Time domain particle tracking methods for simulating transport with retention and first‐order transformation

Abstract

Particle tracking in the time domain has received increasing attention as a technique for robustly simulating transport along one‐dimensional subsurface pathways. Using a stochastic Lagrangian perspective, integral representations of transport including the effects of advection, longitudinal dispersion, and a broad class of retention models are derived; Monte Carlo sampling of that integral leads directly to new time domain particle tracking algorithms that represent a wide range of physical phenomena. Retention‐time distributions are compiled for key retention models. An extension to accommodate linear transformations such as decay chains is also introduced. Detailed testing using first‐order decay chains and four retention models (equilibrium sorption, limited diffusion, unlimited diffusion, and first‐order kinetic sorption) demonstrate that the method is highly accurate. Simulations using flow fields produced by large‐scale discrete‐fracture network simulations, a transport problem that is difficult for conventional algorithms, demonstrate that the new algorithms are robust and highly efficient.