Solute transport in dual‐permeability porous media

Abstract

A dual‐advection dispersion equation (DADE) is presented and solved to describe solute transport in structured or layered porous media with different nonzero flow rates in two distinct pore domains with linear solute transfer between them. This dual‐permeability model constitutes a generalized version of the advection‐dispersion equation (ADE) for transport in uniform porous media and the mobile‐immobile model (MIM) for transport in media with a mobile and an immobile pore domain. Analytical tools for the DADE have mostly been lacking. An analytical solution has therefore been derived using Laplace transformation with time and modal decomposition based on matrix diagonalization, assuming the same dispersivity for both domains. Temporal moments are derived for the DADE and contrasted with those for the ADE and the MIM. The effective dispersion coefficient for the DADE approaches that of the ADE for a similar velocity in both pore domains and large values for the first‐order transfer parameter, and approaches that of the MIM for the opposite conditions. The solution of the DADE is used to illustrate how differences in pore water velocity between the domains and low transfer rates will lead to double peaks in the volume‐ or flux‐averaged concentration profiles versus time or position. The DADE is applied to optimize experimental breakthrough curves for an Andisol with a distinct intra‐ and interaggregate porosity. The DADE improved the description of the breakthrough data compared to the ADE and the MIM.