Thermal Separation Processes

Klaus Sattler, Hans Jacob Feindt

Thermal Separation Processes

0 VCH Vcrlagsgescllschaft mbH, D-60451 Wcinheim (Federal Rcpuhlic ot Germany). IWS

Distribution:

VCH, P.0. Box 10 1161. D-69451 Weinheim. Federal Kcpublic of Germany

Switzerland: VCH. P.O. Box. CH-4020 Bascl. Switzerland

LJnitcd Kingdom and Ireland: VCH, 8 Wellington Court. Cambridge CBI 1HZ. United Kingdom USA and Canada: VCH, 220 East 23rd Street. New York, NY 10010-4606. USA

Japan: VCH. Eikuw Building, 10-9 Hongo 1-chomc. Bunkya-ku, Tokyo 113. Japan

ISBN 3-527-28622-5

Klaus Sattler, Hans Jacob Feindt

Thermal Separation Processes Principles and Design

Weinheim - New York Base1 - Cambridge - Tokyo

Prof. Dipl.-Ing. Klaus Sattler Fachhochschule fur Technik Speyerer Stral3e 4 D-68163 Mannheim

Dr. Hans Jacob Feindt BASF AG Abteilung Verfahrenstechnik D-67056 Ludwigshafen

This book was carefullyproduced. Nevertheless, authors and publisher donotwarrant 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. Weinheim (Federal Republic of Germany) VCH Publishers. New York. NY (USA)

Editorial Directors: Philomena Ryan-Bugler, Louise Elsam, Karin Sora Production Manager: Claudia Gross1

Library of Congress Card No. applied for A catalogue record for this book is available from the British Library

Die Deutsche Bibliothek - CIP-Einheitsaufnahme Sattler, Klaus: Thermal separation processes : principles and design / Klaus Sattlcr ; Hans Jacob Feindt. - 1. ed. Wcinhcim ; Ncw York ; Bascl ; Cambridge ; Tokyo : VCH, 1995 ISBN 3-527-28622-5 (Weinheim ...) N E : Feindt, Hans Jacob:

0VCH Verlagsgesellschaft m b H , D-69451 Wcinhcim (Federal Rcpublie of Germany), 1995 Printed on acid-free and low-chlorine paper

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form-byphotoprinting,microfilm.or anyother means-nortransmittedartranslated intoamachinelanguage without written permission from the publishers. Registered names, trademarks, etc. used in this book. even when not specifically marked as such, are not to bc considcrcd unprotected by law. Composition: Filmsatz Unger & Sommcr GmbH, D-69469 Weinheim Printing and Bookbinding: Druck haus ,Thomas Muntzer" GnibH, D-99947 Bad Langcnsalza Printed in the Federal Repuhlie of Germany

Foreword

The separation of gaseous and liquid solutions into their components and the drying of wet products have always been an integral part of the manufacture of products in the chemical, petroleum, food, and pharmaceutical industries. As environmental protection has become an increasingly important consideration to industry, separation processes have become more important in direct proportion. This book provides a clear fundamental development of the technology of important separation processes. As indicated by the title the book deals with separation processes in which heat is an input to the complete process of separating the constituents of a mixture. The flow of heat in the process is clear in distillation, crystallization and drying but is not so obvious in absorption, extraction and adsorption, where the heat flow is required to regenerate the solvent or adsorbent.

Each of these six subjects is given thorough coverage in its own chapter. These chapters follow a comprehensive development of the physical chemistry and engineering which provide the principles upon which the separation processes are based. The individual process treatments cover computational algorithms, equipment design criteria and energy conservation. The overall treatment permits the evaluation of competing separations techniques and the choice of the optimal process. This book is intended as a college or university level text for students in chemical engineering and related fields. It is also complete enough and detailed enough in its development of each topic to be useful as a reference for practicing engineers both new to and experienced in the area of separations. CCNY, New York May 1994

Prof. H. Weinstein

Preface

This book, transformed from the original German by Dr. H. J. Feindt, is based on two German editions “Thermische Trennverfahren”, published by Prof. K. Sattler. They have been successfully used as textbooks for university and college students and as reference texts in seminars and training programs for practising engineers in Germany, Austria and Switzerland. The book presents a clear and very practice-oriented overview of thermal separation technologies. An extensive introduction elucidates the physical, physico-chemical, and chemical engineering fundamentals and principles of the different unit operations used to separate homogenous gaseous and liquid mixtures. The introduction is followed by a concise text with many explanatory figures and tables referring to process and basic design, flow-sheets, basic engineering and examples for the application of the unit operations distillation, absorption, adsorption, drying, liquid-liquid and solid-liquid extraction, evaporation and crystallization of solutions, melt crystallization and desublimation. A comprehensive reference list allows follow up of special separation problems. The book enables the reader to choose and evaluate thermal separation processes and to model and design the necessary separation plant equipment.

Chemical and mechanical engineers, chemists, physisists, bio-technologists in research and development, plant design, production, environmental protection and administration and students in engineering and natural sciences will find this treatment of exceptional value and practical use. Due to the quantity of the topics covered exercises could not be included in this book. An additional collection of illustrations with reference to basic engineering and design of the necessary equipment of thermal separation units is available in German (Sattler, K. : Thermische Trennverfahren. Aufgaben und Liisungen, Auslegungsbeispiele) and will be translated into the English language. We are very much obliged to Prof. H. Weinstein, City University of New York for his advice and his Foreword to this book. Many thanks are also given to Philomena Ryan-Bugler, Louise Elsam, Karin Sora and the production team of VCH Verlagsgesellschaft for the accurate lectorship and book production. Special thanks are also given to Paul Fursey, University of Bradford, United Kingdom, for his assistance in copy-editing. Briihl, Ludwigshafen December 1994

K. Sattler H. J. Feindt

Contents

Frequently Used Nomenclature XV

1

Basic Concepts 1

1.1

Principles of Thermal Separation Processes

1.2

Thermal Separation Process Modes

1.3 1.3.1 1.3.2 1.3.3

Mass Balance, Energy Balance, Exergy Balance Mass, Energy and Heat Balances 8 Exergy Balance 12 Calculation of Balance Equations 13

1.4 1.4.1 1.4.1.1

1.4.6

Phase Equilibria 14 Basic Concepts 14 General Differential Equation for the Equilibrium Between Two Phases 17 The Gibbs Phase Rule 18 Liquid-Liquid Equilibrium 19 The Nernst Distribution Law 19 Representation of Liquid-Liquid Phase Equilibrium 23 Vapor-Liquid Equilibrium 28 One Component Systems 28 Two and Multicomponent Systems 30 Henry’s Law, Gas Solubility 44 Boiling Equilibrium of a Solid Solution, Decrease of Vapor Pressure and Increase of Boiling Point 51 Gas-Solid Phase Equilibrium 52 Gas-Solid Phase Equilibrium, Sublimation 52 Gas-Solid Phase Equilibrium with Adsorption/Desorption and Convective Solid Drying (Adsorption Equilibrium) 54 Liquid-Solid Phase Equilibrium 60 Solubility of Solids in Liquid Solvents 60 Melting Pressure Curve 62 Decrease in the Freezing Point 63 State Diagrams of Binary Systems for Solid and Liquid Phase Equilibrium 65 Enthalpy of Phase Changes 65

1.5

Separation Factor and Relative Volatility

1.6

Minimum Separation Work

1.4.1.2 1.4.2 1.4.2.1 1.4.2.2 1.4.3 1.4.3.1 1.4.3.2 1.4.3.3 1.4.3.4 1.4.4 1.4.4.1 1.4.4.2 1.4.5 1.4.5.1 1.4.5.2 1.4.5.3 1.4.5.4

67

1

7

67

8

X

Contents

1.7 1.7.1 1.7.1.1 1.7.1.2 1.7.1.3 1.7.2 1.7.3 1.7.3.1

Mass Transfer Fundamentals 68 Mass Transfer by Molecular Diffusion 69 Steady-State Diffusion 69 Unsteady-State Diffusion 70 Diffusion Coefficient 70 Mass Transfer by Convection 72 Overall Mass Transfer 74 Two Film Theory, Mass Transfer Coefficient and Turbulence Theory

1.8

Steady-State Cocurrent Operation

1.9 1.9.1 1.9.2

1.9.4 1.9.4.1 1.9.4.2

Steady-State Countercurrent Operation 79 Theory of Separation Stages 79 Method to Determine the Number of Theoretical Separation Stages for a Countercurrent Column 82 Calculation for Counterflow Columns 86 Mass Balances 89 Phase Equilibrium Relationship 89 Enthalpy Balances 89 Stoichiometric Conditions for the Sum of the Concentration at Each Equilibrium Stage 90 Kinetic Theory for the Counterflow Separation of a Mixture 90 Two-Directional Mass Transfer Between Phases 91 One-Directional Mass Transfer 92

1.10

Steady-State Crossflow Operation

1.11

General Procedure to Design Equipment for the Thermal Separation of Mixtures 94

2

Distillation and Partial Condensation 101

2.1

Concepts of Simple Distillation, Rectification and Partial Condensation 101

2.2 2.2.1 2.2.2 2.2.3 2.2.4

Discontinuously and Continuously Operated Simple Distillation, Flash Distillation 103 Discontinuously Operated Simple Distillation 103 Continuously Operated Simple Distillation 107 Heat Requirement of Simple Distillation Units 109 Flash Distillation 111

2.3

Carrier Distillation

2.4

Vacuum and Molecular Distillation

2.5 2.5.1 2.5.1.1

Countercurrent Distillation (Rectification) 119 Process Variations of Rectification 119 Continuously Operated Rectification in Rectification Columns with Enriching and Stripping Zones 119 Stripping (Exhausting) Column 120

1.9.3 1.9.3.1 1.9.3.2 1.9.3.3 1.9.3.4

2.5.1.2

75

77

94

113 116

Contents

XI

2.5.4 2.5.5 2.5.6 2.5.6.1 2.5.6.2

Enrichment Column 121 Carrier Rectification 123 Combinations of Different Variations 123 Rectification with an Entrainer 123 Heteroazeotropic Rectification 129 Two Pressure Operation 130 Diffusion Distillation 131 Overpressure, Low Temperature and Vacuum Rectification 132 Continuous Adiabatic Rectification 134 Flow Rates 135 Heat Requirement of a Column 136 Energy Saving Steps 138 Determination of the Number of Separation Stages and Column Height for Heat and Mass Transfer 147 Minimum Reflux Ratio, Optimal Economic Reflux Ratio 157 Feed Stage 157 Discontinuous Adiabatic Rectification 158 Amount of Overhead Product 160 Heat Requirement 161 Still Diameter, Free Vapor Space, Column Diameter 162 McCabe-Thiele Method to Determine the Number of Theoretical Separation Stages 163 Semicontinuous Adiabatic Rectification 163 Determination of the Column Diameter 164 Internals in Rectification Columns 165 Column Trays 167 Random Packing, Packing with Regular Geometry 196

2.6

Choice, Optimization and Control of Rectification Units

2.7

Rectification Units Accessories 218

2.8

Parallel Flow Distillation

2.9

Nonadiabatic Rectification

2.10

Partial Condensation

3

Absorption

3.1 3.1.1 3.1.2

Principle of Absorption and Desorption, Processes and Process Examples 239 Concepts and Process Examples 239 Process Examples 240

3.2

Requirements of the Wash Liquid or Solvent, Solvent Consumption 243

3.3

Enthalpy and Heat Balances

3.4

Cocurrent Phase Flow Absorption

2.5.1.3 2.5.1.4 2.5.1.5 2.5.1.6 2.5.1.7 2.5.1.8 2.5.1.9 2.5,l. 10 2.5.2 2.5.2.1 2.5.2.2 2.5.2.3 2.5.2.4 2.5.2.5 2.5.2.6 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.5.3.4

216

222 222

230

239

246 248

XI1 3.5 3.5.1 3.5.2

Contents

Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns 248 Determination of the Column Cross-Sectional Area 248 Determination of the Number of Stages and Column Height for Mass and Heat Transfer 250

3.6

Types of Absorber

3.7

Regeneration of the Solvent, Desorption

4

Adsorption 281

4.1 4.1.1 4.1.2

Principles of Adsorption and Desorption, Processes and Examples 28 1 Concept 281 Processes and Examples 282

4.2 4.2.1 4.2.2 4.2.3

Adsorbents, Selection of Adsorbent 291 Adsorbents 291 Requirements for the Adsorbent, Adsorbent Selection 291 Technical Adsorbents, Characteristic Data of Adsorbents 293

4.3

Adsorption Kinetics

4.4 4.4.1 4.4.2 4.4.3

Variation of Adsorption, Design of Adsorbers 301 Single Stage Adsorption in a Vessel Adsorber with Adsorbent Packing Multistage Adsorption with Cross Flow of Gas and Adsorbent Phases 307 Multistage Countercurrent Adsorption 308

4.5

Adsorber Types 310

4.6

Desorption, Regeneration of Loaded Adsorbent

5

Drying

5.1

Concepts, Processes and Examples

5.2

Characteristics of the Moist Product, Movement of Moisture

5.3

Properties of Wet Gases, h-X Diagram

5.4

Mass and Heat Transfer in Convection Drying

5.5

Drying Kinetics, Course of Drying, Drying Time

5.6 5.6.1 5.6.2 5.6.3

Convection Drying 340 Drying Gas and Heat Requirements in Convection Drying Steps in Energy Saving 343 Variations of Convection Drying 346

5.1

Contact Drying

5.8

Radiation Drying

262 263

293

311

317

349 351

317 320

324 331 335 340

301

Contents

5.9

Dielectric Drying

5.10

Freeze Drying (Sublimation Drying) 355

XI11

352

Design of Dryers 357 Overview of Dryers, Dryer Selection and Design 357 Individual Presentation of Selected Dryer Types with Design Aids 363 Chamber Dryer 363 Tunnel Dryer 364 Belt Dryer 364 Multiple Plate Dryer 364 Rotary Dryer 364 Fluidized Bed Dryer 366 Air-Flow Dryer, Pneumatic (Flash) Dryer 374 Spray Dryer 377 Drum Dryer 381 Thin Film Evaporation Dryer (Vertical and Horizontal Dryer) 381 5.1 1.2.11 Contact-Mixing Dryer 381 5.11.2.12 Contact Dryer with Continuous Product Movement due to Gravity 385 5.11.3 Process Control of Dryers 387 5.11 5.11.1 5.11.2 5.1 1.2.1 5.11.2.2 5.1 1.2.3 5. 11.2.4 5.11.2.5 5.11.2.6 5.11.2.7 5.1 1.2.8 5.11.2.9 5.1 1.2.10

6

Extraction 393

6.1

Basic Concepts and Processes 393

6.2 6.2.1 6.2.2 6.2.3 6.2.3.1 6.2.3.2 6.2.3.3 6.2.3.4 6.2.3.5 6.2.3.6 6.2.4 6.2.4.1 6.2.4.2 6.2.5

Liquid-Liquid Extraction 395 Fields of Application and Process Examples 395 Solvent Requirements, Selection of Solvent 399 Liquid-Liquid Extraction Variations 400 Single Stage Extraction 400 Differential Stagewise Extraction 403 Multistage Cross-Current Extraction 403 Multistage Countercurrent Extraction 407 Countercurrent Extraction with Extract Reflux 421 Countercurrent Distribution 424 Design Forms of Extraction Apparatus 424 Mixer-Settler, Mixer-Settler Cascade 425 Countercurrent Columns with and without Energy Supply 426 Selection and Design of Extraction Apparatus 456

6.3

Solid-Liquid Extraction (Leaching) 458

6.4

High Pressure Extraction (Distraction) 463

XIV

Contents

7

Solvent Evaporation, Crystallization 475

7.1

Basic Concept and Processing Modes of Crystallization

7.2 7.2.1 7.2.1.1 7.2.1.2 7.2.1.3 7.2.1.4 7.2.1.5 7.2.2 7.2.2.1 7.2.2.2 7.2.3 7.2.4 7.2.5 7.2.6 7.2.7

Crystallization from a Solution 484 Concentration of Solutions by Evaporation 485 Single Stage Solution Evaporation 486 Multistage Solution Evaporation 487 Solution Evaporation with Mechanical and Thermal Vapor Compression 492 Multistage Flash Evaporation 498 Types of Evaporators to Concentrate Solutions 500 Balancing of Crystallizers 500 Crystal Product Rate 500 Heat Exchange During Crystallization 506 Crystallization Kinetics, Crystal Seed Formation, Crystal Growth 508 Design of Crystallizers for Mass Crystallization from a Solution 511 Criteria for the Selection and Design of Crystallizers 516 Freezing 519 Fractional Crystallization of a Solution 520

7.3

Crystallization from a Melt

7.4

Crystallization from a Vapor Phase, Sublimation and Desublimation

8

Documentation and Calculation of Physical Characteristics 533

General References 537 Index 539

475

521 524

Frequently Used Nomenclature

A

Area

m2

AQ

Cross sectional area, cross section

m2

D D,D

Diffusion coefficient

m2/h

Vapor; vapor flow rate

kg, kmol; kg/h, kmol/h

E

Enrichment ratio, stage efficiency factor

F

Force

N

F

Loading factor for column trays

m/s

fiF

Feed; feed flow rate

kg, kmol; kg/h, kmol/h

F

Free internal energy

kJ

G, G

Gas; gas flow rate

kg, kmol; kg/h, kmol/h

G

Free enthalpy, Gibbs free energy

kJ

H

Enthalpy

kJ

HE TS

Height equivalent to one theoretical stage

m

HTU

Height of a transfer unit

m

K*

Phase equilibrium constant, distribution coefficient

L, L

Liquid; liquid flow rate

kg, kmol; kg/h, kmol/h

Lc M

Characteristic length

m

Molar mass

kg/kmol

N

Number of stages

NTU

Number of transfer units

Q,Q

Heat; heat flow rate

kJ; kJ/h, W

R, R

Reflux; reflux flow rate

kg, kmol; kg/h, kmol/h

R

Gas constant

kJ/(kmol K)

S

Entropy

k J/K

.

v m

+

=

1/pa

XVI

Frequently Used Nomenclature

T

Absolute temperature

K

U

Internal energy

kJ

V, V

Volume; volumetric flow rate

m3; m3/h

Molar volume

m3/kmol

Work

kJ

Ratio or loading of key component in liquid or heavy phase (moles i/moles inert, kg i/kg carrier (inert))

-

v

W

x

Y

Ratio or loading of key component in vapor or light phase (moles i/moles inert, kg i/kg carrier (inert))

Z

Length or height for heat and mass transfer

a

Activity

a

Specific volumetric area

m2/m3

cp, Cp

Specific heat

kJ/(kg. K), kJ/(kmol. K)

c

Molar concentration

kmol/m3

cw

Resistance coefficient

d

Diameter

m

dP

Particle diameter

m

ds

Sauter diameter

m

f

Fugacity

bar

Specific free internal energy

kJ/kg, kJ/kmol

gravitational acceleration

m/s2

Specific free enthalpy

kJ/kg, kJ/kmol

h,

Specific enthalpy

kJ/kg, kJ/kmol

Ah, A&

Latent heat

kJ/kg, kJ/kmol

k

Overall heat transfer coefficient

W/(m2. K)

k

Overall mass transfer coefficient

m/h

rn, m

Mass; mass flow rate

kg; kg/h

n, n

Number of moles; molar flux

kmol; kmol/h

P

Total pressure

bar, Pa

P,

Partial pressure of component i

bar, Pa

.Lf g g9

E

m

Frequently Used Nomenclature

XVII

Po, i

Saturated vapor pressure of component i

bar, Pa

AP

Pressure drop

mbar, Pa

4

Specific heat requirement

kJ/kg

4

Specific heat flux

kJ/(m2 h), W/m2

r

Radius

m

r

Reaction rate

kmol/(m3 h)

s, s

Specific entropy

kJ/(kg. K), kJ/(kmol K)

S

Characteristic distance (transfer distance)

m

t

Time

h

t,n

Mean residence time

h

u, ii

Specific internal energy

k J/kg, k J/kmol

W

Velocity

m/s

W

Mass fraction, weight fraction of component i

X

Molar fraction, heavy phase

Y

Molar fraction, light phase

Z

Variable distance length or height

Az

Tray spacing

-

m

Greek a

Separation factor

-

a

Heat transfer coefficient

W/(m2. K)

Mass transfer coefficient

m/h

Activity coefficient Film thickness, layer thickness

m

Porosity, void fraction of a bed of solids, fraction of free volume Yield

-

Dynamic viscosity

Pa s

-

Temperature

"C

Slope, gradient angle, inclination

0

Thermal conductivity

W/(m . K)

Chemical potential

k J/kg, kJ/kmol

XVIII

Frequently Used Nomenclature

V

Reflux ratio, solvent ratio, adsorbent ratio

-

V

Kinematic viscosity

m2/s

e

Density

kg/m3

0

Surface tension

N/m

v?

Relative humidity

-

Subscripts

H

Steam

T

Carrier

g is J

Gas phase Component

1

Liquid phase

0

Above, surface

P

Effective, practical

S

Solid phase

t

Theoretical

U

Below

U

Loss

a

Start, entry

0

End, exit

Thermal Separation Processes: Principles and Design Klaus Sattler, Hans Jacob Feindt copyright 0VCH

Verlagsgesellschaft m h H , 1995

Basic Concepts

1.1 Principles of Thermal Separation Processes In a chemical production plant, products are produced by the chemical and physical conversion of raw materials or intermediate products. The production unit is a completely integrated technical operating unit on the site. It is connected with other units on the site by transportation and personnel routes, and pipelines for raw materials, auxiliary substances, products, utilities, and energy. It usually consists of the actual production unit and several off-site facilities, as shown in Fig. 1-1. The main unit contains the unitprocesses and operations, such as separation, combination, division, formulation, heat transfer, conveying, storage, packing. Figure 1-2 shows a general set-up which is independent from the type of process. The combination of unit processes and operations with respect to product properties depends on the product produced. During the chemical conversion of raw materials, homogeneous and heterogeneous mixtures (Figs. 1-2 and 1-3) are generated. Both reactants and products may be found in these mixtures, according to the yield and conversion of the chemical reaction. By means of thermal separation processes these mixtures must be treated to obtain the desired products to a demanded purity and to enable the raw materials to be recycled. Processes to separate physically homogeneous (one phase) and heterogeneous (two or multiphase) mixtures are listed in Table 1-1. The driving force of the separa-

tion process usually forms the criteria for the separation. Homogeneous mixtures with a molecularly dispersed distribution of individual components may only be separated by means of a thermal separation process. Thermal separation processes are mass transfer operations, driven by molecular forces. Mass, and often heat, is exchanged between at least two phases of different composition. The phases are the mixture phase(s) and a selective auxiliary phase. The auxiliary phase is generated by either adding heat and/or by means of an auxiliary substance. The required driving forces, concentration, and temperature gradients, are formed due to the auxiliary phase. In Fig. 1-4 thermal separation processes are listed and are denoted by the phases contributing to mass transfer in Table 1-2. Thermal separations of mixtures are carried out in the following individual steps :

Step 1: An additional phase is generated by supplying energy to the system, or by adding an auxiliary component. - Step 2: Mass, and often simultaneously heat, is exchanged between phases. This is achieved by the addition or removal of energy. - Step 3 : After completion of the interchange process, the phases are separated. Together with the separation of the phases a (partial) separation of the mixture occurs. -

All thermal separation processes follow this order of events. The basic principles of thermal separation processes are now formulated and will be discussed in detail.

2

1 Basic Concepts

Main plant Process consisting of physical and chemical unit operations to produce desired products Off-sites, auxiliary equipment

- process control of the main plant

control room sometimes with a process control computer, control devices for drives, production lab, instrument air station

Inputs Energy

-+

-+

- supply of energy to main plant, generation and distribution

--*

Excess energy

- transport to the process unit of the raw material and auxiliary

-+

materials, transport of the products (roads, rail connections, harbor)

Main products

-+

By-products

+

Waste

of electrical power, heating system for heating media such as

hot water, steam, dyphil, salt melts - provision of auxiliary materials (adjuvants) such as heat

Raw materials Auxiliary materials

-

transfer media, coolants, catalysts, solvents, inerts ~~~

~_~

~~

- storage of raw and auxiliary materials, and products, spare parts, tools and materials for repair work and maintenance

_~

-

__ __

- disposal

treatment of waste gas and wastewater, reprocessing of solid residue and waste disposal

+ Waste gas

Wastewater

- facilities for the operating personnel

Fig. 1-1. General production process set-up.

Raw material

I

metering, preheating

i

Main product ready for storage or shipment

~

Path of raw material or product

Fig. 1-2. Basic flow chart for the main part of a production plant.

1.1 Principles of Thermal Separation Processes

3

Y 1 Y 1 A

Y

r

Reaction mixture

A b : : +

Phases in Cocurrent Flow (Principle of Parallel Flow)

Phases in Countercurrent Flow (Principle of Counterflow)

Phases taking place in mass and heat transfer are guided in cocurrent flow through the separation apparatus. The maximum efficiency of this separation apparatus is the same as that for a single theoretical separation stage.

Phases taking place in mass and heat transfer are guided in countercurrent flow through the separation apparatus. In this case it is important to disperse the phases with the aid of internals, thereby achieving intensive mixing of the phases. Thus the

.............................

............................ I

I

1 I

: I

Rectification (counterflow distillation) counterflow crystallimtion from a melt Counterflow sublimation Counterflow liquid-liquid extraction Fractionating, Counterflow processes

i

1

Partial distillation Partial condensation Absorption Extraction Adsorplion Cristallization from a solution Drying

~

~

phase transformation

Thermal \epnratioii

I_._________..-.....

L

I

Procesres with auxiliary materials

Absorption Adsorption Convective drying Carrier distillarion Extractive distillation Extraction Entrainer gas sublimation

Principle of classification. Distillation Partial condensation Crystallization Drying (except convective drying) Vacuum d h m a t i o n

Fig. 1-4. Summary of thermal separation processes.

,_r -- -- -_,l

Simple phase transfomiation t) fractionating

Auxiliary product: required for separation tf not required tor separation

4

1 Basic Concepts

Table 1-1. Summary of separation processes. Classes of separation processes

Driving force of separation process

Nature of mixture

Separation processes

Mechanical separations

Gravity Centrifugal force Pressure

Heterogeneous

Sorting (s - s) Dense-media separation (s - 1) Flotation (s - 1 - g) Sedimentation (s - 1) Filtration (s - 1) Pressing (s - I) Centrifugation (s - 1) Hydrocyclone separation (s - 1) Classification Sieving (s - s) Air classification (s - g) Hydraulic classification (s - 1)

Membrane separation

Pressure Electrical field Concentration gradient

Heterogeneous Homogeneous

Ultrafiltration (s - 1) Reverse osmosis (hyperfiltration) (s - 1) Dialysis (s - 1) Electrodialysis (s - 1) Electrophoresis ( s - 1) Permeation (1 - 1, g - g) Gas diffusion (g - g)

Electrical separation

Electrical field

Heterogeneous

Electro osmosis (s - 1) Electrical dust removal (s - g)

Magnetic separation

Magnetic field

Homogeneous

Magnetic separation (s - s)

Thermal separation

Concentration gradient Temperature gradient

Homogeneous

Distillation (1 - 1) partial condensation (g - g) Absorption (g - g), (A) Adsorption (g - g, s - I), (A) Chromatography (g - g, 1 - 1) Extraction (s - s, 1 - I), (A) Sublimation (g - g) Crystallization ( s - 1, 1 - 1) Drying (s - 1) Thermal diffusion (g - g, 1 - 1)

~

Abbreviations: s solid, 1 liquid, g gas to characterize the state of the components of the mixture to be separated, (A) thermal separation process with auxilliary component.

maximum possible interfacial area (phase boundary) for mass transfer is obtained and, hence, the highest possible mass transfer coefficient values. Figure 1-5 shows a “separation column” with stages connected in series in which the key component i of a

mixture is exchanged from the heavy phase to the light phase. Both phases may contain all components of the mixture. A closer inspection of stage n shows that the heavy phase, with a mole fraction of x,, is in contact with the light phase with a

5

1.1 Principles of Thermal Separation Processes

Table 1-2. Characteristics of thermal separation processes by the phases in which mass and heat transfer occurs. ~~

Phase Phase All components Not all components are in both phases 1 2 are contained Phase 2 One (several) comin both phases Phase 1 pure pure ponent (s) is (are) in both phases ~

Immiscible phases in contact

Miscible phases in contact

g

1

g

S

Distillation Partial condensation

Concentration of solutions

Gas drying

Counter current sublimation

g

g

1

1

Liquid-liquid extraction

1

S

Crystallization from a melt

S

S

g

g

Thermal diffusion

1

1

Thermal diffusion

S

S

~~

Absorption Desorption by stripping Adsorption Drying

Crystallization from a solution

Solid-liquid extraction (leaching) Adsortpion

-

Abbreviations: g gas phase, 1 liquid phase, s solid phase.

mole fraction of Y , , - ~ .If x, and are not phase equilibrium concentrations, the fed phases of stage n are not in phase equilibrium, and mass and heat transfer take place. The key component i becomes enriched in the light phase up to a final concentration y,, while the heavy phase is reduced in component i from x,,to x , - ~ . With stage n as a theoretical separation stage, the leaving phases are in equilibrium and no further mass or heat transfer is possible. Therefore, y, and x , - ~ are phase equilibrium concentrations. The heavy phase, with concentration x,, - arrives at stage n - 1 and comes into contact with the light phase, with concen-

tration y n P 2 .An exchange, similar to that in stage n, takes place. The discussed example shows that for countercurrent phase flow, single stages are connected in series in one separation apparatus. The light phase leaving a stage is guided to the following stage whereas the heavy phase is guided to the previous stage. A theoretical stage is that part of a separation apparatus where mass or heat transfer take place in which entering phases are not in phase equilibrium, while the leaving phases have reached phase equilibrium (see Chapter 1.4). In a practical separation stage, equilibrium is often not achieved. The efficiency

6

1 Basic Concepts

transfer ratio, depending on whether y is only locally valid or constant across the cross section of the column.

Phases in Cross Flow (Cross Flow Principle)

LP

HP

L-l---r Fig. 1-5. Countercurrent flow of two phases in a separation apparatus. n - 1, n Stages connected in series LP Upflowing light phase HP Downflowing heavy phase Molar fraction of the key component in x the heavy phase Molar fraction of the key component in y the light phase

Phases taking part in mass and heat transfer flow across through the separation apparatus at an angle of 90" to each other. The separation efficiency depends on the equilibrium location and the ratio of the phase fluxes, but is often low in an individual separation stage. To separate a mixture and obtain pure products, several separation stages are connected in series. This is done most effectively with countercurrent phase flow. Phase cross flow and parallel feed of one phase to individual separation stages are sometimes used. However, cocurrent flow is of non importance.

compared with a theoretical stage is ex- ~i~~ Requirement pressed as the stage efficiencyfactor, E (exchange ratio, enrichment ratio, MURPHREE The time needed to separate a mixture in a efficiency) (Fig. 1-5): discontinuous operation is the effective residence time. For continuous operation, it is separation effect of a practical stage the mean residence time t,, of the mixture E= in the separation apparatus: separation effect of a theoretical stage E=

Yn-Yn-1 Yn*-Yn-1

(1-1)

t,

V

=T

V

where

where

y,* - y,-,

possible theoretical enrichment of the key component in the light phase ( y ; phase equilibrium concentration at x, y , - y n p 1 actual enrichment of the key component in the light phase

I/

This often has to be distinguished as a local transfer ratio, as opposed to an overall

Short-, medium- and long-term separation processes can be distinguished depending on the time requirement:

filled volume of the mixture in the separation apparatus (determined by the volume of the apparatus and the degree of filling) effective volumetric flow of the mixture

1.2 Thermal Separation Process Modes

Short-term processes (t, < 30 sec). Examples: Spray drying, gas adsorption, precipitation crystallization. - Medium-term processes (30 sec< t, < 2h). Examples: Absorption, rectification, drum drying, pneumatic-conveyor drying, sublimation, extraction, crystallization, liquid adsorption. - Long-term processes (1 h < t , < 1 d). Examples : Rotary drum drying, vacuum tumbling drying, vacuum freeze drying, fractionation crystallization. -

Energy Supply For the thermal separation of a mixture in an apparatus, energy has to be supplied in the form of: -

Heat, to increase the sensible heat of the flowing masses and to supply latent heat.

-

7

Flow energy, for pressure drops in the ap-

paratus and the connecting pipework. Mechanical energy, for example for dispersing, pulsing, stirring and pump circulation devices. - Work, to operate peripheral machines such as compressors and vacuum pumps. -

1.2 Thermal Separation Process Modes Apparatus for the thermal separation of mixtures may be operated both discontinuously (intermittently, batch production, stagewise operation) and continuously (steady-state). In the following section, the operating modes are briefly illustrated. The advantages and disadvantages are listed in Table 1-3.

Table 1-3. Comparison of continuous and discontinuous operation to achieve the same separation

problem.

Comparison criteria

Operating mode Continuous

Mathematical description of the separation process, modeling Investment cost of separation unit Operating cost of separation unit Operation of separation unit Automatic control of separation process Working stress on unit components Environmental pollution, possibility of accident Operation reliability, flexibility in the case of breakdown of separation unit parts, safety buffer Flexibility to adjust to other mixtures to be separated

Discontinuous

Simpler Less Less Easier Possible with less expense Less Less

Higher Better

8

1 Basic Concepts

Continuous Operation : In continuous operation the mixture being separated is continuously fed to the separation device. It is continuously separated into two or more fractions, which are continuously withdrawn from the separation device. An ideal binary mixture can be separated into almost pure components in a separation column operated continuously with countercurrent flow. To separate a mixture of k components, k - 1 columns connected in series are needed. Discontinuous Operation: With discontinuous operation the mixture being separated is charged to the separation device. During a time period, the “batch period”, the mixture is separated mainly into two fractions of defined different compositions. One fraction is continuously withdrawn from the separation device, while the other remains in the device and is withdrawn at the end of the batch time. Discontinuously operated processes mainly in one stage - allow incomplete separation of a mixture; the obtained fractions are treated in subsequent stages (this is the case for multistage discontinuous separation). Alternating Operation : If in a separation apparatus after a loading process (separation of a mixture) an unloading process (the regeneration of a substance aiding separation) is required, at least two sets of equipment are operated alternately. Therefore, steady separation of the mixture is guaranteed. In the case of the adsorption of a substance from a gas phase in a container adsorber (see Chapter 4), for example, a solid

[

f s u m of amount) entering the system (transport)

+

[

adsorbent adsorbes adsorbate (key component in the gas phase). Adsorption continues to an upper loading limit. After the maximum load has been reached in the first adsorber, operation is switched to the second adsorber. The loaded adsorber is then regenerated by dampening, drying and cooling. After the regeneration cycle is finished, the adsorber is ready for loading again.

1.3 Mass Balance, Energy Balance, Exergy Balance In general, the first step in the design of a separation plant is the balancing of individual apparatuses and parts of the plant. Balances are done with respect to energy and mass fluxes, in connection with a schematic representation of the process (flow diagram).

1.3.1 Mass, Energy and Heat Balances The balancing of chemical engineering systems follows the sequence listed in Fig. 1-6. Of the variables listed for process design, mass and energy (usually in the form of heat, enthalpy, and exergy) are of most interest. These variables may also be used for planning, evaluation of systems, analysis, and synthesis. Based on the laws of conservation of mass, energy and momentum, balance equations are set up [1.1] - [1.5]. For a general open system

f sum of amount ) generated in = the system (transformation)

1

f s u m of amount) leaving the system (transport)

1 f

-k

increase of \ mass stored in the system (accumulation)

1.3 Mass Balance, Energy Balance, Exergy Balance

9

Determination of the balance area of the system by defining real or imaginary boundaries (unit complex, unit, part of the unit, individual apparatus, part of an apparatus, volume element)

Determination of the balance size of measured or valuable system properties (total mass, component mass, atomic mass; state variables such as enthalpy, entropy; momentum; cost)

Process description Flow sheets

4l

Formulation of balance eauation to obtain a list of all balance variables of interest in a quantitative form

1

+

~

Solution of the balance equations

I Optimization

Environmental requirements Safety provision requirements Safety requirements

Dertermination of process --* control equipment

+

Precalculation and economical calculations

Fig. 1-6. Balancing of processes (schematic simplification of the concepts) [1.1].

Depending on the problem or task a integral or differential balance equation is generated : 0

Differential, to investigate a process in a differential volume element or at an interfacial surface element

0

Integral to determine the streams entering and leaving the system

Differential balance equations lead to velocity, concentration, and temperature profiles in the system, or at the boundary surfaces, after solving the corresponding differential equation system with suitable bound-

10

1 Basic Concepts

ary conditions. Integral balance equations give a basis for evaluation of the total system with respect to energy and mass. Results of integral balance equations are often presented in a table or in a flowchart (product and energy scheme, mass and heat flowchart, etc.).

The material balance for an individual component k is

c i

-

-

m i j , * Wi,k,a

c mi,, i

*

m , k =

wi,k,w

+ mS,k

(1-4)

where Mass Balance

mi,a

Material balances (mass or quantity balances) can be general or total material balances over the complete system and must be distinguished from material balances for individual mixture components (Fig. 1-7). Using the terms in Fig. 1-7, for an open system the general integral balance equation is

wi, k, a 9 wi, k, o

c mi,a+ i

mQ =

c i

+ m,

(1-3)

In steady-state operation (continuous feed and withdrawal of material without start up and shut down procedures) the accumulation terms mQ and m, are not required.

m i ,w

rfzp ms, I j z Q , k ,

mass flux i (a feed, o product) mass fraction of component k in stream i ms,k intensity of sources (Q) and sinks (S)inside the balance area generally with respect to component k

m Q , k and m $ k take, for example, chemical reactions involving k into consideration. If k is a reactant in j single reactions taking place simultaneously in the balance area, for steady-state operation,

m l , a ~W l . k , a , '1.a

BA

-BB

-

Fig. 1-7. Balance scheme to derive the balance equations. BB Balance boundary BA Balance area

1.3 Mass Balance, Energy Balance, Exergy Balance

11

the balance area and uj,k is the stoichiometric ratio of k in the reaction j . dnk Instead of mass and mass fractions, it is 'j = (1-6) convenient to use another kind of substance Vj,k * I/. dt flow or concentration units to set up mateis the equivalent reaction rate of the reac- rial balance equations. Useful conversion tion j , V is the volume of reaction mass in relationships are given in Table 1.4. where

Table 1-4. Conversion between concentration scales of a mixture component.

Mass fraction wi

Molar fraction

Partial density

xi

ei

Mole ratio of component i ') x m ,1

Mass fraction m;

wi

Molar fraction

ni x . = __

C.i i

c-M; ei

e

i

Partial density

Wi'

e

ei

xi * Mi M -

e

Molar ratio of component i in the inert or carrier phase

I) Reference is the mass of the remaining mixture excluding component i, expressed as carrier mass m 1

c mi

2,

')

i

Density e = - @ = L e i V i n. Molar ratio carrier load X i = n1

Used variables: mi mass of mixture component i number of moles of mixture component i

ni

M =

_f

c xi Mi mixture mean molar mass of the i

9

V

total volume of the mixture

ml

mass of reference component 1

c mi total mass of the mixture c total number of moles of the mixture i

i

ni

12

1 Basic Concepts

For a complete mass balance over a balance area at steady-state, in which only I physical transformation of matter occurs, an equilibrium system consisting of Eq. I (1-3) and k - 1 equations (1-4) for k active components over the balance area, must be where set up. Due to the valid stoichiometric con- hi,,, hi,, dition, for the individual phases, the kth equation (1-4) gives Q cwk=l

(1-7)

k

Ways to formulate material balances for differential volume elements as the balance area, and methods to solve this differential equation system may be found in, for example [1.1] and [1.3]. Energy and Heat Balances

c Ei,a+ EQ i

= E,

+ c Ei,, + Es

(1-8)

i

where E . . E,,E,

Ei,, EpEs

.

QQ,Qs

specific enthalpy of mass flux ki entering and leaving additional heat flow supplied heat flow lost intensity of heat sources (Q) and sinks ( S ) in the balance area

QQ,Qs account for the exothermic and endothermic nature of phase transformations and chemical reactions under steady-state conditions. If, for example, over the balance area, chemical reactions involving component k occur QQ- Qs = - v * h/r,

Based on the law of conservation of energy, an energy balance analogous to the material balance may be set up for any bounded balance area. Using the terms from Fig. 1-7 for the energetic and materialistic open system, the energy balance becomes Ea+

Qu

(1-9)

includes all energy forms, such as potential and kinetic energy, binding energy, heat energy flow through the system boundary, supplied (a), or removed (0) energy supplied or removed by the mass flux mi intensity of the heat sources or sinks inside the balance area

In process design, a heat balance is often sufficient. From the first law of thermodynamics, for the balance area in Fig. 1-7, the mthalpy or heat balance equation is

- c rj - vj, - hhR, = j

=

- u k Ai;,

*

*

Wi,k,a

(1-10)

i

where AhR,j reaction enthalpy for component k in reactionj AhR the total reaction enthalpy for component k (ALR> 0 for endothermic reactions, Ah;, < 0 for exothermic reaction) U, total conversion of k hfk molar mass of k

1.3.2 Exergy Balance When the economics of plants are considered, the cost of raising primary energy causes a domination of energy costs over investment costs. The optimum cost of a process corresponds to minimum use of energy. Therefore, it is necessary to investigate processes which have high energy consumption in order to optimize energy usage.

1.3 Mass Balance, Energy Balance, Exergy Balance

To evaluate the energy utilization, energetic and exergetic process analyses are used. Since exergetidanergetic flowcharts show local internal and external irreversibilities, the locations and quantities of heat losses may be detected, leading to thermodynamic optimization from the consideration of process energy improvements. According to Fig. 1-7 the exergy balance equation, for a steady-state open system, under isobaric conditions, is

=

GE,w+

c

___

dQ,

+

+

G,,w AG, i

(1-11)

where exergy of input Ea and output E, energy fluxes Gj,a,Gi,w exergy of input Yizi,a and output m;,w mass fluxes Qm heat flow supplied G E , a , GE,@

G; = Yiz; * [(hi - h,) - T, . (s; - s,)]

entropy temperature, enthalpy and entropy, referred to surrounding conditions or to a particular system state reference exergy losses due to irreversibilities

AG,

AG,

(1-12)

=

T, * AS,

(1-13)

More information on energetic and exergetic analysis can be found in the literature [1.6- 1.91. The exergetic analysis of a rectification unit is given as an example in [1.10].

13

1.3.3 Calculation of Balance Equations Calculation of mass, energy and exergy balances for the total separation plant are usually done sequentially from apparatus to apparatus. They are occasionally carried out simultaneously by an iterative method, considering the corresponding equation system for the total separation process. In this case, it is necessary to develop a calculation flowchart with coded interface and ramification. The process structure is conveniently presented graphically. After mathematical formulation of the process, the number and values of the independent system variables are determined. Finally, the balance equations are solved sequentially. To calculate the balance data using a computer [1.1, 1.11-1.161 a flexible programming system is required. The main program controls and organizes by assigning priorities to the calculations via references to the corresponding process steps, mass fluxes, and computation parameters. It organizes the intermediate storage of calculated mass fluxes and state variables, and transfers these as input variables to the following stages. Initial variables for each stage are calculated in subroutines, based on stage specific theoretical and empirical models. By including the graphical methods in the balance, economic optimization by, for example, minimizing the energy flow [1.17] or optimization with respect to complete safe operation of the process can be performed [1.18]. It is often convenient to present the results for a balance over a single piece of equipment, a process unit or total processes, and, if necessary, for combined processes. They can be quickly understood in clearly arranged flowcharts (SANKEYdiagram).

14

1 Basic Concepts

1.4 Phase Equilibria 1.4.1 Basic Concepts With thermal separation of mixtures, usually in open systems, an exchange of heat and mass occurs at the phase interface. When phase equilibrium is reached, no further heat or mass transfer takes place. Basic concepts and equations are now introduced [1.20], in order to describe phase equilibria:

- Thermodynamic Systems: Any quantity

-

-

-

-

-

-

of matter that is separated from its surroundings by rigid or imaginary boundaries and whose properties may be unequivocally and completely described by thermodynamic, macroscopic state variables. Open Systems: Thermodynamic systems in which matter and/or energy may transfer with the surroundings, through the boundaries. Closed Systems: Thermodynamic systems in which only energy may be exchanged with the surroundings. The system is closed, containing constant mass, but is not isolated. Adiabatic (thermally) Isolated Systems: Thermodynamic systems in which no heat or mass transfer with the surroundings takes place, although exchange of energy in other forms, e.g., shaft work, is possible. Closed (isolated) Systems: Thermodynamic systems in which no exchange of energy or matter occurs with the surroundings. Homogeneous Systems: Single phase systems with identical macroscopic properties in each volume element. Heterogeneous Systems: Two or multiphase systems with at least one abrupt change in macroscopic properties at the boundar(y/ies) between the phases.

Phase: A physically homogeneous region of a system, contained within a phase boundary. Each volume element in one phase has identical macroscopic properties. The change of state variables, i. e., those not dependent on mass, such as temperature, pressure, composition, etc., are continuous and time independent (without, for example, a step change). - Dispersed (discontinuous) Phase: A phase consisting of homogeneous matter, which is scattered in space, and dispersed in the continuum of the other mainly coherent phase. - Continuous Phase: A uniform, nondispersed phase. - Free (Gibbs free) Enthalpy (thermodynamicpotential), G : The relationship between the enthalpy H, entropy S and internal energy U is defined as

-

G=H-T.S or G = U + p . V-T-S

(1-14)

Therefore, the Gibbs free enthalpy is that part of the enthalpy which, at a reversible change of state, can be converted into other types of energy. For a closed system (constant mass or for a pure phase), the total differential for the free enthalpy d G is dG =

(z)p (g) - dT+

T

.dp

(1-15)

and, from Eq. (1-14) dG=dU+p*dV+ V*dp-

T-dS-S. dT

(1-16)

For a reversible change of state it follows from the first law of thermodynamics that: d U -tp . dV = T . dS

(1-17)

1.4 Phase Equilibria

(dG), = ,ul dn,

and therefore dG= V-dp-S-dT

(1-18)

With constant mass, the free enthalpy is only a function of pressure and temperature. Comparison of the coefficients in Eq. (1-15) and (1-18) gives:

(g)p= -S

and

(5)

=

V (1-19)

T

For an open system, the free enthalpy is not only a function of pressure and temperature, but also a function of the amount of mass n of each individual component. G = G(T,p,n1,n2,...)

(1-20)

The change of free enthalpy is therefore given by

.dnl +

an2 p,T,n,,n3 ... + (E)

By integrating this equation under the assumption of constant pressure and temperature, the free enthalpy of the system shows a definite dependency on the composition and chemical potential of the components of the mixed phases in the system. G = p l . n , + p 2 - n 2 +...

(1-24)

For a change of chemical potential it follows from Eq. (1-24) that (dc),,, = n1 dp,

+ n2 - dp2 + . . .

(1-25)

and with the requirement of dG = 0 at equilibrium,

n, . dp, + n2 - dp,

+ . .. = 0

(1-26)

or

This is the Gibbs-Duhem equation in two different forms and is of fundamental significance in proving the consistency of precalculated or experimentally determined equilibrium data.

. dn2 + . . .

hence dG = - S . d T + V . d p

(1-23)

(1-27)

d G = - S * d T + Vedp-t p. T , n 2 . . .

+ p 2 . dn, + . . .

15

+ (1-21)

For individual components the isothermal and isobaric change of state is

or by introducing the chemical potential p of the individual components, we can write

Chemical Potential (partial molar free enthaipy): An expression for the change of the free enthalpy of a system, which consists of a mixture, if 1 mole of the mixture component i is added to a n infinite amount of the mixture. Hence,

(1-28)

In a mixture the chemical potential of a component i can be expressed as

16

1 Basic Concepts

where poi is the standard chemical potential, i. e., the chemical potential of the component i at the standard state. For any component of a gas mixture, the standard state is the same as for the standard state of a pure gas component at the temperature and pressure of the system. For any component of a liquid mixture, the standard state is the same as the standard state of a pure liquid component at the temperature and pressure of the mixture. The partial molar free mixing enthalpy A& is

A p i = i ? . T . ln(y,.xi)

(1-30)

-

where y i xi is the activity and yi is the activity coefficient of the component i of the mixture. The activity coefficient here is defined as lim yi = 1

(1-31)

X,'l

Equilibrium: A system is at equilibrium if, in fixed surrounding conditions, no change on a macroscopic scale occurs in the system. Therefore, there is no tendency toward an exchange of matter and energy between the phases. Exchanges of matter and energy between phase boundar(y/ies) of the heterogeneous system are reversible. The equilibrium between the phases (the phase equilibrium) is sensitive to changes in the surrounding conditions. Compositions of the phases at the desired phase equilibrium are independent of time, the amount of material and the direction from which equilibrium is reached. Equilibrium Conditions: Equilibrium between the phases of a heterogeneous system is reached if the following conditions are valid: no local pressure differences exist with respect to time and space (mechanical equilibrium) dp = 0 therefore p1 = prl = . . .

(1-32)

and no local temperature difference exists with respect to time and space (thermal equilibrium) d T = 0 therefore

T, = T,, = . . .

(1-33)

These two conditions meet the requirements to describe an isolated system in a state of equilibrium. The system is stable, when the system entropy reaches a maximum, hence dS = 0

(1-34)

The equilibrium condition for a closed system may be derived from the fact that any infinitesimal change of state at equilibrium is reversible. For example, we have dU=dQ+dW=T*dS-p.dV

(1-35)

or

d H = T -d S i - V* dp

(1-36)

The equilibrium conditions for an adiabatic and isochoric change of state are given by, (dU)v,, = 0

(1-37)

for the adiabatic and isobaric change of state,

(CW),,, =0

(1-38)

for the isothermal and isochoric change of state,

(W" ,=0

(1-39)

and for the isothermal and isobaric change of state,

The internal energy U, the enthalpy H , the free internal energy F, and the free enthalpy G , must be at a minimum for a system to be at equilibrium. This is comparable to a me-

1.4 Phase Equilibria

chanical system where the potential energy is a minimum at equilibrium. Combining Eq. (1-21) and (1-28) gives dG= -S.dT+ V-dp+zpi.dni

(1-41)

The equilibrium condition for an isobaric and isothermal change of state for an open system is (dG),,

=

-

p i dni = 0

(1-42)

At equilibrium, mass transfer between the phases of a system is reversible and a material balance requires (1-43)

dn,,, = -dni,,, and so it follows that p r. , = ~ p. I , I I - Pi,III

=

. ..

(1-44)

Therefore, phase equilibrium is reached when the chemical potential of each chemical species in the system is the same in all phases. For the equilibrium of two phases I and 11 using Eq, (1-291,(1-30) and (1-44) it follows that

Rearrangement defines the “distribution coefficient” (%equilibrium constant’? K:, giving

xi,II= KT * xi,,

(1-46)

and the relationship (1-47) with . - fi or,II . APoi = P or,,

(1-48)

17

Knowledge of the distribution coefficient or the equilibrium relationship = f(xiJ as a function of pressure and temperature is essential for the design of thermal separation processes. The relationship is found in three steps: - Step 1: Evaluation of the activity coefficient yi Of each component in each phase at a different temperature, pressure and composition, measured experimentally or determined from an appropriate correlation. - Step 2 : Determination of the differences in the chemical Potential APoi of each component under the same conditions (see Step 1). - Step 3: Evaluation of KT or the equilibrium relationship x ~ ,=~f ,(xi,,).

1.4.1.1 General Differential Equation for the Equilibrium Between TWO Phases

The criterion for the equilibrium of two phases is p i , , = pi,II or dp,,, - dpi,,, = 0. The general differential equation for the equilibrium of two phases I and I1 may be written:

(1-49) This relationship links the state variables of pressure p , temperature T and molar fraction xi of the component i in both phases I and 11. The enthalpy A ~ Z ~ ,and , , ~ , the volume AK,I,II are partial molar phase transfer quantities. The partial molar quantities of a binary mixture may be determined by graphical method if the appropriate quantities are known as a function of the mixture composition (Fig. 1-8).

18

1 Basic Concepts

q P

vl,p&,p

v

X

Example:

-

Partial molar volume of both mixture components Molar fraction of component 1 Mixture volume

-.Ah;,,,

R *T

R - T2

(1-53)

or dP dT

-

The molar volume Vof a real fluid mixture is

__ -

V = x l . I / , , + x , . T -/ 2 , p = x 1 -. 1 / , p +

where

+ (1 - Xl)

(1-50)

G,p

where q,, and 1/2,p are partial molar volumes of components 1 and 2 of the mixture. The mole fraction x1 of component 1 varies between the limits 0 and 1.

-

q,#=v-x,.=

av

(1-51)

ax1

V + (1 - x,) .

aV ~

ax,

Ah1.1, T -A4.11

Ahi,ii = Ah,,g

AI/,Il =

dp/dT

-

VI

(1-54)

the molar evaporation enthalpy of the components at a given p and T the differences in the molar volumes of the saturated vapor and liquid of the system components, at a given p and T the slope of the vaporpressure curve

(1-52)

In Fig. 1-8 the measured volume of the mixture V is plotted against the molar fraction xl, A tangent from point A of the v(x,)curve gives the points D and E. Points B

1.4.1.2 The Gibbs Phase Rule The Gibbs phase rule describes how many state variables of a muitiphase system may vary independently (degrees of freedom of

19

1.4 Phase Equilibria

the system) without disturbing the systems equilibrium :

P+F=K+2

(1-55)

where

F the degrees of freedom of the system at equilibrium (chosen from the state variables pressure, temperature, concentration of each component in each phase); number of variables describing the state of the system which may be varied independently without disturbing the system equilibrium P number of phases of the heterogeneous system (one gas phase, one or more liquid phases depending on the miscibility of the components, one - at mixed crystal forming - or several solid phases according the number of crystal types) K number of components; the minimum number of components of the system forming the phases which must be independently declared

F = 0 invariant system F = 1 monovariant system F = 2 divariant system, etc. The phase rule is important for thermal separation processes as, if certain process parameters are choosen, it establishes which state variables are cogently fixed at an arbitrarily adjusted phase equilibrium (Table 1-5).

1.4.2 Liquid-Liquid Equilibrium 1.4.2.1 The Nernst Distribution Law

For a dissolved substance S in two nonideal, immiscible, liquid solvents such as T and L at constant pressure and temperature the distribution according to Eq. (1-45) is

pas,, + R . T.ha,,,

=

+ . T . lnczs,II

(1-56)

= pos,II R

where as is the activity of S. For phase equilibrium of two liquid phases, the standard state of both phases is the same (normalized to pure liquid S). It follows that POSJ

(1-57)

= POS,II

and therefore including Eq. (1-56) as,1 = as,II

or

YS,I * *S,I = YSJI

. XS,H

(1-58)

To describe the concentration dependance of the activity coefficients Y , , ~and Y , , ~ ~the , computational methods shown in Table 1-8 may be used, for example the NRTL or UNIQUAC methods. For a substance S distributed in phase I (raffinate R) and phase I1 (extract E) with a small concentration of cS,, and c ~ , the ~, Nernst Distribution Law is an approximation given by

A substance is distributed between two liquid phases so that the same concentration ratio appears in both phases. It is independent of the total amount of phases at constant pressure, constant temperature and similar molecular forms in each phase. For separation by liquid-liquid extraction, the Nernst distribution law describes the equilibrium between raffinate and extract phases if the carrier component T and solvent component L are not miscible (see Chapter 6). Table 1-6 shows additional variations of the Nernst distribution law.

5. Selected thermal separation processes. Examples of the Gibb’s phase rule. separation Phases

on o f binary

Number Type 2 1, g

2

quid n

2

orption

2

orption

3

on of le binary , carrier on of one nt

21 Ig

1, g

s, g

1, 1

Components Number Type 2 Miscible liquids

2

3

3

3

Immiscible liquids

Degrees of freedom 2

1

3

Carrier Key component Solvent

3

Inert gas Adsorbate Adsorbent

3

Inert gas Absorbate Solvent

Process parameters Pressure, concentration o f one component, e.g., in the liquid phase Pressure

Consequences for the remai variables describing the syst explanations Concentration of the second nent in the liquid phase, the tration of both components vapor phase, and the temper all fixed (boiling point diagr Concentrations and tempera strongly fixed, no simple se possible (boiling point diagr

If the concentration of the ponent in the raffinate rema concentration of the extract fixed (distribution equilibriu

Pressure, temperature, concentration of the key component in the liquid phase

Fixed loading of the compo adsorbed in the absorbent ( tion isotherm)

Pressure, temperature, partial pressure o f the absorbate in the gas phase

Concentration of absorbate liquid phase is fixed (absorp isotherm)

Pressure, temperature, partial pressure of the absorbate in the gas phase

. (continued) separation Phases Number Type

Components Number Type

Degrees of freedom

Process parameters

Consequences for the remain variables describing the syste explanations

Components without mixed crystals load

ion

Dissolved substance Solvent

ration and m llization

Concentration of the dissolv substance fixed by the solubi curve

Pressure temperature

Dissolved substance Solvent

zation from n ooling llization

Solid phase concentration an temperature are fixed (solidu liquidus lines)

Pressure, concentration of one component in the liquid phase

Components forming a mixed crystal

ation from

Moisture content of the prod Pressure, temfixed (sorption isotherm, 1st perature, partial pressure of the period) moisture in the gas

Dry product Moisture Dry gas

pic product ng period)

Dry product Moisture Dry gas

on drying groscopic by hot gas g period)

Pressure temperature

Pressure

Temperature

Fixed saturation loading of t product with moisture (sorpt isotherm and 2nd drying per

Boiling point temperature of saturated solution is strongly by the pressure (vapor-press curve of the saturated soluti Temperature determines the pressure of the sublimable c ponents, corresponding to th sublimation pressure curve

tions: s solid phase (solid), 1 liquid phase (liquid), g gas phase (gas).

22

1 Basic Concepts

Table 1-6. Additional formulae of the Nernst distribution law. Correlations and conversion relationships for the distribution coefficient K . 0

Mole fractions x, y are used as the concentration scales for the distributed substances S Y x

-=

0

K?(tP)

Mass fractions w substance S wS. E ~

wS, R 0

= K:(B)

~ and, w~ ~ are, used ~ as the concentration scales for the distributed

(1-61)

.

Molar ratios X , Y are used as the concentration scales for the distributed substance S Y X

- = K$(B) 0

(1-60)

.

(1-62)

.

Relationship between the distribution coefficient

(1-63) 0

Correlation for the distribution coefficient K: [1.21 K$

A , + A z . wS,R

(1-64)

+ A , . w ~ , +R A,. w;,R

Specific substance constants for Eq. (1-64)at tP = 25 "C. System

I

I1 I11

A,

A2

7.1957 0 1.1888 0 1.5569 0

A3

A4

-1022281.0 50722.0 -3.3775 2.0970 - 3.6840 -0.7462

System examples : I Water/toluene/aniline [1.21] 11 Water/benzol/dioxane 111 Watedmethyl isobutyl ketone (4-methyl-2-pentanone)/acetone

Nomenclature used in Eqs. (1-59) to (1-64):

VE

volume of the extract phase nS,R

CS,E = __ nS'E

vE

'S,E

molar concentration of the substance S in the extract phase number of moles of S in the extract phase

C S , R = __ 'R

molar concentration of S in the raffinate phase

IIS,R

number of moles of S in the raffinate phase

VR

volume of the raffinate phase

1.4 Phase Equilibria

23

mole fraction of the substance S i n the raffinate phase mole fraction of the substance S in the extract phase number of moles of extract or raffinate phase weight fraction of S in the extract phase weight fraction of S in the raffinate phase mass of S in extract or raffinate phase mass of extract or raffinate phase mole ratio of S in the raffinate phase number of moles of carrier mole ratio S in the extract phase number of moles of the solvent molar mass of extract and raffinate phase density of extract or raffinate phase A schematic distribution diagram for liquid-liquid extraction is shown in Fig. 1-9. The Y, X distribution diagram is essential for the design of separation apparatus.

1.4.2.2 Representation of Liquid-Liquid Phase Equilibrium

Industrial extraction process systems with three or four liquid components are common. In addition to a vapor phase two or

X-

Fig. 1-9. Schematic presentation of the liquidliquid phase equilibrium, the loading diagram. EC I Equilibrium curve with a constant distribution coefficient EC 11, Equilibrium curve for a concentrationEC I11 dependent distribution coefficient P Plait point Y = X , 45" line AL Mole ratio of S in the extract phase Y Mole ratio of S in the raffinate phase X

three pairs of liquid phases are possible. Now equilibrium of liquid-liquid phases for ternary systems will be discussed in more detail for cases where partial miscibility of carrier liquid and solvent cannot be neglected, and presentation by means of an equilibrium diagram similar to Fig. 1-9 is insufficient. A practical way at constant temperature and pressure to graphically describe the data of phase equilibrium of a ternary system uses an equilateral triangle (Gibbs' triangle). Figure 1-10 shows an equilateral triangle representing a three component mixture. Each apex of the triangle corresponds to one of the pure components T L and S. Any point on the sides TS, TL and LS char-

24

1 Basic Concepts XTXL-

0 0

(1-65)

XS‘l

S

In the case of a liquid-liquid extraction operation, the solvent L must be chosen such that it is very miscible with the solute of the original binary mixture T/S yet immiscible with the carrier liquid 7: Simple extraction processes for a common type of ternary mixture with components T, L, and S are presented in Fig. 1-11. A vapor phase and two liquid phases (in the two phase region) coexist in the heterogeneous system. S is completely soluble in T and L. In the area between A and B, T and L are insoluble in each other. The binary mixture of A and B, x1.l XT= 0 according to point M, will separate into two XL: 0 XLXL- 1 liquid phases of compositions A and B corxs.0 XS‘ 0 XT responding to the mass ratio m/MB. Until for example, the substance S is Fig. 1-10. Equilateral triangle (Gibb’s triangle) for the representation of ternary mixtures. added isothermally to the binary mixture, A Binary mixture state point with molar according to point M, the ratio m M / B fractions of x, = 0.7 and xL = 0.3 will change if the liquid phase with the B,L State points of two ternary mixtures highest concentration of S disappears. Now M State point of a ternary mixture the ternary system is homogeneous. This is resulting from the mixing of B and C xL,xT,xsMolar fractions of L, T, and S in the true at point M’, the saturation point. Similarly, this is valid for points P, P’ and Q, Q‘. ternary mixture at state point M Curve A, M , P’, Q’, B is the line connecting the saturation points or the solubility curve, solubility isotherm or binodal curve acterizes a binary mixture. Point A, for ex- (Fig. 1-11). ample, is a two component mixture with a Below the binodal curve the ternary syscomposition of 0.7 parts of T and 0.3 parts tem is heterogeneous; elsewhere it is a hoof L. Any point within the triangle repre- mogeneous solution of one liquid phase. A sents the composition of a ternary mixture, mixture, such as R in Fig. 1-11 b, below the for example B, C and M; the graphical binodal curve will form two conjugate liqmethod to derive the fractions xT, x, and uid phases, represented by points C and D x, in Fig. 1-10 will now be explained in on the binodal curve. The connecting line more detail. between C and D is the tie line and deIf n, kmol of the ternary mixture at scribes the state of the phase equilibrium of point B is added to n2 kmol of the ternary the conjugate liquid phases. The more submixture at point C, the composition of the stance S the conjugate liquid phases connew mixture lies on the line This is tain, the shorter the tie lines. The equilibshown by means of a material balance. The rium points C and D move toward each location of the mixing point M follows the other on the binodal curve to finally reach lever, or mixture, rule such that the “critical point” P, the plait point.

-

m.

1.4 Phase Equilibria

A 9 z const

a)

b)

25

S=const

A

o'/ I

TA

i

Q

I

i

I

P

\

\

M

BL

Definition of the binodal curve [binode) A Q' P' M' B Binodal curve

Fig. 1-11. Representation of a liquid-liquidphase equilibrium in an equilateral triangle. a) Definition of the binodal curve (binode)

AQ'P'M'B Binodal curve b) Interpolation procedure to determine the tie lines CPD ... Binodal curve CD Tie line PK, K,K3 Conjugation line

If, for example, several tie lines are found experimentally, additional tie lines may be constructed via the interpolation procedure, linking conjugate liquid phases in phase equilibrium, shown in Fig. 1-11b (for additional interpolation methods, see [6.1]). The conjugation line connects the intersecting points that are generated by the lines parallel to the triangle axes TS or E. The starting point occurs at the intersection of the tie lines and the binodal curve. The value of K* for horizontal lines is unity, corresponding to the Nernst Distribution Law and according to Eqs. (1-59)-(1-63). For tie lines inclined to the horizontal the coefficient values are K* > 1 or K* < 1. It is uncommon in extraction processes to find ternary systems of T, L and S where

I Interpolation procedure t o determine the tie lines C P D . . . Binodal curve CD Tie line P K, K, K, Conjugation line

two partially immiscible substance pairs exhibit a miscibility gap at equilibrium as shown in Fig. 1-12. To simplify the procedure of solving extraction problems, equilibrium curves may be transposed from triangular coordinates to rectangular coordinates [0.1, vol. 2, p. 5461. Figure 1-13 shows different graphical methods used to represent the distribution equilibrium. An increase in temperature usually leads to an increase in mutual solubility. The area of heterogeneity under the binodal curve decreases and the tie lines may also change their slopes. This is shown schematically for a liquid-liquid phase equilibrium in Fig. 1-14. The influence of pressure is negligible with regard to technical accuracy.

26

1 Basic Concepts

Closed system with miscibility gap between L and S

Open system with miscibility gap between L and S

Open system with miscibility gap between T and S

System with decomposition of mixture into three phases in region I11

Fig. 1-12. Phase equilibrium of ternary systems with two partially inmiscible substance pairs. I One phase region

I1 Two phase region

111 Three phase region Type A Closed system with miscibility gap between L and S Type B Open system with miscibility gap between L and S Type C Open system with miscibility gap between T and S Type D System with mixture decomposition into three phases in region I11

The liquid-liquid equilibrium data are determined by a straight forward experimental procedure [0.1, vol. 2, p. 5561 or [6.2]. A heterogeneous ternary system is used in the analysis to obtain the tie lines. After intensive mixing, the system is separated isothermally into two conjugate

phases. Both phases are weighed and analyzed and the state points entered on the Cibbs phase diagram. The lever rule for the phases (Eq. 1-65) can be used as a control method. The mixture point R, and the state points of the two conjugate phases C and D form a straight line; the tie line (Fig. 1-11).

1.4 Phase Equilibria al

I

S

27

I

L

X--b

t Y

I

L

Fig. 1-13. Phase equilibrium for a solvent extraction process. a) Closed system of two partially miscible liquids T and L b) Open system of three liquids, T/L and L/S partially miscible R ,,R,, R3 Raffinate phase E l , E2,E3 Extract phase K , , K 2 ,K3 Tie lines BC Binodal curve EC Equilibrium curve P Plait point at K* = 1 Mole fraction of the key component in the raffinate and extract phases x, Y Mole ratio of the key component in the carrier and the solvent X, Y 45" degree line used to transfer equilibrium concentration points x =y

The ratio of the distances CR/m must correspond to the ratio of the mass fractions of the conjugate phases. To determine the binodal curve by the tilration method, the third component must be added slowly to either one of the homogeneous binary mixture, T/S or L / S . If the binodal curve is reached, the mixture becomes cloudy. The analysis gives one point on the binodal curve (point E in Fig. 1-11).

Binodal curves found experimentally may be described by empirical correlations (parabolic approach for system of type C and Hlavaty approach for system of type D in Fig. 1-12 [1.21, 1.221). In the case of a low concentration of S distributed in the raffinate and extract phase, Eq. (1-64) can be used to calculate the distribution coefficient. The activity coefficient in Eq. (1-58) should be calculated according to Table 1-8.

28

1 Basic Concepts 5

S

1

P

L

Fig. 1-14. Temperature effect on ternary liquid equilibria [0.8]. P Plait point T, L, S Components

Data for liquid-liquid equilibria can be found in [1.23-1.301.

1.4.3 Vapor-Liquid Equilibrium 1.4.3.1 One Component Systems The phases of a one component system are usually presented on a p,19diagram. Figure 1-15 shows a p , I9 diagram for water. The diagram is divided into three areas, the solid phase (ice), the liquid phase (water), and the vapor phase (steam). At a higher pressure, due to the existence of additional solid phases, further regions are added (polymorphic). Inside each area the system is divariant; pressure and temperature may be varied independently. The lines separating the regions are the melting or fusion curve, the vaporization

curve and the sublimation curve. These lines generally connect points between the phases at which each of the two coexisting phases are in equilibrium. According to the Gibbs phase rule, a one component system with two phases is monovariant at equilibrium. If the pressure p is changed, then, according to the saturation pressure, the temperature B must also change. The pressure p and temperature 19 are related by the corresponding equilibrium curve. The differential Eq. (1-49) gives the relationship between the two phases at equilibrium. A brief review of the equilibrium conditions, according to Eq. (1-40) gives the following: dgsystem at equilibrium = dgsystem at equilibrium = dgI - dgII =

(1-66)

29

1.4 Phase Equilibria

t I

P 218 Ibarl

From the latent enthalpy of phase transition from I + I I follows

IMC

~

Ah

A S = __

0.987

0.00611

(1-70)

T

Substituting Eq. (1-69), it follows that dp - A h d T T. A V

~

(1-71)

u 0.0075 100

31oc1

37L

Fig. 1-15. p , &Diagram of water. TP Triple point (coexistence of three phases, invariant system) MC Melting or fusion curve (coexistence of solid phase and liquid phase at equilibrium, monovariant system) VC Vaporization curve (coexistence of liquid phase and gas phase (steam) at equilibrium, monovariant system) SC Sublimation curve (coexistence of solid phase and gas phase at equilibrium, monovariant system) C P Critical point p Pressure B Temperature

where dg,, dg,, are the change of free enthalpy in phases I and 11. Substituting into Eq. (1-18), dg1= - S , . d T + q . d p = d g I I = - -311

*

d T + 61. dp

(1-68)

The slope dp/dT of the equilibrium curve between two coexisting phases is therefore

(1-69) where A i is the difference in the molar entropies, and A the difference in molar volumes of phases I and 11.

v

This is the common form of the ClausiusClapeyron equation, also known as the Clapeyron equation. The equation is generally valid and describes all forms of two phase equilibria for one component systems. In the following text, vapor-liquid equilibrium will be discussed. The equilibrium curve is the vaporization line beginning at the triple point and ending at the critical point where the liquid and gas phase are “identical”. Substituting the molar vaporization enthalpy Ah,,g, at the equilibrium temperature T, and the difference of the molar volumes A V of vapor (g) and liquid (I) (TI)into Eq. (1-71), the slope of the vaporization curve is

(6,)

dp

d~

G

-

T.

g

(q,- q)

(1-72)

At a certain distance from the critical point, the molar volume becomes negligible in comparison with GI. Furthermore, if the vapor phase behaves like an ideal gas, may be substituted by RT/p. Eq. (1-72) therefore becomes

q

6,

dlnp ~

dT

Ahl,g %-

R - T2

(1-73)

Upon integration, the following approximation for the vapor-pressure curve is then found :

30

1 Basic Concepts

l n p = - _'his' .R

T

+ const

(1-74)

If Q GI, a plot of Eq. (1-74) as l n p against l/T yields a straight line. This implies the assumption of ideal behavior for the vapor and a vaporization enthalpy independent of temperature and pressure. A better correlation for vapor pressure is as presented by ANTOINE

cal temperature of the components in the mixture. In absorption processes, the temperature is usually higher than the critical temperature of the dissolved gas components. Nevertheless, distillation and absorption processes may be discussed together with respect to relevant phase equilibria. With the equilibrium condition for two phases expressed by Eq. (1-45) or derived from Eq. (1-49), the general equation for gas-liquid phase equilibrium is

(1-75) A, B, and Care substance related constants. Additional methods for computing vapor pressure are listed in [1.58]. If two points on the vapor pressure curve are known, such a s p , , and p z , T,, the vaporization enthalpy may be estimated using the integral form of Eq. (1-73)

1

*

(&

-

":T>

. dp]

P

(1-77)

where mole fraction of component i in the vapor phase pressure of the system at equilibrium p T temperature of the system at equilibrium I? the universal gas constant q,G partial molar volume of component i at pressure p and temperature T yi activity coefficient of i in the liquid phase (see Eq. (1-31)) xi mole fraction of component i in the liquid phase Q L molar volume of liquid component i at temperature T and saturated vapor pressure poi f , fugacity of the pure substance i at temperature T and the corresponding saturated vapor pressure poi yi

(1-76) Methods for computing the vaporization enthalpies are documented and critically examined in [8.1]. Figure 1.16 shows two common presentations of vapor pressure curves for a few different substances. For practical use, vapor pressure data may be found in [8.3, 8.41. 1.4.3.2 Two and Multicomponent Systems The Basic Equation for Vapor-Liquid Equilibrium

The basic equation for the vapor-liquid phase equilibrium forms the major design criteria for apparatus that separate liquid mixtures by distillation or selective absorption. In distillation, the process or actual working temperature is lower than the criti-

The fugacity f , is defined by the chemical potential of a real gas, as postulated by LEWIS:

pi =poi + R . T . lnf,

(1-78)

1.4 Phase Equilibria 1c

[bad

a a’

tP 6

10

[bar] 7 6

5 L

b’

t:

log P

1.c

: 0

0.E

0.7 0.E

0.E 0.4

0.; Fig. 1-16. Vapor-pressure curves of some substances. a) p, T-diagram b) logp, l/T-diagram M Methanol W Water T Toluene E Ethanol B Benzol

31

32

1 Basic Concepts

Fugacity is used to replace the pressure of

an ideal gas pi by a “corrected pressure” A of a real gas i, to produce a universally valid relationship. At zero pressure a real gas behaves like an ideal gas, and fi lim =1 PI’O

(1-79)

Pi

A discussion and derivation of Eq. (1-77) can be found in [0.12, 1.581. Eq. (1-77) is universally valid, and should be applied if real behavior of vapor and liquid phases is to be considered. Considering the influence of pressure on the vapor and liquid properties of a substance, the real saturated vapor pressure p$ is

(1-80)

The molar volume vmay be computed with an appropriate equation of state for v(p,T). Eq. (1-82) can then be integrated. Useful correlations which may be used to calculate state variables are listed in Table 1-7. These equations may be applied to both pure gases and gas mixtures. Most correlations used to calculate the activity coefficients are based on the dependence of the free mixing enthalpy on the activity coefficient for each individual component in the mixture. If two pure components are mixed, the entropy AS, increases. A positive and/or negative change of enthalpy (“heat of mixing”) AH,, and a decrease of the free enthalpy, the free mixing enthalpy AG,, occur. It can be shown that AGM+ T . AS,

AH,=

(1-83)

The free mixing enthalpy Ag,, one kmol of the mixture, is P

Ag, = R . T .

Eq. (1-77) becomes y..p = y;.

xi. p*. 01

(1-81)

AgM = R . T .

For the design of distillation and absorption apparatus, it is necessary to know the equilibrium relationship yi (xi) either as an analytical, homogenous equation, or at least as an equilibrium curve. According to Eq. (1-77), the fugacity or the fugacity coefficients can be calculated or found experimentally to be a function of pressure, temperature and phase composition. An expression for the fugacity is V - E ) . d p

T-

C xi. h a i i

1xi i

*

-

ln(yi x i )

(1-84)

Therefore

Calculation of Vapor-Liquid Equilibrium Data

In- =

=

related to

(1-82)

1xi. lnx, + i

+ E . T.Cxi.lnyi

(1-85)

i

In Eq. (1-85) the first term is the change of enthalpy during the mixing of ideal liquids, a free mixing enthalpy. The second term, change of excess enthalpy AgME, takes into consideration the behavior of real liquids in the mixing process. AgME=R.TCxj*lnyj i

(1-86)

1.4 Phase Equilibria

33

Table 1-7. Method to calculate p, V, T data for real gases and gas mixtures*. Method

Characteristics

Literature

Benedict, Webb, Rubin method ,,BWR equation"

Equation with 8 constants dependent on mixture concentration. Originally developed for light hydrocarbons, but modified and validity region expanded

BENEDICT,M., WEBB,G. B., RUBIN,L. C., .lChem. Phys. 8 (1940) 334. BENDER,E., Habilitationsschrift, Ruhruniversitat Bochum. ORYE,R.V., Znd. Eng. Chem. Des. Dev. 8 (1969) 4, 579.

Redlich-Kwong method

Equation with 2 constants determined by the critical data of a substance, many times extended and improved

Virial equation Wohl method

Correlation for second virial coefficients

WOHL,K., Z. Phys. Chem. 2 (1929) 77

Prausnitz, Gunn method

Correlation for second virial coefficients

PRAUSNITZ, J.M., and GUNN,R.D., AZChE. J. 4(1958) 430.

*

REDLICH,O., and KWONG,J., Chem. Rev.

44 (1949) 223.

Additional methods in [1.70].

Applying a partial mole fraction derivative to Eq. (1-86), the activity coefficients of the components are given by

For example, the activity coefficients of a binary mixture y1 and y2 are

(1-88) and

Some examples for practical use are given in Table 1-8. Each method has been selected and tested on many substances, and their possible applications are given. All of the listed computation methods need not only be used for variables of pure substances, but also for state variables of the mixture. One or more points on the equilibrium curve of a binary system should be found experimentally.

Experimental Investigation of Vapor-Liquid Equilibrium

The procedure to find vapor-liquid equilibrium data by experimentation is as follows: A sample of a liquid mixture, with a known mole ratio in equilibrium with a vaThe methods used to compute A g M L . por phase, is selected and analyzed. Equiincluding Eqs. (1-87)-(1-89), lead to the librium data at constant temperature or methods of VAN LAAR,MARGULES, WOHL, constant pressure can be found. This comREDLICH-KISTER, WILSON, and PRAUSNITPmon procedure is explained in detail by to compute the activity coefficient. HALA,PICKet al. [1.58, 1.591.

34

1 Basic Concepts

Table 1-8. Methods to Calculate Vapor-Liquid Equilibrium Data [1.70, 1.711. Method

Characteristics

Literature

Method of WOHL (VANLAAR,MARGULES,SCATCHARDHAMER)

Effective Volumetric Ratio Polynomial Equation for the excess Gibb's energy, interaction parameters, relatively simple to use

WOHL,K., Trans. Am. Chem. Eng. 42 (1946) 215 [1.13].

Extended Van Laarmethod

For nonpolar binary systems with large dilution in the region up to the critical region

MUIRBROOK, N. K., Dissertation, Univ. of California, Berkeley (1964) CHUEH,P. L., and PRAUSNITZ, J. M., Computer Calculations for HighPressure Vapor Liquid Equilibria. Prentice Hall Inc., 1968.

Scatchard-Hildebrand Solubility parameters and partial Equation, Chaomolar volumes are referred to Seader method 25 "C, suitable for hydrocarbon systems

CHAO,K.C., and SEADER,J.D., AIChE. J 7 (1961) 4, 598.

Wilson equation

Interaction method for the excess Gibb's energy; suitable for totally miscible systems, not applicable for systems with limited miscibility since only the binary parameters are used, applicable to multicomponent systems; only valid for small and medium operating pressures

WILSON,G.M., J. Am. Chem. SOC. 86 (1964) 127.

NRTL equation (non random two liquids)

Method based on the Wilson equation with nonrandomness parameter which can be applied to systems with limited miscibility and nonideal systems; use of binary parameters to calculate multicomponent data; only valid for small and medium operating pressures

J. M., RENON,H., and PRAUSNITZ, AZChE. J 14 (1968) 135. RENON,H., and PRAUSNITZ, J. M., Ind. Eng. Chem. Dev. 8 (1969) 3, 413.

Uniquac equation (universal quasi chemical)

Method based on the principle of the local compositions, similar to the Wilson and NRTL equations, which are derived as special cases; also describes ,,real" liquid phases; only valid for small and medium operating pressures

GMEHLING, J., ANDERSON, T.F., and PRAUSNITZ, J.M., Ind. Eng. Chem. Fund. 17 (1978) 269.

Unifac equation (uniquac functional group activity coefficient)

Contributions of individual functional groups; prediction of the interaction between the activity coefficients of functional groups by interaction parameters, only valid for small and medium operating pressures

J., FREDENSLUND, A., GMEHLING, and RASMUSSEN, P., Vapor-Liquid Equilibria using Unifac. Elsevier Publ. 1977.

1.4 Phase Equilibria

35

n

Fig. 1-17. LABODEST apparatus for the determination of vapor-liquid equilibria. Vacuum, ambient and over pressure operation at temperatures up to 250°C. Presentation according to data of Fischer Labor- und Verfahrenstechnik, Meckenheim near Bonn [1.61]. 1 Flow evaporator with electrical immersion heater Phase mixing chamber to adjust the equilibrium 2 3 Phase contact path 4 Phase separation chamber Solenoid valves to take samples 5 6 Sample take-off, vapor phase 7 Sample take-off, liquid phase 8, 9 Sample take-off, circulation streams 10 Gaseous sampling of vapor phase, i. e., for systems with a miscibility gap

36

1 Basic Concepts

Figure 1-17 shows an experimental apparatus introduced by FISCHER[1.61] to find vapor liquid equilibrium data.

(1-92) In Fig. 1-18, the method used to check consistency is applied to a binary mixture of acetone and trichloromethane. The equilib-

Consistency of Equilibrium Data To check for accuracy, thermodynamic consistency, and lack of contradiction in the equilibrium data found, many methods and criteria using both experimentation and correlations are available t1.62- 1.661. A simple method used to check the consistency of data for a binary system is discussed below: At a constant temperature, it follows from Eqs. (1-21)-(1-26) that (1-90)

a1

I

0

1

10

0.2

x1 0,L

05

0.8

1,O

- 0.1

-0.2

h

- - 0,3

This leads to a simplified Gibbs-Duhem Equation particularly for a binary mixture

The logarithm of the activity coefficients in Eq. (1-91) may be plotted against the mole fraction of component 1. For a consistency check of the values for logy,(x,) and log y 2 (x2)data, the following requirements should be satisfied: Over the complete range of mole fractions the curves should have opposite slopes At the point x1= 0.5 the slope of the curves should be equal but opposite If the curves do not show a minimum or maximum, all y-values should be either larger or smaller than 1 (all data points for both logy(x,) curves should be on the same side of the log y = 0 line) The integral, or rather the area below the log ( y 1 / y 2 )(xI) curve has to be equal to 0

-0.3I Fig. 1-18. Proof of consistency of vapor-liquidequilibrium data for an acetone-trichloromethane system at 1.013 bar. a) log y,,x,-diagram to prove Eq. (1-91) b) log ( y 1 / y 2 ) , x,-diagram to prove Eq. (1-92), 1 Acetone, 2 Trichloromethane

1.4 Phase Equilibria

rium data is supplied by the DECHEMA service for substance properties. The calculation was done with the aid of the Uhde-substance property compiler using the Van-Laar Method. In process engineering the proof of published vapor-liquid equilibrium is of particular interest. In [1.67-1.701 and [1.72-1.851 data collections and bibliographies are listed. Particular attention is given to a collection of vapor-liquid equilibrium data by GMEHLING et a1 and published by DECHEMA [1.72]. Ideal and Real Mixtures

Depending on miscibility and effects resulting from mixing (volume contraction, volume dilation, heat of mixing) of different kinds of liquids, real and ideal mixing behavior and real and ideal mixtures can be distinguished. In an ideal mixture, components are miscible in any mole ratio. The attractive force between different types of molecule, is the same as that between similar types of molecule. During mixing there are no volume effects or heats of mixing. In practice, only approximately ideal behavior is found, for example, in the mixing of substances such as isotopes, optical antipodes, stereo isomers, structural isomers and neighbors in a homologous series. For an ideal mixture, Raoult’s law follows from Eq. (1-81)

y I . p = p . = p O,I. . X i

(1-93)

Definition of Raoult’s law: The partial pressure pi of component i in the vapor phase is at an adjusted equilibrium proportional to the mole fraction xi in the liquid phase. The saturated vapor pressure po,i depends on the equilibrium temperature. For a real mixture the attractive force between different types of molecule is not the same as that between similar types of mole-

37

cule. Molecules are described as similar if they have similar size, structure, and chemical nature. If in a particular mixture, the attractive force between different types of molecule is smaller than that between similar types of molecule, the molecules in the mixture are held together with a smaller force than those in a pure liquid. Thus, the effect during mixing is an endothermic volume expansion and an increase in vapor pressure. There is a positive deviation from Raoult’s law which leads to a pronounced maximum for the vapor pressure, and therefore to a minimum boiling point (for example, ethanol-water mixture). If the attractive force between different types of molecule is larger than that between similar types of molecule, the molecules in the mixture are held together with a stronger force than those in a pure liquid. This results in an exothermic volume contraction during mixing. There is a negative deviation from Raoult’s law, leading to the development of a minimum in the vapor pressure curve, and a maximum boiling point (for example, nitric acid - water mixture). In Table 1-9, different approaches to describe the liquid-vapor (or gas) phase equilibrium are listed. In distillation processes, the operating pressure is usually in the range ca. 0.05-5 bar. It is sufficient to treat the liquid phase as a real liquid, while the vapor phase may be assumed to be ideal. Gas absorption processes are often carried out under relatively high pressure conditions. The real behavior of the vapor phase must be taken into consideration. Representation of the Vapor-Liquid Equilibrium for Binary Mixtures

For the graphical representation of vapor liquid equilibrium of binary mixtures, there

38

1 Basic Concepts

Table 1-9. Gas - liquid equilibrium relationship. Liquid phase Ideal Partial pressure p i of component i in the vapor phase

-

Ideal

PI = Po,1 . XI

Real

1)

-

-

Gas phase

Ideal

PI = Po,1.

Y1

. XI

Real - Real

PI =Po*,[‘ Y1 . XI

Distribution coefficient KT = y ;/x; Relative volatility (separation factor) ai,k Partial pressure p i of the super critical component in the gas phase ’)

Raoult’s Law.

’)

ai,k =

Po. i

Y1 . P0,l Yk’P0.k p I. = H I. . y .l . x l.

ai,k =

Po, k

~

p I. = H I. . x2) 1

~

ai,k =

P,*,i

Yi ~

Yk

*

Po*, k

p I. = p *0,1. . y I. . x I.

Henry’s Law.

are three diagrams of practical importance: the pressure diagram, the boiling diagram, and the equilibrium diagram.

Pressure Diagram: The partial pressures p 1 and p 2 of both components of the mixture, in the vapor phase, and the pressure p, the system or total pressure of the liquid and vapor phase, are plotted against the mole fraction of the liquid phase at constant temperature. Boiling Diagram: The boiling line and dew line are plotted at constant pressure. The boiling line L9(x) connects the bubble points at boiling temperature as a function of the composition of the liquid mixture. The dew line L9(y) shows the condensation temperature Of the saturated vapor mixture as a function of its composition in the vapor. Equilibrium Diagram: For the case of constant operating pressure, the equilibrium composition of the vapor phase is plotted as a function of the liquid phase composition.

Figure 1-19 shows the three diagrams for an ideal binary mixture (for example, a nearly ideal binary system is benzol-toluene). The pressure diagram for an ideal mixture may be described by Raoult’s law. The partial pressures p1(x,), p2(x2)and the overall pressure p(xl) are straight lines. Boiling lines and dew lines for an ideal mixture at a given pressurep may be derived from Dalton’s and Raoult’s laws to give P=CP;

(1-94)

i

and (1-95)

p,I = y 1, .

Therefore, the equation describing the boiling line is

x1(L9,p) =

P - Po,z(d) Po, 1 (8) - Po,2 (19)

(1-96)

and the equation describing the dew line is

1.4 Phase Equilibria

0

x,l%l b)

f

3

100 OC

90

"0

20

XI,

LO

~1160

100

f

-

80 x 1%1

cl

x2

100

8o

Y

[%I 60 Yl

40

20

0'

20

XiLO

60

80

x[%l

-

100

39

Fig. 1-19. Pressure diagram, boiling diagram and equilibrium diagram for the almost ideal mixture benzol-toluene. a) Pressure diagram for a mixture of boiling point temperature 100 "C p 1(xl),p2(x2)Partial pressure lines of benzol and toluene p(xl,xz) Total pressure line X1 Molar fraction of benzol in the liquid phase Molar fraction of toluene in x2 the liquid phase b) Boiling diagram at a total pressure of 1.013 bar I Liquid phase region I1 Steam or vapor phase region 111 Two phase (wet steam) region B Bubble point line D Dew point line L9 Temperature c) Equilibrium diagram at a total pressure of 1.013 bar y Molar fraction of benzol in the vapor x Molar fraction of benzol in the liquid phase -- Conceptional lines to generate the equilibrium diagram from the boiling diagram

Similarly, the equilibrium curve of an ideal mixture may also be derived from Dalton's and Raoult's laws to give Po, 1

yI = P0,l

XI

f

*

XI

(1-98)

P0,2 x 2

The relative volatility a1,2,independent on concentration (see Chapter lS), is (1-99)

Boiling lines and dew lines may be calculated stepwise for a chosen temperature 8. po,l and po,z are the saturated pressures of pure components 1 and 2 corresponding to temperature 8.

y, =

a1,2 * X l

1 + x1 *

@1,2

- 1)

(1-100)

The equilibrium curve may also be developed graphically from the boiling diagram,

40

1 Basic Concepts Fig. 1-20. A schematic of the equilibrium behavior and important thermodynamic functions of a binary system according to Rock [1.861, a) Pressure diagram b) Boiling diagram c) Equilibrium diagram d) Activity coefficient diagram e) Relative volatility diagram f ) Free excess enthalpy of the mixture g) Mixing enthalpy and excess entropy 1st Column: Ideal mixture 2nd Column: Real mixture showing positive deviation from ideal behavior (for example; ethanoltoluene) 3rd Column: Real mixture showing negative deviation from ideal behavior (for example; acetonechloroform)

yressur e diagram

I

x1 Boiling diagram I

bl

0

1

1

0

u XlYl

0

1

P=const

Equilibrium diagram

1 0

1 0

Cl

P =const.S=const

Activity coefficient diagram

dl

Relative volatility diagram

enthalpy Free excess of

dSE

I loo~oc~n

0

the mixture

fl

1oi

/1

__c

Mixing enthalpy and excess entropy

41

x1

3xonst,p=const

O M T-A;, 0

T*AZE

dii

41

1.4 Phase Equilibria

according to the requirement that the system is at thermal equilibrium. In Fig. 1-19 the graphical development of the procedure is shown. This is generally valid and includes real mixtures. Distillation processes are influenced by the working pressure, as shown in Fig. 1-19. With a reduction in pressure, at the same mole fraction x1 in the liquid, the vapor fraction y , increases; hence the separation of the mixture is more efficient at lower pressure. To describe phase equilibria for real binary mixtures, the equations listed in Table 1-9 can be used. Pressure, boiling, and equilibrium diagrams, and other plots showing system behavior characteristics for a real mixture, are given and discussed in Fig. 1-20. According to Raoult's law, and therefore applying to ideal behavior, the activity coefficient can have positive (yi> 1) and negative (yi < 1) deviations. Pressure, boiling, and equilibrium diagrams for the steam distillation of common and important binary mixtures of partial miscibility are shown in Fig. 1-21. Azeotropism An azeotropic point is characterized by the following : 0

0

Pi

X2,ac = Y2,ac

(1-101)

The relative volatility of an azeotropic mixture a,,= 1, therefore (1-102) hence

-

P2

XI

Ylxi

cl

IP iPl

-

iP1 XI

-

YI XI

p=const

-

p=const

t __

x1oc XI

-----c

1

0

-x1oc

x1

I

Fig. 1-21. Pressure diagram (a), boiling diagram (b) and equilibrium diagram (c) of a binary mixture with a miscibility gap over the complete concentration range (left column) and a binary system with a limited miscibility gap (right column). x ~ Azeotropic , ~ ~ concentration B Bubble point line D Dew point line

The equilibrium composition is the same for both vapor and liquid phases X1,ac = Y l , a c

I

P

0

(for an explanation of Eqs. (1-102) and (1-103), see Chapter 1.5) For an azeotropic mixture the isothermal partial pressure curve p 1(xl),p2(x2),the isobaric boiling line t?(xl) and dew line d ( y J and the isobaric equilibrium curve y 1(x,), exhibit maxima/minima (maximum boiling or bubble point and therefore minimum vapor pressure; minimum boiling or bubble point and therefore maximum vapor pressure see Fig. 1-20)

It is not possible to separate an azeotropic mixture by simple distillation. To

42

1 Basic Concepts

t

s,

X-

Fig. 1-22. Influence of the operating pressure on the azeotropic point. A, Azeotropic point at an operating pressure of

PI

A, Azeotropic point at an operating pressure Pll cpz capillary condensation

adsorbate in the gas mixture is higher than the partial pressure, corresponding to the adsorbent load X i at equilibrium. Desorption occurs if the concentration of the adsorbate in the light phase is lower than the corresponding equilibrium concentration. If rpi is almost equal 1 condensation of adsorbate takes place. If the structure of the solids consists of a capillary system with small pore sizes, even with pi < 1, capillary condensation of adsorbate with wetting behavior occurs. According to the Gibbs-Kelvin equation (1-134)

where 0

surface tension (N/m)

Mi molar mass of the adsorbate (kg/kmol)

el,; density of the adsorbate in the liquid r

state (kg/m3) radius of curvature (m), negative for wetting (concave surface) and positive for nonwetting- (convex surface) in Eq. (1-134) bl

al

scopic, if the partial pressure p , is equal to the saturated vapor pressure of the adsorbate the partial pressure p iis then only a function of temperature, and only the heat of vaporization is necessary for drying. In practice often low concentrations of the gas phase adsorbate must be handled. The adsorption equilibrium curve is therefore characterized by high loading rates of the adsorbate into the adsorbent at low adsorbate partial pressures in the equilibrium gas phase (approximate vertical tangent of the adsorption isotherm at pi 0, Fig. 1-34). Adsorption takes place when the partial pressure p i or the relative saturation rp, of +

PL

-

t

k

:"i

9-

- - - Capillary condensation

Fig. 1-36. Adsorption isotherm (a), sorption hysteresis (b). Ad Adsorption isotherm De Desorption isotherm X Loading of adsorbent with adsorbate p , Equilibrium partial pressure p Relative humidity

1

35

1

30

25

1/x

20 15 10

5

0 I1

0

0.21 I

01

I I

1.o

106

;

x,y-

08

I

I

I

I

1

I

X

0.6

0.4 0.2

02

I

02

I

01

1

06 x.y

08

1

10

I

I

f 0.8

0

0

04

06

Y-

08

I Adsorption equilibrium data for the system oxygen/nitrogen/active carbon. Presented in a triangular diagram using mass fractions as the concentration scales (8 = - 150"C, p = 1 bar). A,B State points of active carbon loaded with pure oxygen and pure nitrogen, respectively. Curve A.. E.. B Locus of the state points of active carbon loaded with gas mixture. RE Conode TI Adsorption system : Acetylene/ethylene/silica gel ( 8 = 25 "C, p = 1 bar). I11 Adsorption system: Acetylene/ethylene/active carbon (8 = 25"C, p = 1 bar). X Loading of the adsorbent by the key component (adsorbate), in kg key component/kg adsorbent x Molar fraction of acetylene in adsorbate y Molar fraction of acetylene in the gas mixture

58

1 Basic Concepts

1 1

X

0

0

1.0

1.0-

t

1 Y-

Fig. 1-38. Influence of pressure on the course of the adsorption isotherm for the coadsorption of two gases [0.8]. X Loading of the adsorbent by the key component x Molar fraction of the component which is more easily adsorbed in the (key component free) adsorbent y Molar fraction of the more easily adsorbed component in the gas mixture

At the concave surface of a wetting adsorbate in the liquid state, for a capillary of radius r, the adsorbate vapor pressure (po,i ) r is lower than the vapor pressure po,i for a flat surface. For a nonwetting adsorbate, b0Jr > capillary condensation does not occur. Due to capillary condensation, with a monomolecular layer at the adsorbed surface the adsorbate concentration is considerably higher than the saturation concentration X,,, (Fig. 1-36). The adsorption isotherm can be found experimentally using volumetric or gravimetric methods. Special methods to measure proportional properties to detect the change in the occupation of the adsorbate on the surface of the adsorbent are also available (see [1.32, 4.1, 4.21). For the correlation and extrapolation of equilibrium data for adsorption processes with one adsorbate component useful approximations are listed in Table 1-12. Experimentation has shown that different adsorption isotherms are occasionally obtained, for data taken during adsorption or desorption under the same conditions. This hysteresis in the sorption isotherm (Fig. 1-36) must be considered in the design of adsorbers and thermal dryers. The hysteresis phenomena can be explained by capillary condensation. For the adsorption in an adsorbent composed of two components from a gas or vapor mixture, the adsorption equilibrium may be conveniently represented using a triangle. The triangular axes are then l/X, y, and y,x mole fractions or mass fractions. Figure 1-37 shows some practical examples from [0.8]. The effect of the operating pressure of the adsorber can be seen in Fig. 1-38. Published adsorption equilibrium data for binary and ternary mixtures can be found in [1.40]. Adsorption equilibria for two component and multicomponent systems may be calculated using the correlations listed in Table 1-13.

1.4 Phase Equilibria

59

Table 1-12. Correlations and methods for the extrapolation of equilibrium data for one component adsorption. 0

Freundlich equation [1.33] X = k, * pk2

k,, k2 Temperature dependent constant determined experimentally. Freundlich's method is valid for the description of adsorption isotherms of form 5 given in Fig. 1-35. 0

Langmuir equation [1.34] X=

k~ . Xmax . p 1+ k A ' p

kA Adsorption coefficient, Xma,maximum monomolecular layer loading of the adsorbent by the key component (adsorbate).

k System specific adsorption constant (usually k = 1); heat of vaporization of absorbate. AfiAd Adsorption enthalpy, Langmuir equation is valid to the point that the monomolecular layer is saturated. kA and Xma,are experimentally determined. 0

Brunauer, Emmet, Teller equation (,,BET" equation) [1.36] kA*p

x = xma, ' -. 1-p

1 -(n+l).p"+n.p"+'

1 + (kA - 1) * p - kA * p n t '

(In the range 0 < p < 0.35 simplification according to X=

k~ . P (1 - a) . (1 - + kA * Xmax.

and rearranging, gives

-.-

-

1

kA

-1

+ .P Xmax*kA X m a x . k ~

X 1-P the linear relationship in the 1/X. p/(p - l), p diagram. Basis for the determination of the BET surface [4.26]).

n Number of molecular layers of the adsorbed component on the adsorbent (for n = 1 Langmuir equation).

BET equation is valid for multilayer adsorption. Modified BET equation also applicable for systems with capillary condensation [1.36].

0

Dubinin equation i1.371

V Adsorbed volume at the adsorbent

V, Adsorbent saturation volume at p = 1

C Structural factor (depends on the pore structure of the adsorbent)

p Affinity constant, m exponent, characteristic for adsorption system

1 Basic Concepts

60

Table 1-13. Calculation of the adsorption equilibrium of binary and multicomponent systems. 0

Modified Langmuir equation [1.40]:

1

e Experimentally determined adaption parameter X,,,,, Monomolecular layer of component i or of all m components (no uniform fixed value)

k, Adsorption coefficient of the ith component (determined by the adsorption isotherm of i ) 0 0

Modified Dubinin equation [1.41] Ideal Adsorbed Solution Theory (IAST) of MYERSand PRAUSNITZ [1.42], Real Adsorbed Solution Theory o f COSTA et al. [1.43].

1.4.5 Liquid-Solid Phase Equilibrium 1.4.5.1 Solubility of Solids in Liquid Solvents If a solid with an amorphous or crystalline structure is dissolved in a large excess of solvent, the dilute solution gives one homogeneous phase. If more solid is added to the diluted solution, up to the point where the solid can no longer be dissolved, the solution is saturated or at solubility equilibrium. The maximum solubility or the maximum capacity of the solvent to dissolve the solid has then been reached. The solubility of the substance to be dissolved in the solvent depends on the temperature, molar amount of solvent in the crystals, and hence the form of the crystals; the dependence on pressure is only minor. For the same crystal form, solubility usually increases with a higher temperature. If the molar volume of the solid decreases during

dissolution, increasing the pressure also increases the solubility. Figure 1-39 shows a schematic section of the phase diagram for a binary system (solvent - dissolved substance), including the eutecticum. The eutectic of solutions diluted with water is called the cryohydrate. It appears in all solvent - dissolved substance systems. In Fig. 1-39, cooling a solution from point A down to the solubility curve SC, causes crystallization to take place (the case of over solubility will be discussed later). The mass fraction of solvent in the solution thus increases because of partial crystallization of the dissolved solid. During the cooling process, the change of state of the solution moves along the solubility curve SC until the eutectic point E is reached, the solution then freezes completely. If a solution is cooled from B, then the solvent freezes when the ice curve IC is reached. The dissolved substance becomes enriched (the concentration of the solution is increased because the fraction of solvent

1.4 Phase Equilibria

I"C1

W-

Fig. 1-39. Phase diagram for a binary solvent/ dissolved substance system with eutectic point without solvate formation. I Homogeneous solution region I1 Two phase region, solution, and solvent as the bottom layer 111 Two phase region, solution, and solid as the bottom layer I V Region of solid phase, solvent, and eutectic point V Region of solid phase, solute, and solvent IC Ice curve SC Solubility curve E Eutectic point (cryohydrate) ~5 Temperature w Mass fraction of the dissolved substance in the solution Phase. -+ Change of the solution state by cooling from A and B

is decreased by freezing the solvent). During the cooling process, the change of state of the solution moves along the ice curve IC until the eutectic point E is reached; the solution then solidifies. No further separation of solvent or dissolved solid by cooling is possible while passing through the eutectic point E. Therefore, the eutectic temperature is the limit for crystallization by cooling. The closer the

61

system is to the eutectic point the more difficult it becomes to separate the dissolved substance from the solvent. The effect of temperature on the solubility is shown by the solubility curve SC. In crystallization processes, the solubility is expressed as a function of the loading X (kg/kg) of the substance dissolved in the solvent. In the solubility-temperature diagram, the saturation concentration or solubility X i s plotted against the temperature r9, with the result being the theoretical solubility curve or saturation line X ( v )(Fig. 1-40). In Fig. 1-41, if a solution is cooled carefully without a crystallization seed, the following is observed: despite the fact that the saturation line has been crossed no dissolved solid crystallizes. After passing the first oversolubility curve, single crystal seeds may be observed, whilst on passing the second oversolubility curve, small crystals develop spontaneously. The area of the stable, unsaturated solution is followed by the area of the metastable, over-saturated solution between the saturation line and the second over-saturation line. It follows that the area where seeds are spontaneously formed is the area of unstable two- or multiphase systems. The range of practical crystallization processes carried out inside the important metastable area depends upon many process parameters, including solution concentration, intensity of mixing in the crystallizer, cooling rate, initial temperature, number of crystal seeds and the crystallizer shape (surface condition). In order to crystallize an over-saturated solution within the metastable area, inoculate crystals must be present when the solubility curve is crossed. If the crystal seeds are present when the metastable area is entered, the over-saturation of the solution will be reduced; this is because the over-saturation is mainly used by the crystal seeds for growth although a few new crystal seeds are formed. Both crystal growth and seed formation occur and

62

1 Basic Concepts

f

2.

t

%

Ig/lOOgl

Region of unstable solution // 1.

oc oc

k Miers-region) /'

Region of stoble solution (subsatured solution)

Fig. 1-41. Temperature-solubility diagram. SC Theoretical solubility curve (saturation line) 1. O C First super solubility curve 2. OC Second super solubility curve X Solubility r9 Temperature

are dependent upon the over-saturation of the solution (see Chapter 7.2.3). For practical use of crystallization processes, data and references regarding the solubility of solids in solvents can be found in [0.17, 1.46-1.50, 7.21. Calculations of the effect of temperature on solubility can be found in [1.111].

tr-l-l-.-pI \ 2

'0

20

LO

60

80 [ O C ] 100

9-

Fig. 1-40. Temperature-solubility diagram, solubility curves for different salts in water. Representation according to PERRY[0.17]. X Loading of solvent with dissolved substance, g of water-free substance in 100 g water (gA00 g H,O), solubility 6 Temperature

1.4.5.2 Melting Pressure Curve The solid-liquid phase equilibrium of a pure substance is described in the state diagram (see Fig. 1-15) by the melting pressure curve p ( T ) . This curve is formed by the connection of state points, where the liquid and solid phase coexist at phase equilibrium. For crystallization processes which start from the melting point, a knowledge of this curve is important. The melting pressure curve may be given based on the general form of the CLAUSIUSCLAPEYRON equation in a similar manner to the vapor pressure and sublimation curves (Eq. (1-71))

1.4 Phase Equilibria

A&, 1 dP dT T . -

(1-135)

(6 V,)

--

where dp/dT is the slope of the melting pressure curve, Ahs, the melting enthalpy, dependent upon temperature and pressure, and the molar volumes in the liquid and solid state, respectively and T the equilibrium temperature. The molar volumes and are almost the same. It is not allowed to simplify Eq. (1-135) by neglecting 5, el 0 and the melting temperature increases with increasing pressure. This is common for many substances, especially metals.

c,

Case2: A l / < O , 5 < el >@,. From Eq. (1-135) it follows that dT/dp < 0 and the melting temperature decreases with increasing pressure. For example, this applies to water, gallium, and bismuth. For some substances the sign of A V changes with increasing pressure, (for example with rubidium, caesium and graphite) the sign changes from plus to minus. A maximum temperature for the melting pressure curve then is when A V = 0 or el = e,. Different approximations for the melting pressure curve are discussed in [1.88].

YGas

Solid phase

St-

phase

T-

Fig. 1-42. Lowering of the solution freezing

point.

- T Lowering of freezing point

VC

VCS

SC p

T

Solvent vapor pressure curve Solution vapor pressure curve Solvent sublimation pressure curve Pressure Temperature

64

1 Basic Concepts (1-1 3 7)

where A & , is the melting enthalpy of the pure solvent and x, is the mole fraction of the soluted substance in the solution. Therefore, for an ideal solution, the decrease of the freezing point is proportional to the mole fraction of the solute in the solution. As shown by Eq. (1-128), for solutions, electrolytes, in which dissociation of the solute occurs, the number of molecules n2

t

h

Crystalline phase

t.-i

A

h

x-

B

x-

A

nlB

B+M

AIB-M A/B-M +BlA-M

AiB-M B/A.M A/B M - W A - M

~~

A

x-

0

A

x----t

of solute has to be replaced by the number of ions n;. Replacing the mole fraction x2 of the solute by its molality c, = n2/m,, in Eq. (1-137) gives

=

c,

a

c,

where C, is the cryoscopic constant of the solvent, and is defined within the brackets. C, is the decrease of the freezing point of a

Fig. 1-43. Melting point diagram of some binary systems. Type I Miscibility in the liquid and solid state of components A and B, mixed crystal formation over the entire concentration range. Type I1 Miscibility in the liquid state, immiscible in the solid state, melting point B diagram exhibits eutectic point. Type I11 Miscibility in the liquid state, partial miscibility in the solid state, melting point diagram shows eutectic point and mixed crystal region. Type IV Miscibility in the liquid state, partial miscibility in the solid state, melting L+B/A-M point diagram with peritectic point and mixed crystal region. Miscibility B/A gap reaches temperature region in which mixed crystals are formed. B Type V Compound formation by the components, immiscibility of the solid phases, development of two eutectic points, E, and E,. L Melt Mixed crystals M A/B-M A/B-Mixed crystal (excess of A) B/A-M B/A-Mixed crystal (excess of B) Eutectic point E Peritectic point P Connection A/B VAB Liquidus line LL Solidus line s

65

1.4 Phase Equilibria

solution when 1 kmol of the solute is dissolved in 1 kg of solvent. Table 1-14 shows the cryoscopic constants C, for some solvents. Table 1-14. Cryoscopic constants of several solvents. Solvent

Water Benzol Bromoform Cyclohexane Nitrobenzene Naphthalene Acetic acid

Melting point at 1.013 bar (“C)

Cryoscopic constant C, (K . kg/mol)

0 5.5 7.8 6.5 5.7 80 17

1.86 5.12 14.4 20 6.9 6.8 3.9

In an ideal solution, the increase in the boiling point and the decrease in the freezing point for a chosen solvent is only dependent on the concentration of the dissolved substance, and not the type (colligative properties). The increase in the boiling point and decrease in the freezing point may be used to calculate the molar mass of a soluted substance. 1.4.5.4 State Diagrams of Binary Systems

for Solid and Liquid Phase Equilibrium

For the basic calculation of crystallization starting from a melt, the state diagrams (melting diagrams, 7;x-diagrams) for the partial separation of binary mixtures must be known. A thermal analysis is carried out by the experimental detection of cooling curves. The temperature during cooling is measured as a function of time in solutions of different composition (see, for example, [1.89]). Methods for calculating crystallization equilibrium are presented in [1.112].

Figure 1-43 shows characteristic diagrams for binary systems with explanations given in the caption.

1.4*6 Enthalpy

Of

Phase Changes

For an isobaric phase transition of a substance, the enthalpy change is usually considerable. If a substance is exchanged between two or more phases in a heterogeneous system, a considerable positive or negative heat of evolution is expected. This is because an exchange of substances between phases always has a n associated exchange of heat. The enthalpy change of a substance associated with the isobaric transition from one phase to another at equilibrium may be described analogously to the CLAUSIUSCLAPEYRON equation as dlnZi - Ahi

~

dT

-

_

l?- T 2

_

(1-139)

where Zi is a characteristic quantity for the phase change and is dependent on temperature, the type of substance, and often pressure and concentration. This is explained for important thermal separation processes in Table 1-15. Usually Zi(7‘) is the phase equilibrium curve, or the line that divides the area at the different states of the phases. If, for example, in a one component system, the vapor pressure Zi is equal to the saturation vapor pressure po,i of substance i in the liquid phase, p J T ) is the vapor pressure curve of substance i. Areas of liquid and vapor (gas) phases are separated by the vapor pressure curve; single points on it represent phase equilibria (see Fig. 1-15). If a chemical reaction takes place, in separation apparatus at constant pressure, Z ( 7‘) is the chemical, temperature dependent, equilibrium constant. Eq. (1-139) is

5. Variable Zicharacterizing the phase change and phase change enthalpy Ahi.

nge of substance i between phase 1 and 2 Phase 2 Number of system components 1 S

3, n

1

2, n

g

2, n

g

1

g

2, n

g

1

g

2

1

1 2, n

1 1

Characteristic phase change variable Z j

Phase separation curve (phase equilibrium curve)

Phase c enthalpy

Thermal process

Recrystallization Melting Solidification (crystallization from a melt) Dissolving Liquid-liquid extraction Crystallization from a solution Sublimation Desublimation Adsorption Desorption Drying Evaporation Condensation Distillation Partial condensation Absorption Desorption Liquid-liquid extraction

Recrystallization pressure Melting pressure

Recrystallization pressure curve Melting pressure curve

Recrysta enthalpy Melting

Solidus line Liquids line

Vapor pressure curve

Vapor pressure

Sublima

Sublimation pressure curve Adsorption isotherm Desorption isotherm

Gas load of the solid Moisture load of the solid

Differen solubilit

Saturation curve (solubility curve)

Solid load of the solvent

Sublimation pressure

Partial vapor pressure Henry constant absorption coefficient Gas load of the solvent Distribution equilibrium constant

Bubble point line Dew point line Absorption isotherm

Sorption isotherm

Adsorpti

Evapora Evapora Absorpti

Mixing differenc

tions: s solid phase, 1 liquid phase, g gas phase.

67

1.6 Minimum Separation Work

then the Van-Hoff’s isobar, with reaction enthalpy Ahi. An average value of the differential enthalpy Ahi of the phase change may be assumed, by integrating Eq. (1-139) in the temperature interval T, q.This may be done, if no measured data is available, and the shape of the equilibrium Zi(7‘) is known, using +

Ah, =

R e T, -T2.(lnZi,r,-1nZi,r,)

G-T,

(1-140)

1.5 Separation Factor and Relative Volatility The separation factor a is generally defined as

The separation factor is therefore a direct measure of the separation efficiency of a separation unit or the whole process, and is thus of practical importance. It is usually dependent on pressure, temperature, and phase composition. Large values for the separation factor characterize a process whith a low separation effort. The more a approaches unity, the more difficult the separation. When a = 1 separation is impossible. The separation factor a is the relative volatility in distillation processes. The light phase is the vapor phase and the heavy phase is the liquid phase; the component with the lower boiling point is the “light” component. Taking Dalton’s and Raoult’s laws into account, Eq. (1-142), the relative volatility of the lighter component 1 referred to the heavier component 2, becomes

a1,2 =

Y1 ‘P0,l ~

.

Y2 P0,2

(1-141)

= f (p,

XI,. ..)

(1-144)

For ideal mixtures, Eq. (1-144) becomes where X, is the mole ratio of the key component leaving the separation unit or separation apparatus in the heavy phase, and Y, is the mole ratio of key component leaving the separation unit or separation apparatus in the light phase. Substituting the mole concentration Xl and Y, with the mole fraction x1 and y1 (see Table 1-4) the separation factor a,,2is a1.2 =

Y1 ‘ X 2 ~

Y2 +

x1

(1-142)

where 1 represents the key component and 2 represents the reference component. For a binary mixture Eq. 1-142 becomes (1-143)

a1,2 =

P0,l ~

Po,2

=f(p, T )

(1-145)

In this case, a1,2is dependent only on pressure and temperature and not on the composition of the mixture. A reduction of the working pressure p in distillation processes causes an increase in the relative volatility a and the separation becomes more efficient.

1.6 Minimum Separation Work The mixing of pure substances increases the entropy. The entropy of the mixture is the mixing entropy ASM plus the sum of the

68

1 Basic Concepts

entropies of the pure substances before mixing. Since the entropy increases, the free energy (free internal energy AF, in isochoric processes, free enthalpy AG, in isobaric processes) decreases. Thermal separation operations are isobaric apart from pressure drops which occur in the separation apparatus. During mixing the change of the free enthalpy ACM of the system, the free mixing enthalpy is equal and opposite to the minimum separation work Wmin required to separate the mixture into its pure components. Wmi,

=

(1-146)

-AGM

When k components are mixed to obtain 1 mol of a real mixture, as discussed in Chapter 1.4.1, the free mixing enthalpy AgM, is k

agM= R . T C xi.h a i < 0

(1-147)

i=1

AgM is negative for the entire concentration range, as seen in Eq. (1-147). The minimum separation work required to separate 1 mol of the k component mixture is k

qmin= - E . TCxi.lnai>O

(1-148)

i= 1

Work must be supplied to the system thus values of Wmin are positive. The actual work supplied to separate the mixture is usually higher than the minimum separation work, as given by Eq. (1-148). Additional energy is required to create additional phases if necessary, to divide phases using mechanical means, to mix or to disperse. The energy losses of the separation units, and the pump work necessary to transport the liquid are not considered in Wmin.

For a given mixing enthalpy AH,, the mixing entropy ASM may be derived from the definition of the free mixing enthalpy

(In ideal mixtures the mixing enthalpy AH, = 0; therefore ASM = - AG,/T and therefore ATM = - R . C xi lnxi > 0.) +

1.7 Mass Transfer Fundamentals The basic principles of mass transfer are discussed in detail in [1.95-1.971. Thermal separation processes are actually mass transfer processes; matter is transported between phases and across phase interfaces. Mass transfer is caused by differences in concentration within a phase and by disturbances of the phase equilibrium. The time taken to return to the phase equilibrium depends mainly on mass transfer, but also on heat transfer (heat is transported not only by convection and radiation at higher temperature, but also by mass). For the design of thermal separation processes, along with a knowledge of phase equilibria, it is also important to have a detailed understanding of how equilibrium is reached and the time required, taking into account restrictions in the mass transfer rate. There are two ways in which matter may be transported by the concentration gradient (the driving force):

Molecular Diffusion: Transportation of molecular size matter. Molecular diffusion takes place in solids and phases with no motion or in phase boundaries Convective Diffusion or Convection : Matter is transported in groups of molecules with the concentration gradient as the driving force, along with the free or forced flow. Under the operating condi-

1.7 Mass Transfer Fundamentals

tions chosen in thermal separation processes, convective mass transfer always occurs in liquid and gas phases Heat and mass transfer are analogous processes. Molecular diffusion in homogeneous materials or phases is similar to heat transfer. Convective diffusion or convection in homogeneous materials or phases corresponds to heat transfer by convection. Mass transfer at the phase boundary corresponds to heat conduction. Mass transfer between phases occurs like heat transfer in several chronological steps. The slowest step controls the rate of the entire process. Thus the mathematical descriptions of heat and mass transfer operations are analogous. Calculation methods and approaches to calculate the heat transfer coefficients may similarly be used to calculate mass transfer coefficients. (See Table 1-18 in Chapter 1.7.2 for the analogy of heat and mass transfer.)

1.7.1 Mass Transfer by Molecular Diffusion 1.7.1.1 Steady-State Diffusion Analogous to Newton’s law of momentum transport and Fourier’s law of heat transfer by conduction, Fick’s first law for mass transfer by steady-state equimolar diffusion, is

x

Dj

69

x coordinate of the diffusion space diffusion coefficient of component i in the diffusion space (m2/h)

Introducing the partial pressure of gases as measure of concentration, Fick’s first law becomes

oi.A n 4,x = - _ . R.T or m I., x =

-

apj

oi-M ~A. R.T

(kmol/h)

ax

api *

~

ax

(kg/h)

(1-150)

(1-151)

Fick’s first law describes equimolar diffusion, in which all components of the system may diffuse independent from each other. During thermal separation processes, matter is transported through phase boundaries. If a phase boundary is selectively permeable to one component, only one-directional diffusion is possible (an especially important case for absorption, adsorption, and drying). For one-directional diffusion, STEFAN’S law gives (1-152)

where c is the sum of the molar concentration of all components in the observed phase, and i is the diffusing component. For gases, Eq. (1-152) becomes

where rate of mass flux of substance i in direction x perpendicular to the area A (kmollh) diffusion area (m2) A aci/ax concentration gradient in the direction of the diffusion flux (kmol/ m3/m) Hi,x

where p is the system pressure. The difference in the flow rate fij,x as calculated by Eqs. (1-149) and (1-152), is the factor c/(c - cj), which is due to the additional superseding one-directional diffusion (“Stefan flux”). The amount of mass flux transferred by diffusion is therefore larger

70

1 Basic Concepts

with one-directional diffusion than with equimolar diffusion.

only for simple geometric cases (for example, plate, cylinder, sphere).

1.7.1.2 Unsteady-State Diffusion

1.7.1.3 Diffusion Coefficient

In unsteady-state diffusion processes, the concentration distribution (or concentration gradient) changes with time and position. Fick's second law for unsteady-state diffusion is analogous to the Fourier equation for unsteady heat transfer

The diffusion coefficient D generally depends upon temperature, pressure, the concentrations of the components and the substance mixture components to be diffused. Diffusion coefficients for several systems are listed (see, for example, [1.47, 1.49, 1.90-1.921) or may be calculated empirically [0.8, 8.1, 8.2, 8.16, 8.171. Diffusion coefficients for some systems are shown in Table 1-16 and simple calculation methods are presented in Table 1-17.

(1-154) Solutions of the partial differential equation for given boundary conditions exist

Table 1-16. Diffusion coefficient for different systems [0.1]. Diffusing component

2"d Mixture component (diffusion medium) (solvent)

Pressure

Temperature

(bar)

("C)

100 300 1095 1249 178 428

Gold

Lead

Silicon

a-Iron

Copper

Silver iodide

Benzol Carbon disulfide Methanol

n-Heptane n-Heptane Water

Benzol

Air

1.013

Benzol

Hydrogen

1.013

Benzol

Carbon dioxide

1.013

0

Steam Steam Steam

Air Hydrogen Carbon dioxide

0.981 0.981 0.981

45 0 0 0

25 25 18 0 45 0 45

Concentration

Diffusion coefficient

(m2/h)

4.5 to 7.1

0.83 . 0.54. 0.54. 1.80. lo-' 0.48. lo-' 1.23. lo-'

50 50 0.25

0.89. lo-' 1.28 * lo-' 0.49. lo-'

0.03 to 0.09

0.0270 0.0364 0.1058 0.1437 0.0189 0.0257 0.083 0.278 0.051

1.7 Mass Transfer Fundamentals

71

Table 1-17. Simple calculation methods for the diffusion coefficient. Diffusion in the gas phase The diffusion coefficient D l , 2of gas 1 into gas 2 under moderate pressure may be approximated using the critical data of the gases according to CHENand OTHMER[8.15]

(1-155) Where M I ,M2 Molar mass, kg/kmol Tk, Critical temperature, K J $ 2 Critical molar volumes of gas components 1 and 2, m3/kmol T Absolute reference temperature, K P Reference pressure, bar Dl,2 Diffusion coefficient, m2/s (To convert to different reference conditions and to therefore compute a rough estimate of the diffusion coefficient at different temperatures and pressures, a diagram is given by SLATTERY and BIRD [S.l5]).

5,

0

Diffusion in the liquid phase In large dilution of a solution without dissociation, the diffusion coefficent D l , 2of component 2 in a solvent 1 may be calculated using an equation given by WILKEand CHANG [8.15]

(1-156) Where D l , 2 Diffusion coefficient, cm2/s T Reference temperature, K q1 Dynamic viscosity of solvent, CP M I Molar mass of solvent, kg/kmol & Molar volume of dissolved substance referred to the boiling point at 1.013 bar, cm3/mol C Association factor (C = 2.6 for water, C = 1.9 for methanol, C = 1.5 for ethanol, C = 1.0 for benzol, ether and heptane as a solvent) The temperature dependency of the diffusion coefficient D l , 2 is approximated by the Stokes-Einstein-Term [0.17] (1-157)

The influence of the concentration on Dl,2is discussed, for example, in [0.17].

72

1 Basic Concepts

1.7.2 Mass Transfer by Convection According to the method used to calculate heat transfer by convection, the convective mass transfer under steady state conditions is

PB

I

t

I

,_

Phase I Ci,G

hi = p; * A * ( q k- Cj,G) = A * Ac;

Y

Phase II

L

(1-158)

X-

Fig. 1-44. Illustration of mass transfer.

See also Fig. 1-44, where: convective flow rate of substance i (kmol/h) area of phase boundary (m2) A cLK,c , concentration ~ of substance i in the bulk of the observed fluid Phase and at the phase boundary, respectively (kmol/m3) Pi mass transfer coefficient (m/h) ti;

PB Phase boundary 6 Boundary layer thickness c, Concentration of key component x Space coordinate

matter is only transported by molecular diffusion. Eqs. (1 - 149) and (1 - 158) are then

For gases, Eq. (1-158), gives

ti = I

P;-A -*

R-T

(pi,k

- P I ,G)

=

P,.A

Re T

. Apl (1-159)

where the partial pressures of the gas i, pi,K and pi,Gare those in the bulk of the gas phase and at the phase boundary, respectively. Eq. (1-158) describes generally the transition of a substance from within the bulk fluid to a phase boundary, or from a phase boundary into the bulk fluid (for the latter case, Eq. (1-158) must be appropriately modified). The concentration of the component in the kernel c ~ is , assumed ~ to be constant throughout the fluid. A concentration gradient Aci occurs only in the vicinity of the phase boundary (see Fig. 1-44). Furthermore, it is assumed that a laminar current exists in the boundary layer and that

and the mass transfer coefficient is

p.=-Di

'

s

(1-161)

where 6 is the thickness of the boundary layer. From this equation, the dependency of the mass transfer coefficient Pi on the diffusion coefficient 0; and the boundary layer thickness 6 of the fluid flow, may be seen. The laminar boundary layer and turbulent bulk cannot be distinguished exactly, due to the continous transition; the boundary layer thickness 6 is, therefore, a formal complementary variable. The mass transfer coefficient P depends upon fluid mechanics (free flow, forced flow), the physical characteristics of the exchanging matter system and the properties of the substance in the fluid phase, and may

1.7 Mass Transfer Fundamentals

73

Table 1-18. Analogy between mass and heat transfer. Analogous variable

Heat transfer

Mass transfer

Transfer variable

Heat flux Q (kJ/h)

Mole flux ri (kmol/h) Mass flux m (kg/h)

Driving force

Temperature gradient A 8 ("C)

Concentration gradient Aci (kmol/m3) Partial densitiy gradient Aei (kg/m3) Partial pressure gradient Api (bar)

Thermal conductivity

Diffusion coefficient D (m2/h)

Heat transfer coefficient a (W/(m2. K))

/3 (m/h or kg/(h . m2. bar) or

Transport coefficient Transfer coefficient

1 (W/(m. K))

Mass transfer coefficient

kmol/(h . m2 . bar) ( k is used as overall mass transfer coefficient)

Dimensionsless numbers to consider -

Gr, modified Grashoff number (see [1.31])

free flow Grasshoff number

-

Re

forced flow Reynolds number

=

W.1 ~

V

Reynolds number

- flow

Galilei number

F, Fr=-=-

- flow

w2

Fg

(.g Froud number

- two phase flow

Weber number - two phase flow

Eotvo's number -

physical characteristics

v

pr=-=a

V.Cp'Q

1

Prandtl number [ratio of molecular momentum transfer (friction, or viscosity effect) to molecular heat transfer (heat conduction)]

V

sc = -

D

Schmidt number [ratio of molecular momentum transfer (friction or viscosity effect) to molecular mass transfer (diffusion effect)] (continued next page)

74

1 Basic Concepts

Table 1-18. (continued) Analogous variable Dimensionless numbers used to calculate the transfer coefficients

Heat transfer

Nu=-

Mass transfer

a.1

Sh =

I

p.1 ~

D

Nusset number (ratio of total heat transfer over heat conduction alone)

Sherwood number or second Nusset number (ratio of total mass transfer over molecular mass transfer)

Nu = f ( G r , , P r )

Sh

for free flow

for free flow

Nu = f(Re, Pr,

. ..)

=f

(Grs,Sc)

Sh = f(Re, Sc,

... )

for forced flow

for forced flow

Nomenclature : Fg gravitational force, F, inertial force, Fq viscosity force, F, surface force, I = L , characteristic length, q dynamic viscosity, v kinematic viscosity, I heat conductivity, a temperature conductivity, e fluid density, surface tension of fluid(s), g gravity constant (9.81 m/s2), w flow velocity of fluid, thermal volumetric expansion coefficient of the fluid (for Grashoff number)

known physical characteristics and heat transfer area. In mass transfer, the fluid phases are in contact, and are separated by a phase boundary. The interfacial area depends upon the internals in the apparatus, fluid mechanics, and the properties of the substances making up the phases. Therefore, the dimensions of the surface of the phase boundary are not easily determined. At the phase boundary, equilibrium between the phases is assumed. This equilibrium at the phase boundary must be considered in mass transfer operations.

be calculated in a similar way to the heat transfer coefficient a , by means of dimensionless numbers. The most common dimensionless groups are listed in Table 1-18, including those essential for the calculation of the mass transfer coefficient.

1.7.3 Overall Mass Transfer Overall mass transfer is the transportation of matter through a phase boundary, from one fluid phase into another. Resistance to the mass transfer is analogous to resistance to heat transfer in that it may be considered as being divided into individual resistances; this will be demonstrated later. The main differences between mass transfer and heat transfer are: 0

In heat transfer, the fluid phases are separated by a defined, solid wall with

0

Individual resistances in heat transfer operations may easily be determined by experimentation. In mass transfer operations between two fluid phases, only the total resistance can be found experimentally, and only under complex experimental conditions. During heat transfer the individual resistances are: resistance due to convection in fluid 1, heat conduction

1.7 Mass Transfer Fundamentals

resistance of the wall, and resistance due

to convection in fluid 2. In mass transfer

operations, a mass transfer resistance has to be considered in each phase of the system. Most approaches (two film theory, theory of surface renewal) assume that there is no transfer resistance in the surface of the phase boundary which is not true for every case. For example, surface inhibition occurs at the boundary if active boundary substances are enriched within the boundary. If the substance exists in both phases under different conditions or forms, there may also be surface reactions. The mass transfer may also be considerably influenced by eddies at the boundary (turbulence in the boundary surface layer, Marangoni effect).

75

PB

t u

Fig. 1-45. Illustration of mass transfer, the twofilm theory.

PB Phase boundary (Interfacial area) Concentration of key component x Space coordinate c

where 1.7.3.1 Two Film Theory, Mass Transfer Coefficient and Turbulence Theory

The two film theory [0.4] describes the mass transfer between two adjacent phases. The main resistance occurs in the two boundary layers at either side of the interface. In these laminar boundary layers, matter is only transported by molecular diffusion. With a phase equilibrium at the interface, the interface itself offers no resistance to the mass transfer. Mass transfer is very fast in the bulk of the phase, due to turbulent convection. The concentrations c ~and , cKII ~ are uniform throughout the bulk phase (see Fig. 1-45). As shown in Chapter 1.7.2 and Fig. 1-45, the mass flux from phase I to phase I1 is

ri

mass flux across interface mass transfer coefficient in phase I and phase I1 c ~ , cK,[, ~ , bulk concentration of the substance of interest in the bulk of phase I and phase 11, respectively A interfacial area c ~ cG,II , ~ , concentration of the substance at the interface

P,,PII

The existing phase equilibrium at the interface means that the concentration is (1-164)

CG,I = K * . CGJI

where K* is the equilibrium constant (see Chapter 1.4 and Fig. 1-46). The concentration gradient in phase I is (1-165)

Matter leaving phase I enters phase I1 through the interface and therefore,

and in phase I1 is n

(1-166)

76

1 Basic Concepts

C

Introducing an overall mass transfer coefficient kll, related to the overall mass transfer resistance in phase 11, it follows that 1

1

1

k11

PI1

K * *PI

-=-+-

CII

therefore the molar flux ri is

-

(1-172)

Fig. 1-46. Concentration diagram for mass transfer. BL Balance or operating line

EC Equilibrium curve c1 Concentration of key component in phase I cII Concentration of key component in phase 11

Considering the concentrations cK,I and cK,,, related to the equilibrium concentrations cy and c;"l c K , ~= K " .

~fi

(1-167)

cl*

(1-168)

and

c,,,,

1

=-

K*

(1-171)

Eq. (1-165) may now be written as

where all the variables refer to phase 11. Analogously, referred to phase I 1

1

kl

PI

- _ --

K*

+-

(1-173)

PI1

and

li = k, . A *

(CK,1

- )c:

(1-174)

Eqs. (1-171) and (1-173) Show how the aPpropriate reciprocal value of the mass transfer coefficient is used to calculate the total mass transfer resistance of phases I and 11. When PI1% P, is k, = PI, and the total mass transfer resistance is essentially controlled by the resistance in phase I. When PI % PII is k,, =DI1 and the total mass transfer resistance is essentially controlled by the resistance in phase 11. The ratio (1-175)

combining Eqs. (1-166) and (1-169) gives (1-170) The concentration at the interface cG,1 1 , which is not easily determined experimentally, has been eliminated.

is derived from Eqs. (1-162) and (1-163) and gives the slope of the line connecting PI and Pz in Fig. 1-46. The two film theory is only an approximation of the real mass transfer in thermal separation processes. Nevertheless, it is used for the evaluation of mass transfer measurements. In the thermal separation of mixtures, the interface between phases is usually not

1.8 Steady-State Cocurrent Operation

fixed; it is constantly changed and renewed by the effect of the flow of the phases. More accurate descriptions of mass transfer are shown by HICHBIE[1.93] in his penetration theory and DANCKWERTS [1.94] in his rheory of surface renewal. Both theories take into account the change of the surface of the interface. According to turbulence theory, the mass transfer coefficient /3 is proportional to the square root of the diffusion coefficient D (see Eq. (1-161)).

/3-@

(1-176)

77

(multicomponent) carrier and the component to be exchanged. The total mass balance of the unit (see balance area BAI in Fig. 1-47 and Chapter 1.3) gives the following equation for the exchanged component La * X , - L , . X ,

where . . L a ,L ,

x,, x,

=

Gu . yW - G, . ya (1-177)

entry and exit flux of phase I mole fraction of transferred component at the entry and exit of the unit (phase I) entry and exit flux of phase I1 mole fraction of transferred component at the entry and exit of the unit (phase 11)

1.8 Steady-State Cocurrent Operation

Ga, G, y,, y ,

The cocurrent principle, mentioned in Chapter 1.1, is the basis for the following general discussion of steady-state cocurrent operations. Figure 1-47 shows two immiscible phases Ph I and Ph 11, guided in cocurrent flow through a separation device. Both phases may be mixtures of components, and during the contact of the two phases, one component is transferred from Phase I to Phase 11. Therefore, both phases consist of a

Due to selectivity, only one component is assumed to be transferred between both phases, thus the total flux of each individual phase changes throughout the separation unit. But the flux of the inert components in each phase remains unchanged. Therefore, it is convenient to relate the mole fraction x and y to the inert carrier fluids L, and G, as a mole ratio of component i in

Fig. 1-47. Steady-state cocurrent operation. PhI Phase I PhII Phase I1 BAI Balance area I (Complete separation unit) BAII Balance area I1 (Partial separation apparatus)

78

1 Basic Concepts

the inert (moles i/moles inert). Eq. (1-177) then becomes LT*( X , - Xu) = GT*(Y, - Y,)

tl

(1-178)

In a X X coordinate system, this equation gives a straight line of slope -LT/GT between the points PI (X,, Y,) and P2(X,, Y,) (see Fig. 1-48). Considering only one part of the separation unit (balance area BAII in Fig. 1-47), the mass balance of the exchanged component is L T * ( X , - X ) = G , * ( Y - Y,)

(1-179)

XG

xu x

xu

X----t

Fig. 1-48. Loading diagram for a steady-state cocurrent mass transfer operation from phase I to phase 11. EC Equilibrium curve BL Balance line Y Loading of phase I1 X Loading of phase I

In a K X plot, it also gives a straight line of slope -LT/GT between the points P, (X,, Y,) and P ( X ,Y) (see Fig. 1-48). The line is the balance line, or operating line, of the separation in a steady-state process with cocurrent flow. It is identical to the line given by Eq. (1-178). Points on the balance line represent any chosen cross section of the separation unit, with the corresponding concentration X and Y. P, characterizes the entry cross section into the unit and P2 the exit cross section. (According to Eq. (1-177), if the mole fraction is the concentration scale given by Eq. (1-179), the balance line becomes a curved line. This is also the case if the inert fluxes LT and GT are not constant along x 4 the length of the separation device.) The equilibrium curve Y ( X )of phases I Fig. 1-49. Loading diagram for a steady-state and 11, based on the loading of i, Y and X , cocurrent mass transfer operation from phase I1 is now added to the Y,X diagram in to phase I. Fig. 1-48. The intersection Q(X,, Y,) of EC Equilibrium curve the operating line and the equilibrium curve BL Balance line represents the conditions at the exit cross Y Loading of phase I1 section. This is called a theoretical transfer X Loading of phase I unit, and equilibrium between the phases leaving the transfer unit is reached. If component i is transferred from phase I1 into phase I, the operating line is above ally (for example, cocurrent distillation and the equilibrium line, as shown in Fig. 1-49. cocurrent drying). Countercurrent flow of Cocurrent operation, in thermal separation the phases, which will be discussed in the of homogeneous mixtures is used occasion- following chapter is of more practical use.

tI

1.9 Steady-State Countercurrent Operation

79

1.9 Steady-State Countercurrent Operation a)

Based on the principle of countercurrent flow presented in Chapter 1.1, steady-state countercurrent flow operations are generally discussed in the following section. The separation of a mixture in a single stage does not normally separate the mixture into fractions of the required purity. To increase the separation effect, single stages may be connected to form a cascade (Fig. 1-50). A cascade is a separation device consisting of several similar stages, or several separation units connected in series. If the phases are in countercurrent flow, a serial connection of single stages similar to a countercurrent flow cascade, can be achieved in a countercurrent flow column (Fig. 1-51). This is a practical, simple and economic method of multiplying a single stage separation effect. It is not necessary for countercurrent flow phases to be in stagewise contact (as in tray towers). Constant contact of the phases throughout the length of the column is possible. For the design of countercurrent flow columns, essentially two theories are used,

[ IF M

A

Fig. 1-51. Countercurrent flow column. a) Reflux principle b) Flow through principle F Feed to be separated E Top product A Bottom product I . . .V Separation stages in the countercurrent flow column

the theory of separation stages and the kinetic theory of separation of mixtures in countercurrent flow. The theory applied depends mainly on the type of countercurrent flow process, the internals in the column, the type of mixture to be separated, and its physical and chemical properties.

1.9.1 Theory of Separation Stages

Fig. 1-50. Series connection of individual separation stages (Cascade). I, 11, 111 Equivalent separation stages F. . Feed L , , L,, . . . Individual fraction flows

In separation processes, a common problem is a mixture of a certain composition to be separated into two fractions, where after separation each fraction is of the required composition. If the separation is carried out in a countercurrent flow column, the

80

1

Basic Concepts

necessary height for heat and mass transfer must be determined. The height of the column depends on the number of separation stages connected in series, where each stage represents a single theoretical separation stage (see Chapter 1.1). The actual height of the countercurrent flow column is fixed by the number of theoretical stages and the "stage efficiency factor" (amplification ratio). Determination of the number of required stages is now discussed. Figure 1-52 shows two immiscible phases PhI and PhII flowing countercurrently through a column. Both phases consist of a multicomponent mixture but only one component is transferred from phase 1 to phase I1 during the contact of the phases. Therefore, the phases are composed of a (multicomponent) carrier or solvent and the component to be transferred. Phl PhII

Fig. 1-52. Countercurrent flow column. PhI Phase I PhII Phase I1 BAI Balance area I (total separation column) BAII Balance area I1 (a column section) CC Countercurrent column

Using the notation given for cocurrent flow, a mass balance for the whole separation column (balance area I in Fig. 1-52) for the component to be transferred is

L a .x, + 6,. ya = i, - x, + G, .y ,

(1-180)

where the mole fraction is the concentration scale, or the loading

A mole balance over a section of the column (balance area I1 in Fig. 1-52) with respect to the component to be transferred, gives

and

G,* ( Y - Y,) = i, . (X-X,)

(1-183)

Eqs. (1-181) and (1-183) are plotted on a X X coordinate system and straight lines are produced between the points PI (X,, Y,) and P2(Xa,Y,) and between the points P,(X,, Y,) and P ( X , Y ) .These are the balance lines, or operating lines, with slope LT/GT,the ratio of the flow rates of the carriers. When a component is transferred from phase I into phase 11, the balance line is below the equilibrium line. When a component is transferred from phase I1 into phase I (see Fig. 1-53), the balance line is above the equilibrium line. If the carrier fluxes L, and G , are not constant along the length of the separation device, or other concentration scales are used, the balance line is curved. Points on the balance line link the related mole concentrations X and Y at any cross section of the separation unit. The greater the distance between the balance line and the equilibrium curve, the higher the concentration gradient, i. e. the driving force, for the mass transfer, or the "disturbance from equilibrium". Driving

1.9 Steady-State Countercurrent Operation

Fig. 1-53. Loading, or operating diagram of a countercurrent flow process. BL Balance line EC Equilibrium curve Y Loading of phase I1 X Loading of phase I

forces vary along the column height, as shown in Fig. 1-53. If the balance line touches the equilibrium line, the driving force is zero. The phases in contact at that particular cross-sectional area are in equilibrium, no mass transfer occurs. The separation processes discussed so far consider phase I as a fresh feed into the column. This is important for separation processes such as absorption and extraction. For these processes it is practical to use mole ratio as a concentration scale based on the solvent or inert flux, since the flow remains constant, or will only change negligibly, along the column height. If phase I is generated by phase transition or phase reversal from phase I1 in a heat exchanger on top of a counterflow column, a reflux principle is used instead of the simple flow-through principle (see Fig. 1-51). Phase I is no longer a fresh feed to the column but is the reflux generated by converting phase I1 into phase I; this is the case in countercurrent distillation or rectification. The liquid phase I, the reflux, is generated by partial or total condensation of the

G,y

81

t t

LeX PhII PhI

Fig. 1-54. Reflux principle in a countercurrent flow column.

CC Countercurrent flow column C Condenser BA Balance area PhI Phase I (reflux) PhII Phase I1 (vapor phase)

upflowing vapor phase I1 in a condenser at the top of the column. A mass balance over the upper part of the counterflow column, as shown in Fig. 1-54, at constant vapor flux G and constant reflux with total condensation of phase 11, gives G=L+E

(1-184)

and for the component to be transferred

-

G y

=

i . x + I?.X,

(1-185)

From this, the balance, or operating, line of the rectification column is given by (1-186) where the reflux ratio v is the ratio of the downflowing reflux L = R to the leaving product at the top of the column E

82

1 Basic Concepts

R

(1-187)

V = 7

E

and following from Eq. (1-186)

1.9.2 Method to Determine the Number of Theoretical Separation Stages for a Countercurrent Column

A discussion of a method of determining (1-188) the number of theoretical separation stages v+ 1 required to separate a mixture in a counterflow column follows. Eq. (1-188)is plotted on a y,x diagram (see Fig. 1-55) as a straight line if the slope v/(v + 1) of the balance or operating line is McCabe-Thiele Method constant, or rather if v is constant. A graphical method to determine the theoretical stages of counterflow columns which is easy to use was introduced by MCCABE [1.98]. and BIELE The McCabe-Thiele method is based on the idea of theoretical stages (theoretical separation unit, theoretical tray). From Chapter 1.1, a theoretical stage is that part of a separation apparatus in which heat and/or mass transfer occurs between two phases in contact. Both phases leaving the theoretical separation unit are at phase equilibrium. For a given separation task, the counterFig. 1-55. Operating diagram for a binary system flow column contains the required number EC Equilibrium curve. of theoretical stages in series. To calculate BL Balance or operating line the number of theoretical stages, the x (tan x = v / [ v + I]) Gradient McCabe-Thiele method is applied, for exyo (yo = x E / [ v+ 11) Ordinate intercept ample, to a rectification column for the parx Molar fraction of the low-boiling compotial separation of a binary mixture. In this nent in the liquid phase case, the molar vaporization enthalpies of y Molar fraction of the low-boiling compothe components of the mixture are assumed nent in the vapor phase to be equal and the enthalpy changes of the vapor or the liquid are negligible. Then, the balance line is straight. (A method to calcuWhen, at the phase contact, an equal late a solution to this separation problem amount of matter is converted from phase under different conditions is shown in I (liquid) into phase I1 (vapor) and vice Chapter 2.5.2.4). Fig. 1-56gives a schematic versa the mass fluxes G and L are constant diagram for a rectification column with n along the length of the column. In adiabatic theoretical stages and also the correspondoperation of the column this is only valid if ing y, x diagram according to MCCABEand the components of the mixture have equal BIELE. The vapor flux G leaving the nth stage molar vaporization enthalpies and exhibit with composition yn of the lower-boiling ideal behavior.

y = - . xV+ v+l

XE

1.9 Steady-State Countercurrent Operation

83

Fig. 1-56. Schematic of a rectification

Yn-1

Yn-2

Yn-3

I

I

1 I

&Phase

+Phase

X - - t

I1 (vapor phase) I

(liquid phose. reflux)

component is totally condensed in the condenser. Some of the condensate leaves the top of the column as product E with composition y, = x,. The rest of the condensate, L = G - E, is the reflux at stage n with composition x,. Vapor with composition y , and reflux with composition X , are linked by the balance line given by Eq. (1-188), where in particular y , = x,. The balance line intersects with the y = x line at the point A (xE,yn= xE) in the McCabe-Thiele diagram. For a given reflux ratio v, it follows that yo = x,/(v 1) and therefore point B (O,y,) on the balance line AB is fixed. In general, the balance line combines the mole fraction y,-, and x, of two stages.

+

~

V y,-1 =-. x, + XE v+l v+l ~

(1-189)

Since stage n is a theoretical stage, the vapor leaving the stage yn is in phase equilibrium with the reflux x, leaving stage n. On the McCabeThiele diagram, this gives the point A, with the coordinates x, and y , on

column for the separation of an ideal binary mixture, and the corresponding McCabe-Thiele diagram. C Condenser RC Rectification column n, n - 1,. . . Theoretical separation stage number, indice for the vapor and reflux mole ratio of the low-boiling component EC Equilibrium curve BL Balance or operating line y Molar fraction of the low-boiling component in the vapor x Molar fraction of the low-boiling component in the reflux

the equilibrium curve. The points A,, A,, and A characterize a theoretical stage n. The following stages n - 1, n - 2, etc., can be constructed in the same way, by extending the steps between the balance line and equilibrium curve. For every counterflow separation process, the number of theoretical stages can be found by this simple graphical procedure. Each stage is constructed between the equilibrium curve and balance line, starting with the initial point and finishing at the end point. Obviously in Fig. 1-56 the separation of a binary mixture with the given reflux ratio v gives a top product with composition x, and a bottom product of composition x > xmin. xmi,can only be reached with an infinite number of theoretical stages. Therefore, the reflux ratio v is the minimum reflux ratio for xmi,(see Chapter 2.5.2). If xminshould be reached by the separation, the reflux ratio v has to be raised accordingly (for more details see Chapter 2.5.2). A method similar to the McCabe-Thiele method exists for the graphical determina-

84

1 Basic Concepts

tion of theoretical separation stages for counterflow columns where phase I is not a reflux but a fresh feed phase. The number of theoretical stages is found by the construction of steps between the equilibrium curve and the balance line (see Fig. 1-57). The ratio L T / G T is of particular importance. With practical separation stages installed in counterflow columns, phase equilibrium cannot be reached. Therefore, the efficiency of a practical stage is lower than that of a theoretical stage. For the installation of practical stages in a column, the stage efficiency E (exchange ratio, MURPHREE Efficiency, introduced in Chapter 1.1) is found by a comparison of the number of practical stages and theoretical stages. E may be related to either one of the phases. Relating E to the upflow phase gives

Phl

Egm =

yd yd

- yu - yu,h

(1-190)

or Egm =

yu - yd

'uth - yd

(1-191)

depending on whether the reference component is transferred from phase I into phase I1 or vice versa (see Fig. 1-58). YUthis the mole fraction of the upflow phase for a theoretical separation stage. The method used to determine stage efficiency is demonstrated in Fig. 1-58. The concentrations of the component of interest are experimentally determined in relation to the reference components of the entering and leaving fluxes Xu and xd.For a given

PhII

a)

b)

Fig. 1-57. Schematic of a countercurrent flow column with mass transfer from phase I1 to phase I (a) and an operating diagram to determine graphically the number of theoretical separation stages (b). EC Equilibrium curve BL Balance line n, n - 1,. . . Theoretical separation stages, refer to the loading of the key component in phases I and I1 as indices Y Loading of phase I1 with key component X Loading of phase I with key component

1.9 Steady-State Countercurrent Operation

85

current separation stage

Ph I Ph II a1

bl

Cl

Fig. 1-58. Definition of the stage or Murphree efficiency factor for a countercurrent flow column with the theoretical and practical maximum change in key component loading in a particular stage with mass transfer from phase I1 to phase I and vice versa.

EC Equilibrium curve BL Balance line Y,,, Phase equilibrium loading at X ,

equilibrium curve and balance line, the stage efficiency Egmis the ratio of the distance between these lines. The stage efficiency EI, is related to the downflow phase, and is thus similar to Eqs. (1-190) and (1-191). The stage efficiency varies from stage to stage according to the course of the equilibrium curve and balance line. It is dependent on the design of each separation stage, the process parameters in the column and the properties of the phases in contact. Usually the efficiency is determined experimentally. Empirical approximations may only be used to calculate the stage efficiency factor for a few simple cases. (Due to the nonideal mixture of the phases leaving the separation stage, the stage exchange rate Egmis the mean value of the local exchange rate Eg over the cross section of the stage, see Chapter 2.5.6.1. The latter value can only be calculated if the fluid mechanics of the phases at the cross section are known.) If E,, is the average of all stages, the approximate number of stages Np to be installed in t h e e m n is

Nt

Np = _ _

(1-192)

Egmm

where Nt is the number of theoretical stages, determined by computation or graphically. Where the slopes of the equilibrium curve and balance line are very different this approximation can lead to significant errors. For this case a “pseudo-equilibrium curve” between the equilibrium curve and balance line as shown in Fig. 1-59 may be introduced. Its course is determined by the vertical distances between the equilibrium curve and balance line divided by the stage exchange rate Egnl: a = Egm.b

(1-193)

The number of practical stages Np is determined by constructing steps between the balance line and pseudo-equilibrium curve. In Eq. (1-193), the exchange rate Egmis used repetitively in the interval X , + Xu. If trays are used as internals in a column, the theory of separation stages is particularly important for the determination of the actual column height (see Chapter 2.5.6.1).

1 Basic Concepts

PEC -4

5‘

/

Fig. 1-59. Determination of the number of practical separation stages. EC Equilibrium curve PEC Pseudo-equilibrium curve BL Balance line Y Loading of phase I1 X Loading of phase I

The values of n, and HETS depend on the form of the packing material, the type of packing (or the geometry in general), the operating conditions, and the properties of the two counterflow phases. nt can only be computed in particularly simple cases. The value is usually determined experimentally. If the number of theoretical stages Nt is determined, (for example by the graphical McCabe-Thiele method or by computation), and n, or HETS for the chosen packing are known, the height Z for mass and heat transfer of the packed column can now be calculated with Eqs. (1-194) or (1-195), respectively.

1.9.3 Calculation for Counterflow Columns

Graphical methods for the determination of the required number of theoretical stages discussed so far, are easy to use and are of practical importance for first approximations for separation processes of binary mixtures, or for systems with inert carrier mixtures and a single component to be transferred. If several components are transferred between the phases in contact, the number of separation stages can only be (1-194) calculated with the aid of a computer; graphical methods can only be partially apwhere n, is the number of theoretical plied. stages, which corresponds to the height Z of Methods of calculating the separation of a packed column and Nl is the number of multicomponent mixtures in counterflow theoretical stages that are effective along columns are based on the two “stage-tothe height of the packed column. Therefore, stage” methods by LEWISand MATHESON the reciprocal value HETP = HETS is the [1.99], or THIELE and GEDDES[1.100]. Both height of the packing, which has the same methods are iterative and usually exhibit usage as a theoretical stage (HETP: Height bad convergence, as well as needing a lot of Equivalent to one Theoretical Plate, HETS: computing time and power. Thus, until Height Equivalent to one Theoretical 1960, several approximation methods, or Stage). “short cuts” were developed and modified using simple assumptions to simplify the 1 HETP = (1-195) column design [1.101]. These short cuts are still of practical interest for an estimation nt

Heat and mass transfer in counterflow phases usually only takes place within the area of the trays. The theory of separation stages is also valid for packed columns. Since single stages cannot be distinguished, an evaluation number n, or its reciprocal value HETP or HETS is introduced

1.9 Steady-State Countercurrent Operation

87

been developed. However, a method giving sufficient and rapid convergence for a general design problem does not yet exist. Methods to calculate counterflow columns exactly are based on a column model. The column model gives a system of nonlinear equations, the task of each method is to solve this system. The equation system contains an overall mass balance and also a balance for each component, enthalpy balances, equilibrium relationships and the stoichiometric conditions for the sum of the concentrations for the theoretical stages of a counterflow column (see Fig. 1-60). In the equation system, the following nomenclature is used: Lj

Fig. 1-60. Model of a countercurrent column. i Flow rate of phase I (downflowing phase) SL Flow rate of side stream phase I F Feed 1, .. .j , . . .,n Theoretical separation stages (1 < j < n) j Stage index BA Balance area G Flow rate of phase I1 (upflowing phase) SG Flow rate of side stream phase I1 Q Heat flow

of the design of the column, and as first iteration variables for an exact check. If strong heat effects along the column height or pronounced nonideal behavior of the mixture occur, the short cuts fail. Since 1960, several methods for the exact calculation of a counterflow column have

flow rate of downflow phase leaving the jthstage Gj flow rate of upflow phase leaving the jthstage SLj flow rate of side stream leaving the jthstage (same state as the downflow phase) flow rate of side stream leaving SGj the jthstage (same state as the upflow phase) feed 6 .cj part of feed (same state as the downflow phase) FJ . (1 - c j ) part of feed (same state as the upflow phase) j index, characterizes the actual separation stage; starting at the top of the column, j is counted from 1 to n, from top to bottom heat flow from stage j Qj

6.

The column model in Fig. 1-60 is generally valid for rectification, counterflow absorption, and counterflow extraction. For rectification (see Chapter 2.5.2), the nomenclature used is : stage I (j=1)

condenser at the top of the column

88

1 Basic Concepts

SG, = O with total condensation SG,=O FI * E ] = O valid for normal cases, not F2=0 valid for a stripping column heat flow out of condenser Ql top product flux SL, vapor stream to condenser G reflux from condenser i, heat loss from an actual stage Qj (under approximately adiabatic operating conditions of the column) side stream, vapor SGj side stream, liquid SLj stage n

reboiler

F, =O

valid for normal cases, not valid for an enrichment column

(J =n>

F,+I= O heat supply to the reboiler bottom product flux vapor mixture generated in reboiler

- Qn

SL, Gn

and for counterflow absorption (see Chapter 3.5):

Fl . c1 F,+l

SG] SL,

feed of solvent needed to absorb the key component (washing liquid) (el = 1) feed of gas mixture to be treated ( E , + , = 0) flow rate of treated gas mixture leaving the column flow rate of loaded washing liquid leaving the column

Except for the listed flow rates, all other F,, SGj, SL,, and Qj are virtually zero. In an absorption column operated with an intermediate coolant as the washing liquid, Qj is substantially different than zero. For the case of counterflow liquid-liquid extraction (see Chapter 6.2.3.4)

F,.

E .,

F,+,

feed of heavy phase feed of light phase

SGl L,

s

light phase exit flow rate heavy phase exit flow rate

Usually no side streams are withdrawn ( s L j= 0, s G j = 0 ) and side feeds are not considered (5 = 0). At normal conditions, heat flux Qj through the sides or column walls is negligible. The following approximations are made for the calculation of a counterflow column : The concentration of the phases in one stage (on a tray) are uniform over the cross-sectional area of the column The phases leaving the stage are at phase equilibrium [the stage efficiency coefficient (enriching factor) may be used throughout the calculation] The column is operated at steady-state conditions (an exception being simulation of the start up of the column using dynamic methods; for example see [1.102]) In absorption and extraction processes, the assumption of phase equilibrium of the phases leaving the stage is less valid than in rectification processes. The exact calculation for a counterflow column using the theory of separation stages is generally carried out for rectification processes. The following discussion of a system of nonlinear equations, based on the column model, is particularly valid for rectification, but this may be applied to all other counterflow processes. Before the equation system can be formulated the variables used to describe the state of the counterflow system must be expressed. According to the column model in Fig. 1-60 they are

6

T.F

'.i

SLj s Gj

8;

i';

feed temperature of feed liquid fraction of the feed leaving side stream, liquid leaving side stream, vapor heat flux reflux flow rate

1.9 Steady-State Countercurrent Operation

Gj

T,, Pj x. 1 3 J.y y 1,J .. . z.[ , J.j L ’ z.1J.G

n

vapor stream temperature and pressure of the stages (on the column tray) molar fraction of key component i in the reflux stream L, and the vapor stream Gj molar fraction of the key component i in the liquid and vapor part of feed F j total number of separation stages (trays)

Equations showing the relationships of these variables are given in the following chapters.

1.9.3.1 Mass Balances The overall mass balance over the upper section of the column (see balance area BA in Fig. 1-60) gives J

(F, - SG, - SL,)

+

k=l

+ 1. The first point C on the stripping line occurs at the intersection of a vertical at x, and the 45" diagonal ( y = x = x,). Its position, and the intersection at point S with the enrichment line, are

Fig. 2-44. McCabe-Thiele diagram for a binary system, column with stripping and enriching section. EC Phase equilibrium curve OLE Operating line, enriching section OLS Operating line, stripping section IL Intersection line Mole fraction of the low-boiling compoy nent in the vapor phase Mole fraction of the low-boiling compox nent in the liquid phase

152

2 Distillation and Partial Condensation

must be condensed to preheat it to its boiling conditions, and A & = G* - G = F . ( f - 1)

(2-61)

Hence, the reflux R* is therefore larger than the corresponding sum l? + l? A mass balance over the feed cross section (Fig. 2-46) gives

(R* - ri) . x - (G* - G) ' y - F . x,=

0

(2-62) Fig. 2-45. Material balance of the stripping section. BA Material balance area

governed by the condition of the feed F (concentration x, and thermal state) and the reflux ratio v. The intersection point S gives the conditions of the mixture at the feed cross section (see Fig. 2-44); this is the cross section where the stripping column changes into the enrichment column and vice versa (Fig. 2-46). The factor f is introduced to describe the thermal state of the feed mixture. f.F=R*-R

(2-60)

If the feed is at its boiling temperature, f = 1. If the feed is subcooled, some of the vapor leaving the stripping column AG

where x and y are the molar fractions of the key component (the lower-boiling component) in the liquid and in the vapor, well above the feed cross section. Combining Eqs. (2-60) to (2-62) gives a straight line for the locus of intersections. (2-63) This intersects with the 45" diagonal at point D ( y = x = xF), with the abscissa at point E ( y = 0, x = x F / f )and with the enrichment and the stripping line at point S (see Fig. 2-44). (The coordinates of S, xs and ys describe the composition of reflux and vapor above the feed cross section.) The caloric factor f is obtained from a heat balance over the feed cross section. Since for the preheating of a subcooled feed to boiling conditions the condensation of vapor AG, is necessary.

F . (f - 1)

*

Ah!,g = F * (&s - &F)

(2-64)

From this it follows that (2-65)

Fig. 2-46. Balance of a feed cross section.

where hs and &F are the enthalpies of the mixture at boiling and feed conditions, respectively, and is the vaporization en-

2.5 Countercurrent Distillation (Rectification)

thalpy referred to the conditions at the feed cross section. Different thermal feed conditions and the corresponding position of the locus of intersections are listed in Table 2-13. The point S is fixed by the intersection of the enrichment line and the locus of intersections line, and thus the second point of the stripping line is determined. This is the connection for C and S in the McCabeThiele diagram (Fig. 2-44). The required number of theoretical separation stages Nt is obtained by the construction of steps between the equilibrium curve and the operating lines of the stripping and enrichment zones, as described in Chapter 1.9.2. The example in Fig. 2-44 contains = 4 theoretical steps, including the reboiler in the stripping section, and 2 4 theoretical steps in the enrichment zone. In this case, a feed of composition x, is separated into an overhead product of composition x, and a bottom product of composition x,, of the lower-boiling key component. The stage with a state point on the

153

equilibrium curve closest to S* is said to be the feed stage. If a side stream of composition x, is withdrawn out of the enrichment column, the reflux ratio v reduces to a reflux ratio v,, well below the output . . R-S v, = (2-66) E

s

~

The enrichment line then shows a bend at

x,. Below x, the slope changes according to v, < v resulting in additional number of

separation stages required compared to a separation process without the side stream (Fig. 2-48). If the molar vaporization enthalpies of both of the components of the mixture are not equal, or if considerable enthalpy changes in the liquid fluxes appear, the fluxes are no longer constant in the column section of interest. The stripping and enrichment lines become curves that are determined from point to point in the McCabeThiele diagram. According to HAUSENand

Table 2-13. Thermodynamic state of feed mixture and the resulting position of the intersection line in the McCabe-Thiele diagram. Thermal state of the feed

Temperature

Enthalpy

Calorific factor f

Slope Path of the (see Fig. 2-47) intersection

Subcooled liquid

I9FO

Boiling liquid

8 F = 8s

hF= h,

1

Wet vapor (partially vaporized) (liquid + vapor)

8 F = !Ys

ii, > r;,



+ Ah,,,

> 19S

* 8, Boiling point of the feed.

&F

0 1, f = 0, f < 0) given by Table 2-13. OLS Operating lines, stripping section

9 f

XF

XS

XE

X - - c

Fig. 2-48. Rectification column with side stream in the enriching- section. a) Schematic representation b) McCabe-Thiele diagram OLE1 Operating line, enriching section above sidestream take off Gradient tan H, = vo/(vo+ 1) OLE2 Operating line, enriching section below sidestream take off gradient tan x2 < tan x1 OLS Operating line, stripping section IL Intersection line EC Equilibrium curve

KIRSCHBAUMand BILLETthe enrichment line is, neglecting the superheating and mixing enthalpy, (linear bubble point and dew point lines in the h , x diagram of MERKEL cording to BITTERL2.59, 2.601, for a variable reflux ratio of the enrichment column and PONCHON, see Fig. 2-11)

Y=

($T 1_

-

1

vo+l

2). x ~-

c

XE

XE

1 --

+

.

vo

vo+l

xE ~-

c

(2-67)

-

A4g2

Ah,,,, - Ah;,,,

c

X 1 -~

C

With chosen and adapted reflux con&tions according to Eq. (2-69), the enrichment line may be calculated by Eq. (2-54). The ordinate intersection of the enrichment line according to Eq. (2-67), is

(2-68)

Assuming linear bubble and dew lines in the Merkel-Ponchon diagram (Fig. 2-11), ac-

(2-69)

* VO

zp

.

where v, is the adjusted reflux ratio at the column head. c is a factor calculated with the molar vaporization enthalPies Al;f,gi and Ahl,g2,where

c=

V

XE

Yo =

v,. (1

-$)+ 1

(2-70)

2.5 Countercurrent Distillation (Rectification)

The following equations are used to describe the stripping line

where x , and ys are the coordinates of the intersection point S of the stripping and enrichment lines. u is given by

where the reflux ratio vs at the feed cross section is (2-73)

155

and MERKEL[2.62, 2.631 is used in its exact form for the mixture being separated. In contrast to the McCabe-Thiele method, the molar vaporization enthalpies of the components are not assumed to be equal and the enthalpy of mixing not neglected. The Ponchon-Savarit method, therefore, exactly determines the number of theoretical separation stages by taking into account the real caloric conditions of the separation column. However, it is more costly and more complicated to handle than the McCabe-Thiele method and the PonchonMerkel diagram is only readily available for use in a few systems. CHON

Short Cut Method of FENSKE, and GILLILAND UNDERWOOD This method is based on the assumption of constant flow rates, R and G, constant relative volatility a1,2and an infinite reflux ratio v. According to FENSKE and UNDERWOOD [2.64] the required minimum number of theoretical separation stages Nt,min for a binary rectification is

A comprehensive representation of different approaches to obtain the operating lines of rectification columns is given by BITTER in [2.59, 2.601. In practical column operation at higher loading, liquid is entrained with the upflowing vapor. The ratio of the entrainment and the amount of upflowing vapor influences the local reflux ratio and thus the position The reboiler is not taken into account. An infinite reflux ratio v = 00 means no of the operating lines and the enrichment product is withdrawn at the head of the colratio. umn (E = 0); all condensed overhead vapor is returned to the column. In the McCabeThiele diagram, stripping and enrichment Ponchon-Savarit Method lines coincide with the 45" diagonal and therefore the concentration of the feed x, The method of PONCHON and SAVARIT [2.61] is a graphical determination of the number has no influence on the minimum number of theoretical separation stages in counter- of stages Nt,min. For similar values of the relative volatilflow columns. It is particularly applicable to binary mixtures in rectification pro- ity at the top and bottom of the column, the geometric mean is cesses. Exact results are obtained when the a1,2,Eand a1,2,A, enthalpy-concentration diagram of PON- used in Eq. (2-74).

156

2 Distillation and Partial Condensation 1.0

0.6 0.L

t

0.2

0.1

0 0.0; 0.0

Fig. 2-49. Gilliland's diagram for theoretical stages and reflux requirement. EOR Economic operating range

a1,2 = h

,

E

. QV,A

(2-75)

Figure 2-49 shows an empirical relationship between the number of theoretical separation stages N, and the reflux ratio v introduced by GILLILAND [2.64]. For a given rectification problem the minimum reflux ratio vmin and the minimum number of separation stages Nt,,,in may be determined by the McCabeThiele method or calculated by Eqs. (2-74) and (2-77). With these, the required number of theoretical stages for any chosen reflux ratio v is found from the Gilliland diagram. The best economic operating range of rectification columns is

The described short cut methods may also be applied for difficult rectification problems, for example, the separation of azeotropic mixtures. A suitable transformation of coordinates for the equilibrium

Fig. 2-50. Transformation of coordinates, azeotropic binary systems. x, y Coordinates of the azeotrope mixture a > 0.240 for a = y . (1 - x)/[x.(1 - y ) ] ; a = 0.252 k 0.012 for a = r] . (1 - O / [ < . (1- r ] ) ] .

composition of the azeotropic mixture is required, thus the relative volatility of the transformed system should be almost constant in the range of interest (Fig. 2-50).

Calculation of the Number of Stages, Concentration and Temperature Profiles If a multicomponent mixture with pronounced nonideal behavior is to be separated, graphical and short cut methods fail. They also fail if a key component calculation gives insufficiently accurate results. The number of stages or the height for heat and mass transfer of a rectification column are determined by the aid of a computer. Computations are based on an equation system (see Chapter 1.9) consisting of 0 0 0 0

Mass balance equations Phase equilibria relationships Enthalpy balance equations Stoichiometric conditions of the sum of concentrations

2.5 Countercurrent Distillation (Rectification)

157

For equilibrium curves including a turning point, vmin may be found in such a way that the balance line is tangential to the equilibrium curve (Fig. 2-51). Since the number of separation stages cannot be infinite the real reflux ratio must be v > vmin. The operating costs C , of the rectification unit (energy costs for heating and cooling) increase with increasing reflux 2.5.2.5 Minimum Reflux Ratio, ratio. The investment costs C, of the colOptimal Economic Reflux Ratio umn increase with increasing number of installed separation stages and decrease with The reflux ratio v, where increasing reflux ratio. The investment costs R increase slightly with large reflux ratios due v=(2-76) to the high manufacturing costs of columns E with large diameters. The economic optimum reflux ratio vOpt, is the most important operating variable in a rectification process with a set feed condi- is given by the requirement of minimal total tion and operating pressure. v may be varied costs C, = C, + Co of the rectification between the minimum reflux ratio vmin and unit, and is graphically determined as shown in Fig. 2-52. Several variations in the 00. The minimum reflux ratio vminis the reflux ratio requiring an infinite number of rectification unit with different reflux raseparation stages in the stripping and en- tios, are calculated obtaining the curves C,(v) and C,(v) in Fig. 2-52. The richment column to realize the separation C,(v), economic optimum reflux ratio vOpt is thus desired. At constant relative volatility a1,2 found at the minimum of the total costs and with a feed at boiling conditions, vmin curve, C,(V). is according to FENSKE and UNDERWOOD, In practice, operating reflux ratios of v = (1.05 2) vmin and sometimes higher are used. The system is nonlinear and must be solved using a reasonable estimate of the iteration variables (for example, the condition of the product flows at stage to stage calculations, mass, concentration or temperature profiles) [2.66-2.681.

2.5.2.6 Feed Stage The minimum reflux ratio may also be determined graphically from the McCabeThiele diagram, from the requirement that the stripping and enrichment lines intersect at point S* (Fig. 2-44). vmin results from the ordinate intersection yo,min with the enrichment line, giving

v min . =-- xE

1

(2-78)

Yo,min

With unequal molar vaporization enthalpies, vmin is calculated from Eq. (2-70).

The location of the feed stage is chosen in such a way that as few separation stages as possible are needed in the stripping and enrichment column. Figure 2-53 shows examples of early, delayed and correct feed locations in the sense of a minimum number of separation stages. An early feed location increases the number of separation stages required in the enrichment column, whilst a delayed feed location increases the number of separation stages in the stripping column. In the given example, one separation stage is saved when the correct feed location is chosen.

158

2 Distillation and Partial Condensation b)

a)

XA

XF X+

Fig. 2-51. Graphical determination of the minimum reflux ratio. a) Intersection point method b) Tangent methold OLE Operating line, enriching section OLE, Tangential operating line, enriching section, from A out through the equilibrium curve OLS Operating line, stripping section IL Intersection line EC Equilibrium curve T Tangent contact point

2.5.3 Discontinuous Adiabatic Rectification

Fig. 2-52. Reflux ratio for optimum design. CT Total Costs C, Investment costs C, Operation costs

In discontinuous rectification a liquid mixture is charged to a still (Fig. 2-54) and after heating the mixture to boiling point, rectification occurs in an enrichment column operated on top of the still. The vapor leaving the enrichment column is then condensed in a condenser. Some of it is passed back as reflux to the column, the rest is continuously withdrawn as product. After the rectification is finished, the bottom product (distillation residue) is removed from the still. Discontinuous rectification is less costly with respect to equipment than the continuous variation and multicomponent mixtures may even be separated in a single column. Due to the considerable dead times for charging, discharging and heating of the

2.5 Countercurrent Distillation (Rectification)

XA

XE -X

Fig. 2-53. Influence of delayed and early feed mixture entry on the required number of separation stages. a) Early feed b) Delayed feed c) Correctly chosen feed Z Feed stage

RC ~-

Q

159

Fig. S C TC TR RC

2-54. Batch distillation unit. Still Condenser Top product cooler Top product receiver Rectification column

160

2 Distillation and Partial Condensation

still, and the tendency to use continuous operation in chemical plants, discontinuous rectification is seldom used. It is mainly employed for small amounts of mixture, which change irregularly with time and mixture composition. In practice, there are two variations of discontinuous rectification. In the first variation, the reflux ratio at the head of the column is kept constant. The composition of the top product varies with time and with the composition of the still contents. This variation is preferred for the separation of multicomponent mixtures. At the start of the rectification process, a large reflux ratio is used to remove low-boiling components of the mixture during this “first run”. If the desired product component appears in the overhead product, the reflux ratio is decreased. During the “main run” a low reflux ratio is kept constant. At the end of the main run the reflux ratio has to be increased again to obtain as much as

possible of the remaining product from the still mixture. Figure 2-55 shows a typical curve of the temperature of the top product against the amount of distillate, for discontinuous rectification of a ternary mixture. In the second variation, the reflux ratio is continuously adjusted to maintain a constant overhead product composition. This variation is preferred for fractional separation of binary mixtures. Exact mathematical treatment of discontinuous rectification is not simple due to the changing component concentrations in the still contents and the overhead product, and the concentration profile of the column with time. Therefore, only a few important relationships which apply under certain assumptions are given in the following chapter. More details are found in [2.1-2.31.

tI

During a discontinuous rectification process of time t, a liquid mixture B, with a concentration of x, is separated into a top product Eg of concentration x, and distillation residue B, of concentration x,, (see Fig. 2-54). Molar fractions x,,, xE and x, refer to the low-boiling component as the key component. fg is the separation time, fixed by the order of events of the total process. The important cases for process control are constant vapor load of the column and constant heat supply over a time period. These are discussed in detail in [2.2]. If the column is operated with a constant reflux ratio v, a material balance of the column gives analogous to Chapter 2.2

Top product flow

-

Fig. 2-55. Path of the temperature in the top of a column, which depends on the distillate top product flow, for a three component batch distillation process. Area A, B; C, D; E, F Withdrawal of virtually pure product fractions with low reflux ratio Area B, C ; D, E Withdrawal of products of intermediate composition. The intermediate fractions are usually collected separately and feed to the still together with the following charge.

2.5.3.1 Amount of Overhead Product

(2-79)

and the total amount of overhead product

Eg is

2.5 Countercurrent Distillation (Rectification)

Eg = B, - B,

= B,

*

Eg The simplest ways of solving the integral expressions in Eqs. (2-79) and (2-80) are graphical or numerical means. Table 2-14 shows the order of the steps which are required. The time mean composition of the distillate x ~is , ~

fiE

the top of the column and concentration x,, total amount of withdrawn top product during the rectification process molar enthalpy of the top product

By neglecting the liquid contents in the column and condenser, according to Eq. (2-82), the amount of top product E ( x ) is xB, -

(2-81) If the reflux ratio v is adjusted at a time to obtain a constant overhead product concentration X E , , the total amount of produced overhead product is

161

E=B,*-

xEa -

(2-84)

Table 2-15 describes the course of action to evaluate Eq. (2-83). If the reflux ratio v is kept constant at the column top, the total heat requirement Q of the column is

(2-85)

2.5.3.2 Heat Requirement With constant top product concentration

xEa,the total heat requirement Q is

Now A&,,g and f i E depend on X , and hence on E. Analogous to Eq. (2-84), the amount of top product E ( x ) is (2-84)

where Ah,,, enthalpy of vaporization of the top product, referred to the pressure at

x

~is the , ~time mean molar fraction of low-boiling component in the top product, which is analogous to Eq. (2-81)

Table 2-14. Step-by-step evaluation of the integral terms in Eqs. (2-79, 2-80). 0 0 0 0

I

Determination of the number of theoretical stages Nt (see Chapter 2.5.3.4). Selection of x values in the range of interest (xe, > x > xe,) Graphical determination of x, corresponding to x, considering v = const. and at constant Nt Plotting of xE(x) and evaluating the integral I

162

2 Distillation and Partial Condensation

Table 2-15. Step-by-step determination of the heat requirement Q with constant top product composition x,. 0 0

0

Selection of the reflux ratio v in the interval v, < v < v, where v, and v, are the initial and final values of the reflux ratio Graphical determination of the still concentration x corresponding to v using the McCabeThiele diagram at fixed number of separation stages Nf(see Chapter 2.5.3.4) Calculation of E using Eq. (2-84) and plotting v ( E ) + 1 against E Graphical evaluation of the integral term in Eq. (2-83) and calculation of Q

xE,m =

B;x

Bil

-B*x

B,-B

(2-87)

According to Eq. (2-79) the still contents B is given by

s-)

XB.

B=B,.exp(-

dx

x, - x

(2-88)

The course of action to evaluate Eq. (2-85) is described in Table (2-16). In discontinuous rectification practice, for the important cases x,, = const., v = const., the heat requirement calculated from Eq. (2-83) or (2-85), is approximately the heat supplied to the distillation still during the total time period of rectification tg. The change in the heat required during the rectification process, resulting from the change of the liquid contents in the still from B, to B,, is neglected. Therefore, the calculation of the heat exchange area and

the flow of the heating medium already includes a design safety factor. To heat the still contents after filling B, to boiling point, the heat requirement Q,, is

where ha and hs are the molar enthalpies of the mixture B,, to be separated at the filling temperature and boiling point, respectively.

2.5.3.3 Still Diameter, Free Vapor Space, Column Diameter

The diameter dof the distillation still and the height of the free vapor space Z , may be calculated by means of Eqs. (2-7)-(2-10) given in Chapter 2.2. The calculation of the column diameter is discussed in Chapter 2.5.5.

Table 2-16. Steps in the determination of the heat requirement Q with constant reflux ratio. 0

0

Determination of B for Eq. (2-88) as described in Calculation of x ~using , Evaluation of the integral tion of Q

assumed x values within the interval xB, > x > x B , using Table 2-14. Eq. ~ (2-87) and E using Eq. (2-86) term in Eq. (2-85) with fixed A&,,g( E ) and h E ( E )and calcula-

163

2.5 Countercurrent Distillation (Rectification)

2.5.3.4 McCabe-Thiele Method to Determine the Number of Theoretical Separation Stages With discontinuous rectification processes, vapor generated in the distillation still is guided through the column. The column is operated in enrichment mode, the reflux is part of the condensate from the condenser and flows countercurrently with the upflowing vapor (Fig. 2-54). The vapor concentration y and reflux concentration x at a particular cross section, are linked by the equation for the enrichment line (Eqs. (2-54) and (2-67)). The required number of theoretical separation stages is derived by constructing stages between enrichment line and equilibrium curve, as shown in Fig. 2-56 for a binary mixture. It has to be kept in mind, that due to the continuous withdrawal of top product, the composition of the still contents also continuously changes the mole fraction, the low-boiling fraction decreases from the initial value x,, of the rectification process to the value x at the point in time of interest. The mole fraction of the low-boiling component in the

top product decreases from x,, to x, during the rectification time t with a constant number of separation stages and constant reflux ratio v. Otherwise, to produce a top product of constant concentration x,,, with a constant number of separation stages, the reflux ratio at the top of the column has to be increased and adjusted constantly. The minimum reflux ratio vmin for a mole fraction X , of the low-boiling component in the still, is (2-90) where X, and y B determine the coordinates of the intersection of the enrichment line and the equilibrium curve.

2.5.4 Semicontinuous Adiabatic Rectification In semicontinuous rectification, a fractionally generated vapor mixture is separated into continuously downflowing fractions in

b)

a1

t X - - c

Fig. 2-56. McCabe-Thiele-diagram for calculating the number of theoretical stages for the batch distillation of a binary mixture. a) Constant reflux ratio v = const b) Constant composition of the overhead product xE, = const

164

2 Distillation and Partial Condensation

a rectification column consisting of enrichment and stripping sections (Fig. 2-57). Since the fraction of the low-boiling component in the still continually decreases during the rectification process, the composition of top and bottom products may be kept constant only by continuously increasing the reflux ratio.

containing ethylene glycol, is charged directly back to the reactor. Mathematical treatment of semicontinuous rectification processes is found in [2.2].

2.5.5 Determination of the Column Diameter The cross-sectional area A Q and diameter d for a rectification unit, result from a flow equation in which the vapor is the reference phase

Fig, 2-57. Semicontinuous distillation unit. DS Distillation still or batch reactor RC Rectification column SC Stripping column C Condenser R Reboiler

Semicontinuous rectification processes are of practical importance for vapor mixtures generated in a discontinuous chemical reaction. These then have to be separated into a component continuously fed back to the reactor and a discharging fraction. For example, the main task during the transesterification of dimethyl teraphthalate with ethylene glycol is to continuously separate methanol from the reaction mixture. The reaction equilibrium is then shifted toward the product. Methanol is the top product of the column which is connected directly to the transesterification reactor. The high-boiling, or heavy, bottom product,

where V,,,,, is the maximum possible effective volumetric flow rate of vapor through the column, w ~is the , maximum ~ ~ ~ allowed velocity, referred to the free crosssectional area of the column, Gmax is the maximum possible flow rate, Q, is the vapor density, and Mg its molar mass. With Gmaxin kmol/h, w ~ in ,m/s,~ operating ~ ~ temperature T in K and operating pressure p in bar, the column diameter d is

d

= 0.00542 *

(2-92)

Ideal behavior of the vapor phase is assumed. It is recommended to compare the result from the calculations for four reference cross sections; the cross section at the column head, the cross sections above and below the feed tray and the cross section of the column bottom. The maximum allowed vapor velocity w ~depends , ~ on~the~type and geometry of the column internals, on the reflux load, and the properties of the phases in contact.

2.5 Countercurrent Distillation (Rectification)

2.5.6 Internals in Rectification Columns In order to reach the most possible intensive contact between the counterflow phases (vapor and reflux) and hence good mass and heat transfer, the rectification column is equipped with internals. Internals include trays, rotating devices and packing. Columns with stepwise phase contact, e. g., tray columns, and columns with rotating internals, and wetting columns with a continuous phase contact, e.g., packed columns can be distinguished. In tray columns with controlled flow, the liquid reflux passes via an inlet downcomer from the upper tray to the horizontal tray immediately below it. The liquid then flows across the tray as a continuous phase and flows from this tray to the next lower tray via a downcomer (Fig. 2-58a). The desired liquid content is ensured by installing a weir in front of the downcomer. Vapor enters the tray directly through openings in the bottom of the tray (drilled holes, slits, throats, etc.) or via rigid or flexible caps where the vapor forms bubbles which are dispersed in the liquid. In overpressure operation, with large weir heights and small vapor loadings, a bubbling bed forms on the trays. In vacuum operation, with small weir heights and large vapor loadings, the reflux liquid is dispersed in droplets and a droplet bed forms. With medium loading conditions, depending on the vapor load a two phase region forms between the trays, consisting of bubbling zone and a spray zone in which liquid droplets are entrained (splash zone). Heat and mass transfer take place in both bubbling and spray zones. Therefore, the transfer area is the total surface of the vapor bubbles and the liquid droplets. On trays with controlled vapor and liquid flow (reflux), the basic flow pattern is cross flow. In columns without controlled liquid guidance, the flow pattern is counterflow.

165

No phase contact between the spray layer and the next upper tray is possible in columns with forced flow control; both phases flow separately in counterflow. The maximum vapor loading of a tray column has to be adapted to the liquid loading, so that no liquid is carried by the vapor to the next upper tray. With minimum vapor loading, reflux should not drain through the floor drilling and the column should not become empty. In packed columns, liquid reflux flows as a falling film, or as a streamlet, from top to bottom counterflow to the upflowing vapor. Both liquid and vapor phases are in continual contact (Fig. 2-58 b and c). Mass and heat transfer occur at the inside and outside surfaces of the randomly packed filling material or the arranged packing elements in reflux film. The exchange area is the surface area. In the case of spraypack fabrics, the reflux liquid is sprayed. The contact area is the total surface area of the liquid droplets. Maximum gas and liquid throughput rates of packed columns depend on the type of packing and packing geometry, the relative free void fraction and the physical properties of the mixed phases. The column becomes flooded beyond a certain volumetric flux of the vapor at a given flux of the reflux. A controlled counterflow of the phases then does not exist; the separation efficiency of the column is reduced drastically. In rotary columns, the reflux is sprayed by means of a rotor with a funnel shaped distributor or is distributed by means of a rotor as a film on a heated tube wall. The phase contact upflowing vapor-downflowing liquid is stepwise in the first case and continuous in the latter (Fig. 2-58d). In Table 2-17, important criteria for the selection of column internals are listed. Technical considerations include separation efficiency, maximum loading and pressure drop. To date, it has not been possible to

166

2 Distillation and Partial Condensation

tD 1

C)

d)

1 --

RC

RO

4

Vapor phose

Liquid phose

Fig. 2-58. Rectification column internals. a) Tray column D Downcomer ID Inlet downcomer BZ Bubbling zone SZ Spray zone b) Random packed column R P Random packing c) Wetted packing column MP Regular mesh or extended metal packing SP Spraypack d) Rotary column RO Rotor with funnel shaped distributor RC Reflux collector ? Vapor phase 1 Liquid phase

large variety of rectification trays, random and structured packings available. In general, trays should be used as column internals, if: 0

0

0

0

Large throughputs require a large column diameter With throughput variations sufficient flexibility is important Larger tray pressure drops under coarse vacuum, normal pressure, or overpressure operation are tolerated A possibility of contamination and incrustation occurs

Random packings in smaller column diproduce internals with maximum exchange ameters are characterized by efficiency accompanied by maximum loading and minimum pressure drop. Instead, 0 High specific loadability the column internals have to be chosen ac- 0 Good separation efficiency cording t o the particular requirements of 0 Small specific pressure drop the rectification problem. This explains the 0 Low costs

2.5 Countercurrent Distillation (Rectification)

167

Table 2-17. Considerations for the assessment and selection of column internals.

0 0 0 0

0

Effectiveness, separation effect (enrichment ratio, NTS, HETP-value) Loading ability, loading range (highest allowed vapor velocity, smallest possible vapor velocity, reflux stream density) Pressure drop, equivalent pressure drop for a theoretical stage Flexibility for loading variations Sensitivity against fouling and crusting Possibility of manufactoring of materials resistant to different mixtures Acceptable column costs

This type of filling material is particularly useful with normal pressure and under coarse vacuum operation. Structured packings are better than random packings with respect to separation efficiency and loadability. Since they cause smaller specific pressure drops, though at higher costs, they are suitable for difficult separation tasks in vacuum operation. A detailed discussion of column internals and a rating with respect to costs are given by BILLETin [2.2, 2.14, 2.691. Table 2-18 gives a detailed overview of technical columns in counterflow of gasliquid, designed by MANTEUFEL [2.108]. 2.5.6.1 Column Trays Liquid Flow The flow pattern on column trays is usually controlled. Due to the design arrangement of the entry and exit, including an exit weir, the reflux liquid flows across the tray while the vapor flows upward (Fig. 2-59). Vapor and liquid therefore flow in a cross currentcounter-flow manner through the column. With trays without controlled liquid flow, vapor and liquid flow countercurrently through the same openings in the tray. Holdup of the liquid on the tray for sufficient heat and mass transfer is obtained only under certain flow conditions.

Important Types of Column Trays

Column trays are horizontally arranged elements of plate, formed and strengthened by channel sections. In general, trays are assembled as individual plates or as packages of several trays, mounted at the column wall with a liquid-tight seal (Fig. 2-60). Trays may be accessible by means of manholes in the column wall and service openings on the trays for maintenance, cleaning and reconstruction purposes (Construction details are found in [2.2, 2.70, 2.711). The following groups of column trays are important : Trays with drilling or slits in the base plate. Liquid flow controlled across the base plate or drops downward through the base plate openings where the vapor flows counterflow upward, e. g., sieve tray, turbogrid tray) Trays with vapor flow through throats, or chimneys covered by bells, hoods, or caps, dipped in the liquid. The liquid flows in a controlled manner across the base plate (e. g., bubble cap tray, cross flow tray, Thormann tray, Streuber tray) Trays with drilled holes in the base plate, which are covered by movable and adjustable load valves. Liquid flows in a controlled manner across the tray (e. g.,

8. Overview of full-scale technical columns with countercurrent flow of gas and liquid phases *.

Empty

Empty

Bubbles

Drops

Continuous Countercurrent

Continuous Countercurrent

Bubble column

Spray column

Only at top on

with

Tray column without reflux drain

Stagewise Countercurrent cross flow Bubbles/drops

-

Stagewise Countercurrent Bubbles/drops

Horizontal directors (trays) (radial) Liquid weir on each tray

Bubble cap trays Sieve trays (hole trays) Tunnel-cap tray (Thormann) Valve tray Perforated tray Sieve turbogrid tray Sieve bubble cap tray

Only at top

Wire mesh tray (Turbogrid) Ripple tray Perforated tray Kittel tray Corrugated sieve tray

Random packed column

Continuous Countercurrent Film/bubbles Random packing

Structured packing

Continuous Countercurrent Film Vertical dividers (axial)

C C Fi dr C

Sulzer packing P Stedrnan packing Spraypack Braided metal packing Braided metal spiral packing (Montz)

Raschig rings Tube bundle Saddel (Berl-) (Kuhn) Pall rings Tube bundle (Brauer) Intos-Ring Plates Perro-Ring (Adolphi, G) Intalox Grid Novalox Square grid Ralox Spring Interpack Random (Montz) Trickle wire weave packing packing (Stage!

Every 1-3 m O or only at top

Only at top or several intermediate distributors

Only at top or several intermediate distributors

Jet tray Centrifuge tray Perform contact tray MD-sieve tray Film tray Metal

Metal

(i. e., Multifit, Hyperfit)

Shaped-metal trickle packing

100-300

100-200

Metal Ceramic

Ceramic Metal Plastic

60,

450-800

Po (c M Pl

Metallic weave Plastic Porcelain

ing

2-3

2-4

1-2

1-2

2-2.5

1.5-2.5

1-2.5

0.5-2 1-3

3-

10-6

10-2.5

1-

5-2

5-0.5

2-3

2-3

2-

olumn

hange [2.109]

[2.109]

[2.731,[2.74]

[2.73],[2.74]

5

10

0.5- 0.3

0.5-0.25

1-0.3 1.5 i2.1101

0.1-0.4

0.1-0.2

P.21

v.21

1

1

0.

ture : olume-specific surface (m2/m3) loading factor F, = w g . f separation stages: number of stages per unit column height n, = N , / Z olumn volume: per unit vapor volumetric flow and per separation effectiveness required column volume hange: ratio of effective gas velocity through the gas openings and gas velocity related to the column cross sectional ntation according to MANTEUFEL [2.108]

6

170

2 Distillation and Partial Condensation a) Section 1-1

1

Vapor

4

Section 11-11

Reflux

Fig. 2-59. Column cross-flow trays. a) Single-pass tray, available up to ca. 2 m diameter b) Four-pass tray for large column diameters and high liquid loading c) Radial flow tray d) Stepped tray to even out different liquid levels at high liquid loadings e) Reverse flow tray for small liquid loadings t Vapor 1- Reflux

2.5 Countercurrent Distillation (Rectification) 2

L

171

c’

3

Fig. 2-60. Attachment and sealing of trays. Representation according to Montz, Hilden. a) Tray with attachment device b) Tray sealing with spiral spring c) Function of the tray sealing 1 Shell 2 Cage of spiral spring 3 Spiral spring 4 Tray 5 Spacer 6 Bolt 7 Bolt attachment 8 Tray support ring

0

Glitsch valve tray, Stahl valve tray, Koch flexitray) Specially constructed trays with specially designed vapor openings, cause an increase in the cross flow due to a deflection of the vertical vapor jet (e. g., perforated valve tray, Kittel tray, jet tray, perform contact tray)

Well known types of column trays are presented and explained in Tables 2-19 and 2-20 with respect to their operating mode and important design data. ~

Figure 2-62 shows different areas of a cross section of a tray which is common to all cross flow trays. These areas must be considered in the fluid mechanical design of the tray. Table 2-21 compares some important column trays. For the detailed evaluation of economical efficiency or optimization calculations, experimentation with the separation mixture in pilot-scale plants is required [2.69, 2.721.

Loading Range, Operating Range The operating or loading range of a tray column is limited by the type and geometry of the trays and also by the properties of the phases in contact. From the viewpoint of large throughputs and good flexibility, a tray column should have the largest possible operating range. Figure 2-63 shows qualitatively the operating range with controlled flow. The following loading limits must be considered :

172

2 Distillation and Partial Condensation

Tab. 2-19. Commonly used column trays with explanation and brief description of the design and operation [2.73]. ~~

~

~

Tray Explanatory sketch

Design and operation principle

Column trays without guided liquid flow Sieve tray without downcomer

Sieve plate without downcomer, countercurrent vapor and liquid flow through the same openings. Liquid rains in dispersed droplets from tray to tray and sprays when landing on next tray. Minimum vapor velocity must be obeyed to keep a liquid layer on the tray as the heat and mass transfer area.

[2.74]

Ripple tray

Approximately sinusoidally ribbed sieve plates or shaped metal surface. In order to guarantee a good liquid distribution, plates are placed with a 90" shift, with reference to the plate above. Countercurrent vapor and liquid flow, the vapor mainly flows through the ribbed plate peak openings and preferentially the liquid drops trough the plate valley openings.

[2.74]

Grid or shaped plate, countercurrent vapor and liquid flow, both phases flow interchangeably through the slits. The liquid is thereby dispersed as droplets. Trays used with and without liquid guidance.

[2.74] [2.75] [2.76]

References

, 0

0 0 0 0

0 0

1: .

Turbogrid tray

2.5 Countercurrent Distillation (Rectification)

173

Tab. 2-19. (continued) Tray Explanatory sketch

Design and operation principle

Kittel tray without downcomer

Shaped metal trays, vapor and liquid flow through the same slits. The slits are arranged such that the vapor imposes the direction of movement of the liquid. The liquid on each tray is pushed from the edges to the middle and drains there preferentially. On the neighboring trays the flow direction is opposite.

[2.74]

Column trays with guided liquid flow

Sieve plates with tray openings for the vapor flow and feed or drain appliances. Minimum vapor velocity must be obeyed such that liquid does not rain through the trays. As in the case of sieve slit trays, additional slits can be stamped into the surface of the sieve plate, through which some of the vapor is reflected in the direction of the liquid flow. This is advantageous with large liquid loadings. More downcomers can also be ordered as in the case of MD (Multi Downcomer) Trays.

12.21 [2.74] [2.77] [2.78] [2.91]

Sieve tray

ID Inlet downcomer OD Outlet downcomer

References

(continued next page)

174

2 Distillation and Partial Condensation

Tab. 2-19. (continued) Tray Explanatory sketch

Design and operation principle

Bubble cap tray')

Cross-flow tray with openings or chimneys for the vapor flow, covered by caps with smooth, slitted or peaked edges. The upflowing gas phase is directed up through the caps and flows out in parallel to the tray base through the liquid, such that a bubbling layer for heat and mass transfer forms. The cap submergence remains fixed by the distance between the top of the downcomer and the bottom of the cap, and is the submergence of the vapor path through the bubble layer. A decrease in the bubble cap diameter increases the separation effectiveness but enables an increase in the loading. The modern flat or low-riser cap designs show good effectiveness with higher loadings and low pressure drops. For higher vapor loadings, rectangular ( - 100 x 50 rnm) cross-wise arranged caps are used (cross-flow cap trays).

I

I

Section 1-1

1

2

a

I

-b

3

-- a nnnn

L

b C

6 d

e

a

Cap designs 1 Conventional cap') 2 Low-riser') 3 Sigwart cap') 4 Umbrella cap') 5 Varioflex cap') 6 Varioflex cap with valve plates2) (nozzle discharge disc) a Vapor opening (tray opening, chimney) b Cap c Vapor outlet slit with guide plate d Nozzle disc lift stop e Valve plate (nozzle disc)

References P.21 [2.74] [2.80] [2.81]

2.5 Countercurrent Distillation (Rectification)

175

Tab. 2-19. (continued) Tray Explanatory sketch

Design and operation principle

Channel tray3)

Cross-flow trays work to the same principle as bubble cap trays; they have length-wise vapor chimneys which are fixed by the U-shaped channels and hood covers. The channel breadth, chimney breadth, chimney height and hood submergence depend upon the operating conditions. Parallel (STREUBER system) or channels mounted crosswise to the (THORMANN system) liquid-flow direction are used. Annular channels are also used, in which case the flow on the tray is radial. The type and design of the head slits define the direction of the vapor flow and, therefore, an acceleration or deceleration of the liquid ( ~ O R M A N Ntray). 1 Channel tray with cross-liquid flow defined by the channels and hoods (THORMANNsystem) 2 Liquid flow through a channel tray (THORMANN system) 3 Addition of a hood with alternating folded slits 4 Slit sketch of a vapor chimney and hood

References K2.21 [2.85]

(continued next page)

176

2 Distillation and Partial Condensation

Tab. 2-19. (continued) Tray Explanatory sketch

Design and operation principle

References

~

KSG cross-flow tray3) 1

KSG-S

Cross-flow tray with punched in vapor chimney with rounded edges (types KSG-S, KSG-0) or with direct punched-out gas outlets (type KSG-E). Chimneys are covered by hoods with outlet slit. To avoid an impact on opposite vapor fluxes neighboring vapor fluxes cross each other under a 90" angle due to the opening arrangement of the exchange devices (positive effect on pressure drop and entrainment). Depending on the vapor load on the KSG-S tray, vapor flows through either one or both output slits arranged on top of each other (wide operating range; operating characteristic like a valve tray). 1 Cross-flow tray 2 Vapor chimney with hood

KSG-0

-& KSG-E

Perforated valve tray4)

Froth

rl

Froth

Tray with slits arranged at side. Vapor or gas is guided through the horizontally flowing liquid. Thus, with a small liquid holdup a long contact time is achieved. Type A Liquid always flows from the outer edge radially across the tray to the center (radially in the same direction)

[2.90]

2.5 Countercurrent Distillation (Rectification)

177

Tab. 2-19. (continued) Tray Explanatory sketch

Design and operation principle

1

S-Tray (Uniflux tray)

1-

Valve tray5)

bl

References

Type B Alternative liquid flows from outside toward the center and from the center toward the Froth outside (radial opposing)

Cross-flow tray with across-mounted S-shaped elements including trapezoid slits. Liquid accelerated in downcomer weir direction by the vapor leaving the chimneys.

12.21 [2.74]

Cross-flow sieve tray with large holes (hole diameter = 40 mm). The holes are covered by guided movable ballast valves, plate valves or lever valve (float valve). Valve lift and, therefore the opening for the vapor flow is adjusted automatically by the momentum of the upflowing vapor. While exiting the valve vapor is diverted under the valve cap to flow parallel to the tray base plate into the liquid. Thus good vaporliquid mixing is provided by the valve caps over a wide vapor load range. To avoid draining of the tray a minimum vapor load is required. Different valve designs are: 0 “Three-leg” valve (glitsch valve, ballast valve) guided by three internal legs

12.21 [2.74] [2.82] [2.87] [2.88]

(continued next page)

178

2 Distillation and Partial Condensation

Tab. 2-19. (continued) Tray Explanatory sketch

Design and operation principle

CJ

9

L

7

1

0

2

6

5

9

3

L

6

5

L

?

1

0 0

2

6

5

3

6

5

L

Square “four-leg” valve (Speichim capsule tray) Valve disc with smooth or venturi tube shaped vapor entry guided in a cage mounted on the tray (Koch Flexitray, Stahl Varioflex-cap with valve disc) Rectangular float valve (Nutter float valve tray) Cross-wise mounted area valves guided by internal legs (Montz cross-flow valve tray) Valve disc attached to the grid (Krupp “grid valve”) a) Valve tray (schematic) b) Operation principle of a ballast valve in fully open position c) Assembling of a ballast valve

1 Ballast unit 2 Tray sheet metal (base plate) 3 Vapor flow 4 Initial opening limitation (closed position) 5 Lower ballast unit 6 Maximum opening limitation 7 Initial opening area 8 Maximum opening area 9 Centripetal vapor exit

0

Kittel tray with downcomer2)

Expanded-metal tray as previously described with controlled liquid flow 1 Expanded-metal segment 2 Channel 3 Downcomer 4 Inlet weir

3

References

P.21 [2.74]

2.5 Countercurrent Distillation (Rectification)

179

Tab. 2-19. (continued) ~~

Tray Explanatory sketch

Design and operation principle

Jet tray

Cross-flow tray with half stamped out slots. The flap opening acts as a nozzle. The vapor jet forms parallel to the tray and forces the liquid to flow across the tray to the downcomer. To avoid draining of the tray a minimum vapor velocity is required.

[2.74]

Cross-flow tray made of expandedmetal segments. Vapor outlet aperture - vapor blow direction - are shifted by 90". To increase the active surface of the tray and to avoid entrainment of liquid baffle expanded-metal deflectors are mounted in a sharp angle against the vapor flow direction. 1 Baffle 2 Downcomer 3 Upper tray downcomer and weir

v.21 [2.88]

Cross-flow tray for vacuum operation. Flat plates including downcomers are arranged at a small distance. The liquid flows as a film across the plates in constant contact with the vapor. Liquid and vapor both flow through the downcomer to the next tray.

12.21

_ -

t

' \__ >._ /'

Perform contact tray5)

1

2

3

Film tray

') *)

3, 4,

5,

Representation Representation Representation Representation Representation

References

according according according according according

to to to to to

ACV Dr. Stage, Schmidding, Heckmann, Koln-Niehl. Stahl GmbH, Viernheim. Montz GmbH, Hilden. Kiihni, Allschwil. Gutehoffnungshutte AG, Oberhausen-Sterkrade.

180

2 Distillation and Partial Condensation

Table 2-20. Geometrie and fluid dynamic characteristics of important column trays [0.1, 0.6, 2.73, 2.741. Tray type, sizes (mm) and operating variables

Vacuum rectification

Normal pressure operation

Overpressure rectification, absorption

500- 8000 80- 160 1.25 . d, (0.5-0.6) . d 20-30 0.7. h, 500-800 (0.7-1.2) * ego.’

500- 8000 80- 160 (1.25-1.4). d, (0.6-0.75) . d 30-70 0.8 * h, 400- 600 (0.7-1.5) * ego.’

500- 8000 80- 160 1.25 . d, 0.85 ’ d 40-100 0.9. h , 300-400 (0.6-1.4) . ego.’*)

(8.4- 12.5) . w

(10-16)

0.05-0.15 0.20-0.30

0.10-0.30 0.35-0.75

0.15-0.40 0.55- 1

500-8000 80- 150 300- 600 20- 30 500- 600 (0.8- 1.2) . e[O.’

500-8000 80- 150 300- 600 40- 60 400- 600 (0.7-1.5). Q[O.’

500- 8000 80- 150 300- 600 60- 80 300- 500 (0.6-1.4) . ego.’

Bubble-cap trays Tray diameter d Cap diameter d, Cap spacing t (division) Weir length I , Discharge weir height h , Weir outflow height h, Tray spacing Az Gas(vapor) velocity w (m/s) Gas(vapor) velocity in chimney Weff (m/s) Pressure drop A p dry (kN/m2) total (kN/m2)

(5.5-8.4)

*

w

.w

Channel trays Tray diameter d Channel width Channel length Discharge weir height h , Tray spacing Az Gas(vapor) velocity w (m/s) Gas(vapor) velocity in chimney weff (m/s) Pressure drop A p dry (kN/m2) total (kN/m2

(6.3-8.4)

*

w

(8.4-10)

.w

(10-12.5)

.w

0.10-0.1 6 0.22-0.30

0.15 -0.30 0.35-0.60

0.20-0.40 0.45-0.70

500-10000 50- 150 820 2040 1.5 . d, 0.22-0.32

500 - 10000 50- 150 820 3050 (1.7-2.2) . d, 0.16 - 0.24

500- 10000 50- 150 820 4070 (2-3). d, 0.12-0.16

500-800 (8- 14) * ego.’

400- 600 (10-18) ego.’

300-500 (8-14) . Q ~ O . ’

0.20-0.30 0.30-0.40

0.30-0.40 0.40-0.65

0.35-0.50 0.50-0.90

Valve trays Tray diameter d Valve diameter d, Valve lift Discharge weir height h, Valve spacing (division) t Valve arealtray area (scale for active tray area) Tray spacing Az Maximum gas (vapor) velocity in the openings (m/s) Pressure drop Ap dry (kN/m2) total (kN/m2)

2.5 Countercurrent Distillation (Rectification)

181

Table 2-20. (continued) Tray type, sizes (mm) and operating variables

Sieve trays Tray diameter d Openings (drill hole) diameter dd Hole spacing (division) t Opening areahray area (opening ratio) Discharge weir height hw Tray spacing Az Minimum gas (vapor) velocity in the openings w e f f , m (m/s) Gas(vapor) velocity in the openings weff (m/s) Pressure drop dry (kN/m2) total (kN/m2)

Vacuum rectification

Normal pressure operation

Overpressure rectification, absorption

500- 4000 2.5-15 (2.5-3). dd 0.12-0.20 10- 20 500-800

500-4000 2.5- 15 (3-4) . dd 0.08-0.15 20- 50 400- 600

500-4000 2.5-15 (3.5-4.5) . dd 0.06-0.10 40- 80 300-400

10 *

g

10

ego.’

eg0.5

. @p0.5

1.8 . Weff,m

1.8 . Weff,m

1.8 . Weff,m

0.08-0.20 0.20-0.30

0.08-0.30 0.35-0.60

0.08-0.35 0.55-0.90

500- 4000 3- 12 0.25-0.35

500- 4000 3- 12 0.15 -0.25

500- 4000 3- 12 0.12-0.18

Grid trays Tray diameter d Slit width Slit arealtray area (opening ratio) Liquid level on the tray Weir height Tray spacing Az Gas(vapor) velocity w (m/s) Ratio of minimum gas and vapor velocity in the slits w e f f , m (m/s) Pressure drop Ap dry (kN/m2) total (kN/m2) *)

8- 10 12- 28 30- 50 no weir existent; no guided liquid flow 400- 600 300- 400 250- 300 (1.5-2.3). ego.’ (1.1-1.6) ego.’*) (1.4-2) . Q;’.’ 10 . ego3

10 . ego5

10 *

0.06-0.10 0.10-0.20

0.08-0.12 0.20-0.40

0.08-0.12 0.40-0.65

eg Gas (vapor) density (kg/m3)

Fig. 2-61. Explanation sketch for Table 2-20. Section 1-11

Az d

Active tray area Outlet downcomer area Inlet downcomer area Spacing Weir length Discharge weir height Weir outflow height Tray spacing Tray diameter

Section 1-11

--t

Gas (vapor) p h a s e phase

- - C Liquid

eF0.5

182

2 Distillation and Partial Condensation 0

0

-ES -LB

0

-BS

0

Fig. 2-62. Sections of a cross-flow tray. WA Working area IDA Inlet downcomer area LDA Liquid distribution area DA Disengaging area (outgassing area) ODA Outlet downcomer area DS Dead section BS Bubbling or froth section ES Entrainment section LB Liquid backup in downcomer to form a gas(vapor) seal T Gas, vapor 1 Liquid

Minimum vapor load (weeping, draining): if the vapor load is too low, instability of vapor distribution on the tray and weeping, leaking of liquid through the tray occur Minimum liquid load (minimum crest over weir, weir overflow): if the liquid load is too low, a constant weir overflow and a perfect liquid distribution on the tray are not guaranteed Maximum vapor load (entrainment, flooding): if the vapor load is too high, liquid droplets are entrained in a considerable amount or even flooding occurs Maximum liquid load (downcomer blockage, foam disintegration): if the liquid load is too high, the downcomer capacity is not sufficient and the too low residence time in the downcomer does not allow a complete separation of vapor and liquid (foam disintegration)

A detailed overview of the dependency of selected trays on the operating range, the tray geometry and the operating parameters, is given by MOLZAHN and SCHMIDT in [2.92]. For example, an increase in the tray spacing gives an increase in all loading limits. An increase in the free area gives an increase in the vapor load limit, while the liquid load limit remains unchanged. Increasing the height of the weirs expands the operating range of the liquid, but reduces the vapor load range. An increase in the downcomer height shifts the operation range to higher liquid loads, but decreases the range altogether. The maximum possible vapor load F, or wg,, is reached under a given liquid load when the height of the two phase layer on the tray of interest is equal to the distance between the two trays. A liquid droplet of diameter d , is then suspended between the two trays. The weight of the droplet, reduced by the buoyancy, is then equal to the resistance of the flow.

183

2.5 Countercurrent Distillation (Rectification)

Table 2-21. Comparison of some important column trays [2.74]. Tray type

Operating range Crnax/Grnin

5

4 6 8 8

Flexi- Total bility pressure (Vo)*) drop of the tray at 85% of the maximum loading (mm H2O) (10 Pa)

(-1

at 85% of the maximum loading

(->

Bubble cap tray(+) 4 to Channel tray (+) 3 to Thorman tray 4 to Valve tray (Koch) 5 to Valve tray 5 to (Glitsch) (+) Sieve tray (-) 2 to Kittel tray 2 to Drain sieve 2 to tray ( +1 Turbo grid 1.5 to tray ( + 1

Tray efficiency in the allowable range of loading changes

0.8 0.6 to 0.8 0.6 to 0.7 0.55 to 0.65 0.85 0.7 to 0.9 0.8 0.7 to 0.9 0.8 0.7 to 0.9

80

50 80 80 80

45 to 50 to 45 to 45 to 40 to

80 85 60

60

0.7 0.7

0.7 0.6 0.5

300 to 400 300 to 500 300 to 500

0.5

300 to 500

60

40

3

0.7 to 0.8 0.7 to 0.8 0.6 to 0.8

10

30 to 50 20 to 50 30 to 40

2.5

0.7

0.6 to 0.8

10

25 to 40

3

55

(-)

900 to 800 to 400 to 400 to 400 to

0.8 0.8 0.75

3

Equiva- Weight lent cost (N/m2) related to the bubble cap tray

1

0.8 0.8

1400 1400 700 700 700

Tray works well with polluted liquids Tray works badly with polluted liquids Flexibility, the part of the operating range in which the tray efficiency exhibits only a +15% swing G,,, Gas (vapor) loading at the top limit of the operating range Gmin Gas (vapor) loading at the lower limit of the operating range

(+) (-) *)

from Eq. (2-93) ~OIIOWS (2-93) where w , , ~is the maximum vapor velocity referred to the tray area and diameter d, of the droplet. Droplets with a diameter < d, are carried out; droplets with a diameter > d, fall back into the bubble regime. c , ~ is the frictional coefficient (c, = 0.4 with turbulent flow past immersed single drops). Introducing the F-factor

F,,,

=

3 * c,

(2-95)

where F, is the maximum F-factor to the droplet diameter d,. SOUDERS and BROWN [2.93] include the first root expression as the loading factor k,. This depends on tray construction, tray spacing, flow pattern of the phases, properties of the mixture, and particularly on the size of the droplets which is influenced by the surface tension. The loading factor k, has to be found ex-

2 Distillation and Partial Condensation

184

I

I

I

Flooding

rc.; .....................r........

Downcomer

ition

/

-

Weepinq, Draining

[m3/(mZ h)l

Fig. 2-63. Tray columns with guided liquid flow, range of operation [2.14, 2.921. Aps Height or stage specific pressure drop 7

v, Liquid loading wn Vapor velocity

perimentally and is usually given by the 80% vapor load related to the flooding manufacturer of the trays. Figure 2-64 al- point; the column diameter d, the number lows a first approximation of k , for sieve of exchange elements n and the outlet and bubble cap trays. For valve trays, k , may be assumed to be 30% larger. Empirical approximations are given in Table 2-22 to calculate the loading factor k , for important types of trays. The column diameter d can be computed by Eq. (2-92), after the velocity w related to k,Q.OL the free cross-sectional area AQ is calcu- [rnlsl lated with F, in Eq. (2-95) and a safety allowance is added. An alternative method by STICHLMAIR 0 0 2 [2.97] to compute the column diameter d and the tray spacing Az is explained in I I / Table 2-23. Since the loading factor k ,is 200 300 LOO 600 800 1000 m m not used, the use of this method is advanAz Irnml tageous. In practice, design charts are sometimes Fig. 2-64. Load factor k, for sieve and bubble given by the column manufacturer. Hence, cap trays with weir height of 30 mm. Representawith the charts, as shown in Fig. 2-66 start- tion according to MERSMANN [0.1], Vol. 2. ing with the density ratio Q,/,Q,, tray spac- Az Tray spacing ing Az, volumetric vapor flow Vg and an k, Load factor

t

2.5 Countercurrent Distillation (Rectification)

185

Table 2-22. Empirically fixed estimates for the calculation of Souders, Brown correlation factors k , for the upper loading limit of selected column trays [2.2], [2.95]. 0

Souders, Brown correlation factor for the upper loading limit of tray columns

F w

eg, el

0

F Factor (see for example [O.l]) Gas or vapor velocity, related to the free column area (m/s) Gas or vapor density, liquid density (kg/m3)

Souders, Brown correlation factor for the upper loading limit of bubble cap trays k , = 0.05

Az

z,

d,

0

VKZZ,

vz

Tray spacing (mm) Cap height (mm) Cap diameter (mm)

Souders, Brown correlation factor for the upper loading limit of sieve trays

dd 0

.

determined for an opening ratio of 8 % Hole diameter (mm)

Souders, Brown correlation factor for the upper loading limit of Koch valve trays

4

Reduced gas or vapor loading (m3/s) System factor which is characterized by the mixture foam formation tendency (fs= 0.85 for vacuum operation, f,= 0.75-0.80 for normal and overpressure operation) Factor which considers the influence of tray spacing Column diameter (m) D

Vg.r = ~. 3600

ME

-. Qg

1

f , . f ~* , ~

Molar mass of the gas or vapor (kglkmol) Maximum gas or vapor flow rate in the column section of interest (kmol/h)

Reduced liquid loading (m3/h) Reflux or solution flow (kmol/h) (continued next page)

186

2 Distillation and Partial Condensation

Table 2-22. (continued)

Reduced liquid load

?,r

[rn3/hl-

Fig. 2-65. Diagram for the estimation of the diameter d of Koch A type valve tray [2.96] (see also Fig. 2-59).

Table 2-23. Scheme to determine the column diameter d and tray spacing Az by STICHLMAIR 12.971

I

Calculation of the maximum F-factor F,,,: F, = 2.5 . [p2 where a, = a,

AH ~

A ok

01

- (el -eg) g]”4

Relative free cross section

Initial estimation (e.g., a, = 0.1)

AH Hole area, slit area (m2) A,, Active area (m2) O/ Surface tension (kg/sZ)

el e,

g

Liquid density (kg/m3) Gas or vapor density (kg/m3) Gravitational acceleration (m/s2)

(2-96) (2-97)

187

2.5 Countercurrent Distillation (Rectification) Table 2-23. (continued) 0

Calculation of the allowable F-factor and, therefore, fixing of the upper loading limit F=0.7*Fm

0

(2-98)

Calculation of relative gas or vapor velocity wg on the active tray area and calculation of the active area A,,

wg =

F

(2-99) (2-100)


0 (n,),= 0

v

(2-148)

The smaller the reflux ratio, the more the separation effect decreases with maldistribution. To restrict maldistribution of the liquid by channeling or flow at the wall, the total height of the packing Z is separated into single packing heights 2, each with its own support and cover grids, and liquid distributor [2.118].

2.5 Countercurrent Distillation (Rectification)

3 = 2.5 - 3.0 d ' k

-

d

zk

= 5.0 - 8.0 saddles

-3

d

Rasching rings

5.0 - 10.0 pall rings

(2-152)

(2-153)

(2-154)

Calculation of the separation effect in advance is difficult due to the large number of variables. Also, scale up of HETP or n, found by experiments at pilot-plant scale is not easily done due to an increase in unfavorable liquid distribution in a full-scale plant. A method to calculate the separation effect of packed columns is introduced by BILLETand MACKOWIAK [2.126], where the variable n, is given by

AP (2-155)

as a function of the pressure drop Ap of the packing, the number of transfer units related to the gas phase NTU,,, and the stripping or strip off factor 1

L h=m.G

(2-156)

(rn is the slope of the equilibrium curve and L and G are the liquid and gas flows, respectively). A simple estimation is possible by Eq. (2-130), according to BECK[2.118]. For the stripping and enrichment section the variable n, has to be calculated separately, followed by a control calculation for the single packing of height 2,. Figure 2-79 shows the dependency of the efficiency of selected packing elements on

215

the gas loading. The efficiency is greatest in the holdup region (area 111, Fig. 2-75) between the lower loading limit point and the flooding point. The efficiency increases with smaller dimensions of the packing elements and with a larger reflux or larger liquid load, respectively. The required packing height Z for mass and heat transfer between counterflow phases may be calculated in two different ways as discussed in Chapter 1.9.2. After determination of the desired number of theoretical separation stages Nt by numerical or graphical means, and the separation efficiency experimentally under conditions close to the operating conditions and suitable for scale up, the packing height is

Z = N t .HETS = 4 nt

(2-157)

The packing height may also be determined by the NTU-HTU method (see Chapter 1.9.4.1) based on the kinetic theory of counterflow mixture separation. In rectification processes, mass transfer resistance in both phases must be considered. The mass transfer coefficients in both the vapor and liquid phases should be known in order to evaluate HTU The NTU-HTU method is of no importance for rectification in contrast to absorption. This is mainly because no secured data and no valid calculations for the partial mass transfer coefficients are given for wide ranges. Liquid Holdup of Trickled Packing

Liquid holdup is comprised of the static and the dynamic contents. The static contents remain in the stagnant volumes, gussets, etc., of the packing due to surface tension. The dynamic contents are constantly renewed by the liquid flow. If liquid no longer flows on top of the packing, a cer-

216

2 Distillation and Partial Condensation

tain amount of liquid volume remains in the packing due to adhesion. Calculations of the static and dynamic liquid contents are given in the work of GELBE[2.128] and KURTZ [2.129].

-r-----

0

1-

I

I

I

1 F[Pa”’I

I

1

2

15 10

1 7

3 [ rnb a r /m ] 2 APS

1

0.5 0.5

0.7

1

1.5 F[P~”’]

2

3

2.6 Choice, Optimization and Control of Rectification Units For the initial selection of column internals for rectification columns, knowledge of the vapor load and operating pressure is sufficient. With small vapor loads and, therefore, small column diameters, random packings are used close to the lower limit of the coarse vacuum range. If good separation efficiency at low pressure drops - even with large column diameters and a wide operating range - is required, packings with regular geometry are preferred. If a large column throughput requires a large column diameter and the pressure drop with an ambient operating pressure is of secondary importance, trays are used as column internals. For the final selection of column internals, mixture behavior, operating conditions, characteristic performance figures, costs, pressure drop, and other criteria are important. Substantial criteria are listed in Table 2-31. Different evaluation criteria prove to have an opposite influence. For example, the requirement of good separation efficiency leads to a higher pressure drop and higher costs. The selection of column inter-

Fig. 2-79. Separation efficiency and specific pressure drop of selected packings as a function of the vapor load. Representation according to Vereinigte Fullkorper-Fabriken GmbH, Ransbach-Baumbach. 1 Pall ring I” 2 VSP 25 3 Pall ring 1.5” 4 VSP 40 5 Pall ring 2” 6 Top-Pak size 1 (height 45 mm) n, Number of theoretical separation stages per m packing height Ap, Specific pressure drop per m packing height F Vapor load factor System: Isooctane - toluene; operating pressure:1.013 bar; column diameter: 400 mm; reflux ratio: 03

2.6 Choice, Optimization and Control of Rectification Units

Table 2-31. Column internals selection criteria.

0

Product specification (top product, bottom product, sidestreams) Mixture properties Thermal sensitivity, contamination tendency, foaming properties, material properties Operation condition Operation form, operating pressure, reflux ratio Performance figures of column internals, technical data Liquid load, vapor load (loading factor, operating range) Partial load behavior, separation efficiency (no. of theoretical separation stages per m) Stage specific pressure drop Required specific column volume (column volume/vapor flow rate) Costs Column costs, peripheral equipment costs, operating costs Reliability

0

Influence by process or system*

0

0

0

Main resistance of transfer process in liquid phase in gas or vapor phase Discharge of intermediate fractions required Constant temperature along tower required Foaming tendency Clogging tendency (suspending solid) Diswetting tendency Corrosive medium Viscous liquid Heat exchange required Hydrodynamic properties Low liquid holdup allowed Low pressure drop allowed Wide range of gas and liquid rates Large gas loading Very small liquid rate Equipment demands Frequent cleaning required Low weight allowed Low construction height Small base area 0 less suitable

x very suitable

* Representation according to REICHELT [2.109].

Tray column

X

0

Trickle packed tower apparatus 0 X

X

0

0

X

0

X

X

0 0

X

0 0 (XI

X X

Tower with packed tubes

0

X

0

X

X

0

X

0

(XI

X X

trickle packing tower 0 0

0

X

X

0

217

218

2 Distillation and Partial Condensation

nals and the commitment of the operation conditions results from an economic compromise. The main criteria for rectification units that are looked for are minimum total costs, safe operation and no environmental pollution. If the investment costs of column internals are to be compared, the solution of a separation problem is first analyzed. Suitable internals have to be specified with criteria for comparison purposes, such as the specific column volume v, as the column volume per vapor or gas load, and separation efficiency for the optimum operating condition. For random and regular packing, 71

&-.Z 4

Z

HETS

(2-158) For trays with a constant tray spacing Az, 71

d’*--N,* A z 4

Performance figures and cost data are given in Fig. 2-80 and Table 2-32. Economical optimization of a rectification unit regarding the reflux ratio is discussed in Chapter 2.5.2.5, Fig. 2-52. Further optimization, especially with a view to a heat network are presented by BILLET[2.2, 2.141. Several opportunities exist for process control of rectification units, depending on the requirements [2.2, 2.130-2.132, 2.1431. Figure 2-81 shows a simplified section of a flow sheet for a rectification unit with the usual process control equipment.

2.7 Rectification Unit Accessories In addition to the internals (trays, random packing, regular packing) required to increase the phase surface area, additional elements are provided in the column [2.2]: 0

0 0

AZ

0

(2-159)

T~ obtain the specific column costs c for comparison of different types of internals, only has to be multiplied with the interrials specific costs, C, per m3 column volume. c, has to be determined for each thosen column diameter d

c = v.c,

(2-160)

A comparison and evaluation of different column internals is given by BILLETin [2.2].

Support plates for filling material (Fig. 2-82) and support grid for packings Hold-down plates (Fig. 2-82) Liquid distributor for filling material and packings (Table 2-33) and liquid redistributors (Fig. 2-82) Demister between rectification trays and in front of vapor lines (wire gauze or plastic gauze with a strengthened cover [2.134], etc.)

Tube evaporators with thermosiphon circulation or continuous flow evaporators are mainly used in rectification facilities. Falling film evaporators or film evaporators are seldom used. The vapor is condensed in a horizontal liquid-cooled tube bundle heat exchanger or air-cooled finned-tube heat exchangers [2.135].

2.7 Rectification Unit Accessories

219

L \

..-

I " I

0

Carbon steel column shell

I

I

I

1

2

Tower diameter Iml-

I I

3

Fig. 2-80. Relative column costs related to the empty column as a function of the column diameter. Representation according to REICHELT[2.109]. Column data: d = 1 m, I/= 1 m3 -. -. Pall rings St. 50 x 50 - Bubble cap tray - .. . - Pall rings St. 25 x 25 Centrifugal tray Pall rings St. 15 x 15 Channel tray - _ _ Interpack 20 x 20 ..... Valve tray 1 m3 packing with shell 1 m 3 column volume including trays and shell, tray spacing 0.5 m

Table 2-32. Performance figures and pressure drop [OJ], [2.132]

*,

Column internals

F-factor

Number of theoretical

Specific tray pressure drop Ap/N, (N/m2)

Kittel centrifugal expanded-metal tray Valve tray Sieve tray Channel tray Bubble cap tray Grid packing, coarse Metal gauze packing Grid packing, fine Pall ring 25 x 25 x 0.6 Pall ring 5 0 ~ 5 0 ~ 1 . 0 Interpack filling 20 x 20 x 0.4

2.89 2.22 2.12 1.74 1.54 3.04 2.82 2.59 2.30 2.47 2.18

0.65 1.43 1.40 1.52 1.34 0.75 3.69 0.71 3.02 2.18 2.08

558 535 576 936 694 171 140 414 242 238 46 1

*

Values are obtained with the system ethyl benzene - styrene at 133.3 mbar, at 80% of the flooding point, and a reflux ratio (v = 03). Tray spacing Az = 0.5 m.

220

2 Distillation and Partial Condensation

HE1

d

Fig. 2-81. Simplified process flow diagram of a rectification unit. C 1 Column TIC 1 Overhead product, temperature H E 1 Reboiler control FIC 1 Feed control HE 2 Condenser Top product cooler HE 3 FR 1 Top product, flow, recorded Bottom product cooler, feed Bottom product, flow, recorded HE 4 FR 2 preheater Bottom product, temperature, TR 2 recorded V 1 Top product receiver PIC 1 Steam pressure indicator and control, Process control keys: P Pressure possible response to total column L Level pressure drop F Flow PdI 1 Pressure drop, indication T Temperature PI 1 Top column pressure I Indication Bottom column pressure PI 2 LIC 1 Level control, bottom R Recording TR 1 C Control Overhead product temperature, recorded FRRC 1 Reflux ratio control, possible response to top product temperature

2.7 Rectification Unit Accessories

221

1. Support plates*

a) Corrugated expanded grid or perforated plate welded on a frame, diameter up to 1000 mm and a low load (one piece)

b) Frame with flat profile grid for small and intermediate diameters, and intermediate load, with and without expanded grid (also used as hold-down tray)

c) Braun support grid, one piece, for diameters up to ca. 600 mm made from standard parts (500x 250), edge segments are adjusted, suitable for every diameter, grid height up to 150 mm

d) Standard support tray made from single beams, for diameters larger ca. 950 mm, light and heavy model

2. Hold-down plates** (bed-limiter)

e) Sieve or expanded metal plate for a diameter up to ca. 1200 mm Fig. 2-82. Packed tower internals.

0 Sieve or expanded metal including weight for diameters larger ca. 1100 mm

222

2 Distillation and Partial Condensation

3. Liquid redistributors**

g)

Rosette redistributor for diameters up to

600 mm

h) Redistributor for diameters larger ca. 1200 mm

Fig. 2-82. (continued)

* Representation according to Vereinigte Full-

korper-Fabriken GmbH & Co., RansbachBaumbach. ** Representation according to Norton GmbH, Wesseling.

2.8 Parallel Flow Distillation With parallel flow distillation [Oh] vapor and liquid are guided in parallel flow through a column in contact zones, mainly tube bundles (Fig. 2-83). Upflowing vapor drags liquid upward on the inner tube wall in the form of a film, where mass and heat transfer occur in a similar manner to rectification. In general, during phase contact, vapor is enriched with the low-boiling component, while the liquid phase is reduced. At the respective ends, phases are separated by a separator; vapor enters the next higher tube bundle, while liquid flows to the next lower tube bundle. Vapor arriving at the top of the column is condensed in a total condenser. The condensate is divided into the overhead product and the reflux which is fed back to the column. Some of the bottom product is discharged, and the rest is fed back to the distillation still. With counterflow distillation, vapor velocities are 1-3 m/s, whereas in parallel

flow distillation considerably higher gas velocities, up to 50 m/s, are possible. The separation efficiency decreases at increasing allowable vapor velocity, with increasing diameter of the individual tubes in a tube bundle. More intensive phase contact with developed two phase flow is reached by vortex flow or devices to reinforce spray vortex flow, compared with pure liquid flux. Internals for counterflow columns in distillation and absorption are currently being developed. The use of this type of column on an industrial scale is not yet known.

2.9 Nonadiabatic Rectification Nonadiabatic rectification (thermal rectification, redistillation) is a thermally gentle separation process of high-boiling liquid mixtures, using a combination of partial distillation and partial condensation. The fractionator is a special thin-layer evaporator, with externally heated columns and an externally cooled rotor (Fig. 2-84). The vapor mixture, generated in a thinlayer or falling film evaporator, flows countercurrently in the fractionator, with the downward liquid reflux at the heated inner wall of the evaporator. By repeatedly vaporizing and condensing some of the

2.9 Nonadiabatic Rectification

4

4

223

downflowing liquid and the upflowing vapor, the low-boiling mixture components are enriched in the vapor, while the higherboiling components are enriched in the reflux. Vapor at the top of the fractionator condenses in a condenser. Some of the condensate is withdrawn as overhead product, the remaining forms the reflux which returns to the fractionator. Reflux leaving the sump of the fractionator flows back to the distillation unit and is there withdrawn as the bottom product. Depending on the separation task, the fractionator may be operated only as an enrichment column, only as a stripping column or in a normal operating mode as shown in Fig. 2-84. The thin-layer evaporator is most effective when the ratio of the mass flows vaporized and condensed on the side is equal to 1 [2.136]. Therefore, the separation efficiency of the fractionator depends on how often the generated vapor mixture is condensed and revaporized in the unit. At infinite reflux ratio and at constant relative volatility a, the separation efficiency in the concentration range of interest is Vapor phase Liquid phase

Fig. 2-83. Two stage cocurrent tube bundle distillation unit. ST Still TC Tube bundle column C Condenser TP Top product RF Reflux BP Bottom product SE Separator EA Entrainment area

(2-161) where the vapor concentration at the top and bottom of the fractionator n, = N,/Z Number of theoretical stages per m of the fractionator z height for mass and heat transfer of the fractionator (chosen upper limit of the dimensions of a thin-layer evaporator : 850 mm diameter, 9 m height)

yo, yL?

224

2 Distillation and Partial Condensation

Table 2-33. Liquid distributors. Presented by MANTEUFEL [2.133]. System

Method

1

Construction

Drain-

Liquid flux per drain

Om

No. of drains per m2

Liquid rate (m3/(m2 h))

> 10

40-400

Medium >1

40-1000

Medium to very large

+

liquid jet # '3

,

3'6

.

Hole

1. Hole or sieve tray distributor with or without vapor riser (tube) 2. Channel or trough-type distributor Tube distributor (straight or concentric)

like liquid

>5

1. Spout or riser distributor 2. Channel or trough-type distributor

2.9 Nonadiabatic Rectification

Operating range

Energy

con-

sumption

Free vapor area

Functional range

Column diameter (m)

Performance

Pros

Cons

225

Limited 51

No

20-40% > 50%

Normal pressure overpressure

Up to 2.5 2 0.6

Sensitive to dirtying or fouling

Equal single drain fluxes

Few drains

Unlimited

No

20-40% > 50%

Normal pressure overpressure

Up to 2 20.6

Sensitive to dirtying or fouling

Wide operating range

Not for small liquid rates

(continued next page)

226

2 Distillation and Partial Condensation

Table 2-33. (continued) System

Method

Atomization to droplets or fog

1

t! I

' 111

\\

I/ 11\ I/ 11 1I 11

Construction

Liquid flux per drain Wh)

No. of drains per m2

Liquid rate (m3/(m2 . h))

-

M

Small to very large > 0.2

30-1600

\\\

1 1 1

Nozzle

1. Solid-cone nozzle

Flat-spray nozzle Slot nozzle Perforated die (sprinkler) Beam nozzle Deflector nozzle Two-fluid nozzle 2. Pipe distributor with nozzles Perforated pipe distributor

$1 6o

20 - 5000 Mechanical A drive

+' Effective side pressure

Roloiion

Atomization to droplets or fog Liquid jet or droplet discharging

-

> 100

a63 Rotary disk

Segner sprinkler, single or several arms

03

3

2.9 Nonadiabatic Rectification

227

Operating range

Energy consumption

Free vapor area

Functional range

Column diameter (m)

Performance

Pros

Cons

Limited N - CH - C H3C Na,AsO, + H,S + Na3As03S+ H 2 0 A Na3As0,S + 1/2 0, Na,AsO, + S Re -+

-

3.2 Requirements of the Wash Liquid or Solvent, Solvent Consumption

245

Table 3-2. Requirements on solvent and wash solution. Selection aspects. 0 0

0

0

0 0 0 0 0 0 0

0

Sufficiently good solubility of the key (gas to be absorbed) component (favorable absorption equilibrium properties). High selectivity to the key component (solvent acting physically (physisorption) maximum selectivity is 5 : 1, i. e., at least 1/5 of the absorbed molecules are of other components of the gas mixture than the key component. In chemically acting solvents selectivity is considerably higher). Simple to regenerate (no azeotrope formation between solvent and absorbed component, no formation of chemical compounds which are not or only costly to regenerate, high boiling point difference between solvent and absorbed component, favorable desorption equilibrium properties). Low vapor pressure at absorption temperature to avoid solvent loss by evaporation and, therefore, impurities of the cleaned gas flow by solvent vapor. Moderate boiling point to separate the dissolved component by partial solvent evaporation. Low melting point to tolerate a high temperature gradient between absorber top and bottom. Large specific heat to buffer absorption heat due to solvent heating. Low viscosity. Chemical and thermal stability to avoid corrosion and solvent decomposition. Good availability, low price. If possible the solvent should not be toxic or should not have any environmental impact, the solvent flash point should be high, and it should not have a tendency to foam by itself or with elutriated gas components. Low solvent residue should not have an impact on the absorption product value.

where Y,, Y, concentration of the key component i in the gas phase at the entry and exit of the absorber (kmol i/kmol inert carrier) X , , X , concentration of the key component in the solvent (liquid) at the entry and exit of the absorber (kmol i/kmol liquid phase solvent)

(The use of the molar loads instead of mole fraction offers an advantage in calculations. In particular the balance line Y(X) at GT = const. and L , = const. are straight lines in the Y(X)-loading diagram, which will be shown later.) The molar flow rates GT and L , valid in Eq. (3-1) are

(3-2) and L,=--

LCl

1

+xa- L,

*

(1 - x u )

(3-3)

where G, and L , are the entry flow rates of the gas mixture and solvent, and xu and y, are the absorbed component and absorbent entry mole fractions of the liquid and gas phase, respectively. If evaporation of the solvent and solubility of the inert carrier has to be considered, the total flow rates L and G, and the mole fractions x, y are used. At least three bal-

Y h

i

/

4 I

Fig. 3-4. Material and enthalpy balances of cocurrent (a) and countercurrent (b) absorbers.

ance equations are obtained describing the mass balance over the absorber. It is sometimes practical, to recycle some of the loaded solvent, with intermediate cooling through a section of the absorber, or to recycle through the entire absorber (Fig. 3-5). Therefore, the requirement for fresh solvent is (3-4)

Xa.1

=

Xa+r-Xw r+ 1

(3-6)

An increase in the recycled solvent flow rate L,, and hence the recycle ratio r, implies a saving in wash solution, but also a decrease in the mean driving force for the transfer of absorbate from the gas into the liquid phase (see Fig. 3-7). The result is a necessary increase in the interphase surface for mass transfer.

and

r=7

LTU LT

(3-5)

where r is the recycle ratio between the flow rate L,, of the recycled solvent and the fresh or regenerated wash liquid L,. A mass balance over the mixing stage (Fig. 3-5) for the key component gives an absorbed component loading X u , , for the wash solution fed to the absorber

3.3 Enthalpy and Heat Balances An enthalpy or heat balance for an absorber without heat losses as Shown in Fig. 3-4 gives

.

Ga ' &,a + =

*

Zi,a f

I% ' + (Ya-Yw)

Gu * hg,@+ L , . hC,@+ Q

*

1

f i ~ b=

(3-7)

3.3 Enthalpy and Heat Balances

iT x, I

? G a s ph.ase

4

Liquid phase

Fig. AS C P

3-5. Absorber with solution recycling.

Absorber Cooler Pump

MS Mixing stage

where

hgLh, enthalpy of gas and liquid phases Ah,, Q

absorption enthalpy heat flow removed from the absorber by cooling (Q = 0 under adiabatic absorber operation)

During the absorption of gases in solvents the heat of absorption is released and absorption is therefore an exothermic process. The heat of absorption is mainly taken up by the solvent, as heat transfer within the gas flow is poor and negligible. Therefore, during an adiabatic absorption process the temperature of the solvent increases

247

due to the heat of absorption from an entry temperature V/,a to a n exit temperature V,,,. V , , may be estimated by Eq. (3-7) with the assumption, that all of the heat of absorption is taken up exclusively by the solvent. Since an increase in the temperature from 8,, to 8,, occurs, this causes a decrease in the solvent absorption capacity of the soluted substance according to Henry’s law. The absorption efficiency reduces due to an unfavorable equilibrium position at the higher temperature, (see Chapter 1.4.3.3). Consequently, isothermic absorption is aimed for in practice. The heat flux to be removed under isothermal absorption at (V1,@= LP/,) follows from Eq. (3-7). Continuous removal of the heat of absorption is very difficult. The absorber is cooled stagewise if the absorption heat is considerable. If a volatile solvent is used, some of the absorption heat is used up by vaporization of solvent. For this case, the heat flow of vaporization is added in Eq. (3-7) on the right side. (To calculate the exact temperature and concentration profile over the active absorption column height, the appropriately adapted equation system in Chapter 1.9.3 is used.) With isobaric absorption, the absorption enthaQy AEAbis the specific heat of absorption for a kmol absorbed substance. This depends on the temperature, the absorbate-solvent system and the absorbate concentration in the solution. If the absorbate is soluble as a gas, the absorption enthalpy is the solution enthalpy. This may be determined, for example, from the temperature dependency of Henry’s constant Hi

(3-8) If the absorbate condenses under the absorption conditions, the condensation en-

248

3 Absorption

thalpy is added to the mixing enthalpy. The absorption enthalpy then becomes

where y i is the activity coefficient and h/,, is the vaporization enthalpy of the absorbed component. With chemisorption the heat effect is caused by a phase change enthalpy and a reaction enthalpy. The reaction enthalpy hRis calculated by means of the formation enthalpy fiij for each reactant j which participates in the reaction

ing diagram are governed by the solvent ratio v for each absorption stage. For example, an absorbate balance, for stage AB1 (Fig. 3-6a) gives

Cocurrent absorption is usually carried out in spray or jet scrubbers and film absorbers. Cocurrent absorption is mainly used for the absorption of chemically acting wash liquids and only small residence times are needed to obtain the required absorption yield also at a large throughput.

(3-10) where vj is the stoichiometric ratio of the reactant j . A graphical method to determine the absorption enthalpy for physical systems by the aid of the enthalpy-concentration diagram is described in [3.1]. Absorption enthalpies for practical use are given in [3.16].

3.4 Cocurrent Phase Flow Absorption In absorption processes with cocurrent flow, the feed phase flows parallel with the solvent phase through a single absorber or through a series of absorbers. Figure 3-6 shows a schematic for a cocurrent two stage absorption unit. The loading diagram corresponds to the case of the leaving phases just reach equilibrium. (If phase equilibrium is not reached, which is usually the case, a curve must be used which takes into account the true exit loading of each stage X ,, e f f , , e f f , etc., instead of the equilibrium curve in Fig. 3-6.) The slopes of the operating lines in the load-

3.5 Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns During absorption with countercurrent flow, the feed gas phase flows upward into the absorption column. The solvent phase, which is introduced at the top and withdrawn at the bottom, flows against the gas phase. Internals in the column provide stepwise (trays, spray zones, rotating discs) or continuous (random packing, regular packing, etc.) phase contact.

3.5.1 Determination of the Column Cross-Sectional Area The column cross section AQ and column diameter d result from a flow equation with the gas phase as the reference phase (3-12)

3.5 Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns

249

b)

a)

Y2-

y,

L 4,

2

Fig. 3-6. Cocurrent two stage absorption unit. a) Absorption unit with feed of fresh or regenerated wash solution to each stage b) Absorption unit with solution reflux (recycle) c) Operating diagram to (a) d) Operating diagram to (b) AB 1, AB 2 Absorber 1 + 2 BL 1, BL 2 Balance line for the 1'' and 2nd absorption stage EC Equilibrium curve

x,

x

-

250

3 Absorption

V,,,,, is the maximum possible effective volumetric flow of the gas phase through the absorber. It is recommended to calculate the volumetric gas flow with respect to the absorber entry and exit cross-sectional area. In that way, losses of absorbate from the gas phase, solvent evaporation, pressure drop, and increase in the temperature under adiabatic absorption are considered. The maximum allowable velocity of the gas phase, referred to the free absorber ,,, on the floodcross section w ~ , ~depends ing point or upper loading limit for the selected internals, for example, as calculated by the methods presented in Chapter 2.

units (“HTU-NTU concept”) according to Chapter 1.9. Basic equations are listed in Table 3-3. The required number of theoretical stages Nt for a countercurrent flow absorber can be graphically obtained by drawing the stages on to the operating diagram between the balance or operating line and the equilibrium curve (Fig. 3-7). From an absorbate balance over the top section of the absorption column, according Fig. 3-4, the equation of the balance line is

3.5.2 Determination of the Number of Stages and Column Height for Mass and Heat Transfer

The balance line is linear if the solvent ratio v = LT/GT in the concentration range of interest Y, > Y > Y, is constant. Solvent vaporization and carrier gas solubility are disregarded. The course of the equilibrium curve is fixed by the relationship given in Chapter 1.4.3.3

The column height Z for mass and heat transfer is determined using the concept of theoretical stages or the concept of transfer

(3-13)

Table 3-3. Basic equation to determine the number of theoretical separation stages Nf and the number of transfer units NTU,, of countercurrent absorbers [3.9]. Stage concept (Balance around a theoretical stage)

HTU, NTU-concept (Balance around a differential height element)

Concentration change

AY; = Y, - Y;*

dY; = ( Y ;- Y ; * ) .dNTU,,

Mass balance

6,. AY; = L,. AX;

Enthalpy balance *

L,. cp,l * A19 = G,. A Y ; . AfiAD,;

6,. dY; = L,. dx; L,. cp,, . d19 = G,. d Y i . AhAb,;

Phase equilibrium

*

Absorption heat is only transfered to the liquid phase, heating of the gas phase may be neglected. i Absorbate component, key component cp,, Specific heat of solution A , , B, Constants

3.5 Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns

251

'S

xu X--b

Fig. 3-7. Determination of the number of theoretical stages in an operating diagram of a countercurrent absorber including equilibrium curve and balance line, depending on the solvent ratio and recirculation ratio. BL Balance line for the case of a single solvent pass through the absorber ( r = 0; v = tanx) BLM Balance line for the case of a minimum solvent ratio and a single solvent pass through the absorber ( r = 0; v = vmin= tammin) -. BLR 1 Balance line for the case of solvent recirculation ( r = r ) BLR 2 Balance line for the case of maximum solvent recirculation ( r = rmax)EC Equilibrium curve Y Gas load X Liquid load

Y -H i X ____-.___ 1 + Y p 1+x

(3-14)

(From Fig. 3-7 it is seen that recirculation of loaded solvent decreases the amount of solvent required, but due to the lower driving forces for the transfer of absorbate leads to an increased number of separation stages in the absorption column.) The solvent ratio v is an important operating variable for absorption, similar to the reflux ratio for rectification. It controls the slope of the balance line for an absorption problem and has to be larger than a minimum solvent ratio vmin. vmin is obtained by graphical means from the slope of the balance line through the points A and S (Fig. 3-7) or calculated by

are linked by where Y, and X,,,,, Eq. (3-14). With the minimum solvent ratio vmin the required degree of absorption could only be carried out with a n infinite number of separation stages. Chosen solvent ratios for practical absorber operation are usually in the range v = (1.3 . . . 1.6) vmin. The operating costs of absorption are increased with increasing solvent ratio and therefore a higher consumption of solvent. The investment costs as a consequence of a decreasing number of theoretical separation stages of the absorber with an increasing solvent ratio are decreased. Therefore an economical, favor-

252

3 Absorption

able solvent ratio voptis gained from a diagram where operating, investment and total absorber costs are plotted against v. vOptis the solvent ratio which gives a minimum for the total costs. In the concentration range Y, > Y > Y, with a constant solvent ratio v and a constant slope rn for the equilibrium curve, the absorption factor A is constant (3-16) Then the number of theoretical stages can be calculated with

In A

(3-17)

Absorption is especially economical with absorption factors A between 1.25 and 2.0. Determination of the number of theoretical stages for desorption using countercurrent solvent flow stripping, by means of a stripping gas is analogous. In this case, the fact that X, is the entry concentration and X , the exit concentration of the solvent to the stripper must be considered. According to the operating conditions, the course of the desorption equilibrium curve is different from that for the absorption equilibrium curve. The balance line is now below the equilibrium curve and so the reciprocal value of the absorption coefficient is required. The relation for the stripper is similar to Eq. 3-17

X u - Xa -

--x, Ya rn

?;( );(

A

-1

(3-19) is the ratio of the actual amount of scrubbed absorbate to the maximum possible amount when phase equilibrium between the scrubbed gas and feed solution has been reached. The scrubbing degree EA represents the yield of the absorption achieved. EA corresponds to the absorption coefficient with A < 1 and a large number of separation stages Nt. With A > 1 and a large number of separation stages N,, the scrubbing degree is approximately 1. This means that the amount of absorbate absorbed is the maximum possible. The scrubbing number

Ez =

1 Ni+ 1

where m is the slope of the desorption equilibrium curve, Nt is the number of theoretical separation stages of the stripper and X,, X,, Y,, Y, are the loadings according to Fig. 3-4. Fig. 3-8 gives an estimate of the number of theoretical stages required for absorption and stripping as a function of the absorption factor and the residual gas load. Since data in Fig. 3-8 are calculated by means of Eqs. (3-17) and (3-18), which are based on linear equilibrium curve and balance line, an appropriate concentration scale for the solvent and gas has to be used. Apart from the absorption factor A , the scrubbing degree EA and scrubbing nurnber Ez are also important. The scrubbing degree

(3-18)

Y , - rn . X,

Y, - rn X,

(3-20)

is a measure of the investment expenditure for the absorption. The smaller the difference Y, - rn. X, at the top of the ab-

3.5 Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns

253

1.o 0.8

0.6 0.L

0.3 0.2

t

0.1 0.08 0.06

-75 0.01 'C c

0.006 0.OOL

0.003

0.002 0.001 0.0001

0.000~ O.OOO!

Fig. 3-8. Number of theoretical stages of absorbers and strippers for the case of linear equilibrium curve and balance line, and constant absorption coefficient. A Absorption parameter 1/A Stripping paramter Nl Number of theoretical separation stages

sorber, the closer is the desired approach to the equilibrium between the remaining gas and feed solution, the larger must be the number of separation stages of the absorber. Basic equations for mass and enthalpy balances, phase equilibrium relations, and the formulation of the concentration differ-

ences are listed in Table 3-3. These equations form an algebraic equation system which is the basis for stage-to-stage calculation methods for a computer [3.22-3.241. These equations are extended, if necessary, by the inclusion of stoichiometric conditions if mass or mole fractions are used for the concentration scales.

254

3 Absorption

The number of actual stages Np or trays in an absorption column is

Egm =

(3-22)

the tray efficiency is found experimentally under conditions as close as possible to the operating conditions. (To calculate E,, see Chapter 2.5.6.1). The height of the absorption column 2 for mass and heat transfer is given by

(3-21) where E,, is the mean tray efficiency for the gas phase in the concentration range of interest. (Direct graphical determination of Np may be carried out using an operating diagram as shown in Fig. 3-7. The separation stages can be drawn between the operating line and an auxiliary line, which is constructed by dividing the distance Y - Y* into the ratio 1 : Egm,y for each stage. is the efficiency at Y on the absorption concentration profile.) According to Chapter 2.5.6 and Fig. 3-9,

Z = Nt * HETS

(3-23)

where HETS is the active column height with a separation effect equivalent to one theoretical separation stage. HETS is also found by experiment under conditions as close as possible to the operating conditions (see Chapter 2.5.6.2).

b)

a)

xn-1

y , - Yn-1 Y, - Y;-1

cu

*I

i I

I

yn

I I Xn-f

Xn

X-

Fig. 3-9. Determination of the tray efficiency Ex, in an absorption column. a) Schematic b) Operating diagram BL Balance line EC Equilibrium curve X,-], X,, Absorbate load of solution found experimentally under conditions as close as possible to operating conditions Y,- I , Y, Related absorbate load in the gas phase Y:-, Equilibrium load at X,, Y Absorbate load of the gas mixture X Absorbate load of the solution

3.5 Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns

If the HTU-NTU concept is to be applied to determine the column height Z (height of filling material, packing height) for mass and heat transfer then according the discussion in Chapters 1.7 and 1.9,

255 (3-26)

and (3-27)

dY

z=kg,Y GaeT .AQ. Ys,- Y - Y " *

= HTU,,

9

NTUog

(3-24)

or

where j3g,y, PI,, are the mass transfer coefficients for the gas and liquid phases and m is the slope of the equilibrium curve. In the range of validity of Henry's law (see Chapter 1.4.3.3) and under small loadings, (3-28)

= HTU,,

*

NTU,,

(3-25)

where

.

.

carrier gas flow rate, solvent flow rate (kmol/h) volume specific effective mass ae and heat transfer surface (corresponds nearly to the true wetted packing material surface) column cross section AQ kg,Y* k1,X overall mass transfer coefficient related to the gas and liquid phases absorbate loading of the carrier x,Y flows. (Under low key component concentrations, which is common in absorption practice, the loadings are approximately the mole fractions, y = X x = X . If this simplification can not be made, molar fraction are expressed as concentration scales in Eqs. (3-24) and (3-25).) GT, LT

According to Chapter 1.7.3.1 the mass transfer coefficients are given by

where Hi is Henry's constant and p is the absorption operating pressure. Pg,y and PI,, are related to the loading, and bgand PI to the molar fractions, the conversions are

where eg,el are the mean densities and Mg, M, are the mean molar masses of the gas and liquid phases. NTU,, and NTU,, are found by numerical or graphical evaluation of the integral expressions in Eqs. (3-24) and (3-25) (see Chapter 1.6.3). For an approximately linear equilibrium curve and balance line, the approximate result according to Eq. (1-218) applies. The heights of the transfer units HTU,,, HTU,, in Eqs. (3-24) and (3-25) are strongly governed by the total mass transfer coefficients kg,y, k , , and the specific transfer area a,. Therefore, the product kg,y.a, and hence HTU,, or kl,x. a, and HTUoI,should be found by experiment under conditions as close as possible to the operating conditions for scale up purposes (Fig. 3-10).

256

3 Absorption

Fig. 3-10. Height of a transfer unit HTCJogfor different Montz packings with regular geometry as a function of different gas and liquid loads. Representation according to Montz GmbH. Absorptions system: air, ammonia/water f Specific liquid load

a) Gas load effect 0 ,* i = 10.55 m3/(m2+h) + i = 15 m3/(m2. h) 0, A i = 10 m3/(m2. h)

Z p (m) (m) @bar) 0.29 1.36 998

Symbol Montz-Pak d O

*,

A

B1-100

+ c1-200 B1-300

0.29 1.43 992 0.22 1.0 991

b) Liquid load effect 0 ,* F = 1 r i a A F = 1.6m

257

3.5 Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns

Calculation of the overall mass transfer coefficients is done using Eqs. (3-26), (3-27), and (3-29) after computation of the mass transfer coefficients Pg and P,. For example, to calculate the mass transfer coefficient PI of the liquid, empirical correlations are applied in the form

-

Sh, = C, Re;" . Sc; . Gap

(3-30)

where the dimensionless numbers are PI . L, Sh, = ___

Dl

Sherwood number of the liquid phase

L, characteristic length

D,diffusion coefficient in the liquid phase Re, =

l*L, ~

Dl

Reynolds number of the liquid phase

I sprinkle density, volumetric solvent flow rate of the column cross section v, kinematic viscosity of the solution VI

Sc, = - Schmidt number of the liquid Dl

phase

Gal = * " Galilei number v:

The calculation for the gas phase mass transfer coefficient, Pg using empirical correlations are of the form =

C,

. Re,' - Sci

Dg

Schmidt number of the gas phase

Dg diffusion coefficient in the gas phase Suitable correlations to calculate the mass transfer coefficient for absorption and desorption are listed in Table 3-4. Figure 3-11 shows the product of the volumetric mass transfer coefficient Pg and effective volume specific surface for mass transfer, a, as a function of gas and liquid loads for different types of random packings, found by empirical means. If a chemical reaction takes place between the absorbate A and absorbent B (chemisorption), the equations listed in Table 3-4 to calculate the mass transfer coefficient may be applied, especially when the resistance to mass transfer is mainly in the gas phase. However, if the mass transfer is controlled by the mass transfer resistance in the liquid phase, the mass transfer coefficient of the liquid phase is increased in the case of fast chemical reactions. This increase is expressed by the enhancement factor E which is defined as the ratio of the liquid phase mass transfer coefficients, P / R with and P, without chemical reaction

(3-32)

g acceleration due to gravity

Sh,

V

Sc, = -K

(3-31)

where the dimensionless numbers are

w -L , Reg = - Reynolds number of the vg gas phase

E depends on the order of the reaction, the reaction rate constant k and the diffusion coefficient D of the reactants. For a first order irreversible reaction, given, e. g., by [3.34], (3-33) In absorption practice a second order irreP versible reaction of the form A + v,B frequently appears. E is then found from the Hatta number Ha (Fig. 3-12) where -+

w superficial gas velocity vg kinematic viscosity of the gas phase

4. Correlations to calculate the mass transfer coefficient [3.68]. 4a. Liquid phase mass transfer coefficient

Packing type

2 . Ref.59. S C ~. .Gay.“ ~ 5 . Rep” . Sc?’

. Gaf.17

PI.

Characteristic length L, in

L,=4

Berl saddle

L, =

L, = dp

Raschig rings

Sh,

Re,

6

Lc=4

Gal L, =

4

Lc=d,

L, = l/ab*’ Raschig rings . Ref’3 . Sc-’.’ . (a . 4)0.4 Pall rings Berl saddle Cylinder

:I

__ 9)’12

.

( .i. . (T

d~

@I

Volume Validity range with respect to specific packing dimension surface of the packing [mm] Re, a

a

ab*)

10 5 dp 5 50 10 5 dp 5 50

6 5 dp

72

3 5 Re, 5 3 . lo 3 5 Re, 5 3 . lo

0.4 5 Re, 5 lo3

Ceramic packing

Raschig rings Saddles Spheres

a

nal diameter of packing (mm)

1

ecific wetted packing surface

L, = - Valid for all dimensionless numbers E

~

g

We,=

L, . w2. @

Weber n

(T

Relative void fraction

Fr, =

i . L,

(T,

Froude number, liquid

Critical surface tensio complete wetting [cos 0 = 1 (0Contact

Gas phase mass transfer coefficient Packing type

. ’

.

for for

2

. S CE” ~ . (a .$,)-2

CL,2 15 mm

4 < 15 mm

__ 3 1 ’ 3

w E

Raschig rings Pall rings

p,. Characteristic length Lc in

L = 4 . -&

E Lc = 4 . a

Sh,

Re,

1 Raschig =C rings a Berl saddle Spheres Miscellaneous packings

a

1

Volume Validity range with respect to specific packing dimension surface of the packing [mm] Re, a Raschig rings 10 5 Re, 5 lo4 10 5 dp, 5 50 Pall rings a6 *)

L, = -

4 = 50 10 s dp s 50

1 5 Re, 5 lo3

R

[

[

a

[

. dp > 1000 . V,

7 Raschig rings (ceramic) 30 Saddles (ceramic) 73 Spheres (ceramic)

. ent

. Sc0.33 2

,

. R e y 2 . Sc0.33 rcurrent 4

. w,

__

-

a va

, Sh,=- p g

’

[

Tower with packed tubes Pall rings Tower with packed tubes Pall rings dh

Dg

draulic diameter of packing

260

3 Absorption

a)

[s-’I 1

2

1

-

3 6 8 1012 ;.lo3 ~ r n ~ / ( r n ~ . s ) ~

2

1

3 L 6 /.lo3 [rn3/(rn2.s)l

8 1 0

2

LO

d)

t

2o

pg .a, .lo3 [s-’I10 8

6 I

I

I

I

I

I

~ I ~ I

1

2

L

6

8 10

15 20

Fig. 3-11. Gas phase volumetric mass transfer coefficient p g .a, as a function of the liquid rate. [3.47]. Representation according to BILLETand MACKOWIAK a, b) System: Ammonia/air-water, p = 1 bar, T = 288 K, d = 0.3 m a) Packing height 0.9 m, F = 1 . 2 1 p a (Hiflow ring 25 mm, PP, 45500 l/m3, F =1.621/% (Pall ring 25 mm, PP, 55 180 l/m3) b) Packing height 1.35 m, F = 1.161/Pa, 50 m m Pall ring, PP, 6425 l/m3; 50 mm Hiflow ring, PP, 6450 l/m3 c, d) System: Carbon dioxide/air-water, p = 1 bar, T = 295.9 K, F = 0 . 5 5 m , d = 0.3 m c) Packing height 0.85 m, 25 mm Hiflow ring, plastic, 46100 l/m3; 25 mm Pall rings, plastic, 55180 l/m3 d) Packing height 1.35 m, 50 mm Hiflow rings, PP, 6400 l/m3; 50 mm Pall rings, PP, 6765

i Ha

urn3

Specific liquid rate

=

reaction rate mass transfer rate (3-34)

and a parameter ERi= 1

+-

CB

v B * ‘AG

(3-35)

where cAGis the concentration of the absorbate A in the phase boundary, and cB the concentration of the reactant B in the liquid phase. The effective specific surface for mass and heat transfer, a, is mainly found experimentally, along with the mass transfer coefficient. In general a, does not correspond either to the possible theoretical geornetric specific surface a of the packing (see Tables 2-26, 2-27) or to the true wetted

3.5 Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns

I

261

E 100

10

1

0.1

1

100

10 Ha

1000

Fig. 3-12. Enhancement factor E as a function of Hatta number Ha, as a ratio of the reaction rate and mass transfer rate of an irreversible 2”dorder reaction (parameter ERi according to Eq. (3-35). Ha Hatta number E Enhancement factor

specific surface a b . The wetted surface ab is normally smaller than the geometric surface a because of stagnant flow volumes and zones as a result of poor wetting, especially in random packing. Again a, is smaller than ab, due to the formation of coherent liquid zones in packing elements or liquid gussets. (The additional defined hydraulic surface is the sum of the nonwetted surface and the surface for mass transfer of the packing.) The active volume specific phase interfacial area for mass and heat transfer, a, depends predominantly on the sprinkle density v//Ae, the properties of the liquid phase and the wettability of the packing surface. A small sprinkle density (e.g., in vacuum rectification operation), large surface tension CJ and high viscosity ql leads to a small a,. The poor wettability of plastic packing material to aqueous liquids or other polar liquids is improved by hydrophilizing the surface of the packing material [3.42]. Only with column operation above the lower loading point (see

Fig. 2-75) the gas load is also important, which increases a,. An estimate of the surface area of the packing, a, for mass transfer by physical absorption according to PURANIKand VOGELPOHL[3.43] for the liquid phase is

- I

(3-36)

including the Reynolds number

i

Re, = ____ vI. a

(3-37)

and the Weber number (3-38) The “critical” surface tension uCfor wetting is for packing material steel 71, pottery 61, PVC 40 and glass 73 N/m. More

262

3 Absorption

calculation methods for a,, are given in [3.44-3.461. For further design and optimization of absorption units with countercurrent flow and solvent regeneration, see [3.4, 3.253.301. The calculations for adiabatic operated absorbers, in which large heat effects have to be considered, are described in [3.31]. Process control of absorption columns can be found in [3.32]. The dynamic behavior of absorption tray columns is discussed in [3.33].

3.6 Types of Absorber In principle all types of gadliquid contact apparatus are suitable for use as absorber. For selection it has to be ensured that 0

0

0

0

The available driving force for the absorption is used to its maximum The minimum input of conveying or mixing energies (energy dissipation) obtains a maximum phase surface area with good surface renewal With high phase turbulence, mass transfer coefficients are large Special absorption problems such as unusual loading, treatment of corrosive substances, possibility of incrustation, strong heat effects etc., are considered

flow scrubber; scrubber with rotating internals such as rotation, cross haze, and disc scrubber) 0 Gas comes into contact with the liquid, which has the form of a film on a fixed or moving base, gas and liquid phase remain continuous (column absorber with random or regular packing, falling film or surface absorbers) Some important absorber types are discussed in Table 3-5 (see pages 264-273) with references made to particular literature. Figure 3-28 compares selected absorbers with respect to the volumetric specific phase surface a as a function of the specific conveying or dispersion power input, which is

lobT

L

I

I

1

1- --1

rn3

Gas and liquid come into contact in three different ways : 0

0

Gas is dispersed into the wash liquid, the liquid phase remains continuous (column absorber with transfer trays, bubble columns, vessel absorber, dispersing agitator) Wash liquid is sprayed into the gas, the gas phase remains continuous (free board scrubber without internals such as venturi srubber, injector srubber, spray srubber, annular-flow srubber, radial-

O2

w[5] -

Fig. 3-28. Specific contact surface of different absorbers as function of specific power input. Representation according to MERRSMANN, HOFER,STICHLMAIR [3.9]. a Volumetric or specific interfacial area W Specific power input

3.7 Regeneration of the Solvent, Desorption

where A is the phase interfacial area between gas and liquid, V, is the absorber volume, W is the induced conveying or dispersion power; C, q and r are factors depending on the absorber design; 1 - E is the relative gas content and E is the relative liquid content [3.34-3.361. Packed columns are mainly employed in absorption processes. They are distinguished by having a low pressure drop (ca. 2-5 mbar/m), allowing a variable gas load and - similarly to tray columns - enable high numbers of separation stages. Spray scrubbers with one or at the most a few separation stages, are employed as chemical scrubbers if small residence time is sufficient. The pressure drop is very low at ca. 0.1 mbar/m. Venturi scrubbers with a liquid atomizer have a high gas pressure drop but provide very intensive phase contact. They are particularly suitable for scrubbers with short residence times in absorption processes and, in combination, for fine dust separation. Bubble columns, dispersion agitators and vessel absorbers, have a relatively large liquid volume, but small gas loading and a high pressure drop. Since the residence time of the liquid is large, slow running absorption processes suit these apparatus [3.9].

3.7 Regeneration of the Solvent, Desorption Absorption is favored at raised pressure and low temperature. Therefore, the reverse process, desorption, favors low pressure and high temperature. With desorption the absorbed component is removed from the absorbent; the solvent is degassed and regenerated before reuse. On the whole, desorption is carried out in four ways, which can either be applied individually or in combination:

263

Simple expulsion of the absorbed gas component of the absorbent by reducing the pressure. This desorption option is advantageous if the absorption was carried out under a higher operating pressure 0 Expulsion of the absorbed gas component under higher temperature, usually linked to rectification and combined with pressure release steps. The boiling point of the solvent limits the operating temperature 0 Expulsion of the absorbed gas component by an inert gas or steam flow (stripping) which is mainly carried out in packed or tray columns. Inert gas flows countercurrently to the loaded solvent. The absorbed gas component travels from the liquid phase into the gas phase, in which its partial pressure is kept low by the continuously fed inert gas 0 Formation of a chemical compound between absorbed component and a regeneration auxiliary substance (chemical regeneration). The absorbed component reacts with the auxiliary substance which is insoluble with the absorbent or solvent, and precipitates. Downstream to the regeneration unit is a thickener, and the solid is separated from the absorbent in the subsequent filter (e. g., the double alkali process to separate sulfur dioxide from flue gas. Sulfur dioxide forms a sulfite with an alkali solution used as an absorbent. When calcium hydroxide is added calcium sulfite is formed, which is insoluble in water and therefore precipitates. This is then separated from the alkali solution). Some regeneration processes for loaded solvent are shown in Fig. 3-29. 0

Another example for the separation of an absorbed component from the washing liquid (regeneration) is given in Fig. 3-30. In the presented Wellmann Lord process, sulfur dioxide is separated from flue gas using

. Absorber types (type, assembly, and operation principle, references). le column [3.48-3.531, vessel absorber

le columns without liquid circulation ') stage

ple bble lumn

Bubble column cascade

b) tered te

Jltistage -

(Sieve t r a y ) (Single hole t r a y ) Bubble column with cascade tray

Columns with gas distributor (porous sintered plate, plate, sieve tray, spigots, nozzles), gas flows cocurrently currently through a continous liquid phase in form of gas jets; homogenous (quasi-laminar) bubble flow, is ch by a large interfacial area and little backmixing with equ at a superficial gas velocity wg < 0.05 m/s. Bubble coal form larger bubble, bubble splits, heterogenous (turbule flow may be observed at wg > 0.05 m/s. wg,,, = 1 m/s; ing range ca. 0.01 -0.2 m3/(m2 . s); ratio height/diamet diameter 0.1 - 10 m; in large dimension and inexpensive t high gas flow rates possible at large liquid residenc movable internals. Fig. 3-13. L liquid phase, G gas phase.

a)

Perforated plate

Gas ____

-200 prn

Sieve tray

-Gas

+

One-hole tray

Liquid-

depending on

0.5-5 mrn

tg/f,

Fig. 3-14. Devices used to generate bubbles'). db Hole diameter Volumetric flow rate of gas and liquid phase

c,

0’lj--j;~

columns with liquid circulation ’) l tion G

0

Forced

0

LQ

othir mp)

slip stream-

Jet-

L Jet tubereactor

L

b)

mixing

d)

C)

Ring Furminozzle gating

1

Ejector nozzle

0

G

Recycle reactor [3.48, 3.543 with natural circulation t central tube (mammoth recycle reactor), with cocu stream of liquid and gas phase (slip stream recycle re internal tube (jet tube recycle reactor) (Fig. 3-15 a-c).

Jet tube reactor [3.55, 3.561 with momentum exch (“ejector nozzle”) above the ring nozzle to inte distribution and to keep the gas in the range of the (Fig. 3-15 d). Jet reactor [3.48, 3.561 with a gas distribution by a t nozzle and liquid circulation preferential in the low section (Fig. 3-15e).

Jetreactor

Recycle reactor ___ )

zle

ber

Fig. 3-15

el

Venturi

3-5d-d-

tube

80 kJ/mol of adsorbed substance and decreases with increasing extent of cover of the adsorbent surface. Accordingly, the exothermic bond energy is required to release the adsorbed substance from the surface of the adsorbent. Desorption is an endothermic process.

282

4 Adsorption

The reverse process to adsorption, desorption, is favored by a pressure reduction and an increase in temperature. With desorption, the loaded component or adsorbed component, is removed from the surface of the adsorbent. After regeneration of the adsorbent and treatment by drying and cooling, the adsorbent is ready for reuse.

4.1.2 Processes and Examples In practice, gas-phase adsorption is mainly carried out in a vessel adsorber with fixedbed packing mounted on a support grid, like a sieve. Since the treated gas phase flows continuously, a fixed-bed adsorption unit consists of at least two vessels. One vessel is “loaded”: from the flowing gas the adsorbent adsorbs adsorbate until the adsorbent becomes saturated, at which point the adsorbate is no longer adsorbed and is detected at the exit of the adsorber (adsorption phase). During the adsorption phase of the first vessel, the second vessel is considerably regenerated (desorption phase, regeneration phase). This is done by a temperature increase (temperature change), decrease of pressure (pressure change) or by

rinsing with an auxiliary desorption substance (displacement desorption). A combination of these variations also exists. The regenerated adsorbent is left to dry and is then returned to the adsorption operating conditions (cooling, pressure build up). Figure 4-1 shows schematically pressure swing adsorption (PSA) applied as the BF process to generate nitrogen from air, including notes and explanatory diagrams. Durink the adsorption phase, oxygen is adsorbed from compressed cooled air on carbon molecular sieve packing in a vessel switched to “load”, the remaining nitrogen leaves the vessel as product gas. From storage, nitrogen is then supplied to users. The time-controlled adsorption phase is achieved when the oxygen reaches a certain level in the product gas. In the subsequent regeneration phase, desorption starts by pressure reduction (pressure compensation with the previous regenerated vessel) and expulsion of oxygen. After the desorption phase, the pressure in the vessel is increased before starting the next adsorption phase. Figure 4-2 shows the participation of solvent recovery by adsorption. The LURGI-SUPERSORBON process shown in Fig. 4-3 uses steam as a desorption fluid for the recovery of water insoluble solvents. During the adsorption phase, solvent-rich

Fig. 4-1. BF-N, process (a) and pressure swing diagram (b) to produce nitrogen from air by pressure b swing adsorption. Representation according to data of Bergbau-Forschung GmbH and INCA mbH, Essen [4.12]. Adsorption cycle: Adsorption of oxygen on a carbon molecular sieve CMSN2 (loading period 60 s) Desorption cycle: Pressure compensation and withdrawal of remainder by means of a vacuum pump (desorption period 60 s)

Adsorption pressure/desorption pressure 1M0.1; 3.5/0.1; 8/1 bar Variations: Plant size 1-2000 m3,/h, variation 8/1 bar Output pressure 5-7 bar N, Purity 95 - 99.9 “70 H,O Dew point < -50°C CO, Concentration < 5 PPm Energy consumption of nitrogen production 0.2-0.7 KW/m3

--

I

Nitrogen product gas I

v c

_ _ _ _Control _ _ _ _ _ _ _ai _ I

Wastewater Pressure

Solubility in water Recovery process

Adsorption on active carbon

Adsorption on active carbon

I

I

Partially soluble

Insoluble

Treatment (water separation)

,

Separation (Phase separation]

I Enrichment condensation

I Enrichment condensation and distillation

Complet Adsor active

I Chemical drying

I

I

Decomposition

Examples

I

J r I Distillation I

Acetic ether, MEK. MIBK, MEK/toluene, THF/toluene. alcohoVtoluene

Toluene, xylene. benzene. hexane. chlorohydrocarbon

Ethanol, is acetone. T

Fig. 4-2. Solvent recovery by adsorption *. Representation according to KRILLand WIRTH[4.13].

*

Sometimes water washing is advantageous (e.g. at DMF)

4.1 Principles of Adsorption and Desorption, Processes and Examples

air flows through the active carbon fixed bed, switched to “load”, in which solvent vapor is mainly adsorbed. Clean gas leaves the vessel. If a breakthrough of solvent occurs, after a certain time and at a certain solvent exit concentration, the controller is switched to a regenerated adsorber. In the regeneration phase, the loaded active carbon desorbs by using steam in the opposite

285

direction to the loading direction. The solvent is expelled as vapor and condensed. The water and solvent are separated in a gravity separator. The active carbon, treated with ,steam has to be dried and cooled with the carrier gas containing the solvent at the start of the loading phase. If the adsorption process is operated continuously with respect to the adsorbent, Adsorber

Adsorber

Active carbon

b Solvent-rich waste air

I

I

t

I

T

Condenser

Water

Fig. 4-3. Simplified flow diagram of the Lurgi-SUPERSORBON process to separate solvent vapor from waste air. Representation according to data of Lurgi GmbH, FrankfurUMain [4.14].

Process data: Adsorbent:

Cylindrically shaped active carbon, particle diameter 4 mm, specific surface 1240- 1250 m3/g 1000-400000 m3/h Gas throughput: up to 99% Adsorption yield: Steam (2-4 bar, overpressure): 2-4 kg/kg +- 1-1.5 kg/kg for recPower consumption: tification (in case of water soluble solvent) Electric power consumption : 0.15-0.45 kWh/kg 30-60 kg/kg (heating by 30°C) Cooling water: 0.5 - 1 kg/t Active carbon losses:

286

4 Adsorption

the absorbent must pass through the adsorption, desorption, drying and cooling zones in a continuous cycle. For example, a continuous adsorption process to recover solvent, the Lurgi KONTISORBONprocess, is

shown in Fig. 4-4. The solvent-containing exhaust air is precleaned, if necessary, by mechanical means and enters through a control system at the bottom of the adsorption zone the unit. Together with the active

Secondary adsorber

-Two-stage

Ey!?-

Cooler -

Solvent Pneumatic conveyer

Air

-

4.1 Principles of Adsorption and Desorption, Processes and Examples

carbon, stored on perforated metal sheets, it forms a multistage fluidized bed where the adsorption of the solvent takes place. Cleaned used air leaves the unit at the top. The loaded active carbon falls from the lower gas distributor into a sluice tube which separates the air rich adsorption zone from the inert desorber. After the secondary adsorber, the regeneration zone, the active carbon passes through three tube bundle heat exchangers mounted on top of each other. The downflowing active carbon is heated in the two stage heaters. Steam or thermal oil is used as heating medium. Nitrogen flows countercurrent to the carbon and strips the desorbed solvent, which is then released when the carbon is heated. Solvent is condensed and removed as liquid in an external condenser. Nitrogen saturated with solvent passes from the condenser into the secondary adsorber, where the active carbon moves down and adsorbs the solvent. Nitrogen is recycled to the sec-

ond heating stage with a blower. The regenerated active carbon passes a direct cooling zone, the third heat exchanger, and reaches the top gas distributor of the adsorption zone via pneumatic conveying. Liquid phase adsorption is used mainly to bind turbid substances, to purify and decolor solutions, and to separate organic pollutants. Grained active carbon is employed as an adsorbent, mixed in a pulverized form with the liquid or as particles in a percolation process. A schematic for wastewater treatment by adsorption of waste substances, for example, is shown in Fig. 4-5. The adsorption process is carried out discontinuously with grained active carbon or continuously with grained or pulverized active carbon. Figure 4-6 shows a discontinuously operated adsorption unit including three adsorber vessels connected in series, and filled with active carbon beds for the pretreatment of wastewater. Regeneration

Lurgi KONTISORBON process. Representation according to data of Lurgi, FrankfurUMain I4.15, 4.161.

4 Fig. 4-4.

Cooling water

1 x 1 Heating medium

a

Nitrogen Nitrogen - solvent mixture Active carbon

nAir r T d Solvent Process data:

287

Superficial gas velocity of fluidized bed: 0.8-1.2 m/s Pressure drop (total): 10-18 mbar (ca. 25-5070 of pressure drop of packed bed units) Height of each fluidized bed: 0.025-0.05 m Adsorbent: Active carbon, particle diameter 0.7 mm Active carbon losses: ca. 2%/a (referred to the circulating carbon mass) Inert gas feed: ca. 0.05% of clean exit air Regeneration energy consumption: 30-4070 of a packed bed heat requirement

288

4 Adsorption

0)

W a s t e w a t e r composition

I

I

f

substances

Settling substances

Floating substances

I I

I

z-

Suspended substances

substance

I

substance

Nonbiode-

substances

__ I 1 /Sedimentation

i

Filtro tion

1

1

i

substances

b

Wastewater gathering points 1-5

Adsorption

c

Adsorption

-

Biology

Adsorption -

+Active c a r b o n (pulverized) C

Fig. 4-5. Systematization of wastewater composition (a) and adsorptive wastewater treatment (b). Representation according to UHDE [4.17]. a) Partial flow treatment b) Adsorption of toxic components prior to biological treatment c) Continous feed of active carbon into the activated-sludge tank d) Further treatment of persistent (e. g., biocide) wastewater components

4.1 Principles of Adsorption and Desorption, Processes and Examples

289

Fig. 4-6. Discontinuous adsorption unit for pretreatment of wastewater. Representation according to UHDE [4.17, 4.191. 1 Adsorber vessel with active carbon packing 2 Condenser 3 Gravity separator

or reactivation of active carbon is carried out by steam or outside in an reactivation oven. Figure 4-7 shows a continuously operated unit for the downstream cleaning of pretreated wastewater. Biologically treated wastewater enters the countercurrent adsorber from the bottom via a distribution system, and leaves by means of a chute system. The upflow velocity is ca. 6.5 m/h. Active carbon continuously slides through the adsorber and is discharged by an air lift pump. Transport water and carbon are separated by a sieve. The carbon is then dosed by a screw feeder into a two stage rectangular fluidized bed oven employed as a reactivation oven. With a flue gas temperature range from 20O-105O0C, active carbon is reactivated and withdrawn glowing. After quenching in a water bath, the active carbon is transported by water back to the adsorber. Flue gas loaded with expelled organic substances from the reactivation oven

are treated in an secondary-burning treatment unit. Table 4-3 gives an overview of technical application of adsorption used for gas drying, separation of gas mixtures, gas generation, gas enrichment, gas cleaning, and wastewater treatment by means of selected examples. Table 4-4 gives the effective pore size of different molecular sieves and adsorbate molecule diameters. The following advantages characterize adsorption as a thermal separation process : 0

0

0

It may be carried out under ambient temperature and hence under favorable energetic conditions. The process is positively influenced by special treatment of the adsorbents It is possible to treat mixtures with low adsorbate concentrations if a suitable adsorbent is available Simultaneous separation of several mixture components is possible

290

4 Adsorption Exit water (clean wastewater)

I

-

Active carbon reflux

-

I

Flue gas t o chimney

Pretreated wastewater Gas or oil

Fig. 4-7. Adsorption unit for continuous treatment of wastewater. Representation according to UHDE[4.17, 4.181. 1 Countercurrent adsorber 2 Air-lift pump 3 Drain screen 4 Active carbon feed 5 Desorption and reactivation in a two stage fluidized-bed furnace 6 Quench vessel 7 Bin for active carbon make-up 8 Postcombustion unit

Table 4-1. Actual data of a plant to separate dioxane*. Process parameter Wastewater input Loading rate Contact time (3 adsorber) Dioxane feed concentration Dioxane exit concentration Degree of reduction Adsorption capacity (referred to dioxane and active carbon) Holdup time Stripping time Steam consumption (referred to active carbon)

*

(m3/h) (m3/(m2 . h)) (h) (mg/l) (mg/ 1) (070)

Representation according to data of UHDE [4.17, 4.191.

Design

Operating state

16 3 2.5 100

25 4.7 I .6 16 1

2

98

94

4.2 Adsorbents, Selection of Adsorbent

291

Table 4-2. Actual data of a plant for subsequent treatment of 3000 m3/d wastewater*.

Loading before adsorption (mg/l)

Loading after adsorption (mg/l)

BOD5

BOD5 COD

COD TOC

20 50-80 20-60

TOC

5

1-27, mean 7 2-30. mean 8

BOD 5 Biochemical oxygen demand within 5 days Chemical oxygen demand Total organic carbon

COD TOC

* Representation according to UHDE [4.17, 4.191.

4.2 Adsorbents, Selection of Adsorbent 4.2.1 Adsorbents Adsorbents are solids characterized by a high specific mass or volume surface area. There are a large number of homogeneous and heterogeneous active centers on the surface where free bonds are provided by the solid for the adsorption of adsorbate molecules. The high specific surface is mainly due to the internal surface of the adsorbent body, which consists of a macro-pore system and a particularly important micropore system with external excess. Pore sizes are commonly : 0

0 0 0

Macropores with a diameter dpr > 50 nm Mesopores with 50 > d,, > 2 nm Micropores with 2 > dpr > 0.4 nm Submicropores with dpr < 0.4 nm

The pore size distribution characterizes the pore system and hence the specific surface and the adsorbate loading capacity of the adsorbent (measurement techniques to de-

tect micro- and macropore systems are found in [4.20, 4.261). Theselectivity of the adsorbent and hence the possibility of gas mixture separation by adsorption, is based on three effects, the equilibrium effect, the steric effect, and the kinetic effect. The equilibrium effect causes the key component to be bonded more strongly to the adsorbent than the others. With the steric effect, micropores of the adsorbent only allow molecules with a diameter smaller than the pore sizes to pass (sieve effect with adsorbents of uniform and very narrow micropore size distribution). In the case of the kinetic effect, key component molecules diffuse faster into the pore system of the adsorbent than less movable and slow molecules [4.11].

4.2.2 Requirements for the Adsorbent, Adsorbent Selection To ensure economic, safe, and nonpolluting operation, the adsorption process has to meet certain requirements. These requirements, which at the same time are aspects of adsorbent selection, are listed in Table 4-5.

292

4 Adsorption

Table 4-3. Adsorption application (selected examples). Process

Adsorbent

Air and gas drying

AA, SG, Zeolith-MS

Gas production, gas mixture separation, gas enrichment H2 N2 0 2 0 3

nho-Separation from hydrocarbon mixtures (see Table 4-4)

Gas purfication Solvent recovery

Production stage Ad De

+

Remarks Process Company PSA, “Heatless Drying” PSA

Zeolite-MS/AT C-MS C-MS Zeolite-MS C-MS Zeolite-MS/SG Zeolite-MS

AC AC SG

+

+ +

+

+

+

+ +

+

+ +

UCC/HYSIV Linde/UCC BF-N2-process Linde/BF-process BF-02-process Linde-Ozon-process UCC-IsoSiv-process

Supersorbon-process (Lurgi) Kontisorbon-process (Lurgi)

AC

+

ADSOX-process

Separation of SO2

AC, MS ACO

+ +

Babcock-BF-process

Separation of NO, and SO2 Separation of H,S, CS2 Separation of H2S

ACO AC, MS, AA Fe(OH),-rich adsorbent (hydrated iron oxide etc.) AC, AA, Biofilter

Solvent enrichment with subsequent oxidation Flue gas treatment

Deodorization

Wastewater ireatment (Separation of turbid matter, organic matter, etc.) ~~

AC

+ + +

BF-Uhde-process Giulini-Saar-Ferngasprocess

+ (if possible)

~

Abbreviations : Ad Adsorption; De Desorption; AC Active carbon; AA Active alumina; ACO Active coke; C Carbon; MS Molecular sieve; SG Silica gel; PSA Pressure swing adsorption

4.3 Adsorption Kinetics

293

Table 4-4. Effective pore diameter of different molecular sieves and corresponding adsorbate with smaller critical molecular diameter [4.1 I]. Effective pore diameter (lo-'' m)

Adsorbate

3-3.8

He, Ne, Ar, CO, NH,, H2, 02,N,, H20, CO,

4.2

Kr, CH,, C2H6, C2H4, C2H2, SO2, CH30H, CpH50H

5 .O

n-C3H, to C,,H3,, C2H5C1,Cyclopropane

8.0 9.0

i-C4Hlnto i-C14H3n, Dioxane, Cyclohexane 1.3,s-Triethylbenzene

Table 4-5. Adsorbent requirements and selection aspects.

0 0 0 0 0 0

0 0

Even at low adsorbate concentration in the gas or liquid phase high additional load of absorbed material (additional load is the adsorbent load with adsorbate when the adsorption process is finished minus the residual load after desorption). Large useful capacity. High selectivity to certain adsorbates. Good desorption behavior, easy to regenerate, low residual load of the key component. High adsorption rate, short adsorption or mass transfer zone, MTZ. High stability to heat and vapor. Good chemical restistance, low ignitability. High abrasion resistance. Low specific packing pressure drop. Low price

4.2.3 Technical Adsorbents, Characteristic Data of Adsorbents Technical adsorbents include active carbon, active coke, silica gel, active argillaceous earth or aluminum oxide gel, bleaching earth and molecular sieves (Table 4-6). In Tables 4-7 and 4-8, some properties of the adsorbents are described.

ity Xst,see Chapter 1.4.4.2) and adsorption kinetics. The adsorption rate is described as a function of the limiting transport phenomena for the adsorbate transfer from the bulk of the carrier phase to the inner of the adsorbent particle. Individual transport steps are (Fig. 4-9): 0

0

4.3 Adsorption Kinetics The design of adsorbers depends on the adsorption equilibrium (static loading capac-

0

0

Free diffusion out of the carrier phase into the boundary layer around the adsorbent particle (exterior mass transfer) Diffusion through the boundary layer (boundary layer diffusion, outer diffusion) Diffusion inside the pore system of the adsorbent Addition at the inner pore surface (actual adsorption)

294

4 Adsorption

Table 4-6. Applied adsorbents. Adsorbent based on carbon [4.4, 4.20, 4.561 Active carbon, active coke, carbon molecular sieve, carbon fiber mat, carbon fiber paper [4.54, 4.551. 0 Carbon content >go%, others are inorganic salt and ash. 0 Base material and manufacturing: wood, brown coal, pit coal, peat, saw dust, coconut shells, petrol coke. Carbonization including following pore structure increased by steam activation or chemical activation using phosphoric acid solution or zinc chloride solution, if necessary oxidation using air or steam. 0 Amorphous solid structure, graphite lattice of microcrystallite, powder coal, granular coal of particle size ca. 0.25-4 mm. 0 Hydrophobic nature, especially suitable to bind nonpolar substances, flue gas cleaning, gas cleaning, solvent recovery, deodorization, respiration filter, catalyst carrier, separation of gas mixtures, deoiling, degreasing, liquid decoloration; organic substance removal from drinking water, feed water, and wastewater; chlorine and ozone removal from water.

Active argillaceous earth, aluminum oxide gel, alumina gel 0 0 0

> 8 5 % A1,0,, others are inorganic salt. Surface active aluminum oxide, activated by calcination, pellets or extrudate, particle size ca. 2-8 mm. Suitable for gas drying, gas enrichment, polar substance adsorption from solutions, catalyst carrier

Silica gel [4.21, 4.221 0

0 0

Granulated, porous amorphous form of silica dioxide, produced with sulfuric acid and sodium silicate hydrate, >99% Si02,others are inorganic oxides, dry pellets (size 3.5 mm) contain ca. 3 % A1203. Narrow pores and wide pores, pellet size ca. 2-8 mm. Suitable for gas drying and catalyst carrier.

Molecular sieve-zeolite (MS) [4.23, 4.241 0

0 0

0

0

Natural or synthetic tecto silicate with - a three dimensional aluminum silicate crystal lattice consisting of S i 0 4 and AIO, tetrahedron - a system of cavities inside the lattice connected by pores of defined and absolute equal pore diameter - free movable cations, exchangeable in a solution, to compensate the negative charge of the acid ion lattice - the general formula x[(M',M",,~) * A102]ySi0, . zHzO (MI, M" monovalent cation and divalent cation, i. e., Na or Ca) for example: Na12(A102)12(Si02)12 . z H 2 0 MS 41 nm Preparation by crystallization of gels generated in aqueous alkaline silicate- o r aluminatesolution, also by adding amine or ammonium compounds. Large adsorption area (800- 1000 m2/g), high electrostatic adsorption force, feed pores of defined diameter classify different molecule sizes (screening effect), pore diameter according to MS-type 30- ca. 100 nm. Delivery forms: powder, pellets, particle size ca. 0.3-5 mm. Suitable for gas drying, gas cleaning and gas mixture separation, as well as catalysis purposes.

295

4.3 Adsorption Kinetics

Table 4-7. Adsorbent characteristics for evaluation. Specific surface area a: outer and inner adsorbent surface area referred to its mass unit (m2/g). Experimentally determined by N2-adsorption isotherms with respect to space requirement of an N2-molecule (BET-surface area). Density, adsorbent porosity, packed bed porosity Solid density (true density, skeleton density) Q ,

m,

Skeleton mass, V, Skeleton volume

Particle density (apparent density)

e mL

m

v

= = I

m,+m,

K+G

dry adsorbent

-- m, v,+G

(4-2)

Air mass in the pore system, Vp Pore volume

Particle density

Q

~ of ,adsorbent ~

ep,x = ep * (1

X

eP of

plus adsorbed component

+ x)

(4-3)

Adsorbent load with adsorbed component (dimensionless)

Adsorbent porosity cp

= -m, =

m,

v, V . ( l - E p ) e p = e, . (1 - Ep) @

=

Packed bed density (bulk density) ing volumeter)

mb

v,

&

m V.(l-Ep)

=-1

ep

-Ep

n (4-5)

@ b (adsorbent

bulk density after tapping using a stamp-

Packing mass (for example adsorbent packed bed mass) Packing volume Packing porosity (packed bed voidage) (continued next page)

296

4 Adsorption

Table 4-7. (continued) 0

Approximate values of density and porosity Adsorbent

@$

@p

( W ) (Wl) ~

Active carbon Active carbon, fine-pored Active coke Silica gel, fine-pored Silica gel, wide-pored Active argillaceous earth Molecular sieve

2.2 2.0 1.9 2.2 2.2 3.0 2.6

@b

(Wl)

EP

-

-

~~

~~~

0.6 0.8 0.9 1.1 1.1 1.2 ca. 1.3

ca. ca. ca. ca. ca. ca. ca.

0.4 0.45 0.6 0.75 0.60 0.75 0.75

0.73 0.60 0.53 0.50 0.50 0.60 0.50

0.33 0.44 0.33 0.32 0.45 0.38 0.42

Pore size distribution of the micropore system determined by the water adsorption isotherm using the Gibbs-Kelvin equation; determined for the macropore system by mercury penetration and mercury or helium displacement, an example is given in Fig. 4-8. Fig. 4-8. Differential pore size distribution of a Linde molecular sieve and molecular sieve carbon [4.27]. W

L

0

Pore radius-

0

Adsorption capacity X (adsorbed component capacity of the adsorbent)

mi

ST

Maximum mass of adsorbed component Adsorbent mass

The static adsorption capacity, “static activity” X,,may be derived from the respective adsorption isotherm (see Chapter 1.4.4.2). A steep course of the isotherm in the log XJlog p i diagram gives a favorable adsorption. Additional adsorbent consumption has to be taken into account during design to consider adsorbent ageing, adsorbent damage, adsorption displacement etc. [4.28, 4.29, 4.341.

Catalytic properties If an adsorbate has to be converted into a chemical compound, i. e., separation of SO2 or

H2S from flue gas, a catalytic activity of the adsorbent is desired. Due to the catalytic activity of active carbon the following reactions are favored: SO2 + H2O + 1/202 + H2SO4 H,S+ 1/20, + H , O + S SO2+2H,S - j 2 H 2 O + 3 S If the adsorbate has to be recovered, no adsorbent catalytic activity is allowed.

Adsorbent properties [4.9, 4.10, 4.13, 4.25, 4.271.

500-1000

0.25-0.30 0.30-0.40

100-400

0.40 0.10

700-850

250-350

0.30-0.45 0.05-0.10

400- 800

600-850

0.35-0.45 0.10

700-800

100

0.05-0.10 0.20-0.30

600

e

600- 1000

0.25 -0.40 0.40-0.50

400-500

on

1000-1500

0.30-0.50 0.50- 1.10

300-500

on

(cm3/g)

(kg/m3)

Pore volume

Bulk density

s sieve 600-900

- Micropores - Macropores

(nm)

(m2/g)

Mean pore diameter

Specific surface

20

Specific heat (kJ/(kg. K))

Thermal conductivity (W/(m. K))

Desorp temper ("C) 100-1

0.84 0.84

100- 1

0.84 21 100

30-35

3-10

0.92 0.92 0.85-1.05

0.95- 1.05

0.20 0.20 0.12

0.13

120-2 120-2 150-3

200- 3

Boundary layer

.........

Pore diffusion

Surface diffusion

........

?[ .... ....

dpr w , ~ ~ ) d) Slugging (wg > wmfl) e) Fast fluidization (wg& w , ~ ~ ) SB Slumbed bed or fixed bed FB Fluidized bed CFB Circulated fluidized bed (pneumatic conveying)

I

i

PC

ICFB)

I1 Pressure drop versus superficial gas velocity MF Minimum fluidization; SCO significant carry over starts SB Slumbed bed FB Fluidized bed PC Turbulent bed, start of circulated fluidized bed (pneumatic conveying) NPD Narrow particle size distribution WPD Wide particle size distribution Ap Pressure drop 111 Heat transfer coefficient versus superficial

gas velocity wmf Minimum fluidization velocity w I Particle terminal velocity wg Superficial gas velocity a Heat transfer coefficient

5.11 Design of Dryers

flowing. Bed heights of 250-1,500 mm allow large residence times. Vibrating fluidized beds are mounted on plate springs which vibrate on a base frame with counterweights. Vibrators generate oscillations in the direction of product movement or conveying. Relatively small bed heights of up to 250 mm, and little backmixing of the fluidized bed (“plug-flow like”), in combination with the vibration, allow a narrow residence time distribution. Vibrating fluidized bed dryers are suitable for treatment of products which are difficult to fluidize or which tend to agglomerate or stick together. If additional heat exchanger equipment is put into the fluidized bed, heat transfer between the gas and heat exchanger and the product and heat exchanger, are superimposed to give the mass and heat transfer between the gas and the product. The transfer rate is significantly increased compared to a bed without a heat exchanger of the same area. The advantage is that the drying gas requirement is smaller, and hence the expenditure for exhaust gas treatment is reduced. The higher thermal efficiency also makes a higher evaporation rate at a lower temperature level favorable. Fluidized bed dryers with additional heat exchangers are operated with bed heights over ca. 400 mm, to treat fine granular products which are easy to fluidize. With dryers employed as spray-fluidized beds, the flowable product to be dried (solution or suspension) is sprayed onto an already dry product which acts as a receiver in the fluidized bed. During the following drying process, individual particles grow due to the sprayed product. Through a stirring effect and the convective mass transfer caused by the rising bubbles in a fluidized bed, intensive particle motion is observed. This is favorable for the mass and heat transfer between the gas and product and for the heat transfer between product and heat exchanger. Due to good solid mixing an almost uniform ternpera-

369

ture inside the whole bed is achieved. The large exchange area of gas and product particles is also favorable as is the liquid-like behavior that simplifies the handling of the product. The disadvantages are particle attrition, erosion of internals, and carry over of solids due to eruption of bubbles at the bed surface. Application of conventional fluidized bed technology with fines is problematical and limited economically, particularly with a specific light product having a high initial moisture content. The transformation of the fluidized bed principle into the centrifugal field offers some advantages [5.109]. Table 5-9 gives some indication of the fluid mechanics, the mass and heat transfer in fluidized beds, and their design. Fig. 5-33 shows a simplified operating range diagram according to REH I5.541-[5.56]. Gasisolid systems are classified into three operating ranges: fixed bed; pneumatic conveying; and an area which includes fluidization and classifying of solid particles. In Fig. 5-34 the operating ranges of a fluidized bed dryer and other dryers are shown. The Reynolds number Reg of the gas phase, calculated with particle diameter dp, is (5-102) and is plotted against a number including the Froude number, Fr

The parameter is the mean porosity of the bed E. A grid with lines of constant Archimedes number A r (5-104)

370

5 Drying

0)

Exhaust gas t o scrubber

bl

t I "

W e t product

"Plug- f I0w '* fluidized bed zone

Preliminary

Drying zone

t

t

Hot air

Hot air

t

Cold air

Dry Product

5.11 Design of Dryers

371

Wet feed Exhaust air t o cyclone

(1)

Side elevation

Adjustable weir

Hot air

I

Dried product

Plan view

(111) Plan view

Plan view

Feed

Feed

+ m t

Product

L7-

Product

Product

Feed

Fig. 5-32. Fluidized-bed dryer. and data of Babcock-BSH AG, Krefeld. Representation according to POERSCH Drying unit 1 Fluidized bed 2 Gas distributor 3 Charging device, wet material 4 Dust separator 5 Blower 6 Gas heater I Weir 8 Cooling section 9 Dry material discharge Fluidized-bed dryer Continuous “plug flow” fluid bed dryer: (I) straight path; (11) reversing path; (111) spiral path. Geldart [5.112].

5 Drying

372

Table 5-9. Indication of fluid mechanics, mass and heat transfer and design of fluidized beds.

Fluidized-bed cross-sectional area A , (5-106) Drying gas mass flow rate of density eE,kg/s m, Optimum fluidization superficial gas velocity, m/s wg Slumbed bed or packed bed height 2, of wet product Z , =mGLI .

t,=0.2

... 1 m

(5-107)

@s ’

mG,/

e, t,

Wet product mass flow rate, kg/h Wet product density, kg/m3 Required drying time, h

Gas phase pressure drop 0 Gas passing upwards through a polydisperse packed bed with minimum fluidization velocity wmf [5.57, 5.581

0

(5-108)

Gas passing through a fluidized bed Weight =

- particle buoyancy

Bed cross-sectional area

Gas passing through the gas distributor

a,, Emf

Zmf

wmf

ylg

-

A , * Zmf* ( 1 - emf). (e, - e,) g = const A, ( 5 -1 09)

ApD= (0.1 . . .0.2) . Ap, = 20 mbar (approximate value) Volume specific surface of the particles, m2/m3 Bed voidage at minimum fluidization (gas fraction, void fraction) Bed height at minimum fluidization velocity, m Minimum fluidization velocity, m/s kg * s Dynamic viscosity of gas, . m2

(5-110)

~

Minimum fluidization velocity wmf (Transition between slumbed bed and fluidized bed, see Fig. 5-31) [5.58]

(from Ap = Apn, Eqs. (5-108) and (5-109)) Kinematic viscosity of gas, m2/s.

vg Optimum fluidization velocity wg Determination by Fig. 5-34 based on operational experience or, for example [5.59] by W E= 7.5 . (5-112) at maximum heat transfer between fluidized bed and immersed transfer surfaces.

5.11 Design of Dryers

373

Table 5-9. (continued) Approximate value: wg = (1.5. , .2) . wmf for grainy, free-flowing particles wg = ( 5 . . .lo) wmf for particles with tendency to agglomerate

dp

(5-113) (5-114)

Mean particle diameter, m

Bed voidage emf at minimum fluidization 4 . m, (5-115) Emf = 1 x ' e, * d 2 . Zmj Mass of powder in a bed, kg m, d Bed diameter Height of incipient fluidized bed (determined experimentally or from expansion Zmf diagrams [5.60]) Fluidized-bed height Z , total height Zeffof fluidized bed and free board (disengaging space) (5-116) (5-117)

Zeff= z+ z , Reg, A r Reynolds and Archimedes number (see Eqs. (5-102) and (5-104)) & Bed voidage Free board height for allowable solid entrainment, m Z, Bubble formation, bubble growth, jet penetration [ 5 . 5 8 , 5.61, 5.111, 5.1121. Particle entrainment from fluidized beds [5.68, 5.69-5.71, 5.111, 5.1121 Mass and heat transfer in a fluidized bed 0 Estimate of mass and heat transfer coefficient in a fluidized bed without internals by empirical correlations (5-118) at Re, c; 100 [5.55] Nu = 0.3 . (5-119) at 0.1 < Reg< 15 L5.551 Sh = 0.374 . 0

(for a more detailed calculation see [5.59, 5.111, 5.1121). Estimate of the heat transfer coefficient a, between fluidized bed and immersed surfaces by empirical correlations

Nu, =

4

= 0.79

.Ar0.Z2.

( - y),.,, 1

-

[5.67]

(5-120)

10 < Ar < 2 . lo4 for For the case of horizontal, quadratic shifted tube bundles of tube diameter dR and of tube separation s (favorable values of a, are at wg = (2.5.. . 3 ) . wmf and s = (4.. .6) . dR),(for a detailed calculation see [5.59, 5.60, 5.63, 5.641). Dimensionless numbers Re,, Nu, Nu, and Ar are based on the particle diameter dp as the characteristic length Heat conductivity of gas, W/(m. K). I,

374

3

--Fr,

c

5 Drying

e,1 e, - e,

Re,

-

Fig. 5-33. State diagram of gaslsolid systems simplified for fluidized beds range of operation by REH [5.54-5.561. Representation according to POERSCH,Fa. Babcock-BSH AG, Krefeld.

5.11.2.7 Air-Flow Dryer, Pneumatic (Flash) Dryer [5.1, 5.21

and (5-105) helps to ease handling. (Nomenclature for Eqs. (5-102)-(5-109) is given in Table 5-9). With the knowledge of the particle size dp these diagrams provide an estimate of the fluidization velocity wg and the gas velocity for the other dryer types are found. Alternatively, with a chosen gas velocity wg the size dp of the particle is determined, which, for example, is either definitely carried over or just transported by pneumatic conveying. Figure 5-35 shows common residence time ranges for different convective dryers plotted against corresponding particle sizes.

In an air-flow dryer [5.7, 5.73, 5.741 powdery, granular, wet products are dried in parallel flow quickly and gently (Fig. 5-36) while being conveyed through an air-flow tube or ring channel [5.75, 5.761. The length of the dryer tube, the drying time and moisture vapor flow are decisive functions of the particle diameter of the product. Since the dryer has little product holdup during the drying, the operation may be adjusted for a rapidly changing moisture content and different feed flows. The advantage is also the low heat requirement and operational demand as well as the space saving vertical arrangement. The terminal velocity of the product particles is

375

5.11 Design of Dryers 10:

10

ps 1

3 . F r1 L

e,-e,

lo-’

lo-:

10‘:

lo-’

lo-:

-

10’

100

lo-’

10-2

Re,

102

lo3

1oL

Fig. 5-34. Ranges of operation of different convective dryers. Representation according to POERSCH, Babcock-BSH AG, Krefeld.

w,= f:.dp.-.-

e, - e g eg

g

c,

(5-121)

where c, is the resistance coefficient of a spherical particle, dependent on the gas Reynolds number Reg c w 3= q g + 1 y

(5 -122)

Mass and heat transfer in an air-flow dryer [5.74] are described using the Prandtl number Pr, and the Schmidt number Sc, (see Table 1-18), and are

Sh =

~

’’

dp = 2

D

+ 0.664 - SC;’/~Re;/2 (5-124)

With the relative velocity wre, between the gas velocity wg and the particle velocity w,, the Reynolds number is calculated

376

5

Drying

- 1 min

10-2

lo-’

1

d, [ m m l

-

10

Fig. 5-35. Ranges of residence time of different convective dryers. Representation according to POERSCH, Babcock-BSH AG, Krefeld. dp Particle diameter t Residence time

The nomenclature used in Eqs. (5-121)(5-125) is given in Table 5-9. The residence time tp of a particle in an air-flow dryer of length Z is (see also Fig. 5-35) (5-126) To dry a wet product with different particle sizes, the dryer has to act as a classifier. In a conventional air-flow dryer the classification effect is not sufficient: during the residence time in the first drying stage coarse

particles may not become dry while fine particles can reach too high a temperature. With other short-time dryers, the product motion is in the form of a vortex flow driven by the hot gas which increases the residence time. This can be achieved with hot gas jets tangentially entering the drying area (vortexflowdryers such as helical flow tube with nozzles and annular flow dryer [5.77]), with displacement internals including gas guide vanes (spiral tube pneumatic dryer [5.78, 5.79]), or with tapered inclined perforated screen (cyclone dryer [5.80]). The convex dryer [5.81, 5-82] combines the functions of drying and classifying. With a

5.11 Design of Dryers

t

I "

I -

.T

3e

C

b

' if

Fig. 5-36. Pneumatic dryer and helical flow dryer. Representation according to BabcockBSH AG, Krefeld. a Fresh gas fan b Gas heater c Helical flow tube with nozzles d Pneumatic tube e Exhaust gas fan f Circulating gas heater g Circulating gas fan h Dried material discharge by rotary valve i Wet material supply by feeding centrifuge

combination of a fluidized bed dryer and an air-flow dryer, i.e., a spinflash dryer, pastes, filter cakes, slurries, etc., can be processed [5.83].

5.11.2.8 Spray Dryer

In a spray dryer or suspendedparticle dryer (atomizing dryer) [5.1, 5.2, 5.7, 5.84-5.891

377

(Fig. 5-37), materials ranging from a liquid (solution, suspension) to a wet liquid-pasty product, can be sprayed as a liquid mist into the hot gas flow. In the case of a disc atomizer, the liquid product is pumped into a quickly rotating spray disc and leaves, driven by centrifugal forces, through specially designed openings at the outer edge of the disc. Depending on the number of revolutions of the disc and the wet product viscosity, particle sizes can range approximately from 5-250 pm [5.90-5.921. In spray atomizing of wet products, onecomponent nozzles give hollow spherical, free-flowing and relatively coarse products, while high or low pressure two-component nozzles, operated with propellants, give a fine product [5.93]. The mist droplets generated during atomizing are mixed with hot gas, which is centrally charged at the tower head. Some of the hot gas may be introduced tangentially to superimpose a rotation on the main flux of gas and product. In the cylindrical section of the spray tower, the product droplets sink downward in parallel or countercurrent flow to the gas. Droplets are therefore dried in seconds or fractions of a second. The obtained powder is discharged at the tower cone and fed to the conveying system by swinging lids, rotary-vane feeders, screw feeders, etc. A small amount of the fines (10-15%) reach the waste gas cleaning area with the waste gas, and is discharged there. With knowledge of the parameters influencing the particle size distribution of spray dried powders, and process experience with different products, new spray dryers with, for example, integrated fluidized beds are developed. Production of almost dust-free powders is now possible [5.110]. The height of the spray dry tower, Z is calculated from the sedimentation velocity w, of the droplet, the required drying time tg and the gas velocity wg.Referring to the largest droplet,

378

5 Drying

Fig. 5-37. System Buttner-Balfour spray drying unit. Representation according to Babcock-BSH AG, Krefeld. 1 Cooling gas fan 2 Gas distribution 3 Gas twisting baffles 4 Rotating spray disc 5 Filter the particle diameter, discharge velocity, 6 Gas fan spray angle, density ratio, drying time, etc., 7 Gas heater are given [5.94]. 8 Wet material vessel During the evaporation from the droplet 9 Spray tower 10 Exhaust gas discharge tube surface, which is generally the case for a 11 Cyclone droplet travelling in the spray dryer, the 12 Exhaust gas fan mass and heat transfer for in the gas distrib13 Dry material pneumatic conveyor uted droplets are [5.7] 14 Cyclone 15 Rotating valve

Nu = 2.0 + 0.6 . Re0.’

Sh 2 = tg * (w,k wg)

(5-127)

(+ applies for parallel flow, - for countercurrent flow of wet product and hot gas). For a quick estimate of the tower diameter and height, nomograms may be used if

= 2.0

+ 0.6

Re’.’

(5-128)

a

Sc0.33

(5 -129)

The characteristic length in the dimensionless number is the droplet diameter. The velocity is the relative velocity between the droplet and the drying gas (Eq. (5-125)). Table 5-10 presents some characteristic data for convection dryers.

0. Some characteristic data for convection drying.

5-15

free-flowing product, pulverized, pasty, lumpy

r

5-20

blocky, bulky, fibrous in large quantities, pasty product

r

5-18

large quantities of pellet-like to pasty products

yer

5000- 6000

6-20

agricultural products

6000-15000

0.15-1.5 for product gas overflow 0.1 - 12 for product gas through-flow

Specific heat requirement, water evaporation (kJ/kg)

Specific water evaporation rate (kg/(m2 . h))

e

Product condition

dryer pellet-like, pasty small quantities

3500-5000

4000-5000

4400-5000 in convection drying 3000-3800 in contact drying

Dryer type

- design data

Layer thickness on a kiln: 20-100 mm

Layer thickness: 150-200 mm Air velocity: 0.2-1 m/s Layer thickness: 20-50 mm Tunnel length: 20-60 m Tunnel width: 3-6 m Air velocity: 2-3 m/s 1-5 belts on top of each other Effective belt length: 5-50 m Effective belt width: 0.5-3 m Effective belt area: 3-100 m2 Belt velocity: 0.3-0.6 m/min Air velocity: 2-3 m/s Disc diameter: 2-5 m Disc area: 20-900 m2 Revolutions: 0.5-3 min-' Layer thickness: 10-20 mm Air velocity: = 2 m/s Power consumption: 6-25 kW

ions: c continuous, b batch

(continu

0. (continued) e

yer

r

ic

er

1.5-50 kg/(m3. h)

liquid (solution, suspension) to liquid-paste like products

25-500 kg/(m3 . h)

pulverized, crystalline, fine products, products able to be pneumatically conveyed

10-600

grainy, pulverized short-fibrous products, products able to be fluidized

4000- 6000

25-50 kg/(m3 . h) with direct heating up to 200 kg/(m3 . h)

nonsticky, lumpy pulverized or crystalline products, large throughput

Specific heat requirement, water evaporation (k J/kg)

Specific water evaporation rate (kg/(m2 . h))

Product condition

3500-6000

4000-5000

4000-6000

Dryer type - design data

Drum diameter: 1-4 m Ratio drum length/drum diameter: 4-7 Drum revolutions: 0.5-10 min-' Drum inclination: 1-6" Air velocity: 2-3 m/s Fluidized-bed area: 0.5-40 m2 Bed height: ca. 0.2-1.5 m

Riser diameter: 0.3-1.2 m Riser length: 15-30 m Superficial gas velocity: 10-40 m/s Particle size: 0.01 - 10 mm Drying time: 2-8 s Power consumption: 15-100 kW Tower diameter: up to =8.5 m Height: up to = 20 m Specific air necessary: 8-45 mh/kg water Power consumption: 0.1 -0.3 kW/kg water

5.11 Design of Dryers

5.11.2.9 Drum Dryer

In a drum dryer (rolling dryer or “adhesion-layer dryer”) [5.1, 5.2, 5.95, 5.961 a thin film of fluid or semifluid material (low viscosity to pulpy products) is evenly distributed by a spreader knife and retained on a drum, which slowly revolves with internal heating. The product is dried during one revolution of the drum (Fig. 5-38). Shortly before the drum dips again, the product is continuously scraped from the drum surface in the form of flakes or scales by means of scraper knives. Depending on the pressure and temperature in the drying room, the drying process is usually only contact or evaporation drying, or with the presence of a drying gas, a combination of contact and convection drying. According to the wettability, viscosity, and surface tension of the wet product, different charging devices should be used (Fig. 5-38). Drum dryers are manufactured with single or double drums as a single stage, or in series of two double drums with two stages. The residence time of the wet product in the drum t , is controlled by the revolutions n in such a way that it corresponds to the drying time, tg (5-130) where 7 is the angle between charging and discharging of the product on the drum.

5.11.2.10 Thin Film Evaporation Dryer (Vertical and Horizontal Dryer) The thin film evaporation dryer [5.28, 5.97, 5.981 enables concentration of soluted or suspended solids, to form a crystalline or powdery dry substance by evaporation of the solvent from a thin layer, under vacuum. The wet liquid product is fed over the

381

heating zone and, by means of a rotor, applied in a thin film to the heated wall. In the preheating and crystallization zone, the first crystals form and are thickened in the following slurry zone to a crystalline pulp. In the final powder zone the product is dried. Mounted swinging wipers prevent powder depositions and incrustation on the heating surface. Figure 5-39 shows schematically a thin-film evaporation dryer and a two stage thin-film evaporation drying unit. 5.11.2.11 Contact-Mixing Dryer With contact-mixing dryers [5.1, 5.21 the product is mechanically mixed, redistributed and intensively dried. Milling and scraping devices may be installed for lumpy products. Drying is usually carried out at atmospheric pressure or under vacuum conditions. In a plate dryer [5.29, 5.30, 5.461 (Fig. 5-29), without hot gas peripherals, free-flowing product is moved across heated discs using wiper arms, turnover blades, side scrapers, rakes, etc. The product is constantly overturned and alternately transferred from disc to disc through central openings or openings in the dryer walls and dried in this way. With a paddle dryer (Fig. 5-40) the liquid, pasty, or free-flowing wet product is evenly distributed by rotating paddles over the heated areas (jacket, hollow shaft, and paddles) and discharged at atmospheric pressure or under vacuum. Other contact-mixing dryer designs are based on the paddle dryer with the possibility of continuous operation. For example, the AP-dryer reactor [5.99, 5.1001 includes two parallel stirring gears, a main shaft, and a cleaning shaft. The main shaft is equipped with discs and mixing ingots. On the faster rotating cleaning shaft (counterrotation/synchronous) disc elements and knead ingots are also mounted. Due to the

382

5 Drying

I

f

W@

M

b

Fig. 5-38. Cylinder dryer, design Biittner. Representation according to Babcock-BSH AG, Krefeld.

I Single drum dryer 1 Heated drum 2 Vapor hood 3 Wet material trough 4 Roller for wet material 5 Charging roller 6 Scraper 7 Dry material discharge screw 11 Drum dryer arrangements.

Representation according to Krauss-Maffei AG, Munich. a) Feeding rolls for pasty materials b) Drum dryer arrangement for viscous materials and slurries c) Dip feeding for fluid materials d) Roller-feeding for fluid materials e) Spray-feeding by rotating sieve basket for thermally sensitive materials

5.11 Design of Dryers

c11:

383

Cooling water

cuurn pump

WF

d

VA

Sealing liquid

WF

Condenser

diL Raw product

t

Feed Pump

DM

llate drawal

Fig. 5-39. Thin-film evaporator-dryer. Representation according to Luwa - SMS Verfahrenstechnik, Zurich/Butzbach. a) Vertical thin-film evaporator-dryer b) Combined vertical and horizontal evaporator-dryer WF Wet material feed DM Dry material discharge VA Evaporated moisture (vapor)

384

Steam

5 Drying

I1 l l

Condensate

Cooling

water

Fig. 5-40. Paddle dryer. Representation according to Buss AG, Basel. BO Body RO Rotor with paddles DR Drive FR Frame VF Vapor filter VC Vapor condenser DD Discharge device VP Vacuum pump

special arrangement of discs and mixing ingots an intensive mixing and kneading effect is achieved as well as a 90% self cleaning of the heat transfer areas. On the shaft helically inclined welded mixing ingots cause an axial product transport. In a Discotherrn (operated continously or batchwise), [5.100], [5.101] interrupted disc elements with knead ingots or mixing hooks are mounted on the rotor shaft. In

t

A

the shell area not covered by the rotating kneading or mixing ingots, counterhooks are fixed at the shell. Due to the interaction of rotating kneading/mixing ingots and the fixed counterhooks an intensive mixing and kneading motion and a 90% self cleaning effect are achieved. In a Druvatherm, the wet product is flung, whirled and intensively mixed by shovels similar to plowshares. Between the shovels, agglomerates are destroyed by knives mounted on a head. Therefore, products showing a tendency to form lumps or which are normally difficult to dry can be processed. In a Drais dryer, which is designed similarly to the Druvatherm, the complete mixer may be removed in the axial direction for cleaning purposes.

5.11 Design of Dryers

385

5.11.2.12 Contact Dryer with Continuous Product Movement due to Gravity

(Fig. 5-41). The drying process is a batchwise operation.

Tumbler Dryer [5.30, 5.1021

Double Cone Dryer [5.102]

In a tumbler dryer, free-flowing products are dried under vacuum. Through a shift in the axis of rotation and the vessel axis, the jacket-heated drying vessel has a tumbling motion. The product inside the dryer follows this motion due to gravitational forces

In a double cone dryer (“mixing dryer”) a drying drum with the form of a double cone revolves around an axis of rotation, which is perpendicular to the drum axis. Bulk material with a poorer flow behavior is dried in batches, usually under vacuum conditions.

Fig. 5-41. Vacuum tumbler drying unit for polymer chips. Representation according to Babcock-BSH AG, Krefeld.

Tumbler dryer Scrubber Rotary piston pump Condenser Rotary gate valve pump Condensate receiver Heating and cooling agent unit

386

5 Drying

5.11 Design of Dryers

387

Contact Rotary -be Dryer (Contact Drum Dryer) [5.30]

acteristic data for a selection of contact dryer designs.

The rotary dryer in Fig. 5-30, with a jacket heated by flue gas, for example, is also suitable for free-flowing and dusty products. In a contact rotary tube dryer, the product is guided through the rotary drum by arranged tube bundles. The heat required for the drying is transferred from a heating medium flowing in the shell. Other contact dryers are described in detail in t5.1, 5.21. Table 5-11 gives some char-

5.11.3 Process Control of Dryers Process control of dryers is discussed, for example in [5.2, 5.103, 5.1041. Applications of process control computers to drying technology are described in [5.105]. A spray drying unit is presented in Fig. 5-42 as an example of the representation of process control installations and equipment.

4 Fig. 5-42. Flow and instrumentation diagram of a spray drying unit, pilot scale. Represented by Krauss-Maffei AG, Munich. 16 Mixed vessel 1 Fresh air filter with louvrc 17 Slurry dosing pump 2 Fresh air fan 18 Dosing pump 3 Hot gas generatiodgas burner 19 Filter 4 Hot gas distribution assembly 20 Homogenizer 5 Drying tower with hot-gas spiral 21 Spinning-disk atomizer distributor, sieve-tray top, tangential hot 22 Control device for spinning disk atomizer gas channel, air brush 23 Wet product ring line including lance 6 Dry product storage nozzles and atomizer pressure nozzle 7 Cyclone 8 Vibrated convcyer chute P Pressure 9 Venturi scrubber AP Pressure drop 10 Circulation pump T Temperature 1 I Compressed air sack filter F Flow 12 Main blower M Motor 13 Silencer I Indication 14 Fan C Control 15 Paste mixing bin A Alarm

388

5 Drying

Table 5-11. Characteristic data for a selection of contact dryer designs [5.1, 5.2, 5.45, 0.61. Dryer type

Product condition

Specific water evaporation rate (kg/(m2 * h))

Specific heat requirement for water evaporation (kJ/kg)

Cylinder dryer

liquid to pasty

15-75

3000 -4000

Thin-film dryer

liquid to pasty -muddy

50- 100

3000

Paddle dryer

liquid Pasty free-flowing

5-20

3000-3500

Drais-dryer

liquid Pasty free-flowing

10-30

3000

Contact rotary tube dryer

grainy free flowing

4-8

3200- 3600

Tumble dryer

granular free flowing

2- 10

3000

Abbreviations: c continuous, b batch

5.11 Design of Dryers

Operating mode

Design data

C

Cylinder diameter 0.6- 1.5 m Cylinder width: 0.8-3.6 m Effective cylinder circumfence: 75-90070 Cylinder revolutions: 2-20 min-' Heating area (per cylinder): 1.5-17 m2 Layer thickness: 0.1 - 1 mm Power consumption: 3-25 kW Diameter: 0.2-1.1 m Height: 2-12 m Heating area: 0.25-18 m2 Throughput: 10000 kg/h Driving power: 133 kW Diameter: 0.5-2.2 m Nominal volume: 1- 16 m3 Heating area: 1-60 m2 Construction length: 2-6 m Driving power: 1.5-50 kW

b, c

Content: 0.05-30 m3 Heating area: 0.5-60 m2 Driving power: 5-700 kW Throughput: 3600 kg/h

C

Drum diameter: 2-5 m Drum length: 4-8 m Drum inclination: 8- 15" Drum revolutions: 3-8 min-' Heating tube diameter: 100-130 mm Heating area: 200-3000 m2 Particle size: vmin Y Solvent load with key component X Carrier load with key component

410

6 Extraction

vmin implies that the feed and the leaving extract phase are in phase equilibrium. This is only possible with an infinite number of separating stages or with an infinite transfer time. Therefore, the actual solvent ratio v has to be chosen such that it is larger than vmin. The value of v for extractor design and operation should result from cost estimates according to Fig. 6-16. With the known course of the equilibrium curve for fixed extraction conditions, the required number of theoretical stages Nt is determined by drawing steps between the equilibrium curve and the balance line, analogous to the McCabe-Thiele method (see Chapter 2.5.2.4 and Fig. 6-18). If the distribution coefficient K* is constant in the loading range of interest X u 2 X 2 X,, the equilibrium curve is linear in the operating diagram. The required number of theoretical stages Nt is then calculated from

/Ec

Fig. 6-18. Graphical determination of required number of theoretical stages. EC Equilibrium curve BL Balance line Y Solvent load with key component X Carrier load with key component

If two fluxes, characterized by the state points A and B, are mixed, the state point of the mixture M, lies on the connecting line between A and B. However, if from Nt = -1 flow rate mA a part mBis removed, the state In E point M2 of the remaining mixture mA - rhB (6-32) also lies on the connecting line AB,but instead lies outside A and B on an extension where E is the extraction factor (see Chapter 1.4.2). Application of Eqs. (6-34)-(6-36) im(6-33) plies: the state points of the fictitious mixtures b must lie on an extension of the connecting line between the state points F and In the case when the carrier T and solvent E, or R , and La or R and E, respectively. L are considerably miscible, countercurrent All three fictitious differential flow rates D extraction calculations have to be carried have a common state point which is named out using triangular coordinates (Gibbs tri- the “pol” P, and is the intersection of the angle). Molar balances over the top section extended lines FE, and R,,,if the state of the column and over the total column, points F of the feed mixture 8 E, of the extract phase E,, R, of the raffinate phase with the nomenclature in Fig. 6-15, give A , and L, of the solvent phase L , are . . F - E, = fi - E = D (6-34) given. P gives the fictitious composition of the two phase system for fixed flow rates of (6-35) R and 8,and remains in the same place 6, - L o = R - E = D during the extraction process. The pol loca. . (6-36) tion is fixed by the feedkolvent ratio F - E , = R, - L , = D

6.2 Liquid-Liquid Extraction

(6-37)

According to a graphical method by HUNTERand NASH [6.17], the required number of theoretical separation stages Nt for the distribution of the key component between the extract phase E , and the raffinate phase R,, may then be determined using the Gibbs triangle. One has only to consider that the state points of phases in equilibrium leaving the respective stages lie on the binodal curve and at the end of the common tie lines of phases in contact in a common cross section lie on the binodal curve and on a common pol or cross-section line The Hunter-Nash method is illustrated in Fig. 6-19. The state points F and E, are connected by the top pol line. F is the state point of the mixture entering the top sepa-

A

411

ration stage. E, is the state point of the extract phase leaving the top stage E,. If the top stage acts as one theoretical separation stage, the leaving phases must be in phase equilibrium. R, is the state point of the raffinate phase 6,and lies on the binodal curve at the intersection with the tie line through E,. The raffinate phase 6,and extract phase come into contact in the cross-section below the top stage. State point El of El has to lie on the binodal curve and the pol line passing through R,, and is therefore known. When selecting the state points R,, R,, . . . and E,, E,, . . ., according to the method as described for the top stage, the number of stages is found from the number of the raffinate state points in the diagram. The minimum solvent ratio is referred to the feed, p =

Lmin ~

F

=,*.

L T min =A

F

(6-38)

and is derived from Fig. 6-20 by the Lever rule for the phases, with the assumption of phase equilibrium between the leaving extract phase E, and the feed I? Therefore, the state point of the extract phase Em,, will then lie on a tie line passing through F.

T

P

Fig. 6-19. HUNTER and NASHmethod to graphically determine the number of theoretical stages of

countercurrent extraction units. BC Binodal curve TL

PL

Tie line Pol line

L Pure solvent (triangular corner) F, E,, R,, La State points of feed and leaving phases

412

6 Extraction

S

tray efficiency Ed. If there is plug flow then the relationship between &d and Ed is (6-39.2) where

L

P

Fig. 6-20. Determination of minimum solvent ratio vkin. BC Binodal curve TL Tie line PL Pol line

(6-39)

E

is the extraction factor.

Generally, the mass transfer between two liquid phases in liquid-liquid extraction is substantially slower than that for rectification processes. Small values of the tray efficiency factors therefore follow. With average extraction, tray efficiency factors range from 0.3-0.7 with sieve trays, and 0.3-0.6 with Koch cascade trays. Only in mixer-settler cascades and with centrifugal extractors is the actual tray efficiency almost the theoretical tray efficiency. Introducing the concept of height of a theoretical separation stage, HETS to evaluate the actual height of an extraction column giving the same effect, the total height of the column Z for mass transfer is

(Since the initial load Y, is usually very small, imin is approximately equal to &,,in. The minimum solvent ratio v A * , ~ ~ ~ corresponds to the minimum solvent ratio Z = N t .HETS (6-40) referred to the feed, ~4,). To determine the actual number of re- For the determination of the separation efquired stages Np for the extraction column, ficiency which is characterized by the enthe number of theoretical stages Nt and the richment ratio or HETS in the case of liqstage efficiency factor EMd (MURPHREE uid-liquid extraction, results from experistage efficiency factor) have to be known. ments on a pilot-plant scale, are required to For the case of mass transfer from the con- a greater extent than in rectification. tinuous to the disperse phase with respect to The separation effect in extraction prothe dispersed phase, EMdis cesses is not only a function of common variables such as the phase column loads, Y n -Yn -1 but also of variables which depend on the (6-39.1) EMd = internals, the concentration profile along Y*(xn)- Y n - 1 the column, the substance compositions, where yn, y n - , are the concentrations of and substance properties. These additional the key component in the disperse phase variables and their influence make scale-up above and below the stage of interest, re- to production units, based on the results spectively, and y*(xn)is the stage exit con- found in pilot-scale plants, questionable. centration in equilibrium with the concen- The variables specific to extraction are tration of the continuous phase x,. For the listed in Table 6-3. Besides the mass transfer coefficient, the limiting case of ideal mixing in the separation stage, EMd corresponds with the local separation effect is mainly influenced by

6.2 Liquid-Liquid Extraction

413

Table 6-3. Specific extraction variables influencing the separation effect (exchange ratio, height of a theoretical separation stage HETS, height of a transfer unit HTU). ~

~~

Variable

Effect

Fluid mechanics Droplet formation Droplet size, droplet size distribution Droplet swarm motion Droplet coalescence

Small droplets and a narrow droplet size distribution favor mass transfer

Interfacial effects Interfacial tension gradient Viscosity gradient Marangoni effect (near interfacial liquid layers move from area of low interfacial tension to areas of higher interfacial tension)

Interfacial turbulences caused by interfacial tension gradient increase the mass transfer to the interphase compared to the mass transfer by only diffusion

Mixing effects Longitudinal mixing, back mixing (axial carriage of smallest droplets by the continuous phase, continous phase dragged by droplets in the wake) Cross mixing (radial mixing caused by cross flow diffusion)

Compared to the ideal case of plug flow the driving force for mass transfer is reduced by mixing effects

the mass transfer surface, which is directly proportional to the holdup of the dispersed phase and inversely proportional to the droplet diameter. Therefore, the effects of coalescence have a large impact on the separation effect. Stage-to-stage calculations are easy to do if the miscibility of the carrier and solvent may be considered as being negligible. For example, a molar balance for the key component over a three-stage countercurrent extractor (Fig. 6-21) gives the equation system: 1. Stage

-

T * X , + LT Y2= T X I

-I-L ,

*

Y,

(6-41)

References

3. Stage T . X2

+ LT

*

Y, = T * X3 + L

-3

(6-43)

In the case of distribution equilibrium in each stage, (6-44)

Introducing the solvent ratio, v = L T / T and the extraction factor E = K* . v, a system of three linear equations is finally achieved, with the unknowns X I , X 2 , and X 3 , and, therefore, q , &, and &

- (1 + C) . X I + E * Xz =

-X ,

X ~ - ( l + & ) . X 2 + & * X=3o

X , - (1

+ E)

*

(6-45) (6-46)

X,= - v Y, (6-47) *

414

6 Extraction

D=

1

-(1

+ &) 1 0

-(1

E

+ &) 1

-(1

+ &) (6-49)

XI

\'

L

is the coefficient determinant, DXi is the determinant for the respective unknown X i , following from D.In the equation system Eqs. (6-45)-(6-47) the coefficient of Xi is replaced by the components of the solution vector

yz

( -5) - v * Y,

For any number of stages the coefficient determinant D and the solution vector can be appropriately extended. If the initial solvent load is negligible, Y, = 0, the calculation is then considerably simplified. For any number of stages, n 3 N,,

3. Stage

xu-

x,

~-

Fig. 6-21. Material balance of a three-stage countercurrent extractor.

E-1

En+'-

1

(6-50)

From Fig. 6-22, based on Eq. (6-50), the required number of theoretical stages N,may be derived for an extraction yield 7 (Yo), if the extraction factor E is given. (6-51)

X I ,X , and X , may be calculated by following the Cramer rule for this equation system,

(6-48) if the entry loads X , , Y,, the solvent ratio v, the distribution coefficient K*, and the extraction factor E are given, where

HTU, NTU Concept Using the concept discussed in Chapters 1.7 and 1.9 for LLE, the height required for mass transfer Z for a countercurrent extraction column is

-

6.2 Liquid-Liquid Extraction

415

100 -

I

Jt

10

-

1

I

-

I

99.9

99

7[%1

I

I

90

0

Fig. 6-22. Determination of extraction yield. Representation according to BRUNNERand Westfalia Separator AG, Oelde [6.20]. Nt Number of theoretical separation stages q Extraction yield

= HTUo,.

NTUoE

(6-52)

where cross-sectional area of the extraction column kE,kR overall mass transfer coefficient referred to the extract and raffinate phases

AQ

or

where the key component loadings X and Y of the carrier and solvent, respectively, are referred to as the concentration scale

-= - + kR PR

BE,PR

(6-55) DE

mass transfer coefficient, referred to extract and raffinate phases

416

6 Extraction

effective specific volumetric mass transfer area (phase boundary area) loadings of the raffinate and exX,Y tract phases by the key component in one reference cross-section of the column (see Fig. 6-18) X*, Y* phase equilibrium loadings referred to X and Y (see Fig. 6-18) HTU,,, height of the transfer unit referred to extract and HTU,, raffinate phases, respectively NTU,,, number of the transfer units referred to extract and NTU,, raffinate phases, respectively ae

The heights of a transfer unit HTU,, and HTU,, are found empirically under conditions as close as possible to the operating conditions from the product of k E .a, and k, . a,. Transformation of the results obtained in an experimental column to a technical column is only possible based on scafe-i.rp relations~ips found empirically. For example, according to BAUER[6.21], for agitated columns

(2)

1/3

HTU, = HTU, ’

(5-56)

and according to TRORNTHON [6.22] for pulsed tray columns, HTU, = HTU,,. exp[C. (d, - d,)]

(6-57)

where d is the column diameter and the index t refers to the technical column and v to the experimental column. The constant C in Eq. (6-57) is, according to REISSINGERet al. [6.23], 1.64 for column diameters up to 300 mm. For larger diameters, C has to be reduced. Generally, no measurement of the concentration profile for the determination of the operating line Y ( X )is transferable. The balance line in Fig. 6-18 must be used to determine NTU, but its form assumes

plug flow in the column. The evaluation of the integral expressions in Eqs. (6-52) and (6-53), follows the method presented in Chapter 1.9.4. When small columns and technical columns are compared, it is observed that, for a given extraction effect, a column with a larger diameter requires a larger height for mass transfer Z,,,. This is due to axial and radial mixing effects which cause deviations from a uniform, fluid particle residence time distribution in both the disperse phase and the continuous phase. The driving forces are reduced by this mixing, compared with the ideal case of plug flow. The mixing effects are caused by: 0

0

0

0

Molecular and turbulent diffusion in axial and radial directions Carrying of continuous phase in the wake of a droplet Carrying of the smallest droplets by the continuous phase Cross flow

The negative influence increases with increasing column diameter. Figure 6-23 shows the concentration profile of both phases along the column height z for the cases of ideal plug flow and pronounced longitudinal mixing. With longitudinal mixing a distinct increase in concentration occurs at the point where the phases enter, due to mixing of the column contents. Mixing therefore causes a partial equalization of the concentrations along the extraction column length and hence a decrease in the driving force. To compensate this effect, a larger height for mass transfer, Z,,, is required compared with the height Z found by a plug flow model. Eqs. (6-52) and (6-53) are used to calculate Zefl, in which either HTU or NTU have to corrected ( T U , NTU) to consider the mixing, so

417

6.2 Liquid-Liquid Extraction

a)

Z

1

EC

-0 0 0

a

t

VI

0

L

a

Z

c

V

2

c

X

W

0

y,

x, Y

-

XU

Xa Raffinate phase load

X-

Fig. 6-23. Influence of axial mixing on concentration curves (a) and number of separation stages (b). a) --- Concentration curve at plug flow

- Concentration curve at pronounced mixing

b) EC

OL BL Y X

Equilibrium curve Operating line at pronounced mixing Balance line at plug flow Extract phase load Raffinate phase load

or

Z,,,

0

= HTU.NTU

(6-59)

From Eq. (6-58), the apparent height of a transfer unit is

HTU = HTU f HDU

(6-60)

when the mixing effect is considered. According Eq. (6-60), F U is the sum of the height of a transfer unit HTU for plug flow and the height of a dispersion unit HDU. Mixing effects may be found experimentally, by measuring the residence time distribution of the phases. Mixing flow models are used to convert the results into half empirical correlations (see, for example, [0.4]):

0

The cell model (stage model) describes hydrodynamic flow in countercurrent columns analogously to the flow in a number of equal, ideally mixed vessels, as individual mixing stages (cells). Between the individual mixing stages, no mixing takes place. The number of cells is the adjustable parameter for the measured residence time distribution in the mixing cell cascade. Stronger backmixing leads to a smaller number of cells, or to a larger cell height. In the more complicated backfiow model, where the column is also divided into individual mixing cells, as in the cell model, additional longitudinal mixing between the cells in form of “mixing flow” is included.

418

6 Extraction

The dispersion model (diffusion model) explains the deviation of the real flow profile from the ideal plug flow profile due to dispersion analogously to molecular diffusion. For example, in the continuous phase, the axial distribution of the key component is (6-61)

where dispersion molar flow rate of the key component in the continuous phase (current density) density and molar mass of the continuous phase concentration gradient of the key component axial diffusion coefficient in the continuous phase

nD, c

ec9Mc

dx/dz

D ,C

The Bodenstein number Bo is the ratio of pure convective axial mass transfer and mass transfer due to longitudinal mixing, and is a measure of the substance dispersion in the real column flow and the mixing effects. Large values of Bo characterize narrow, small values but strong scattered residence time spectra. Bod and Bo,. must be known to calculate HDU. If the extraction factor E = 1, which is true for many technical applications, the apparent height of a transfer unit HTU considering Eqs. (6-62) and (6-63) is __

HTU = HTU + ___ wc

Du~,c

HDU

-

1

L,.

-+-

Bod

0.8 lne + L , . E I.,.(&- 1)

(6-64)

0.33

(6-65)

(6-62) (%)?

BO,.

where Bod and Bo, are the Bodenstein numbers ( E extraction factor, Lc characteristic length, height, wd, w,. flow velocities of the dispersed and continuous phases)

wd

For example, to calculate the dispersion coefficient for a Rotating Disc Contactor (RDC), given in [6.24],

Calculation of the axial flow dispersion assumes knowledge of the dispersion coefficients for the continuous and dispersed phases, as a function of their variables. The dispersion model is valid if the mixing effects are small. Characteristic parameters of the dispersion and cell model are interchangeable. The height of a dispersion unit HDU is calculated according to ZEMERDINGand ZUIDERWEG I6.241, [6.25] 1

Dax,d + -_

where

I*):(

[(%)? -

(6-66)

P

dispersed phase fraction (holdup) Re,,Re, Reynolds numbers of the stirrer and the continuous phase

Re,, =

d; . n ~

VC

, Re,.=

d

*

W,

__ VC

(6-67)

w, = n . d, . n circumferential velocity of wd, wc,

d, d,,d,,

zz

n

the stirrer flow velocity of the dispersed and continuous phases, number of stirrer revolutions diameters of the column and impeller and the stator ring height of mixing cell

Application of the one-dimensional dispersion model gives the differential equations ~0.41

(6-68)

d=

1/-

v$

6.2 Liquid-Liquid Extraction

4.r;;

71

wi

*

= 1.128

419

(6-70)

The maximum phase velocity wi, similar to the other countercurrent flow columns, is related to the phase velocity at the flooding point wif wi

(0.5

... 0.8)

*

Wif

(6-71)

Most of the concepts used to calculate two phase flow in extraction columns are based on a simple model of two countercurrent liquid phases (the two phase model of GAYLER,ROBERTS,and PRATT[6.27]). The relative velocity w,, between the phases is the sum of the effective phase velocities (6-72)

(6-69) With known overall mass transfer coefficients kd and kc, specific volumetric interface area a, and axial dispersion coefficient, Duxthe solution gives the actual concentration profile of the key component in the column. In [6.26], methods to measure the longitudinal mixing in countercurrent extraction columns are described and approaches to calculate the Bodenstein number and the axial dispersion coefficient for common extractor designs are given.

Column Diameter, Holdup, Interface Area The diameter of an extraction column d is determined by the throughput of one phase i (extract or raffinate phase) and the maximum superficial velocity or volumetric flux, w iper unit cross-sectional area of the column

where w d is the velocity of the disperse phase, w, the velocity of the continuous phase, and y) is the holdup of the dispersed phase. A reduction factor 6 has to be introduced for columns with internals reducing the cross-sectional area (Eq. (6-72)). This is the void fraction of packed columns; introduc ing the relative void fraction it is (6-73 According to ~ O R N T O N[6.28] the relative velocity w,, is a linear function of (1 - 9). Extrapolation of the holdup for a single droplet ( y ) 0) gives the characteristic velocity of a droplet J +

WreI

wd

=-

9

WC + ___ = J . (1 - 9)

1-y)

(6-74)

(where V an apparatus and substance-specific variable, is similar to the terminal velocity of an individual droplet with phase

420

6 Extraction

velocity w, = 0 and small holdups of the dispersed phase (p-0). However, V is smaller than the real terminal velocity of single fluid particles in the continuous phase, and does not correctly describe the real physical behavior. Therefore, newer concepts based on droplet swarm relationships are used to calculate the relative velocity with p -+ 0, the steady-state velocity of a single droplet (see, for example, [6.29]). Phase throughput and phase velocities wdr w,,respectively, reach a maximum at the flooding point. The flooding point is the hydrodynamic loading limit of the column, exceeding its limit disturbs the phase flow. Either the dispersed phase is then carried out by the continuous phase, or the dispersed phase coalesces to streaks or drops. The column is now partially or total blocked, and phase inversion from the disperse phase to continuous phase occurs. The maximum values wdF and wcF, according to THORNTON [6.28], are obtained from Eq. (6-74) by differentiation of the phase velocities with respect to holdup

lid,

Following from Eq. (6-74) with the maximum value of the holdup pF in Eq. (6-78), (6-80)

and the loading limit of the column is


0.001 N/m) or small density differences (A@> 30 kg/m3) Disadvantages: - Sensitive to fouling and incrustation - At trays with low opening ratio narrow loading range

Advantages:

-

0

445

446

6 Extraction

Table 6-10. Common extraction columns with rotating internals. Design, principles, characteristic data and references [6.23, 6.31, 6.46, 6.521. Principles Characteristic data

Agitated column type Design Rotating Disc Contactor (RDC)'),

[6.53]In a rotating disc contactor phase mixing is caused by a disc mounted [6.56] on a rotor. Stator rings subdivide the column into individual compartments to reduce backmixing. Suitable for large throughputs as well as mixtures containing soil. Column diameter: up to 8 m Column height: up to 12 m Max. cross-sectional load: ca. 40 m3/(m2 . h) Separation efficiency: 0.5- 1 m-l Density difference: h e 2 5 0 kg/m3 Maximum throughput: 2000 m3/h

*)

Variable speed drive Light phase outlet

--Rotor

disc

, JHeavy

phase outlet

Asymmetric Rotating Disc Contactor (ARD)3, -\

Partition

Baffle

Troy

Shaft Disc

path

Assembly

Ref.

In an ARD-extractor the asym[6.57] metrical stator consists of trays and [6.58] baffles to divide the column into [6.59] extraction zones and linked transfer zones. On the rotor mixing discs are mounted. The extraction zone is limited by the stator partition and is separated by the trays into chambers. Phase transport and separation take place in the settling zone behind the partition. Compared to the RDC smaller throughput but better separation efficiency. Column diameter: up to 4 m Max. cross-sectional load: ca. 20 m3/(m2 . h) Max. throughput: 250 m3/h Separation efficiency: 1-3 theoretical stages/m Density difference: h e > 10 kg/m3.

6.2 Liquid-Liquid Extraction

447

Table 6-10. (continued) Agitated column type Design

Principles Characteristic data

Scheibel Column') Oldshue-Rushton Column')

In a Scheibel Column phase mixing [6.60] is caused by blade mixers or blade [6.61] mixers with mounted baffles. Wiremesh packing or filling material of one to three times the height of the mixing zone acts as the settling zone. Operation mode is like the mixer-settler principle. Separation efficiency ca. 3-5 theoretical stages/m.

Scheibel

H P Heavy Phase LP Light Phase

Kuhni Kuhni

W

a b c d e f

central shaft mixing blade baffle breake plate mixing zone separation zone

Oldshw-Rulhton

Ref.

The Oldshue-Rushton Column is [6.62] similar to the RDC. Instead of a disc rotor a turbine mixer is used. The individual chamber height is larger and is approximately the same as the column diameter. Mixing zones are separated by narrow passage holes. Separation efficiency: 1-3 theoretical stagedm with narrow stator rings and 0.8-1 theoretical stages with wide stator rings.

In Kuhni columns mixing zones [6.63] (with centrifugal mixers) are sepa[6.101] rated by perforated plates where the opening ratio (free cross-sectional area) may be adjusted to the desired operating conditions. Possible operating are mixer-settler mode and dispersion mode. Column diameter: up to 3 m Max. throughput: 350 m3/h Max. specific cross-sectional load : ca. 50 m3/(m2 . h). Separation efficiency: up to 10 theoretical stages/m, depending on the free cross section of the stator disc and operating conditions.

(continued next page)

448

6 Extraction

Table 6-10. (continued) Agitated column type Design

Principles Characteristic data

QVF Mixing-Cell Extractor (MCE)2)

QVF-MCE: Mixing zones (with blade [6.46] mixer, four elements) are separated by [6.64] partitions with specially designed openings (central circular with meandershaped weir to promote a channeling of both phases). Behind the weir a settling zone is formed to separate the phases. The heavy phase flows through the opening in the upper weir section into the circular area and passes downward. Analogously the light phase flows upward. At different points each phase passes through the opening area to increase the throughput and to decrease back-mixing. Column diameter: up to 1 m Opening ratio: 10, 20, 40% Max. cross-sectional load: ca. 15 m3/ (m2. h) depending on opening ratio Separation efficiency: cell efficiency 40-60%, i. e., 5-8 theoretical stages/m.

w

B Blade mixer with 1 elements P Partition W Meander shaped weir

EC Extraction Column STEINER)’) (System HARTLAND,

c

Basic design

Grid installation

Ref.

[6.65] In an EC (enhanced coalescence) [6.66] column mixing zones (blade mixer) are separated by grids made of thin metal sheet to support coalescence and axial flow. Due to special treatment of the grid surface the disperse phase coalesces at the grid openings and blocks part of the free area. Thus, an opening ratio adjusted to the respective load is achieved. The EC column is marked by a high loading flexibility and sufficient separation efficiency over the total loading range. Separation efficiency increases at underload operation. Max. cross-sectional load: ca. 80 m3/(m2 . h) Separation efficiency: ca. 2-6 theoretical stageslm.

6.2 Liquid-Liquid Extraction

449

Table 6-10. (Continued)

Agitated column type Design

Principles Characteristic data

SHE E~tractor’)~)

In an SHE column (self-stabilizing[6.66] high performance) mixing zones (with [6.67] paddle mixer) are separated by special installations. Rotationally symmetric installations in the phase separation zone force each phase to pass through channels which are tapered in the flow direction. In the case of overload the dispersed phase is stacked up in corresponding channels to the edge of the installations. If the overload still increases, the disperse phase flows through the channels reserved normally for the heavy phase. By simple reduction of the throughput or reduction of mixer revolutions a stable operating point is restored. SHE columns are marked by a high specific cross-sectional load. Max. cross-sectional load: ca. 100 m3/(m2 . h) Separation efficiency: ca. 3 theoretical stages/m, low load dependency.

M Mixer

C Conical

installation

Ref.

Controlled phase flow in conical installations

(continued next page)

450

6 Extraction

Table 6-10. (Continued) Agitated column type Design

Principles Characteristic data

Graesser Contactor')

[6.64] The Graesser contactor consists of a horizontal column divided into in- [6.68] dividual chambers by partions and a rotor with circulating dipping tubes. Phases to be contacted flow countercurrently through the column. Phase mixing occurs in the chambers. Via a gap between the circulating partitions and the column shell the mixture is passed from chamber to chamber. Due to gentle phase mixing the Graesser contactor is especially suitable for systems which form emulsions that are difficult to separate. This contactor is unqualified for systems with large density differences and large surface tension. The throughput is small and the length of a theoretical stage is approximately the drum radius. Column diameter: up to 1.8 m Max. throughput: ca. 25 m3/h Max. cross-sectional load: ca. 1-2 m3/(m2 h) Residence time: 3-15 min per theoretical stage. 1

') *)

3, 4,

5, ')

Representation Representation Representation Representation Representation Representation

according to according to according to according to according to according to

BRANDT, REISSINGER, S C H R ~ E[6.31]. R PILHOFER, SCHROTER [6.46]. Buss AG, Winterthur. M ~ G L[6.63]. I QVF Glastechnik GmbH, Wiesbaden. GAUBINGER, HUSUNG, MARR[6.67].

Ref.

I

22

20

-t 15

!

-1

I T

' I

7

f

N

E m

E

I

'rn

i I

10

\ I

\

I

\

-1 l

ips= 10 8%

I

cl

5

0.2-

4& . f i t-I

120

110

1

I

t

-

160 180 200 n [rnin-'I

-I-t

220 2LO

I

260

E Ln 0.1 kW

I

Fig. 6-41. Load ranges and efficiency of a QVFMCE and a Kiihni column. Representation according to PILHOFER,

-l$:--: I

-v-i'

.

-

8-

12

14 13

10

--

8

+/

0

t

I

!

~

'

I

~

I stator Load range cross of sections a QVF-MCE ps as afor function different of free the d l o.2 number of mixer revolutions -E m, Water/Acetone/Toluene A Water/Acetone/Butyl acetate 0.1 B Total load w I n Mixer revolutions I1 Separation efficiency of a QVF-MCE and Kiihni column as a function of the mixer revolutions n and the total load B. 0

m3/(rnZ.hl

..

~~

A

3

L..,

4

F

-

8-

12

10

I

;,/

i~---

~

8

I I

rn3/(rnZ.hl

452

6 Extraction

-

6 [rn3/(m2.h)]

0

0

10

20

30

LO

b [rn3/(m2.h)]

50

60

6.2 Liquid-Liquid Extraction

453

t

4 Fig. 6-42. Loading limits and efficiency of

SHE extractor and EC column. Representation according to data of QVF Glastechnik GmbH, Wiesbaden.

Ne

10

a) Loading ranges of an SHE-extractor -Toluene-Water _ _ _ _ Butyl acetate-Water b) Efficiency of a SHE extractor System: Toluene/Acetone/Water d-c Mass transfer direction, column diameter 100 mm c) Efficiency of an EC column System: Toluene/Acetone/Water Parameter: Revolutions per minute n, Theoretical stagedm & Total cross-sectional load

Fig. 6-44. Torque M, as the Newton number, Ne of one cell as a function of the Reynolds number Re for a rotating disc contactor RDC. Representation according to HUSUNG[6.69].

Ne Newton number Ne =

Re Reynolds number d

Mz

. n 2 . Q, Re = n . d;/v, d,'

Column diameter Z , Height of mixing cell n Revolutions d,. Diameter of rotor disc Q, Density, continuous phase v, Kinematic viscosity, continuous phase

8 !

-1

I

I e 2 -

1 0

I

10

-

20 30 nr [rnin-ll

LO

50

Fig. 6-43. Separation efficiency of a Graesser contactor. [6.70]. Representation according to STICHLMAIR System : Toluene/Acetone/Water Vd/< = 1.5 Tube diameter 100 mm Active length: 1 m Cell length: 0.025 m n, Number of theoretical stages per m n , Rotor revolutions

angular velocity o = 2 - x . n, and number of revolutions n. Therefore, centrifugal extractors allow treatment of systems with low phase density differences (A@2 20 kg/m3) and a tendency to form emulsions. At the periphery of the rotating extractor rotors filled with liquid, there is considerable pressure of 100 bar or more. Therefore, the extraction process in a centrifugal extractor is not isobaric, and this may affect the location of the distribution equilibrium I6.721. The total throughput and allowable pressure in the inlet and outlet for both liquid phases fix the operating range of the centrifugal extractor. For the design (Sauter diameter, droplet velocity, pressure profile, residence time distribution, flooding load, etc.) see [6.71, 6.73 -6.751. Extractor selection and operatine Darameters have to be determined exper" I

454

6 Extraction

Table 6-11. Selected centrifugal extractors. Design, principles and characteristic data [6.20, 6.31, 6.711. Extractor type Design

Principles Characteristic data

Lurgi-Westfalia Extractor (Luwesta-Extractor) [6.20]

Disc separators, divided into mixing chamber and separation chamber with conical discs. The liquid is distributed in thin liquid layers thus causing a short droplet path. Holes in the discs form rising channels for the upward flowing liquid. The liquid is introduced to the first stage via an inlet pipe and mixed with the extract phase withdrawn from the second stage by a centrifugal catcher. Phase separation and discharge of the final extract phase occur in the disc unit of the first stage. Mixing of the raffinate phase with fresh solvent and phase separation in the disc unit of the second stage, discharge of the raffinate phase. In countercurrent flow the extract phase is brought into contact with fresh feed in the first stage. Since in multistage apparatus the throughput decreases and fault liability decreases, singlestage centrifugal extractors are favored. If necessary single stage apparatus are connected to multistage units.

I--.-

Design')

7-

____-

-Heavy phase Light phase

Phase path2)

Heavy phase

Light phase

S Separator M Mixer ~

~-

Single-stage extractor data: Drum volume: 0.003-0.12 m3 Revolutions: 6500-4400 min-' Flow capacity: 1.25-120 m3/h Data of a BXP-Robatel separator: Volume: 0.017-0.22 m 3 Revolutions: 2900- 1000 min-' Drum diameter: 0.32-0.8 m Flow capacity: 6-50 m3/h

6.2 Liquid-Liquid Extraction

455

Table 6-11. (Continued) Extractor type Design

Principles Characteristic data

Robatel extractor, BXP3) [6.71]

Chamber separator which may be connected to a countercurrent flow unit. Phase mixing by centrifugal mixers at the bottom of the rotating drum, phase separation in the above separation chamber, overflow of phases via a weir system with channels to reach the next stage. Data of a BXP-Robatel separator: Volume: 0.017-0.22 m3 Revolutions: 2900- 1000 min-' Drum diameter: 0.32-0.8 m Flow capacity: 6-50 m3/h

Podbielniak centrifugal extractor') [6.76]

A series-connection of concentric perforated cylinders. The heavy phase is charged via a central shaft and passes, driven by centrifugal forces during rotation, to the outside while the light phase is led inward. Mass transfer occurs during intensive contact of the phases in the cylinder holes. Both phases flow countercurrently. The spacing between the cylinders acts as a phase separation zone. The number of cylinders connected in series corresponds to the number of mixing and separation stages.

Data of Podbielniak extractors: Rotor volume: 0.6-983 L Revolutions: 10000-1600 min-' Flow capacity: 0.23- 132 m3/h Separation stages: 3-5 per apparatus Density difference: A@2 50 kg/m3

')

*)

3,

Representation according to MULLER[0.1, Vol. 21. Representation according to BRUNNER[6.20]. Representation according to GEBAUER, STEINER, HARTLAND [6.71].

456

6 Extraction

imentally under condition as close as possible to the operating conditions. Table 6-11 illustrates the assembly and operating modes of selected centrifugal extractors and gives some geometrical and operational data. Centrifugal extractors are noted by their small space requirement, small holdup and hence short residence times, fast phase separation, and high throughput. These apparatus are particularly suitable for the treatment of substances which have a tendency to form emulsions, with an unstable key component, and also for small phase density differences. The main disadvantages are the high investment costs, maintenance costs, and energy expenditure.

6.2.5 Selection and Design of Extraction Apparatus Table 6-12 shows a strategy diagram for the solution of an extraction problem. If the substance system, type of operation, process variations, and required number of separation stages are fixed, the type of extractor can be selected. Figures 6-45 to 6-47 give an indication of the selection. However, for the final selection and design, experiments under conditions as close as possible to the operating conditions, and scaleup knowledge are required. Figure 6-48 gives a brief summary of the separation efficiency of columns, with in-

Table 6-12. Strategy to solve an extraction problem * 0 0

0 0 0

0 0

0

0

0 0

0

Analysis of extraction problem (& x,, xu) Selection of solvent (Chapter 6.2.2) Determination of operating mode, operating conditions and process Analysis of distribution equilibrium (Chapter 1.4.2) and further physical properties (e, q, CJ etc.) Balancing, determination of total throughput, determination of ya from optimization considerations of extraction requirements and solvent regeneration, determination of solvent ratio (Fig. 6-16) Choice of disperse and continuous phase (Chapter 6.2.3.4) Calculation of the required number of theoretical separation stages by graphical or arithmetical means, determination of the theoretical extractor height (length) by the aid of the HTU/NTU concept (Chapter 6.2.3) Selection of extractor type (Chapter 6.2.5) Experimental investigation of fluid mechanics and mass transfer under conditions as close as possible to operating conditions (droplet formation and size, droplet size distribution, droplet movement, coalescence, separation behavior, mass transfer, HETS or HTU with respect to surface (interfacial) tension and mixing effects), selection of the optimum operating point (Chapter 6.2.4) Transfer of experimental results to the production unit by considering experimentally gained scale-up experience Extractor geometry (cross-sectional area, height or length, opening ratio, size of internals) and energy input (Chapter 6.2.3 or 6.2.4) Determination of the optimum operating point (mixer or rotor revolutions, pulsation intensity etc.) (Chapter 6.2.3 or 6.2.4)

* The presented order has not to be followed strictly. Sometimes iterative loops are required.

6.2 Liquid-Liquid Extraction

457

L-J Process

Separator, centrifugal extractor

holdup

b' form emulsion, poor separation

limited

Lowno.of theoretical stages required

Separator, Mixer-Settler cascade with separation aid Centrifugal extractor, Graesser, RDC, ARD

yes

1

r

Mixer-Settler cascade Centrifugal " extractor Small floor space

All column types Centrifugal extractors

theoretical stages required Graesser

I

no Small floor space

I

1

yes r

-'

Pulsed sieve-

High throughput

extractor

I I

I

no

throughput

Fig. 6-45. Selection of extractor types. Representation according to BRANDT, REISSINGER, S C H R ~ E[6.31]. R

ternals reducing the cross-sectional area as a function of the total cross-sectional load. Figure 6-49 gives a comparison of the capability of selected extraction apparatus with standard dimensions, for the system toluene/acetone/water.

C=

I

I

load range Wide load range

Pulsed packed column Karr column Scheibel (OldshueRushton)

The optimal apparatus is the apparatus which best solves the extraction problem with minimum investment costs. In Fig. 6-49 the course of the characteristic cost value for different extractor types C, is presented

costs ($) throughput (m3/h) number of separation stages

(6-130)

458

6 Extraction

Fig. 6-46. Qualification of different extractors according to data of the companies Podbielniak and Luwa. Representation according to MULLER[0.1, Vol. 21.

This is equivalent to the investment costs according to STICHLMAIR [6.77]for different types of extraction apparatus, over the total throughput. The design of an extractor usually begins with experiments in a pilot-scale plant. The present correlations for the phase flow, coalescence behavior, mass transfer, etc., for different extractor types, are functions of the apparatus geometry, operating conditions, and substance properties. They mainly describe the behavior in observed experiments. Coalescence times, number of stages and height, flooding point, holdup, and optimal operating conditions (optimum value of the residence time) are found experimentally. They are used with applicable scale-up methods from the manufacturing companies, to design and dimension the full-scale extractor.

6.3 Solid-Liquid Extraction (Leaching) Solid-liquid extraction [0.1, 0.8, 6.20, 6.77-6.801 is mainly applied as percolation extraction in cross-flow and countercurrent flow and as immersion extraction in discontinuous or continuous modes. With percolation extraction, the mechanically ground and decomposed solid is moved through the extraction apparatus from stage to stage and sprayed with solvent. In this case, the solvent is enriched with the key component. Percolation extraction may only be applied to solids which allow the throughflow of solvent in a packed bed state. When the permeability of the solid is too low, immersion extraction is used. Here the solid is suspended in the solvent or is intermediately

6.3 Solid-Liquid Extraction (Leaching)

459

extracted and then separated from the enriched liquid phase, either discontinuously or by using a decanter, or continuously using special extraction apparatus. Solid-liquid extraction can be distinguished from liquid-liquid extraction by the following characteristics : 0

Fig. 6-47. Qualification of different extractors. The size of rectangle in each field is a scale of how good the extraction apparatus fulfills the quality factor. Representation according to MULLER[0.1, Vol. 21. Quality factors 1 Investment costs 2 Operating costs 3 Possibility of high stage number 4 Possibility of large throughput 5 Flexibility (reliable operation at fluctuating operating conditions) 6 Low holdup of both phases 7 Low holdup of either one of the two phases 8 Required floor space 9 Required structural height 10 Ability to treat system with emulsion formation tendency 11 Difficulties to scale-up from experimental scale to production scale

Extrmtor types I I1

I11 IV

V VI VII VIII IX

X

Spray column Packed column Sieve tray column Rotating disc contactor Mixed column Graesser contactor Pulsed column Mixer-Settler cascade Mixer-Settler tower Centrifugal extractor

0

No defined distribution coefficients exist for the distribution of the valuable or key component in the feed and solvent phase. A true equilibrium state is hardly ever reached since the solid always contains undissolved key component inside the capillaries and the enriched solvent contacts the solid surface with different key component loadings. An apparent equilibrium is reached when the solution inside the capillaries is of the same concentration as the free solution. The time required to reach this apparent equilibrium is a decisive function of the type, particle size and porosity of the solid, the solubility of the solvent, and the temperature. Usually, a temperature increase favors solid-liquid extraction. Some of the solvent, the “bonded solution”, remains bonded to the solid particle surface due to adsorption. The higher the percolation velocity, the lower the fraction of bonded solution.

Solid-liquid extraction may also be presented in a simplified equilateral triangle. With cross-current leaching, fresh solvent is added to the solid stagewise. For example, in the first extraction stage, fresh solvent is added to solid with an initial concentration w, at the state point F (Fig. 6-50). The mixing point P, lies at the intersection of the line FL with the line SP, representing the chosen solvent ratio v = i/f In the first extraction stage, the extract phase has the state point Q1. (Q, lies at the intersection of the extension of TP, and the triangle side KL,according to the separation of the mixture into the pure carrier P, and

460

6 Extraction

a1

I

bl

n, [rn-

0

10

20

30

6 [rn3/(m2-hl]-

50

LO

Fig. 6-48. Maximum efficiency of different extractor types as a function of total load. Representation according to PILHOFER, S C H R ~ E[6.46]. R

a) System: Toluene/Acetone/Water Symbol Extractor type ps[ 0701 U

V I 0

+

0

MCE Kuhni column

PSE PSE

PSE PSE

10.8 11.8

22.0 33.0 39.0

50.0

b) System: Toluene/Acetone/Water n EC column A SHE column