The Space-Time Adaptive Smoothing Approach to Reactive Random Walk Particle Tracking

Lagrangian methods such as Random Walk Particle Tracking (RWPT) are often employed to simulate solute transport in heterogeneous porous media. They are free from the numerical dispersion and instability problems that affect Eulerian methods, and they are mass-conservative by definition, among other advantages. Until very recently, the main limitation of RWPT has been the incorporation of complex (nonlinear, equilibrium, multicomponent…) chemical reactions. We present our most recent advances on reactive transport modeling with RWPT, which allow us to simulate all kinds of nonlinear kinetic and equilibrium reactions between numerical particles, by means of time-evolving and space-adaptive smoothing functions that provide an optimal link between particle positions and solute concentrations. These smoothing functions (kernels), which can be understood as mathematical representations of the particle support volume, are optimized in size and shape to minimize the error in a local environment. The kernels are efficiently applied and stored in the form of matrices, and they are corrected to account for impermeable boundaries. The same principles can be used to control the error through particle splitting and merging. Finally, we introduce our latest work on the upscaling of lower-scale mixing-limited reactions through an extension of the presented methodology. In this variation, we compute the solute concentrations at two different scales: The model-scale concentration (given by smoothing) and the particle-scale concentration, which drives the reactions. The parameters that control the interplay between these two concentrations can be linked to the statistical description of the local-scale medium heterogeneity, or they may be inferred from experimental results.