Two-Dimensional Modeling of the NAPL Dissolution in Porous Media: Heterogeneities Effects on the Large Scale Permeabilities and Mass Exchange Coefficient

In this paper, we are interested by the dissolution of NAPL (Non-Aqueous Phase Liquid) contaminants in heterogeneous soils or aquifers. The volume averaging technique is applied to 2D systems with Darcy-scale heterogeneities. A large-scale model is derived from a Darcy-scale dissolution model in the case of small and large Damkholer numbers, i.e., for smooth or sharp dissolution fronts. The resulting models in both cases have the mathematical structure of a non-equilibrium dissolution model. It is shown how to calculate the resulting mass exchange and relative permeability terms from the Darcy-scale heterogeneities and other fluid properties. One of the important finding is that the obtained values have a very different behavior compared to the Darcy-scale usual correlations. The large scale correlations are also very different between the two limit cases. The resulting large-scale models are compared favorably to Darcy-scale direct simulations.