Interlayer Diffusive Transfer and Transport of Contaminants in Stratified Formation. II: Analytical Solutions

Abstract

Transverse diffusive transfer of solute mass between regions of mobile and immobile water is a key mechanism causing tailing and reduced peak concentrations. In Part 1, we developed a two-dimensional first-order rate model that describes reactive solute transport averaged across the thickness of a two-layer system. The model describes the capacitance effect of low-permeability layers to store and release solute by diffusive-type mass transfer, under quasi-steady conditions. In this paper, we develop two-dimensional analytical solutions for the first-order rate model in an infinite porous medium, using the methods of Fourier and Laplace transforms and superposition. The solutions consider a rectangular source with (1) an instantaneous release of a contaminant mass and (2) an exponentially decaying source applied at a fixed rate. Simulations show that increased pore-water velocity produces a more dispersed mobile solute and pronounced tailing. Comparison of the theory with the Borden aquifer data indicates that the first-order rate model can describe the early dispersion of the chloride tracer, on the basis of diffusive interlayer mass transfer.