Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media

TL;DR

This paper introduces a global random walk (GRW) method for simulating reactive transport and biodegradation in heterogeneous porous media, offering computational efficiency and direct concentration modeling without rescaling particle densities.

Contribution

The paper presents a novel GRW-based numerical framework for coupled flow and reactive transport in porous media, handling nonlinearity and heterogeneity effectively.

Findings

GRW schemes demonstrate numerical convergence against analytical solutions.

Coupled flow and reactive transport problems are successfully simulated.

Flow nonlinearity and heterogeneity significantly influence biodegradation outcomes.

Abstract

Flow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number of the lattice sites is updated with a global random walk (GRW) procedure which spreads the particles from a lattice site with computational costs comparable to those for a single random walk step in sequential procedures. To cope with the nonlinearity and the degeneracy of the Richards equation the GRW flow solver uses linearization techniques similar to the $L$-scheme developed in finite element/volume approaches. Numerical schemes for reactive transport, coupled with the flow solver via numerical solutions for saturation and water flux, are implemented in splitting procedures. Diffusion-advection steps are solved by GRW algorithms using either biased or unbiased random walk probabilities. Since the number of particles in GRW simulations can be as large as the number of molecules involved in chemical reactions, one avoids the cumbersome problem of rescaling particle densities to approximate concentrations. Reaction steps are therefore formulated in terms of concentrations, as in deterministic approaches. The numerical convergence of the new schemes is demonstrated by comparisons with manufactured analytical solutions. Coupled flow and reactive transport problems of contaminant biodegradation described by the Monod model are further solved and the influence of flow nonlinearity/degeneracy and of the spatial heterogeneity of the medium is investigated numerically.