MATHEMATICAL SIMULATION OF FLOW THROUGH HOLLOW FIBRE MEMBRANE UNDER CONSTANT HYDRAULIC CONDUCTIVITY

Abstract

Distilled water flow through a virgin hollow fibre membrane, HFM is considered as steady
nonuniform since the fibre’s wall hydraulic conductivity coefficient is kept constant along the fibre
and unchanged during the operation. Under these conditions, two well known laws were used to
mathematically simulate the hydraulic flow through the HFM. These two laws are: the Darcy’s
Law, to simulate the flow thought the fibre wall, and the Hagen-Poiseuille’s Law, to simulate the
laminar flow through the fibre channel. Laboratory measurements were carried out to provide necessary data for the calibration and verification of the mathematical model that was developed based on the Darcy’s and Poiseuille’s laws. A good agreement was obtained between the measured and predicted flowrate values under the same conditions.The developed Mathematical model can be used as a tool to investigate the hydraulic performance of commercial HFM modules. A comparison was made between two commercially available of HFM modules of the same material but differ in the fibre sizes; it was found that there is a difference between its performance and the efficiency of the operation energy.