Membrane Filtration 111 CAMBRIDGE. A Problem Solving Approach with MATLAB GREG FOLEY UNIVERSITY PRESS. Dublin City University

Transcription

1 Membrane Filtration A Problem Solving Approach with MATLAB GREG FOLEY Dublin City University 111 CAMBRIDGE UNIVERSITY PRESS

2 Contents Preface Abbreviations page xv xviii 1 Introduction to membrane filtration of liquids Introduction Definitions and terminology Dead-end and crossflow configurations Key process parameters in membrane filtration Solute and particle rejection Membranes and their properties Membrane materials Membrane morphology Membrane modules Flat sheet and spiral wound modules Shell-and-tube modules Stirred cells Flux characteristics in membrane filtration Dead-end filtration Crossflow configuration Conclusions 14 References 15 Additional reading 15 2 Dead-end filtration Introduction to dead-end filtration The filtrate flux equation The specific cake resistance Cake compressibility Effects of particle and liquid properties Filter aids Analysis and design of batch dead-end filtration Analysis and design of batch DEF at constant pressure Analysis of batch DEF at constant filtrate flux 31

3 viii Contents Analysis of batch DEF with a centrifugal pump Continuous filtration Modelling product transmission in DEF Conclusions 41 References 42 Problems 43 Further problems 45 3 Crossflow microfiltration Introduction Modes of operation Flux characteristics during continuous operation Theories of crossflow microfiltration Concentration polarisation and shear-induced diffusion The force balance approach The spatial dependence ofthe flux A simple kinetic model of CFMF Steady state behaviour Dynamic behaviour Constant flux operation Linking the kinetic model with force balance theory Flux dynamics with a transition flux Process design and analysis Analysis of a continuous feed-and-bleed system Modelling the dynamics of batch CFMF Fed-batch operation Cake properties in CFMF Improving the flux Backflushing Crossflushing Air sparging Product recovery in CFMF Conclusions 83 References 84 Problems 85 Further problems 86 4 Ultrafiltration flux theories Introduction Concentration polarisation Prediction of mass transfer coefficients Prediction of diffusion coefficients Prediction of solution viscosity 95

4 Contents ix 4.4 The limiting flux (LF) model The osmotic pressure (OP) model Flux characteristics predicted by the osmotic pressure model The osmotic pressure model with viscosity effects Is the VOP model 'correct'? Conclusions 116 References 116 Problems 117 Further problems Ultrafiltration process analysis and design at the limiting flux Introduction Continuous feed-and-bleed ultrafiltration Analysis of a single-stage system Analysis of a multi-stage system Analysis of a multi-stage system using ordinary differential equations Analysis of a multi-stage system using a graphical method Design of a single-stage system Design of a multi-stage system with equal areas Optimisation of multi-stage systems Design with viscosity dependent mass transfer coefficient Batch ultrafiltration Calculation of final conditions for a fixed time Calculation of batch time by solution of governing ODE Calculation of batch time using special functions Approximate methods for calculating the batch time Fed-batch operation Single pass operation Single pass analysis with viscosity independent mass transfer coefficient Single pass analysis with viscosity dependent mass transfer coefficient Single pass design with constant mass transfer coefficient Membrane fouling and limiting flux operation Conclusions 148 References 148 Problems 149 Further problems Diafiltration at the limiting flux Introduction Discontinuous diafiltration 152

5 x Contents Volume reduction method Dilution method Constant volume diafiltration Water consumption in CVD Time taken for CVD Ultrafiltration with constant volume diafiltration (UFCVD) UFCVD time optimisation with viscosity dependent mass transfer coefficient Economic optimisation of UFCVD Economic optimisation with viscosity dependent mass transfer coefficient Optimisation of UFCVD when Ca( < caopt Dynamic modelling of UFDF processes Dynamic modelling of UFCVD Dynamic modelling of variable volume diafiltration (WD) Generalised WD processes and dynamic optimisation Diafiltration of suspensions Continuous diafiltration Two-stage continuous UFDF Counter-current diafiltration Dialysis Conclusions 190 References 190 Additional reading 191 Problems 191 Further problems Ultrafiltration and diafiltration with incomplete rejection Introduction Quantifying rejection Concentration polarisation Flux dependence of the apparent rejection coefficient Continuous feed-and-bleed ultrafiltration Analysis and design of a single-stage system Solving single-stage problems using a graphical method Analysis and design of two-stage systems Batch ultrafiltration Batch UF with constant apparent rejection Batch UF with constant intrinsic rejection Fed-batch ultrafiltration Single pass ultrafiltration Constant volume diafiltration Computation of diafiltration time 211

6 Contents xi UFCVD with arbitrary rejection coefficients Dynamic modelling of UFCVD Optimisation of UFCVD with arbitrary rejection coefficients Variable volume diafiltration Conclusions 219 References 220 Additional reading 220 Problems 220 Further problems The osmotic pressure model applied to ultrafiltration and diafiltration Introduction Analysis and design of continuous feed-and-bleed UF Analysis and design of single-stage systems Multi-stage systems Dynamic modelling of batch UF Batch UF with constant mass transfer coefficient Batch UF with viscosity dependent mass transfer coefficient Fed-batch ultrafiltration Single pass ultrafiltration Constant volume diafiltration Optimisation of UFCVD Optimisation of UFCVD - constant mass transfer coefficient 235 viscosity dependent mass transfer coefficient Ultrafiltration with constant wall concentration The osmotic pressure model with incomplete rejection Single-stage feed-and-bleed UF Dynamic modelling of batch UF Constant volume diafiltration Product transmission in CFMF Conclusions 249 References 250 Additional reading 250 Problems 250 Further problems Reverse osmosis and nanofiltration Introduction to reverse osmosis Reverse osmosis theory Combining RO theory with concentration polarisation theory Predicting osmotic pressures Process configurations in RO Analysis of a continuous feed-and-bleed system 260

7 xii Contents 9.6 Analysis of a single pass system Reverse osmosis software Introduction to nanofiltration Nanofiltration theory Fed-batch nanofiltration Conclusions 270 References 270 Additional reading 271 Problems 271 Further problems Membrane fouling Introduction The 'blocking' view of fouling Empirical modelling Dead-end filtration Incompressible cakes Compressible cakes Crossflow microfiltration The apparent specific resistance Ultrafiltration Membrane fouling and the limiting flux Flux dynamics at constant composition Dynamics of continuous feed-and-bleed UF Constant volume diafiltration Ultrafiltration with constant volume diafiltration (UFCVD) Reverse osmosis and nanofiltration Conclusions 296 References 296 Problems 297 Further problems 298 Appendix: Mathematical and computational background 299 A.l Introduction 299 A.2 Calculus and symbolic computation 299 A.2.1 Differentiation 300 A.2.2 Series approximations to functions 303 A.2.3 Integration 304 A.3 Numerical solution of non-linear algebraic equations 306 A.3.1 The Newton-Raphson method 306 A.4 Numerical solution of ordinary differential equations 310 A.4.1 Euler's method for numerical solution of an ODE 310 A.4.2 Solution of systems of ODEs with the MATLAB function ode45 312

8 Contents xiii A.4.3 Differential algebraic equations 314 A.5 Numerical integration 315 A.6 Numerical differentiation 316 A.7 Non-linear regression 318 A.8 Conclusion 319 Further reading 319 Practice problems 320 Index 323