A probabilistic, flux-conservative particle-based framework for transport in fractured porous media

作者：Ranit Monga, Rajdeep Deb, Daniel W. Meyer, Patrick Jenny · 发表于：Advances in Water Resources · 年份：2023 · DOI：10.1016/j.advwatres.2023.104368 · 被引用次数：6 · 研究领域：Groundwater flow and contamination studies、Hydraulic Fracturing and Reservoir Analysis、Enhanced Oil Recovery Techniques

Advection dominated transport processes in sub-surface formations are characterized by discontinuities in the fields of transported quantities, and realistic predictions are challenging for Eulerian transport schemes because they suffer from numerical diffusion. Henceforth, we have focused on developing a Lagrangian particle-tracking scheme for modeling advective solute transport in fractured media. To this end, we adopt an Embedded Discrete Fracture Model (EDFM) for fractured media with a permeable matrix. The flexibility to use non-conformal fracture–matrix discretizations makes EDFMs a compelling choice in field-scale flow problems. Unaffected by the numerical diffusion, Lagrangian transport schemes complement the potential of EDFMs by allowing the use of sufficiently large grid cell sizes for flow field computations. In an EDFM framework, the inter-continuum fluid mass exchange cannot be quantified by the particle trajectories/pathlines due to the unresolved fracture–matrix interfaces and different dimensionalities of the matrix and fracture discretizations. These constraints motivate the use of a stochastic particle-tracking scheme, and thus, we formulated a pathline-specific probability of inter-continuum particle transfer based on mass conservation of an elementary solute/fluid mass. The particle’s transfer probability is calculated for the maximum residence time period in its associated fracture/matrix control volume, thus making the scheme time-adaptive. In addition,...