Heat and mass transfer in a randomly packed hollow fiber membrane module: A fractal model approach

Hollow fiber membrane modules are widely used in various industries. The disordered nature of hollow fiber distributions in the module exhibits the existence of a fractal structure formed by the voids between the fibers. The area fractal dimension of the voids on the module cross section is obtained. Then the shell side flow distribution and convective heat and mass transfer are investigated based on the fractal theory developed. An experimental work where an air flow in the shell side is humidified by a water flow in the tube side is performed to validate the model. It is found that the model predicts the flow distribution and the heat and mass transfer deteriorations well with local data for a triangular array. With the model, friction factor and Sherwood number deteriorations which take into account of the degree of irregularity, in terms of fractal dimension, are analyzed. The results show that the higher the packing density is, the less the fractal dimension is, and the less the non-uniformity of the flow distribution is. The Sherwood and Nusselt numbers of a randomly distributed fiber module are only 1–5% of a uniformly spaced tube array. Correlations are proposed for the estimation of friction factor and Sherwood numbers considering the degree of irregularity. The predictions are also compared to the available mass transfer correlations in the literature.