A comprehensive mathematical model is developed for simulation of ion transport through nanofiltration membranes. The model is based on the Maxwell-Stefan approach and takes into account steric, Donnan, and dielectric effects in the transport of mono and divalent ions. Theoretical ion rejection for multi-electrolyte mixtures was obtained by numerically solving the “hindered transport” based on the generalized Maxwell-Stefan equation for the flux of ions. A computer simulation has been developed to predict the transport in the range of nanofiltration, a numerical procedure developed linearization and discretization form of the governing equations, and the finite volume method was employed for the numerical solution of equations. The developed numerical method is capable of solving equations for multicomponent systems of n species no matter to what extent the system shows stiffness. The model findings were compared and verified with the experimental data from literature for two systems of Na2SO4+NaCl and MgCl2+NaCl. Comparison showed great agreement for different concentrations. As such, the model is capable of predicting the rejection of different ions at various concentrations. The advantage of such a model is saving costs as a result of minimizing the number of required experiments, while it is closer to a realistic situation since the adsorption of ions has been taken into account. Using this model, the flux of permeates and rejections of multi-component liquid feeds can be calculated as a function of membrane properties. This simulation tool attempts to fill in the gap in methods used for predicting nanofiltration and optimization of the performance of charged nanofilters through generalized Maxwell-Stefan (GMS) approach. The application of the current model may weaken the latter gap, which has arisen due to the complexity of the fundamentals of ion transport processes via this approach, and may further facilitate the industrial development of nanofiltration.

Nanofiltration Maxwell-stefan Membrane Mass Transfer Numerical Simulation

Baker RW, Wijmans JG, Athayde AL, Daniels R, Ly JH, Le M, J. Membr. Sci., 137(1-2), 159 (1997)
Bowen WR, Mukhtar H, J. Membr. Sci., 112(2), 263 (1996)
Levenstein R, Hasson D, Semiat R, J. Membr. Sci., 116(1), 77 (1996)
Bowen WR, Cassey B, Jones P, Oatley DL, J. Membr. Sci., 242(1-2), 211 (2004)
Bowen WR, Welfoot JS, Williams PM, AIChE J., 48(4), 760 (2002)
Bowen WR, Welfoot JS, Chem. Eng. Sci., 57(7), 1121 (2002)
Deon S, Dutournie P, Bourseau P, AIChE J., 53(8), 1952 (2007)
Deon S, Dutournie P, Limousy L, Bourseau P, Sep. Purif. Technol., 69(3), 225 (2009)
Deon S, Escoda A, Fievet P, Chem. Eng. Sci., 66(12), 2823 (2011)
Fadaei F, Hoshyargar V, Shirazian S, Ashrafizadeh SN, Desalination, 284, 316 (2012)
Fadaei F, Shirazian S, Ashrafizadeh SN, Desalination, 281, 325 (2011)
Geraldes V, Alves AMB, J. Membr. Sci., 321(2), 172 (2008)
Mohammad AW, Hilal N, Al-Zoubi H, Darwish NA, J. Membr. Sci., 289(1-2), 40 (2007)
Szymczyk A, Fatin-Rouge N, Fievet P, Ramseyer C, Vidonne A, J. Membr. Sci., 287(1), 102 (2007)
Krishna R, Chem. Eng. J., 35, 19 (1987)
Krishna R, Wesselingh JA, Chem. Eng. Sci., 52(6), 861 (1997)
Wesselingh JA, Krishna R, Mass transfer in multicomponent mixtures, Delft University Delft, Netherland (2000).
Taylor R, Krishna R, Multicomponent mass transfer, Wiley (1993).
Mitrovic J, Int. J. Heat Mass Transf., 40(10), 2373 (1997)
Gavalas GR, Ind. Eng. Chem. Res., 47(16), 5797 (2008)
Sircar S, Golden TC, Sep. Sci. Technol., 35(5), 667 (2000)
Krishna R, van Baten JM, Ind. Eng. Chem. Res., 45(6), 2084 (2006)
Do HD, Do DD, Chem. Eng. Sci., 53(6), 1239 (1998)
Hung HW, Lin TF, Baus C, Sacher F, Brauch HJ, Environ. Technol., 26, 1371 (2005)
Li S, Tuan VA, Noble RD, Falconer JL, Environ. Sci. Technol., 37, 4007 (2003)
Hogendoorn JA, van der Veen AJ, van der Stegen JHG, Kuipers JAM, Versteeg GF, Comput. Chem. Eng., 25(9-10), 1251 (2001)
Lehnert W, Meusinger J, Thom F, J. Power Sources, 87(1-2), 57 (2000)
Runstedtler A, Chem. Eng. Sci., 61(15), 5021 (2006)
Kaczmarski K, Cavazzini A, Szabelski P, Zhou D, Liu X, Guiochon G, J. Chromatogr. A, 962, 57 (2002)
Banat FA, Al-Rub FA, Shannag M, Heat Mass Transf., 35, 423 (1999)
No HC, Lim HS, Kim J, Oh C, Siefken L, Davis C, Nucl. Eng. Des., 237, 997 (2007)
Szymczyk A, Fievet P, Ramseyer C, Desalination, 200(1-3), 125 (2006)
Vezzani D, Bandini S, Desalination, 149(1-3), 477 (2002)
Szymczyk A, Fievet P, Desalination, 200(1-3), 122 (2006)
Yaroshchuk AE, Adv. Colloid Interface Sci., 85, 193 (2000)
Bargeman G, Vollenbroek JM, Straatsma J, Schroen CGPH, Boom RM, J. Membr. Sci., 247(1-2), 11 (2005)
Straatsma J, Bargeman G, van der Horst HC, Wesselingh JA, J. Membr. Sci., 198(2), 273 (2002)
Mehta GD, Morse TF, Mason EA, Daneshpajooh MH, J. Chem. Phys., 64, 7 (1976)
Noordman TR, Wesselingh JA, J. Membr. Sci., 210(2), 227 (2002)
Mason EA, Lonsdale HK, J. Membr. Sci., 51, 1 (1990)
Wesselingh JA, Vonk P, Kraaijeveld G, The Chemical Engineering J. and the Biochemical Engineering J., 57, 75 (1995).
Lali AM, Khare AS, Joshi JB, Nigam KDP, Powder Technol., 57, 39 (1989)
Patankar S, Numerical heat transfer and fluid flow, CRC Press (1980).
Deon S, Dutournie P, Fievet P, Limousy L, Bourseau P, Water Res., 47, 2260 (2013)
Afonso MD, de Pinho MN, Ind. Eng. Chem. Res., 37(10), 4118 (1998)
Bowen WR, Mohammad AW, Hilal N, J. Membr. Sci., 126(1), 91 (1997)
Schaep J, Vandecasteele C, Mohammad AW, Bowen WR, Sep. Purif. Technol., 22-23, 169 (2001)
Bandini S, Vezzani D, Chem. Eng. Sci., 58(15), 3303 (2003)