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

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.