On using particle tracking methods to simulate transport in single-continuum and dual continua porous media

The use of particle tracking methods to predict transport in single continuum and dual continua (mobile-immobile systems and fractured media) is studied. The accuracy of the particle tracking methods with different interpolation and tracking techniques is evaluated, and its transport predictions are compared to analytical solutions, finite element solutions (e.g. SUTRA) and finite difference solution (e.g. MT3D). For a two-dimensional problem with homogeneous conductivity and pulse injection of contaminant, the particle tracking solution matches the analytical solution better than those using standard finite difference and finite element techniques, which suffer from numerical dispersion. Furthermore, the particle tracking method accurately predicts the mean and variance of the stochastic concentration distribution and compares favorably with MT3DMS that employs a total variance diminishing technique for discretizing the advection term. For modeling matrix diffusion in fractured media and mass transfer in dual porosity (mobile-immobile) systems, two approaches are studied and compared. A semi-analytical approach is compared to a particle tracking technique that accounts for matrix diffusion using particle transfer probabilities. An empirical relationship that can be used to map the governing parameter of the semi-analytical approach to the corresponding panicle transfer probability is derived. The similarities and differences between these two techniques and their suitability for practical applications are also discussed.