MODPATH-RW: A Random Walk Particle Tracking Code for Solute Transport in Heterogeneous Aquifers

Random walk particle tracking (RWPT) is a discrete particle method that offers several advantages for simulating solute transport in heterogeneous geological systems. The formulation is a discrete solution to the advection-dispersion equation, yielding results that are not influenced by grid-related numerical dispersion. Numerical dispersion impacts the magnitude of concentrations and gradients obtained from classical grid-based solvers in advection-dominated problems with relatively large grid Péclet numbers. Accurate predictions of concentrations are crucial for reactive transport studies, and RWPT has been recognized for its potential benefits for this kind of application. This highlights the need for a solute transport program based on RWPT that can be seamlessly integrated with industry-standard groundwater flow models. This article presents a solute transport code that implements the RWPT method by extension of the particle tracking model MODPATH, which provides the base infrastructure for interacting with several variants of MODFLOW groundwater flow models. The implementation is achieved by developing a method for determining the exact cell-exit position of a particle undergoing simultaneous advection and dispersion, allowing for the sequential transfer of particles between flow model cells. The program is compatible with rectangular unstructured grids and integrates a module for the smoothed reconstruction of concentrations. In addition, the program incorporates parallel processing of particles using the OpenMP library, enabling faster simulations of solute transport in heterogeneous systems. Numerical test cases involving different applications in hydrogeology benchmark the RWPT model with well-known transport codes.