MATHEMATICAL SIMULATION OF UNSTEADY FLOWTHROUGH HOLLOW FIBER MEMBRANE

Abstract

Water flowing through hollow fiber membrane comprises two types of flow each having its
own hydraulic characteristics. The first is the flow inside the fiber channel, and the second is the
flow through the fiber porous wall. Water flow through hollow fiber membrane, HFM, is unsteady
nonuniform flow due to the accumulation of rejected material on the fiber surface causing a change
in the hydraulic resistance along the fiber length with time. Under these conditions, a mathematical
model was developed to simulate water flow through hollow fiber membrane based upon the
equations governing the flow inside the fiber channel and through the fiber wall, equations
governing conditions imposed by flow boundaries, and implicit finite difference technique for
solving partial differential equations. The model was verified by using published laboratory
experimental data. A very good agreement was obtained between the measured and predicted
flowrate values under the same conditions.
 The mathematical model was applied to three types of commercially available fiber modules
to investigate variation of flux, the transmembrane pressure, the thickness of the rejected materials
along the fiber length, the flowrate, and the effect of the pot length on the fiber hydraulic
performance. It was found there is considerable variation in the hydraulic performance of the three
types of fiber. Therefore, the mathematical model provides a tool to work on finding the optimal
design of the hollow fiber membrane.