Abstract
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.
Highlights
Numerical works of modeling of dissolution ([24] [25] [26] [27]) were carried out. These numerical studies show that: 1) the effectiveness of the dissolution of NAPL depends on the heterogeneity of the aquifer which controls the trapping of NAPL; 2) the deviation of the aqueous phase flow resulting from the heterogeneity and the reduction of relative permeability due to the trapping of NAPL prolongs times of dissolution ([26]); 3) the morphology of the NAPL source zone, determined by heterogeneity of the porous medium controls dissolution, in other words the precise characterization of the location of the trapped clusters is essential to predict the dissolution flux [27]; 4) when the initial residual saturation is discontinuous, pure water entering in the NAPL source zone can come out again with a certain concentration different or non-equilibrium concentration
This result confirms those obtained previously in the case of the “local equilibrium” assumption for the flows perpendicular to the strata ([31] [38]), the correlations of the mass exchange coefficients used for each case are very different. These mass exchange coefficients grow in both cases with average saturation for the three volume fractions of region considered. As in the former studies [38], one notices that the mass transfer during the dissolution of NAPL in heterogeneous porous medium is amongst other things controlled by: ‒ quantity of residual pollutant contained in poral space; ‒ installation of this pollutant in the porous medium, certainly marked by the influence of heterogeneities or hydrodynamic instabilities
In this paper we have proposed a large-scale model describing NAPL dissolution for stratified heterogeneous systems
Summary
The mechanisms of migration in aquifers of partially miscible pollutants to water (oil, hydrocarbons...), later denoted NAPL for Non-Aqueous Phase Liquid, are well-known. Numerical works of modeling of dissolution ([24] [25] [26] [27]) were carried out These numerical studies show that: 1) the effectiveness of the dissolution of NAPL depends on the heterogeneity of the aquifer which controls the trapping of NAPL; 2) the deviation of the aqueous phase flow resulting from the heterogeneity and the reduction of relative permeability due to the trapping of NAPL prolongs times of dissolution ([26]); 3) the morphology of the NAPL source zone, determined by heterogeneity of the porous medium controls dissolution, in other words the precise characterization of the location of the trapped clusters is essential to predict the dissolution flux [27]; 4) when the initial residual saturation is discontinuous, pure water entering in the NAPL source zone can come out again with a certain concentration different or non-equilibrium concentration. The two-dimensional problem is considered: a large-scale NAPL, local non equilibrium dissolution model is built using a volume averaging technique and effective properties such as the large scale relative permeability to water and the large scale mass exchange coefficient are estimated for situations of the study
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