Pore‐scale simulation of dispersion and reaction along a transverse mixing zone in two‐dimensional porous media

Abstract

Several studies have demonstrated that the success of natural and engineered in situ remediation of groundwater pollutants relies on the transverse mixing of reactive chemicals or nutrients along plume margins. Efforts to predict reactions in groundwater generally rely on dispersion coefficients obtained from nonreactive tracer experiments to determine the amount of mixing, but these coefficients may be affected by spreading, which does not contribute to reaction. Mixing is controlled only by molecular diffusion in pore spaces, and the length scale of transverse mixing zones can be small, often on the order of millimeters to centimeters. We use 2D pore‐scale simulation to investigate whether classical transverse dispersion coefficients can be applied to model mixing‐controlled reactive transport in three different porous media geometries: periodic, random, and macroscopically trending. The lattice‐Boltzmann method is used to solve the steady flow field; a finite volume code is used to solve for reactive transport. Nonreactive dispersion coefficients are determined from the transverse spreading of a conservative tracer. Reactive dispersion coefficients are determined by fitting a continuum model which calculates the total product formation as a function of distance to the results from our pore scale simulation. Nonreactive and reactive dispersion coefficients from these simulations are compared. Results indicate that, regardless of the geometrical properties of the media, product formation can be predicted using transverse dispersion coefficients determined from a conservative tracer, provided dispersion coefficients are determined beyond some critical distance downgradient where the plume has spread over a sufficiently large transverse distance compared to the mean grain diameter. This result contrasts with other studies where reactant mixing was controlled by longitudinal hydrodynamic dispersion; in those studies longitudinal dispersion coefficients determined from nonreactive tracer experiments over‐estimated the extent of reaction and product formation. Additional work is called for in order to confirm that these findings hold for a wider variety of grain sizes and geometries.