Triple-porosity analysis of solute transport

Abstract

As an extension to the traditional dual-porosity approach, a triple-porosity model is presented to study the solute transport in heterogeneous porous media where the transport processes are distinctly different between macropores, mesopores and micropores. The distinctions in terms of conductance and storage in the respective pore domain are characterized by the fact that: (a) macropores are primary flow paths where both dispersion and convection are prevalent; (b) mesopores are intermediate flow paths where convection becomes dominant and (c) micropores are supplemental flow paths and mass storage spaces where only diffusive flow is manifested. In cascading coupling, the solute interchange between micropores and mesopores is maintained by assuming micropore diffusion as internal sources (sinks) attached to mesopore skins. A comprehensive solute exchange between macropores and mesopores is preserved. A mathematical model is constructed in accordance with the physical conceptualization. The coupled partial differential equations are solved in a one-dimensional geometry using Laplace transform, and the subsequent coupled ordinary differential equations are circumvented via the method of differential operators. Semi-analytical solutions are obtained.