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 > sigma > 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 %. The mass transfer coefficient and the membrane model parameters are determined by using an optimization technique-the Simplex Search. The data for phenol separation obtained on a laboratory scale 139 HFRO experimental setup and the experimental data available in literature are used for the estimation of the model parameters as well as the mass transfer coefficient in the B9 module. These estimated parameters are then used to predict and compare performance at some other operating conditions. The theoretically predicted and the experimental values for both present and previous studies are found to be in good agreement. The analysis of the phenol separation data clearly shows the two parameter membrane transport model used in previous studies may not be sufficient for accurate design and analysis of a radial flow hollow fiber system for many solute-membrane systems. Finally, the mass transfer correlation for the shell side of the hollow fiber module is also developed and compared with the correlation available in literature. (C) 2004 Elsevier B.V. All rights reserved.