BENCHMARKING THREE-DIMENSIONAL VARIABLE-DENSITY FLOW IN FRACUTED POROUS MEDIA

Variations in fluid density can greatly affect fluid flow and solute transport in fractured rock. Numerical models are often used to simulate variable-density flow in groundwater. A useful model must be tested and model testing is carried out by comparing model performance with “benchmark” problems. Several benchmark problems exist to verify a new variable-density flow model in porous media. However, few test cases exist to verify a new variable-density flow model in fractured porous media. Results presented by Shikaze et al. (1998, JCH) and Graf and Therrien (2005, AWR) can be used to verify dense plume migration in 1D vertical and inclined fractures embedded in a 2D porous matrix. Caltagirone (1982) and Weatherill et al. (2004, AWR) have presented analytical solutions for the onset of convection in homogeneous media. The solutions can be applied to vertical and inclined fractures by introducing a cosine weight to account for fracture incline. However, application of the Caltagirone (1982) and the Weatherill et al. (2004, AWR) analytical solutions requires that the rock matrix be impermeable. We conclude that, to date, a robust and well-accepted benchmark problem for variable-density flow in 2D fractures oriented in 3D and embedded in a permeable 3D rock matrix does not exist.

In this paper, we present a new benchmark problem for variable-density flow in a non-planar fracture embedded in a 3D porous matrix. We modify the HydroGeoSphere model to solve variable-density flow in 3D fractured rock and the modified model is verified using analytical and numerical test cases. With the extended model, variable-density flow in a single non-planar fracture is benchmarked where the porous matrix consists of regular 3D hexahedral elements and the fracture consists of 2D triangular elements. The transient benchmark simulation describes advection, dispersion, and diffusion in both fracture and porous matrix and fracture-matrix diffusion. We provide detailed data on mass fluxes, tracer breakthrough curves, concentration contours and tracer penetration depth to ensure rigorous objective testing of a new model. We also give details on the numerical methods used to ensure further rigorousness of the new benchmark problem. The new benchmark allows numerical intercomparison with a new variable-density flow model in a 3D framework.