HTUOV = f(Fv)
( if "L = const.)
Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
(33)
32
3
Experimental determination of packing performance
I
s
ob"S
Alternatively, it can be expressed as a function of wL if Fv is constant, i. e. HTUOV = f ( M J (if / v = const.)
(34)
The pressure drop per unit height of bed Ap/H is also a function of Fv if uL is constant, i.e.
A/?/// = f (Fv) (if wL = const.)
(35)
3.2
33
Evaluation of measurements
a
c 'EH
o
u
If the resistance to mass transfer is entirely in the liquid phase, the desorption efficiency is given by $LaPh, the product of the mass transfer coefficient 3L and the interfacial area per unit volume aPh. In this form, it is referred to as the volumetric mass transfer coefficient and is expressed either as a function of the liquid load uL at a constant gas capacity factor Fv {Eqn (36)} or as a function of the gas capacity factor at a constant liquid load {Eqn (37)}: fiLaPh = t(uL)
(if Fv = const.)
(36)
fiLaPh = f(Fv)
(if uL = const.)
(37)
34
3
Experimental determination of packing performance I
&

I
'
^
$
l
d5 = 450 mm ds= 300 mm
&  •
l
Z = 730 1/m2 Z = 1350 1/m2
Fig. 3.3. Perforatedpipe distributor for pilot columns
d s =220 mm
Z = 2150 1/m2
Fig. 3.4.
Capillary distributor for pilot columns
Likewise, the liquid holdup hL can be expressed either as a function of the liquid load at a constant gas capacity factor {Eqn (38)} or as a function of the gas capacity factor at a constant liquid load {Eqn (39)}: hL = f(uL)
(if F v = const.)
(38)
hL = f(Fv)
(if uL = const.)
(39)
3.2
d s =450mm
Evaluation of measurements
1/m2
Z = 380 1/m2
Fig. 3.5. Profiledslot distributor for pilot columns
d s =500 mm
Fig. 3.6. Nozzle distributor for pilot columns
.
Z = 610 1/mz
35
36
3
Experimental determination of packing performance
= 800 mm
Z = 490 1/m 2
Fig. 3.7. Funnel distributor for pilot columns
Normally, flooding represents the condition for the maximum capacity of a packed column. In other words, the dynamic load at the flood point Fv FJ/VQ^ is a measure for the upper capacity limit under operating conditions. It can be determined from its relationship to the dimensionless flow parameter \), which is defined by Eqn (13). Hence, Qv VQL
\ V V 6L
(310)
The relationship expressed by Eqn (310) can be obtained by experiment. The height HTUOV of an overall mass transfer unit is related as follows to the heights of the transfer units in the gas HTUV and liquid HTUL phases: HTUQV
= HTUV + X HTUL
(311)
where X is the stripping factor and is given by (312) in which myx is the average slope of the equilibrium curve in the range of concentrations concerned.
3.3
Test systems
37
The height of a transfer unit in the liquid phase HTUL is obtained from the corresponding number of transfer units NTUL: HTUL =  J ^
(313)
The volumetric mass transfer coefficient $LaPh in the liquid phase is given by
The numerical value of HTUOV is obtained from the number of overall transfer units NTUOyin the gas phase for a given liquid load uL. i.e.
Once the values for HTUOV and $LaPh are known, the height of a gas transfer unit HTUV can be determined from HTUV = HTUOV  myx j . J±±
(316)
In absorption tests with an ammonia/airwater system, the resistance to mass transfer is located in both the gas and liquid phases. On the other hand, resistance to mass transfer is entirely in the liquid phase in desorption tests with a carbon dioxidewater/air system. These two systems have practically identical diffusion characteristics. Thus, data derived from tests on the one system may be applied to the other system. For instance, if HTU0V for the absorption system is known, the corresponding value of HTUV can be calculated by inserting the value of 3L1
Ar
70
/
A~—0
0.4
0.8
Y
uvwn\ene
TTT 1.2
1.6
2.0
Vapour capacity factor F v [m'
1/Z
2.4 1
2.8 3.2 1/2
s" kg ]
Fig. 3.8. Liquid load as a function of the vapour capacity factor in systems operated at atmospheric pressure and under vacuum. Valid for total reflux
3.4
Experimental results
41
The physical properties of the gasliquid systems selected for the mass transfer studies are reviewed in Tables 3.5 to 3.8. If the system's resistance to mass transfer is mainly in the liquid phase, Table 3.5 applies; if it is mainly in the gas phase, Table 3.6; and if it is in both the gas and liquid phases, Table 3.7. The physical properties relating to rectification, i.e. vapourliquid, systems are entered in Table 3.8; and Fig. 3.8 indicates the wide range of liquid loads encompassed by the rectification tests performed under total reflux with these systems. The figures listed in Table 3.9 describe the range of capacities and the physical properties of all the mass transfer systems that were evaluated. Two systems listed in Table 3.10 were selected to study absorption processes in which mass transfer is accompanied by a fast chemical reaction in the liquid phase.
3.4 Experimental results Some of the results determined in experiments on fluid dynamic behaviour and mass transfer efficiency are presented in Figs. 3.93.50. They are representative for the comprehensive test program and were obtained by systematic evaluation of Eqns (31)  (310) and Eqn (317). Thus Figs. 3.93.17 show the efficiency and pressure drop chararacterics for random beds of metal packings in pilot columns of various diameters. They apply for rectification at atmospheric pressure and under vacuum with total reflux. Figs. 3.18 and 3.19 show the corresponding relationships for random beds of plastics and ceramic packings. It is evident from Figs. 3.203.22 that geometrically arranged metal packing has a low pressure drop per theoretical stage and a very high separation efficiency that depends very little on the load. The results represented in these diagrams were obtained in vacuum rectification. As opposed to this, the efficiency of metal gauze packing depends greatly on the load (Fig. 3.23). This can be ascribed to the fact that the surface of the gauze exerts a capillary action, which is particularly effective at low liquid loads, under which it spreads the small amounts of liquid uniformly over its surface and thus gives rise to a higher efficiency. Typical loglog pressure drop diagrams for random beds of packing produced from different materials are reproduced in Figs. 3.243.29. An increase in the slope of the pressure drop curves indicates that the loading point has been exceeded. Figs. 3.30 and 3.31 provide unmistakable evidence to the effect that, if the liquid load is kept constant below the loading point, the liquid holdup is practically independent of the gas load. On the other hand, it increases considerably in the loading range and attains a maximum at the flood point. The curves shown in Figs. 3.323.38 are characteristic for the relationship between the liquid holdup and the liquid load when the gas load is constant. Figs. 3.32 and 3.33 illustrate the effect exerted by the dimensions of the packing; Fig. 3.34, the effect of the material from which the packing was produced; Fig. 3.35, the effect of the shape of the packing; and Fig. 3.36, the effect of the system. Although geometrically arranged packing presents by far the greater area per unit volume, its liquid holdup is only slightly more than that of random packing (Figs. 4.36 and 4.37).
1.187
293
15.1
15.1 4.7 2.2 15.9 15.6 15.6 15.6 15.5
v v 10 6 m2 / s
15. 4
23.8 14.9 12.2 13.1 12.9 10.8 16.5 12.4
Dv10 6 m2 / s
= negative system;
p
= positive system
33 67 133 267 533 1000 103 133 267 1000 133 13 1000 1000
Chlorobenzene / ethylbenzene" Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene11 Chlorobenzene / ethylbenzene" Toluene / noctane11 Toluene / noctane11 Toluene / noctane11 Ethanol / waterp Ethylbenzene / styrene" trans1 cwDecahydronaphthalene" Methanol / ethanol11 1,2Dichloroethane / toluene"
n
Pr mbar
Rectification systems
314 329 345 364 385 407 321 327 345 352 350 336 343 365
Ts K 0.140 0.268 0.510 0.967 1.827 3.241 0.373 0.473 0.900 1.294 0.483 0.066 1.303 3.200
Qv
kg/m 3 52.4 28.7 15.8 8.8 4.9 2.9 19.1 15.3 8.5 8.2 15.9 105.8 8.4 3.2
Vv10 6 m 2 /s
0.980
0.633 0.317 0.185 1.220 1.208 1.452 0.950 1.246
64.8 35.8 19.9 11.1 6.3 3.7 21.0 17.0 9.5 14.5 19.9 120.0 9.1 4.0
Dy10 6 m 2 /s
Table 3.8. List of properties of the systems investigated in the rectification studies
1.188 1.763 4.929 1.150 1.297 1.162 1.162 1.168
293 301 295 303 297 300 300 298
Ammoniaair/water Ammoniapropane/water AmmoniaFreon 12/water Sulfur dioxideair/water Sulfur dioxideoxygen/water Acetoneair/water Methanolair/water Ethanolair/water Carbon dioxideair/ 1 M NaOH in water
QV kg/m 3
T K
Systems with resistance in the gas and liquid phases
0.809 0.803 0.793 0.791 0.785 0.780 0.908 0.904 0.894 0.567 0.798 0.881 0.929 0.806
Scv
1043
999 996 998 989 998 997 997 997
QL
956 941 926 908 887 866 779 774 758 787 835 846 739 968
kg/m 3
QL
kg/m 3
0.59 0.52 0.45 0.39 0.34 0.30 0.53 0.50 0.43 0.53 0.45 1.24 0.54 0.35
6 v L •10 m2 /s
1.20
1.03 0.84 0.96 0.99 0.92 0.86 0.86 0.89
v L 10 6 m 2 /s
Table 3.7. Properties of the gasliquid systems for which allowance had to be made in the evaluation of mass transfer
28.5 26.9 25.1 23.2 21.1 19.0 23.1 22.5 20.7 25.7 21.0 26.0 17.2 22.3
a L 10 3 kg/s 2
75.0
72.7 72.0 72.4 70.0 72.3 72.1 72.1 72.2
a L 10 3 kg/s 2
2.33 2.85 3.50 4.33 5.41 6.67 2.33 2.53 3.18 3.42 3.64 1.04 4.75 4.86
D L 10 9 m 2 /s
1.77
1.72 2.01 1.79 1.87 1.66 1.18 1.44 1.09
D L 10 9 m 2 /s
255 181 128 89 62 45 195 171 118 82 123 1019 113 70
ScL
678
597 418 536 530 556 728 600 819
ScL
jars'
B
3.4
Experimental results
43
Table 3.9. Loading ranges and properties of the systems investigated Gas capacity factor Liquid load
F v [m"1/2 kg1/2 s uL [m3/m2 h]
Liquid density Liquid viscosity Liquidside diffusion coefficient Surface tension Gas density Gas viscosity Gasside diffusion coefficient Schmidt number of liquid Schmidt number of gas
QL [kg/m3] vL [m 2 /s] D L [m 2 /s] aL [kg/s 2 ] Qv [kg/m 3 ] vv [m 2 /s] D v [m 2 /s] ScL
0.00292.773 0.2563118.20 7581237 0.301.66 1.046.50 17.274.0 0.0664.929 2.2126.2 3.787.4 451186 0.1852.122
SCy
Number of packings investigated Number of absorption and desorption measurements Number of rectification measurements Absorption and desorption systems investigated Rectification systems investigated
67 2605 665 31 14
Table 3.10. Absorption systems embraced by the experiments System
NH3  Air/H 2 O 3
QV [kg/m ] 3
QL[kg/m ] 2
r]v/Qv [m /s] 2
D v [m /s] Transfer component dissolved by Conditions
NH3  Air/H 2 O + H2SO4 1.18
1.18
1.18
1032.7
998.2 15.210"
6
2.3810"
15.210 5
Physical absorption in the solvent
SO2  Air/H 2 O + NaOH
1039.4 15.2lO"6
6
2.3810
5
Chemical absorption: 2NH 3 + H2SO4+ H2O = (NH4)2 SO4 + H2O
1.2lO"5 Chemical absorption: SO2 + 2 NaOH = Na2SO3 + H2O
System operated at standard temperature and pressure
Fig. 3.39 gives an impression of the relationship between the flood load and the flow parameter for geometrically arranged metal packing of various sizes. As opposed to this, Fig. 3.40 clearly shows that the shape of packing exerts a not inconsiderable effect on the load at the flood point, even if the packings compared are of the same nominal size. Characteristic results of absorption experiments are presented in Figs. 3.41 and 3.42; and of desorption experiments, in Figs. 3.433.45. The effects of the packing dimensions are also revealed in the latter. It is evident from Fig. 3.46 that, in the range below the loading point, mass transfer in systems with resistance on the liquid side is independent of the gas load. Fig. 3.47 demonstrates that, if mass transfer in absorption systems is predominantly in the gas phase, it can be improved by increasing the gas or liquid load.
44
3
Experimental determination of packing performance
In the course of the studies, it was observed that when new, freshly installed beds of packing were first taken on stream the liquid holdup was slightly less than that of the packing a few days later. The same applies to the mass transfer, as is evident from Fig. 3.48, which is valid for a desorption system. In experiments with an absorption system (cf. Fig. 3.49), the differences in mass transfer were significantly greater, and the efficiency became stable after an operating period of a few days. Other studies were performed on plastics packing that had been given a surface finish, e.g. rendered hydrophilic. They led to the conclusion that the surface treatment did not increase the efficiency to a level higher than that attained by unfinished packing after an operating period of one week at the most (cf. Fig. 3.50):
Raschig rings, metal, ds=500mm, Z = 600 1/m2 Ethylbenzene/Styrene, 67 mbar, L/V = l. H = 2 m
cu .—.
£==
A.
2
D
\
r\ \
—.—•o—
O~
24
f
—o— —o—
20 O
^
—A—
16
j
50 mm 25 mm 15 m m
9 /
/ /
12 CO '
•
y'
/
'
S5
S
A
o CO CO
a>
a E
Q.
c^
o cu
Q.
6 4 2
I
1 1
1 j
1
/
J
V
CDCO
0 0.4 0.6 0.8 1.0 12 1.4 16 1.8 2.0 2.2 2.4 Vapour capacity factor Fv [m' 1/z s"1 kg" 2 ] Fig. 3.9. Performance data for metal Raschig rings showing the effect of packing size
3.4
45
Experimental results
Raschig rings, metal, ds= 500 mm, Z = 600 1/m2 Ring size 50 mm, H = 2 m, ratio L/V=1
20 "Z 16 a „
•••••• 1,2Propylene/Ethylene glycol 6.7mbar  ©  Ethylbenzene/Styrene 34 mbar  ©  Ethylbenzene/Styrene 67 mbar Methanol/Ethanol 1 bar
a
JZ*
/
"a «_ . a CO
T
/
Q
^— 0.4 0.6 0.8
1.0
1.2 1.4
1.6
1.8 2.0 2.2 2.4 2.6
Vapour capacity factor Fv [m" 1/2 s"1 kg 1/2 ] Fig. 3.10. Performance data for metal Raschig rings showing the effect of the system and the test conditions
46
3
Experimental determination of packing performance
Pall rings, metal, ds = 500 mm, Z = 600 1/m2 Ethylbenzene/Styrene, 67 mbor, L/V = 1, H = 2 m ^
"
3
cr" o—••
CF—6O
—O"
o
A
12 10
a
/
>[3
 — u — bu mm — o — 25 mm —A— 15 mm
r
/
t .
^"'
/
•
y
, —
oS7 CD •
6
1
/ /
'
CD < ] QCO
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Vapour capacity factor Fv [m~ 1/2 s"1 kg 1/2 ]
Fig. 3.11. Performance data for metal Pall rings showing the effect of packing size
3.4
47
Experimental results
Pall rings, metal, ds = 500 mm, Z = 600 1/m2 Methanol/EthanolJ bar, L/V = 1. H = 2 m
"
_r—
4
^
cz
—^
o
.
i
'• •
•
o— —o =
12 10
co CD
i A
vsb
ZD CO
D—^ ]
•
— o — 50 mm — a — 25 mm — A — 15 mm
' 3 
yr
^
Q .
O
/ /
I d
V ./
^.
> > —O"
A
u
!
i
CO CO CD
Ja D
E
(—>
o CD CDCO
cr
ID
M
M
0.4 0.6 0.8
—
1.0 1.2
—
1.4
1.6 1.8 2.0 2.2 2.4 2.6 2.'
Vapour capcity factor Fv tm" 1/z s"1 kg 1/2 ] Fig. 3.12.
Performance data for metal Pall rings showing the effect of packing size
48
3
Experimental determination of packing performance
Pall rings, metal, ds= 500 mm, Z = 600 1/mz Ring size 50 mm, H = 2 m, ratio L/V = 1
1,2Propylene/Ethylene glycol ©• Ethylbenzene/Styrene  ©  Ethylbenzene/Styrene
_
6.7 mbar
6
/
a .
^
•
2 ••ir
0.8
1.0 1.2 1.4 1.6
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
Vapour capacity factor Fv [m" 1/z s"1 kg 1/z ] Fig. 3.13. Performance data for metal Pall rings showing the effect of the system and the test conditions
3.4
49
Experimental results
Metallic rings, ds=220 mm, Z=2036 1/m2 Chlorobenzene/Ethylbenzene, 67 mbar, L/V=1, H=15 m
38mm Pall ring N=14301 irr3 — o — VSP ring 1 N = 30948 rrr3 —^— 50mm Pall ring N=6000 m"3 — o  VSP ring 2 N = 7621 m"3 ••••A
a Z3 CO
i 6 E
•te _ co CO
6
/
fcr .
•
*
0 o CD CD.
0
0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Vapour capacity factor Fv [m~1/2s~1 kg 1/z ]
Fig. 3.14. Performance data for various metal rings determined in tests on the same system and under the same conditions
50
3
Experimental determination of packing performance
50mm rings, metal, ds=220 mm, Z=2036 1/m2 Chloro/Ethylbenzene, 67 mbar, LAM. H=1.45 m 1.8 .a ^
/ A
1.4
—TT
VP
^ _ . \ / Or
\
3 &—• TOPPok. N = 6880 m
Pall rings. N=6360 nr 3
> /
/
/
0.4
0.8
1.2 1.6 2.0 2.4 2.8 3.2 Vapour capacity factor Fv [m 1/2 s~ 1 kg 1 / 2 ]
Fig. 3.18. Performance data for plastic Hiflow rings showing the effect of packing size
3.6
54
3
Experimental determination of packing performance
50mm rings, ceramic, ds=220 mm, Z=2036 1/m2 Chloro/Ethylbenzene, 67 mbar, L/V1, H1.5 m 2.5 CD
1.5
o
0.5 12 10
•=
.a— Pall ring N6195 1/m3  *  INTALOX saddle N = 8175 1/m3 o— Hiflow ring = 4684 1/m3
^
6
(ZL
< ^
^ ^ o— —•—
Sulzer packing BX Montz packing A1
o CD
rf
—on.
C_>
Q.
"•oE
B1IOC 1 1.5
0.6 0.6
o.; y y ^y°
1
1.5 2 3 4 6 3 Liquid load uL10 [m 3 /m 2 s
Fig. 3.33. Liquid holdup data for metal Montz packing of three different sizes
1.3'i1.43r
10
n
15 20
64
3
Experimental determination of packing performance
50mm Pall ring, d s = 0.3m, H = 1 1.4 m Air/Water, 1 bar,293 K. F V ;J
 M o n t z packing Bl300, met al r
Fh uL>Fi and hL)Ft. They follow logically from the physical model, and the mathematical description applies to the entire loading range.
4.2 Resistance to flow The resistance factor § allows for the geometry of random packing or of the flow channels in systematically stacked beds. It also allows for the transition from laminar to turbulent liquid flow and thus depends on the vapour and liquid loads. The application of Eqn (415) to evaluate experimental results has revealed that § is analogous to the friction factor in pipe flow in that it is a function of Reynolds number Rey for the gas phase. This is evident from Fig. 4.3, which shows the correlation between gas and liquid flow in both circular pipes and packed beds. It can be seen that the slope is practically the same in all cases.
4.2
Res is tan ce to flo w
11
ZD TD
ID
Gos or vapour load u v
o a o
Fig. 4.2. Qualitative relationship between the liquid holdup and the phase loads in a packed column
Liquid holdup hL
The resistance factor § also depends on the liquid holdup, which is defined as the volume of stationary liquid that exists in the form of a film on the surface of the packing or is present in voids, dead spots, and phase boundaries in the bed of packing within a twophase countercurrent column during the period in which the liquid phase descends at a constant rate onto the surface of the bed. There are two components of liquid holdup: a static hLst and a dynamic hL>dyn. Thus hL>dyn
(416)
The dynamic component flows downwards, and the static remains within the bed. As the liquid load increases, the difference between the two components becomes progressively greater, until the stage is reached when the static can be regarded as nonexistent. In most industrial mass transfer processes, the dynamic component preponderates by several orders of magnitude. An expression for hL that is valid over the entire loading range can be obtained by rearranging Eqn (415). Thus
78
4
Fluid dynamics in countercurrent packed columns
Gas Reynolds number Re V(Packing
fe
&
o 3.
00 CD Cd
CO
oo CD
Gas Reynolds n u m b e r R e j Fig. 4.3. Qualitative loglog relationship between the resistance factor and the gas Reynolds number in the channels of a packed column with the liquid Reynolds number as parameter. The corresponding relationship for flow in tubes is presented as a comparison.
hL =
g 3
WiJ
(417)
a
„ 4
/IL) 2
The basic assumption in this case is that the flow of liquid over the packing is laminar. It differs from flow in the vertical channels of the model in that it continually changes direction and is interrupted at boundaries. Another point in which the theory departs from reality is that laminar flow in the film applies only at comparatively low liquid loads. The critical Reynolds number, above which flow becomes turbulent, has been derived from numerous measurements. According to definition, uL
ReL,cr = 10
(418)
For laminar liquid flow in the vertical channels of the model, the exponent n in Eqn (418) is exactly n = V3; and a figure of n = 2/3 has been determined for flow in systematically arranged beds of packing. The value changes at higher loads, and the following relationship for turbulent film flow was established by experiment on about 50 different types of packing dumped at random:
N\\ lh
n = \— ,a
(419)
where h is the height and d the outer diameter of an individual element of packing, N is the number of elements per cubic metre, and a is the surface area per unit volume in m2/m3.
4.2
79
Resistance to flow
Although Eqn (417) can be solved only by iteration, its great advantage is that it is analogous to the equation for twophase countercurrent flow in vertical tubes. The curves presented in Fig. 4.4 convincingly verify this analogy. The first step in their compilation was to rearrange the equation to solve for §, i.e.
hL(zhLf\
uL
1
(420)
UyQv
Values of  thus calculated for flow in a bed of metallic Bialecki ring packing were plotted against the corresponding Reynolds numbers with the liquid load uL as parameter. The values for the Reynolds numbers were derived from the following relationship:
Pipe flow
Bialecki rings
\
VV \ \ \V\ \^\ \ A V .^
100 70
\
V
\\
\\
50 40
V_
30
\ S
20
\
£
\\^ V\ \ \ \ \ \ \ \ \ \
S 5 4
\ \
\ \
10
\
\\
\ \^
3
\
2
L
41'
\
\ V
\V A
\ \ y_N\^\ _^.\
\ !^_ K\
w
ct:
10 Y 2.8
0.7 0.5 0.4

0.3
\
\N
\ ^ y.
\
\ \ \
\ \\ ^ \\ \\\
S
\ \
\
>
\\\ \\
0.2
01
30
= 80m 3 /m 2 h
\\v \\\ \\\ s V L 40 \ Nv v \ \ \ \ NVAS. \ A \ \\ v > v y \ \\
\ \ 0 " X \ \v
CO CD
ri ^g tQl N =78323 1/m3 a =331 m z /m 3 e =0.9381  Syslem: Air/Water 1 bar ; 298 K
5mni Biale :ki
\s
\ \ \— A sy \ \\\> \\ \ yX
u = 80m /m h" V \
J
2
50
100
300 500
1000
r
r" •2.8 3000 5000 10000
Gas Reynolds number Rev Fig. 4.4. Resistance factor as a function of the gas Reynolds number for a packed column and a tube with the liquid load as parameter. Valid for an air/water system at STP.
80
4
Fluid dynamics in counter cur rent packed columns UyidlSp)
Qy
(421)
Key —
The corresponding curves for twophase pipe flow, calculated from the standard equations cited in the literature, have been included in the diagram. The fact that the two sets of curves are largely parallel in the range of laminar gas flow provides striking evidence of the analogy and confirms the validity of the model based on flow in vertical channels in packed columns. The relative positions of the two sets of curves show that the resistance factors are higher in the bed of packing. However, this is only to be expected, because the pressure drop for gas flow in beds of packing is considerably greater than that in vertical smooth pipes. Evaluation of the results obtained on all the packings investigated led to the following relationship: = C Rey2 ReL°
(422)
in which C is a constant that is characteristic for individual types of packing and must be determined experimentally. Numerical values for C at the loading and flood points for various types of packing are presented in Table 4.1. A relationship that is more useful in practice for the determination of § at the loading and flood points in specific separation tasks is (423) C2
rMlL
where r L /ry is the viscosity ratio for the two phases and W is the wellknown flow parameter described by Eqn (13), i.e.
Table 4.1. Data for determining the loading and flood points in random beds of packing Dumped Packing
Pall ring
Ralu ring
Material
Size mm
N 1/m3
Metal
50 35 25
6242 19517 53900
112.6 139.4 223.5
0.951 0.965 0.954
2.725 2.629 2.627
1.580 1.679 2.083
Plastic
50 35 25
6765 17000 52300
111.1 151.1 225.0
0.919 0.906 0.887
2.816 2.654 2.696
1.757 1.742 2.064
Ceramic
50
6215
116.5
0.783
2.846
1.913
Plastic
50 50 hydr.
5770 5720
95.2 95.2
0.938 0.939
2.843 2.843
1.812 1.812
CFI
8
m 3 /m 3
4.2
81
Resistance to flow
Table 4.1. (continued) Dumped Packing
Material
Size mm
N 1/m 3
a m 2 /m 3
m 3 /m 3
E
Cs
cFI
NOR PAC ring
Plastic
50 35 25 6 25 10
7330 17450 50000 48920
86.8 141.8 202.0 197.9
0.947 0.944 0.953 0.920
2.959 3.179 3.277 2.865
1.786 2.242 2.472 2.083.
Hiflow ring
Metal
50 25
5000 40790
92.3 202.9
0.977 0.962
2.702 2.918
1.626 2.177
Plastic
50 50 hydr. 50 S 25
6815 6890 6050 46100
117.1 118.4 82.0 194.5
0.925 0.925 0.942 0.918
2.894 2.894 2.866 2.841
1.871 1.871 1.702 1.98?
Ceramic
50 38 20
5120 13241 121314
89.7 111.8 286.2
0.809 0.788 0.758
2.819 2.840 2.875
1.694 1.930 2.410
Glitsch ring
Metal
30 PmK 30 P
29200 31100
180.5 164.0
0.975 0.959
2.694 2.564
1.900 1.760
Glitsch CMR ring
Metal
1.5" 1.5" T 1.0" 0.5"
60744 63547 158467 560811
174.9 188.0 232.5 356.0
0.974 0.972 0.971 0.952
2.697 2.790 2.703 2.644
1.841 1.870 1.996 2.178
TOPPak ring
Alu
50
6871
105.5
0.956
2.528
1.579
Raschig ring
Ceramic
50 25
5990 47700
95.0 190.0
0.830 0.680
2.482 2.454
1.574 1.899
VSP ring
Metal
50 25
7841 33434
104.6 199.6
0.980 0.975
2.806 2.755
1.689 1.970
ENVIPAC ring
Plastic
80 60 32
2000 6800 53000
60.0 98.4 138.9
0.955 0.961 0.936
2.846 2.987 2.944
1.522 1.864 2.012
Bialecki ring
Metal
50 35 25
6278 18200 48533
121.0 155.0 210.0
0.966 0.967 0.956
2.916 2.753 2.521
1.896 1.885 1.856
Tellerette
Plastic
25
37037
190.0
0.930
2.913
2.132
Hackette
Plastic
45
12000
139.5
0.928
2.832
1.966
Raflux ring
Plastic
15
193522
307.9
0.894
2.825
2.400
DINPAC
Plastic
70 47
9763 28168
110.7 131.2
0.938 0.923
2.970 2.929
1.912 1.991
hydr. = made hydrophilic
82
4
Fluid dynamics in countercurrent packed columns
(4 24)

The one and only constant C in Eqn (423) describes the shape and surface of the packing. The viscosity m and load nL exponents are practically independent of the type of packing, and the form of Eqn (423) has been confirmed for all the types of packing investigated.
4.3 Loading conditions If inertia forces are neglected and steadystate conditions exist in the main loading range, it is assumed for the purpose of drawing up the model that the shear forces and the force of gravity are in equilibrium in a layer of any given thickness between 5 = 0 and s = s0 within the liquid film. It is also assumed that the frictional force exerted by vapour of density QV and velocity uv acts at the surface of the liquid film (cf. Fig. 4.1). At a given liquid load wL, the liquid commences to hold up when its velocity at the interface with the vapour becomes zero, i.e. when ML,S — 0 at s = s0'. UL>S = 0
(ifs
= so)
(425)
The corresponding vapour velocity is the upper limit for the absolutely stable hydrodynamic range defined by
s, as defined by Eqn (426), for uvin Eqn (415) yields the following theoretical relationship for the liquid holdup at the loading point: Solving for hL>s and inserting in Eqn (426) yields the following equation for the vapour velocity at the loading point:
—
i/12 8
12 rw UL QL
8
QL
LI nV/ Qv
As has already been mentioned, the resistance factor § 5 allows for the shape of the flow channels and is therefore dependent on the packing geometry and on the vapour and liquid loads; and it also allows for the transition from laminar flow in the liquid phase. It can be expressed as a function of the flow rate LIV, density QV/QL, and viscosity r\L/r\v ratios by combining Eqns (423) and (13). Thus,
4.3
Loading conditions
83

ci
(429)
Qv QL
In this equation, the load point constant C5, which is specific for the packing, and the exponent ns must be determined empirically. The equation has been confirmed by experiment and is presented graphically in Fig. 4.5. It can be seen from this diagram that a discontinuity, which correlates with the phase inversion, divides the function into two linear sections. The large majority of masstransfer processes take place within the section represented by the lower values of flow parameter on the axis of abscissae. The values at the further end
Phase inversion
Continuous phase :gas ) Disperse phase : liquid S CO
on
0.4
Flow porameter I
ff
V I pL W Fig. 4.5. Qualitative loglog relationship between the resistance parameter and the modified flow parameter
of the axis correspond to very high liquid loads, and the high slope of the linear relationship in this range indicates an increase in the resistance factor 5s and a proportionally greater pressure drop in the gas phase. It can thus be concluded that the intersect of the two straight lines, i.e. the discontinuity, is the point at which phase inversion occurs. In other words, this is the point at which the gas becomes the disperse phase; and the liquid, the continuous. It is given by (430) The associated values for the liquid load correspond to phase inversion at 50100 m3/m2h. Data on the higher loading range are not yet available for all the packings investigated. An example of a known relationship is presented in Fig. 4.6. Accordingly, the values for the constant Cs and the exponent ns in Eqn (429) depend on the loading range. It has been found that the following empirically determined numerical values of ns apply in common for all types of packing in the loading ranges concerned:
84
4
Fluid dynamics in counter cur rent packed columns
(431)
£ W i*> 0.4*„, =0.723
(432)
35mm Bialecki ring, metal, System: Air/Water, 1 bar, 293 K
**
*^
<s
0.1
0.2 0.3 0.4 0.50.6 0.8 1 Flow parameter   / ^ ( A
2
3 4 56
N
Fig. 4.6. Resistance parameter for a bed of metal packing
Numerical values of the constant Cs for specific types of packing are listed in Table 4.1 (randomly dumped) and Table 4.2 (systematically stacked).
4.4 Flooding conditions The flood point in a bed of packing can be described physically by empirical curves in which the liquid holdup hL has been plotted against the gas load uv with the liquid load uL as parameter; or plotted against uL with the gas load uv as parameter. Curves of this nature are presented qualitatively in Fig. 4.2. In the upper diagram, the curves are vertical at the flood point, and can thus be described by the following equations: —— = 0;
uv^
uv>Fl
JJ^ = 0; uL * uLtFl
(tor uv = uv>Fl)
(for uL = uL>Fl)
(433) (434)
Applying these equations to Eqn (415) for n = % leads to the following theoretical flood point correlations:
4.4 Flooding conditions
85
Table 4.2. Data for determining the loading and flood points in geometrically arranged beds of packing Arranged packing
Material
Size mm
N 1/m3
a m2/m3
m3/m3
Pall ring
Ceramic
50
7502
155.2
0.754
Bialecki ring
Metal
35
20736
176.6
0.945
Ralu pack
Metal
YC250
250.0
Mellapak
Metal
250 Y
Gempak
Metal
Impulse packing
Montz packing
Euroform
CFI
8
3.793
3.024
0.945
3.178
2.558
250.0
0.970
3.157
2.464
A2T304
202.0
0.977
2.986
2.099
Metal
250
250.0
0.975
2.610
1.996
Ceramic
100
91.4
0.838
2.664
1.655
Metal
B1200 Bl300
200.0 300.0
0.979 0.930
3.116 3.098
2.339 2.464
Plastic
Cl200 C2200
200.0 200.0
0.954 0.900
2.653
1.973
PN110
110.0
0.936
3.075
1.975
Plastic
for the gas load uV}Fi,
i / T T (ehL>Fl)2 \lhLZL and for the liquid load, 1
QL
(436)
For a given liquidgas mass flow ratio L/V, these equations are related as follows:
u
L,Fl —
Qv Qv QL
Tv
V
(437)
U
V,Fl
It follows that
I  8) =
~y
g
V
s range is a function of uL only and that the gas stream exerts hardly any effect. Therefore, applying the boundary condition implied by Eqn (425) gives rise to the following relationship for the liquid holdup in the uv < uvs range:
4.7
Liquid holdup in packed beds
Fv>e range. Since the efficiency attains a maximum in this loading range (cf. upper diagram in Fig. 4.12), it can be assumed that the droplets are redeposited in the packing. As a result, the area of contact between the phases would be increased, and mass transfer would thus be intensified. Actual flooding does not commence until the liquid load becomes even greater and an increasing quantity of the liquid film or lamella is supported by the energy of the gas stream, as is expressed by a significant rise in the liquid holdup. The fluid dynamics model developed in Section 4.1 is thus confirmed, and it is physically unjustified to describe the onset of flooding in terms of descending liquid droplets when the equilibrium of forces has been attained. In actual fact, it can be deduced from Fig. 4.12 and the arguments presented above that packed columns are also eminently suitable for separating liquid droplets, and this fact has long since been exploited in industrial practice.
4.9 Phase inversion in packed beds Strictly speaking, the flow model presented in Section 4.1 is not valid unless the assumptions made in its development apply. Experimental studies have revealed that the relationships for the loading and flood points derived from the model can be applied in the loading range described by a load parameter of i> < 4 without reservation and to within an accuracy that is adequate for practical purposes. However, if this value of load parameter is exceeded, phase inversion occurs, i. e. the original disperse phase  the liquid  becomes the continuous phase, and the previously continuous gas phase becomes the disperse phase. This stage sets in at the comparatively high liquid loads encountered in a number of absorption processes and, particularly, in highpressure rectification. It ought to be possible to express phase inversion in physical terms by altering the exponent in the relationship for the resistance factor §, as is indicated by the example shown in Fig. 4.6. This assumption has, in fact, been confirmed experimentally in numerous studies, some results of which have been collated in Figs. 4.13 to 4.15. The associated diagrams apply to packing of various geometries and textures produced from various materials and with flow channels of various dimensions. It can be derived from them that the point at which phase inversion can be expected is at a flow parameter, as defined by Eqn (424), of ip = xps = 0.4
(480)
The physical interpretation of these relationships is as follows (cf. Fig. 4.16). If the transition point is reached at a given liquid load uL>i, the associated liquid holdup can be expressed as a fraction / of the relative void fraction, i.e. hL,i = {hLtS)t
= is
(481)
4.9
Phase inversion in packed beds
103
Nominal packing size 25 mm o Air/Water 1 bar 293 K; OToluene/nOctane133mbar • Chlorobenzene/Ethylbenzene 67 mbar A Air/Ethylene glycol; v Air/Methanol.1 bar, 293 K
•c — * > ^ .
i i
Raschig ring, ceramic
s
«. 0.8 a > i < ^
n Pall ring, plastic
1 0.8 Z 6 =
r
3
—.
2
s.
Bialecki ring, metal
0.8 Fig. 4.13. Resistance factor as a function of the modified flow parameter
0.06 0.1
0.2 0.3 0.4 0.6 0.8 1
2
k
3 4
>c
6 810
Modified flow parameter s (  p )
The corresponding vapour velocity at the loading point (uv?s)i can then be derived from Eqn (426). Thus
KS)/ = (iQVn/irA/v\/ 
(482)
and the corresponding theoretical liquid load, from Eqn (427), i.e.
.i = («u)i
=
12
(483)
104
4
Fluid dynamics in countercurrent packed columns
Nominal packing size 50 mm oAir/Water 1 bar 293 K ; sEthanol/Wateri bar 0 Chlorobenzene/Ethylbenzene 67;133mbar b •
^
4
^
3
i
i L
• Raschig ring , ceramic
1 a

I
I
i
!
pi i
k
i_
a a.
I
p
i
k
"GO
D
all
o
rin
ramie 1
a; S o
0.06 0.1
0.2 0.30.4 0.6 0.8 1
Fig. 4.14. Resistance factor as a function of the modified flow parameter
2 3 0.4
Modified flow parameter
^s(^p v T
lv>
Now, the following relationship exists between (uLS)i and (uv,s)i'L V
=
(uL>s)j
QL
(uv,s)i
Qv
(484)
Rearranging Eqn (424) gives (485) The relationship between §5>; and / then follows from Eqns (481) to (485), i. e. (486)
4.9
105
Phase inversion in packed beds
o Air/Water 1 bar 293 K D,mChlorobenzene/Ethylbenzene 67133 mbar c
4 3 ? a m = hLiS — hLi, equating Eqn (426) with Eqn (435) would give (490) Equating the theoretical relationship derived from the model for the liquid holdup at the loading point {Eqn (427)} with that at the flood point {Eqn (438)} gives rise to
4.9
Phase inversion in packed beds
107
0.16 (hUs), e
0.14
*
\Q 0.12
^ ^
^
•
^ ^
o o
=
==—=
.
/
0.
o CO
/ ^ System: Air/Water at STP
.£ 0. / 0.06 0.04
f 0
50
100 150 200 250 300 350 400 450 500 Packing characteristic qs10"6[m^2S"2]
Fig. 4.17. Relationship between the phase inversion coefficient and the packing characteristics for an air/water system at STP
chloride solution 1 Air /Calcium chloride solution 1 Air/Methanol
150
200 250 300
350 400 450 500
Packing characteristic qs10~6[rrr2 s~z] Fig. 4.18. Relationship between the phase inversion coefficient and the packing characteristics for various systems
108
4
Fluid dynamics
in countercurrent
packed
columns
o a> ZD CO CO CD
Fig. 4.19. Qualitative pressure drop function
Gas or vapour load u v
(491) The theoretical boundary condition is defined by (492) In this case, the liquid holdup is given by (493) In other words, the liquid holdup accounts for onehalf of the void fraction. It therefore follows that the resistance factors are all of the same magnitude, i. e. %m = h,t = &
(494)
As a consequence, Eqn (490) can be reduced to Eqn (493). Theoretically, the liquid holdup defined by Eqn (493) can be attained if the liquid load assumes the limiting value given by Eqn (483) (for i = 0.5), i. e.
"v.suKFI
%
a2
^
(495)
4.9
Phase inversion in packed beds
109
The corresponding vapour load is obtained from Eqn (482) (for / = 0.5), i. e.
The liquid holdup in the uL < uLi range is given by hL,m = m
(497)
where n < /2The corresponding vapour load follows from the general theoretical relationship to describe the liquid holdup at the flood point, i. e. Eqn (438). Thus,
Since UL>FI > 0 and, consequently, (3n  1) > 0, it follows that %>n>
%
(499)
If Eqn (498) is applied to the conditions at the phase inversion, it can be equated to Eqn (483) to obtain the formal relationship between i and n, i. e. i = n 3V2(3nl)
(4100)
At the phase inversion, the relationship between them is given by (cf. Fig. 4.16) mt = nli
(4101)
where m is the ratio of the liquid holdup at the flood point to that at the loading point, i.e. m = ^ L hus
(4102)
Hence, if i is known from Eqn (488), n can be determined from Eqn (4100); and m, from Eqn (4101). The relationships n = f(qs) and mf = f(qs) for various systems at standard temperature and pressure are presented graphically in Fig. 4.20. Rearranging Eqn (489) gives rise to Q= (—)=— qs \a I a
\ a
(4103)
110
4
Fluid dynamics in counter current packed columns
inversion
4.0
CD CO O
*•
3.5 3.0
c:
i
/
\ \ \
2.5
^/ >^
.
^ —
—
= n 0.39 0.38
i
— Air/Calcium chloride solution 1
—
•^. A —»
—— ——
0.37 ——
——* —
—

^—
Air/Water
— « ,
—
• .
I 1.5 /
i
,
V
2.0
i
Ar ...
^ +
\
H \\
d.
itio rr
— Nitrogen/Heav / oil 
—
0.36
QJ O O
0.35
—I—I—J — — 0.34 ^n (I 
i
i/
i
i\
1.0
0.33 0
50
100 150 200 250 300 350 400 450 500 Packing characteristic q s 10" 6 [m~ 2 s " 2 ]
Fig. 4.20. Characterization of the phase inversion point in various systems Substituting for e3la2 in Eqn (483) then gives the liquid load at the phase inversion, i.e. uL.i = ^ T ^3 « —
—
(4104)
This expression for the liquid load at the phase inversion is shown as a function of the area per unit volume a with the void fraction e as parameter in Fig. 4.21. Substituting ne for hL>m {Eqn (497)} and it for hL>s {Eqn (4105)} in Eqn (4102) gives 1
(4105)
Since the liquid holdup at the flood point is very difficult to determine by experiment, the values of m derived from it are not very accurate. The average is m — 2.2 for lowviscosity systems (cf. Section 4.7). The following theoretical value of m is obtained by substituting hLyFllz for n in Eqn (4105): (4106) 1 In analogy to Eqn (440), the holdup at liquid loads of uL < uL>i can be estimated from (4107) where ri = 0.349.
4.9
111
Phase inversion in packed beds
120
V
System: at
e = 0.98
Air/Water STP
•7
//
•
£ 80
Cs 3.5 /£
a
=
'""\?
cr
e0.9(]
40
• — — .
W.I'.r
Phase inversion 20 50
100
150
200
250
300
350 z
400
450
500
3
Area per unit volume a [m /m ] Fig. 4.21. Liquid load at the phase inversion point as a function of packing characteristics
If r\L = r\w, inserting values of hLjFilz thus obtained in Eqn (4106) would again yield a value of about 2.2 for m. Solving Eqn (4105) for n would then give rise to n = 0.349. The flow pattern is altered once the flow parameter exceeds the value i^ at which phase inversion commences (cf. Figs. 4.13 to 4.15). If the set of equations in the model is to be formally retained, this alteration would be expressed as a change in the exponents and constants in Eqns (429) and (441) for the resistance factors § 5 / and I=F/)I respectively. Numerical values for the exponents can be obtained from Eqns (432) and (443). The following condition must be satisfied at the phase inversion: 55 
(4108)
55,i
Eqn (429) can therefore be converted into ("s  ns,i)
Cs,i = Cs
(4109)
Inserting the numerical values then gives
CSi = 0.695 C 5 [ —
(4110)
Another condition that must be satisfied at the phase inversion is (4111)
112
4
Fluid dynamics in countercurrent packed columns
Eqn (441) can therefore be converted to yield the following relationship for the constant: (nFlnFl,i)
\0.2
(4"112)
ZT) The simplified relationship in this case is thus
(
^
0.1028
—
(4113)
Consequently, the vapour load at the loading and flood points can be formally determined by Eqns (428) and (435), even in the range above the phase inversion. The values of ^s and §F/ required for the calculations and corresponding to n$ = nSj, Cs = Cs,i, HFI = nFiti, and CFl = CFiA can be obtained from Eqns (429) and (441) respectively.
4.10 Relationship between loading and flood points The range between the loading and flood points is of utmost importance in the design and operation of packed columns. The liquid holdup and thus the pressure drop within this range increase at a higher rate than they do in the range below the loading point. The design load uVD, at which the column volume is a minimum, then lies between uV}s and uym, i e. uv,s ^ uV}D < uVyF{
(4114)
Substituting for uvs from Eqn (426), f$ from Eqn (457), ^L from Eqn (459), and fw>s for fw in Eqn (458) gives rise to the pressure drop per unit height (Ap/H)s in the uv = uV;S loading range, i.e.
Likewise, the pressure drop per unit height (Ap/H)Fi at the flood point uv = uVtn can be derived from Eqns (435), (457), (458), and (459) a n d / w = fWiFl. Thus,
The pressure drop ratio is therefore &PFI
„ fw,Fi = 2— fw,s
hLjm
e  hLjS
hLiS
e
Substituting m for hLiFilhL>s {cf. Eqn (4102)} then gives
(4117)
4.10
113
Relationship between loading and flood points
It follows from Eqns (497) and (4102) that (4119)
Hence, the pressure drop ratio can be expressed by the following simple relationship: ApFl n fw,Fl , x — = 2 ^r— (m  n) Aps Jw,s
,. 1 o m (4120)
Alternatively, it can be expressed as follows by substituting the righthand side of Eqn (4105) for m:
fw,s \ 3 V2(3nl)  n
(4121)
The factor n can be obtained by combining Eqns (497) and (4107), i. e. /^ r
«uL < ut =
0.349
\0.05
(4122) r\wlQw
The factors fw>s and fw,Fi m Eqn (4121) are defined by Eqn (456) as the ratios of the effective area ae to the area per unit volume a at the loading and flood points respectively. The effective area ae is that of the surface of the flow channels of hydraulic diameter dh in which the pressure drop would be the same as that encountered in the bed of packing under consideration. The hydraulic diameter dh is defined by (4123)
fwa
The pressure drop per unit height at the loading and flood points can be derived from Eqn (458). Thus, Uy,S
.
H Ap
(4124 a)
?5
is
E
2
1  hLyFi I
dhiFtfs
(4124 b)
Substituting ne for hL>m {cf. Eqn (497)} and zn/m for hLfS {cf. Eqn (4119)} in the ApFi/Aps ratio thus obtained gives rise to the following equation:
%Fl
fw
fw,S
1
n
m 1  n
(4125) UV,S
114
4
Fluid dynamics in countercurrent packed columns
The ratio of the vapour load at the flood point to that at the loading point can be derived by equating Eqns (4120) and (4125). Thus, (4126) uv,s
Substituting the righthand side of Eqn (4105) for m in this equation then gives (I")2 uv,s
(4127)
«V2(3wl)
where n is defined by Eqn (4122) and the term h,s^Fi is the ratio of Eqn (429) to Eqn (441), i.e.
(nS 
Im
(4128)
n
Fl)
This ratio can also be estimated by applying Eqn (459). Thus,
fw,Fl
(4129)
fw.S
In this case, the ratio of this equation, i.e.
can be calculated from Eqn (467) or expressed in terms
64 lL,Fl
• +
hL,Fi \ ° ' 3 Rev,Fi
hL,s 1
64
 +
Re v,s
1.8 Reom 1.8 • Re v,s •
 hLtFl
\~
(4130)
The expression within the square brackets in this equation can be equated to (uViS/uViFif08 = 0.97. Applying Eqns (497) and (4119) then gives rise to 0.97
1n
 t ,,
(4131)
t s
The fw,Filfw,s ratio is thus known from Eqn (459), and the pressure drop ratio can therefore be obtained from Eqn (4121). Eqn (4127) can also be derived by substituting Eqns (497) and (4119) for hLiFt and hLS, respectively, in Eqn (452). The flood point exponent n depends fundamentally on the system and the flow parameter \p and can be calculated from the model. The liquid holdup hL>s accounts for only a fraction of the relative void fraction 8, i. e. it differs from e by a factor/. Thus hL.s = f e
(4132)
4.10
115
Relationship between loading and flood points
Hence, in analogy to the derivation of Eqn (488) for the determination of the phase inversion coefficient /, the following relationship applies for the factor /:
f
144
df)2'
s2 *
(4133) QL)\QL
Equating Eqns (497), (4102) and (4132) gives (4134) Substituting f o r / o n the lefthand side of Eqn (4105) then gives /5 _ (I/) 2
n5[2(3nl)f3 {ln[2(3nl)]V3}2
(4135)
Three systems with different physical properties were taken as examples for evaluating the relationships discussed above: air/water, air/calcium chloride solution, and nitrogen/heavy oil, each at STP in the loading range below the phase inversion, i. e. \p < 0.4. Fig. 4.22 shows the relationship obtained from Eqn (4131) between the flow parameter i> and the modified resistance parameter ratio R, which is given by (4136)
R =
«
2 8
i —
O
—
S 2.4 i_ CD
——— — .1
1 2.0
i
.
_
—
—
—
—
—
\\\0
«—'
a
s
1
y / i
•55 1.2
1 0.8
/ / *
1 bar, 293 K
TZJ
04
1 1 0
0.04 0.08 0.12 0.16 0.2
0.24 0.28 0.32 0.36
Flow parameter i) Fig. 4.22. Modified resistance parameter ratio as a function of the flow parameter
0.4
116
4
Fluid dynamics in counter current packed columns
Thus Fig. 4.23 would be obtained for packing with a CFilCs = 0.6 ratio. Fig. 4.24 was plotted from Eqns (4133) and (4135) and shows the coefficient n for the liquid holdup under flooding conditions as a function of the flow parameter IJ. It also shows the corresponding function for ra, which is the ratio of the liquid holdup at the flood point to that at the loading point and was determined from the relationship between m and n expressed by Eqn (4105). Finally, if the functions n = f(ij) and §5/^7 are known, the following can also be determined as functions of the flow parameter ip: the ratio of the resistance factors ^L,FI^L,S {Eqn (4131)}; the vapour load ratio WV;F//"KS {Eqn (4127)}; and the pressure drop ratio ApFl/Aps {Eqn (4120)}. These relationships, as determined on some metal packings and an air/water system at STP, are shown as an example in Figs. 4.254.27.
_, 1
1
dx
AJC
DLr\La
(521)
where doL/dx is the rate of change in surface tension along the height of the column with respect to the composition x in the liquid phase; AJC is the difference between the concentration in the bulk to that at the surface of the liquid and is given by (cf. Fig. 1.5)
5.3 Vapourliquid phase boundary
127
a cz a a
CO
a
QJ
CZ
a
a
0.2 Fig. 5.4. Hydraulic and phase contact areas as functions of the liquid load
10
15
20 25 30 35 40
Liquid load uL [m 3 /m 2 h]
= xx*
L
=
(xxe)
(522)
The difference in concentration depends on the distribution of the resistance to mass transfer in the two phases, i. e. on the ratios HTUJHTUOL for the liquid phase and HTUvIHTUov for the vapour phase. These two ratios are related as follows: HTUL HTUQL
~
HTUV ~ HTU
~
kov ~ I3
(523)
where v is given by HTUV HTUL
(524)
128
5
Mass transfer in countercur rent packed columns
The ratio v can be determined from Eqns (129), (55), and (514). Thus, _5_
£k.
JL
MX.
v = Cv myx ML
QL_ ( V Q V ) 2 QV 
J_
DL2

where ML and Mv are the molecular masses of the respective phases. The difference in concentration can then be calculated from the following equation: Ax = ~^(xxe)
(526)
The evaluation of numerous studies on rectification systems has shown that the area aPh of the phase boundary remains constant in positive and neutral systems and that Eqn (516) can thus be applied. In negative systems, however, the interfacial area aPh is reduced by the surface tension gradient and surface destabilization. Allowance for this effect can be made by —
= (1  2 . 4 • 104MflL0'5)  ^
(527)
The mass transfer efficiencies HTUOv {Eqn (311)} determined by experiment in rectification systems differ from those calculated from Eqns (527), (54), and (513) by an average of 14 %. The increase in liquid holdup within the range above the loading point also causes an increase in the area aPh of the phase boundary. It can be now assumed that, in analogy to Eqn (470), the following relationship applies above the loading point: _ = + \ a }Uv>Uvs a \ a a / \ uv>m Thus the interfacial area at the flood point will be given by
ow I
a
In this case, the volumetric mass transfer coefficient for the range in question can be calculated from the above equations. Figures 5.5, 5.6, and 5.7 convincingly demonstrate the good agreement between the efficiencies determined by experiment and those calculated from the NTUHTU concept, including the model equations developed above. They show the relationship between the packing efficiency and the capacity for absorption, desorption and rectification systems. The packing concerned in each case was Hiflow rings of various sizes and materials.
5.3
129
Vapourliquid phase boundary
50mm Hiflow rings, metal. ds= 0.45 mm. Z = 2400 1/m2 AmmoniaAir/Water. 1 bar. 293 K. uL = 10 m 3 /m 2 h. H = 1.45 m •a?
"
4
5 a.
=n
CO
^
/
Experimental data
z
•— / / Model calculated curve
—V
CO
a
0.4
0.8
1.2
1.6
2.0
2.4
Gas capacity factor Fv [m~
2.8 1/2
3.2
1
s" kg
1/z
3.6 4.0
]
Fig. 5.5. Comparison of the loadefficiency relationship calculated from the model correlation with that determined in desorption experiments
50mm Hiflow rings, plastic. ds= 0.3 mm. Z = 1400 1/m2 Carbon dioxideWater/Air, 1 bar. 293 K. uL = 15 m 3 /m 2 h, H = 1.33 m
 E xperime ntal data CD
^
\
° S co
D
V
^
a g
§ i 3
"B"—U
"EH:3—nHol M LJUcl
a
D
n ^—
V— / /
rnlnilnfnrl U
0.4 0.8
1.2
1.6
rnr\;
UUI V
1
t
0.2
2.0 2.4 2.8
Gas capacity factor Fv lm"
\
1/2
1
3.2 3.6
12
s" kg '
Fig. 5.6. Comparison of the loadefficiency relationship calculated from the model correlation with that determined in absorption experiments
130
5
Mass transfer in counter cur rent packed columns
25mm Hiflow rings, plastic, d s = 228 mm, Z = 2036 1/m2 Chlorobenzene/Ethylbenzene, 67 mbar, L/V = 1, H = 1.5 m en
I Experimental data 1 } ° C
CD
—o—
/
txr°
a—£Q ,.J
o o
io
—
Model calc jlated (:urve
o
0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.4
Vapour capacity factor F v [m 1 / Z s"1 kg 1 / z ] Fig. 5.7. Comparison of the loadefficiency relationship calculated from the model correlation with that determined in rectification experiments
5.4 Relationship between mass transfer and fluid dynamics The factors that influence fluid dynamics and mass transfer in beds of packing are the flow velocities of the phases and the physical properties of the system, e.g. the density, viscosity, and diffusion coefficient. Other parameters are introduced by the packing, e.g. the void fraction, the surface area per unit volume, and a factor that allows for the shape and surface structure of the packing. They are all related by the pressure drop per transfer unit, which is referred to here as the specific pressure drop and is defined by &p NTUn
H
HTUn
(530)
The equation can be applied if mass transfer is predominantly in the vapour phase, which is the case in most rectification and many absorption and desorption systems. Under these circumstances, mass transfer is a function of Reynolds number Rev (and thus the capacity factor Fv) and the Schmidt number Scv acccording to Section 8.3, i. e. approximately HTUQV
=
HFv
uL = const.
(531)
The following simple relationship for the specific pressure drop at a constant liquid load uL can be obtained by combining Eqns (530) and (531):
NTUn
Sc,
=
C
ty
uL = const.
(532)
The liquid load uL depends on the mass flow ratio L/V, the densities of the vapour QV and the liquid o L , and the vapour capacity factor Fv, i.e.
5.4
Relationship between mass transfer and fluid dynamics
131
In other words, the specific pressure drop modified by the Schmidt number is a function of the liquid and gas loads. According to a recent suggestion, it can be expressed as follows in terms of the various parameters:
This equation allows the results of rectification studies to be correlated and compared with those obtained in absorption experiments. The phase ratio L/V can be determined by rearranging Eqn (533), i.e.
T"ft; T,
Rectification experiments are often performed at a phase ratio of L/V = 1. In this case, Eqn (534) becomes t
= 1=AF?
(536)
V
In most absorption studies, however, the liquid load is kept constant, and the gas load is varied or vice versa, as is evident from the diagrams presented in Chapter 3. The equation that applies in this case is derived from Eqns (534) and (535), i. e. A
—
• Scv
3
= B uLn F{?n = BULFV"
(537)
Figures 5.8 to 5.10 show the results of rectification experiments under total reflux, i.e. L/V = 1; and Fig. 5.11, absorption tests in which the load in the one phase was kept constant and that in the other was varied. It can be seen that they confirm the above relationships, the general form of which is shown qualitatively in Fig. 5.12. Fig. 5.11 indicates that packing may have two ranges of liquid loads  in one of which n < 0; and in the other, n = 0 . The latter can be expected at liquid loads of u^ > 1015 m 3 /m 2 h, i. e. in absorption processes. The liquid loads in vacuum rectification are quite often less. A comparison of Eqn (532) with Eqn (537) reveals that the exponents in, m, and n are theoretically related by in = m + n
(538)
If the liquid loads are higher than about 15 m 3 /m 2 h, uL no longer exerts an effect on the modified pressure drop per transfer unit, with the result that the exponent n in Eqn (537) becomes zero. Consequently, it is only in this higher loading range that rectification and absorption experiments can be described by a common exponent, i.e.
132
5
Mass transfer in countercurrent packed columns
100
e_
80 •eg. imm Hiflow ring.meta ii =0.22m.H=U8m M:=39435 1/m3 N 2 z = 600 1/m a iloro/Ethylbenzene 40 pr = 67mbar,L/V=1
/
1 Q
30 /
i/
20 Rectificat on L/V=1
i5m3/m2h = m
(539)
It can be derived from the above equations that the constants A and B are related by B = A
QL
(540)
The only case in which the constants are the same is that of higher liquid loads, when n tends to zero, i.e. m 3 /m 2 h

(541)
5.4
133
Relationship between mass transfer and fluid dynamics
60
3
n 25mm NORPAC.PP (Js=0.3m,H=1.40m 3 1s=47837 1/m 40 2 i?=600 1/m 30 %Air/H 2 0,u L =10rn 3 /m 2 h p=lbar.T = 293K
JT 20
Absorp tion uL = 10m:/ m 2 h ^
10
q
1 J
A¥
If
4
M T ILi
f
— RecTiTication t/V=1
i
"g
4 /
Fig. 5.9. Modified specific pressure drop as a function of the capacity factor in rectification and absorption
0.6
0.8 1
G25mm NORPAC.PVDF ds=0.22m.H = U 7 m N = 45400 1/m3 Z = 2250 1/m2 Chloro /Ethylbenzene p T 67mbar.L/Vl 2 1/2

3 1
1/2
Capacity factor Fv [m" s" kg ]
These equations were evaluated in the light of the results obtained in numerous studies on pressure drop and mass transfer in the rectification and absorption systems listed in Table 5.3. It was thus revealed that the difference between the calculated and experimental figures are slight if the numerical values listed in Table 5.4 are allotted to the exponents m, m and n. Numerical values for the constant A that were determined for dumped packing are presented in Table 5.5; and for regularly stacked packing, in Table 5.6. Inserting the numerical values for m and n in Eqn (534) yields relationships for the pressure drop per transfer unit in the range of lower {Eqn (542)} and higher {Eqn (543)} liquid loads, i. e.
134
5
Mass transfer in countercur rent packed columns
40
30 h
e50mmHiflowring,PVDF hydroph.
_ 20 
d s =0.22 m, H=1.47m N=7163 1/m3 Chtoro/Ethylbenzene P T =67mbar ,L/V=1
10
L/V= 1
en Q.
Absor ptinn 3 2 u L =10rn /m h
3
o a>
CL
2
1 0.8 0.6 0.6
u
4 / / \
6
e drop
&plNTUv. In the ammoniaair/water system, in which the resistance to mass transfer is divided between the two phases, the height HTUV of a transfer unit in the gas phase can be obtained from Eqn (316). Examples of comparisons between physical and chemical absorption on the basis of the modified specific pressure drop per gasside transfer unit are shown in Fig. 5.18. The relationship is practically independent of the system and can be expressed by
NTUV
Ap HTUV Scv213 = f(Fv) = CF? H
(547)
The height of a transfer unit HTUV for absorption systems with rapid chemical reaction in the liquid phase can be obtained from the values of Ap/NTUV determined from Eqn (547) and Ap/H from the following approximate equation:
5.6
Mass transfer in absorbers accompanied by chemical reaction in the liquid phase
Vm 2 , uL=i0 m 3 /m 2 h, NTP
d s =300 mm, CD
0.4
_ NH 3 Air/H 2 0*H 2 5q, •1 NH3 Air/H20 c3
_ 0.3 S £ o
o a> cDco
143
• 0.2 \
\
r—
• ^^"^
"•«
0.1
^
•
0.5 0.4 c: co CT> c:
g
>
0.3
s
n
SB'
•—•* '
•
!••
V
0.9 1.0 1.2 CO
f 5 1.6
25mm N0RPAC . m N = 478371/m3
TD
5 2.0
50mm Hiflow H = 14 m N=69971/m 3
2.5 3.0 4.0 0
Fig. 5.16.
8 16 24 32 0 8 16 Specific pressure drop Ap/NTU0V [mmWG]
Process engineering data for evaluating physical and chemical absorption
U
CTQ
92.
o
o
uat ing
3,
CD
o
o
cal abs
5"
T3_
CO
—» CD
Gas capacity factor Fytrn'^s' 1 kg1/2]
c o r>o CD e n
metol II
CO
zr
3
CD CD CD
II
o§ 3 3 ^3
II
CL d . "— oo
CD Kj
\ \ i
\
\
CD CO
\
4
Ht. In this case, the values to be determined are the equivalents of the separation efficiencies Na and Nb in beds of Ha and Hb height and the efficiency Nd at H = 0 (cf. Fig. 6.5). The results are correlated by means of the following two equations: Na = Nd + ANt + Ha
dN dH lH>Hi
(617)
Nb = Nd + AN; + Hb
dJV \ dH j H > H i
(618)
in which Hb is greater than Ha by a multiple q, i.e. Hb = qHa
(619)
These relationships give rise to a correlation that permits the positive or negative inlet effect ANt to be calculated from the measured values of 7Vfl, Nb and Nd, viz. (620)
ZD
Fig. 6.5. Scheme for modelling the inlet effect in scaling up
Packed height H
154
6
End effects in packed columns
As is evident from Fig. 6.5, the height AHt of the inlet zone can be estimated graphically if a minimum of two measured values of TV for the inlet zone, i.e. H < Htj suffices to allow the shape of the curve to be described, at least roughly, as follows:
N=i(H)H o
^
=3
^
•>. .— " " " " " • *
^\ r
2
3
?.9O •10" m
3

^
b
0 0
0.5
1.0
1.5
Packing height H [m] Fig. 6.9. Efficiency of a packed desorption column as a function of the height
6.4 Column design and scaleup It is evident from the relationships discussed above that it is absolutely essential to make allowance for end effects in designing industrialscale separation columns. In the first place, experimental data on the efficiency of the intended packing and the relationships derived from them must be checked in order to determine under which conditions they are valid. An efficiency of (N/H)P, as determined in pilotplant experiments in a column of effective height HP, generally differs from the value (N/H)T for a technicalscale column of height HT = HP. Thus the figure for a pilot column is given by
158
6
End effects in packed columns
47mm DINPAC. plastics; ds = 288 mm Z = 490 1/m2 CO2H2O/Air at STP, Fv = 0.94 rTr l / 2 s'kg 1 / 2 NTUL/H, dNTUL/dH
"^ 6 ^—
~ 4
'
I 2
3 3 2 UL=J5 97 in~ m /m
a
Z
0
— — 
i i
i
i
i
i
i
i
i
i
i
i
i
u
i i .
io .g •
, H
4
L_U
, '
2
2 •10"
3
m3/m2 Q
n 0
0 0.5
1.0
1.5
Packing height H t m ] Fig. 6.10.
Efficiency of a packed desorption column as a function of the height
6.4
Column design and scaleup
159
70mm DINPAC, plastics ; d s =288 mm Z = 490 1/m 2 C0 2 H 2 0/Air at STP, Fv = 0.94 m 1 / 2 s 1 kg l / 2 NTUL/H,
(JNTUL/CJH
D •
4
——I — — ——
•^ — —
2
^—*
— — ^
'
•
— —
—
•••H
Y0*0*
4 =i95 1 •1U V
s
\ *^
£ 4
^il
__!_• 
— —

1
—
4
g
•
10"
"CD
s
O
1
OO CD
CJ
c cz 0 .9^ o
.##
. — ——— .
^^
•
Z.90 •10" 0.5
Y
•
— — • •
_^ —^^
0
^
2J
U L = 5.97
•
k —^ »——.—— —•» ^——
—*— jQr
6
3
3
2
m / in
1.0
Packing height H [ m ] Fig. 6.11. Efficiency of a packed desorption column as a function of the height
—
—
—
t_LJ
4 2
1.5 0
160
6
End effects in packed columns
H\
[H/p
dN i\dHlp \
H>H.
Nd \
Hp
(622)
ip
and that for a technicalscale column, by N_\ =(AN_\ +{Nd HJT \dHJT>H>Hi
+
(623)
Combining Eqns (622) and (623) gives
HlT
\HjP
\\
Nd + ANt \ _lNd + ANA }_\!dN_\ H jp \ H j T \ [\dHJp
50mm Pall ring,metal, d s = 500 mm, Z = 600 1/m 2 Methanol/Ethanol 1 bar L/V = 1 ; dn t /dH.
I8
(624)
nt/H
1.5 2 Capacity factor F v [ r r r 1 / 2 s " 1 k g l / 2 ]
QJ
_IJN\ \ dHJT
2.5
6 «= o
4 >
Fv = 2.5 m 1 / 2 S"1 k g 1 / z 0 0 Fig. 6.12.
1
2 Packing height H i m ]
3
Efficiency of a packed rectification column as a function of the height
6.4
Column design and scaleup
50mm Pall ring.metal, d s = 800. Z = 490 1/m 2 ; L / V = 1 Ethylbenzene/Styrene 130 mbor dn t /dH,
161
nt/H
15 2 Capacity factor F v [ m~ 1 / z s" 1 k g 1 / 2
CD r _Q U
4 F v = 2 5 ; 1 5 ; 0 7 5 m'm s" 1 kg 7 .9*
2
o
0
0
1
2
3
o
Packing height H [ m l Fig. 6.13. Efficiency of a packed rectification column as a function of the height The end effects in the technicalscale column can be regarded as identical to those in the pilot plant if the phase distributors and support plates are of the same design in both cases, if the column diameters dSj and ds>P do not differ significantly from one another, or if the packing has no tendency to maldistribution. In these cases, the following applies for the inlet Nd
Nd H
(625)
H
and the following, for the zone of fully developed flow:
id///p
\d///r
(626)
Eqn (624) can then be simplified to give (627)
162
6
End effects in packed columns
12 10
35mm Pall ring,metal ds = 500mm, Z = 600 1/m2
o 2 1.5 2 Capacity factor Fv [rrr 1 / 2 s"1 kg 1/2
10 CD
.Q
I l l Ethylbenzene / Styrene 130 mbar dn t /dH, n t /H
8
e 6
0 0
2
1
3
Packing height H [ m ] Fig. 6.14.
Efficiency of a packed rectification column as a function of the height
Hence the efficiency ratio r\T for columns of different height, i. e. HP and HT, is given by
H N_
H ip
1 N_ H IP
J
(628)
The significance of this equation is clearly illustrated by Fig. 6.16, in which it is presented qualitatively as a general function, i.e.
(629)
6.4
12 10
~a> o
Column design and scaleup
I I I I T 35mm Pall ring,metal ds=800 mm, Z = 490 1/m2
1.5
Ethytbenzene/Styrene 130 mbor L/V = 1. dn,/dH, n,/H I I I i i i i \ i r 2 2.5 Capacity f a c t o r F v [ m ~ 1 / 2 s " 1 k g 1 / 2 ]
F v =15 m 1 / 2 s " 1 k g 1 / z Packing height H i m Fig. 6.15. Efficiency of a packed rectification column as a function of the height
Fig. 6.16. Ratio of the efficiency in an industrialscale plant to that in a pilot plant as a function of the column height
Packed height HT
163
164
6 End effects in packed columns
The curves shown in the diagram apply for experimental beds of different height, HP1 and HP2 > HP]. They tend towards a theoretical limit at a height HT^> °°, i. e. (T\T)HT^X^>
\ 
N d
+
ANl
(630)
If HT —» HP, the limit is unity, i.e. (Tlr)/fr>//,> 1
(631)
Under the given conditions, the following relationship must apply in the zone of completely developed flow: ldN_\ \dHJH>Hi
=
NTNp HTHp
_ AN AH
K
}
Rearranging to solve for HT yields HT=Hp + (NT  NP) r—\
(633)
Hence, the height of bed HT required to achieve a separation efficiency corresponding to a value NT can be obtained direct from the results of a pilotscale experiment in which (dN/dH)H> Hi has been determined, in which case the one experimental point Np for the case of HP > Ht suffices. If the height HT of the bed is to be determined from the efficiency per unit height (N/H)P of the pilot column, the value obtained would be too small by an amount AH/HT, which is given by
AH HT
NT (N/H)
T
NT (NIH)P
NT (N/H)T
(634)
AH/HT can also be expressed in terms of the efficiency ratio r\T, as defined by Eqn (629), i.e.
Theoretically, AHIHT can be expressed as a function of the total number of theoretical stages NT, which is given by NT=Nd
+ ANt + HT  ^ \ an /
(636)
6.4 Column design and scaleup
165
The requisite height of bed HT can then be determined by rearranging Eqn (636), i. e. (637)
dH lH>Hj If the efficiency of the pilot plant were to be taken into consideration, the height of the packed bed would be given by
(638)
The figure thus obtained is less than that derived from Eqn (636) by the following amount:
The term AH/HT can be expressed as a function of NT by combining Eqns (637), (638), and (639) or by combining Eqn (39) with Eqns (633), (638), and (622). Thus, ^ HT
1
'
N N Ndd + ANj NT
1 N + AJV 1 HP IdN\
(640) ; Hi The values thus obtained lie between the following limits:  for the limiting case of NT —» NP, (641) T I Nr + NP
 and for the limiting case of an infinitely large number of theoretical stages NT I AH \HT
1 1 +
HP
I dN\ \ dH ) H> Hi
If there are no end effects, Eqn (640) would be reduced to
f] "• T f{Nd
0 + A Nt) + 0
(643)
166
6
End effects in packed columns
A special case arises if Eqn (67) does not apply, i.e. if dN Q\H
(644)
=£ const.
If the differential coefficient were thus to change over the entire height of the column, the relative increment of height AH/HT would have to be determined from the following relationship, which can be derived from Eqns (629) and (635): N AH
= 1
(645)
 = HH)
In this case, the relationship N = f (H) would have to be determined experimentally.
Raschig ring,ceramic 8mm.Fv=Q.84 ml/2s1kgl/2ids=1OOmrn.Z=l65O 1/m2 — 25mm,Fv=1.32 m1/2s1kg1/2Jds=750mm,Z=425 1/m2 Ethanol/Water 1 bar, L/V=1 1
s s,
>
 Hp ^^
1^
s
0.9
— —
I 0.8
— —— —— —
0.7
—
m
1 3 Packing height H i m ] 0.3
»——— — i
& 0.2
r/
CD
i0.1
/ —
CD
*. ,. — \— ^—»—
"
Effect of t h e n u m b e r
of
liquid distribution points on the rectification efficiency
7.3 Maximum packing efficiency in inlet zones A term introduced to evaluate experimental results is the relative efficiency e of the packed bed. In rectification studies, it is defined by nA j nA )
(713)
7.3 Maximum packing efficiency in inlet zones
111
and in absorption and desorption studies, by (NTU/H)Z m /m h v
C "
Fv=1 m"l/2s"1kc
07
3
n /(Ti
NH3Air/H20. ds ] ; UL = 10 r = 0.45 m 0.7 0.8 0.9 1 1.5 Height ot packing H [m]
2
ii
•
2.5
Fig. 7.19. Efficiency ratio as a function of the bed height in a packed desorption and absorption column
188
7
Liquid distribution at the inlets of packed columns
If the number of liquid distributor outlets is Z < Zopt, substituting Eqn (729) for C, Eqn (730) for n, and Eqn (715) for q in Eqn (728) gives rise to the following expression for the relative efficiency in random beds of packing: ( f o r L / V = \\H=
1.5)
(731)
This relationship between e and Z is, strictly speaking, valid for a reference height of H « 1.5 m and LIV = 1 and is presented graphically in Fig. 7.20. If the relative efficiency ratio, as defined by Eqn (725), is taken into consideration to allow for different values of LIV and the value of qopt remains unchanged, C and n will depend on LIV. In this case, the relationship shown in Fig. 7.21 would apply, i. e. 0 04
C= 1.13

(for/f = 1.5)
(732)
(for//=1.5)
(733)
Surface area per unit volume a [rn 2 /m 3 ] 50
100
Dumped packing
75
100
150
200 250
0.9 0.8
150 200 300 400 500 750 1000 1500 2000
Number of distributor outlets Z [ 1 / m 2 ] Fig. 7.20. Relative efficiency as a function of the dimensions in a packed column and the number of liquid distribution points
7.6
Estimation of relative efficiency
189
Substituting Eqn (732) for C, Eqn (733) for n, and Eqn (715) for q in Eqn (728) and allowing for the relative efficiency ratio, as defined by Eqn (725), yields an expression for the relative efficiency in random beds for the case in which LIV > 1. Thus, I 8 L \0.04 4JIZ e = 1.13 rV / \a
01
/f\ 0.25
W
(for H = 1.5)
(734)
Relative efficiency of arranged packing The corresponding values for C and n in systematically arranged beds of packing of the types investigated for the case of LIV = 1 and H = 1.5 are as follows: Carr = 1.14
(for LIV = 1; H = 1.5)
(735)
narr = 0.07
(for LIV = 1; / / = 1.5)
(736)
Thus, if Z < Z op ,, substituting Eqn (735) for C, Eqn (736) for n, and Eqn (715) for q in Eqn (728) yields the relationship that corresponds to Eqn (731) for random beds, i. e. (for L/V = 1; H = 1.5)
earr = 1.361 [ —
(737)
i a
Although insufficient experiments have been performed to reveal the effect of the phase ratio LIV on the relative efficiency of stacked packing, it is reasonable to assume that Eqn (725) can be applied for rough estimates.
0.5 10
10
10
Distribution coefficient q
Fig. 7.21. Relative efficiency as a function of the distribution coefficient in packed columns with the liquidvapour ratio as parameter
8 Scaleup for end effects and phase distribution In Chapters 6 and 7, it was demonstrated that the evaluation of measurements to determine the column efficiency in a pilot plant must allow for end effects and the initial distribution density realized by the liquid distributor. Otherwise grave errors may occur in scaling up on the basis of these measurements or relationships derived from them. The necessity arises because the most pronounced changes in efficiency can generally be anticipated in the upper zone of the column immediately below the inlet. It is only in the lower zones that the efficiency can be expected to remain in equilibrium. Typical curves plotted from the results of systematic studies will again be taken as an example to explain this fact. They are reproduced in Figs. 8.1 and 8.2 and strikingly demonstrate the extent to which the inlet efficiency of a column is affected if the number of liquid distributor outlets is greatly reduced. According to the diagrams, there are two main zones in the bed of packing: the inlet zone, in which the local efficiency continuously changes; and the lower zone, in which the local efficiency remains constant, i.e. the number of transfer units, NTUi in desorption or NTUOv m absorption, increases almost linearly with the height H. It is also evident from the diagrams that the increase in NTU is independent of the number of liquid distributor outlets Z. In other words, the NTU = f (H) curves for Z = constant are practically parallel in the lower zone. The conclusion can thus be drawn that the development of twophase flow is complete in the zone of constant local efficiency and depends
1
1
I
.
\
A
,
\
CO d
4
o
~
o
°
6
CD _O
i —i
*—•—
m
0
u
0.2
•
U
s—'
_1 —— \5 
k
.—•—'
^——«
2 i
1
..
:
1
1
• '
1 bar 38.4 rcr/m2h _
ZD
£
i
i i —i—i—•
4
i

co2 H20 /Air
^
'i

 25mm Hiflow rings PP, ds= 0.288 m Fv = 0.66m" 1/2 s" 1 kg 1/2
E
l r—
J
MH3Air/H20. 1 bar JL= 5.4 m 3 /m 2 h
1
.
I I I .
Ai
'—i
i
0.4
0.6
0.8 1 1.2 1.4 Packing height H i m ]
1.6
1.8
2
Fig. 8.1. Efficiency as a function of the height of bed with the number of liquid distribution points as parameter
Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
192
8
Scaleup for end effects and phase distribution
Absorption NH3Air/H20.1 bar, Fv = 1 firms' 1 kg1/z, uL = 38.4 m J /rrh 1
1
1
1
1
1
1
50mm Hiflow rings, plastic
•I 6 =3
* * *
^
. 
. —
E
r
t—"
*
* . — 
. — — •
d s = 0.45 m 
ii
i
0 0
0.2
0.4
0.6
0.8 1 1.2 1.4 Packing height H [ m ]
1.6
1.8
i
2
2.2
Fig. 8.2. Efficiency as a function of the height of bed with the number of liquid distribution points as parameter
solely on the packing's selfdistribution characteristic and no longer on the effects of the inlet current distribution. An explanation to this effect has already been given in Chapters 6 and 7. Another fact that is known from Chapter 6 and can also be derived from the diagrams is that there is a certain number Zo of liquid distributor outlets that gives rise to hardly any inlet effects. Thus the flow pattern that is characteristic of the packing's selfdistribution effect already exists in the inlet zone, and the local separation efficiency is theoretically constant over the entire height of the column. The inlet efficiency is improved if Z > Z o , because the liquid distribution at the head of the column allows more effective exploitation of the area available per unit volume, i.e. the average dN/dH is higher in the inlet zone. However, if Z < Zo, the inlet efficiency is negative, because the surface of the packing in the inlet zone is only moderately wetted, i.e. the average dN/dH is comparatively low. Yet another fact that arises from the diagrams is that the relationships tend towards a finite value at H = 0. It can be ascribed to external end effects, e.g. reflux distributors and support plates, that are embraced by the measurements under certain sampling arrangements and are thus normally included in the evaluation of packing efficiency; but this has already been mentioned in Chapter 6. A qualitative impression of the relationship between end effects and the relative efficiency can be obtained from Fig. 8.3. The N = f(H) curves in the lower part of the diagram qualitatively represent the efficiency determined by experiment and were derived from the quantitative curves presented in Figs. 8.1 and 8.2, in which N = NTUOv and N = NTUL. The associated relative efficiency is represented by the set of curves in the upper part of the diagram. Two cases of efficiency, e and e, are shown: in the one, the end effects Nd have been included {Eqn (81)}; and in the other, deducted {Eqn (82)}, i. e.
8
Scaleup for end effects and phase distribution
193
Assumption: Nd independent of Z
CD O
a a. QJ
Fv = const; u L or L/V = const
Nd
Packing height H Fig. 8.3. Efficiency as a function of the height of bed with the number of liquid distribution points as parameter (qualitative)
N
= f(H)
(81) (82)
In the light of these relationships, it can be appreciated that a knowledge of the experimental conditions is essential in scaling up separation columns from experimentally determined values for the efficiency. In other words, design calculations must be based on known values for the height HP of the pilot column, the end effects Nd, the relationship between the efficiency and the inlet characteristic, and the relative efficiency e, which depends on the number of liquid distributor outlets. Relationships of this nature assume the form of Eqns (732), (735), and (738) in Chapter 7.
194
8
Scaleup for end effects and phase distribution
8.1 Scaleup model Once a sound basis for planning has thus been established, the model shown in Fig. 8.4 can be derived. It allows a qualitative comparison of the relationship between the number of separation units and the height of the bed of packing that exists in a pilot plant (Case a), an industrialscale plant with the maximum number of liquid distributor outlets (Case b), and an industrialscale plant with fewer liquid distributor outlets (Case c). In Case a, the height is HP, and the number of transfer units pertaining to Zmax liquid distributor outlets is NPjmax\ in Case c, in which Z < ZmflJC, it is merely NP. The number of separation units that must be realized in Cases b and c is NT. If the number of distributor outlets is Zmax, the minimum bed height required is HT>min\ and if Z < Zmax, the height required would be HT > HTjmin. The limiting value for the efficiency at a bed height of if = 0 is the contribution made by the end effects Nd. The quantities AN{ and ANi>max are characteristic of the effect exerted by
Industrialscale columns
Pilot column
Packing height H Fig. 8.4. Graph for modelling the effect of the number of liquid distribution points on the efficiency and in scaleup
8.1 Scaleup model
195
the inlet current and therefore depend on the number of liquid distributor outlets Z and Zmax respectively. The qualitative TV = f (//) diagram in Fig. 8.4 is based on the assumption that the height HP in the pilot plant and the heights HT>min and HT in the technicalscale plant are greater than that of the inlet zone Hi, in which the local efficiency dN/dH is subject to continuous change. In the H > Ht zone, dN/dH is constant and, owing to the geometry of the model, identical to the following ratio: dtf \
=
dH)H>
Hi
(1e)^,^ HT
( g 3 )
HTj
The relative efficiency e in this equation is defined by Eqn (713) for rectification systems and by Eqn (714) for absorption and desorption systems. It is fixed by the efficiency ratio that corresponds to the height of the pilot plant HP, i.e.
(«)*, = —^
(84)
The maximum efficiency per unit height that can be achieved by the optimum number of liquid distributor outlets Zmax and a height HP is given by
(8 5)
nr = (f) lip

\tijpjmax
In this case and if Z > Zmax, the requisite height of an industrialscale column would be
(8 6)
"
r"
Hence, HT is always greater than HT>min by an amount that is equal to the second summand in Eqn (86), and this summand, in turn, depends on e = f (Z). In other words, the increase in bed height that is necessitated by nonoptimum liquid distribution is given by Hrfhnun_n
H n T.min
JN\
( 1 e )
^
1
H,
\ " I P,max H= 1
kg11/z
\ I
\ M
ii
0.95
INd
'
\ \ \
_ 0.90
\
\
\
\
1 0.85
Zp" : Zmax.
\
\
\
N
* %
1 0.80 o .
'
LiJ
0.75
•
~JOn
•••V/fi

^
*

•
0.75
1.5
2.5 3.5 Packing height H, [m]
=E 0.35
•—• —
4.5
1
i
S 0.30
\
_ 0.25 /
CT) QJ
/
0.20 0.15
]_
t
15 25 Number of separation units NT
35
Fig. 8.11. Effect of the number of liquid distribution points on scaleup, if the number of distribution points in the industrialscale plant differs from that in the pilot plant
206
8
Scaleup for end effects and phase distribution
If e < e0, it would be logical to assume that NP/HP < NT/HTj i.e. that the inlet effect is negative. As has already been mentioned, there is a certain number of liquid distributor outlets that gives rise to a situation in which no positive or negative inlet effects occur. This limiting value Zo corresponds to a relative efficiency of (eo)Nd = o, as defined by Eqn (821), and to an efficiency per unit height of N
Nd HP
iP,max p,max;Nd
=0
(822)
Zo can be obtained by substituting e = {eg) Nd = o for £ m Eqn (734). Thus, [0.1
(L/V)025]1
(823)
An
1.13
Values of Zmax and Zo determined in two different beds of packing are listed in Table 8.1. A comparison of these figures gives an impression of the great extent to which Zo is less than Zmax. Table 8.1. List of characteristic operating values in a pilot plant for determining the number of liquid distribution points that is unlikely to give rise to either positive or negative end effects Packing
L/V
AN,.max
Pall, metal 50 mm
112.6
0.951
1
0.3
DINPAC, PP 47 mm
135.3
0.921
2.8
1
NP,
5.6
Nd
N H [1/m T7
0.5
1.67
335
92
1
3.07
516
73
8.5 Effect of phase maldistribution The efficiency of packed columns is affected not only by the number Z of distributor outlets per unit area but also by the uniformity with which the phases are distributed over the column crosssection. This applies particularly to the liquid phase. If it is not uniformly distributed and if the ratio of the column diameter ds to the size of the packing d is djd > 10, an impairment in separation efficiency NIH is likely, as has been confirmed in practice. If the degree of liquid maldistribution M is 0 < M < 1, the deterioration in separation efficiency AE can be estimated from the column efficiency Ec by means of the following equation: ' N\ IN H H (824) AE = = \Ec N
8.5
207
Effect of phase maldistribution
According to the Huber and Hiltbrunner theory, the column efficiency Ec is given by the following equation if the maldistribution M takes effect over the entire height of the column: 1
Ec =
(825) r + 1
where djd is the ratio of the column diameter to the size of an element of the packing and r is the reflux ratio. An idea of the extent of the theoretically feasible loss in efficiency can be obtained from Fig. 8.12, which was derived by evaluating Eqn (825). According to this diagram, hardly any significant loss in efficiency need be anticipated in columns with the diameter ratio mostly encountered in pilot plants, viz. djd < 10, even if the values of M are comparatively large. In modern, uniformly dumped or geometrically stacked beds of packing with no tendency to channelling, the distributor characteristic largely governs the degree of maldistribution M in the inlet zone and the extent to which the surface of the packing is wetted. It can be seen from Fig. 8.13 that the number of distributor outlets is a not inconsiderable factor and is generally much higher in pipe and related types of distributors than in simple box types. Hence the quality of liquid distribution depends not only on the number Z of the outlets but also on the uniformity with which they are fed. The mass transfer experiments described in Chapter 5 were performed in pilot columns to evaluate the characteristics of packed beds. The liquid phase was uniformly fed in accordance with the aspects mentioned above, and the number Z of distributor outlets was sufficiently large to ensure the utmost efficiency. The ratio of the column diameter to the size of the packing was about djd = 10 or less; in other words, the likelihood that liquid maldistribution M could affect the packing efficiency could be almost ignored {cf. Eqn (825)}.
0.5 *
Vapour /Liqijid ratio L/V =1
3 0.4
&0.3 y
0.2
>
0.1
•IT  " •
10 Fig. 8.12. (825)
\^
^' 14
_4
— — —
18 22 26 30 34 38 42 Ratio column diameter/packing diameter rjs/d
46
50
Efficiency as a consequence of maldistribution and calculated from Eqns (824) and
208
8
Scaleup for end effects and phase distribution
0.4 hWater STP—N ID
I 0.2 •XD
— ——
\
0.1 ZJ
•JU ]/
— 
•
10 12 14 16 Liquid load UL in m3/m2h
18
Fig. 8.13. Maldistribution caused by troughtype and perforatedpipe distributors
At ratios of djd > 10, maldistribution M is likely to occur and effect a loss in efficiency. The higher the ratio, the greater the loss. For instance, if djd = 50 and M = 0.2 apply over the entire packed height, the loss in efficiency may be theoretically as high as 50 %. Maldistribution M over the height of the column is undoubtedly a characteristic of the packing. Consequently, it may depend on the vapour load fv {cf. Eqn (717)} in the column as well as on the quality of the distribution at the inlet. Thus = t(fy) = i(FvIFy,Fl)
(826)
The curves shown in Fig. 8.14 were plotted from the results obtained on rectification systems in columns of various diameters packed with metal Pall rings. The liquidtovapour ratio was LIV = 1. They show the column efficiency Ec as a function of the diameter ratio djd with the relative vapour load factor fv as parameter. The corresponding equation is
Pall rings.metal.d = 15.25.35.50 mm. L/V = 1
15 20 25 30 35 40 45 50 Ratio column diameter/packing size d s /d Fig. 8.14. Column efficiency of beds of metal Pall rings as a function of the diameter ratio of the column and the rings
8.5
Effect of phase maldistribution
_ f tds_ . ~ \d'Tv
209 (827)
It can be seen from the diagram that the larger the value of fv and thus the greater the load, the higher the efficiency and the less the effect of the djd ratio. If the stripping factor \, as defined by Eqn (130), is I ~ 1, Ec can be estimated by the Schliinder equation, i.e.
1 1M
(828)
1 1+M
If the liquid is uniformly distributed over the inlet crosssection of the column and the quality of the distribution is retained throughout its entire path, the efficiency can be expected to remain constant over the entire height of the bed. A proviso is that the Schmidt number, i.e. the quotient of the kinematic viscosity and the diffusion coefficient, and the Marangoni number of the liquid phase in negative systems do not undergo any significant change along the concentration profile. In measurements on an ammonia/airwater system in columns of 0.3, 1.0 and 1.4 m diameter, no loss in efficiency was observed in beds of modern reticulated packing, e.g. Norpack rings. The yardstick adopted for the efficiency was the HTU, and the points plotted for these 25mm and 50mm rings all lay on their respective curve (cf. Figs. 8.15 and 8.16). It can therefore be concluded that the liquid distribution in beds of Norpack rings is uniform regardless of the column diameter.
NH3Air/WQter  ds=1.4 m 
10
9
I
s
Q.
H.
Nr
0
Fig. 9.2.
Hf
 With nr redistributors
Packing height H Graphical model to illustrate the effect of redistribution on the column efficiency
Now let Y\T be the ratio of the efficiency of the column without redistributors (N/H)T to the efficiency (N/H)r of an individual zone in a column with nr distributors, i.e. N T[T
(914)
=
and let Nr
«, + i
U ,
'
(915)
9.1
Estimation of optimum number of phase redistributors
217
Substituting y\T from Eqn (914) and (N/H)r from Eqn (915) in Eqn (913) then gives ,
Nd + ANt I 1
1 \
,
Nd + ANt I
Hr
H)r The ratio AH/H, which is essential for the evaluation of Eqns (95), (96), (97), and (910), can be related to T)rby rearranging Eqn (912) and expanding to give AH _HTH_ H H
NT/(N/H)TNT/(N/H)r NT/(N/H)r
_
I r,r
lV
"1/J
Hence, if the height of a column without distributors exceeds the effective height of a column with nr distributors by an amount AH (cf. Fig. 9.1), the relative increase in height AHIH is given by AH H
1 (N/H)r Nd + ANt
1
NT Nd + AN,
I
1
1 1 Hr HT
1 1 1
(918)
I +
I
Eqn (917) can be further rearranged to give
^W = ^W~l
(9 19)
"
The term HT in Eqn (919) is the height of a bed without redistributors and can be defined by substituting NT for N and HT for H in Eqn (911) and rearranging. Thus HT = [NT  (Nd + AW,)] —  \
(920)
The term H is the effective height of a bed with rcr redistributors and is given by (921) H)r Substituting Eqn (920) for HT and Eqn (921) for H in Eqn (919) then gives rise to AH
/
Nd
+
AAM/jV\ ^
218
9
Phase redistribution in columns
Alternatively, Eqn (911) can be rearranged to solve for N, and the following expression can thus be obtained for Nr: Nr =
t
6N\
+ Hr
(923)
J
Inserting this relationship in Eqn (922) then gives Nd
Nd Hr
Nr
dN\
1
(924)
If the expression on the righthand side of Eqn (922) is substituted for AH/H in Eqn (97), a relationship can be found for the height Hr of the one section in a column with nr distributors, i.e. K
1 N NT
nr
1
(925)
)\H)rldN
The total bed height H in a column with nr distributors can be obtained by substituting H for (nr + 1) Hr {cf. Eqn (92)} in Eqn (97). Thus 1
H = nrK —)
(926)
) / Eqn Eqn (922)
The limiting case of a very large number of separation stages NT, corresponding to HT> oo, follows from Eqn (918), i. e. AH\
I
1 (N/H)r Hr Nd + ANt
(927)
It also follows from Eqn (922), which gives rise to Eqn (928), and from Eqn (924), which gives rise to Eqn (929). Thus AH
1 cUV\
AH
Nd + ANt
H
Hr
1
(928)
(929)
9.2
Costs relationships
219
Equating Eqns (927) and (928) or Eqns (928) and (929) yields the following relationship for the height of one section if the number of separation stages tends to infinity:
^
N_\
_ldN\
(930)
Since NT, it follows that nr also tends to infinity. In this case, Eqn (925) becomes
A comparison of Eqn (930) with Eqn (931) leads to the conclusion that, if very great values of NT are realized, the costs for columns with redistributors will not be on the same level as those for columns without redistributors unless the costs factor K tends towards the following limit:
K
^T
Nd + AJV,.
(932)
According to the model, this relationship is valid if the following applies:
One incontestable fact that emerges from these considerations is that the bed height Hr at which redistributors can be economically installed cannot be determined by a simple rule of thumb. The factors that really count in its determination are the end effects at the inlets, the efficiency in the zone of completely developed flow, and the acquisition costs for the redistributors. If the costs factor K, as defined by the expression on the righthand side of Eqn (96), is greater than the value calculated from Eqn (932), Hr must be higher than the figure obtained from Eqn (930).
9.2 Costs relationships The spacing at which redistributors can be economically installed between sections of packing of Hr height is governed by the costs factor K, which is defined by Eqn (96). Eqn (932) clearly states that the limiting value KNT _+ ^ for this costs factor is fixed by the ratio of the end effects and efficiency in the inlet zone to the efficiency in the zone of completely developed flow. Rectification and desorption experiments to verify these relationships were performed in pilot plants on packing produced in various shapes and sizes from various
220
9
Phase redistribution in columns
materials. The main dimensions of the columns in the pilot plants and the distribution density of the liquid distributors were varied. The results of these experiments, which have already been discussed in Chapter 6, are reproduced in Figs. 9.3 and 9.4. The values required for the determination of the limiting costs factor KNT _ oo can be read off from the curves in this diagram in conjunction with the qualitative diagram presented in Fig. 9.2. These values are listed in Table 9.1. An important outcome of the studies is that the costs for a column with redistributors cannot be the same as those for the corresponding column without redistributors unless the factor K defined by Eqn (96) is identical to a limiting value that depends on the efficiency in the inlet zone and is defined by Eqn (932). It can be easily proved that the number of redistributors nr and their spacing Hr are irrelevant if this condition applies. In other words, the costs C remain constant as long as Hr is greater than Ht. According to Eqn (94), the costs for a column with nr redistributors is given by C = H\—
d} cP + JT dscs) + nrcr = HcPs + nrcr
(934)
where cPs are the costs per unit height of column for the bed of packing and the column shell, as defined by Eqn (96), i.e. (935)
= ~7 ds cP + Jt dscs
14 A o
12
Ethanol/Water, 1 bar Ethylbenzene /Styrene, 130 mbar Methanol /Ethanol, 1 bar
10
Z) CI
a CDCD
0
1
3
Packed height H [m] Fig. 9.3.
Number of theoretical stages as a function of bed height in rectification
9.2
221
Costs relationships
DINPAC plastics, ds288 mm Z = 490 1/m2 C02H20/Air, STP uL=5.97 m 3 /m 2 s, Fv=0.9410"3 m 3 /m 2 s
47mm racKing "
— — •
——'
—CD to
a
«
?
no ~ n r n 11 n f
§ "2
Uc
i f
l
Jr * — — — ——— I —
s
^ ^ ^— 70mm Pac king — i
i
1.5
0.5 1.0 Packed height H [m] Fig. 9.4.
Number of transfer units as a function of bed height in packed desorption columns
Table 9.1. Empirical data for describing inlet effects in packed columns. Used to evaluate the diagrams in Figs. 9.69.10. Material
H [1/m2]
Nd
ANi
[m] 500
600
0.5
0.5
(if)
K lim
1.9
0.526
Pall ring 50 mm
Metal
Pall ring 35 mm
Metal
800
490
0.5
1.9
2.125
1.129
Raschig ring 25 mm
Ceramic
750
900
0.5
1.5
3.125
0.64
Tellerette 70 mm
Plastic
288
490
1
0.8
1.53
1.176
Tellerette 47 mm
Plastic
288
490
1
0.65
2.05
0.805
System
jctifica
o
&
Desorption
Packing
222
9
Phase redistribution in columns
cPs is related by the factor K to the costs of the redistributors cr as follows:
Cps =
cr K
(936)
Rearranging Eqn (923) to solve for Hr gives
Hr = [Nr  (Nd
(937)
dN
The relationship between NT and Nr is obtained from Eqn (915), i. e. NT = Nr (nr + 1)
(938)
Hence the total costs are given by
=
1
cPt\[NT(nr
nrK\
in
ldN
(939)
The limiting value for the costs factor K can be found by differentiating Eqn (939) with respect to nr and equating the derivative to zero, i.e. dC = 0 dnr
(940)
The result is the same as that given by Eqn (932) and is independent of the number of redistributors nr and thus of their spacing Hr. The following relationship can be derived from Eqns (923), (934), (935), and (936): K
C = cPs NT Nd + ANt + Hr
K dN dH
NT
(941)
The limiting value for the costs factor K can again be found by differentiating this equation with respect to Hr and equating the derivative to zero, i.e. dC_  0 dHr
(942)
Again, the result is the same as that given by Eqn (932). The case in which no distributors are installed can be represented by substituting nr = 0 for nr in Eqn (939). Thus,
9.2
1 1 dN\ dH
L
Costs relationships
223 (943)
H.
Since Hr = HT in this case, it can be seen that Eqn (943) is identical to Eqn (920). Therefore, HT — CpstiT
(944)
— Cnr
Eqns (939) and (941) apply for Hr > H(, i.e. for the range in which the spacing Hr between two redistributors is equal to or greater than the height Ht of the inlet zone, in which the efficiency dN/dH generally changes. If Hr < Ht, the relationship to apply would be that derived from Eqns (923) and (941), i. e. C = cPs N7
1
1 +
K
K
Hr
NT
(945)
The functional relationships between the characteristic costs and design parameters are illustrated qualitatively in Fig. 9.5. The various parameters represented as functions of the spacing Hr between redistributors are defined as follows:
T = packed height without redistributors
c o ZD CD
o "a a
Fig. 9.5. Qualitative relationship between packed height, costs, and the number of redistributors
Packed height between redistributors Hr
224
9
Phase redistribution in columns
the costs ratio per separation unit by C
1
(946);
the various costs factors by (947);
lim < K < Klin
the number of liquid distributors by (948),
in which case Nr is obtained from the relationship TV = f(//) or from Eqn (923) if Hr > Ht; and the relative reduction in bed height by (949).
0.6 <J
CJ)
/ m 3 /m 3 /s
244
11 Overall evaluation of packing
aspect is the costs as determined from Eqn (111). From the engineering aspect, however, the tendency to fouling would be another factor to be taken into consideration. Frequently, the decision in favour of a particular type of packing is based on an analysis of the total costs with due regard to specific local conditions, e.g. the layout of the equipment. If different types of column internals are compared on the basis of Eqn (111), a fundamental distinction must be drawn between cases in which Fv = 0.8 FFh where Fm is the capacity factor at the flood point, and those in which Ap/nt is a constant. The latter is important for evaluating all separation processes in which a limit is imposed on the pressure drop.
11.3 Evaluation for the separation of thermally unstable mixtures The parameters that influence the thermal stability of a substance are the operating temperature and the residence time. The latter is governed by the volume of liquid / retained in the bed of packing and the liquid flow rate VL or  if the liquid velocity uL and the height H of the bed are given  by the liquid holdup hL, i.e.
The specific residence time tjnt is defined as the period during which the liquid is held up over a bed height that corresponds in terms of efficiency to a theoretical stage, i.e.
nt
(114)
uL \ ntIH
It attains its lowest value in column internals for which the term hL/(nt/H) is a minimum when uL remains constant. Eqn (114) can also be writen in the following form: ^ = hL^LVV=KhVy nt uL
(115)
In other words, the specific residence time tjnt is directly proportional to the column volume per unit of efficiency vv. The constant of proportionality Kh is a dimensionless hydrodynamic quantity that is specific for a given type of packing and is given by h
L
L
^
L
Thus, for a given column volume per unit of efficiency vv and a given liquid/vapour ratio L/V, the bed of packing with the shortest residence time will be that in which the liquid holdup hL is lowest for the load factor concerned. Hence, the average total residence time of the liquid in the bed is a function of parameters that depend on the load, i.e. hL and vv, and parameters that are defined by the separation task, i.e. the number of theoretical stages nt and the volumetric phase ratio, i.e.
11.3
Evaluation for the separation of thermally unstable mixtures tL = Kh vv nt = hL vv nt ——
245 (117)
uL The volumetric phase ratio in this case is given by
The product of hL and vv is identical to the liquid holdup h'L per unit of separation efficiency and vapour volumetric flow rate, i.e. h'L = hL vv
(119)
Consequently, the suitability of column internals for the rectification of thermally instable mixtures is essentially defined by two equations, i.e.
—
= f(FV)
LI V,PT = const
(H10)
nt —
= f(
The following relationship can be obtained by combining these two equations: ) t
(1112)
I L/V,pT = const
The terms (tLlni)um and (Ap/nt)um define the maximum permissible limits for the specific residence time and the temperature at the foot of the column. If they are known, it can be determined which of the columns under investigation represents the most favourable costs. The condition that must be satisfied in this case is (1113)
Another condition that must be met is that the choice should be in favour of the column with the lowest costs per unit of column efficiency and unit volumetric flow rate, as defined by v,C
= j  ^ Kh
(1114)
nt
where C is the costs per unit volume of the packed column. Eqn (1110) relating to plastics packing is presented graphically in Fig. 11.3. It can be seen that the minimum residence time coincides with the vapour capacity at the loading point, above which the liquid holdup rises considerably with an attendant, renewed increase
246
11
Overall evaluation of packing
in the residence time. This minimum corresponds to a pressure drop per theoretical stage lS.plnt = 2.2 mbar. Eqn (1112) is presented graphically in Fig. 11.4. In this case, the example taken to plot the curve was metal packing in the range below the loading point. Another fact that can be derived from Figs. 11.3 and 11.4 is that the residence for the liquid is less in beds of packing with a large area per unit volume a than in beds with smaller values of a.
Chlorobenzene/Ethylbenzene 67 mbar. L/V=1
CD
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
Vapour capacity factor F v [m" 1/2 s"1 kg 1 ' 2 ] Fig. 11.3. Specific residence time of the liquid phase in a column packed with plastics Hiflow rings as a function of the capacity factor
20
i
i
i
i
i
i
Chlorobenzene/Ethylbenzene 67 mbar. L/V1 10
X CMR
1.5 Turbo ,a=173rn 2 /m 3 
Metal^ ^\ —.»
7^1—.
Gempak2AT,a = 200m 2 /m r 3 0.1
0.2
0.3 0.4
^ —
0.6 0.8 1
Spec, pressure drop Ap/n t [mbar]
Fig. 11.4. Specific residence time of the liquid phase as a function of the specific pressure drop in a random and in an arranged bed of metal packing
11.4
Evaluation in terms of minimum column volume
247
11.4 Evaluation in terms of minimum column volume Rectification is the most energyintensive thermal separation process. The planning stage involves thermodynamic and hydrodynamic analyses of the design, materials, and operating parameters and a knowledge of the process engineering parameters required for the evaluation of the intended column internals. The only means of ensuring optimized energy consumption and minimum column volume is to instal efficient highperformance packing with a low inherent pressure drop. Considered from this aspect, the volume Vc of the enrichment section in a rectification column of height H through which vapour with a molar mass \iv and a density QV flows at a velocity uv and a molar flow rate V is given by VC = V— QV
—H
(1115)
Uy
The molar flow rate V is given by V = D (r + 1)
(1116)
where D is the molar flow rate of the overhead product and r is the reflux ratio. Eqn (1116) applies to the entire enrichment section of the column if the individual components of the mixture have almost the same vaporization enthalpy. Strictly speaking, it applies to the stripping section only if the mixture to be separated flows through the column at its boiling point, i.e. tF = tb. The terms nt/H and vv associated with the vapour capacity factor Fv can be introduced by means of the relationship expressed in Eqn (136). Eqn (1115) then becomes yc = D iiv — vv (r + 1) nt
(1117)
Qv
Other parameters that affect the volume Vc are the operating pressure and the nature of the system to be separated. The following two general relationships then apply: QV, r, nt = f (/?, system)
(1118)
vv = f (p, system, internals)
(1119)
The term (r + 1) governs the energy consumption, and the separation term (r + l)nt exerts a great influence on the column volume. This product passes through a minimum at a certain reflux ratio r, i.e. VC,min
n = f (Ap//Ir)
(1120)
If the rectification process involves a large number of theoretical stages, this minimum value increases with the pressure drop per theoretical stage Ap/nt, as is clearly evident from the example shown in Fig. 11.5. It is also obvious from the diagram that modern packing is
248
11 Overall evaluation of packing
Ethylbenzene/Styrene. pj =51 mbar, tp = t b x F 0.591 , x D 0.992 . x B = 0.0035 60
\
\
\
» 55
s
\ X \
X
I SO
^ r
^ 45
1
—.
o
^ .
—»
40 460
N ___
\
440
\
1 •
—i
\
420
, —
cT
T 400
H
iI
OfV
/
/
J 380 X /'
g 360
•K >
— —
^1
340 i
320
—~*
300 rpi ^
re "'^
rr. rr yn bU °^ '^ ReflUX ratio r
7r ' ^
pn "^
Fig. 11.5. Effect of the specific pressure drop on the column dimensions in the vacuum rectification of an ethylbenzene/styrene mixture
definitely superior to traditional fractionating plates from the aspect of the volume Vc of the enrichment zone, because it gives rise to much lower values of Ap/nt and vv. Since a decrease in the value of Ap/nt entails a reduction in the reflux ratio r {cf. Eqn (149)}, another great advantage of lower pressure drops in separation processes that involve a large number of theoretical stages is a substantial cut in the energy consumption. According to Eqns (148) and (149), the reflux ratio in a real column r exceeds that in a theoretical isobaric column riso by a factor vG, which  in turn  exceeds the minimum rmintiso by a factor v. There must be a value of v that corresponds to the minimum volume Vc,min
11.4
249
Evaluation in terms of minimum column volume
and the separation term [(r + l)nt]min and to which Eqn (1120) would apply. The relationship to the pressure drop per theoretical stage would then be / Ap\ [(r + \)nt]minVG
= f —
(1121)
]> V
n
t
\
The additional energy consumed by this pressure drop is given by vGQiso
riso + 1
v 1
(1122)
rmin,i,
It can be expressed as follows as a function of the presssure drop per theoretical stage: / Ap \
= ff
(H23)
Ethylbenzene / Styrene , pT = 51 mbar . t F = t b x F : 0,0591 ,x D = 0,992 , xB0,0035 S "5
18
^—
X
h r
•
'm n. sc
«
1.4
3
1.2
[(r*1)nt]min
0.3
03 a ,
CD
a c
—•
AQ /QIS0
;0.2
GU
ci
0.2 Js
\

CD C 3 C/) iso can also be expressed as a function of the pressure drop per theoretical stage, i.e. l(r + l ) n l ] m i 
= fH 
n
t,iso
\
n
t
(H24) I
These relationships are presented graphically in Fig. 11.6. The data taken as an example were derived from Fig. 11.5. The effect of the pressure drop on the energy consumption and the number of theoretical trays is immediately evident. The curves apply to the case in which the column volume Vc is a minimum. In other words, they need not necessarily correspond to the operating conditions under which the minimum total costs, i.e. the sum of the capital investment and running costs, can be expected. The extent to which the two cases agree depends on the local costs for energy and the materials of construction.
11.5 Theoretical considerations in the design of column internals Modern manufacturing and finishing techniques allow column packing to be realized in multitudinous geometrical forms with a wide variety of surface structures, as is evident from the designs discussed in Chap. 2. Thus great scope is available in varying the hydrodynamic and performance characteristics. The materials of construction represent another important design factor. It is obvious from the preceding sections of this chapter and the remarks on the experiments discussed in Chap. 3 that there is no single type of packing that can provide a perfect answer to all the demands that are encountered in practice: high outputs, low pressure drops, short residence times, immunity to corrosion, resistance to fouling, and low costs. Consequently, a logical procedure in selecting packing would be to apply Eqns (111) and (112) in order to determine which would be most economical of the types that have previously been screened for compliance with process requirements, e.g. short residence time and low pressure drop in the rectification of thermally unstable mixtures. Many aspects on separation efficiency have to be considered in addition to the operating requirements and the properties of the system. Most importance is attached to the basic geometry and dimensions of the packing. The volumetric mass transfer coefficient, i.e. the product of the mass transfer coefficient p and the area of contact aph at the phase boundary, is a useful performance criterion (cf. Chap. 5). It is defined in terms of the phase load u in a horizontal crosssection of the column and the height of a transfer unit HTU (or the number of transfer units NTU per unit column height H), i.e.
The specific column volume, in analogy to Eqn (136), can be introduced in this equation, i. e. 1
uNTUIH
HTU
u
' $aPh
(1126)
11.5
Theoretical considerations in the design of column internals
251
According to the theory of nonstationary diffusion, the mass transfer coefficient 3 for the phase concerned depends on the corresponding diffusion coefficient D and the period of contact required for renewal of the phase boundary, i.e.
P =  \ / 
(H27)
where — = constant = 2jt~ 05 . c The duration of contact can be reduced by design measures. For instance, it is known that small packing separates more efficiently than large; and regularly stacked packing with interrupted flow channels, more efficiently than fallingfilm. In both cases, x is small, with the consequence that both the specific column volume v {cf. Eqn (1128)} and the total volume Vc, through which the phase in question flows at a volumetric rate V {cf. Eqn (1129)}, are also small:
— Vc = vVNTU
(1128) (1129)
A knowledge of the residence time in the column is particularly important in planning the rectification of mixtures that are sensitive to heat. It depends on the liquid holdup {cf. Eqn (113)}, the liquid load uL, and the volume Vc {cf. Eqn (1117)} of a column of height H and diameter ds. The value for the liquid phase is given by
L
(
UL 
)
d}
The value for the vapour phase can be obtained from this equation by introducing the terms for the effective void fraction ee for the gas {Eqn (455)} and the superficial gas velocity uv, i.e.
tv
=
£eVc
= ^H
JT 2 — ds Uy
(1131)
Uy
The residence time tL is related to the duration of contact xL through the liquid holdup hL, which depends on the length lx of the path of contact over which the surface of the liquid is renewed in the bed of packing concerned. The average liquid velocity over this path is given by uL = —
(H32)
252
11
Overall evaluation of packing
The total number of paths of contact per unit height of column, i.e. for H = 1, that is permitted by the geometry of the packing is given by
«c = 7
(H33)
1
Therefore, rL and tL are related by the following equation:
Substituting for tL from Eqn (1130) then yields the following relationship between the duration of contact and the liquid holdup: xL =  ^ uLnc
(1135)
Finally, substituting for nc from Eqn (1133) gives xL =  ^
(1136)
This equation states that the less the product hLlx of the liquid holdup and the path of contact for a given liquid load, the less the duration of contact xv. It is an unambiguous statement that must be observed in designing packing geometry. In analogy to Eqn (1132), the average superficial velocity of the gas or vapour phase is given by Uv=— xv
(1137)
In other words, the vapour traverses the path lx in a period of time xv, which is related as follows to the residence time tv: (1138) Substituting for tv from Eqn (1131) gives rise to Eqn (1139); and combining Eqns (1133) and (1139), to Eqn (1140): TV = —^—
uvnc Uy
(1139)
77.5
Theoretical considerations in the design of column internals
253
These equations relate geometric parameters for the packing, i.e. the void fraction 8 and the length of the path of contact / t , to certain operating conditions, i.e. the liquid holdup hL and the superficial gas velocity uv. Hence, the duration of contact of an entire phase depends on the local phase velocity and the number of paths of contact per unit of effective column height. The figure for the liquid phase can be obtained from Eqn (1141), which is derived by combining Eqns (1132) and (1137); and for the gas phase, from Eqn (1142), which is derived from Eqns (1133) and (1137):
xL = ^J— uLnc
(1141) (1142)
uvnc The corresponding residence time for the liquid phase is given by Eqn (1143); and for the gas phase, by Eqn (1144):
tL = ¥
(1143)
UL
tv=^
(1144)
Uy
According to these two equations and to Eqns (1130) and (1131), a definite relationship exists between the residence time, the load, and the height of the bed. If the liquid load uL is given: the smaller the product of the liquid holdup hL and the height H, the shorter the residence time tL. If the vapour load uv is given: the smaller the product of the effective void fraction ee and the height //, the shorter the residence time tv. Rearranging Eqn (1128) allows the duration of contact e to be expressed in terms of the specific column volume v, the area of contact at the phase boundary aph, and the coefficient of diffusion D, i.e. (1145) It follows from this equation that if the duration is short, the product of the specific column volume v and the area of contact aph must be small. Its value for the vapour {Eqn (1146)} and liquid {Eqn (1147)} phases can be obtained by further rearrangement of Eqn (1145). Thus
aph = c Vj±
(1147)
254
11
Overall evaluation of packing
According to Eqn (111), the price of a rectification column is governed by the product of the specific column volume and the costs per unit volume. Consequently, development work must be aimed at selecting design parameters that involve the minimum outlay on materials of construction and machining. Combining Eqns (1140) and (1146) gives rise to (1148) It follows from this equation that, if the void fraction 8 is given, the specific column volume vv relating to the vapour phase can be reduced by shortening the length of the path of contact lx. Analogous information can be derived from the corresponding equation for the specific volume vL relating to the liquid phase, which is obtained by combining Eqns (1136) and (1147), i.e. V
L = —
\
ITTli
(H49)
Design measures aimed at frequently interrupting the flow paths for the two phases, and thus their redistribution, have a beneficial effect on mass transfer and therefore reduce the specific colume volumes. The liquid holdup hL also depends on the design and the loading conditions, and the advantageous effects that can be achieved if its value is low are evident from Eqn (473). The area a per unit volume and the area of contact aph at the phase boundary can be best exploited by packing that permits high vapour velocities and can be uniformly wetted. According to Eqns (1148) and (1149), low values for the specific column volumes vv and vL can thus be attained. An illustrative example is given by Table 11.3, in which the specific column volume Vy for a random bed of Pall rings is compared to that for stacked Pall rings operated at the same pressure drop per theoretical stage Ap/nt. It can be seen that the column space occupied by the stacked bed is only about 40 % of that of the random bed.
Table 11.3. Difference in specific column volume between random and geometrically arranged beds of Pall rings. Comparison based on the specific pressure drop Metallic Pall ring packings, ring size 25 mm Ap/nt [mbar] » vv^ [m3/m3/s]
Dumped Stacked
0.5
1
5
0.453 0.180
0.244 0.080
0.093 0.036
77.6
State of the art in the development of packing
255
11.6 State of the art in the development of packing The properties expected of packing are great separation efficiency and a high superficial velocity, yet the minimum possible pressure drop in the stream of gas or vapour. The more that these requirements are met, the less the volume of the internals that are required for a given separation task, i.e. that necessary to achieve a specified capacity and overall efficiency. Thus a measure for the efficiency is the specific column volume vv {cf. Eqn (134)} that is required to cope with a given liquid load or a given phase ratio. Its reciprocal can be regarded as the volumetric efficiency of the packing. A criterion that is frequently adopted for evaluating packing is the pressure drop per unit of efficiency, which is referred to as the specific pressure drop. If it is low, the packing is eminently suitable for the separation of mixtures that are sensitive to heat, because it allows operation at moderate product temperatures. Packing with a low specific pressure drop is essential for the realization of optimum energy consumption in separation equipment. In many cases, it also entails a reduction in capital investment costs, particularly for vacuum rectification processes that involve a large number of transfer units. Hence the specific column volume and the specific pressure drop decisively govern the economics of column packing. The operating characteristic for the packing is another criterion for selection. Some of the numerous products that have to be separated on an industrial scale tend to foul or corrode the packing in a column. Experience has shown that the simpler the geometry of the packing and the smoother its finish, the less this tendency. An example of suitable geometry is honeycomb packing, in which parallel rows of sheet metal, foil, or plastics film are stacked crosswise in a regular geometric arrangement. The only means of finding out the extent to which the performance of random and stacked beds of packing can be improved is to determine by experiment the parameters that specify the geometry and texture. The wide differences in the thermodynamic behaviour and physical properties of the various systems to be separated by thermal techniques entail corresponding differences in the operating conditions. Thus the liquid loads in vacuum rectification are usually much less than those encountered in rectification at atmospheric or higher pressures or in absorption and desorption processes. Consequently, the liquid/vapour load ratio in a column may vary considerably from the one process to another. Moreover, the efficiency of most beds of packing depends on the load and pressure; and the maximum load, on the liquid/vapour ratio and the pressure. It can thus be seen that there is no one type of packing that gives optimum performance in each and every industrial application. This also explains the numerous designs of packing on the market. In view of these facts, engineers responsible for planning thermal separation plants often have difficulty in selecting the optimum packing for a given application, particularly since the pertinent empirical values derived from laboratory or plant studies are not always available. However, evaluation of the results presented in various publications permits the performance of packing of different geometries and textures to be assessed in outline. The criterion that is generally adopted in evaluating various types of packing is: the greater the area per unit volume a, the better the mass transfer. However, this applies only if the yardstick for packing performance is the specific column volume vv. Another criterion is: the greater the effective void fraction, the less the pressure drop and the larger the bed capacity.
256
11
Overall evaluation of packing
A measure for the degree to which the area available per unit volume in the bed of packing can be exploited is the performancerelated area a'. It represents the area per unit efficiency and unit vapour volumetric flow rate, and is given by (1150)
a — a vv
The volume of packing material v' present in a bed can be expressed in terms of the separation efficiency and the flow rates, i.e. (1151)
— a s vv = — a' s = (1  e) vv
If vv has been determined for various beds, the area required to realize the one theoretical stage and unit vapour volumetric flow rate can be obtained from the function (1152)
a' = f(fl)
These conclusions have been verified by the results of comprehensive studies of recent and later date that were performed under comparable conditions on various beds of packing and that embraced different design principles, different materials, and different surface structures, e. g. expanded metals, fabrics, and smooth surfaces (Fig. 11.7). The results obtained in evaluating the less recent studies are presented in Fig. 11.8, which shows the performancerelated area a ' a s a function of the area per unit volume a for some packings of completely different geometries and textures (cf. Table 11.4). The points plotted Table 11.4. Symbols for traditional types of packing as illustrated in Fig. 11.8 Packing
Dimensions
Symbol
Metal gauze
Sulzer
BX
T
Sheet metal, folded and perforated
GHH
Square
•
Metal grid
Glitsch
Fine
Metal grid
Glitsch
Course
• •
Ceramic, rough
Raschig ring
25 mm
A
Plastic, corrugated and performated
BASF ring
25 mm
O
Sheet metal, smooth
Raschig ring
25 mm 35 mm 50 mm
A A
Sheet metal, discontinuous
Pall ring
15 mm 25 mm 50 mm 80 mm
O O
Structure
Expanded metal, discontinuous
Pall ring
25 mm 50 mm
A
o 6 e e
77.6
State of the art in the development of packing
257
PacMiam
Gutsch 3no, .jjorjc
b!;iS,".!*; bfiCl,
Fig. 11.7. Examples of traditional packing for geometrically arranged and random beds
metal
Pail ring, exp. met
in the diagram were derived from experiments performed in the same pilot plant, with the same test system, and under the same conditions. It allows the limits to be estimated within which the separation efficiency can be influenced by design measures. According to the diagram, the degree of exploitation of the available surface decreases with an increase in its area a, i.e. more area a' has to be installed per unit efficiency and unit flow rate. Figure 11.8 also permits the conclusion that changes in the surface structure of packing of given basic geometry merely lead to a moderate change in the efficiency per unit area. Despite the very expensive material of high interfacial activity that is required for its production, metal gauze packing is less efficient per unit area than, say, a random bed of traditional metal Pall rings. In qualitative terms, this entails that, if the one theoretical stage is adopted as a measure for the efficiency under conditions that correspond to about 80 % of the maximum possible capacity, the area per unit volume of the gauze packing required to realize this
258
Is*
Overall evaluation of packing
on o/) — c
*E e
11
max. loac
A
.  —
c ^« «— ^*
—
^—,
—
•
—•
.—
in
,—
, zu a
g 10 " S 40
Ethylbenzene/Styrene 133 mbar Liquid/Vapour ratio L/V = 1
—
a CD
aopt
(1157)
If the column is of large diameter, the effect exerted by the costs Ks corresponding to the area as is reduced. Four types of metal packing, one of them structured, will now be taken as an example to illustrate these relationships. The specific column volume vy, as defined by Eqn (134), is shown as a function of the area a per unit volume in Figs. 11.14 to 11.18. The relationship can be described by an equation of the following form:
264
11
Overall evaluation of packing
VV=
WA+.
(1158)
where A and B are constants. The costs function follows from Eqns (1156) and (1158), i. e. (1159) The costs Cp per unit of packing installed are given by Eqn (1160); and the costs Cs per unit area of column shell, by Eqn (1161): Cp = C + Da
(1160)
Cs = E + Fds
(1161)
where C and D are costs factors that apply to a specific packing, and E and F are the corresponding factors for the column shell. Eqn (1161) applies if the column diameter ds and thickness s lie in the range ds < 1 m, s = 6 mm through ds ~ 2 m, s = 8 mm to ds ^ 3 m, s = 10 mm and the material of construction is stainless steel (18 Cr 10 Ni 2.5 Mo  German steel number 1.4571). The total costs K are therefore given by —+ B a
a(C + Da)
4[^ + F
(1162)
Numerical values for the factors A and B (derived from Figs. 11.15, 11.17, and 11.18) and for C, D, E and F (estimated from manufacturers' data) are listed in Table 11.6. Eqn (1162) is presented graphically in Figs. 11.19, 11.20, and 11.21. The curves are valid for traditional random packing (represented by Pall rings), modern random packing
Nominal ring size d [mm "e
13
50
35
25
15
yre le ' 33 nba r, t V ma>:. ccipac it v CO .80 f^eto 1 R DSCflio rino
F hyl "IPfTIGDG \
kH i 10
100
Fig. 11 14. rings
200 300 Area per unit volume a [m 2 /m 3 ]
7
400
Relationship between the specific column volume and the area of beds of metal Raschig
11.7
265
Optimum area per unit volume in beds of packing
(represented by Glitsch Cascade MiniRings), and stacked packing (represented by Montz Bl). It can be seen that the total costs K depend greatly on a and ds and that the optimum area aopt per unit volume is a function of ds.
50
Nominal ring size d [mm ' 25
35
3 13 CL>
t 12 \ 11
15
' ' I r Q /C> t .thy Iben zene/ o tyrene 133 mbar,  =
\\
1
c:a.8 0% max. capacity
Metal Pall rings
"i 10
i
r 100
200
— 400
300
Area per unit volume a [m 2 /m 3 ]
Fig. 11.15. Relationship betwen the specific column volume and the area of beds of metal Pall rings
Nominal ring size d [ m m '
50 35 12
15
25 1 1
11
Methanol/Ethc nol i 1
9 \ _ O
i
10
i_
DCir.
L
'
V
r:a.80°/«3 mo* r.nn acity
\
N
\
«1etc I Pall f"innc 1 200
—
400
300 2
3
Area per unit volume a [m /m ]
Fig. 11.16. Relationship between the specific column volume and the area of beds of metal Pall rings
11
266
Overall evaluation of packing
Nominal ring size d[inches]
2.5
2
1.5 1.5T
1T
\ 1e\
PL
0.5
1
/ C 1L . .1 U _. _
Ihiuruuenmi e/t thylDenzene o/ muui, V 1 
c ^\
: a . 8 0 % max. capacityI \
o 7 ^"•^^
IB S.
5
— —
letal Gl tsc ) C 3SC(ide Mini Ri igs 1 1 1 n
100
200
300 2
•o
400
3
Area per unit volume a [m /m ] Fig. 11.17. Relationship between the specific column volume and the area of beds of Glitsch CMR packing
10
i I I I :•  Chlor Dbenzene/Ethylbenzene 67 mbar,4 = 1
c a . 8 0 % max. capacity
/ )
^ 7 >
Mellapak 250 Y
S.
° 6
Lh
"o 5
—^
f^lontz niGta [ I
200
300
i
pprl^inn •a
500
400 2
3
Area per unit volume o [m /m ] Fig. 11.18. Relationship between the specific column volume and the area of arranged beds of packing
11.7
Optimum area per unit volume in beds of packing
267
Differentiating Eqn (1162) with respect to a gives rise to aopt, as is indicated by Eqn (1157). Thus ^ + F\= alpt (AD + BC) + 2 BDalpt
(1163)
If the numerical values for the factors A to F listed in Table 11.6 are inserted in Eqn (1163), the graphical relationship illustrated in Figs. 11.22, 11.23, and 11.24 can be obtained by plotting the optimum area aopt per unit volume against the column diameter ds. According to the curves reproduced in Fig. 11.22, the value of aopt corresponding to a shell diameter of ds > 2 m is aopt < 120 m 2 /m 3 , and the associated optimum diameter of the Pall ring is d > 50 mm. The value for stacked Montz Bl or packing of similar geometry and efficiency is aopt = 200/300 m 2 /m 3 . The dashed lines in the diagrams apply for the case in which the costs of the packing may vary by ± 25 %. If D = 0, Eqn (1163) is simplified to
Substituting Cs for (E + Fds) {Eqn (1161)} and Cp for C {Eqn (1160)} then gives
In other words, the optimum area aopt per unit volume is governed by the costs ratio CJCp and the column diameter ds.
Table 11.6. Costs function factor for some types of packing Factors for cost functions
Ethylbenzene/ Styrene 133 mbar Pall ring
Chlorobenzene/Ethylbenzene 67 mbar Glitsch CMR Montz packing Bl
A (m2/m3/s)
7
4
16
B (m /m /s)
0.07
0.04
C (DM/m2)
14
6
0.018 22 + 6/ds
D (DM/m)
0
0.077
0
3
3
E
(DM/m2)
F
(DM/m3)
640 for 0 .5 m < ds < 4 m 180 for 0 .5 m < ds < 4 m
268
11
Overall evaluation of packing
Ethylbenzene/Styrene133 mbar, L/V=1, Fv = 0.8F Vmax Nominal ring size d [mm] 80 50 35 25
Area per unit volume a [m 2 /m 3 ] Fig. 11.19. Effect of the diameter of a column packed with metal Pall rings on the total costs and the area that permits minimum costs
Chloro/Ethylbenzene 67mbar, L/V=1, Fv0.8F Vmax. Nominal ring size d [inches] 2.5 2 1.5 1
700 en
costs Kit
_E
600 500 400 300
15E
\
800 \ \
v \ V \\
\ \
1E
i Kmin
\
> A
y/
^—
7
s
/
7 /
y /
^\y
/
/
/ />
/ ^
Metal Glitsch CMR 200
i
i
i
100 200 Area per unit volume a [m z /m 3 ]
300
Fig. 11.20. Effect of the diameter of a column packed with metal Glitsch CMR on the total costs and the area that permits minimum costs
11.7
Optimum area per unit volume in beds of packing
269
ChloroZEthytbenzene 67mbar,L/V=l
1100
\
\
1000
Kmin \
0
?5rr)
\
= 800
\j
.
\
7.5
y
——. 
\
4? 900
7
/
at ?
1 700 1
a
*
— — — 
— —
. 
d—
—. ———
° 600
4
500
m
Ann,
[
r7
n
1
ne
L II ietci I
200
PIjcki

—
—
— ———
"
— — —
m



——
Bl
300 2
400 3
Area per unit volume a [m /m ] Fig. 11.21. Effect of the diameter of a column packed with metal Montz Bl on the total costs and the area that permits minimum costs
250
Stainless Steel Pall ring
\ 200 s
o
150
\\ \
s
***
CD
a
25
°
•
100
^
—
•
35 •*
*—' —«. —•
•
^•—
'75 •cP
m
—
CD
— — ——  —
50 M _ __
50 0
1.0
1.5
2.0 2.5 3.0 3.5 Column diameter d s Im]
4.0
4.5
5.0
Fig. 11.22. Optimum area as a function of the diameter of columns packed with metal Pall rings
270
11
300 ^ "
1 1
1 1
250
a. o
Overall evaluation of packing
200
a
Stainless ste el GlitschC MR
V
£ 150 a "a
I
1— r—
— —. — * —
• 2.5
'——.
p ~~
•
50
0.5
1
1.5
2
2.5
3.5
3
Column diameter ds [ m ] Fig. 11.23.
Optimum area as a function of the diameter of columns packed with metal Glitsch CMR
400
1 1 • Stainless steel
\ \
350 \
\
 Montz packings B1
\
I
\
°° 300
•cP
O QJ
r
I
250  ^
5 °
z
c
•
—
0.5
1.0
1.5
2.0
—
. —
•
—
—
.
•

*
2.5
——
—
—. * 
—
—
—

^"7—
P
200
—
3.0
3.5
4.0
•
>—

4.5
r 5.0
Column diameter ds [ m ] Fig. 11.24.
Optimum area as a function of the diameter of columns packed with metal Montz Bl
11.8 Limits to the further development of packing It is evident from the above analysis that the design measures that can lead to a noticeable improvement in efficiency per unit area are restricted in number, regardless of whether they are applied individually or combined for modifying existing packing or for developing new types. In many cases, the improvements that can be achieved are no better than moderate. As is evident from Fig. 11.25, the enlargement of the area per unit volume always leads to a reduction in the specific column volume vv and thus to an increase in the volumetric efficiency Ev, which is defined by
E J2t,y —
—
vv
a
(1166)
11.8
_ 28
1
1 \
Ethylbenzene/Styrene 133 mbar
\
1
\
Chlorobenzene/Ethylbenzene 67 mbar \
L/V1 Specific pressure drop 3 mbar \
\
u
\
16
\
\
\
"V
60
•—.
ckino •—«.
20
I rQdit'mr)nl •—«. •——
_
P" — —
100 140
— 
1
180
220
=====
260
300 340 z
380
420
460 500
3
Area per unit volume a [m /m ] Fig. 11.25. Specific column volume and volumetric efficiency as functions of the area for beds of traditional and modern packing
The curves in Fig. 11.25 were derived from those shown in Figs. 11.8 and 11.10 and from the following relationship:
Vy
=
(1167)
They reveal the limits that are imposed on the development of column packing. The limit to which the volumetric efficiency Ev tends corresponds to an area per unit volume a — 350 m 2 /m 3 , and cannot be significantly improved at higher values of a. The process engineering criteria adopted for the technical evaluation of column packing include the liquid holdup hL per unit column volume, the vapour flow rate at the loading uVjS and flood uv>Fi points, the pressure drop per unit height of bed Ap/H, and the volumetric mass transfer coeffients in the liquid 3Lap^ and vapour ^yaPh phases. These parameters also govern the packing performance from the economics aspect, because they decide the specific column volume vv. The relationships for their determination are dealt with in Chapter 4 and 5. The other parameters in these relationships concern the system to be separated, the operating conditions, and the design. The system parameters are the phase densities QL and QV and dynamic viscosities r\L and r\v; the operating parameters are the volumetric flow rates uL and uv and the liquid/vapour ratio L/V; and the design parameters are the packing's area per unit volume a, the relative void fraction 8, and the empirical factors that define the packing's shape and surface, i.e. the factors in the relationships for the liquid holdup Ch, the flow rate at the load Cs and flood Cpi points, the pressure drop Cp, and the volumetric mass transfer coefficients on the liquid CL and gas Cv sides.
7 8 9 10 12.5 15 20 25
QJ O
eff
•
(_>
'olu metr
20
271
Limits to the further development of packing
272
11
Overall evaluation of packing
The relationship for the liquid holdup (hLS)P follows from Eqns (473) and (474), i. e. h L t S = Ch a 0 5 1 6
(1168)
The relationship for the vapour flow rate at the load point uVyS for a given system is obtained from Eqns (426) and (429), i.e.
fs = Cs (e  hLiS) A/ ^f
~ uv,s
(H69)
The corresponding relationship for the vapour flow rate at the flood point can be derived from Eqns (435) and (441), i. e.
=
/F/
Another factor that affects hydrodynamic evaluation is the pressure drop per unit height of bed (Ap/H)s at the loading point. In the model, it is described by Eqn (458), with 5L = ^s/w> and Eqn (426) with uv = uvs The relationship for the theoretical design factors that influence the pressure drop at the loading point in the model can be obtained from these two equations, i.e.
JAp,S '•
It can be concluded from Eqns (54), (513) and (516) that the design parameters that affect mass transfer on the liquid side are the area per unit volume a and an empirical constant CL, which is characteristic for the packing geometry and texture and is given by fL = CLa1/6~?>LaPh
(1172)
Likewise, mass transfer on the gas side depends on the area per unit volume a, a factor Cv that is characteristic for the packing geometry and texture, and the void fraction available for the flow of vapour (e  hL), i.e. (H73) Pall rings have been used successfully in industry for more than 35 years and are a convenient reference for comparing the hydrodynamic parameters selected for evaluation. Thus differences in the liquid holdup hL can be expressed by the ratio of the value for the packing concerned to that for 50mm Pall rings, i.e. ru hL s
'
=
h£ hL,s (Pall50)
=
fhis
!h±± (Pall50)
(U 1
K
11.8
Limits to the further development of packing
273
Differences in the flow rates at the loading and flood points can be expressed by the corresponding ratios, i.e.
Uv Fl
'
Uy,S
fs
uvs (Pall50)
/ 5 (Pall50)
uv>Fl (Pall50)
(1175) (1176)
fViFt (Pall50)
The ratio for the pressure drop at the loading point is
hP,s p
'>
(Ap/H)s
(Pall50)
(1177)
fAp>s (Pall50)
The corresponding ratios for mass transfer on the liquid rL and gas rv sides are given by the following equations:
h $LaPh (Pall50)
(1178)
fL (Pall50)
ftyflp/, fy
(1179)
rv = § a (Pall50) " f (Pall50) v Ph v
Three types of packing have been chosen to demonstrate the application of Eqns (1172) to (1179) in the light of the results of experimental studies (Table 11.7). Two of them are
Table 11.7. Characteristic data for some types of metal packing Glitsch rings
PModifications 30 P
No. 0.5
30 PmK
CMR 304
Shape in metallic version
d[m]
0.030
0.030
h[m]
0.030
0.030
0.510
s [m] 3
N [1/m ] 2
3
a [m /m ] 3
w [kg/m ]
0.28lO"
0.005 3
0.2 10 3
32509
28445
560811
169
180
357
0.958
8
3
0.015
319
0.975 200
0.955 348
11
274
Overall evaluation of packing
similar, viz. the 30 P metal and the 30 PmK Glitsch rings. They differ from one another in wall thickness s and in the fact that the ends of the former are smooth and those of the latter form a collar; in other words, the parameters that differ are a and 8. The third packing to be discussed is the CMR Glitsch ring No. 0.5, whose shape and size differ completely from those of the other two. The values measured for the liquid holdup are shown as a function of the liquid and vapour loads in Figs. 11.26 to 11.28. After the loading point has been exceeded, the liquid holdup rises rapidly until, in the bed of CMR Glitsch No. 0.5 rings, it attains a value as high as 30 % of the void fraction at the flood point. The corresponding pressure drop measurements have been plotted in Figs. 11.29 to 11.31. The pronounced rise in pressure drop with an increase in the liquid load, and thus in the holdup, is clearly evident.
PT 10
^
8 . Air /hl 2 O.1bar,293K  Glitsc h 30P metal 6 lm.N=32509m3  H=1.3fDm. Z=1013 m2
r
cr
cr
£
Fv =1nH'
1
1.5 2
3
4
1 kgi/2
6 3
1—
8 10 3
15
2
Liquid load 10 U_[m /m s ]
0.3 0.4
0.6 08 1.0
Gas capacity factor F v [nr
1.5 2.0 1/2
1
3.0 1/2
s" kg ]
Fig. 11.26. Liquid holdup as a function of load in a random bed of metal Glitsch 30 P packing as listed in Table 11.7
11.8
275
Limits to the further development of packing
Figure 11.32 shows the results of the separation efficiency experiments and the corresponding pressure drop measurements. The Glitsch 30 P and 30 PmK rings have practically the same efficiency, but the associated pressure drops differ considerably over the packed bed. Both the efficiency and the pressure drop of the Glitsch ring No. 0.5 CMR 304 are decidedly higher than the corresponding figures for the other two packings. The relationship between the specific column volume Vy and the pressure drop per theoretical stage lS.plnt is given by
Vy
=
Qv
(1180)
Fv (nt/H)
Figure 11.33 shows that, at any given value of Ap/nt, the value of vv required to achieve the one theoretical stage and unit vapour capacity is significantly less for the Glitsch ring No. 0.5 CMR 304 than for the other two packings. Figure 11.34 demonstrates that the Glitsch ring No.5 CMR 304 is also superior to the other two in respect of the volume of packing required to achieve unit efficiency and unit volumetric vapour load v' {cf. Eqn (1151)} at a given pressure drop per theoretical stage. The diagram includes the corresponding curves for the specific mass of the packing vv', which is related to v' through the weight per unit volume w of packing, i.e.
i—
hz = 1 m1/2
i
s 1
I
jj
B
S1
kg n
i
Air/H20,1bar. 293 K . Glitsch 30 PmK ds=0.3.N=284< H=l.32m.Z=10 13m2
•s ZD
CJ
1.5 2 3 4 6 8 10 Liquid load 103uLlm3/m2 s]
I
15
1 10
4u o •V. o  o oc o  ol —
•UL=
o
53 Fig. 11.27. Liquid holdup as a function of load in a random bed of metal Glitsch 30 PmK packing as listed in Table 11.7
0.4
r
i
r \ J
30
CKXX
20rriVm2h
I i
—ok>—•opcoo 10
0.6 0.8 1.0
1.5 2.0
3.0
Gas capacity factor F v l n r 1 / 2 s1 kg 1/z ]
15
11
276
Overall evaluation of packing
(1181)
w = v w
Numerical values for the area per unit volume a, the thickness of an element of packing s, and the weight of unit volume of packing w are presented in Table 11.7, and Eqns (1151) and (1152) were evaluated with values of vv taken from Fig. 11.33. Yet another feature that underlines the superiority of the Glitsch ring No. 0.5 CMR 304 in this comparison is the average liquid residence time per theoretical stage tLlnt {cf. Eqn (115)}, which is an important factor in the separation of thermally unstable mixtures. The relevant functions are presented in Fig. 11.35. Factors on which the residence time depends are the liquid holdup hL, the separation efficiency nt/H, and the liquid flow rate uL, which in this case is given by QV
(1182)
_ 20 n
f
,5
>n
1kCVI
Fv=1m'
jy
=2 10
 A ir/H 2 0.1 bar.293K bl tsch No.0,5C ^IR3U4 dc;=0.3m,N=560 811m3 H=1.11m, Z=101: 1m 2
§•
5 6 15
2
3
4
6 3
8 10 3
15
2
Liquid load 10 Ui [m /m s] 40 n
30
V0
20 ZD CD
4
 °n
15 o10 8 6
u
>—
I
JH1
>ooc
! ZOmVmZh 0
n
\J 5
o
yet*
0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 Gas capacity factor F v [rrr 1/2 s"1 kg 1/2 ]
Fig. 11.28. Liquid holdup as a function of load in a random bed of metal Glitsch No. 0.5 CMR 304 packing as listed in Table 11.7
11.8
277
Limits to the further development of packing
Characteristic geometrical data and (separately determined) model parameters for the three Glitsch packings discussed above are listed in Table 11.8 together with the corresponding values for 50mm Pall rings. Table 11.9 lists the results obtained in evaluating Eqns (1173) to (1179). Again, 50mm Pall rings were taken as reference. The above relationships for the performance of column packing give an idea of the limits within which packing elements of given basic geometry may be developed. According to Eqn (24), the relative void fraction increases with a decrease in the thickness s of the packing element. Substituting this relationship for in Eqn (1169) gives rise to the following for the design parameters that influence the loading point: (1183)
Air./H 2 0.1bar. 293K Glitsch 30 P metal ds=0.3m, N=32509m3 H=1.36m, Z=1013m2 Fig. 11.29. Pressure drop as a function of load in a random bed of metal Glitsch 30 P packing as listed in Table 11.7
0.4
0.6 OS 1.0
Gas capacity factor
1.5 2.0 F v [nr
1/2
3.0 4.0 j
s~ kg V2 ]
278
11
Overall evaluation of packing
200
i
150 o 100 h o 0 © 60 • 50
„
i?
] 0 10 20 30 40
A
& I'Kr
ffffi A /
3
i
I°
MA
Sk
1 . 20
m
I \ \ \\ \ \ \ 0
>
\
tyfi \ ^
^ s
• * • —
*  — ^ —  ,
•—»
CD CO
0.5 1 1.5 2 2.5 Spec, pressure drop Ap/n t [mbar]
—
—
Fig. 11.34. Volume of material and mass of packing, both expressed in terms of the efficiency and the volumetric vapour flow rate, as functions of the specific pressure drop for the various metal packings listed in Table 11.7
11.8
283
Limits to the further development of packing
Tables 11.10 and 11.11 list process engineering parameters required for the global evaluation of random and stacked beds. The reference value selected for the comparison is the pressure drop per theoretical stage Ap/nt, which is responsible for differences in the load factor Fv and the column diameter ds. The yardsticks adopted for the material requirements are the specific column volume vv and the weight w' and area a' of packing per unit of separation efficiency and throughput. Significant factors in evaluating packing for systems that are sensitive to heat are the liquid holdup h'L per unit of efficiency and throughput and, as a consequence, the liquid residence time per theoretical stage tLlnt. Another factor to which consideration must be given in the design of random and stacked beds of packing is the mechanical strength or the physical constants of the material. The idealized stressstrain diagrams shown in Fig. 11.39 for 50mm Pall rings illustrate this point. The assumptions made in plotting the graphs were that the load is always applied in the radial direction and that the open joint lies in the centre of the ring. The applied pressure in terms of bed height was calculated from theoretical considerations. As would be expected, the thickness of the ring exerts a considerable effect on the load under which plastic deformation occurs. In further experiments, it was ascertained that the deformation in rings with spotwelded joints was only onequarter of that in unwelded rings. It is obvious from the above remarks that fluid dynamic and efficiency studies are absolutely essential in the design of column packing and that they necessitate wellequipped pilot plants. Some of the author's pilot plants are illustrated in Chapter 3 and in Fig. 11.40
20 ,
15
h
61Itr,
10
b
S
'tsch
6
%
13
^
1.5
~ A D O
1 0.1
2.3 2.1 1.9 0.2
'
30,
?Op ^
05 n
rtr
LMfx
Loading capac ty 2
;
[ m i/2
0.4
si
Chlorobenzene/Ethylbenzene 67 IT bar, L/V = 1
" ^
ka V 2 l
0.6 0.8 1
1.5 2
3
4
5 6
Specific pressure drop Ap/n t [mbar] Fig. 11.35. Relationship between the specific liquid residence time and the specific pressure drop in rectification columns with the metal packings listed in Table 11.7
284
11
Overall evaluation of packing
Table 11.10. Parameters for comparing random beds of highperformance metal packing Dumped packing
Ap/n t [mbar]
Glitsch No. 1 CMR w = 390 kg/m 3 a = 249 m 2 /m 3 E = 0.969 N = 169930 nr 3
Fv [ m  ¥ k g 1 / 2 l v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] h[ [m3s/m3] t L /n t [s]
1.56 0.127 49.53 31.623 2.03 • 10"3 7.18
2.28 0.076 29.64 18.924 1.5510"3 5.49
2.88 0.041 15.99 10.209 0.96610' 3.42
Glitsch No. 1.5 CMR w = 306 kg/m 3 a = 186 m 2 /m 3 e = 0.972 N = 64495 m3
Fv [m¥kg1/2] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]
1.8 0.1327 41.92 25.48 1.7510"3 6.2
2.48 0.083 25.40 15.44 1.6610"3 5.87
2.96 0.055 16.83 10.23 1.110"3 3.89
Glitsch No. 1.5 T CMR w = 215 kg/m 3 a == 173 m 2 /m 3 8 = 0.970 N = 62432 nr 3
Fv [m^'VV' 2 ]
v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] h' [m3s/m3] t L /n t [s]
1.8 0.137 29.46 23.70 1.86103 6.58
2.5 0.082 17.63 14.18 1.510"3 4.985
3.1 0.056 12.04 9.69 1.1410"3 4.05
Pall rings 25 mm w = 390 kg/m 3 a = 215 m 2 /m 3 e = 0.942 N = 53200 nr 3
F v [m^'Vkg 1 ' 2 ] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] h[ [m3s/m3] t L /n t [s]
1.34 0.154 60.06 33.11 1.84510"3 6.542
1.92 0.108 42.12 23.22 1.59510"3 5.656
2.4 0.072 28.08 15.48 1.23610' 4.384
Pall rings 50 mm w  210 kg/m 3 a = 113 m 2 /m 3 8 = 0.942 N = 6358 irr 3
F v [m^'V'kg 1 ' 2 ] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]
1.6 0.248 52.08 28.02 2.773 • 10"3 9.832
2.26 0.171 35.91 19.32 2.334 • 103 8.277
2.74 0.127 26.67 14.35 1.92710" 6.832
Hiflow rings 50 mm w  173 kg/m 3 a = 92 m 2 /m 3 e = 0.977 N = 4739 nr 3
F v [m^V'kg 1 ' 2 ] v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]
2.04 0.192 33.22 17.86 2.147 • 10~3 7.612
2.68 0.134 23.18 12.46 1.79710"3 6.372
3.02 0.101 17.47 9.39 1.41910" 5.032
11.8
Limits to the further development
of packing
285
Table 11. 11. Parameters for comparing types of highperformance structured metal packing Packing
Ap/n t [mbar]
0.5
1
2
3
Gempak 2AT  304 w = 165 kg/m 3 a = 200 m 2 /m 3 8 = 0.979 dr = 0.63 mm
F v [m s kg v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]
1.76 0.133 22.02 26.69 1.510 5.31
2.46 0.087 14.44 17.5 1.285 10 4.55
3.24 0.055 9.075 11.0 0.966 • 10 3 3.425
3.6 0.048 7.92 9.6 0.919 io 3 3.259
Mellapak 250 Y w = 200 kg/m 3 a = 250 m 2 /m 3 8 = 0.96 d, = 0.96 mm
Fv [rn^Vkg v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]
2 0.086 17.2 21.5 1.098 l O 3 3.894
2.56 0.067 13.4 16.75 0.962 10" 3.414
3.025 0.053 10.6 13.25 0.889 • 10"4 3.152
3.3 0.078 15.6 19.5 0.432 • IO 5.078
Ralupak 250 YC w = 290 kg/m 3 a = 250 m 2 /m 3 8  0.965 dx = 0.84 mm
Fv [nr^Vkg v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]
2.2 0.073 21.17 18.25 2.098 • l O 3 7.439
2.7 0.056 16.24 14.0 2.012 107.135
3.1 0.048 13.92 12.0 1.839103 6.522
3.22 0.064 18.56 16.0 2.5559.059
Montz packing BI  300 w = 242.1 kg/m 3 a = 300 m 2 /m 3 8 = 0.93 d, = 1.4 mm
Fv [ m ^ V k g v v [m3s/m3] w' [kg s/m3] a' [m2s/m3] hi [m3s/m3] t L /n t [s]
1.8 0.077 18.64 23.1 0.923 • l O 3 3.271
2.35 0.06 14.53 18 0.862 10~3 3.057
3 0.051 12.35 15.3 0.8143 • 103 2.888
3.25 0.048 11.62 14.4 0.8814 103.125
286
11
Overall evaluation of packing
2.0 INTALOX sa jdle 1.8 Bialecki ring
1.6 
1.2 i
>/ / /
/
—
/
/
/
/ 1:
0.8
u>
7^
0.6
/ /.
0.4
/ •y, >
0
V jr
/
V
/
/
ririg 
,* Bialeck i
N0RPAC ring
ri
, L Plast ic
/
0.2
yep
^ Pall ring
/
/
/.' I y.
Packing size 50 mm
/
1 / . / .'
f
/, f
1
1.0
/. /
Pall ring ^
/
/
/
y
/
V*
/^/ .
ng.
Hiflow r
/
•*
/
o cz o
/
.•
/
> /  /_
/x
1.4
V
/
1
2
4
i
6
/I
8 10 0 2 Liquid/Gas ratio L / V
Metal 6
8
10
Fig. 11.36. Resistance coefficient at the loading point as a function of the liquidgas ratio in packed columns, system air /water at STP
11.8
Limits to the further development of packing
287
2.8 i
\
Metal
 Plastic 
\ \
2.6 \
^
2.4
1= 5 2.2
6 2.0 3 3
1.8
i\
NORPA C ring
iT
/VSP r
\
I ji~T
\
V
.Pali ring
\ \ \
V
\ \*
CO
a
CO
min > nt>minyiso, and rmin > rmin>iso. As is evident from Figs. 1.7 and 1.8, the number of theoretical stages in real rectification, when Aplnt > 0, is also greater, i.e. nt > nt>iso; and, according to Eqn (152), the reflux ratio as well, i. e. r > riso. The procedure outlined below permits calculation of the savings in energy and the reduction in the number of theoretical stages that can be achieved by retrofitting and makes due allowance for the specific pressure drop Aplnt. The steps (a)(p) can be deduced from Figs. 1.7, 1.8 and 12.1 and the thermodynamic fundamentals and relationships that describe rectification processes. (a) The nature of the task implies that the mole fractions of the more volatile component in the feed xF, overhead product (distillate) xD, and bottom product xB are given. The pressure pT at the top of the column is also given and can theoretically be optimized to allow minimum separation costs. Known parameters are the molar enthalpy of the feed hF and h'F at the inlet and boiling temperatures, respectively, and the molar condensation enthalpy Ahv of the vapour stream in the inlet crosssection. Hence the factor / that describes the thermal state of the feed can be calculated from Eqn (112). (b) The relative volatility aIjiso of a molar mixture with a concentration x*tso, yfjso at the intersect / of the equilibrium curve and the gline can be determined by iteration from phase equilibrium equations. Thus, the following applies for an ideal binary mixture:
Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
292
12 Retrofitting columns by the installation of packing
1
X F /f Xp Liquid mole fraction x
Fig. 12.1. Qualitative diagram representing the minimum number of theoretical stages and the enrichment curve required to obtain the minimum reflux ratio in isobaric and real rectification
xn1
where Au A2, Bj, B2, C7, and C2 are the Antoine constants for a given boiling point T and the corresponding pressures of the more volatile Pj and less volatile P2 components 1 and 2. The phase equilibrium concentration of the more volatile fraction x*iso can then be obtained from the following equation, which is valid for a = aI>iso, y = y*iso, x = x*iso and a pressure /?/ = pT:
f xUso (a[Jso

'
•

/
_
XF
(122)
!
(c) Once aItiso and x*iso have been obtained, the phase equilibrium concentration of the less volatile component y*iso can be calculated from the following equation:
xUso
(aUso

(123)
12.1 Advantages of retrofitting
293
There is no need for iteration if the feed is admitted into the column at the boiling point, i.e. if hF = hF and / = 1, in which case x*iso = xF. Under these circumstances, a*wo = a* corresponding to pt = pT and T(xF) can be determined direct from Eqn (121); and thus yfJso = yFJso, from Eqn (123). (d) It is evident from Fig. 12.1 that the minimum reflux ratio in isobaric rectification is given by (124) (e) Thus the reflux ratio r in real rectification can be obtained from Eqn (149) by assuming a value for the factor vg\ and the energy parameter e can therefore be calculated from Eqn (147). In Fig. 1.8, the value of s, the stagenumber parameter, can then be read off on the axis of ordinates against this value of e and the corresponding pressure drop per theoretical stage Ap/nt. This step is demonstrated in the qualitative diagram shown in Fig. 1.7. A knowledge of the parameter s is essential for determining the number of theoretical stages in real rectification from Eqn (145). (f) The term nt>min>iso in Eqn (145) applies to the minimum number of theoretical stages in isobaric rectification. It can be defined by the Fenske. equation if the mean relative volatility amJso in the range of concentrations under consideration can be accepted, without reservation, as being sufficiently accurate for practical purposes. Thus In nt,min,iso =
lxB
xD  xD
xB
J
J In a.m,iso
 1
(12"5)
The minimum number of theoretical stages required in the enriching zone of the column, in which the mean relative volatility is am}enr!iso, is given by In ^t,min,enr,iso
XD
lXF
xD
xF
 1
(126)
(g) Eqn (145) can be rearranged to give the total number of theoretical stages nt in real rectification, i. e. (127) The number of these stages that is accounted for by the enriching zone is given by ^ t, min, enr, iso
n,,enr =
\
s
' $
, ._
.
(128)
(h) The pressure pF in the crosssection of the feed inlet can now be obtained from nlenr, i. e. (129)
294
12 Retrofitting columns by the installation of packing
(i) The relative volatility a7 applies to the intersect of the curves that are valid for the feed inlet crosssection. As described in step (b), it can be determined by means of Eqn (121), but applies in this case to real rectification. Therefore, x7*can be obtained from the following relationship:
im
r
i+*;(«,!)*'
/i
(1210)
/I
(j) Now that Jt*and a7 are known, the phase equilibrium concentration yf can be determined from
Again, iteration is unnecessary if the mixture is at the boiling point when it flows into the column, because x*= xF and a 7 = aF at /?7 = pF and T(xF). (k) The minimum reflux ratio rmin for the real column can then be obtained from y*
The following relationship ought to exist between rmin and the minimum reflux ratio in an isobaric column rminjiso Xl iso
 (r • i \ y*'™ r 'mm ~ \rmin,iso ^ l) *
' *
i ^
Xl iso
>
*
±L i * — 1
n? ITl V 1 ^" 1 " 3 /
(1) The reflux ratio in isobaric rectification can be obtained by rearranging Eqn (152). Thus Fmin, iso
/ 1 /» 1 A \
riso =
r = vrmin>iso
(1214)
The factor v in Eqns (148) and (150) can then also be determined. (m) Since rmin>iso and v are now known, the energy parameter for isobaric rectification eiso, as represented on the axis of abscissae in Fig. 1.7, can be calculated from Eqn (146). (n) The value for siso corresponding to eiso on the isobaric (Apfnt = 0) curve in Fig. 1.8 can be read off on the axis of ordinates. Rearranging Eqn (144) and inserting this value for siso then gives the number of theoretical stages in the isobaric column, i.e. nUlso =
H
t
~ 1
+ Siso
(1215)
$iso
(o) The values obtained for nt and nt>iso in steps (g) and (n) can be taken to calculate the theoretical column efficiency r\c from Eqn (142). Alternatively, r\c can be calculated from Eqns (153), (154) or (155), because the terms in these equations are now also
12.1
Advantages of retrofitting
295
known. Yet another means by which r\c can be obtained is to determine the increase in the number of theoretical stages Ant that is caused by the specific pressure drop Ap/nt, i.e.
Ant = nt nt>iso =
_*~i"° ^1
T Km,*™ + 1)
S) {L
(1216)
Siso)
In this case, the theoretical column efficiency, i. e. the number of theoretical stages in a theoretical isobaric column, expressed as a ratio of that in a column with pressure drop, is given by
=
n,Mo + An,
An, 1 +
(p) The amount Ar by which the reflux ratio in a real column exceeds that in an isobaric column is defined by Ar = r riso =
* ~ 6iso
(rminMo
+ 1)
(1218)
yi  e) {i  eiso)
It allows an expression to be obtained for the efficiency in terms of energy r\e, i. e. the energy consumption in a theoretical isobaric column to be expressed as a ratio of that in a real column. Thus
u
=
riso + 1 riso + Ar + 1
= l +
1_ Ar riso + 1
v
;
Relationships for the relative increase in the energy consumption QIQiso and in the number of theoretical stages Ant/nt)iso can be obtained by following the steps (a)(p) in the procedure outlined above. With the aid of Fig. 1.8, they can be expressed as functions of the pressure drop per theoretical stage Aplnt, i.e.
4^ Qts
An, nt,iso
—  1 = f (Ap/n,) 1
 1 = f(Ap/nt)
(1220) (1221)
T\C
Both relationships are presented graphically in the numerical example given in Fig. 12.2. The diagram convincingly demonstrates the advantages that can be derived from installing packing instead of plates. The upper curve was plotted from the sole aspect of achieving the utmost savings in energy, i.e. for a constant number of theoretical stages (nt = const.), and the parameters that were taken into consideration were nt>min>iso, riso and s. The two lower curves represent the case in which the intention was both to save energy and to reduce the
12
296
Retrofitting columns by the installation of packing
number of theoretical stages, i. e. the minimum reflux ratio factor was constant (v = const.) and the parameters were rminJso, ntMnMo and ntJso. The headings on the diagram indicate the ranges of pressure drops that apply to arranged packing, random packing, and plates.
12.2 Potential for retrofitting with lowpressuredrop packing It is clearly evident from Fig. 12.2 that the energy consumption and the number of theoretical stages in intensiverectification columns can be substantially reduced by substituting lowpressuredrop packing for fractionating plates. Theoretically, it is also feasible to retrofit the column so that the number of theoretical stages remains unchanged. In this case, the severity or the fineness of the cut can be increased, and purer products can be obtained.
Regular or corrugatedsheet packing 0.30
Dumped pack ag
Trays
11M Tt1
0.20
^
r t min.is o=27.4 n t = 58 r,s044 s  0.5,?
e:D 0.15 CO
0.10 0.08
si
/
! )\
0.03
3—
ft
/
/+ 3
4
/
y
/
s W
y /
=
^
0.20 0.15
0.06
"
0.04
nt,iso=52
0.03
.
6
0.30
nt m i n . i s o " L11 'QJ v = 1.3
k
/
0.10 0.08
i
/ min.iso
y
0.015
y
y
yA
0.02
A
y
/
/
/
y y
/
y
/
/
A
y /
y
j
/
/
0.06 0.04
y/
—
y
/ 3—/ y
y
/
CD
0.02 0.015 8 10
15 20
40
60 80
Specific pressure drop A p / n t [mm WG ] Fig. 12.2. Increase in energy consumption and in the number of theoretical stages as a function of the specific pressure drop in vacuum rectification involving a large number of theoretical stages. Evaluated with the aid of Fig. 1.8.
72.2
Potential for retrofitting with lowpressuredrop packing
297
The condition for equilibrium at the point y = yt\ x = xj is —
(1222)
Consequently, the minimum reflux ratio rmin is given by (cf. Fig. 12.1) a, ^"min
(1223)
1x?
a7
The rate of heat emission Q is described by Q =
h'Bh'F
xD  xB
(1224)
where v is the factor for the minimum reflux ratio {cf. Eqn (150)} and rmin depends on the pressure pF in the feed crosssection and thus, according to Eqn (129), on the pressure drop per theoretical stage Ap/nt. Another means of determining the effect of Ap/nt on Q arises from the following equation, which can be obtained by rearranging Eqn (147): • • \' pc 'r min,iso
(1225)
1 e
Consequently, the following relationship can also be derived from Eqn (157); and it can be evaluated with the aid of Fig. 1.8:
CD
a
ID C=
Hnin.iso t V g " " i )
Fig. 12.3. Application of Fig. 1.8 for retrofitting estimates
Energy parameter
298
12 Retrofitting columns by the installation of packing XF 
XB
*
1e
Ahv
+ h'D  h'B\ + h'B  h'F
(1226)
The significance of the pressure drop per theoretical stage Ap/nt in retrofitting and designing separation columns is further demonstrated in Figs. 12.3 and 12.4. These diagrams represent a method of comparing column internals with different pressure drops per theoretical stage, i.e. (Ap/nt)j and (p/nt)2. The two types of column compared are denoted by the subscripts 1 and 2, and the method permits a comparison in the following five cases: (A) The minimum reflux ratio factor v, as defined by Eqn (150), remains constant. (B) The reflux ratio r {Eqn (1225)} and thus the energy parameter e remain constant. (C) The number of theoretical stages nt {Eqn (127)} and thus the stagenumber parameter s remain constant. (D) The product vapour load V remains constant. (E) The column is operated at a constant pressure drop per theoretical stage Ap/nt. In Cases (A) and (B), the difference in the number of theoretical stages is given by An't = nh  nh =
^ " ^
(nt,min,iso
+ 1)
(1227)
In Cases (A) and (C), the difference in reflux ratio is given by Ar' = r2  n =
e 2 (1_ e 2~^_ei)
(rminjso + 1)
(1228)
Eqns (1227) and (1228) can be solved numerically with the aid of Fig. 1.8. The percentage reduction in the number of theoretical stages that can be achieved by installing the internals denoted by the subscript 1 instead of those denoted by the subscript 2 can be determined from the following equation: 100 = ^ nh
100
(1229)
nt.
The corresponding savings in energy can be calculated from the following equation: Ql
~QQl
100 = y ^ y y
100
(1230)
In Case (A), the reduction achieved in the number of theoretical stages is less than that in Case (B), and the savmgs in energy are less than those in Case (C). On the other hand, no energy is saved in Case (B), and no reduction in the number of theoretical stages is effected in Case (C). In Case (D), the opportunity of retrofitting with stacked packing with a low pressure drop can be exploited to increase the capacity F. If the vapour flow rate V is the same in both cases, i. e. V = const., the distillate flow rate D in a real column can be compared to that in a theoretical isobaric column Diso by means of the following equation: V = Diso (riso + 1) = D (riso + 1 + Ar)
(1231)
72.2
Potential for retrofitting with lowpressuredrop packing
299
The inlet capacity in the isobaric case is given by Eqn (1232); and that in the real case, by Eqn (1233): F 1
XD
=D
ISO
J^lSt
F= D
XF
xD
xB xB
(1232)
xB
(1233)
xFxB The efficiency in terms of capacity is therefore given by F 1
1
ISO
(1234)
1 +
where Ar is as defined by Eqn (1218). In other words, the efficiency is the same in terms of capacity r\F as it is in terms of energy r\e, as defined by Eqn (1219). The lower the value of Ap/nt, the greater that of v]F. As a consequence of the pressure drop in a theoretical stage Ap/nt, the capacity in real rectification is less than that in theoretical isobaric i.e. AF
F
 F
r
r
iso
F iso
= 1 x\F =
i(Ap/nt)
(1235)
F
x
ISO
Hence, the following equation applies if column internals with a specific pressure drop (Ap/nt)2 are replaced by internals with a lower value (Ap/«,)/ and the vapour flow rate is assumed to be the same, i.e. Vj = V2 = const, (cf. Fig. 12.4): = D2 (r2
Product vapour rate V
< O
Fig. 12.4. Qualitative comparison of column internals with various specific pressure drops Case D: if the vapour load is kept constant Case E: if the specific pressure drop is kept constant
CD d. CO
Capacity factor Fv
(1236)
300
12
Retrofitting columns by the installation of packing
The inlet capacity F2 in Case 2 and that Fj in Case 1 are given by
F2
D
F,  D
~ xB
XD
xF
• X
XD
xF
~
B
xB • X
(1237)
B
The percentage increase in capacity is therefore FjF2 i
F2
100
(1238)
r2 + 1
in which Ar' is as defined by E q n (1228). In Case ( E ) , an increase in capacity F can also be achieved by retrofitting, because the loads permitted by modern packing of appropriate dimensions are higher than those obtained by plates of equivalent Ap/nt. It is evident from the qualitative diagram shown in Fig. 12.4 that the increase in capacity in this case is given by Fi ~ F2
— P  — 100 r2
FVi  Fy2
—
tv2
100
(1239)
where FVl and Fy2 are the vapour capacity factors at which the value Ap/nt = constant in packings 1 and 2. The benefits offered by highperformance packing with small values of Ap/nt are reviewed in Table 12.1. They apply to both the planning of new and the retrofitting of existing columns. It is evident from the table that advantages can be obtained in the number of theoretical stages nt and thus the column height i7, the reflux ratio r and thus the column diameter ds, the energy consumption Q, and the capacity F. If the calculations reveal that the height of the column to be retrofitted Hj is less than the original height H2, i.e. Hi < H2l full exploitation of the available height H2 will give rise to more cleancut separation, i.e. to improved product quality. An impression of the advantages that modern packing has over conventional sieve plates can be obtained from Table 12.2. The example taken was the vacuum rectification of a mixture with a thermally unstable bottoms product. The principle of the heat pump was applied by compressing the overhead vapour to heat the bottoms. There is no mistaking the considerable improvement that was achieved in the economics of the process by the installation of packing.
72.2
301
Potential for retrofitting with lowpressuredrop packing
Table 12.1. Characteristics for planning new columns and retrofitting existing columns with lowpressuredrop packing (Ap/nt)i < (Ap/n t ) 2 = const.
V =
e = const.
s = const.
V = const.
Ap/n t = const.
n tl < n t2
n t i < nt2 n t] > ntl (v)
n tl = n t2 n t i < n tl (v)
= n t2 n tl An(v)
An; = 0
An; = 0
An; = 0
Ar'(v)
Ar' :> Ar'(v)
Ar' = 0
d S i = ds2 dSi < dSi (v)
d S i < d s2 dSi > dSi (v)
ds, : d s 2
dSi = ds2 dSi < d sl (v)
Q, < Q 2 Qi > Qi W
ri
Ar
IT
PP\/ »
r
^ 
Hi < H, (Vj ri < r2 ri > ri (v)
dd
TT
= r2 < C r i (v)
<S(v)
r
dsi
r, < r, (v)
> d S i (v)
Q, > Q 2 Qi < Qi(v)
>S(v)
F, = F 2
F, : = F 2
Fi = F2
Fi
A
B
c
D
>
Fi > F 2
F2
E
Table 12.2. Economics of applying the principle of the heat pump. Valid for the separation of a mixture consisting of equal parts by weight of ethylbenzene and styrene fed at a rate of 30 tons/hour into the following columns: (a) fitted with perforated plates (b) packed with Mellapak 250 Y. Based on the following prices: electricity 0.06 SFr/kWh, steam 12 SFr/ton, cooling water 0.6 SFr/kWh (SFr = Swiss Francs). With the courtesy of Sulzer AG, Winterthur Operating data
Sieve tray
Mellapak
Pressure at head of column [mbar]
67
67
Temperature at head of column [°C]
58
58
Number of theoretical stages
54
54
Reflux ratio
8.25
6.5
Pressure at foot of column [mbar]
310
127
Temperature at foot of column [°C]
106
81
15
15
Reboiler temp, difference [°C] Compression ratio Compressor costs Energy savings [%]
9.9
4.5
100
60
30
60
302
12
Retrofitting columns by the installation of packing
12.3 Advantages of packing in steam rectification Even if a vacuum is applied, it is not always possible to separate unstable mixtures at temperatures that are low enough to avoid thermal decomposition. This applies particularly to mixtures of fatty acids, and an example is the separation of palmitic and stearic acids in industrialscale rectification columns equipped with 2040 plates. If the pressure at the head of the column is 7 mbar, pressure drops of 4385 mbar occur under normal operating conditions and are responsible for boiling points of between 267 °C and 279 °C. In separation tasks of this nature, it is absolutely essential to restrict the residence time of the products and the pressure drop to the minimum possible values. Even if this demand is met and even if the vacuum applied is justifiable from the engineering and economic aspects, substances that are unstable to heat cannot always be separated under conditions that preclude thermal decomposition. Thermally unstable substances that are encountered in thermal separation practice include higher fatty acids, unsaturated and highmolecularweight organic compounds, and essential oils. They can be separated under very favourable conditions by rectifying with an inert vapour as carrier. Steam is mostly used for this purpose, because many of the organic substances that have to be separated in practice are insoluble in water. An example of the reduction in temperature that can be achieved by this means arises in the distillation of palmitic acid. Thus, if the mass fraction of steam is about 15%, the boiling point at a pressure of 13.3 mbar can be lowered by about 19°C; and at a pressure of 133 mbar, by about 36 °C. Rectification with an inert vapour under vacuum is also resorted to for crude oils that may undergo thermal decomposition at elevated temperatures. For instance, the temperature above which Near East crudes may thermally decompose is about 390 °C. The advantages of steam or inert vapour rectification are offset by the high steam consumption and the extent to which the column crosssection must be enlarged to accommodate the steam fraction additionally imposed. This is evident from the following theoretical considerations. Let a mixture's instability to heat entail that the temperature at a given theoretical stage /, as counted from the head of the column, must not exceed a given value th Then the equilibrium pressure corresponding to this temperature th i.e. the sum of the partial pressures of the mixture's components c = 1 to c = n in the product vapour with a molar flow rate V, is given by (cf. Fig. 12.5): c=n
Pv,i = 2 Pa = const
(1240)
c=l
This equilibrium pressure can be attained and maintained at a constant value if the molar flow rate of steam S is correspondingly large. If the vapour pressure curves for the individual components Pc = f(t) are known, the pressures at the boiling points of the pure components Pi,i,Pc,i,Pn,i can be obtained as is indicated by the qualitative diagram presented in Fig. 12.6. Hence, if the composition of the liquid product phase Xjti,xcj,xn>i leaving the /'th theoretical stage is given, the corresponding partial vapour pressures can be calculated from Pa = la xa Pa
(1241)
303
12.3 Advantages of packing in steam rectification
p T =const. S'V L
Stage 1
Stage j
Stage n t Fig. 12.5. Scheme for describing the product temperature within the column in steam rectification
m PJ.
Top
Pressure p
tj
Ap
m
Botto S.V [ pB=f(pT(ntlAp/nt) tB=f(S/V,pp)
Top Pi
PHJ Pvj'Pcj H V
Fig. 12.6. Qualitative boiling pressure curves in steam rectification
(xc) Stage j Boiling temperature J
A simplifying assumption that can be made for mixtures that obey Raoult's law is that the activity coefficient y is unity. It is valid for most hydrocarbon systems subjected to steam rectification, and considerably simplifies the calculation of phase equilibria. The value thus determined for the equilibrium pressure pv,i of the product vapour at a total pressure pt above the f th theoretical stage allows the partial pressure of the steam at this stage to be determined as a function of the pressure pT at the top of the column and the pressure drop per theoretical stage Ap/nt for the type of packing concerned under the given loading conditions, i.e.
304
12
Retrofitting columns by the installation of packing
Ps,i = Pi ~ Pv,i =PT+
(i  1) —
 Pv,i
(1242)
\ fi I
The total vapour flow rate is the sum of the flow rate of steam and that of the product vapour, i.e. Vtot = S + V
(1243)
If it assumed that the modified Dalton's law of partial pressures applies, the molar fraction of steam will be given by Eqn (1244); and that of the product vapour, by Eqn (1245):
Hence, if the molar flow rate of product vapour V is known, the molar flow rate of steam can be calculated from the partial vapour pressures pSi and pVi, i. e. S = V^~
(1246)
Pv.t
If the individual components each have roughly the same molar vaporization enthalpy, the molar flow rate V of the product vapour and thus its molar fraction yv in the total vapour mixture must be constants, i.e. (yv) v = const = const
(1247)
In this case, the partial pressure of the product vapour can be determined at any given theoretical stage. Thus,
Pv,t = yvPt = yv
Ap
(1248)
Consequently, the phase equilibrium temperature corresponding to the composition xc>i in the liquid phase at that particular stage can be obtained. Now suppose that the thermal instability of the substances to be separated entails that a certain upper operating temperature limit may not be exceeded, e. g. the temperature tt laid down for the fth stage. In this case, the partial pressure pVi exerted by the molar volume above the f th stage must remain constant; its relationship to the total pressure is given by Pi = Ps,i + Pv.i
(1249)
The partial pressure of the steam pSi can be regulated by means of the steam molar flow rate S.
12.3 Advantages of packing in steam rectification
305
The total pressure pt at the /'th theoretical stage is fixed by the pressure pT at the head of the column and the pressure drop per theoretical stage Ap/nt for the packing concerned (cf. Fig. 12.5). Thus, (1250) The partial pressure of the product vapour pVi can be derived by combining Eqns (1249) and (1250). Thus,
Pv,i=Pr+(il)
— Ps,i
(1251)
The following relationship must apply for the partial pressure of the steam: S
(1252)
It therefore follows that the volume flow rate of steam required per unit flow rate of product vapour is given by
The condition for steam rectification must be adhered to, i. e. (Pv,i)ti = const. = const.
(1254)
Consequently, the lower the pressure drop per theoretical stage Aplnt for the packing, the less the flow rate S of steam required. The lowest steam flow rate occurs in an isobaric column, i.e. for Ap/nt = 0, in which case the following applies: %  = £ZLl y
(1255)
Pv.t
If Ap/nt > 0, Siso must be increased by a corresponding amount AS. Since AS is directly proportional to Ap/nt, the pressure drop in an actual column must be compensated by admitting steam at a higher flow rate. This additional rate of steam is given by
It follows from this equation that the lower the pressure drop per theoretical stage, the less the amount of steam that has to be admitted in steam rectification.
306
12 Retrofitting columns by the installation of packing
The ratio of the crosssectional areas of steam rectification columns, the one with Aplnt = 0 and the other with Ap/nt > 0, is equal to the ratio of the squares of their diameters dSyiso and ds. The temperature is the same in both cases, and the density of the steam is thus directly proportional to the pressure. In other words, Eqn (1257) applies for steam rectification with Ap/nt > 0; and Eqn (1258), for Ap/nt = 0: (Qs.dtt = const. ~ Ps,i
(1257)
\Qs,i,iso)ti = const. ~ PS,i,iso
(1258)
Therefore, the increase in the column diameter necessitated by the pressure drop within the bed of packing can be described by
ds 
ds,iso)2
Ps,i
(1259)
"•S, ISO
PS,i,is
Another fact to be taken into consideration is that the ratio of the steam partial pressure in isobaric rectification to that in nonisobaric is equal to the corresponding ratio of their molar flow rates, i.e. (1260) Rearranging Eqn (1259) to solve for ds and substituting from Eqn (1260) yields d5 = ds>iso + Ads = dS}iso + d5>iso \ —lhH£ 7 — = ds>iso 1 + \ / —T— V Ps,i Siso V S
(1261)
Substituting from Eqns (1252) and (1253) then gives
\/ „
T>
S lS
'°
\l
ps.
l Hf
(1262)
This equation states that the amount Ads, by which the diameter dStiso of an isobaric rectification column has to be increased, is directly proportional to the square root of the pressure drop per theoretical stage Aplnt, provided that the vapour load is constant in the column. It also clearly reveals the advantages of replacing existing column internals by lowpressuredrop packing. Consider, for instance, the case in which the pressure drop per theoretical stage of the existing internals is greater than that of the packing intended as a replacement, i.e.
nt /2
(1263)
72.3
Advantages of packing in steam rectification
307
According to the previous remarks, this replacement would result in a savings of AS in steam. Eqn (1264) would then apply for the original internals 2; and Eqn (1265), for the replacement packing 1:
P T
+
d  l ) ( ^
V . ^
(1264)
Pvj pT+(il)  ^ =
pVJ
^
d265)
The molar flow rate of steam, expressed in terms of the molar flow rate of product vapour, can then be obtained by substracting Eqn (1264) from Eqn (1265), i. e.
In other words, the savings ASIV in the molar flow rate of steam is directly proportional to the amount (k 1), by which the pressure drop per theoretical stage of the replacement packing 1 is less than that for the existing internals 2. It can be easily verified by dividing Eqn (1265) by Eqn (1266) that the corresponding relative savings in steam is given by AS ^2
S2S, = —r
k1 =
(1267)
S2
,, ,
PTPVJ
If the total vapour load is kept constant in both cases, the reduction in column diameter that can be achieved by substituting the packing 1 for the existing internals 2 is given by
a
s2
A reduction in capital investment entails that the costs per unit column volume (cf. Chapter 11) for Column 7, as expressed by Eqn (1269), are also less than those for Column 2, as expressed by Eqn (1270): =
(dS2
Adsf df2
CS2 = vV2 C2 where vV2 is the column volume per unit of separation efficiency for Column 2, C2 is the cost per unit volume (m3) for Column 2, and C\ is the cost per unit volume (m3) for Column 1.
(1270)
308
12
Retrofitting columns by the installation of packing
Packing 1 is considered to be more economical only if the total costs CT>1, i. e. capital and running costs, are less than those for the original internals 2. It is quite feasible that, if the costs for the shell and bed of packing are very high, Column 1 may involve the higher acquisition costs, despite the smaller diameter ds>1, yet the total costs may still be less, i.e. CTJ < CT,2 However, if the costs for the shell and packing are extremely high, i.e. Cj ^> C2, CTJ may exceed CTa, even if dsJ < dSy2A flow chart for an oil refinery is shown in Fig. 12.7 to illustrate steam rectification.
Vacuum station
Water Highpressure steam
Vacuum column /
Saturated steam Heater
Fuel ? oil
Fig. 12.7. Crude oil inert steam rectification plant
The five valveballast plates in the distillation zone of a FCC fractionating column were replaced by a bed of Montz Packing Bl/250.60 of 2.6 m total height. A schematic diagram of the upper section of the column is shown in Fig. 12.8. As a result, the separation efficiency was increased from 3 to 4.5 theoretical stages with an associated improvement in the product quality. The packing was arranged in parallel layers, as is shown in Fig. 12.9. Utmost care in stacking the packing is essential in order to maintain the efficiency throughout the height of the bed. Data characteristic of a plant for the distillation of fatty acids before and after changing over from plates to packing are presented in Table 12.3. The advantages achieved from the
12.3
Advantages of packing in steam rectification
309
changeover are immediately evident: the reduction in the pressure drop per theoretical stage allowed a 40 % increase in capacity, a reduction of 25 °C in the temperature at the foot of the column, and 15 % savings in energy. In addition, the column could be operated without carrier steam.
Liquid distributor Distillation zone Fig. 12.8. Example for retrofitting a FCC fractionating column by substituting Montz packing for five valveballast plates in order to improve separation
I I
I I
I I
I I
Liquid collector
I I
Table 12.3. Data relating to the rectification of coconut oil fatty acid in a column formerly fitted with bubblecap plates and after retrofitting with Mellapak packing. With the courtesy of Sulzer AG, Winterthur Characteristic data
Trays
Column diameter ds [m]
2.5
Effective column height H [m]
18.6
Pressure at head of column pr [mbar] Pressure at foot of column pB [mbar]
5 90
Temperature at head of column tD [°C] Temperature at foot of column tB [°C] No. of theoretical stages nt
Energy savings A Q / Q [%]
23
173 255
230
26
32
Capacity increase AF [%] Carrier steam S [%]
Mellapak
40
10 15
310
12
Retrofitting columns by the installation of packing
Fig. 12.9. Montz Pak Bl250 packing elements for a column of 4m diameter. The beds of packing were charged through manholes
12.4 Improvement in product purity caused by restricting the pressure drop in beds of packing The total pressure drop between the head and the foot of the column will obviously be high in rectification processes that involve a large number of theoretical stages. Hence, if it may not exceed a given value owing to the product or the process conditions, undesirable limits may be imposed on the separation efficiency and thus on the purity of the product in plate columns. Examples of the limits that may be set by the process conditions arise in the separation of thermally unstable mixtures; in coupled columns with an integrated heating system, e.g. if the heat content of the bottoms in the one column is utilized for the indirect condensation of the overhead product in the other; or if the overhead vapour in the one column is used to heat the bottoms in another that operates under reduced pressure. In cases of this nature, more theoretical stages can be realized by substituting lowpressuredrop packing for the plates (trays), i.e. nuP > ntJ. This is evident from the qualitative diagram in Fig. 12.10. According to this, the pressure drop must be the same in both cases, i. e. Ap = f^1 ntJ = \^2\ nttP = const. nt IT \ nt JP
(1271)
In other words, the ratio of the number of theoretical stages to the specific pressure drop in the packed column {Eqn (1272)} is greater than that in the plate column {Eqn (1273)}:
12.4
311
Improvement in product purity caused by restricting the pressure drop in beds of packing
uv = const, and A p = const. — n t p > n t T —  ( x D P  x B X
X
D,T
) > (xD
D,P
M
1
Ap= const. n
p
t,I
1 888
X
X
B,I
B,P
Packing
Trays
Vapour load u v
Fig. 12.10. Schematic diagram demonstrating the advantages of packing over plates for improving product quality in separation processes with constant total pressure drop
, nt IT nt,p = 7——r— nuT
(1272)
AEA nt
Jp
AE] r
App = const.
nt JT AE) nt
(1273)
jp
Thus the degree of separation is also increased. A measure for the fraction of high boilers AB remaining in the overhead product D is *B
_
•
_ ^l
*>D)xB = const., Ap = const.
(1274)
It can be expressed in the following form: (1275) This function can be evaluated in the light of the above remarks, to obtain the minimum number of theoretical stages from Eqn (160). Information can thus be derived on the improvement in product quality that can be achieved if the plates are replaced by packing. Likewise, the fraction of low boilers AD remaining in the bottoms B is given by
A
B
—
(XB)XD
= const.,
Ap = const.
(1276)
12
312
Retrofitting columns by the installation of packing
and information on the improvement in the quality of the bottoms can be derived, by analogy, from the following function: (1277) If the overhead and bottom products are of very high purity, the term xD(l  xB) tends towards unity. In other words, if the relative volatility is given, the term xB(l  x^) decides the minimum number of theoretical stages nUmin. This is clearly demonstrated in Fig. 12.11, in which xB(l  xD) is shown as a function of nt and r^p with a as parameter. The following linear relationships are obtained by plotting on semilogarithmic paper:
 xD) xB •
1
(1278)
Thus if xB = const., xD is given by X
~ 1 
D
xB
(1279)
a'
or, if xD = const., xB is given by 1 xB « 1 x D
1 a n, +
(1280)
1
Ratio of specific pressure drops r A p ( n t I = 5 0 ) 1.5
2
2.5
3
3.5
4
10
s e
10'1 2
i 10s
o
103
• \
N
\
\
\
\ \
N
\ \
=3
s\
ioJ 10"
50
\
"i \
100 150 Number of theoretical stages nt
\
1%,200
Fig. 12.11. The advantage of lowpressuredrop packing in improving product quality by the scheme illustrated in Fig. 12.10.
13 Applications for packing in liquidliquid systems Depending on the geometry of their elements and the materials from which they have been produced, random and stacked beds of packing give good results in liquidliquid extraction as well in gasliquid separation processes. This has been confirmed in numerous systematic studies performed in the author's laboratories.
13.1 General aspects More energy is required to separate mixtures by rectification if the differences in the relative volatilities of the components are slight or if the fraction of the one component is small. A typical example of the latter case is the recovery of organic compounds from aqueous solutions in the treatment of industrial effluents. A physical method that can be adopted for this purpose is direct rectification, but the high energy costs involved are a major deterrent. An alternative on which current attention is focused is to extract the organic compounds from the waste water by means of a solvent and to recover the solvent from the extract in a second, rectification stage. Flow charts for both methods are presented in Fig. 13.1. The process with the extraction stage may require much less energy, because the vaporization enthalpy of organic substances is three to five times less than that of water. This is clearly demonstrated by Fig. 13.2. Liquidliquid extraction processes for the recovery of organic compounds from effluents can be successfully carried out in packed columns.
Condenser
b)
Q)
Condenser
Waste water
Extract
Extractor'
Purified
water
Reboiler
Rectification column T I
water
Recycling « ^ _
of solvent
Fig. 13.1. Recovery of organic compounds from production effluents (a) by rectification (c) by liquidliquid extraction and rectification of the process solvent Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
314
13 Applications for packing in liquidliquid systems
1.0 Water  Methanol/ 2 Octanol
0.5
1.0 1.5 2.0 2.5 Solvent/feed ratio C/F [kmol/kmol]
3.0
3.5
Fig. 13.2. Energy saved by combining liquidliquid extraction with solvent recovery instead of direct rectification (cf. Fig. 13.1)
13.2 Experimental The flow chart for the experiments is shown in Fig. 13.3. The diameter of the column was varied up to 0.25 m; and the height of the packing, up to 3.2 m. The types of dumped packing tested are shown in Fig. 13.4; and of arranged packing, in Fig. 13.5. Another packing system that was included in the studies is illustrated in Fig. 13.6. It is known as a tube column and consists of vertical tubes in which the packing elements have been systematically stacked beforehand. The derivation of a generally applicable model to describe mass transfer and flooding in extractions columns filled with these types of packing necessitates a fundamental investigation into the hydraulic characteristics of the packing, because they strongly influence the extraction efficiency and the maximum load. Thus the packing performance is affected by the extent to which the two phases are intimately mixed and uniformly distributed over the entire crosssection of the column. The systems listed in Table 13.1 allowed the effect of the main physical properties  density Q, diffusion coefficient D, dynamic viscosity r\ and surface tension o  to be taken into account over a wide range. In some of the systems, the resistance to mass transfer was in the dispersed phase D only; in others, in the continuous phase C only; and in others again, in both phases. The effect exerted on the performance by the direction of mass transfer was also investigated, i.e. from the continuous to the dispersed phase C —» D or from the dispersed to the continuous phase D —> C. In the diagrams, a C —» D system is denoted by "Dispersed phase / Transfer componentsContinuous phase"; and a D —» C system, by "Dispersed phaseTransfer component/Continuous phase".
13.2
V16
VK
Experimental
V15
Fig. 13.3. Flowchart for one of the pilot plants used in the experiments
Fig. 13.4. Packings investigated in dumped beds
Pall ring 25 mm, metal
Hiflow ring 25 mm, plastic
Bialecki ring 25 mm, metal
Hiflow ring 35 mm, ceramic
315
316
13 Applications for packing in liquidliquid systems
Stacked Bialecki rings,25 mm metal
Montz packing B1300 metal
Montz packing B1300 plastic
Fig. 13.5. Packings investigated in geometrically arranged beds
Tubes filled with packing elements
Fig. 13.6. Extractiontube columns with stacked Bialecki rings
D D D D CD C
Toluene (D)  Acetic acid/Water
Carbon tetrachlor. (D)  Acetic acid / Water
Dichloroethane (D)  Acetic acid/Water
Isobutyl alcohol (D)  Acetic acid / Water Isobutyl alcohol (D)  Acetic acid / Water
Toluene (D)  Acetone / Water Toluene (D)  Acetone / Water
D,C
c D
D D D D,C
Transfer resistance
c c c c
Transfer direction
Extraction system
QDQC
QDFi)2 ( 1  2
hDjFl)
(1316)
The corresponding dispersedphase superficial velocity uD obtained by combining Eqn (1313) with Eqn (132) is hD(lhD)2
uD =
w
(1317)
uDluc
The corresponding position of the dispersedphase flood point is defined by duD dhD }FI
(1318);
and the corresponding equation for the determination of the dispersedphase capacity uD>F/ at the flood point is
324
13 Applications for packing in liquidliquid systems
uD>Fl = 2 CFl 8 u (1  hD>Fl) hlFl
(1319)
Evaluation of Eqns (1316) and (1319) requires a knowledge of the dispersedphase holdup at the flood point, which can be obtained by combining Eqns (1317) and (1319), i. e. , h
=
[(uD/uc)2 + __
SuD/uc]m3uD/uc .
(IjZUJ
4(luD/uc) Numerical values for the floodpoint constant CFi for various types of packing can be obtained by plotting the results, as indicated in Fig. 13.12. Figures thus determined are listed in Table 13.2. Typical curves for the capacity at the flood point are presented in Fig. 13.13. They are valid for a 50mm tube column, as illustrated in Fig. 13.6 and stacked with metallic Bialecki rings, and represent operating conditions without mass transfer. The agreement between the theoretical curves and those plotted from measurements is quite good. Fig. 13.14 indicates the effect of mass transfer. In this example, the load at the flood point was increased by about 25 % when mass transfer proceeded from the dispersed to the continuous phase as a result of rapid droplet coalescence. The bed of packing in this case consisted of stacked 25mm Bialecki rings, which are illustrated in Fig. 13.5. If mass transfer is in the opposite direction, i.e. from the continuous to the dispersed phase, the limiting load would be the same as that without mass transfer.
13.6 Mass transfer in the dispersed and continuous phases From the aspect of industrial applications, the HTU  NTU model described by the following two equations has been found suitable for predicting the efficiency and effective height H of a packed extraction column.
H = HTUQD
' NTUQD
(1321)
H = HTUoc • NTUQC
(1322)
If mass transfer proceeds from the dispersed to the continuous phase, the height of an overall transfer unit HTUQD will be given by HTUOD
= HTUD + E(HTUc)
(1323)
where E is the extraction factor. If mass transfer is in the opposite direction, the following applies: HTUoc = HTUC + 1/E(HTUD)
(1324)
The extraction factor E is governed by the process conditions, i. e. the phase ratio UDI uc, the slope m of the equilibrium curve for the extraction system, and the phase density ratio QDI Qc Thus,
13.6
325
Mass transfer in the dispersed and continuous phases
50mm tube column, metal Bialecki rings d s = 0.0532 m.H = 1.5m
k. r
21)
•>
LI
16 Tc)lue ie([))/H 2o
cu (D)/ H20
k
A
12
Z: ^ \ V
1
on'
^
1/
bar, z.3j r\
Q
0
4 "ISO
Dutanol D)/l
n 0 4 8 12 16 20 24 Continuousphase flood load u CFr 1O 3 [m 3 /m 2 s] Fig. 13.13. Characteristic capacity diagram for a tube column packed with metal Bialecki rings for various liquidliquid systems without mass transfer
25mm stacked metal Bialecki rings ds=0.154m, H = 2.4m \
0
4
8
i r i i i Toluene(D)Acetone/H 2 0Toluene(D)Acetic acid/H20
12
16
20
24
Continuousphase flood load uc,R103[m3/m2s] Fig. 13.14. Influence of mass transfer on the capacity of a column packed with stacked metal Bialecki rings
326
13
Applications for packing in liquidliquid systems
E = m
»!L OS. uc Qc
(1325)
The expression for the height of an overall transfer unit, HTUQD or HTUoc •> contains the term HTUD or HTUC The former is related to mass transfer in the dispersed phase {Eqn (1326)}; and the latter, to mass transfer in the continuous phase {Eqn (1327)}: HTUD =  ^ 
(1326)
HTUC =  ^ 
(1327)
PD aPh
Pc aph
where aph is the phase contact area per unit column volume and (3O (or 3C) is the mass transfer coefficient. The product of aPh and 3 D (or 3C) is referred to as the volumetric mass transfer coefficient. Mass transfer can be adequately described in both directions by the theory of nonstationary diffusion, which Higbie expressed in terms of the diffusion coefficient D in the phase under consideration, the duration of contact x or the length / of the path of contact, and the Fourier number Fo, i.e. (3 = = \ — V jt y x
(for Fo < 100)
(1328)
The Fourier number is defined by Fo = 4  ^
(1329)
Clys
If the duration of contact x or the length / of the path of contact is short and the Fourier number is less than 100, the diffusion coefficient D can be used to determine the mass transfer coefficient 3. Theoretically, a bubble of the dispersed phase remains in contact with the continuous phase over a path of length / and for a time x until it collides with the packing and renews its surface. The time x is defined by x = /e — uD
(1330)
Substituting Cs for hDluD {cf. Eqn (131)} gives
x = Cs I e
(1331)
13.7
Extraction efficiency, test results and derivation of model
327
The characteristic length / depends greatly on the packing geometry. The only means of determining its value if the packing is dumped is by experiment. However, if the packing is systematically stacked, e.g. sheetmetal types or in tube columns, a geometrical relationship exists between / and the characteristic size of the individual packing elements, as is evident from Table 13.2. Another parameter that governs the extraction efficiency is the interfacial area aPh, i.e. mass transfer area per unit volume of packing. It is defined by aPh = 6 e y
(1332)
dyS
where dyS is the mean Sauter diameter of the droplets, which depends on the interfacial tension o at the surface of the droplets and the phase density difference AQ, i. e.
V s ^y
(1333)
where Q is the droplet constant. In the main uc < 0.7 UC,FI loading range, the droplets remain stable. In other words, dvs is independent of load and can be calculated from the droplet constant Cd, for which the following numerical values have been obtained by experiment:
Q = 0.8
(if QD > Qc)
(1334)
Q=1.0
(if
(1335)
QC>QD)
At the flood point, the droplet diameter increases by about 20%, i. e. Q,FZ = 1.2 Q
(1336)
If mass transfer is in the D —»• C direction, i.e. from the dispersed to the continuous phase, the droplet diameter dvs can be expected to increase with an associated decrease in efficiency (cf. Fig. 13.15). If mass transfer is in the C —> D direction, the droplet diameter dvs decreases with an attendant significant improvement in mass transfer (cf. Fig. 13.16).
13.7 Extraction efficiency, test results and derivation of model It has been confirmed by experiments on dumped and stacked packing that the theory of nonstationary diffusion {Eqn (1328)} can be applied to describe mass transfer efficiency in beds of packing, on the assumption that the duration or path of contact is short. The experiments embraced systems with different physical properties, differences in the resistance to mass transfer, and differences in the direction of mass transfer.
328
13
Applications for packing in liquidliquid systems
25mm Bialecki rings, stacked, metal d s =0.1m. H=2.95 m, Toluene(D)Acetic acid/Water, A=0.39 c tkmol/m 3 ] i n l e t o 0.1  o  0.2  ©  0.3 Toluene(D)Acetone/Water, X=1.43
9
£
CD
a
AT Toluene (DJ/Water, uc = (
3 0
2
4
6
8
Fig. 13.15. Mean droplet diameter as a function of the dispersedphase load for stacked metal Bialecki rings
10
Dispersedphase load iiD103[m3/m2s]
25mm Bialecki rings, stacked, metal d s = 0.1 m, H2.95 m 6
1
ug103 =3.372 m 3 /m 2 s uc 103 =2.36 m 3 /m 2 s
5 ^^
m
^
^ 4
 Toluene(D)/Acetone^4J 1 j \\ C direction The packing efficiency, expressed as the height of an overall transfer unit (HTUOD in the dispersed phase or HTUoc m the continuous phase) is shown as a function of the dispersedphase load UD at a constant phase ratio uD/uc in Figs. 13.17 to 13.20. It is evident from the diagrams that the types of packing concerned hold out good prospects in industrial applications. When dumped, Pall and Bialecki rings have almost the same efficiency in extraction columns, and their performance can be considerably improved by stacking (cf. the curves for the Bialecki rings in Figs. 13.17 and 13.18). The extent of the improvement depends on the shape of the rings.
13.7
329
Extraction efficiency, test results and derivation of model
Metal packing, ds = 0.10 m, H = 1.6 m IsobutanoKDlAcetic acid/Water, 1 bar, 293 K i
c=
i
I
i
i
I
i
25mm Pall rings, dumped
1 °8 _u /u =0.85 D
DC
c
o =
o
0.6
25mm Biaecki rings, stacked
CD CD
i
0.4
1
i
i
i
2
I
1
3
I
i
4 3
5 3
6 2
Dispersedphase load uD10 [m /m s] Fig. 13.17. Height of dispersedphase transfer unit as a function of the dispersedphase load for metal packings
Metal packing , ds=0.154mJ H = 2.4m Toluene(D)Acetone/Water, 1 bar, 293 K „
2.0
_§
1.8
1
D
I—
~ CD
c/> cz o
CD CD
Fig. 13.18. Height of dispersedphase transfer unit as a function of the dispersedphase load for metal packings
/
1.6  — •  2 5  m m Bialecki rings, dumped —a—25mm Pall rings, damped 1.4 DC uD/uc=1.429 < 1.2 /25mm Bialecki rings, stacked 1.0 O u u 0
2
4
6
8
10
12 14
Dispersed phase load UDlO3[m3/m2s]
Figs. 13.19 and 13.20 demonstrate that an increase in efficiency can be obtained by reducing the height h of an element of stacked sheetmetal packing. Thus a reduction in height from h = 135 mm to h = 50 mm improved the efficiency in this case by a factor of 1.64. This fact can be explained by the theory of mass transfer in liquidliquid systems. These studies also revealed that, if the resistance to mass transfer is only in the dispersed phase, the efficiency (HTUOD) of 50mm Montz Bl sheetmetal packing hardly differs from that of 25mm metallic Bialecki rings.
330
13 Applications for packing in liquidliquid systems
Montz Bl300 packing Sheet metal, ds=0.157 m. H=2.4 m 1.8
1
/
16
h 0.13 5 m
Z 14
y
C
 To luerie(D )Ac .etic ac id/V\/ate  1 bar, 293 K
cr a
o
* h =0.05m
1.0
/
—n
cp
0.8 —
l
I
0.6
3
3
 uc=2.lMO" m /m^
D
0
8
12
16 3
20 2
Dispersedphase load U0 10 [m /m s]
Fig. 13.19. Height of dispersedphase transfer unit as a function of the dispersedf Montz Bl300 l 3 0 0 packing ki phase load for
Montz Bl300 packing Sheet metal d s = 0.157 m, H = 2.4m
o
2.4
! Tnluen e ( D )  Acetcinp/Wnt Ibar, 293 \(
2.2
o
h  0.135 rr
5 2.0 •s CJ> CD
H
7/
o/
J
^ h = 0.'05m
1.8
1
•
 u D /u c = 1.4?
1.6 0
4
8
12
16 3
3
20 2
Dispersedphase load u D 10 [m /m s]
Fig. 13.20. Height of dispersedphase transfer unit as a function of the dispersedphase load for metal packings
13.7
Extraction efficiency, test results and derivation of model
331
The studies also embraced the determination of the relationship between the volumetric mass transfer coefficient $DaPh and the dispersedphase load uD. The curves thus plotted for dumped ceramic and plastics packing are presented in Fig. 13.21; for tube columns with metallic packing of different sizes, in Fig. 13.22; and for stacked metallic and plastics packing, in Fig. 13.23. The two systems studied are representative of resistance to mass transfer in the dispersed phase and of the direction of mass transfer from the dispersed to continuous phase. The diagrams are selfexplanatory and need no further explanation. An almost linear relationship also existed between the volumetric mass transfer coefficient (3/)flp/j and the superficial velocity of the dispersed phase uD in all the other cases investigated. Mass transfer in the C —> D direction Similar results were obtained when the direction of mass transfer was from the continuous to the dispersed phase C » D. In Figs. 13.24 and 13.25, the height HTUOC of an overall transfer unit in the continuous phase is shown as a function of the continuousphase load wc for a constant phase ratio uDl uc The high extraction efficiency of both dumped and stacked beds of packing in this case is evident from these diagrams. Fig. 13.25 also clearly indicates that large differences may exist between the efficiency of stacked Bialecki rings and that of Montz sheetmetal packing with extraction systems of this nature. In these systems, the resistance to mass transfer is distributed between both phases. It is evident from the relationships discussed in Sect. 13.6 that the two factors that largely govern the efficiency of a liquidliquid extraction column are the mass transfer coefficient 5 and the interfacial area aPh. Their product is referred to as the volumetric mass transfer coefficient pfl/v, and can be obtained by combining Eqns (1311), (1328), (1330), (1332), and (1333). It is thus given by Eqn (1337) for the dispersed phase; and by Eqn (1338), for the continuous phase:
Pz> an = CmuD Pc aph = ^mUD
(a ArTl 3 / 8 r» 1/4 D 1 / 2 igAQ C D
\£
°
^
(1337) (1338)
in which Cm is a mass transfer constant that is representative for a given packing and is given by
c*£][* Eqn (13.38) was adopted to plot the linear relationships shown in Figs. 13.21 to 13.23. The agreement between the theoretical and the experimental results is satisfactory. Allowance can be made for the effect exerted by the direction of mass transfer by means of the following relationship, which was determined by experiment: (Cm)c^D
= 1.5 (Cm)D^c
(1340)
332
13 Applications for packing in liquidliquid systems
[Toluene(D)Acetic acid/Water, 1 bar,293K
2
4
6
8
10
12
Fig. 13.21. Volumetric mass transfer coefficient for the dispersed phase as a function of the dispersedphase load for random beds of ceramic and plastics Hiflow rings
14
Dispersedphase load up •10 3 [m 3 /m 2 s]
Tube columns pocked with metal Biolecki rings
12 z
Dispersedphase load uD 10 [nr/m s
14
Fig. 13.22. Volumetric mass transfer coefficient for the dispersed phase as a function of the dispersedphase load for tube columns packed with metal Bialecki rings
13.7
Extraction efficiency, test results and derivation of model
333
Toluene(D)Acetic ocid/H20;l bar,293K
Fig. 13.23. Volumetric mass transfer coefficient for the dispersed phase as a function of the dispersedphase load for geometrically arranged beds of metal and plastics Montz packing
0
2
4
6
8
10
12 14
3
3
Dispersedphase load uD10 [m /m 2 s]
Metal packing, ds = 01 m, H=1.6 m lsobutanol(0)/Acetic acidWater, I bar, 293 K 0.8  2 5m Tl PCill rings .
dijmp^
i
•Si " i 0.6
c
el
**> 2 5mm bioiecKi rings>. siuik ?d
0.4
no
n
cp
/uc= O.ob1
U 0.2
Fig. 13.24. Height of continuousphase transfer unit as a function of the continuousphase load for metal packings
Ki
0
1
2
3
4
5 3
3
6 2
Continuousphase load u c l0 [m /m s]
13 Applications for packing in liquidliquid systems
334
Metal packing , ds=0.154 m, H = 2.4 m Toluene(D)/AcetoneWater. 1 bar, 293 K 2.2 Montz packing B1300 v h = 0.135m—
1.8
J
1.6 to a o
~
1.4 25mm Pall rings, dumped i\n a 1.2 25"mm Bialecki rings, stacked y o
t
0
12 14
0.8 0.6 2
4
6
8
10
Continuous phase load uciO 3 [m 3 /m 2 s]
Fig. 13.25. Height of continuousphase transfer unit as a function of the continuousphase load for metal packings
In other words, the efficiency of mass transfer in the direction from the continuous to the dispersed phase, i.e. C * D, is 50% higher than that in the opposite direction, i.e. D —» C. This fact can be explained by the corresponding difference in the droplet diameters. The numerical values of Cm listed in Table 13.2 are valid for the C —» D direction. The application of Eqn (1340) to Eqn (13.39) implies the following requirement: {Cm)c
(QV
(1341)
Applying Eqns (1311) and (1333) to this equation yields the following proportional or approximate relationship: (Cm)c
(dys)p{dvs)c
{hD)c{hD)D
(1342)
Substituting the numerical value derived from Eqn (1340) for the lefthand side of Eqn (1341) gives (1343)
13.7
Extraction efficiency, test results and derivation of model
335
In this case, the square root term can be equated to unity. Likewise, substituting the numerical value derived from Eqn (1340) for the lefthand side of Eqn (1342) gives (1344) It also follows from Eqn (1339) that the effective length / of the path of contact is related to the characteristic fluiddynamic constants Ch (for the dispersedphase holdup) and Cd (for the droplet diameter in the dispersed phase) and to the mass transfer constant Cm. The following simple equation thus applies: Ch
/ = 32.41
(1345)
2
(Cm Cd) Combining Eqns (1323) and (1325) to (1327) with Eqns (1337) and (1338) gives the height of an overall dispersedphase transfer unit HTUOD for mass transfer in the D ^ C direction, i. e. 1
1 (
.
x3/8
(g AQ)
n l/2
_l/4
UD
QC
,
+'
m
QD
n l/2
~
DC
QC
(1346)
Likewise, combining Eqns (1324)  (1327) with Eqn (1338) gives the height of an overall continuousphase unit HTUoc for mass transfer in the C —> D direction, i.e. 1
a
UQ
I 1
1
Qc
The effective height H of the column required for extraction can then be obtained from Eqns (1321) and (1322) and the number of transfer units NTUOD and NTUOC
14 Examples for the design of packed columns The relationships discussed in the previous chapters are important for the design and operation of countercurrent packed columns. Examples taken from the fields of desorption, absorption, rectification, and liquidliquid extraction shall now be given to demonstrate how they can be applied in plant engineering. It is presumed that the reader is acquainted with the principles underlying thermal separation techniques. Fig. 14.1 shows a flow chart for a rectification column with a concentration x of low boilers in the feed F, overhead product D, and bottoms B. These fractions are presented qualitatively in the ylx diagram. The example concerned is the separation of a binary mixture; the equilibrium curve ye = f(x) and the operating lines y = f (JC), viz. BI in the stripping zone and ID in the enrichment zone, are given.
Rectification
Reboiler B = FD
Fig. 14.1. Qualitative determination of transfer units in rectification
hF = feed enthalpy hp = feed enthalpy at boiling temperature Ah v =vaporization enthalpy at feed section
Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
338
14 Examples for the design of packed columns
Fig. 14.2 illustrates the principles of absorption and desorption. The factors given are the gas volumetric flow rate V, the concentration of transfer components y in the gas, the liquid volumetric flow rate L, and the concentration of transfer components x in the liquid. The subscript u indicates the bottom of the column; and the subscript o, the head of the column. The gas load Y of transfer component is related to the mole fraction y by
Likewise, the liquid load X of transfer component is related to the mole fraction x by
X
< 14  2 >
= T^
The number of transfer units NTUOv required for rectification between zones with molar fractions ya and yb is given by
NTUov = /a~y"
In 4 ^
Aya  Ayb
(14"3)
Ayb
The terms Aya and Ayb in this equation represent the difference between the equilibrium mole fraction ye>a or ye>b and the vapour mole fraction ya or yb, i.e. &ya = ye,a  ya
(144)
An = ye,byb
(145)
The size of the zones should be selected so that the slope myx of the equilibrium curve is practically the same in each. In contrast, the slopes of the equilibrium curves in absorption and desorption processes can be regarded as constant over the entire range of concentrations between the head and the foot of the column, particularly at low phase loads. In this case, if the gas load is adopted as a measure for the concentration, the number of transfer units in absorption processes will be given by
where Yu and Yo are the gas loads at the foot and head of the column. The terms AYU and AYO are then defined by AYu = YumYXXu
(147)
AYo = YomYXXo
(148)
The corresponding equations for the liquid load are
NTUOL=
ff AXU  AXn
In^ AXn
(149)
14 A X M
_
AX0 =
Examples for the design of packed columns
1 mYX
Y
x
339 (1410)
—YoXo mYX
(1411)
Likewise, the number of transfer units required in desorption processes will be given by Eqns (1412) to (1414) if the gas load is adopted as the measure for the concentration: Y Y u °
AY
(1412)
°
Absorption
Desorption
ye
x,y m yx L/V X,Y L,V r777'
Mole fraction in liquid, gas or vapour Slope of the equilibrium line Molar liquidtogas ratio or slope of the operating line Load fraction of transfer component in liquid /gas Carrier stream of liquid /gas phase L _ Y 0 Y u Y Q = 'U
V
+
*W~
A n — A ii
Fig. 14.2. Qualitative determination of transfer units in absorption and desorption
340
14 Examples for the design of packed columns
Yo = mYXXoY0
(1413)
Yu = mYXXuYu
(1414)
The corresponding equations for the liquid phase are
1 Yo
(1416)
Yu
(1417)
mYX
= xu
1 mYX
In a rectification process, as illustrated in Fig. 14.1, the reflux ratio is given by r
> r*n = T T T T
(1418)
The molar flow rate at the head of the column would then be V= F
XF XB
~ (r + 1) D ~ %B
X
(1419)
In an absorption process, as illustrated in Fig. 14.2 (left), the total liquidvapour ratio must be higher than the ratio of the carrier liquid, i.e. solvent, to the vapour, i.e.
( 14 " 2 °)
Y > T" The flow rate of solvent in this case is given by
Lm = V lu~*°
(1421)
In desorption, as illustrated in Fig. 14.2 (right), the total vapour/liquid ratio must be higher than the ratio of the stripping gas to the liquid, i.e. V
V
The flow rate of stripping gas in this case is given by Vm = L ^ ^ x
o,m
x
u
(1423)
14 Examples for the design of packed columns
341
In absorption and desorption, the total molar flow rate of vapour, consisting of the carrier gas and the transfer components, is given by V =V(\ + Y) where V = Vu (1  yu)
(1424)
and the total molar flow rate of liquid, consisting of the carrier liquid and the transfer components, by L = L(l+X)
where L = Lo(1 x o )
(1425)
The column diameter ds can be expressed in terms of the free crosssectional area As, i. e. ds = \ —As y JI
(1426)
If uv is the superficial gas velocity, As can be defined by As = ^
^
Uy
(1427)
Qy
Thus the column diameter can be calculated from the operating parameters V [kmol/h], uv [m/s], T [K], and p [bar], i. e. ds = 5.4 • 1(T3 \l V — — 17
p
(1428)
Uy
Fig. 14.3 illustrates liquidliquid extraction in which the specific gravity of the continuous phase (Subscript C) is greater than that of the dispersed phase (Subscript D). In this case, the total number of transfer units NTUOc derived from the HTUNTU model is given by NTUoc =
Cc
'°~Cc'u In ^ Aco  Acu Acu
(1429)
where Aco is the driving concentration difference at the head of the column, as defined by Eqn (1430), and Acu is the driving concentration difference at the foot of the column, as defined by Eqn (1431), i. e. Aco = cc,o  ~  cDtO
(1430)
AcM = cc,u  — cD>u
(1431)
Another case to consider is that in which mass transfer is in the C —> D direction and the desired separation efficiency is given by ^E = 1££JL
(1432)
342
14
Examples for the design of packed columns
h CQ.O C
Co
Fig. 14.3. Qualitative determination of transfer units in liquidliquid extraction
Rearranging this equation gives rise to the following: CC,u = (1
(1433)

from which it can be derived that the concentration of transfer components in the continuous phase decreases from cc>o at the head of the column to cc>u at the foot. If the phase ratio in the extractor is uc/uD, the concentration of transfer components in the dispersed phase increases from a value of cD>u at the foot of the column to the following value of cDo at the head of the column: c
(cC,o ~
D,o —
c
D,u
(1434)
UD
Eqn (1322) allows the effective height H to be determined from NTUOc and HTUOc\ and, if the volume flow rate Vc of the continuous phase is given, the column diameter ds can be obtained from the load uc < 0.7 uc, FI from the following equation: (1435)
14.1 Determination of the diameter of an offgas absorption column with various types of packing Polluted air flowing at a rate of 105 m 3 /h STP is to be scrubbed with water in a packed column. The liquidtogas ratio must be varied between LIV = 1 and L/V = 10, depending on the degree of contamination. The maximum permissible load is that at the loading point.
14.1
Determination of the diameter of an offgas absorption column with various types of packing
343
Under these conditions, what diameter would the column have to be if 50mm packing of the following types had to be installed? Plastics packing: Intalox saddles, Bialecki rings, Pall rings, and Norpac rings Metal packing: Pall rings, Hiflow rings, Bialecki rings, and VSP rings Solution Properties of the system Density and dynamic viscosity of the gas QV= 1.19 kg/m 3 TJV = 18 • 10~6 kg/ms Density and dynamic viscosity of liquid QL = 998 kg/m 3 TU = 1 • 10"3 kg/ms The values of Cs required to calculate the resistance coefficients § 5 at the loading point from Eqn (429) are listed in Table 4.1.
Gas, air 100000 m 3 /h, Liquid: water, STP, loading capacity 5.4
/ Packing size 50 mm
j
5.2
/
 I N TALOX 5;adc le 5.0
/
/  Bicilec
Hifl DW
my
y
/
TD
If
1
4.6
= 6.8. What would the error
14.3
Scaling up measurements performed in pilot plants
349
be if the efficiency determined for a height HPa = 1.5 m were to be taken as a basis in calculating the height HT of an industrialscale column required to realize NT = 20 transfer units on the assumption that the inlet distribution remains unchanged? For the purpose of the calculation, assume that the height of the inlet zone Ht is less than HPa = 1.5 m. Solution If no allowance is made for end effects, the height of the column would be
Hw
_ _ g t _ =   L = 5.36 m
If it is assumed that the separation efficiency remains constant in the H > Ht zone, the following applies for Hi < HP dN \
NPbNPa
6.85.6
dHJH>Hi
HP>bHP>a
21.5
„ A , :.4 m
According to the model presented in Fig. 8.4, the end effects (Nd + ANt) can be determined by rearranging Eqn (68) for the case of H = HPa, i. e. ) n lH>Hi = 5 . 6  1 . 5 • 2.4 = 2 The relative difference in height required to compensate end effects can then be obtained from Eqn (815), i.e.
7 1
2Q
^ 1+
JJ'2A
According to Eqn (635), this corresponds to an efficiency ratio of
rjr = 1  4HrT " =
X
" ° 285 = ° 715
The actual column height required can then be calculated from Eqns (635) and (639), i. e.
350
14
Examples for the design of packed columns
The same result can be obtained from Eqn (628). Thus
P_a
Nd + AN(\H
jP,a
1 1.5
2
= 7.49 m 3.733
Hence, the absolute value for the additional height required is AH = 4 ^ " HT = 0.285 • 7.49 = 2.13 m. HT This figure agrees with that for the difference between the values calculated for HT and HT(P), i e.
AH = HTHT(P)
= 7.495.36 = 2.13 m.
Hence, if the column design were to be based on the measured value for (N/H)P>a = 3.733 m"1, the height of the bed would be too short by an amount AH
HT
100 = 28.5%.
14.4 Design of an absorber for removing acetone from process air The spent air from a production plant contains 1 % mol of acetone and flows at a rate of 2000 m 3 /h at 27 °C. The acetone has to be removed to a final concentration of 100 mg/m 3 by absorption in water in a column packed with 50mm metal Pall rings. The main dimensions of the column, which is operated at the loading point, have to be determined for the case in which the water consumption is 1.4 times higher than the minimum. Solution Average properties of the gas phase \iv
= 28.96 k g / k m o l
QV
= 1 . 1 6 2 kg/m3
T]v
= 18.13 • 10~ 6 k g / m s
Dv
= 10.8 • K T 6 m 2 / s
1^
= 58.08 k g / k m o l
Molar mass of acetone
14.4
Design of an absorber for removing acetone from process air
Average properties of the liquid phase \iL = 18.02 kg/kmol QL = 997 kg/m 3 T) L = 0.857 • 10"3 kg/ms DL = 1.18 • 10~ 9 m 2 /s oL =12 10 3 kg/s 2 Slope of equilibrium curve for the acetoneair/water absorption system YYlYx = 2.314
Packing characteristics (Tables 4.1, 4.3, 4.6 and 5.1) a = 110 m 2 /m 3 E = 0.952 m 3 /m 3
C 5 = 2.725 CL = 1.192 Cy = 0.410
CP = 0.763 Ch = 0.784
Product streams (Fig. 14.2, left) Vu
= 2 0 0 0 ^ • , 1 ^ 2 v ^ m 3  = 80.25 kmol/h ft 28.96 kg/kmol
yM
= 0.01 kmol/kmol
yM
=
V
= 80.25 (10.01) = 79.45 kmol/h
°^^
= 0.01 kmol/kmol
=ino
m3
28.96 kg/kmol 58.08 kg/kmol 1.162 kg/m 3
= 4.291 • 10"5 kmol/kmol 4 291 • 10~5 4 2 9 1
1 4,291 = 4322
"10
kmol/kmo1
3 kmol/kmo1
L
= 1.4 • 183.04 = 256.26 kmol/h = Lo
x
= 0 + T 9 ; 4 ^ (0.01  4.291 • 10' 5 ) = 3.087 • 10~3 kmol/kmol 256.26
u
351
352
14 Examples for the design of packed columns Lo
= 256.26 kmol/h • 18.02 kg/kmol = 4617.7 kg/h
Vo
= 79.45 (1 + 4.291 • 1(T5) = 79.45 kmol/h = 79.45 kmol/h • 28.96 kg/kmol = 2301 kg/h
Resistance coefficient {Eqn (429)} 9.806 2.7252
= 0.629
L162
\ 18.13 • 10~6
2301 \ 997 /
Vapour velocity at the loading point {Eqn (428)}
uv,s =
9.806 0.629 12 9.806
0.952 1101
12 9.806
no1
0.857 • 10~3 uL 997
1/6/
997
0.857
uL 997
\i/2
1.162
Liquid velocity at the loading point {Eqn (1182)} for uL and uv = uv,s 4617.7
1.162
Gas velocity at the loading point determined by solving Eqns (428) and (1182) by iteration uv>s = 1.988 m/s Crosssectional area of column {Eqn (1426)}
A
2300.9/3600 1.162 • 1.988
°277
Column diameter {Eqn (1427)} ds=\—'
0.277 = 0.594 m
Column diameter selected for planning: ^ = 0.6 m Crosssectional area of planned column As = — • 0.62 = 0.2827 m2
2
14.4 Design of an absorber for removing acetone from process air Vapour and liquid loads in the planned column
Uv=
^
=
2300.9/3600 1.1620.2827
=1
4617.7/3600 997  0.2827
= 44 5 555
945m/s 3
'
'
1100
3 2 mm / m S
Theoretical liquid holdup {Eqn (427)} 0.857 • 103 • 4.55 • HT3 • HO2 \ 1/3 )
/
Particle diameter {Eqn (466)} dp = 6 •
1
 ^ p 9 5 2 = 2.618 • 103 m
Wall factor {Eqn (457)} /
\"1
A
= 0.9429 Reynolds number for gas flow {Eqn (465)}
v
1.945 • 2.618 • 10~3 • 1.162 (10.952) 18.13 • 106
°9429 
Reynolds number for liquid flow {Eqn (469)}
u
4.55 • I P 3 • 997 110.0 • 876 • 10 3 "
4 8 1 2
Wetting factor for the packing {Eqn (468)}
Resistance factor in gas flow {Eqn (467)}
Pressure drop per unit height in gas flow {Eqn (458)} Ap H
110 ()R2
(0.952  0.0387)
3
1.162 • 1.9452
1
2
0.9429
= 277.2 Pa/m
353
354
14 Examples for the design of packed columns
Hydraulic diameter {Eqn (515)} rf, = 4
. ^ f = 0.0346m
Phase contact area {Eqn (516)} Eh. — a . n QS? 0  5
a "
3
°952

1 110 • 0.857 • 103
(4^55 • 1 0  y 997 \015 ( (4.55 • 10' 3 ) 2 110 , 0.072 110 / \ 9.806
— U.u/^
Height of transfer unit in the liquid phase {Eqn (55)} 3 0.857 • 101.192 \ 997 • 9.806
L
\ 1/2 /4.55 • 10
0.0346 9
1.18  KT /
\
110
/
\ 0.672 /
= 0.539 m Height of a transfer unit in the gas phase {Eqn (514)} HTTJ HTUv =
l
^^ (0'952 " °° 3 8 7^) T ^ rnos?
n ^ ^ i / 2 003461/2
1.945
10.8 • 106
/IIP  18.13 • IP"6 \ 3 / 4 /l0.8 • IP' 6 • 1.162 \ 1/3 / 1 \ \ 1.945 • 1.162 ) \ 18.13 • 10~6 / \ 0.672/ = 0.456 m Differences in gas loads {Eqns (147) and (148)} AYU = 0.012.314 • 3.807 • 10~3 = 2.864 • 10~3 kmol/kmol AYO = 4.291 • 10~5 2.314 • 0 = 4.291 • 10"5 kmol/kmol Overall number of gasside transfer units {Eqn (146)} 0.014.291  H P 5
MTTI NTUov
=
2.864  IP' 3
2 . 8 6 4  1 0  3  4 . 2 9 1  1 0  5 ' l n 4.291 • 10"5
Stripping factor {Eqn (168)}  2.314 • I9*™1* ^ 0.7174 256.26 kmol/h
=
U
^
14.5 Design of a desorber for removing carbon dioxide from process effluents Overall height of a transfer unit {Eqn (162)} HTUov = 0456 + 0.7174 • 0.539 = 0.843 m Height of bed of packing without allowance for end and distribution effects H = 0.843 • 14.826 = 12.49 m
14.5 Design of a desorber for removing carbon dioxide from process effluents The carbon dioxide content of a process effluent flowing at a rate of 4 m 3 /h is to be reduced from 1.5 kg/m 3 to 0.02 mol/m 3 by desorption with air in a packed stripper column operating at 20°C and 1 bar. The carbon dioxide content of the inlet air is 0.03% vol., and that of the air leaving the desorber outlet must not exceed 1 % vol. The desorption column is to be packed with 35mm plastics Pall rings. Determine its main dimensions. Solution Average properties of the gas phase \iv QV r\v Dv
= = = =
28.96 kg/kmol 1.188 kg/m 3 17.98 • 10~6 kg/ms 15.4 • 10~6 m 2 /s
Data for carbon dioxide \iA = 44.01 kg/kmol QA = 1.818 kg/m 3 Average properties of the liquid phase \iL QL rL DL oL
= = = = =
18.02 kg/kmol 998 kg/m 3 0.998 • 10"3 kg/ms 1.82 • 10~ 9 m 2 /s 72 • 10 3 kg/s 2
Slope of equilibrium curve for the carbon dioxidewater/air system rriyx = 1440 Characteristic data for the packing derived from Tables 4.1, 4.3, 4.6 and 5.1 a = 145 m 2 /m 3 8 = 0.906 nr7m 3
Cs = 2.654 CL = 0.856 Cv  0.380
CP = 0.927 Ch = 0.718
355
356
14
Examples for the design of packed columns
Product streams corresponding to Fig. 14.2, right to
= 4 • 998 = 3992 kg/h = 4 •~ ^ 
X
°
=
= 221.53 kmollh
1 5
" ' 4408l'02998
X
° = 1 + 054 1( Vo4
= 6154
" 10 " 4
kmol/kmo1
= 6 15
 ° • 10"4 k m o l / k m o 1
L
= 221.53 (1  6.150 • 10"4) = 221.39 kmol/h
y
=
"
0 3 10 2 °°0 3 10~ 4I01 I • liliiss3 =°3 °22
kmol/kmo1
4
Yu
=
t
3 02 • 10~ "3 Q 2 1Q_4 = 3.02 • 10"4 kmol/kmol
= 0.01 • ^
; \™
= 0.01007 kmol/kmol
18 09 = 0.02 • 10"3 • —^— = 3.614 • 10~7 kmol/kmol Total mass balance
K
= 13,80 (1 + 0.01017) = 13.94 kmol/h  13.94 • 28.96 = 403.71 kg/h
K
 13.80 • 28.96 (1 + 3.02 • HT4) = 399.77 kg/h 399
 7 7 = 336.50 m 3 /h 1.188
Lu
= 221.39 • 18.02 (1 + 3.614 • 10~7) = 3989 kg/h
Resistance coefficient {Eqn (429)}
2.654
3989.45 399.77
9.806 1.188 1;2 0.998 • 10" 998 / 17.98 • 10"
0.4 10.652
14.5 Design of a desorber for removing carbon dioxide from process effluents Vapour velocity at the loading point {Eqn 428)} 9.806 \ 1/2 [ 0.906 1.980 / [ 1451/6 12 9.806
1/2
/ 12 \ 9.806
0.998 • 10~3 uL 998
0.998 • 10~3 uL \1161 998 998 / \ 1.188
Liquid velocity at the loading point {Eqn (1182)} for uL and uvs 3989.45 399.77
1.188 998
Uy s
'
Gas velocity at the loading point determined by solving Eqns (428) and (1182) by iteration uVjS = 1.195 m/s Crosssectional area of column {Eqn (1426)}
As
=
399.77/3600 1.1881.195
=
Column diameter {Eqn (1427)} ds = \
— • 0.0739 = 0.316 m
Column diameter selected for planning: ds = 0.32 m Crosssectional area of planned column As = —  0.322 = 0.0804 m2 Vapour and liquid loads in the planned column
Uv=
399.77/3600 1.1880.0804
^rn , 163m/s
=1
3989.45/3600 UL =
998 • 0.0804 =
3 13 8
'
'
10
Theoretical liquid holdup {Eqn (427)} 0.998 • 10"3 • 13.8 • 10~3 • 1452 \ 1/3 = 0.0708
357
358
14
Examples for the design of packed columns
Particle diameter {Eqn (466)}
=
= 3.890 • 1(T3 rn
6
Wall factor {Eqn 457}
Reynolds number for gas flow {Eqn (665)} 1.163 • 3.890 • 10~3 • 1.188 (1  0.906) 17.98 • 10~6
0.9206 = 2927
Reynolds number for liquid flow {Eqn (469)}
=
*«•
13.8 • 103 • 998 145 • 0.998
Wetting factor for the packing {Eqn (468)}
Resistance factor in gas flow {Eqn (467)}
o ^"•"'
^2927
' 2927 008 M
™j 0.906
= 1.284
Pressure drop per unit height in gas flow {Eqn (458)} Ap H
_ ~
1.188 • 1.1632
145 '
' (0.906  0.0708)
3
1 = 240Pa/m 0.9206
Hydraulic diameter {Eqn (515)}
dh = 4 • ° ^ — = 0.02499 m 145
Phase contact area {Eqn (516)}
a
=
3
3 • 0.906  (( 138 • 10 • 9983 \ 145 • 0.998 • 10"
p
(13.8 • IP' 3 ) 2  998 \ 0 7 5 / (13.8 • 10"" 33))22 145 \'Q45 = 0.799 0.072 • 145 9.806
14.5
Design of a desorber for removing carbon dioxide from process effluents
359
Height of transfer unit in the liquid phase {Eqn (55)} _ L
1
/ 0.998 • 1(T 3 \ 1 / 6 / 0.02499
~ 0.856 \ 998 • 9.806 j
\ 1 / 2 /13.8 • 10~3 \ 2 / 3 / 9
\ 1 . 8 2 • 10~ f
\
145
/
1
= 0.772 m Height of a transfer unit in the gas phase {Eqn (514)}
145 • 17.98 • 10"6 \ 3M /15.4 • 10"6 • 1.188 \ 1/3 / 1 \ _ 1.1631.188 / 1 17.9810 6 / \o.799/~ °'187
m
Differences in gas loads {Eqns (1416) and (1417)} AXO = 6.154 • 10"4 AXU = 3.614 • 10"7 
° ' 0 i 0 ^ 7 = 6.083 • 10~4 kmol/kmol 1440 3 02 • 10~4 — = 1.516 • 10~7 kmol/kmol 1440
Number of liquidside transfer units {Eqn (1415)}
NTUoL oL
6.154 • 10~4  3.614 • 10~7 ~ 66.083 0 8 3 • 105 1 6 • 10"' lO" 7 1044  1 1.516
/ 6.083 • 10"4 = 8.39 \ 1.516 • 10"
Stripping factor {Eqn (168)}
221.39 kmol/h Height of an overall transfer unit {Eqn (163)} HTUOL
= 0.772 +
X
• 0.187 = 0.774 m
Height of bed if end and distibution effects are neglected {Eqn 165)} H = 0.774 • 8.39 = 6.494 m
\
\ 0.799 /
360
14
Examples for the design of packed columns
14.6 Determination of the difference between the theoretical and the real liquid holdup The purpose here is to determine the differences between the theoretical and the real liquid holdups applicable to the loading conditions under which the columns discussed in Sections 14.4 and 14.5 were operated. Solution Known values in Section 14.4 Ch = 0.784 a
= 110 m 2 /m 3
QL = 997 kg/m 3
uL
= 4.55 • 10~3 m 3 /m 2 s
i\L = 0.857 • 10~3 kg/ms
ReL = 48.12
Froude number for the liquid phase {Eqn (427)} = L
HO (455 • I C Y 9.806
.
=
1Q_4
Hydraulic area {Eqn (475)} — = 0.85 • 0.784 • 48.1 0 2 5 (2.322 • 10~ 4 ) 01  0.760 a Real liquid holdup {Eqn (473)}
= 0.0322 m 3 /m 3 Calculated difference between the theoretical and real holdups AhL
0.03870.0322
=
"TiT
^^
=
°'m
Known values in Section 14.5 Ch = 0.718 a = 145 m 2 /m 3
QL = 998 kg/m 3 r\L = 0.998 • 10~3 kg/ms
Froude number for the liquid.phase {Eqn (427)}
uL = 13.8 • 10"3 m 3 /m 2 s ReL = 95.17
14.7 Additional column height required to compensate maldistribution
361
Hydraulic area {Eqn (475)} — = 0.85 • 0.718 • 95.17 025 (2.816 • 10~3)01 = 1.060 a Real liquid holdup {Eqn (473)}
= 0.0736 m 3 /m 3 Calculated difference between the theoretical and real holdups AhL hL
0.0708  0.0736 =  0.039 0.0708
14.7 Additional column height required to compensate maldistribution In a column of ds = 2250 mm diameter packed with 50mm Pall rings, the liquid distributor gives rise to maldistribution of M = 10%. The phase ratio is LIV = 1. If the maldistribution were to remain effective over the entire height of the column, what would be the additional column height required to compensate the attendant loss in efficiency? Solution The loss in efficiency can be read off from the diagram in Fig. 8.12 against the value 4 _ 2250 _ d ~ 50 ~ 4 5 The numerical value thus obtained is AE = 15%. In other words, the efficiency would be reduced by a factor {Eqn (824)}
Hence, the relative increase in height required to compensate the maldistribution is given by
362
14
Examples for the design of packed columns
14.8 Retrofitting a plate column with packing for steam distillation of crude oil In order to avoid thermal decomposition, the partial pressure of the hydrocarbon vapour must not be allowed to exceed 34 mbar at the lower end of the intermediate zone in a vacuum column (pT = 1 0 0 mbar) designed for fractionating crude oil by steam rectification. The plates previously used (subscript 2) gave rise to a pressure drop of 110 mbar between the head of the column and the intermediate zone. After the column had been retrofitted with lowpressuredrop packing (subscript 1), the pressure drop was only 70 mbar. How much steam has thus been saved? Solution According to Eqn (1250), the pressure drop after retrofitting is given by p PT=
{i  l) ^£] = 70 mbar
The pressure drop before retrofitting is given by
p
PT=
(i  1) (  ^  1 = 110 mbar
According to Eqn (1263), the factor k for the difference in pressure drop is given by
Ano
Ap_\ ~ 70 nt
l57
/i
The relative savings in steam achieved by the installation of packing follows from Eqn (1267), i.e. AS
^T
1.571 = 15? L57 +
10034 = ° 226 ~1Q~
The volume flow rate of steam per unit flow rate of the hydrocarbon vapours after retrofitting is obtained from Eqn (1264), i. e. Sj_= V ~
100 + 7 0  3 4 34
The corresponding flow rate before retrofitting is obtained from Eqn (1265), i.e. $2_ _ 100 + 1 1 0  3 4 V " 34 "
7
14.9
Reduction in height effected by redistributors
363
Therefore, the savings in steam per unit flow rate of product vapour is as follows:
The same figure can be obtained from Eqn (1266), i. e.  ^  = ^ • • 7 0 (1.571) = 1.17 The savings in steam achieved by substituting packing for fractionating plates can be determined from the values obtained for AS IV and S2/V, i. e.
100 =5.17 v^~
10
° = 22  6 %
14.9 Reduction in height effected by redistributors It is intended to separate a mixture in a packed column with 30 transfer units, 35mm metallic Pall rings, and optimum inlet distribution. How much height would be saved by installing three redistributors? Solution Assume that the inlet effect and the data describing the efficiency are identical to those listed in Table 9.1. In this case, the effective height of the column without redistributors is given by Eqn (920), i.e. (HT)nr
=
o = [30  (0.5 + 1.9)] • y j ^ = 13 m
The relative reduction in the height of the bed can be read off against nr = 3 in the upper diagram shown in Fig. 9.7. Thus, AH/HT = 0.26 The absolute reduction in height is therefore AH = 0.26 • 13 = 3.4 m Hence, the total effective height of the bed with three redistributors is (HT)nr = 3 = 1 3  3 . 4  9.6 m
364
14
Examples for the design of packed columns
and the effective height between the redistributors is
r
3 + 1
This value can also be read off on the axis of abscissae against nr = 3 in Fig. 9.7. Assume further that the height occupied by a redistributor in the column is hr = 0.4 m. According to Eqn (950), the relative reduction in the total height would then be F^H
= 1  — [2.4 (3 + 1) + 3 • 0.4] = 0.169
The absolute saving in the height of the column shell is therefore AHS = 0.169 • 13 = 2.2 m
14.10 Advantages of geometrically arranged packing in fractionating fatty acids A modern plant for processing palmkernel oil consists of nine distillation stages in tandem. The plans for process optimization included the improvement of product quality by an appropriate choice of column internals. A Hermann Stage method was adopted for the design.
Solution Since the feedstock is sensitive to heat, the distillation stages were designed with structured packing and fallingfilm evaporators. As a consequence, the residence times were very short, and the bottom temperatures were comparatively low (Fig. 14.5). The effects on the product quality were as follows. The overhead product in each stage ranging from Column 2 (octanoic acid) to Column 5 (myristic acid) is the pure distillate of the unhydrogenated crude acid concerned. Its purity is higher than 99 % during continuous operation and even higher than 99.5 % for lauric (Ci2) and myristic (Ci4) acids. Owing to the unsaturated Cw fraction, the purity of the palmitic acid in the sidestream distillate of Column 8 is only just higher than 97 %. Since the linoleic acid fraction (Ci8») in the feed is higher than that of the oleic acid (Ci 8 ), the sidestream distillate in the next column downstream (Column 9) contains only 85% of oleic acid (Ci 8 H); the remainder consists of 810% of linoleic acid (Ci8») and 4  5 % of stearic acid. If the transfatty acid content is less than 0.5%, the oleic acid content in this fraction is higher than that attained in the Henkel or AlphaLaval detergent processes. The flow chart shown in Fig. 14.5 for a fatty acid fractionating plant includes the continuous cracker, the glycerolwater evaporation unit, and the pure glycerol distillation column. The two latter also incorporate a Hermann Stage process and the associated engineering. The entire plant has been on stream in Malaysia since 1992.
14.11 Recovery of acetone from production effluents by liquidliquid extraction
365
O
W)
14.11 Recovery of acetone from production effluents by liquidliquid extraction A production effluent containing 0.241 kmol/m 3 of acetone is to be purified by liquidliquid extraction with toluene. The packed column is to be designed and operated for 80 % acetone recovery. The intended packing is 25mm Bialecki rings. The column diameter and the effective height of bed should permit the effluent to flow at a rate of 1557 m 3 /h, the column load may not exceed 35 % of that at the flood point, and the extractant is toluene flowing at a rate of 2829 m 3 /h.
366
14
Examples for the design of packed columns
Solution Characteristic data for systematically stacked Bialecki rings (cf. Table 13.2) E /
 0.928 = 0.050 m
Cm = 0.67 Ch = 2.151 Cd = 1
Physical properties of the system QD = 857 kg/m 3
QC = 9 9 8 kg/m3
TD = 0.55 • 10~3 kg/ms DD = 2.478 • 10~9 m 2 /s a = 0.026 kg/s 2 Phase flow ratio uD uc
r c  0.893 • 10"3 kg/ms Dc = 1.3 • 10"9 m 2 /s m = 0.64
2.829 = 1.82 1.557
Dispersed phase holdup {Eqn (1320)} (1822 + 8 • 1.82) 1 / 2 3 • 1.82
u h
3
=
4 ( 1  1 . 8 2 ) ° '
3 7 5 m
3
/m
Droplet velocity {Eqn (133)} 9.81 (998  857) 0.026 9982
= 0.1096 m/s
Velocity of continuous phase at the flood point {Eqn (1316)} uc,m = 0.67 • 0.928 • 0.1096 (10.375) 2 (1  2 • 0.375) = 6.6 • 10~3 m 3 /m 2 s Velocity of continuous phase under operating conditions uc = 0.35 • 6.6 • 10~3 = 2.31 • 10' 3 m3/m2s Diameter of extraction column {Eqn (1435)} 4_ 1.557/3600
_
JT ' 2.31 • 10~3
~
>488
m
Velocity of dispersed phase under operating conditions uD = 1.82 • 2.31 • 10~3 = 4.21 • 10"3 m 3 /m 2 s
14.11
Recovery of acetone from production effluents by liquidliquid extraction
Dispersed phase holdup under operating conditions {Eqn (1311)}
" * Mass transfer constant {Eqn (1339)}
Cm
i v °o5°
Height of overall transfer unit {Eqn (1347)} 0.0265'8
1
TJrTJJ oc
1
~ 37.32 ' [9.81 (998857)] 3 / 8 • 9981/4' 1.82
1 (1.3 • 10" 9 ) 1/2
+
1 0.64
1 (2.478 • 10~9)1/2
998 . 857
„ „A = 1.14
Concentration of continuous phase after extraction {Eqn (1433)} cCu = (1  0.8) 0.241  0.0482 kmol/m 3 Concentration of solvent after extraction {Eqn (1434)} cD,o = ~rzr (0.241  0.0482) + 0 = 0.1059 kmol/m 3 1.82 Driving concentration difference at the head of the column {Eqn (1430)} Aco = 0.241 —^— • 0.1059  0.0755 kmol/m 3 0.64 Driving concentration difference at the foot of the column {Eqn (1431)} Acu = 0.0482  —  — • 0  0.0482 kmol/m 3 0.64 Number of overall transfer units in the continuous phase {Eqn (1429)}
oc
0.241  0.0482 ~ 0.0755  0.0482 '
Effective height of bed {Eqn (1322)} H = 1.14 • 3.17 = 3.61 m
0.0755 n
^
1?
367
15 Recent trends in packing technology Solid particles suspended in the vapour and liquid phases may clog beds of packing in many environmental engineering processes. This likelihood can be overcome by fluidizing the beds. Although fluidization allows higher gas flow and mass transfer rates to be realized, hesitation has been shown in the past in adopting it on an industrial scale for packed towers. The reasons for the reluctance were the lack of design correlations and the difficulties involved in homogeneously fluidizing the bed without an attendant high pressure drop in the bottom grid. Further research on the subject has been instigated by the development of a hollow, thinwall, ellipsoidal packing element, the performance characteristics of which allow excellent prospects to be envisaged in industrial aplications.
15.1 Fluidized beds of packing The design and operation of a fluidized bed consisting of this hollow, ellipsoidal packing on a supporting grid are illustrated in Fig. 15.1. The pressure drop in the gas stream flowing in the void fraction is brought about by the shear forces that act between the gas, liquid, and packing. When it is in equilibrium with the weight per unit crosssectional area of packing and the liquid, the bed will start to expand. This stage is referred to as the onset of fluidization. At gas flow rates higher than that at equilibrium, the bed loosens and the elements of packing are free to flow, with the consequence that the interfacial area available for mass transfer is renewed. If the open area of the supporting grid is higher than about 80 %, the density of the packing is the factor that decides whether the phase load at the onset of fluidization will be lower than, equal to, or higher than the flooding load in a comparable fixed bed (cf. Fig. 15.2).
Demister
Gas outlet
A
.Liquid teed x
^"^
Liquid distributor Retaining grid Supporting grid
Liquid outlet Fig. 15.1. Fluidizedbed contactor (left) before onset of fluidization (right) fluidized Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3527286160
370
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Recent trends in packing technology
a =5
Fig. 15.2. Effect of the density Q of the packing on the operating mode of a fluidized packed bed
Gas capacity factor Fv
Qi > Qi > Q3
According to the literature, packing of density less than 300 kg/m 3 allows scrubbers to operate in the nonflooding mode. The density of the hollow ellipsoidal packing, viz. 160 kg/m 3 , is well below this figure.
15.2 Hydrodynamics of fluidized packed beds The load at which beds of the hollow ellipsoidal packing fluidize corresponds to the flooding load in static beds. The relationship between the pressure drop in the fluidized bed and the gas capacity factor F v at constant liquid loads is shown in Fig. 15.3. The conditions for onset of fluidization, i.e. the minimum gas and liquid flow rates, in beds of hollow ellipsoidal packing can be seen in Fig. 15.4. An increase in the liquid load entails a reduction in the free volume of the bed and thus a lower gas velocity at the onset of fluidization. The velocity in the flow channels within the bed and thus the force of friction between the gas and the packing remain approximately constant. An increase in the gas capacity factor normally leads to higher values of the forces that act on the single elements in the bed. Since the bed continues to expand with an increase in the gas flow rate, high local velocities are avoided, and the pressure drop remains almost constant (cf. Fig. 15.3). The relationship between the extent to which the bed expands and the gas capacity factor is shown in Fig. 15.5.
15.3 Mass transfer in fluidized packed beds Fig. 15.6 shows the results of measurements of the mass transfer efficiency, expressed as the height of an overall mass transfer unit HTUcw, in a fluidized packed bed. The measurements were performed on an ammoniaair/water system in a packed column of 0.288 m diameter. It is important to note that the values of HTUOV in Fig. 15.6 are related to the static bed height. The actual height of the bed can then be obtained from Fig. 15.5. Up to the onset of fluidization, the performance is similar to that in most static beds of packing. Owing to the movement of the bed at higher loads, the efficiency remains almost constant as the gas flow rate increases.
75.3
Mass transfer in fluidized packed beds
Liquid load : u L [ m 3 / m 2 h ]
„
a10,o20(o30
50
/ to,
ex.
\
lu
J 30
/
>
•o—
}—
—(. o—tr^ 33u C
—D
Mr
I 20
d s =0.288 m, H stQt = 0.35 m — 1 bar, 293K,Air/Water
CD
10
V
&
0.5
2.5
1.5 Gas capacity factor F v [rfi
3.5
1
1/z
s" kg ]
Fig. 15.3. Pressure drop in a fluidized bed of 0.35 m static height for various liquid loads uL as a function of the gas capacity factor Fv. Bed packed with plastic 35/50mm Euromatic ellipsoids
Static bed ratio H s t Q t / d s = • 0.3, • 0 . 6 , A 0,9 \M
i
1.3
 Air/Water ,1 bar . 293 K J S = 0.288 m
i
1.2
s r
1.1
I
D
U
1.0
oq 5
10
15
20
Liquid load
25
30 3
35
40
2
u L [m /m h]
Fig. 15.4. Gas capacity factor Fv as a function of the liquid load uL for various ratios of the static bed height to the column diameter Hstat/ds at the onset of fluidization. Bed packed with plastic 35/50mm Euromatic ellipsoids
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15 Recent trends in packing technology
Liqid load : u L [ m 3 / m 2 h ]
o i o , a 2 0 , A 30
J
3.0
H s t a ,/d s = 0.6 d