A semi-analytical model for the simulation of solute transport in a network of fractures having random orientations

A semi-analytical model is developed which accounts for solute transport through a multi-dimensional network of fractures having random orientations and sparse distribution. Transport processes including hydrodynamic dispersion, matrix diffusion, retardation, decay and solute transfer at fracture intersections, are considered. The model is derived by application of the Laplace transform to the governing transport equation for each fracture element. The resulting ordinary differential equations are linked using robust descriptions of mass conservation at the fracture intersections. Solute concentrations are determined by numerically inverting the transformed equations in a sequential fashion. The model is verified using a formal mass balance and through comparison to existing solutions for solute transport in fractured media. To illustrate the use of the model, solute transport in a hypothetical network domain was simulated based on fracture conditions measured at a real field setting in a granitic rock.