Modeling Transport in Dual-Permeability Media with Unequal Dispersivity and Velocity

Porous media such as fractured rock and aggregated soils consist of two pore domains with distinct transport properties. A numerical code was developed to simulate solute concentrations in the two domains using a partitioned solution procedure to efficiently model transport in dual-permeability media. Furthermore, an approximate analytical solution was obtained that allows for different advective and dispersive terms in both flow domains, for a first-type or a third-type inlet condition. Solutions were obtained for local concentrations in both domains as well as effluent concentration and the concentration per medium volume. The problem was solved by decoupling the transport equations using diagonalization. This involves an error for the dispersivity matrix that is related to the difference in dispersivity of both domains. The correctness of the solution was assessed by comparison with numerical results. For low Damköhler numbers the solution was accurate even for a dispersivity ratio of 10. The need for a dual-dispersivity instead of a single-dispersivity model was illustrated with sample breakthrough curves and the solution was applied to optimize experimental breakthrough curves for an Andisol with a distinct intraaggregate and interaggregate porosity.