Rate-Based Design of Non-fouled Cross-Flow Hollow Fiber Membrane Modules for Ultrafiltration

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Although ultrafiltration has replaced many liquid phase separation equipment, it is still considered as a "non-unit operation" process because the sizing of the equipment could not be calculated using either the equilibrium stage or the rate-based methods. Previous design methods using the dead-end and the complete-mixing models are unsatisfactory because the dead-end model tends to underestimate the membrane area due to the use of the feed concentration in the driving force while the complete-mixing model tends to overestimate the membrane area due to the use of the more concentrated rejection concentration in the driving force. In this paper, a cross-flow model for ultrafiltration is developed by considering mass balance at a differential element of the cross-flow module and then integrating the expression over the whole module to get the module length. Since the modeling is rate-based, the length of both modules could be expressed as the product of the height of a transfer unit (HTU) and the number of transfer unit (NTU). The solution of the integral representing the NTU of ultrafiltration is found to be the difference between two exponential integrals (Ei(x)). The poles of the solution represent the flux extinction curves of ultrafiltration. The NTU for ultrafiltration is found to depend on three parameters: the rejection R, the recovery S, and the dimensionless gel concentration Cg. For any given Cg and R, the recovery, S is limited by the corresponding flux extinction curve. The NTU for ultrafiltration is found to be generally small and less than unity but increases rapidly to infinity near the poles due to flux extinction. The complete-mixing model is reformulated in terms of the same parameters used in the cross-flow model. The design of membrane modules for ultrafiltration taken from case-studies of previous authors is performed using both the complete-mixing and the cross-flow models developed in this paper and a comparative study of the results is carried out. The length of the hollow fiber module and the membrane area calculated using the cross-flow model for ultrafiltration are found to be always smaller than those given by the complete-mixing model.

Original languageEnglish
Pages (from-to)1221-1238
Number of pages18
JournalSeparation Science and Technology
Volume39
Issue number6
DOIs
Publication statusPublished - 2004

Fingerprint

Ultrafiltration
Membranes
Fibers
Fluxes
Poles
Recovery
Phase separation
Gels
Liquids

Keywords

  • Cross-flow model
  • Height of a transfer unit
  • Hollow fiber module design
  • Number of transfer unit
  • Ultrafiltration

ASJC Scopus subject areas

  • Chemistry(all)
  • Process Chemistry and Technology
  • Chemical Engineering(all)
  • Filtration and Separation

Cite this

Rate-Based Design of Non-fouled Cross-Flow Hollow Fiber Membrane Modules for Ultrafiltration. / Wan Daud, Wan Ramli.

In: Separation Science and Technology, Vol. 39, No. 6, 2004, p. 1221-1238.

Research output: Contribution to journalArticle

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