Modeling and Performance Characteristics of Nanofiltration by DSPM and ARX Model


  • D. Deepak Membrane Research Laboratory, Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli-620015, India
  • G. Arthanareeswaran Membrane Research Laboratory, Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli-620015, India



The DSPM (Donnan Steric Pore Model) is integrated with osmotic pressure to develop nanofiltration modeling. The new model establishes the relation between the pressure across the membrane to the concentrations of permeate and retentate at a particular solute concentration in the feed. The model is successfully tested against the experimental data. We also developed the nanofiltration modeling with ARX (Auto Regressive Exogeneous), a type of black box model. The data for modeling is obtained by simulation of the first principle model. With the help of identification toolbox, an ARX model is developed considering pressure across the membrane as input variable (manipulated variable) and percentage rejection as output variable (control variable). The model is validated against a data subset used for estimation of model. However, the models are sustained only at low feed concentrations. The model output data are compared to the actual output data and calculate the mean square errors (MSE). The obtained residuals are well satisfactory in the range of 0.99. Hence, the derived modeling sustains for nanofiltration and its control operations.


Hilal, N., Al-Zoubi, H., Darwish, N., A., Mohamma, A. W., Abu Arabi, M. 2004. A Comprehensive Review Of Nanofiltration Membranes: Treatment, Pretreatment, Modelling, And Atomic Force Microscopy. Desalination. 170: 281–308.

Van der Bruggen, B., Manttari, M., Nyström, M. 2008. Drawbacks Of Applying Nanofiltration And How To Avoid Them: A Review. Separation and Purification Technology. 63: 251–263.

Gozálvez-Zafrillaa, J. M., Gómez-Martíneza, B., Santafé-Morosa, A. Evaluation of Nanofiltration Processes for Brackish Water Treatment Using the DSPM Model.

Shaalan, H. F. 2002. Development Of Fouling Control Strategies Pertinent To Nanofiltration Membranes. Desalination. 153: 125–131.

Palmeri, J., Ben Amar, N., Saidani H., Deratani, A. 2009. Process Modeling Of Brackish And Seawater Nanofiltration. Desalination. 9: 263–271.

Geens, J., Van der Bruggen, B., Vandecasteele, C. 2006. Transport Model For Solvent Permeation Through Nanofiltration Membranes, Separation and Purification Technology. 48: 255–263.

Al-Zoubi, H., Hilal, N., Darwish, N. A., Mohammad, A. W. 2007. Rejection And Modelling Of Sulphate And Potassium Salts By Nanofiltration Membranes. Desalination. 206: 42–60.

Chakraborty, S., Bag, B. C., Das Gupta, S., Basu, J. K., De, S. 2004. Prediction Of Permeate Flux And Permeate Concentration In Nanofiltration Of Dye Solution. Separation and Purification Technology. 35: 141–152.

Darvishmanesh S., Buekenhoud, A., Degrève, J., Van der Bruggen, B. 2009. General Model For Prediction Of Solvent Permeation Through Organic And Inorganic Solvent Resistant Nanofiltration Membranes,. Journal of Membrane Science. 334: 43–49.

M. H. F. Rahiman, M. N. Taib, Y. M. Salleh. ARX, ARMAX And NNARX Modeling for Essential Oil Extraction System, IEEE.

Han I. S., Cheryan M. 1995. Nanofiltration of model acetate solutions. Journal of Membrane Science. 107: 107–113.

Li, W., Li, J., Chen, T., Zhao, Z., Chen, C. 2005. Study On Nanofiltration For Purifying Fructo-oligosaccharides. Journal of Membrane Science. 258: 8–15.

Mohammad A. W., Hilal N., Al-Zoubi H., Darwish N. A. 2007. Prediction Of Permeate Fluxes And Rejections Of Highly

Concentrated Salts In Nanofiltration Membrane, Journal of Membrane Science. 289: 40–50.

Mohammad, A. W., Takriff M. S. 2003. Predicting Flux and Rejection Of Multi Component Salt Mixture In Nanofiltration Membranes. Desalination. 157: 105–111.

Otero, J. A., Lena G., Colina J. M., Pradanos P., Tejerina, F., Hernandez, A. 2006. Characterizations Of Nanofiltration Membranes: Structural Analysis By The DSP Model And Microscopical Techniques. Journal of Membrane Science. 279: 410–417.

Pontalier, P. Y., Ismail, A., Ghoul M. 1999. Specific Model for Nanofiltration. Journal of Food Engineering. 40: 145–151.

Román, A., Wang, J., Csanádi J., Hodúr C., Vatai G. 2009. Experimental Investigation of the Sweet Whey Concentration by Nanofiltration. Food and Bioprocess Technology. DOI 10.1007/s11947-009-0192-0.

Teixeira M. R., Rosa M. J., Nystrom M. 2005. The Role Of Membrane Charge On Nanofiltration Performance, Journal of Membrane Science. 265: 160–166

Wang D., Wu L., Liao Z., Wang X., Tomi Y., Ando M., Shintani T. 2006. Modeling The Separation Performance Of Nanofiltration Membranes For The Mixed Salts Solution With Mg2+ and Ca2+. Journal of Membrane Science. 284: 384–392.




How to Cite

Deepak, D., & Arthanareeswaran, G. (2017). Modeling and Performance Characteristics of Nanofiltration by DSPM and ARX Model. Journal of Applied Membrane Science & Technology, 18(1).