Flux-related and Critical Dilution Indices: Quantitative Indicators of Mixing and Mixing-controlled Reactions in Heterogeneous Porous Media

The correct quantification of mixing is of utmost importance for modeling reactive transport in porous media and, thereby assessing the fate and transport of contaminants in the subsurface. An appropriate measure of mixing in heterogeneous porous formations should correctly capture the effects on mixing intensity of various processes at different scales, such as local dispersion and the effect of mixing enhancement due to heterogeneities. In this work, we use the concept of the flux-related dilution index as a measure of transverse mixing. This quantity expresses the dilution of the mass flux of a tracer solution over the total discharge of the system and is particularly suited to address problems where a compound is continuously injected into the domain. We focus our attention on two-dimensional systems under steady-state flow conditions and investigate both conservative and reactive transport in both homogeneous and heterogeneous porous media at different scales. For mixing-controlled reactive systems, we introduce and illustrate the concept of the critical dilution index, which represents the amount of mixing required for complete degradation of a continuously emitted plume undergoing decay upon mixing with ambient water. We perform two-dimensional numerical experiments at bench and field scales in homogeneous and heterogeneous conductivity fields. These numerical simulations show that the flux-related dilution index quantifies mixing and that the concept of the critical dilution index is a useful measure to relate the mixing of conservative tracers to mixing-controlled turnover of reactive compounds. In the end we define an effective transverse dispersion coefficient which is able to capture the main characteristics of the physical mechanisms controlling reactive transport at the field scale. Furthermore we investigated the influence of compound specific local transverse dispersion coefficients on the flux related dilution index and on the critical dilution index.