Interlayer Diffusive Transfer and Transport of Contaminants in Stratified Formation. I: Theory

Abstract

This paper deals with modeling depth-averaged solute transport and lateral-diffusive transfer in a two-layer system of contrasting permeabilities. Two-dimensional transport equations are developed, by averaging the local three-dimensional transport equations vertically across the high- and low-permeability layers. The equations account for interlayer mass transfer and the capacitance of the low-permeability layer to store and release reactive constituents by diffusion. The theory indicates that a first-order rate model can describe the process of interlayer mass transfer under quasi-steady condition. An expression for the mass-transfer rate coefficient α is obtained in terms of the transverse diffusion time (or diffusion rates) across the layers. In particular, the diffusion time in the high-permeability layer is related to transverse-vertical dispersion that accounts for the effect of mechanical mixing on the interlayer mass transfer. For small capacity ratio β< 1 the rate coefficient α shows a linear dependence on the pore-water velocity, and a linear approximation is obtained in terms of a Peclet number, in which the transverse-vertical dispersivity is the characteristic length scale. Application to previously published experimental data highlighted the applicability and limitations of the first-order rate model.