Explicit equation for the determination of the overall mass transfer coefficient in a hollow fiber membrane contactor

•An explicit equation for the overall mass transfer coefficient was obtained.•The method of characteristics was used in the solution of fiber mass balance.•The explicit equation gives reasonable estimations of the mass transfer coefficient.•The procedure was validated using experimental data from the literature.

An explicit equation for the determination of the overall mass transfer coefficient in a hollow fiber membrane contactor is developed. This equation results from the solution of the model equations when the solute concentration in the organic extractant phase can be assumed zero throughout the operation of the system. The method of characteristics is used in the solution of the fibers mass balance partial differential equation. The numerical solution of the system using collocation in finite elements is used to identify and validate the region of applicability of the derived explicit equation, showing that it can be applied with small estimation errors even when the operating conditions are far from those imposed in the derivation. Based on an experimental run, a procedure is suggested to estimate the overall mass transfer coefficient using the explicit equation presented in this work. Finally, the proposed estimation procedure is validated using experimental data from the literature.