Approximate solution to predict the enhancement factor for the reactive absorption of a gas in a liquid flowing through a micriporous membrane hollow fiber

Approximate solutions for the enhancement factor (based on the traditional mass transfer theories) for gas–liquid systems with a liquid bulk have been adapted to situations where a liquid bulk may be absent and a velocity gradient is present in the mass transfer zone. Such a situation is encountered during the absorption a gas in a liquid flowing through a hollow fiber. The explicit solution of DeCoursey [Chem. Eng. Sci. 29 (1974) 1867] for a second-order irreversible reaction has been used as a representative sample of the approximate solutions available in literature. It was chosen because of the accuracy of its predictions and the simplicity in use. The solution of DeCoursey was adapted, but still has limitations at long gas–liquid contact times. Under these conditions, the actual driving force for mass transfer of the gas phase species may not be identical for physical and reactive absorption. Also for these situations, there may be a significant depletion of the liquid phase reactant at the axis of the fiber (which is considered to be analogous to the liquid bulk in traditional mass transfer models). A criterion has been proposed for the applicability of the adapted DeCoursey’s approximate solution for a second-order irreversible reaction. Within the range of applicability, the approximate solution has been found to be accurate with respect to the exact numerical solution of the mass transfer model as well as the experimentally determined values of enhancement factor in a single hollow fiber membrane gas–liquid contactor. The single hollow fiber membrane contactor that has been used in this study has potential for use as a model gas–liquid contactor. This contactor can thus be used, along with the present approximate solution of the enhancement factor, to obtain the physicochemical properties of a reactive gas–liquid system from the experimental absorption flux measurements or vice versa, as described in the present work.