Department of Chemical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111 Mashhad, I.R. IRAN
An artificial neural network has been used to determine the volume flux and rejections of Ca2+ , Na+ and Cl¯, as a function of transmembrane pressure and concentrations of Ca2+, polyethyleneimine, and polyacrylic acid in water softening by nanofiltration process in presence of polyelectrolytes. The feed-forward multi-layer perceptron artificial neural network including an eight-neuron hidden layer has the least error in modeling this non-linear process. The overall agreement between the artificial neural network results and experimental data is very good for both the volume flux and rejections, because the maximum values of normalized bias and error are -0.01122 and 1.0737 respectively.
 Wang, X.L., Tsuru, T., Togoh, M., Nakao, S., and Kimura, S., Transport of organic electrolytes with electrostatic and steric-Hindrance effects through nanofiltration membranes, J. Chem. Eng. Jpn.,28, 372 (1995).
 Bowen, W. R., Mukhtar, H., Characterisation and prediction of separation performance of nanofiltration membrane, J. Membrane Sci., 112, 263 (1996).
 Bowen, W. R., Mohammad, A. W. and Hilal, N., Characterisation of nanofiltration membranes for predictive purposes - use of salts, uncharged solutes and atomic force microscopy, J. Membrane Sci.,126, 91 (1997).
 Bowen, W. R. and Wahab Mohammad, A., Dia- filtration of dye/salt solution by anofiltration: Process prediction and optimisation, AIChEJournal, 44, 1799 (1998).
 Hagmeyer, G. and Gimbel, R., Modelling the salt rejection of nanofiltration membranes for ternary ion mixtures and for single salts at different pH values, Desalination, 117, 247 (1998).
 Diaper, C., Correia, V., Judd, S., Characterisation of zirconium/poly (acrylic acid) low pressure dynamically formed membrane by use of the extended Nernst-Plank equation, J. Membrane Sci., 138, 135 (1998).
 Hoffer, E., Kedem, O., Hyperfiltration in charged membranes: the fixed charge model, Desalination, 2, 25 (1967).
 Jitsuhara, I., Kimura, S., Rejection of inorganic salts by charged ultrafiltration membranes made of sulfonated polysulfone, J. Chem. Eng. Jpn., 16, 394 (1983).
 Soltanieh, M., Mousavi, M., Transport of multi-ion solutes through bipolar membranes, The Inter-national Conference of Polymers, Australia, (1996).
 Soltanieh, M., Mousavi, M., Application of charged membranes in water softening: modeling and experiments in the presence of polyelectrolytes, J. Membrane Sci., 154, 53-60 (1999).
 Spiegler, K. S. and Kedem, O., Thermodynamics of hyperfiltration (reverse osmosis): criteria for efficient membranes, Desalination, 1, 311 (1966).
 Jitsuhara, I. and Kimura, S., Rejection of inorganic salts by charged ultrafiltration membranes made of sulfonated polysulfone, J. Chem. Eng. Jpn, 16, 394 (1983).
 Perry, M. and Linder, C., Intermediate reverse osmosis ultrafiltration (RO UF) membranes for concentration and desalting of low molecular weight organic solutes, Desalination, 71, 233 (1989).
 Schirg, P. and Widmer,F., Characterisation of nanofiltration membranes for the separation of aqueous dye-salt solutions, Desalination, 89, 89 (1992).
 Levenstein, R., Hasson, D. and Semiat, R., Utilization of the Donnan effect for improving electrolyte separation with nanofiltration membranes, J. Membrane Sci., 116, 77 (1996).
 Dornier, M., Decloux, M., Trystram, G. and Lebert, A., Dynamic modeling of crossflow micro-filtration using neural networks, J. Membrane Sci., 98, 263 (1995).
 Niemi, H., Bulsari, A. and Palosaari, S., Simulation of membrane separation by neural networks, J. Membrane Sci., 102, 185 (1995).
 Piron, E., Latrille, E. and Rene', F., Application of artificial neural networks for crossflow micro-filtration modelling: “black box and semi-physical approaches, Comp. Chem. Eng., 21, 1021 (1997).
 Delgrange, N., Cabassud, C., Durand-Bourlier, L. and Laine', J. M., Modelling of ultrafiltration fouling by neural network, Desalination, 118, 213 (1998).
 Delgrange, N., Cabassud, C., Durand-Bourlier, L. and Laine', J. M., Neural networks for prediction of ultrafiltration transmembrane pressure - application to drinking water production, J. Membrane Sci., 150, 111 (1998).
 Bowen, W. R., Jones, M. G. and Yousef, H. N. S., Dynamic ultrafiltration of proteins-A neural network approach, J. Membrane Sci., 146, 225 (1998).
 Hamachi, M., Cabassud, M., Davin, A. and Mietton Peuchot, M., Dynamic modelling of crossflow microfiltration of bentonite suspension using recurrent neural networks, Chem. Eng. and Process, 38, 203 (1999).
 Bowen, W. R., Jones, M. G., Welfoot, J. S., Yousef, H. N. S., Predicting salt rejections at nanofiltration membranes using artificial neural network, Desalination, 129, 147 (2000).
 Razavi, M., Mortazavi, A., Mousavi, M., Dynamic modelling of milk ultrafiltration by artificial neural network, J. Membrane Sci., 220, 47 (2003).
 Razavi, M. A., Mousavi, M., Mortazavi, A., Dynamic prediction of milk ultrafiltration per-formance, A neural network approach, Chem. Eng. Sci.,58, 4185 (2003).
 Razavi, M., Mortazavi, A., Mousavi, M., Application of neural networks for crossflow milk ultrafiltration simulation, International Dairy Journal,14, 69 (2004).
 Tambe, S. S., Kulkarni, B. D. and Deshpande, P. B., “Elements of artificial neural networks with selected applications in chemical engineering, and chemical & Biological sciences”, Simulation & Advanced Controls Ltd., Louisville, KY, USA (1996).
 Tsuru, T., Vrairi, M., Yabe, T., Nakao, S., Kimura, S., Ion separation by reverse osmosis with mono - and bipolar membranes, Proceeding of the International Conference on Ion Exchange, Tokyo, 2-4 October (1991).
 Avami, A., Modeling and simulation of water softening by nanofiltration using artificial neural network, B.Sc. Thesis, Departmant of Chemical Engineering, Ferdowsi University, Mashhad, Iran, (2003).