A hierarchical model for solute transport in fractured media

Abstract

A hierarchical concept for modeling solute transport in a well‐connected fracture network is presented. The approach exploits the presence of dominating fractures to separate a fracture network into a small group of primary fractures that are represented explicitly and a much larger group of fractures that are included within network blocks. The primary fracture network is identified prior to a flow solution using deterministic rules that link fracture characteristics with the likelihood that a fracture may dominate its local flow regime. Equivalent conductance matrices unique to each network block closely approximate the hydraulic connections within the network blocks. This hierarchical structure leads to the formulation of much smaller systems of equations for calculating the flow regime when compared to conventional discrete network simulation. A particle‐tracking scheme is developed that takes advantage of the hierarchical structure in modeling solute transport. Fracture systems considered include Poisson models; war‐zone models; and a fractal, Levy‐Lee model. As the range in the length scales of the fracture sets becomes broader or the variation in the transmissivity of individual fractures increases, it becomes more likely that individual fractures will dominate their local flow regime, that transport through a fracture network becomes less like that through a granular porous medium, and that a hierarchical model will provide a better approximation of transport. Poisson models with a bimodal length scale, and war‐zone and fractal models, which lead to multiscale networks, can be effectively represented by a hierarchical model. For these systems the loss in accuracy due to approximations underlying the separation of the network into primary fractures and network blocks is small relative to the uncertainty inherent in the prediction of transport through fractured media. The hierarchical approach provides a better simulation strategy than one based on elimination of the least‐transmissive fractures from the model structure.