This article examines the influence of heterogeneous chemical reaction on the exchange coefficient, convective coefficient, and diffusive coefficient arising in the study of dispersion in a simplified Cross model fluid flow. The exchange coefficient emanates exclusively from the incorporation of the catalytic wall reaction. The convective and diffusive coefficients are also influenced by the wall reaction. The results show that the dispersion coefficient asymptotically reaches a stationary state after a critical time. This critical time decreases as the absorption at the walls increases. The problem finds application in biomechanics such as transport across a semipermeable membrane, in industries releasing waste into the environment, in crude oil conveyance, and in chromatography.