Transverse mixing of conservative and reactive tracers in porous media: Quantification through the concepts of flux-related and critical dilution indices

The correct quantification of mixing is of utmost importance for modeling reactive transport in porous media and for 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 mixing enhancement due to heterogeneities. In this work, we use the concept of flux-related dilution index as a measure of transverse mixing. This quantity expresses the dilution of the mass flux of a conservative 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 homogeneous and heterogeneous porous media at different scales. For mixing-controlled reactive systems, we introduce and illustrate the concept of 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 critical dilution index is a useful measure to relate the mixing of conservative tracers to mixing-controlled degradation of reactive compounds.