A general mathematical model for the prediction of pressure, flow rate, and flux profiles in an ultrafiltration/microfiltration hollow fiber membrane module whose shell side is filled with beads has been developed. The model was studied for a variety of operational modes in such modules, e.g., ultrafiltration/microfiltration, permeate flow rate control, Starling flow (encountered in hollow fiber bioreactors), and tube-side elution (encountered in filtration-cum-chromatography processes), etc., with or without a bead-filled extended section at the permeate outlet. An algorithm is provided to determine the model parameters from experimental data using the model equations. The solutions developed have been used to study the uniformity of transmembrane pressure profile along the module length using a quantity called the uniformity factor α. This factor shows that the model can be a useful tool for achieving the desired module performance in a number of quite different applications. The model predicts successfully the nature of the transmembrane pressure profile and the solvent flux profile in situations that are quite different, namely, conventional ultrafiltration and Starling flow. The approach used in this study can also be adopted to develop a model for description of other operational modes such as backflushing and shell-side elution used in the processes of filtration-cum-chromatography. Those applications employing similar device configurations may also use this model to predict the pressure and flux profiles to facilitate the design of the process and the operation conditions.
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