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Heat and Mass Transfer
Series Editors: D. Mewes and F. Mayinger
Springer-Verlag Berlin Heidelberg GmbH
Engineering ONLINE LIBRARY
http://www.springer.de/engine/
Hans-J org Bart
Reactive Extraction
With 101 Figures
Springer
Series Editors Prof. Dr.-lng. Dieter Mewes Universitat Hannover lnstitut fiir Verfahrenstechnik CallinstraBe 36 30167 Hannover, Germany
Author
Prof. Dr.-lng. E. h. Franz Mayinger Technische Universitat Miinchen Lehrstuhl A fur Thermodynamik BoltzmannstraBe 15 85748 Garching, Germany
Prof. Dipl.-lng. Dr. Hans-J org Bart Universitat Kaiserslautern FB Maschinenbau und Verfahrenstechnik Lehrstuhl fur Thermische Verfahrenstechnik Gottlieb-Daimler-StraBe 67663 Kaiserslautern, Germany
ISBN 978-3-642-07430-1
Library of Congress Cataloging-in-Publication Data applied for Die deutsche Bibliothek - cIP-Einheitsaufnahme
Bart, Hans-Jorg: Reactive extraction / Hans-Jorg Bart. - Berlin; Heidelberg; New York ; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 2001
(Heat and mass transfer) (Engineering online library)
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under German Copyright Law.
© Springer-Verlag Berlin Heidelberg 2001
UrsprOnglich erschienen bei Springer-Verlag Berlin Heidelberg New York io 2001
Softcover reprint of the hardcover 1st edition 2001
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Typesetting: Camera-ready by author Cover design: de'blik, Berlin
Printed on acid-free paper SPIN: 10775055 61/3020 CU - 5 43210 -
ISBN 978-3-642-07430-1 ISBN 978-3-662-04403-2 (eBook) DOI 10.1007/978-3-662-04403-2
Preface
This booklet is designed to bridge the gap between handbooks and technical literature and aims at graduate students or experienced readers. Commercial flow sheeting simulation software is increasingly available and is used in the early steps of process design in industry. As to this, more sophisticated and precise models based on activities instead of concentrations should be used. After an introductory chapter there is in Chapter 2 an intensive discussion of reactive phase equilibria of ionic and non-ionic solutes based on chemical potentials. Chapter 3 introduces to multicomponent diffusion and mass transfer. However, the main focus is on the reactive mass transfer on rigid and mobile surfaces where the interfacial reaction, molecular diffusion and adsorption layers are decisive. The respective extraction of zinc with a cation exchanger and of acetic acid with an anion exchanger is discussed as case studies. Since adsorption layers and surfactants have a major impact on liquid-liquid extraction efficiency, the final chapter reviews several techniques which make use of polymeric species in an extractive process. A short review is also given on extraction apparatus and the hydrodynamics (hydraulic design, droplet populance balances) of columns.
Much of the booklet is based on the PhD works of C. Czapla (2000), G. Modes (2000), H. Klocker (1996), T. Kronberger (1995), M. Marters (2000), M. Roos (2000), M. Traving (2000) and B. Wachter (1996) who I wish to thank for their fruitful contributions. I also appreciate the stimulating discussions I have had with Dr. M.J. Slater (University of Bradford, Great Britain) and Prof. J.A. Wesselingh (University of Groningen, The Netherlands) which helped clarify my thinking and led me to new ways of presenting some of the material. Special thanks go to my wife Ariane and my secretary I. Behrendt for typing and retyping the drafts, to Prof. Dr. J. Draxler (Montanuniversitat Leoben, Austria) for proof-reading the text and to my co-worker D. Bosse who helped with the text, figures and final tedious layout of the book.
Kaiserslautern, September 2000 Hans-Jorg Bart
Table of Contents
NOMENCLATURE ............................................................................................. IX
1 REACTIVE EXTRACTION ........................................................................ 1
1.1 INTRODUCTION .......................................................................................... 1 1.2 PHYSICAL EXTRACTION SYSTEMS ............................................................. 4 1.3 CHEMICAL EXTRACTION SYSTEMS .......................................................... 10 1.4 PROCESS DEVELOPMENT AND DESIGN ..................................................... 13
2 LIQUID-LIQUID PHASE EQUILIBRIA ................................................ 17
2.1 EQUILIBRIUM CONDITIONS ...................................................................... 17 2.2 NON-IONIC SYSTEMS ............................................................................... 21
2.2.1 The Regular Solution Theory ........................................................... 21 2.2.2 Solvatochromic Models .................................................................... 23 2.2.3 Margules Equation ........................................................................... 26 2.2.4 NRTL Model ..................................................................................... 27 2.2.5 UN1QUAC Model ............................................................................. 28 2.2.6 Group Contribution Methods ........................................................... 30
2.3 ELECTROLYTE SYSTEMS .......................................................................... 32 2.4 ION EXCHANGE EQUILIBRIA IN LIQUID-LIQUID SYSTEMS ...................... 37
2.4.1 Metal/Cation Exchange System ....................................................... 37 2.4.2 Acid/Anion Exchange System ........................................................... 47
3 REACTIVE MASS TRANSFER ............................................................... 51
3.1 INTRODUCTION ........................................................................................ 51 3.2 PHYSICAL MASS TRANSFER ..................................................................... 52
3.2.1 Fick's Law ........................................................................................ 52 3.2.2 The Maxwell-Stefan Law ................................................................. 55 3.2.3 Electrolyte Systems .......................................................................... 61 3.2.4 Bootstrap Relation ........................................................................... 65 3.2.5 Estimation of Diffusion Coefficients ................................................ 66 3.2.6 Mass Transfer .................................................................................. 74
3.3 REACTIVE EXTRACTION KINETICS ........................................................... 82 3.3.1 Suifactants, Zeta Potential and the Initial Reaction Rate ............... 82 3.3.2 Microkinetics ofZn-D2EHPA ........................................... .............. 90 3.3.3 Macrokinetics ofZn-D2EHPA ...................................................... 105 3.3.4 Microkinetics of Acid Extraction with TOA ................................... 119 3.3.5 Macrokinetics of Acid Extraction with TOA .................................. 128
VIII Table of Contents
4 CURRENT DEVELOPMENTS AND APPARATUS TECHNIQUES 131
4.1 LIQUID-LIQUID CONTACTING ............................................................... 131 4.2 POLYMERIC EXTRACTION SYSTEMS ...................................................... 140
APPENDIX A - CONVERSION FROM MOLAR TO MOLAL .................. 150
APPENDIX B - ACTIVITY COEFFICIENT CONVERSION ..................... 153
APPENDIX C - OPERATION AND DESIGN OF A SIEVE TRAY ........... 156
C.1 OPERATING AND DESIGN VARIABLES .................................................. 157 C.2 OPERATING LIMITS .............................................................................. 158 C.3 THE MANY VARIABLES ....................................................................... 159 CA BOUNDARIES OF THE OPERATING RANGE AND DESIGN VARIABLES ... 159
C.4.] Inactive Holes ................................................. ............................... 159 C4.2 Entrainment ................................................................................... 161 C4.3 Column Diameter .......................................................................... 162 C4.4 Height of the Coalescence Layer .................................................. 162 C4.5 Slip Velocity and Flooding .............................................. .............. 164 C.4.6 Tray Operation ............................................. ................................. 166 C4.7 Design a Sieve Tray .................................................. ..................... 168
APPENDIX D - THE LAP MODEL FOR MULTICOMPONENT MIXTURES ................................................................................................ 172
APPENDIX E - PHYSICAL AND CHEMICAL PROPERTIES FOR ZnID2EHPA AND HAclTOA .................................................................... 178
LITERATURE ................................................................................................... 183
AUTHOR INDEX .............................................................................................. 203
SUBJECT INDEX .............................................................................................. 207
Nomenclature
A
A,R,C
a
a
C1 , ••• , C4
C;;, Cu
C¢
c,
D
D
D
D2EHPA
D. '1
Interfacial area [m']
Margules parameter [-]
Area downcomer [m']
Area of holes [m2]
Tray area [m']
Debye-Htickel constant [m312morl12]
Specific interfacial area [m2/m3]
Ionic radius [m]
Activity of species i [-]
Activity of water [-]
Coefficient [-]
Function of the Maxwell-Stefan diffusion coefficients and mol fractions of a mixture [s/m2]
Instability constant [-]
Constant [depends]
Kinetic constants [depends]
Density of energy of cohension [cal/cm3]
Pitzer parameter [-]
Solvatochromic parameter [-]
Molar density of species i [mol/L]
Molar density of solvent [mollL]
Molar mixture density [mollL]
Initial molar density [mollL]
Standard molarity (l mollL) [mollL]
Distribution coefficient [-]
Diameter [m]
Fick's diffusion coefficient (binary) [m2/s]
Di(2-ethylhexyl) phosphoric acid
Fick's diffusion coefficient[m2/s]
X Nomenclature
D,/ Diffusion coefficient at infinite dilution (x,---70) [m'/s]
D ~ Axial dispersion coefficient [m2/s]
Dk Column diameter [m]
[) Maxwell-Stefan diffusion coefficients (binary) [m2/s]
[)'j Maxwell-Stefan diffusion coefficients [m'/s]
DR Rotor diameter [m]
Ds Stator diameter [m]
d Droplet diameter [m-1]
d, Driving force for mass diffusion [m-']
ds Sauter diameter [m]
dh Hole diameter [m]
E Activation energy [llmol]
E Eddy diffusivity [m's-l]
e Elementary charge (1.602 x 10-19 C) [C]
F, Force per mol of species i [N/mol]
F, Force per kg [N/kg]
FR Friction force [m-1]
f Fugacity [Pal
1;2 Friction coefficient [sm-']
5 Faraday constant (9.65.104 x C/mo!) [C/mol]
G Gibbs energy [1]
Gu NRTL Boltzmann factor [-]
GE Gibbs excess energy [1]
GJD Gibbs energy (ideal mixture) [1]
g Partial molar Gibbs energy [llmol]
g Acceleration due to gravity (9.81 m/s2) [m/s']
g(d) Break-up frequency of a droplet with diameter d [S-I]
g' UNIQUAC Gibbs combinatorial energy [llmol]
g' Partial molar Gibbs excess energy [llmol]
gJD Partial molar Gibbs energy (ideal mixture) [llmol]
gij NRTL Gibbs residual energy [llmol]
g" UNIQUAC Gibbs residual energy [llmol]
H Enthalpy [1]
HAc Acetic acid
Hel Hydrochloric acid
I
I
K
k
k"
k
k,
k,,"
k,
l.. 'J
to
m
m,
Compartment height [m]
Enthalpy (ideal mixture) [J]
Excess enthalpy [J]
Henry constant [Pal
Column height [m]
Tray spacing [m]
Nomenclature XI
Partial molar enthalpy [J/morl]
Height of coalescence layer [m]
Partial molar enthalpy (ideal mixture) [J/morl]
Partial molar excess enthalpy [J/mol-I]
Ionic strength [mol/kg]
Current density of a mixture [AIm']
Molar diffusion flux [mol m's-I]
Molar diffusion flux relative to the solvent velocity [mol m-'s-I]
Equilibrium constant [depends]
Mass transfer coefficient [mls]
High flux mass transfer coefficient [mls]
Boltzmann constant (1.38066 x 10-23 J K-I) [J K-I]
Kinetic constant (forward reaction) [depends]
Pseudo kinetic constant (forward reaction) [depends]
Kinetic constant (reward reaction) [depends]
Pseudo kinetic constant (reward reaction) [depends]
Friction factor [-]
Characteristic length [m]
Binary parameter [-]
Film thickness [m]
Film thickness (org. phase) [m]
Film thickness (aqu. phase) [m]
Methyl isobutyl ketone
Molar weight of species i [g/mol]
Molar weight of water [g/mol]
Contamination factor [-]
Molal density of species i [mol/kg]
Standard molality (1 mol/kg) [mol/kg]
XII
N
NaDdS
NaLS
NA
N£
N;
N p
N,
Nh
n
nl
n ,
n w
p
p; 0
p; I
P
P
P
Q
Q
Q,
Qd
q;
r;
RO
R
[RHl
[R2 H,l
r
S
S
Nomenclature
Revolutions per second [s-']
Sodium dodecane sulfonate
Sodium lauryl sulfate
Avogadro number (6.02205 x 10" mol-') [mor']
Number of experiments [-]
Molar flux of a component i relative to a stationary reference frame [mol m-2 s-']
Number of model parameters [-]
Mixture molar flux relative to a stationary reference frame [mol m-'s-']
Number of holes [-]
Number of species in a mixture [-]
Number of ionic species in a mixture [-]
Moles of species i [mol]
Moles of water [mol]
Pressure [Pal
Partial pressure of component i [Pal
Vapor pressure of component i [Pal
Vapor pressure of a liquid mixture [Pal
Standard pressure (0.1 MPa) [Pal
Probability [-]
Throughput [m3s-']
Factor (= p qq) [-]
Continuous phase flow [m's-']
Dispersed phase flow [m's-']
Van der Waals' surface [m']
Van der Waals radius [m]
Initial reaction rate [mol m-3 s-']
Gas constant (8.31441 J K-'mor') [J K-'mor']
Ion exchanger concentration [mol/m']
Ion exchanger dimer concentration [mol/m 3]
Radius [m]
Entropy [J K-']
Constant in the Masson equation cm3mol-'(mollLf'l2]
s
s
T
TBP
TOACl
TOA
TX100
t,
u
u,
U. 'J
v V,
V,
V,
w
x
x,
Llx,
Y,
z
z,
Nomenclature XIII
Source term breakage [-]
Source term coalescence [-]
Partial molar entropy [Jmol-'K-']
Surface renewal frequency [s-']
Temperature [K]
Tributylphosphate
Dodecyltrimethylammonium chloride
Trioctyl amine
Octylpoly(ethylglycolether),o' Triton X-lOO
Time [s]
Exposure time [s]
Transference number [-]
Hole velocity [mls]
Downcomer velocity [mls]
Molar average reference velocity [mls]
Velocity of diffusion of species i [mls]
UNIQUAC interaction parameter [J mol-i]
Velocity of diffusion of solvent [mls]
Volume [m3]
Partial molar volume of component i [m3/mol]
Slip velocity [mls]
Partial molar volume of solvent [m3/mol]
Partial mean molar volume [m3/mol]
Partial molar volume of water [m3/mol]
Velocity [mls]
Droplet rising velocity [mls]
Terminal velocity [mls]
X-direction [m]
Mol fraction of component i [-]
Mol fraction difference between bulk and interface [-]
Experimental value [depends]
Simulated value [depends]
Z-direction [m]
Charge of an ionic species [-]
Downcomer height [m]
XIV Nomenclature
Greek letters
a,
a
a
r
r
'1
y
y
a,
°i
'1
0,)
E
Solvatochromic parameter [-]
Pitzer parameter [-]
NRTL parameter [-]
Langmuir constant [mol/m2]
Daughter droplet distribution density [m- I]
Solvatochromic parameter [-]
Binary Pitzer parameter [-]
Thermodynamic factor (binary) [-]
Thermodynamic factor [-]
Interfacial coverage [mol/m']
Activity coefficient, mole fraction, sym. [-]
Activity coefficient, mole fraction, non-sym. [-]
Activity coefficient, molar scale, non-sym. [-]
Activity coefficient, molal scale, non-sym. [-]
Mean electrolyte activity coefficient [-]
Activity coefficient, infinite dilution [-]
Langmuir constant [mol/m3]
Solvatochromic parameter [-]
Hildebrand-Scott solubility parameter [cal"'cm-3/2]
Kronecker delta (oij = 1, if i = j; Oil = 0, if i * j) [-] Porosity [-]
Dielectricity constant, vacuum (8.85419 r 1C2m-l)
[r1C2m- l ]
Dielectricity constant, relative to vacuum( E = Eo E) [-]
UNIQUAC average segment fraction [-]
Apparent molar volume of an ionic species [cm3/mol]
Apparent molar volume of an ionic species at infinite
dilution [cm3/mol]
Electrical potential [V]
Hold-up [-]
Fugacity coefficient [-]
Osmotic coefficient [-]
/( )
/(,
/(,
o 00 E9 0
J1 i' J1 i' J1 i' J1
v
a
a
"'jjk
Viscosity, dynamic [mPa s]
UNIFAC surface fraction [-]
Electrical potential [V]
Nomenclature XV
Weisz-Prater criterion [-]
Interfacial electrical potential [V]
UNIFAC parameter [-]
Equivalent conductivity, mixture [S/m]
Debye-Hiickel constant [m-I ]
Equivalent conductivity, species [S/m]
Overall forward reaction rate constant [depends]
Overall reward reaction rate constant [depends]
Solvatochromic parameter [-]
Binary Pitzer parameter [-]
Chemical potential [J/mol]
Standard chemical potential [J/mol]
Standard molar chemical potential of solvation
[J/mol]
Viscosity, kinematic [m2s]
Stoichiometric coefficient [-]
Number of structural groups [-]
Solvatochromic parameter [-]
UNIQUAC area fraction [-]
Density, species [kg/m3]
Density, mixture [kglm3]
Density, solvent [kg/m3]
Density, water [kg/m3]
Regression parameter [-]
Interfacial tension [N/m]
Solvatochromic parameter [-]
NRTL resp. UNIQUAC parameter [-]
Ternary Pitzer parameter [-]
Pitzer parameter [-]
Zeta potential [V]
XVI Nomenclature
Further symbols
()
[ ]
[ ]
[I]
Subscripts
ad
aq
av
c
crit
d
D
DIL
elf
h
I
o
P
T
T
tot
w
Superscripts
c
C
E
G
H
lD
L
Vector
Concentration [mol/L]
Matrix
Identity matrix [-]
Overbar denotes organic species
Gradient at constant pressure and temperature
Delta
Interfacially adsorbed
Aqueous
Average between bulk and interface
Continuous phase
Critical
Dispersed phase
Downcomer
Diluent
Effective
Hole
Interfacial
Initial
Particle
Terminal
Tray
Total
Water
Referring to molarities
Combinatorial
Excess
Referring to gas phase
Referring to Henry law
Ideal
Referring to liquid phase
m
R
x
a
f3
o
Dimensionless numbers
Ar= ilp g d p
Pc (1)c / PC)2
il d 2 W Eo= P g h e (J Fr
Dt, Fo=-
d 2 p
u 2 Fr=_h_
g d h
Nu =~ C DC Pc ij
wi Pe=
D
Sc =v/ D
Sh=~ D
Referring to molalities
Residual
Referring to mol fractions
Referring a phase
Referring f3 phase
Referring to infinite dilution
Referring to pure component
Archimedes number
Bodenstein number
Eotvos number
Fourier number
Froude number
Liquid number
Hadamard-Rybcynski factor
Nusselt number
Peclet number
Slip Reynolds number
Nomenclature XVII
Single droplet Reynolds number
Hole Reynolds number
Schmidt number
Sherwood number
XVIII Nomenclature
We= VI; Pd d h Weber number (J
p~" d D~6(WI8 - w;;:,)1J~2 Modified Weber number [Cauwenberg 1995] We mcau , (J
Pc d D; N 2 Rotor Weber number We R -'---'------"--(J