Mathematical modelling of a flow-injection system with a membrane separation module

A mathematical model for a flow-injection system with a membrane separation module based on the axially dispersed plug flow model was developed. It takes into account the geometrical dimensions and dispersion properties of the main sections of the manifold, the mass transfer in the channels of the separation module and the characteristics of the membrane (thickness and diffusion coefficient within it). The model was solved analytically in the Laplace domain. The inverse transformation was found to give satisfactory results for reactor Peclet numbers less than 120. Otherwise a numerical solution based on the implicit alternating-direction finite difference method was preferred. The adequacy of the model was confirmed experimentally on a flow-injection manifold with a parallel-plate dialysis module. The unknown flow and membrane parameters were determined by curve fitting. The membrane parameters were determined also by steady-state measurements. Fairly good agreement between the dynamic and steady-state results and with results given in the literature was observed, which, together with other experimental results, supported the validity of the model and showed that it can be used successfully for the mathematical description and optimization of flow-injection systems with membrane separation modules. In this connection, the influence of the reactor parameters and the sample volume on the performance of such a system were investigated and conclusions for improving its sensitivity and sample throughput were drawn. Other possible applications of the model are in membrane technology for characterizing of various membranes and in process engineering for investigating the mass transfer in different dialysers.