Abstract
This paper deals with two-equation models describing solute transport in highly heterogeneous porous systems and more particularly dual permeability structures composed of high- and low-permeability regions. A macroscopic two-equation model has been previously proposed in the literature based on the volume averaging technique [Ahmadi A, Quintard M, Whitaker S. Transport in chemically and mechanically heterogeneous porous media V: two-equation model for solute transport with adsorption, Adv Water Resour 1998;22:59–86; Cherblanc F, Ahmadi A, Quintard M. Two-medium description of dispersion in heterogeneous porous media : calculation of macroscopic properties. Water Resour Res 2003;39(6):1154–73]. Through this theoretical upscaling method, both convection and dispersion mechanisms are taken into account in both regions, allowing one to deal with a large range of heterogeneous systems.In this paper, the numerical tools associated with this model are developed in order to test the theory by comparing macroscopic concentration fields to those obtained by Darcy-scale numerical experiments. The heterogeneous structures considered are made up of lowpermeability nodules embedded in a continuous high-permeability region. Several permeability ratios are used, leading to very different macroscopic behaviours. Taking advantage of the Darcy-scale simulations, the role of convection and dispersion in the mass exchange between the two regions is investigated.Large-scale averaged concentration fields and elution curves are extracted from the Darcy-scale numerical experiments and compared to the theoretical predictions given by the two-equation model. Very good agreement is found between experimental and theoretical results. A permeability ratio around 100 presents a behaviour characteristic of ‘‘mobile–mobile’’ systems emphasizing the relevance of this two-equation description. Eventually, the theory is used to set-up a criterion for the existence of local equilibrium conditions. The potential importance of local-scale dispersion in reducing large-scale dispersion is highlighted. The results also confirm that a non-equilibrium description may be necessary in such systems, even if local-equilibrium behaviour could be observed.