The focus of this work is on the rate of interfacial mass transfer at the interface between two immiscible fluids in porous media, subjected to variations in velocity and first-order consumption in the bulk medium. Numerical and analytical solutions are presented. We quantify the entrance length scale, which is the typical length in the flow direction over which the local and equilibrium Sherwood numbers () become identical, for Darcy-Brinkman flows in the presence of first-order bulk reactions (presented by Damkohler () number). The study considers the effect of Schmidt number (), viscosity ratios, permeability and bulk reaction coefficients. Results suggest a closed form solution for the entrance length scale. It is also observed that the assumption of equilibrium conditions prior to approaching this length may be violated for lower bulk reaction rates. Numerical and analytical results are in good agreement and suggest limited dependency of equilibrium and , as diminishes.