Simulating pore-scale nonlinear reactions at the fluid-solid interface using random walk particle tracking

Random walk particle tracking (RWPT) methods employ a Lagrangian discretization of solute plumes into point particles to numerically solve the advection-dispersion equation. Their recognized advantages over more traditional grid-based Eulerian methods regarding numerical stability and numerical dispersion make them ideal candidates to simulate complex reactive fronts in heterogeneous media. However, handling nontrivial boundary conditions remains a challenge, restricting the range of interface processes that can be simulated. We derive and validate a new collision-based approach to implement a broad class of generalized Robin-type boundary conditions, representing the balance between diffusive fluxes and an arbitrary nonlinear function of the transported and surface reactant concentrations. This formulation allows for modeling arbitrary coupled sets of nonlinear surface reactions within the classical RWPT framework, thus opening new opportunities for simulating pore-scale reactive transport in the subsurface. The collision-based nature of the proposed technique allows for estimating surface reaction rates based on single-particle collisions with the reactive interface. Thus, it does not require concentration field reconstructions or multi-particle searches. We verify the method for a coupled set of nonlinear mass-action reactions under pure diffusion and for nonlinear kinetics representing calcite dissolution in a model porous medium.