A study of mass transfer in hollow-fiber membrane contactors—The effect of fiber packing fraction

Mass transfer in flow parallel to a bundle of fibers is considered. The study is focused on shell-side mass transfer and in particular on the effect of fiber packing fraction φ, a topic very inadequately treated in the literature despite its significance. The process of liquid–liquid membrane-based extraction is examined, involving solute transfer from an aqueous phase (flowing in the shell) to an organic solvent (hexane). Benzaldehyde and hexanal, at low concentrations in water, are the solutes employed, thus obtaining two systems characterized by high partition coefficient. The four modules used are made of hydrophobic polypropylene fibers covering the range of packing densities φ = 0.093–0.402. Quite complete sets of data are collected over sufficiently broad ranges of Reynolds numbers at shell-side (Rew) and lumen (Reo). The experimental study is backed by theoretical modelling of mass transfer, based on laminar boundary-layer type analysis at shell-side, presented in a companion paper. It is shown that the dependence of shell-side Sherwood number, Shw, on Rew to 1/3 power satisfactorily describes the new data, throughout the packing fraction φ-range tested. The effect of φ on shell-side mass transfer (if any) appears to be very weak, probably buried within the narrow range of experimental error; thus, an appropriate correlation for Shw is recommended, covering the φ-range of practical interest (0.05–0.45). The reliability of the new data (and of the proposed correlation) is supported by the theoretical model predictions, displaying fair agreement with no recourse to any adjustable parameters. Finally, the set of expressions developed and/or tested in the context of this study, for predicting stream exit concentrations in physical membrane-based extraction, are in very good agreement with all the new data.