Basic Equations of the Mass Transport through a Membrane Layer

Basic Equations of the Mass Transport through a Membrane Layer

Volumn , Issue , 2011, Pages 1-329

  Nagy, Endre ^a  

^a UNIVERSITY OF PANNONIA   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85144350364     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/C2011-0-04271-0     Document Type: Book

References (375)

1. D.S. Abrams and J.M. Prausnitz (1975) Statistical thermodynamics of liquid mixtures: a new conception for the excess gibbs energy of partly or completely miscible mixtures. Am. Inst. Chem. 21 116-128.
2. N.R. Amundsen, T.-W. Pan and V.I. Paulsen (2003) Diffusing with Stefan and Maxwell. AIChE J. 49 813-830.
3. R.W. Baker (2004) Membrane Technology and Application 2nd ed. Chichester: John Wiley and Sons
4. R.B. Bird, W.E. Stewart and E.N. Lightfoot (1960) Transport Phenomena New York: John Wiley and Sons
5. J.G.A. Bitter (1991) Transport Mechanisms in Membrane Separation Processes Amsterdam: Shell-Laboratorium
6. P. Flory (1963) Principles of Polymer Chemistry New York: Cornell University Press
7. T.Q. Gardner, J.L. Falconer and R.D. Noble (2002) Adsorption and diffusion properties of zeolite membranes by transient permeation. Desalination 149 435-440.
8. C.J. Geankoplis (2003) Transport Processes and Separation Process Principles 4th ed. New Jersey: Prentice Hall
9. V. Geraldes and A.M. Brites (2008) Computer program for simulation of mass transport in nanofiltration membranes. J. Membr. Sci. 321 172-182.
10. A. Heintz and W. Stephan (1994) A generalized solution-diffusion model of the pervaporation process through composite membrane, Part I. Prediction of mixture solubilities in the dense active layer using the UNIQUAC model. J. Membr. Sci. 89 143-151.
11. A. Heintz and W. Stephan (1994) A generalized solution-diffusion model of the pervaporation process through composite membrane, Part II. Concentration polarization, coupled diffusion and the influence of the porous layer. J. Membr. Sci. 89 153-169.
12. D.L. Hoang, S.H. Chan and O.L. Ding (2005) Kinetic modeling of partial oxidation of methane in an oxygen permeable membrane reactor. Chem. Eng. Res. Design 82 177-186.
13. P. Izák, L. Bartovská, K. Friess, M. Sipek and P. Uchytil (2003) Description of binary liquid mixtures transport through non-porous membrane by modified Maxwell–Stefan equations. J. Membr. Sci. 214 293-309.
14. A. Janquiéres, L. Perrin, S. Arnold, R. Clément and P. Lochon (2000) From binary to ternary systems: general behavior and modeling of membrane sorption in purely organic systems strongly deviating from ideality by UNIQUAC and related models. J. Membr. Sci. 174 255-275.
15. H.D. Kamaruddin and W.J. Koros (1997) Some observation about the application of Fick’s first law for membrane separation of multicomponent mixtures. J. Membr. Sci. 135 147-159.
16. F. Kapteijn, W.J.W. Bakker, G. Zheng and J. Poppe (1995) Permeation and separation of light hydrocarbons through a silicalite-1 membrane. Application of the generalized Maxwell–Stefan equations. Chem. Eng. J. 57 145-153.
17. F. Kapteijn, J.A. Moulijn and R. Krishna (2000) The generalized Maxwell–Stefan model for diffusion in zeolites: sorbate molecules with different saturation loadings. Chem. Eng. Sci. 55 2923-2930.
18. R. Krishna (1990) Multicomponent surface diffusion of adsorbed species: a description based on the generalized Maxwell–Stefan equations. Chem. Eng. Sci. 45 1779-1791.
19. R. Krishna (1993) A unified approach to the modeling of intraparticle diffusion in adsorption processes. Gas. Sep. Purif. 7 91.
20. R. Krishna and R. Baur (2003) Modeling issues in zeolite based separation processes. Sep. Purif. Technol. 33 213-254.
21. R. Krishna and J.A. Wesselingh (1997) The Maxwell-Stefan approach to mass transfer. Chem. Eng. Sci. 52 861-911.
22. R. Krishna, T.J. Vlugt and B. Smit (1999) Influence of isotherm inflection on diffusion in silicalite. Chem. Eng. Sci. 54 1751-1757.
23. R. Krishna, J.M. van Baten, E. Garcia-Perez and S. Calero (2007) Incorporating the loading dependence of the Maxwell–Stefan diffusivity in the modeling of CH 4 and CO 2 permeation across zeolite membranes. Ind. Eng. Chem. Res. 46 2974-2986.
24. K.W. Lawson and D.R. Lloyd (1997) Membrane distillation: review. J. Membr. Sci. 124 1-25.
25. H.K. Lonsdale (1982) The growth of membrane and technology. J. Membr. Sci. 10 81-181.
26. S. Li, J.I. Falconer, R.D. Noble and R. Krishna (2007) Modeling permeation of CO 2/CH 4, CO 2/N 2 and N 2/CH 4 mixtures across SAPO-34 membrane with the Maxwell–Stefan equations. Ind. Eng. Chem. Res. 46 3904-3911.
27. S. Li, J.I. Falconer, R.D. Noble and R. Krishna (2007) Interpreting unary, binary and ternary mixture permeation cross a SAPO-34 membrane with loading-dependent Maxwell–Stefan diffusivities. J. Phys. Chem. C 111 5075-5082.
28. S.J. Lue, F.J. Wang and S.-Y. Hsiaw (2004) Pervaporation of benzene/cyclohexane mixtures using ion-exchange membrane containing copper ions. J. Membr. Sci. 240 149-158.
29. J.G. Martinek, T.Q. Gardener, R.D. Noble and J.L. Falconer (2006) Modelling transient permeation of binary mixtures through zeolite membrane. Ind. Eng. Chem. Res. 45 6032-6043.
30. E.A. Mason and A.P. Malinauskas (1983) Gas Transport in Porous Media: The Dusty Gas Model Amsterdam: Elsevier
31. E.E.B. Meuleman, B. Bosch, M.H.V. Mulder and H. Stratman (1999) Modeling of liquid/liquid separation by pervaporation: toluene from water. AIChE J. 45 2153-2160.
32. Mulder M. (1981) Pervaporation Separation of Ethanol–Water and Isomeric Xylenes. PhD Thesis, University of Twente, The Netherlands.
33. M.H.V. Mulder and C.A. Smolders (1984) On the mechanism of separation of ethanol/water mixtures by pervaporation I. Calculations of concentration profiles. J. Membr. Sci. 17 289-307.
34. E. Nagy (2004) Nonlinear, coupled mass transfer through a dense membrane. Desalination 163 345-354.
35. E. Nagy (2006) Binary, coupled mass transfer with variable diffusivity through cylindrical dense membrane. J. Membr. Sci. 274 159-168.
36. D.R. Paul (1976) The solution-diffusion model for swollen membranes. Sep. Purif. Methods 5 35.
37. M. Pedernera, M.J. Alfonso, M. Menéndez and J. Santamaria (2002) Simulation of a catalytic membrane reactor for the oxidative dehydrogenation of butane. Chem. Eng. Sci. 57 2531-2544.
38. D. Reed and G. Ehrlich (1981) Surface diffusion, atomic jump rates and thermodynamics. Surf. Sci. 102 588-609.
39. P. Schaetzel, Z. Bendjama, C. Vauclair and Q.T. Nguyen (2001) Ideal and non-ideal diffusion through polymers: application to pervaporation. J. Membr. Sci. 191 95-102.
40. A. Seidel-Morgenstern (2010) Membrane Reactors Weinheim: Wiley-VCH
41. P. Silva, L.G. Peeva and A.G. Livingston (2008) Nanofiltration in organic solvents. N.N. Li, A.G. Fane, W.S.W. Ho, T. Matsuura (Eds) Advanced Membrane Technology and Applications New Jersey: John Wiley and Sons 451-468.
42. A.I. Skoulidas, D.S. Sholl and R. Krishna (2003) Correlation effects in diffusion of CH 4/CF 4 mixtures in MFI zeolite. A study linking MD simulation with the Maxwell–Stefan formulation. Langmuir 19 7977-7988.
43. S. Thomas, R. Schafer, J. Caro and A. Seidel-Morgenstern (2001) Investigation of mass transfer through inorganic membrane with several layers. Catalysis Today 67 205-216.
44. A. Tuchlenski, P. Uchytil and A. Seidel-Morgenstern (2001) An experimental study of combined gas phase and surface diffusion in porous glass. J. Membr. Sci. 140 165-184.
45. J.M. Van de Graaf, F. Kapteijn and J.A. Moulijn (1999) Modeling permeation of binary mixtures through zeolite membranes. AIChE J. 45 497-511.
46. A. Vignes (1966) Diffusion in binary solutions. Ind. Eng. Chem. Fund. 5 189-199.
47. J.A. Wesselingh and R. Krishna (1990) Mass Transfer Chichester, U.K: Ellis Horwood
48. J.A. Wesselingh and R. Krishna (2000) Mass Transfer in Multicomponent Mixture Delft: Delft University Press
49. J.G. Wijmans (2004) The role of permeant molar volume in the solution-diffusion model transport equations. J. Membr. Sci. 237 39-50.
50. J.G. Wijmans and R.W. Baker (1995) The solution-diffusion model: a review. J. Membr. Sci. 107 1-21.
51. W. Zhu, J.M. Graaf, L.J.P. Broeke, F. Kapteijn and J.A. Moulijn (1998) TEOM: a unique technique for measuring adsorption properties. Light alkanes in silicalite-1. Ind. Eng. Chem. Res. 37 1934-1942.
52. R.W. Baker (2004) Membrane Technology and Application 2nd ed. Chichester: John Wiley and Sons
53. B. Bird, W.E. Stewart and E.N. Lightfoot (1960) Transport Phenomena New York: John Wiley and Sons
54. Bungay, P.M., Lonsdale, H.K., and de Pinho, M.N. (1983) Synthetic Membranes: Science, Engineering and Application, NATO ASI Series, D. Reidel Publishing Company, Vol 181.
55. R.M. Barrer (1939) Permeation, diffusion and solution of gases in organic polymer. Trans. Faraday Soc. 35 629-643.
56. J. Crank and G.S. Parks (1968) Diffusion in Polymers London: Academic Press
57. P. Dechadilok and W. Deen (2006) Hindrance factors for diffusion and convection in pores. Ind. Eng. Chem. Res. 45 6953.
58. W.M. Deen (1987) Hindered transport of large molecules in liquid-filled pores. AIChE J. 33 1409-1425.
59. E.N. Fuller, P.D. Schettler and J.C. Giddings (1966) Ind. Eng. Chem. 58 19.
60. C.J. Geankoplis Ch.J. (2003) Transport Process and Separation Process Principles 4th ed. Upper Saddle River: Prentice Hall
61. V. Geraldes and A.M. Brites (2008) Computer program for simulation of mass transport in nanofiltration membranes. J. Membr. Sci. 321 172-182.
62. J.Q. Hirschfelder, C.F. Curtiss and R.B. Bird (1954) Molecular Theory of Gases and Liquids New York: John Wiley and Sons
63. G.M. Mavrovouniotis and H. Brenner (1988) Hindered sedimentation diffusion and dispersion coefficient for Brownian spheres in circular cylindrical pores. J. Colloid Interface Sci. 124 269.
64. E.E.B. Meuleman, B. Bosch, M.H.V. Mulder and H. Strathmann (1999) Modeling of liquid/liquid separation by pervaporation: toulene from water. AIChE J. 45 2153-2160.
65. Mulder, M. (1981). Pervaporation Separation of Ethanol–Water and Isomeric Xylenes. PhD Thesis, University of Twente, The Netherlands.
66. E. Nagy (2004) Nonlinear, coupled mass transfer through a dense membrane. Desalination 163 345-354.
67. E. Nagy (2006) Binary, coupled mass transfer with variable diffusivity through cylindrical membrane. J. Membr. Sci. 274 159-168.
68. Y. Qin and J.M.S. Cabral (1998) Lumen mass transfer in hollow fiber membrane processes with nonlinear boundary conditions. AIChE J. 41 836-848.
69. J. Smart, V.M. Starov, R.C. Schucker and D.R. Lloyd (1998) Pervaporative extraction of volatile organic compounds from aqueous systems with use of a tubular transverse flow module. Part II. Experimental results. J. Membr. Sci. 143 159-179.
70. V. Soni, J. Abildskov, G. Jonsson and R. Gani (2009) A general model for membrane-based separation process. Computers Chem. Eng. 33 644-659.
71. W.R. Vieth, J.M. Howel and J.H. Hsieh (1976) Dual sorption theory. J. Membr. Sci. 1 177-220.
72. R.W. Baker (2006) Membrane Technology and Applications 2nd ed. Chichester: Wiley
73. J.G.A. Bitter (1991) Transport Mechanisms in Membrane Separation Processes Amsterdam: Shell-Laboratorium
74. M.V. Chandak, Y.S. Lin, W. Ji and R.J. Higgins (1998) Sorption and diffusion of volatile organic compounds in polydimethylsiloxane membranes. J. Appl. Polym. Sci. 67 165-175.
75. H.S. Carslaw and J.C. Jaeger (1959) Conduction of Heat in Solids Oxford: Clarendon Press
76. J. Crank (1975) Mathematics of Diffusion Oxford: Clarendon Press
77. F. Favre, Q.T. Nguyen, R. Clément and J. Néel (1996) The engaged species induced clustering (ENSIC) model: a unified mechanistic approach of sorption phenomena in polymers. J. Membr. Sci. 117 227-236.
78. N. Follain, J.-M. Valleton, L. Lebrun, B. Alexandre, P. Schaetzel, M. Metayer, et al. (2010) Simulation of kinetic curves in mass transport phenomena for a concentration-dependent diffusion coefficient in polymer membranes. J. Membr. Sci. 349 195-207.
79. A.A. Ghoreyshi, M. Jahanshahi and K. Peyvandi (2008) Modeling of volatile organic compounds removal from water by pervaporation process. Desalination 222 410-418.
80. J. Hauser, A. Heintz, B. Schmitttecker and R.N. Lichtenthaler (1989) Sorption equilibria and diffusion in polymeric membranes. Fluid Phase Equilib. 51 369-381.
81. A. Heintz and W. Stephan (1994) A generalized solution-diffusion model of the pervaporation process through composite membrane. J. Membr. Sci. 89 153-169.
82. P. Izák, L. Bartovská, K. Friess, M. Sipek and P. Uchytil (2003) Description of binary liquid mixtures transport through nonporous membrane by modified Maxwell–Stefan equation. J. Membr. Sci. 214 293-309.
83. W.J. Koros (1980) Model for sorption of mixed gases in glassy polymers. J. Polym. Sci. Phys. Ed. 18 981-992.
84. W.J. Koros, G.N. Smith and V.T. Stanett (1981) High-pressure sorption of carbon dioxide in solvent-cast poly(methyl methacrylate) and poly(ethyl methacrylate) films. J. Appl. Polym. Sci. 26 159-170.
85. R. Krishna and J.A. Wesselingh (1997) The Maxwell–Stefan approach to mass transfer. Chem. Eng. Sci. 52 862-906.
86. A. Kubaczka, A. Burghardt and T. Mokrosz (1998) Membrane-based solvent extraction in multicomponent systems. Chem. Eng. Sci. 53 899-917.
87. E. Meuleman, B.B. Bosch, M.H.V. Mulder and H. Strathmann (1999) Modeling of liquid/liquid separation by pervaporation: toulene from water. AIChE J. 45 2153-2160.
88. Mulder, M.H.V. (1984) Pervaporation Separation of Ethanol–Water and of Isomeric Xylenes. PhD Thesis, University of Twente, The Netherlands.
89. E. Nagy (2004) Nonlinear, coupled mass transfer through a dense membrane. Desalination 163 345-354.
90. E. Nagy (2006) Binary, coupled mass transfer with variable diffusivity through cylindrical membrane. J. Membr. Sci. 274 159-168.
91. E. Nagy (2008) Mass transport with varying diffusion and solubility coefficient through a catalytic membrane layer. Chem. Eng. Res. Des. 86 723-730.
92. D.R. Paul and W.J. Koros (1976) Effect of partially immobilizing sorption on permeability and the diffusion time lag. J. Polym. Sci. Phys. Ed. 14 675-685.
93. P. Schaetzel, C. Vauclair, Q.T. Nguyen and R. Bouzerar (2004) A simplified solution-diffusion theory in pervaporation: the total solvent volume fraction model. J. Membr. Sci. 244 117-127.
94. M.R. Shah, R.D. Noble and D.E. Clough (2007) Measurement of sorption and diffusion in nonporous membranes by transient permeation experiments. J. Membr. Sci. 287 111-118.
95. J.C. Slattery (1999) Advanced Transport Phenomena Cambridge: Cambridge University Press
96. Í. Tosun (2002) Modelling in Transport Phenomena New York: Elsevier
97. L.J.P. van den Broeke, W.J.W. Bakker, F. Kapteijn and J.A. Moulijn (1999) Binary permeation through a silicalite-1 membrane. AIChE J. 45 977-985.
98. J.M. van den Graaf, F. Kapteijn and J.A. Moulijn (1999) Modeling permeation of binary mixtures through zeolite membranes. AIChE J. 45 497.
99. W.R. Vieth (1988) Membrane Systems: Analysis and Design Munich: Hanser Publisher
100. J.A. Wesselingh and R. Krishna (2000) Mass Transport in Multicomponent Mixtures The Netherlands: Delft University Press
101. P.V. Danckwerts (1950) Absorption by simultaneous diffusion and chemical reaction. Trans. Faraday Soc. 46 300-305.
102. P.V. Danckwerts (1970) Gas-Liquid Reactions New York: McGraw-Hill
103. B.S. Ferreira, P. Fernandes and J.M.S. Cabral (2001) Design and modeling of immobilized biocatalytic reactors. J.M.S. Cabral, M. Mota, J. Tramper (Eds) Multiphase bioreactor design London: Taylor & Francis 85-180.
104. A. Julbe, D. Farusseng and C. Guizard (2001) Porous ceramic membranes for catalytic reactors—overview and new ideas. J. Membr. Sci. 181 3-20.
105. J.G.S. Marcano and T.T. Tsotsis (2002) Catalytic Membranes and Membrane Reactions Weinheim: Wiley-VCH
106. A. Mehra (1999) Heterogeneous modeling of gas absorption in emulsion. Ind. Eng. Chem. Res. 38 2460-2468.
107. A. Moser (1988) Bioprocess Technology Wien: Springer
108. E. Nagy (2002) Three-phase oxygen absorption and its effect on fermentation. Adv. Biochem. Eng. Biotechnol. 75 51-81.
109. E. Nagy (2006) Binary, coupled mass transfer with variable diffusivity through cylindrical membrane. J. Membr. Sci. 274 159-168.
110. E. Nagy (2007) Mass transfer through a dense, polymeric, catalytic membrane layer with dispersed catalyst. Ind. Eng. Chem. Res. 46 2295-2306.
111. E. Nagy (2008) Mass transport with varying diffusion- and solubility coefficient through a catalytic membrane layer. Chem. Eng. Res. Design 86 723-730.
112. E. Nagy (2009) Mathematical Modeling of Biochemical Membrane Reactors. E. Drioli, L. Giorno (Eds) Membrane Operations, Innovative Separations and Transformations Weinheim: Wiley-VCH 309-334.
113. E. Nagy (2010) Convective and diffusive mass transport through anisotropic, capillary membrane. Chem. Eng. Process. Process Intens. 49 716-721.
114. E. Nagy and A. Moser (1995) Three-phase mass transfer: Improved pseudo-homogeneous model. AIChE J. 41 23-34.
115. E. Nagy, T. Blickle and A. Ujhidy (1989) Spherical effect on mass transfer between fine solid particles and liquid accompanied by chemical reaction. Chem. Eng. Sci. 44 198-201.
116. E. Nagy, T. Blickle, A. Ujhidy and K. Horváth (1982) Mass transfer accompanied by first order intermediate reaction rate in two phase cocurrent flow with axial dispersion. Chem. Eng. Sci. 37 1817-1819.
117. I.F.J. Vancelecom and P.A. Jacobs (2000) Dense organic catalytic membrane for fine chemical synthesis. Catalysis Today 56 147-157.
118. J. Vital, A.M. Ramos, I.F. Silva, H. Valenete and J.E. Castanheiro (2001) Hydration of α-pinene over zeolites and activated carbons dispersed in polymeric membranes. Catalysis Today 67 217-223.
119. A.A. Yawalkar, V.G. Pangarkar and G.V. Baron (2001) Alkene epoxidation with peroxide in a catalytic membrane reactor: a theoretical study. J. Membr. Sci. 182 129-213.
120. T. Westermann and T. Melin (2009) Flow-through catalytic membrane reactors—principles and applications. Chem. Eng. Process. 48 17-28.
121. K.R. Westerterp, W.P.M van Swaaij and A.A.C.M. Beenackers (1984) Chemical Reactor Design and Operation New York: John Wiley and Sons
122. O.M. Ilinitch, F.P. Cuperus, L.V. Nosova and E.N. Gribov (2000) Catalytic membrane in reduction of aqueous nitrates: operational principles and catalytic performance. Catalysis Today 56 137-145.
123. E. Nagy (2007) The effect of the concentration polarization and a membrane layer mass transport on the membrane separation. J. Appl. Membr. Sci. 6 1-8.
124. E. Nagy (2007) Mass transport through a dense, polymeric, catalytic membrane layer with dispersed catalyst. Ind. Eng. Chem. Res. 46 2295-2306.
125. E. Nagy (2009) Mathematical Modeling of Biochemical Membrane Reactors. E. Drioli, L. Giorno (Eds) Membrane Operations, Innovative Separations and Transformations Weinheim: Wiley-VCH 309-334.
126. E. Nagy (2009) Basic equations of mass transfer through biocatalytic membrane layer. Asia-Pacific J. Chem. Eng. 4 270-278.
127. E. Nagy (2010) Mass transport through a convection flow catalytic membrane layer with dispersed nanometer-sized catalyst. Ind. Eng. Chem. Res. 49 1057-1062.
128. E. Nagy and G. Borbély (2007) The effect of the concentration polarization and the membrane layer mass transport on the membrane separation. J. Appl. Membr. Sci. Technol. 6 9-16.
129. E. Nagy and E. Kulcsár (2009) Mass transport through biocatalytic membrane reactors. Desalination 245 422-436.
130. E. Nagy (2006) Binary, coupled mass transfer with variable diffusivity through cylindrical membrane. J. Membr. Sci. 274 159-168.
131. E. Nagy (2008) Mass transport with varying diffusion- and solubility coefficient through a catalytic membrane layer. Chem. Eng. Res. Design 86 723-730.
132. E. Nagy (2009) Basic equations of mass transfer through biocatalytic membrane layer. Asia-Pacific J. Chem. Eng. 4 270-278.
133. E. Nagy and G. Borbély (2009) Mass transport through anisotropic membrane layer. Desalination 240 54-63.
134. P.V. O’Neil (1987) Advanced Engineering Mathematics Belmont: Wadsworth Inc.
135. R.B. Bird, E. Stewart and E.N. Lightfoot (1960) Transport Phenomena New York: John Wiley and Sons
136. J.D. Brotheton and P.C. Chau (1990) Modeling analysis of an intercalated-spiral alternate-dead-ended hollow-fiber bioreactor for mammalian cell culture. Biotechnol. Bioeng. 35 375-394.
137. V. Calabró, S. Curcio and G. Iorio (2002) A theoretical analysis of transport phenomena in a hollow fiber membrane bioreactor with immobilized biocatalyst. J. Membr. Sci. 206 217-241.
138. K. Damak, A. Ayadi, B. Zeghmati and P. Schmitz (2004) A new Navier–Stokes and Darcy’s law combined model for fluid flow in crossflow filtration tubular membrane. Desalination 161 67-77.
139. V. Geraldes, V. Semiato and M.N. de Pinho (2001) Flow and mass transfer modeling of nanofiltration. J. Membr. Sci. 191 109-128.
140. B. Godongwana, M.S. Sheldon and D.M. Solomons (2007) Momentum transfer inside a vertically oriented capillary membrane bioreactor. J. Membr. Sci. 303 86-99.
141. L.J. Kelsey, M.R. Pillarella and A.L. Zydney (1990) Theoretical analysis of convective flow profiles in a hollow-fiber membrane bioreactor. Chem. Eng. Sci. 45 3211-3220.
142. M. Labecki, J.M. Piret and B.D. Bowen (2004) Effects of free convection on three-dimensional protein transport in hollow-fiber bioreactor. AIChE J. 50 1974-1990.
143. W.S. Long, S. Bhatia and A. Kamaruddin (2003) Modeling and simulation of enzymatic membrane reactor for kinetic resolution of ibuprofen ester. J. Membr. Sci. 209 69-88.
144. J. Marriott and E. Sorensen (2003) A general approach to modeling membrane modules. Chem. Eng. Sci. 58 4975-4990.
145. M. Mondor and C. Moresoli (1999) Theoretical analysis of the influence of the axial variation of the transmembrane pressure in cross-flow filtration of rigid spheres. J. Membr. Sci. 152 71-87.
146. Nagy E., and Hadik P. (2002) Analysis of mass transfer in hollow-fiber membranes, Desalination. 145, 147–152.
147. J.M. Piret and C.L. Cooney (1990) Model of oxygen transport limitations in hollow fiber bioreactors. Biotechnol. Bioeng. 37 80-92.
148. C.J. Richardson and V. Nassehi (2003) Finite element modeling of concentration profiles in flow domains with curved porous boundaries. Chem. Eng. Sci. 58 2491-2503.
149. L. Song (1998) A new model for the calculation of the limiting flux in ultrafiltration. J. Membr. Sci. 144 173-185.
150. D.E. Wiley and D.F. Flechter (2003) Techniques for computational fluid dynamics modeling of flow in membrane channels. J. Membr. Sci. 211 127-137.
151. Bird, R.B., Stewart, W.E., and Lightfoot, E.N. (1960). Transport Phenomena, John Wiley and Sons, New York.
152. A. Bottino, G. Capannelli and A. Comite (2002) Catalytic membrane reactors for the oxidehydrogenation of propane: experimental and modeling study. J. Membr. Sci. 197 75-88.
153. A. Brunetti, A. Caravella, G. Barbieri and E. Drioli (2007) Simulation study of water gas shift reaction in a membrane reactor. J. Membr. Sci. 306 329-340.
154. A. Brunetti, G. Barbieri and E. Drioli (2009) Upgrading of syngas mixture for pure hydrogen production in a Pd–Ag membrane reactor. Chem. Eng. Sci. 64 3448-3454.
155. C. Charcosset (2006) Membrane processes in biotechnology. Biotechnol. Adv. 24 482-492.
156. J. Coronas and J. Santamaría (1999) Catalytic reactors based on porous ceramic membranes. Catalysis Today 51 377-389.
157. R. Dittmeyer, K. Avajda and M. Reif (2004) A review of catalytic membrane layers for gas/liquid reactions. Topics Catalysis 29 3-27.
158. A. Fenu, G. Guglielmi, J. Jimenez, M. Spérandio, D. Saroj, B. Lesjean, et al. (2010) Activated sludge model based on modelling of membrane bioreactor (MBR) processes: a critical review with special regards to MBR specificities. Water Research 44 4272-4294.
159. V. Geraldes, V. Semiao and N.M. de Pinho (2001) Flow and mass transfer modeling of nanofiltration. J. Membr. Sci. 191 109-128.
160. K. Gosiewski and M. Tanczyk (2010) Applicability of membrane reactor for WGS coal derived gas processing: simulation-based analysis. Catalysis Today (doi:10.016/j.cattod.2010.11.042)
161. K. Gosiewski, K. Warmuzinski and M. Tanczyk (2010) Mathematical simulation of WGS membrane reactor for gas from coal gasification. Catalysis Today 156 229-236.
162. E. Heracleous and A.A. Lemonidou (2006) Ni–Nb–O mixed oxides as highly active and selective catalysts for ethene production via ethane oxidative dehydrogenation. Part II: Mechanistic aspects and kinetic modeling. J. Catalysis 237 175-189.
163. S. Judd (2006) The MBR Book: Principles and Application of Membrane Bioreactors in Water and Wastewater Treatment New York: Elsevier
164. A. Julbe, D. Farrusseng and C. Guizard Ch. (2001) Porous ceramic membranes for catalytic reactors—overview and new ideas. J. Membr. Sci. 181 3-20.
165. M.K. Koukou, N. Papayannakos and N.C. Markatos (2001) On the importance of non-ideal flow effects in the operation of industrial scale adiabatic membrane reactors. Chem. Eng. Sci. 83 95-105.
166. O. Levenspiel (1999) Chemical Reaction Engineering 3rd ed. New York: John Wiley and Sons
167. G.Q. Lu, J.C. Diniz da Costa, M. Duke, S. Giessler, R. Socolow, R.H. Williams, et al. (2007) Inorganic membranes for hydrogen production and purification: a critical review and perspective. J. Colloid Interface Sci. 314 589-603.
168. J.G.S. Marcano and T.T. Tsotsis (2002) Catalytic Membranes and Membrane Reactors Weinheim: Wiley-VCH
169. J. Marriott and E. Sorensen (2003) A general approach to modeling membrane modules. Chem. Eng. Sci. 58 4975-4990.
170. E.E. McLearly, J.C. Jansen and F. Kapteijn (2006) Zeolite based films, membranes and membrane reactors: progress and prospects. Microporous Macroporous Mater. 90 198-220.
171. D. Mendes, S. Tobsti, F. Borgognomi, A. Mendes and L.M. Madeira (2010) Integrated analysis of a membrane-based process for hydrogen production from ethanol steam reforming. Catalysis Today 156 102-117.
172. S.S. Ozdemir, M.G. Buonomenna and E. Drioli (2006) Catalytic polymer membranes: preparation and application. Applied Catalysis A General 307 167-183.
173. L. Paturzo, A. Basile and E. Drioli (2002) High temperature membrane reactors and integrated membrane operations. Rev. Chem. Eng. 18 511-551.
174. M. Pedernera, M.J. Alfonso, M. Menéndez and J. Santamaría (2002) Simulation of a catalytic membrane reactor for the oxidative dehydrogenation of butane. Chem. Eng. Sci. 57 2531-2544.
175. J.A.Z. Pieterse, J. Boon, Y.C. van Delft, J.W. Dijkstra and R.W. van den Brink (2010) On the potential of nickel catalysts for steam reforming in membrane reactors. Catalysis Today 156 153-164.
176. M.W. Reij, J.T.F. Keurentjes and S. Hartmans (1998) Membrane bioreactors for waste gas treatment. J. Biotechnol 59 155-167.
177. G.M. Rios, M.P. Belleville, D. Paolucci and J. Sachez (2004) Progress in enzymatic membrane reactors—a review. J. Membr. Sci. 242 189-196.
178. M.L. Rodriguez, D.E. Ardissone, E. Heracleous, A.A. Lemonidou, E. López, N. Pedernera, et al. (2010) Oxidative dehydrogenation of ethane to ethylene in a membrane reactor: a theoretical study. Catalysis Today 157 303-309.
179. A. Santos, W. Ma and S.J. Judd (2010) Membrane bioreactors: two decades of research and implementation. Desalination (10.1016/j.desal.2010.07.063)
180. G. Saracco, H.W.J.P. Neomagnus, G.F. Versteeg and W.P.M. van Swaaij (1999) High-temperature membrane reactors: potential and problems. Chem Eng. Sci. 54 1997-2017.
181. A. Seidel-Morgenstern (2010) Membrane Reactors Weinheim: Wiley-WCH
182. C. Téllez, M. Menédez and J. Santamaría (1999) Kinetic study of oxidative dehydrogenation of butane on V/MgO catalysts. J. Catalysis 183 210-221.
183. L. van Dyk, S. Miachon, L. Lorenzen, M. Torres, K. Fiaty and J.-A. Dalmon (2003) Catalysis Today 82 167-177.
184. J.A. Wesselingh and R. Krishna (2000) Mass Transfer in Multicomponent Mixture Delft: Delft University Press
185. K.R. Westerterp, W.P.M. van Swaaij and A.A.C.M. Beenackers (1984) Chemical Reaction Design and Operation New York: John Wiley and Sons
186. Z. Ziaka and S. Vasieiadis (2011) New integrated catalytic membrane process for enhanced propylene and polypropylene production. Sep. Sci. Technol. 46 224-233.
187. P. Andric, A.S. Meyer, P.A. Jensen and K. Dam-Johanson (2010) Reactor design for minimizing product inhibition during enzymatic lignocelluloses hydrolysis. II. Quantification of inhibition and suitability of membrane reactors. Biotechnol. Adv. 28 407-425.
188. K. Bélafi-Bakó, A. Koutinas, N. Nemestóthy, L. Gubicza and C. Webb (2006) Continuous enzymatic cellulose hydrolysis in a tubular membrane bioreactor. Enzyme Microb. Technol. 38 155-161.
189. G. Belfort (1989) Membranes and bioreactors: a technical challenge in biotechnology. Biotechnol. Bioeng. 33 1047-1066.
190. Bird, R.B., Stewart, W.E., and Lightfoot, E.N. (1960). Transport Phenomena, John Wiley and Sons, New York.
191. J.D. Brotherton and P.C. Chau (1990) Modeling analysis of an intercalated-spiral alternate-dead-ended hollow fiber bioreactor for mammalian cell cultures. Biotechnol. Bioeng. 35 375-394.
192. J.D. Brotherton and P.C. Chau (1996) Biotechnol. Prog. 12(5), 575-590.
193. W.J. Bruining (1989) A general description of flows and pressure in hollow fiber membrane modules. Chem. Eng. Sci. 44 1441-1447.
194. J.M.S. Cabral and J. Tramper (1994) Bioreactor design. J.M.S. Cabral, D. Best, L. Boross, J. Tramper (Eds) Applied Biocatalysis Switzerland: Harwood Academic Publishers 330-370.
195. V. Calabro, S. Curcio and G. Iorio (2002) A theoretical analysis of transport phenomena in a hollow fiber membrane bioreactor with immobilized biocatalyst. J. Membr. Sci. 206 217-241.
196. C. Charcosset (2006) Membrane processes in biotechnology: an overview. Biotechnol. Adv. 24 482-492.
197. T.P. Chung, P.C. Wu and R.S. Jung (2005) J. Membr. Sci. 258 55-63.
198. K. Damak, A. Ayadi, B. Zeghmati and P. Schmitz (2004) A new Navier–Stokes and Darcy’s law combined model for fluid flow in cross-flow filtration tubular membrane. Desalination 161 67-77.
199. M. Farhadian, D. Duchez, C. Vachelard and C. Larroche (2008) Monoaromatics removal from polluted water through bioreactors—a review. Water Res. 42 1325-1341.
200. B.S. Ferreira, P. Fernandes and J.M.S. Cabral (2001) Design and modeling of immobilized biocatalytic reactors. J.M.S. Cabral, M. Mota, J. Tramper (Eds) Multiphase Bioreactor Design London: Taylor & Francis 85-180.
201. D.M.F. Frazeres and J.M.S. Cabral (2001) Enzymatic membrane reactors. J.M.S. Cabral, M. Mota, J. Tramper (Eds) Multiphase Bioreactor Design 2001 London: Taylor & Francis 135-184.
202. L. Giorno and E. Drioli (2000) Biocatalytic membrane reactors: applications and perspectives. Trends Biotechnol. 18 339-349.
203. L. Giorno, L. De Bartolo and E. Drioli (2003) Membrane bioreactors for biotechnology and medical applications. D. Bhattacharyya, D.A. Butterfiled (Eds) New Insight into Membrane Science and Technology: Polymeric and Bifunctional Membranes Oxford: Elsevier (Chapter 9).
204. L. Giorno, E.D. Amore, R. Mazzei, E. Piacentini, J. Zhang, E. Drioli, et al. (2007) An innovative approach to improve the performance of a two separate phase enzyme membrane reactor by immobilizing lipase in presence of emulsion. J. Membr. Sci. 295 95-101.
205. B. Godongwana, M.S. Sheldon and D.M. Solomons (2007) Momentum transfer inside a vertically oriented capillary membrane bioreactor. J. Membr. Sci. 303 86-99.
206. González-Brambila, M., Monroy, O., and López-Isunza (2006) Experimental and theoretical study of membrane-aerated biofilm reactor behavior under different modes of oxygen supply for the treatment of synthetic wastewater. Chem. Eng. Sci., 61, 5268–5281.
207. M. Habulin and K. Knez (1991) Enzymatic synthesis of n-butil oleate in a hollow fiber membrane reactor. J. Membr. Sci. 61 315-324.
208. M.M. Hossain and D.D. Do (1989) Biotechnol. Bioeng. 1989(33), 963-975.
209. R.-S. Juang and H.-C. Kao (2009) Estimation of the contribution of immobilized biofilm and suspended biomass to the biodegradation of phenol in membrane contactors. Biochem. Eng. J. 43 122-128.
210. L.J. Kelsey, M.R. Pillarella and A.L. Zydney (1990) Theoretical analysis of convective flow profiles in a hollow fiber membrane bioreactors. Chem. Eng. Sci. 45 3211-3220.
211. A. Kermanshaipour, D. Karamanev and A. Margaritis (2006) Kinetic modeling of the biodegradation of the aqueous p-xylene in the immobilized soil bioreactor. Biochem. Eng. J. 27 204-211.
212. M. Labecki, D. Bowen and J.M. Piret (1996) Two-dimensional analysis of protein transport in the extracapillary space of hollow-fibre bioreactors. Chem. Eng. Sci. 51 4197-4213.
213. M. Labecki, J.M. Piret and D. Bowen (1995) Two-dimensional analysis of fluid flow in hollow-fibre modules. Chem. Eng. Sci. 50 3369-3384.
214. S. Lackner, A. Terada, H. Horn, M. Henze and B. Smets (2010) Nitrification performance in membrane-aerated biofilm reactors differs from conventional biofilm systems. Water Res. 44 6073-6084.
215. W.S. Long, S. Bhatia and A. Kamaruddin (2003) Modeling and simulation of enzymatic membrane reactor for kinetic resolution of ibuprofen ester. J. Membr. Sci. 219 69-88.
216. M.C.M. Loosdrecht, J.J. Heijnen, H. Eberl, J. Kreft and C. Picioreanu (2002) Mathematical modeling of biofilm structures. Antonie van Leeuwenhoek 81 245-256.
217. P. Lozano, A.B. Perez-Marin, T. De Diego, D. Gomez, D. Paolucci-Jeajean, M.P. Belleville, et al. (2002) Active membranes coated with immobilized Candida Antarctica lipase B: preparation and application for continuous butyl butyrate synthesis in organic media. J. Membr. Sci. 201 55-64.
218. S.G. Lu, T. Imai, M. Ukita, M. Sekine, T. Higouchi and M. Fukagawa (2011) Water Res. 35(8), 2038-2043.
219. J.G.S. Marcano and T.T. Tsotsis (2002) Catalytic Membranes and Membrane Reactores Weinheim: Wiley-VCH
220. S. Matsumoto, A. Terada and S. Tsuneda (2007) Modeling of membrane-aerated biofilm: effect of C/N ratio, biofilm thickness and surface loading of oxygen on feasibility of simultaneous nitrification and denitrification. Biochem. Eng. J. 37 98-107.
221. L.F. Melo and R. Oliveira (2001) Biofilm reactors. J.M.S. Cabral, M. Mota (Eds) Multiphase Bioreactor Design Taylor & Francis, London 271-308. J. Tramper
222. B.V. Merkey, B.E. Rittmann and D.L. Chopp (2009) Modeling how soluble microbial products (SMP) support heterotropic bacteria in autotroph-based biofilms. J. Theor. Biol. 259 670-683.
223. M. Mondor and C. Moresoli (1999) Theoretical analysis of the influence of the axial variation of the transmembrane pressure in cross-flow filtration of rigid spheres. J. Membr. Sci. 152 71-87.
224. E. Nagy (2009) Mathematical modeling of biochemical membrane reactors. E. Drioli, L. Giorno (Eds) Membrane Operations, Innovative Separations and Transformations Weinheim: Wiley-VCH 309-334.
225. E. Nagy (2009) Basic equations of mass transfer through biocatalytic membrane layer. Asia-Pacific J. Chem. Eng. 4 270-278.
226. E. Nagy and E. Kulcsár (2009) Mass transport through biocatalytic membrane reactors. Desalination 245 422-436.
227. M. Nakajima and J.P. Cardoso (1989) Forced-flow bioreactor for sucrose inversion using ceramic membrane activated by silanization. Biotechnol. Bioeng. 33 856.
228. C. Nicolella, P. Pavasant and A.G. Livingston (2000) Substrate counter diffusion and reaction in membrane attached biofilms: mathematical analysis of rate limiting mechanisms. Chem. Eng. Sci. 55 1385-1398.
229. J.M. Piret and C.L. Cooney (1991) Model of oxygen transport limitations in hollow fiber bioreactors. Biotechnol. Bioeng. 37 80-92.
230. V. Qin and M.S. Cabral (1998) Lumen mass transfer in hollow fiber membrane processes with nonlinear boundary conditions. AIChE J. 44 836-848.
231. K.R. Rao, T. Srinivasan and C. Venkateswarlu Ch. (2010) Mathematical and kinetic modeling of biofilm reactor based on ant colony optimization. Process Biochem. 45 961-972.
232. G.M. Rios, M.P. Belleville, D. Paolucci and J. Sanchez (2004) Progress in enzymatic reactors—a review. J. Membr. Sci. 242 189-196.
233. G.M. Rios, M-P. Belleville and D. Paolucci (2007) Membrane engineering in biotechnology: quo vamus? Trends Biotechnol. 25 242-246.
234. G. Salzman, R. Tadmor, S. Guzy, S. Sideman and N. Lotan (1999) Hollow fiber enzymic reactors for a two substrate process: analytical modeling and numerical simulations. Chem. Eng. Progress 38 289-299.
235. A. Santos, I.W. Ma and S.J. Judd (2010) Membrane bioreactors: two decades of research and implementation. Desalination 273 148-154.
236. C.A. Sardonini and D. DiBiasio (1992) An investigation of the diffusion-limited growth of animal cells around single hollow fibers. Biotechnol. Bioeng. 40 1233-1242.
237. H. Satoh, H. Ono, B. Rulin, J. Kamo, S. Okabe and K.-I. Fukushi (2004) Macroscale and microscale analyses of nitrification and denitrification in biofilms attached on membrane aerated biofilm reactors. Water Res. 38 1633-1641.
238. J.A. Schonberg and G. Belfort (1987) Enhanced nutrient transport in hollow fiber perfusion bioreactors. Biotechnol. Prog. 3(2), 81-89.
239. M.S. Sheldon and H.J. Small (2005) Immobilisation and biofilm development of Phanerochaete chrysosporium on polysulphone and ceramic membrane. J. Membr. Sci. 263 30-37.
240. H. Strathmann, L. Giorno and E. Drioli (2006) An Introduction to Membrane Science and Technology Italy: Institute on Membrane Technology
241. W. Yang, N. Cicek and J. Ilg (2006) State-of-the-art of membrane bioreactors: Worldwide research and commercial applications in North America. J. Membr. Sci. 2006(270), 201-211.
242. Q. Wang and T. Zhang (2010) Review of mathematical models for biofilm. Solid State Commun. 150 1009-1022.
243. L.R. Waterland, A.S. Michaels and C.R. Robertson (1974) A theoretical model for enzymatic catalysis using asymmetric hollow-fiber bioreactors. AIChE J. 20 50-59.
244. R.W. Baker (2004) Membrane Technology and Applications 2nd ed. Chichester: John Wiley and Sons
245. R.W. Baker, J.G. Wijmans, A.L. Athayde, R. Daniels, J.H. Ly and M. Le (1997) The effect of concentration polarization on the separation of volatile organic compounds from water by pervaporation. J. Membr. Sci. 137 159-172.
246. D. Bhanushali, S. Kloos, C. Kurth and D. Bhattacharyya (2001) Performance of solvent-resistant membranes for non-aqueous systems: solvent permeation results and modeling. J. Membr. Sci. 189 1-21.
247. S. Bhattacharya and S.-T. Hwang (1997) Concentration polarization, separation factor, and Peclet number in membrane processes. J. Membr. Sci. 173 73-90.
248. R.B. Bird, W.E. Stewart and E.N. Lightfoot (1960) Transport Phenomena New York: John Wiley and Sons
249. W.R. Bowen and A.W. Mohammad (1998) Characterization and prediction of nanofiltration membrane performance—a general assessment. Trans IChemE 76(Part A), 885-893.
250. W.R. Bowen and J.S. Welfoot (2002) Modelling the performance of membrane nanofiltration—critical assessment and model development. Chem. Eng. Sci. 57 1121-1137.
251. L. Braeken, B. Bettens, K. Boussu, P. Van der Meeren, J. Cocquyt, J. Vermant, et al. (2006) Transport mechanism of dissolved organic compounds in aqueous solution during nanofiltration. J. Membr. Sci. 279 311-319.
252. P.L.T. Brian (1966) Mass transport in reverse osmosis. U. Merten (Eds) Desalination by Reverse Osmosis Cambridge: MIT Press 181.
253. J. Crespo (2010) E. Drioli, L. Giorno (Eds) Development in Membrane Science for Downstream Processing, in Membrane Operations Weinheim: Wiley-VCH 245-263.
254. S. Darvishmanesh, A. Buekenhoudt, J. Degréve and B. Van der Bruggen (2009) General model for prediction of solvent permeation through organic and inorganic solvent resistant nanofiltration membranes. J. Membr. Sci. 334 43-49.
255. S. De and P.K. Bhattacharya (1997) Modeling of ultrafiltration process for a two-component aqueous solution of low and high (gel-forming) molecular weight solutes. J. Membr. Sci. 136 57-69.
256. W.M. Deen (1987) Hindered transport of large molecules in liquid-filled pores. AIChE J. 33 1409-1425.
257. M.F.J. Dijkstra, S. Bach and K. Ebert (2006) A transport model for organophilic nanofiltration. J. Membr. Sci. 286 60-68.
258. J. Ennis, H. Zhang, G. Stevens, J. Perera, P. Scales and S. Carnie (1996) Mobility of protein through a porous membrane. J. Membr. Sci. 119 47-58.
259. J. Geens, K. Boussu, C. Vandecasteele and D. Van der Bruggen (2006) Modeling of solute transport in non-aqueous nanofiltration. J. Membr. Sci. 281 139-148.
260. V. Geraldes and A.M.B. Alves (2008) Computer program for simulation of mass transport in nanofiltration membranes. J. Membr. Sci. 321 172-182.
261. S. Kim and E.M.V. Hoek (2005) Modeling concentration polarization in reverse osmosis processes. Desalination 186 11-128.
262. N. Li, A.G. Fane, W.S.W. Ho and T. Matsuura (2008) Advanced Membrane Technology and Application New York: John Wiley and Sons
263. Z. Kovács and W. Samhaber (2008) Characterization of nanofiltration membranes with uncharged solutes. Membrántechnika (in English) 12(2), 22-36.
264. D.R. Machado, D. Hasson and R. Semiat (2000) Effect of solvent properties on permeate flow through nanofiltration membranes. Part II. Transport model. J. Membr. Sci. 166 63-69.
265. G.M. Mavrovouniotis and H. Brenner (1988) Hindered sedimentation diffusion and dispersion coefficients for Brownian spheres in circular cylindrical pores. J. Colloid. Interface Sci. 124 269.
266. M. Mulder (1996) Basic Principles of Membrane Technology 2nd ed. Dordrecht: Kluwer Academic
267. E. Nagy (2009) Basic equations of mass transfer through biocatalytic membrane layer. Asia-Pacific J. Chem. Eng. 4 270-278.
268. E. Nagy (2010) Coupled effect of the membrane properties and concentration polarization in pervaporation: unified mass transport model. Sep. Purif. Technol. 73 194-201.
269. E. Nagy (2011) Nanofiltration of uncharged solutes: simultaneous effect of the polarization and membrane layers on separation. Desalin. Water Treat. 34 70-74.
270. E. Nagy and E. Kulcsár (2009) Mass transport through biocatalytic membrane reactors. Desalination 245 422-436.
271. E. Nagy, E. Kulcsár and A. Nagy (2011) Membrane mass transport by nanofiltration: coupled effect of the polarization and membrane layer. J. Membr. Sci. 368 215-222.
272. L.G. Peeva, E. Gibbins, S. Luthra, S.W. Lloyd, R.P. Stateva and G. Livingston (2004) Effect of concentration polarization and osmotic pressure on flux in organic solvent nanofiltration. J. Membr. Sci. 236 121-136.
273. F. Peng, X. Huang, A. Jawor and E.M.V. Hoek (2010) Transport, structural, and interfacial properties of poly (vinyl alcohol)-polysulfone composite nanofiltration membranes. J. Membr. Sci. 353 169-176.
274. B. Van der Bruggen (2009) Fundamentals of membrane solvent separation and pervaporation. E. Drioli, L. Giorno (Eds) Membrane Operations Weinheim: Wiley-VCH 45-62.
275. B. Van der Bruggen, J. Schaep, D. Wilms and C. Vandecasteele (1999) Influence of molecular size, polarity and charge on the retention of organic molecules by nanofiltration. J. Membr. Sci. 156 29-41.
276. B. Van der Bruggen, M. Manttari and M. Nyström (2008) Drawbacks of applying nanofiltration and how to avoid them: a review. Sep. Purif. Technol. 63 251-263.
277. X.J. Yang, A.G. Livingston and L.F. dos Santos (2001) Experimental observation of nanofiltration with organic solvents. J. Membr. Sci. 190 45-55.
278. R.W. Baker (2004) Membrane Technology and Applications 2nd ed. Chichester: John Wiley and Sons
279. R.W. Baker, J.G. Wijmans, A.L. Athayde, R. Daniels, J.H. Ly and M. Le (1997) The effect of concentration polarization on the separation of volatile organic compounds from water by pervaporation. J. Membr. Sci. 137 159-172.
280. S. Bhattacharya and S.-T. Hwang (1997) Concentration polarization, separation factor, and Peclet number in membrane processes. J. Membr. Sci. 132 73-90.
281. J.G.A. Bitter (1991) Transport Mechanisms in Membrane Separation processes Amsterdam: Shell-Laboratorium
282. T.C. Bowen, S. Li, R.D. Noble and J.L. Falconer (2003) Driving force for pervaporation through zeolite membranes. J. Membr. Sci. 225 165-176.
283. T.C. Bowen, R.D. Noble and J.L. Falconer (2004) Fundamental and application of pervaporation through zeolite membranes. J. Membr. Sci. 245 1-33.
284. R. Clémen, A. Jonquiéres, H. Sarti, M.F. Sosata, M.A.C. Teixidor and P. Lochon (2004) Original structure-property relationships derived from a new modeling of diffusion of pure solvents through polymer membranes. J. Membr. Sci. 232 141-152.
285. P. Delgado, M.T. Sanz and S. Beltrán (2008) Pervaporation study for different binary mixtures in the esterification system of lactic acid with ethanol. Sep. Purif. Technol. 64 78-87.
286. X. Feng and R.Y.M. Huang (1997) Liquid separation by membrane pervaporation: a review. Ind. Eng. Chem. Res. 36 1048-1066.
287. E.A. Fouad and X. Feng (2008) Use of pervaporation to separate butanol from dilute aqueous solutions: Effect of operating conditions and concentration polarization. J. Membr. Sci. 323 428-435.
288. A. Heintz and W. Stephan (1994) A generalized solution-diffusion model of the pervaporation process through composite membrane. J. Membr. Sci. 89 153-169.
289. P. Izák, L. Bartovská, K. Friess, M. Sipek and P. Uchytil (2003) Description of binary liquid mixtures transport non-porous membrane by modified Maxwell–Stefan equation. J. Membr. Sci. 214 293-309.
290. R. Jiraratananon, A. Chanachi and R.Y.M. Huang (2002) Pervaporation dehydration of ethanol–water mixtures with chitosan/hydroxyethylcellulose (CS/HEC) composite membranes. II. Analysis of mass transport. J. Membr. Sci. 199 211-222.
291. R. Jiraratananon, A. Chanachai and R.Y.M. Huang (2008) Pervaporation dehydration of ethanol–water mixtures with chitosan/hydroxyethylcellulose (CS/HEC) composite membranes: II. Analysis of mass transport. J. Membr. Sci. 199 211-222.
292. H.O.E. Karlesson and G. Tragardh (1993) Pervaporation of dilute organic–water mixtures. A literature review on modeling studies and applications to aroma compound recovery. J. Membr. Sci. 76 121-146.
293. H.D. Kamaruddin and W.J. Koros (1997) Some observation about the application of Fick’s first law for membrane separation of multicomponent mixtures. J. Membr. Sci. 135 147-159.
294. R. Krishna and J.A. Wesselingh (1997) The Maxwell–Stefan approach to mass transfer. Chem. Eng. Sci. 52 862-906.
295. F. Lipnizki, R.W. Field and P.K. Ten (1999) Pervaporation-based hybrid process: review of process design, application and economics. J. Membr. Sci. 153 183-210.
296. E.E.B. Meuleman, B. Bosch, M.H.V. Mulder and H. Strathmann (1999) Modeling of liquid/liquid separation by pervaporation: toulene from water. AIChE J. 45 2153-2160.
297. E.E.B. Meuleman, J.H.A. Willemsen, M.H.V. Mulder and H. Strathmann (2001) EPDM as a selective membrane material in pervaporation. J. Membr. Sci. 188 235-249.
298. A.S. Michels (1995) Effects of feed-side polarization on pervaporative stripping of volatile organic solutes from dilute solutions: a generalized analytical treatment. J. Membr. Sci. 101 117-126.
299. Mulder, M. (1981) Pervaporation Separation of Ethanol–Water and Isomeric Xylenes. PhD Thesis, University of Twente, The Netherlands.
300. E. Nagy (2004) Nonlinear, coupled mass transfer through a dense membrane. Desalination 163 345-354.
301. E. Nagy (2006) Binary, coupled mass transfer with variable diffusivity through cylindrical membrane. J. Membr. Sci. 274 159-168.
302. E. Nagy (2009) Basic equations of mass transport through biocatalytic membrane layer. Asia-Pacific J. Chem. Eng. 4 270-278.
303. E. Nagy (2010) Coupled effect of the membrane properties and concentration polarization in pervaporation: unified mass transport model. Sep. Purif. Technol. 73 194-201.
304. E. Nagy and G. Borbely (2007) Effect of the concentration polarization and the membrane layer mass transport on the separation. J. Appl. Membr. Sci. 6 1-8.
305. E. Nagy and E. Kulcsar (2009) Mass transport through biocatalytic membrane reactor. Desalination 245 422-436.
306. J. Olsson and G. Trägardh (2001) Pervaporation of volatile organic compounds from water, I Influence of permeate pressure on selectivity. J. Membr. Sci. 187 25-37.
307. Y. Qin and J.M.S. Cabral (1988) Lumen mass transfer in hollow fiber membrane processes with nonlinear boundary conditions. AIChE J. 41 836-848.
308. M.T. Ravanchi, T. Kaghazchi and A. Kargari (2009) Application of membrane separation processes in petrochemical industry: a review. Desalination 235 199-244.
309. P. Schaetzel, C. Vauclair, G. Luo and Q.T. Nguyen (2001) The solution-diffusion model, order of magnitude calculation of coupling between the fluxes in pervaporation. J. Membr. Sci. 191 103-108.
310. P. Schaetzel, R. Bouallouche, H.A. Amar, T. Nguyen, B. Riffault and S. Marais (2010) Mass transfer in pervaporation: the key component approximation for the solution-diffusion model. Desalination 251 161-166.
311. T. Schafer and J. Crespo (2007) Study and optimization of the hydrodynamic upstream conditions during recovery of a complex aroma profile by pervaporation. J. Membr. Sci. 301 46-56.
312. S.I. Semenova, H. Ohya and K. Soontarapa (1997) Hydrophilic membranes for pervaporation: an analytical review. Desalination 110 251-286.
313. P. Shao and R.Y.M. Huang (2007) Polymeric membrane pervaporation. J. Membr. Sci. 287 162-179.
314. M. She and S.-T. Hwang (2004) Concentration od dilute flavor compounds by pervaporation: permeate pressure effect and boundary layer resistance modeling. J. Membr. Sci. 236 193-202.
315. Smart, J.L. (1997) Pervaporative Extraction of Volatile Organic Compounds from Aqueous Systems with Use of a Tubular Transverse Flow Module. PhD Thesis, University of Texas.
316. J. Smart, V.M. Starov, R.C. Schucker and D.R. Lloyd (1998) Pervaporative extraction of volatile organic compounds from aqueous systems with use of a tubular transverse flow module. Part II. Experimental results. J. Membr. Sci. 143 159-179.
317. B. Smitha, D. Suhanya, S. Sridhar and M. Ramakrishna (2004) Separation of organic–organic mixtures by pervaporation: a review. J. Membr. Sci. 241 1-21.
318. O. Trifunovic and G. Trägardh (2006) Mass transport of aliphatic alcohols and esters through hydrophobic pervaporation membranes. Sep. Purif. Technol. 50 51-61.
319. A. Vane (2005) A review of pervaporation for product recovery from biomass fermentation processes. J. Chem. Technol. Biotechnol. 80 603-629.
320. J.M. Van de Graaf, F. Kapteijn and J.A. Moulijn (1999) Modeling permeation of binary mixtures through zeolite membranes. AIChE J. 45 497.
321. L.J.P. Van den Broeke, W.J.W. Bakker, F. Kapteijn and A. Moulijn (1999) Binary permeation through silicalte-1 membrane. AIChE J. 45 977-985.
322. B. Van der Bruggen, J.C. Jansen, A. Figoli, J. Geens, D. Van Baelen, E. Drioli and C. Vandecasteele (2004) Determination of parameters affecting transport in polymeric membranes: parallels between pervaporation and nanofiltration. J. Phys. Chem. B 108 13273-13279.
323. J.P.G. Villaluenga and A. Tabe-Mohammadi (2000) A review on the separation of benzene/cyclohexane mixtures by pervaporation process. J. Membr. Sci. 169 159-174.
324. S.-L. Wee Sh.-L., C.-T. Tye Ch.-Th. and S. Bhatia (2008) Membrane separation process. Pervaporation through zeolite membrane. Sep. Sci. Technol. 63 500-516.
325. J.A. Wesselingh and R. Krishna (2000) Mass Transport in Multicomponent Mixtures The Netherlands: Delft University Press
326. J.G. Wijmans (2004) The role of permeant molar volume in the solution-diffusion model transport equations. J. Membr. Sci. 237 39-50.
327. J.G. Wijmans and R.W. Baker (1995) The solution-diffusion model: a review. J. Membr. Sci. 107 1-21.
328. G. Wijmans, A.L. Athayde, R. Daniels, J.H. Ly, H.D. Kamanaddin and I. Pinnau (1996) The role of boundary layers in the removal of volatile organic compounds from water by pervaporation. J. Membr. Sci. 109(1996), 135.
329. S. Bandini and G.C. Sarti (1999) Heat and mass transport in vacuum membrane distillation. AIChE J. 45 1422-1433.
330. S. Bandini and G.C. Sarti (2002) Concentration of must through vacuum membrane distillation. J. Membr. Sci. 149 253-259.
331. F.P. Berger and K.F. Hau (1977) Mass transfer in turbulent flow measured by the electrochemical method. Int. J. Heat Mass Transfer 20 1185-1194.
332. P.R. Brookes and A.G. Livingston (1995) Aqueous–aqueous extraction of organic pollutants through tubular silicone rubber membranes. J. Membr. Sci. 104 119-137.
333. V. Calabro, B.L. Jiao and E. Drioli (1994) Theoretical and experimental study on membrane distillation in the concentration of orange juice. Ind. Eng. Chem. Res. 33 1803-1808.
334. M.J. Costello, A.G. Fane, P.A. Hogan and R.W. Schofield (1993) The effect of shell side hydrodynamics on the performance of axial flow hollow fiber modules. J. Membr. Sci. 80 1-11.
335. A. Criscuoli (2009) Membrane contactors. E. Drioli, L. Giorno (Eds) Membrane Operations Weinheim: Wiley-VCH 449-460.
336. L. Dahuron and E.L. Cussler (1998) Protein extraction with hollow fibers. AIChE J. 34 130-136.
337. P.V. Danckwerts (1970) Gas-Liquid Reactions New York: McGraw-Hill, Book Company
338. E. Drioli, A. Criscuoli and E. Curcio (2006) Membrane Contactors: Fundamentals, Applications and Potentialities Amsterdam: Elsevier
339. R. Faiz and M. Al-Marzouqi (2010) CO 2 removal from natural gas at high pressure using membrane contactors: model validation and membrane parametric studies. J. Membr. Sci. 365 232-241.
340. R. Faiz and M. Al-Marzouqi (2011) Insights on natural gas purification: simultaneous absorption of CO 2 and H 2S using membrane contactors. Sep. Purif. Technol. 76 351-361.
341. S. Gaeta (2009) Membrane contactors in industrial applications. E. Drioli, L. Giorno (Eds) Membrane Operations Weinheim: Wiley-VCH 499-512.
342. R. Gawronski and B. Wrzesinska (2000) Kinetics of solvent extraction in hollow-fiber contactors. J. Membr. Sci. 168 213-222.
343. C.J. Geankoplis (1993) Transport Processes and Unit Operations 3rd ed. New York: Prentice Hall
344. V. Gekas and B. Hallström (1987) Mass transfer in the membrane concentration polarization layer under turbulent cross flow. I. Critical literature review and adaptation of existing Sherwood correlations to membrane operation. J. Membr. Sci. 30 153-157.
345. M.A. Izquierdo-Gil and G. Jonsson (2003) Factors affecting flux and ethanol separation performance in vacuum membrane distillation. J. Membr. Sci. 214 113-130.
346. R.B. Jorgensen, A.S. Meyer, C. Varming and G. Johsson (2004) Recovery of volatile aroma compounds from black currant juice by vacuum membrane distillation. J. Food Eng. 64 23-31.
347. K.W. Lawson and D.R. Lloyd (1997) Review: membrane distillation. J. Membr. Sci. 124 1-25.
348. J.L. Li and B.H. Cheng (2005) Review of CO 2 absorption using chemical solvents in hollow fiber membrane contactors. Sep. Purif. Technol. 41 109-122.
349. P. Luis, A. Garea and A. Irabien (2009) Zero solvent emission process for sulfur dioxide recovery using a membrane contactor and ionic liquids. J. Membr. Sci. 330 80-89.
350. A. Malek, K. Li and W.K. Teo (1997) Modeling of microporous hollow fiber membrane modules operated under partially wetted conditions. Ind. Eng. Chem. Res. 36 784-793.
351. L. Martínez-Diez and M.I. Vázquez-González (2000) A method to evaluate coefficients affecting flux in membrane distillation. J. Membr. Sci. 173 225-234.
352. S.A.M. Marzouk, M.H. Al-Marzouqi, M.H. El-Naas, N. Abdullahtif and Z.M. Ismail (2010) Removal of carbon dioxide from pressurized CO 2–CH 4 gas mixture using hollow fiber membrane contactors. J. Membr. Sci. 351 21-27.
353. M. Mavroudi, S.P. Kaldis and G.P. Sakellaropoulos (2006) A study of mass transfer resistance in membrane gas–liquid contacting processes. J. Membr. Sci. 272 103-115.
354. N. Nagaraj, G. Patil, P.R. Babu, U.H. Hebbar, K.S.M.S. Raghavarao and S. Neneb (2006) Mass transfer in osmotic membrane distillation. J. Membr. Sci. 268 48-56.
355. E. Nagy and A. Ujhidy (1989) Model of the effect of chemical reaction on bulk-phase concentrations. AIChE J. 35 1564-1568.
356. E. Nagy, T. Blickle and A. Ujhidy (1983) Untersuchung der Stoffübertragung mit einer chemischen Reaktion erster Ordnung von endlicher Geswindigkeit nach einem einheitlichen Modell, I. Definition und Untersuchung der auf dem Haupstrom der Phasen bezogenen Stoffströme bei irreversiblen und reversiblen Reaktionen mit Hilfe der Zweifilmtheorie. Chem. Techn. 35 307-310.
357. M. Otaishat, T. Matsuura, B. Kruczek and M. Khayet (2008) Heat and mass transfer analysis in dierect contact membrane distillation. Desalination 219 272-292.
358. R. Prasad and K.K. Sirkar (1988) Dispersion-free solvent extraction with microporous hollow-fiber modules. AIChE J. 34 177-188.
359. H.A. Randwala (1996) Absorption of carbon dioxide into aqueous solutions using hollow fiber membrane contactors. J. Membr. Sci. 112 229-240.
360. C. Sisak, E. Nagy, J. Burfeind and K. Schügerl (2000) Technical aspects of separation and simultaneous enzymatic reaction in multiphase enzyme membrane reactors. Bioprocess Eng. 23 503-512.
361. A.H.P. Skelland (1974) Diffusional Mass Transfer New York: John Wiley and Sons
362. M.R. Sohrabi, A. Marjai, S. Moradi, M. Davallo and S. Shirazian (2011) Mathematical modeling and numerical simulation of CO 2 transport through hollow-fiber membranes. Appl. Math. Model. 35 174-188.
363. V. Soni, J. Abildskov, G. Jonsson and R. Gani (2009) A general model for membrane-based separation process. Comput. Chem. Eng. 33 644-659.
364. H. Strahmann, L. Giorno and E. Drioli (2006) An Introduction to Membrane Science and Technology Rende, Italy: Institute on Membrane Technology, CNR-ITM
365. A. Seidel-Morgenstern (2010) Membrane Reactors. Weinheim: Wiley-VCH
366. R. Wang, D. Li and D. Liang (2004) Modeling of CO 2 capture by three typical amine solutions in hollow fiber membrane contactors. Chem. Eng. Process 43 849-856.
367. K.R. Westerterp, W.P.M. Swaaij and A.A.C.M. Beenackers (1993) Chemical Reactor Design and Operation New York: John Wiley and Sons
368. J. Wu and V. Chen (2000) Shell-side mass transfer performance of randomly packed hollow fiber modules. J. Membr. Sci. 172 59-74.
369. J.M. Zeng, Y.Y. Xu and Z.-K. Xu (2003) Shell side mass transfer characteristics in a parallel flow hollow fiber membrane module. Sep. Sci. Technol. 38 1247-1267.
370. H.-Y. Zhang, R. Wang, D.T. Liang and J.H. Tay (2006) Modeling and experimental study of CO 2 absorption in a hollow fiber membrane contactor. J. Membr. Sci. 279 301-310.
371. H.-Y. Zhang, R. Wang, D.T. Liang and J.H. Tay (2008) Theoretical and experimental studies of membrane wetting in the membrane gas–liquid contacting process for CO 2 absorption. J. Membr. Sci. 308 162-170.
372. E. Nagy (2008) Mass transport with varying diffusion- and solubility coefficient through a catalytic membrane layer. Chem. Eng. Res. Design 86 723-730.
373. E. Nagy (2009) Mathematical Modeling of Biochemical Membrane Reactors. E. Drioli, L. Giorno (Eds) Membrane Operations, Innovative Separations and Transformations Weinheim: Wiley-VCH 309-334.
374. E. Nagy (2009) Basic equations of mass transfer through biocatalytic membrane layer. Asia-Pacific J. Chem. Eng. 4 270-278.
375. C. Cebeci, J.P. Shao, F. Kafyeke and E. Laurendeau (2005) Computational Fluid Dynamics for Engineers CA: Horizons-Springer