•   Hisham A. Maddah


Porous high-pressure membranes have been widely used for both brackish water and seawater desalination. However, fouling (concentration polarization) extensively reduces permeate flux in high-pressure membranes such that reverse osmosis (RO) and/or nanofiltration (NF). In this study, we have attempted to understand the effect of membrane fouling on the permeate water flux by modeling the salt concentration profile within a membrane of interest. A parabolic (or diffusion) partial differential equation was used to describe the change in salt concentration inside the membrane. Subsequently, the PDE equation was solved numerically, under certain assumptions, by using forward finite difference (FFD) explicit method. It was found that salt accumulation occurs at the membrane feed-side surface and there was a noticeable decrease in water flux as fouling increased. For waters with an initial salt concentration of 10000 ppm (NaCl) and with an average diffusivity of , results showed that both RO/NF would have flux rates of 74.9, 67.4, 22.5, 0, –37.4, –74.9 LMH for the feed-side surface concentrations 0, 1000, 7000, 10000, 15000 and 20000 ppm, respectively, where negative flux indicates a back-flow scenario.


S. E. Ogbonmwan, “Water for Life Ireland Campaign: Supporting the United Nation Water Campaign,” in The 2nd United Nation Water day, Expo., 2011.

H. A. Maddah and A. S. Alzhrani, “Quality Monitoring of Various Local and Imported Brands of Bottled Drinking Water in Saudi Arabia,” World J. Eng. Technol., vol. 05, no. 04, pp. 551–563, 2017.

A. Alawadhi, “Regional report on desalination-GCC countries.,” Proc. IDA World Congr. Desalin. water reuse, Manama, Bahrain, vol. 8, p. 13, 2002.

B. Van der Bruggen and C. Vandecasteele, “Distillation vs. membrane filtration: Overview of process evolutions in seawater desalination,” Desalination, 2002.

H. A. Maddah, A. S. Alzhrani, M. Bassyouni, M. H. Abdel-Aziz, M. Zoromba, and A. M. Almalki, “Evaluation of various membrane filtration modules for the treatment of seawater,” Appl. Water Sci., 2018.

H. A. Maddah et al., “Determination of the treatment efficiency of different commercial membrane modules for the treatment of groundwater,” J. Mater. Environ. Sci., 2017.

C. E. Drioli E, Criscuoli A, “Integrated membrane operations for seawater desalination,” Desalination, vol. 147, no. 1, pp. 77–81, 2002.

R. Rajamohan, V. P. Venugopalan, D. Mal, and U. Natesan, “Efficiency of reverse osmosis in removal of total organic carbon and trihalomethane from drinking water,” Res. J. Chem. Environ., 2014.

T. Brief, “A national drinking water clearinghouse fact sheet,” Tech Br. Twelve, 1999.

B. A. Qureshi, S. M. Zubair, A. K. Sheikh, A. Bhujle, and S. Dubowsky, “Design and performance evaluation of reverse osmosis desalination systems: An emphasis on fouling modeling,” Appl. Therm. Eng., 2013.

J. Baker and L. Dudley, “Biofouling in membrane systems—a review,” Desalination, vol. 118, no. 1, pp. 81–89, 1998.

F. A. Abd El Aleem, K. A. Al-Sugair, and M. I. Alahmad, “Biofouling problems in membrane processes for water desalination and reuse in Saudi Arabia,” Int. Biodeterior. Biodegrad., 1998.

H. C. Flemming, “Reverse osmosis membrane biofouling,” Exp. Therm. Fluid Sci., 1997.

A. Sagle and B. Freeman, “Fundamentals of membranes for water treatment,” Futur. Desalin. Texas, 2004.

H. K. Lonsdale, U. Merten, and R. L. Riley, “Transport properties of cellulose acetate osmotic membranes,” J. Appl. Polym. Sci., 1965.

A. S. Al-Hobaib, K. M. AL-Sheetan, M. R. Shaik, N. M. Al-Andis, and M. S. Al-Suhybani, “Characterization and Evaluation of Reverse Osmosis Membranes Modified with AgO Nanoparticles to Improve Performance,” Nanoscale Res. Lett., 2015.

AXEON Water Technologies, “Reverse Osmosis Membrane Element Construction,” 2015. [Online]. Available: https://www.axeonwater.com/blog/reverse-osmosis-membrane-element-construction/.

S. C. Chapra and R. P. Canale, Numerical methods for engineers, vol. 33, no. 3. 2015.

W. M. Deen, Analysis of Transport Phenomena, 2nd ed. New York: Oxford University Press, 2011.

H. A. Maddah, “Application of finite Fourier transform and similarity approach in a binary system of the diffusion of water in a polymer,” J. Mater. Sci. Chem. Eng., vol. 4, no. 4, p. 20, 2016.

AUXIAQUA, “Filtration systems: Reverse Osmosis,” 2011. [Online]. Available: http://www.auxiaqua.es/en/sistemas-filtracion/.


Download data is not yet available.


How to Cite
Maddah, H. 2019. FFD Analysis for the Effect of Fouling on the Permeate Flux in High-Pressure Membranes. European Journal of Engineering Research and Science. 4, 1 (Jan. 2019), 12-16. DOI:https://doi.org/10.24018/ejers.2019.4.1.1061.