Modeling of a radial flow hollow fiber module and estimation of model parameters using numerical techniques

A numerical solution is developed for modeling as well as predicting the performance of a radial flow hollow fiber reverse osmosis (HFRO) module. The three-parameter Spiegler–Kedem (S–K) model is used for describing the mass transport across the membrane. The solution proposed considers pressure drops in both permeate and bulk streams and includes concentration polarization. The numerical solution uses finite difference method. Two limiting cases of the system of equations are used to arrive at analytical solutions and check the validity of the numerical solution. The simulation of the above three-parameter membrane model is compared with a two-parameter membrane model and an analytical solution available in literature and the significance of the third membrane parameter, the reflection coefficient, is investigated in detail. It is found that when the reflection coefficient is decreased from its maximum value of one, the permeate flow rates are higher and the permeate concentration differs substantially from that reported by the two parameter membrane model of Sekino [J. Membr. Sci. 85 (1993) 241]. Under the simulation conditions investigated (1>σ>0.9), the maximum difference in the permeate flow rates between the two can be as large as 14% while the differences in the permeate concentrations can be as large as 4431%.