Coupled transport of multi-component solutes in porous media

Coupled convective-diffusive transport of multicomponent solutes in spatially-periodic models of porous media is considered. Species coupling at the micro- or interstitial scale results from a first-order irreversible surface reaction on the bed elements, composing the porous medium, and from the off-diagonal terms of the microscale matrix transport coefficients. The coarse-scale long-time solute matrix properties are calculated, namely, mean effective reactivity, velocity and dispersivity. These coefficients are analyzed in several important particular cases, pertaining to reactive and nonreactive constituents. The solution scheme is illustrated by an example of two reactive solute components with diffusional coupling, flowing in a bundle of tubes model porous medium. The effective matrix axial transport coefficients are analyzed for various values of the dimensionless Damkohler number, Da, associated with the surface-reaction constant. Analytical expressions for the effective axial transport properties are obtained in cases of extreme (small and large) values of the dimensionless Damkohler numbers. The microscale molecular diffusive coupling provides for each solute constituent two diffusive pathways to the reactive tube wall: one - via the direct diffusivity component, another - via the coupling diffusivity. The macroscopic manifestation of this microscale coupling is to give rise to coupling off-diagonal terms in the effective matrix transport coefficients: positive off-diagonal terms in the reactivity matrix and negative off-diagonal terms in velocity and dispersivity matrices. From a physical viewpoint microscale coupling brings about a more uniform solute distribution within the tube cross section, which reduces the effective axial transport.