Modelling of cross-flow membrane contactors: physical mass transfer processes

Traditionally, hollow fiber membrane contactors used for gas-liquid contacting were designed in a shell and tube configuration with shell-side fluid flowing parallel to the fiber-side fluid, either in co-current or counter-current pattern. The primary limitations of these so-called 'parallel flow' contactors are the shell-side flow channeling or mal-distribution due to non-uniform packing of the hollow fibers, higher shell-side pressure drop and relatively lower mass transfer coefficients. These limitations can be eliminated or reduced substantially by placing hollow fibers perpendicular to the flow direction. In these cross-flow membrane contactors the concentrations of both fluids vary in both directions i.e. in the direction of the flow as well as in the direction perpendicular to the flow. Hence, unlike parallel flow contactors, simple logarithmic averaging of the concentration driving force cannot be used to predict performance of the cross-flow membrane contactors. Similar changes in the driving force are also found in the cross-flow shell and tube heat exchanger. An analytical expression based on heat transfer analogy is derived in this work to describe the mass transfer in these hollow fiber cross-flow contactors. However, it was found that when the change in the volumetric flow of the compressible fluid is significant heat transfer analogy cannot be used to predict the performance of the cross-flow gas-liquid membrane contactor. Therefore, a detailed numerical model is developed to analyze the performance of the cross-flow membrane contactor in such cases. The model takes into account the shell-side mixing, change in concentration driving force in all direction as well as cascading two or more cross-flow modules to give overall co- or counter-current flow arrangement. To validate the model and developed analytical expression, carbon dioxide absorption experiments were carried out in cross-flow membrane contactor using water as a solvent. The predictions of the developed numerical model were found to be in good agreement with the experimental results.