Statistical analysis and modeling of particle trajectories in 2-D fractured porous media

Solute transport observed in subsurface formations shows complex behavior, particularly in the presence of fractures. In this work, we focus on formations with fractures that are smaller compared to the domain of interest and which are distributed in a heterogeneous matrix at densities below the percolation threshold. We developed a simplified Lagrangian approach to characterize and predict advective transport in 2-D domains containing differently oriented fractures. To this end, we performed Monte Carlo simulation (MCS) studies using ensembles of random domain realizations and gathered/analyzed tracer particle displacement statistics. The series of displacement steps were defined by the locations of particles entering the matrix after traversing through one or several connected fractures. Then, we identify key correlation structures in the evolution of and between displacement step coordinates, namely, the step length, its orientation and the traverse time. Subsequently, a correlated random walk model was derived which is able to accurately reproduce longitudinal and transverse macrodispersion as recorded in the MCS. Finally, we explored the predictive capabilities of our stochastic model by simulating macrodispersion in stratified media composed of heterogeneous zones with different fracture orientations.