Relevance of local compound-specific transverse dispersion for conservative and reactive mixing in heterogeneous porous media

Different measures of dilution have been proposed to describe solute mixing in heterogeneous porous media. Most of these approaches lead to the definition of effective dispersion coefficients. In order to quantify mixing, these up-scaled parameters should account for both local-scale dispersion and effects of flow variability in heterogeneous formations (e.g., flow focusing in high-conductivity and defocusing in low-conductivity inclusions). The correct quantification of mixing is particularly important for transport of compounds undergoing reactions. Recent results of multitracer laboratory experiments showed a dependency of local transverse dispersion on molecular diffusion over a wide range of flow velocities, implying compound-specific transverse mixing even at intermediate and high Peclet numbers. The goal of this study is to assess the relevance of a compound-specific local-scale transverse dispersion on conservative and reactive mixing in heterogeneous domains at the field scale. We restrict our analysis to steady state two-dimensional flow and transport with continuous injection from a line source. We present numerical simulations in heterogeneous domains with different characteristics of variability in the conductivity field, and apply as measures of solute mixing: (1) the effective transverse dispersion coefficient derived from second central spatial moments, (2) a dispersion coefficient derived from flux-related second central spatial moments, (3) the scalar dissipation rate, and (4) a dispersion coefficient derived from the flux-related dilution index. The results indicate compound-specific transverse mixing behavior also at the field scale which is particularly significant in case of low to moderately heterogeneous porous media. Moreover, we show that measures of dilution calculated in a flux-related framework result in an improved quantification of mixing processes and allow to define up-scaled parameters (i.e., effective transverse dispersion coefficients) affected by a low degree of uncertainty. For mixing-controlled reactive transport we illustrate the importance of compound-dependent local effects on the length of reactive solute plumes.