Simulating solute transport in discretely fractured rocks: Computational limitations and a hybrid method
To investigate the computational limitations arising when simulating large-scale groundwater flow and solute transport using a 3D control volume finite element model (the FE model) in discrete-fracture mode, numerical simulations were matched to a semi-analytical solution for radial divergent solute transport in a single fracture. Discretization parameters and computation times were compared for two sets of simulations. Depending on the model parameters, transport simulations in the FE model can take longer to compute with parallel versus serial processing. The transport solution was the largest limiting factor with respect to computational cost for our models. Transport computations, for example, took 86-98% of the total computation time, and the relative flow and transport times changed little with increasing scale. Next, an efficient hybrid numerical-analytical method (the NA method) for simulating solute transport in 2D fracture networks is proposed. The NA method can be used to compute solute breakthrough curves in a 2D network of fractures of varying aperture and fluid velocity by applying the Tang et al. (1981) solution to an equivalent fracture pathway (EFP) which is generated by a numerical model. The NA method was verified at three different transport scales (i.e., 10m, 50m and 250m) using a range of realistic fracture apertures, matrix porosities and hydraulic gradients, by comparing simulated breakthrough curves to those generated by the FE model. Solute dilution can be accommodated by scaling a breakthrough curve using discharge ratios in the fracture segments before and after dilution. The validity of this method depends on the ratio of the Péclet number and the matrix porosity, which can serve as an indication of the cases in which the NA method will be valid for a given fracture spacing and transport distance. A 2k factorial analysis was also conducted which shows that increasing the number of fracture intersections diminishes the ability of the NA method to match the FE model. Simulations of realistic 2D fracture networks however show that in natural fractured rock systems, the NA method could be a useful tool to simulate solute transport at an up to 85% reduced computational cost.