Bisection method for accurate modeling and simulation of fouling in hollow fiber membrane system

Accurate description and modeling of fouling on hollow fibers imposes a serious challenge to more effective fouling mitigation and performance optimization of the membrane system. Although the governing equations for membrane fouling can be constructed based on the known theories from membrane filtration and fluid dynamics, they are unsolvable analytically due to the complex spatially and temporally varying nature of fouling on hollow fibers. The current available numerical solutions for the governing equations are either unreliable or inconvenient to use because of the uses of unfounded assumptions or cumbersome calculation methods. This work presented for the first time a rigorous numerical procedure to solve the governing equations for fouling development on hollow fibers. A critical step to achieve the goal is the use of bisection method to determine the transmembrane pressure at the dead end of the fibers. With this procedure, fouling behavior in the hollow fiber membrane system under a given condition can be simulated within a second. The model simulations were well calibrated and verified with the published experimental data from literature. Also presented in the paper were simulations for performances of the hollow fiber membrane system under various operation conditions.