The longitudinal dispersion and cross-sectional concentration distribution of chemical species through an annular tube have been studied for oscillatory flows in the presence of heterogeneous reactions between the species and tube wall along with homogeneous reaction in the bulk flow. The species is supposed to undergo kinetic reversible phase exchange and irreversible absorptive reactions at the outer wall material whereas in the bulk of the flow, the species participates in a first-order reaction with the solvent. The velocity distribution has a complex interaction with the reaction parameters and in order to track that, three different kinds of oscillatory flows are considered. For the purpose of estimation of dispersion coefficient, the method of moments Aris (1956)[3] is employed. The unsteady convective-diffusion equation gives rise to integral moment equations and are solved numerically by FDM. The cross-sectional concentration distribution is determined from the relationship between central moments and Hermite polynomials for the unsteady components of the flows. The study reveals the coupled effects of reversible phase exchange, irreversible absorption and bulk flow reaction on the transport of species in a variety of flow situations. © 2020 Elsevier Inc.