Numerical simulation of an unstirred batch ultrafiltration process based on the boundary layer concept

A mass transfer model based on a concentration boundary layer, as suggested by film theory, is proposed in this study. The mass transfer coefficient f or the case of an unstirred batch cell was predicted using an extrapolation technique based on a suitable curve fitted equation. The parabolic partial differential equation resulting from the unsteady state mass balance over the concentration boundary layer was solved by a numerical technique using a second order implicit method. The solution process also couples the osmot ic pressure model for the prediction of flux and an equation from irreversi ble thermodynamics for the prediction of real rejection. All equations were solved simultaneously by the multidimensional Newton-Raphson technique usi ng Broyden's correction factor to enhance the rate of convergence. The fina l predicted flux and rejection was found to be in good agreement with the e xperimental data, and the absolute average deviation in both cases was foun d to be well within 10%. (C) 1999 Elsevier Science B.V. All rights reserved .