Dispersion of a chemically reactive solute in a spatially periodic model of a porous medium

Abstract Diffusive and convective transport of a reactive solute within a spatially periodic model of a porous medium is studied analytically for the case where the solute undergoes a generally inhomogeneous first-order irreversible chemical reaction in the interstitial fluid region and/or on the surfaces of the bed particles. A variant of the Taylor—Aris method-of-moments scheme is used to determine the three Darcy-scale phenomenological coefficients governing the macroscopic transport process, these being the mean solute velocity vector U *, diffusivity dyadic D *, and apparent volumetric reactivity coefficient γ *. These coefficients are shown to be expressible in terms of the respective solutions of the characteristic and adjoint eigenvalue problems associated with the microscale convective—diffusive—reactive volumetric and surface differential operators, and defined within the interstitial region of a single unit cell of the spatially periodic porous medium. Each of these three macroscale phenomenological coefficients is shown to be independent of the initial solute distribution within the porous medium, as well as of the choice of weight function used in averaging the microscale solute concentration over the unit cell ('representative volume'). Contrary to prevailing opinion, microscale chemical reactions are shown to affect both the Darcy-scale solute velocity and diffusivity. These 'converse' effects exist in addition to the well-known 'direct' effects of the microscale solute diffusion and fluid convection upon the Darcy-scale apparent volumetric reactivity coefficient γ *. Several specific examples illustrate the implementation of our general solution scheme. On the basis of these, a novel 'reaction-chromatography' separation scheme is proposed. Finally, doubts are expressed as to the utility of residence-time distribution theory as a rational scheme for the design of chemical reactors, since such distribution functions are generally different for reactive solutes than for inert solutes—at least in circumstances where the specific reactivity coefficient is locally inhomogeneous.