Abstract
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.
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R.W. Baker, J.G. Wijmans, A.L. Athayde, R. Daniels, J.H. Ly and M. Le, J. Membr. Sci., 137, 159 (1997).
W. R. Bowen and H. Mukhtar, J. Membr. Sci., 112, 263 (1996).
R. Levenstein, D. Hasson and R. Semiat, J. Membr. Sci., 116, 77 (1996).
W.R. Bowen, B. Cassey, P. Jones and D. L. Oatley, J. Membr. Sci., 242, 211 (2004).
W.R. Bowen, J. S. Welfoot and P.M. Williams, AIChE J., 48, 760 (2002).
W.R. Bowen and J. S. Welfoot, Chem. Eng. Sci., 57, 1121 (2002).
S. Déon, P. Dutournié and P. Bourseau, AIChE J., 53, 1952 (2007).
S. Déon, P. Dutournié, L. Limousy and P. Bourseau, Sep. Purif. Technol., 69, 225 (2009).
S. Déon, A. Escoda and P. Fievet, Chem. Eng. Sci., 66, 2823 (2011).
F. Fadaei, V. Hoshyargar, S. Shirazian and S. N. Ashrafizadeh, Desalination, 284, 316 (2012).
F. Fadaei, S. Shirazian and S.N. Ashrafizadeh, Desalination, 281, 325 (2011).
V. Geraldes and A. M. Brites Alves, J. Membr. Sci., 321, 172 (2008).
A.W. Mohammad, N. Hilal, H. Al-Zoubi and N. A. Darwish, J. Membr. Sci., 289, 40 (2007).
A. Szymczyk, N. Fatin-Rouge, P. Fievet, C. Ramseyer and A. Vidonne, J. Membr. Sci., 287, 102 (2007).
R. Krishna, Chem. Eng. J., 35, 19 (1987).
R. Krishna and J. A. Wesselingh, Chem. Eng. Sci., 52, 861 (1997).
J. A. Wesselingh and R. Krishna, Mass transfer in multicomponent mixtures, Delft University Delft, Netherland (2000).
R. Taylor and R. Krishna, Multicomponent mass transfer, Wiley (1993).
J. Mitrovic, Int. J. Heat Mass Transfer, 40, 2373 (1997).
G. R. Gavalas, Ind. Eng. Chem. Res., 47, 5797 (2008).
S. Sircar and T. C. Golden, Sep. Sci. Technol., 35, 667 (2000).
R. Krishna and J. M. van Baten, Ind. Eng. Chem. Res., 45, 2084 (2006).
H. D. Do and D. D. Do, Chem. Eng. Sci., 53, 1239 (1998).
H.W. Hung, T. F. Lin, C. Baus, F. Sacher and H. J. Brauch, Environ. Technol., 26, 1371 (2005).
S. Li, V. A. Tuan, R.D. Noble and J. L. Falconer, Environ. Sci. Technol., 37, 4007 (2003).
J. A. Hogendoorn, A. J. van der Veen, J. H. G. van der Stegen, J.A.M. Kuipers and G. F. Versteeg, Comput. Chem. Eng., 25, 1251 (2001).
W. Lehnert, J. Meusinger and F. Thom, J. Power Sources, 87, 57 (2000).
A. Runstedtler, Chem. Eng. Sci., 61, 5021 (2006).
K. Kaczmarski, A. Cavazzini, P. Szabelski, D. Zhou, X. Liu and G. Guiochon, J. Chromatogr. A, 962, 57 (2002).
F.A. Banat, F. A. Al-Rub and M. Shannag, Heat Mass Transfer, 35, 423 (1999).
H. C. No, H. S. Lim, J. Kim, C. Oh, L. Siefken and C. Davis, Nuclear Eng. Design, 237, 997 (2007).
A. Szymczyk, P. Fievet and C. Ramseyer, Desalination, 200, 125 (2006).
D. Vezzani and S. Bandini, Desalination, 149, 477 (2002).
A. Szymczyk and P. Fievet, Desalination, 200, 122 (2006).
A. E. Yaroshchuk, Adv. Colloid Interface Sci., 85, 193 (2000).
G. Bargeman, J. M. Vollenbroek, J. Straatsma, C. G. P. H. Schroën and R. M. Boom, J. Membr. Sci., 247, 11 (2005).
J. Straatsma, G. Bargeman, H. C. van der Horst and J. A. Wesselingh, J. Membr. Sci., 198, 273 (2002).
G.D. Mehta, T. F. Morse, E.A. Mason and M.H. Daneshpajooh, J. Chem. Phys., 64, 7 (1976).
T. R. Noordman and J. A. Wesselingh, J. Membr. Sci., 210, 227 (2002).
E. A. Mason and H. K. Lonsdale, J. Membr. Sci., 51, 1 (1990).
J.A. Wesselingh, P. Vonk and G. Kraaijeveld, The Chemical Engineering J. and the Biochemical Engineering J., 57, 75 (1995).
A.M. Lali, A. S. Khare, J.B. Joshi and K.D.P. Nigam, Powder Technol., 57, 39 (1989).
S. Patankar, Numerical heat transfer and fluid flow, CRC Press (1980).
S. Déon, P. Dutournié, P. Fievet, L. Limousy and P. Bourseau, Water Res., 47, 2260 (2013).
M.D. Afonso and M.N. de Pinho, Ind. Eng. Chem. Res., 37, 4118 (1998).
W. R. Bowen, A. W. Mohammad and N. Hilal, J. Membr. Sci., 126, 91 (1997).
J. Schaep, C. Vandecasteele, A. Wahab Mohammad and W. Richard Bowen, Sep. Purif. Technol., 22-23, 169 (2001).
S. Bandini and D. Vezzani, Chem. Eng. Sci., 58, 3303 (2003).
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Hoshyargar, V., Fadaei, F. & Ashrafizadeh, S.N. Mass transfer simulation of nanofiltration membranes for electrolyte solutions through generalized Maxwell-Stefan approach. Korean J. Chem. Eng. 32, 1388–1404 (2015). https://doi.org/10.1007/s11814-014-0329-3
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DOI: https://doi.org/10.1007/s11814-014-0329-3