Mathematical model of nanofiltration systems

W. G.J. van der Meer*, C. W. Aeijelts Averink, J. C. van Dijk

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)


The present design of nanofiltration systems is based mostly on the design of reverse osmosis systems including such aspects as Christmas tree configurations, six spiral-wound modules per pressure vessel, and no recirculation of the brine. However, the feed and osmotic pressure of NF systems are much lower compared to RO systems due to the lower salt concentration of the feed and the lower rejection for monovalent ions. Therefore the hydraulic pressure losses in NF systems are no longer negligible as they are in RO systems. Thus the configuration of NF systems could be different from RO systems. In order to improve the performance of NF systems by optimizing the configuration and operating conditions, a mathematical model has been developed. The model describes the mass transfer through the membranes by using the homogeneous solution model, which is improved by including the concentration polarization. Hydraulic pressure losses are calculated using a modified Darcy-Weisbach equation. In order to optimize the performance of NF systems, the influence of recirculation on recovery, rejection, permeate production per element, and energy consumption has been studied. First results of this study showed that for a given recovery, a one-stage installation with recirculation produces more permeate per element than a two-stage installation without recirculation. However, application of recirculation leads to a slightly increasing energy consumption and permeate concentration.

Original languageEnglish
Pages (from-to)25-31
Number of pages7
Issue number1-2
Publication statusPublished - 1996
Externally publishedYes


  • Mathematical model
  • Membrane filtration
  • Recirculation
  • RO systems


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