Mathematical model of flat sheet membrane modules for FO process: Plate-and-frame module and spiral-wound module

B. Gu, D. Y. Kim, J. H. Kim, D. R. Yang

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


The forward osmosis process is considered a promising desalination method due to its low energy requirement compared to other methods. In this study, modelling and simulations for a plate-and-frame and a modified spiral-wound module are carried out for the FO process. The mathematical models consist of mass balance, a permeate flux model, and concentration polarization equations. The plate-and-frame model is formulated with consideration of flow directions, and the modified spiral-wound model is formulated with consideration of its geometric characteristics. These two sets of model equations are numerically and iteratively integrated since they are implicit and highly non-linear. The simulation for both modules was conducted by varying 4 types of operating conditions: volumetric flow rate of the feed and the draw solution, the concentration of the draw solution, flow direction, and the membrane orientation. The results for various conditions are also compared. In future research, the developed model could be applied for designing FO modules and finding optimal operating conditions.

Original languageEnglish
Pages (from-to)403-415
Number of pages13
JournalJournal of Membrane Science
Issue number1-2
Publication statusPublished - 2011 Sept 1

Bibliographical note

Funding Information:
This research was financially supported by Ministry of Knowledge Economy ( 2008NFC12J0431502010 ) and Seawater Engineering & Architecture of High Efficiency Reverse Osmosis (SEAHERO) program funded by Ministry of Land, Transport and Maritime Affairs ( 10CPTA-A042522-05-000000 ).


  • Concentration polarization
  • Forward osmosis
  • Modelling
  • Modified spiral-wound module
  • Plate-and-frame module

ASJC Scopus subject areas

  • Biochemistry
  • General Materials Science
  • Physical and Theoretical Chemistry
  • Filtration and Separation


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