Transport Mechanisms in Membrane Separation Processes

ISBN-13: 9781461366362 / Angielski / Miękka / 2012 / 219 str.

J. G. a. Bitter

Opis

The present book contains a comparison of existing theoretical models developed in order to describe membrane separation processes. In general, the permeation equations resulting from these models give inaccurate predictions of the mutual effects of the permeants involved, due to the simplifications adopted in their derivation. It is concluded that an optimum description of transport phenomena in tight (diffusion-type) membranes is achieved with the "solution-diffusion" model. According to this model each component of a fluid mixture to be separated dissolves in the membrane and passes through by diffusion in response to its gradient in the chemical potential. A modified Flory-Huggins equation has been derived to calculate the solubility of the permeants in the membrane material. Contrary to the original Flory-Huggins equation, the modified equation accounts for the large effect on solubility of crystallinity and elastic strain of the polymer chains by swelling. The equilibrium sorption of liquids computed with this equation was found to be in good agreement with experimental results. Also, the sorption of gases in both rubbery and glassy polymers could be described quan- titatively with the modified Flory-Huggins equation without any need of the arbitrary Langmuir term, as required in the conventional "dual-mode" sorption model. Furthermore, fewer parameters are required than with the at least identical accuracy.

Spis treści

1. Introduction.- 2. Types of Membrane Separation Processes, Mechanisms of Separation.- 2.1. Porous Membranes.- 2.2. Liquid Membranes.- 2.3. Tight Membranes.- 2.4. Selection of Membrane Separation Processes and Mechanisms.- 3. Survey of Membrane Separation Models.- 3.1. Irreversible Thermodynamics.- 3.2. Preferential Sorption-Capillary Flow Theory.- 3.3. The Solution-Diffusion Model.- 3.4. Viscous Flow Models; Accounting for Imperfections.- 3.5. Models for the Separation of Gas (Vapor) Mixture.- 3.6. Concentration Polarization.- 3.7. Blocking, Fouling, and Poisoning.- 4. Comparison of Membrane Permeation Models.- 4.1. Liquid Separations.- 4.2. Gas Separations.- 4.3. A New Permeation Model for Gases and Liquids.- 5. Basic Diffusion Equation.- 5.1. Introduction.- 5.2. The Maxwell-Stefan Equation.- 5.3. Equation of Darken, Prager, and Crank.- 5.4. The Modified Maxwell-Stefan Equation.- 6. Solubility of Permeants in Semi-Crystalline and Crosslinked Polymers.- 6.1. Solubility of Liquids in Polymers.- 6.2. Modified Equation for the Partial Molar Entropy of Mixing.- 6.3. Partial Molar Enthalpy of Mixing.- 6.4. The Modified Flory-Huggins Equation.- 6.5. Solubility of Gases in Polymers.- 6.6. The Modified Flory-Huggins Equation for Gases.- 7. Comparison and Experimental Check of the Solubility Equations.- 7.1. Swelling of Polyolefins.- 7.2. Swelling of Natural Rubber in Binary Solvent Mixtures.- 7.3. Swelling of Cellulose Diacetate in Mixtures of Ethanol and Water.- 7.4. Solubility of N2O, CO2, and C2H4 in PMMA.- 7.5. Solubility of CO2 and CH4 in Polysulfone.- 8. Prediction of Diffusivity in Multi-Component Mixtures.- 8.1. Basic Diffusivity.- 8.2. Concentrated Solute Diffusivity.- 8.3. Estimation of Diffusion Coefficients.- 8.4. Mixture Viscosity.- 8.5. Prediction of Diffusivity from Mixture Viscosity.- 9. New Permeability Equations.- 9.1. Introduction.- 9.2. Effect of Crystallinity and Swelling on Permeability.- 9.3. Specific Diffusion Rate.- 9.4. Simplified Calculation Procedure of Membrane Permeation.- 9.5. Stress Distributions Inside Membranes.- 9.6. Effect of Pressure Gradients Inside Membranes on Permeation.- 9.7. Permeability Equation for Gases.- 10. Permeation Experiments (Program and Procedures).- 10.1. Membranes Tested.- 10.2. Pervaporation Experiments.- 10.3. Reverse Osmosis Experiments.- 10.4. Dialysis Experiments.- 11. Results of Permeation Experiments.- 11.1. Effect of Permeation Time on Flux and Selectivity.- 11.2. Effect of Composition and External Driving Force on Flux and Selectivity.- 12. Experimental Check of the Permeation Equations.- 12.1. Concentration Dependence of the Mean Diffusivity.- 12.2. Prediction of Selectivity in Pervaporation.- 12.3. Comparison of Calculated and Measured Permeation in Reverse Osmosis.- 12.4. Comparison of Calculated and Measured Permeation by Dialysis.- 12.5. Mutual Effect of Hydrocarbons on their Permeability.- 12.6. Pervaporation of Ethyl Alcohol/Water Mixtures through Cellulose Diacetate Membranes.- 12.7. Permeability of Gases in Polysulfone.- 12.8. Permeability of Mixtures of CO2 and CH4 in Polyisoprene.- 13. Optimum Choice of Polymers for Membrane Preparation.- 14. Discussion and Conclusions.- Appendix I. Irreversible Processes Near Equilibrium.- I.1. Introduction.- I.2. Theory of Near-Equilibrium Processes.- I.3. Entropy Production in Irreversible Flow Processes.- I.4. Rate of Entropy Production; Dissipation Function.- I.5. Phenomenological Equations.- I.6. Requirements of the Phenomenological Coefficients.- I.7. Application of IT/OR/ORR in Membranes; The Kedem-Katchalsky Mode.- Appendix II. Derivation of the Concentration Polarization Equation of Gases.- II.1. Continuity Equation.- II.2. Transport Equation for Tight Membranes.- II.3. Experiments and Results.- Appendix III. Derivation of The Maxwell-Stefan Equation.- Appendix IV. Derivation of the Modified Maxwell-Stefan Equation.- Appendix V. Theory of the Entropy of Mixing.- V.1. Derivation of the Entropy Equation.- V.2. Entropy of Elastic Strain.- Appendix VI. Partial Molar Mixing Enthalpy of Multicomponent Mixtures.- Appendix VII. Solubility Equation for Gases in Polymers.- Appendix VIII. Evaluation and Estimation of Swelling Parameters.- VIII.1. Crystallinity.- VIII.2. Coordination Number.- VIII.3. Partial Molar Volume.- VIII.4. Partial Molar Heat of Mixing.- VIII.5. Activity of Permeants and Permeant Mixtures.- VIII.6. Elastic Strain Factor.- Appendix IX. Self-Diffusivity in Multicomponent Mixtures.- Appendix X. Viscosity of Multicomponent Mixtures.- Appendix XI. Estimation of the Geometric Diffusion Resistance.- Appendix XII. Approximate Solution of the General Differential Equation of Membrane Permeation.- Appendix XIII. Derivation of the Gas Permeation Equation.- List of Symbols.- References.