Guidelines for the application of a stationary model in the prediction of the overall mass transfer coefficient in a hollow fiber membrane contactor

A dynamic model describing the behavior of a hollow fiber membrane extractor, working as a closed system, is developed. Plug flow of both the aqueous and organic phases inside the fiber module is supposed while the reservoirs are considered to be perfectly mixed. The resistances to mass transfer between the phases, inside the module, are lumped in an overall mass transfer coefficient. This dynamic model shows that the system behavior is controlled by five dimensionless parameters: one equilibrium, one mass transfer, two volume ratios and one ratio of space times. A parametric study is conducted and the influence of each parameter on the system behavior is assessed independently. When a pseudo-steady state approximation is made, considering the module in steady state, the currently used stationary model is obtained [N.A. D’Elia, L. Dahuron, E.L. Cussler, Liquid–liquid extraction with microporous hollow fibers, J. Membr. Sci. 29 (1986) 309–319]. The operating region for the determination of the global mass transfer coefficient between the aqueous and organic phases using this simplified model is identified by the comparison of the histories of solute concentrations inside the respective reservoirs, obtained by the solutions of both the dynamic and the stationary models. Based on this comparison, guidelines for the application of the simplified model are given both in terms of the dimensionless parameters and of the operating variables.