A modified Lagrangian-volumes method to simulate nonlinearly and kinetically sorbing solute transport in heterogeneous porous media

Transport in subsurface environments is conditioned by physical and chemical processes in interaction, with advection and dispersion being the most common physical processes and sorption the most common chemical reaction. Existing numerical approaches become time-consuming in highly-heterogeneous porous media. In this paper, we discuss a new efficient Lagrangian method for advection-dominated transport conditions. Modified from the active-walker approach, this method comprises dividing the aqueous phase into elementary volumes moving with the flow and interacting with the solid phase. Avoiding numerical diffusion, the method remains efficient whatever the velocity field by adapting the elementary volume transit times to the local velocity so that mesh cells are crossed in a single numerical time step. The method is flexible since a decoupling of the physical and chemical processes at the elementary volume scale, i.e. at the lowest scale considered, is achieved. We implement and validate the approach to the specific case of the nonlinear Freundlich kinetic sorption. The method is relevant as long as the kinetic sorption-induced spreading remains much larger than the dispersion-induced spreading. The variability of the surface-to-volume ratio, a key parameter in sorption reactions, is explicitly accounted for by deforming the shape of the elementary volumes.