Mathematical Simulation of Unsteady Flow through Hollow Fiber Membrane


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.