A benchmark for variably saturated variable-density variable-viscosity flow and solute transport in porous media

Abstract

In natural environments, fluid density and viscosity can be affected by spatial and temporal variations of solute concentration, for example, due to saltwater intrusion in coastal aquifers, leachate infiltration from waste disposal sites, and upconing of saline water from deep aquifers. Potentially unstable situations may arise in which a dense fluid overlies a less dense fluid. This situation can produce instabilities manifested by dense plume fingers moving vertically downwards counterbalanced by vertical upward flow of the less dense fluid. The resulting free convection increases solute transport rates over large distances and times relative to constant-density flow. Unstable brine flow is further complicated if the porous medium is variably saturated. The results from a laboratory experiment of variably saturated variable-density flow and solute transport from Simmons et al. (2002) are used as the physical basis to define a new mathematical benchmark. This benchmark aims at realistically reproducing the experimental fingering patterns. Random hydraulic conductivity fields were used in the simulations as a numerical perturbation method to realistically mimic the observed dense plume fingering. The HydroGeoSphere code coupled with PEST are used to calibrate the parameter set that defines the benchmark. A grid convergence analysis is performed to obtain the adequate spatial and temporal discretizations. The new mathematical benchmark is useful for model comparison and testing of variably saturated variable-density flow in porous media. Simmons CT, Pierini ML, Hutson JL (2002) Laboratory investigation of variable-density flow and solute transport in unsaturated–saturated porous media. Transp Porous Media. 47(2): 215–244, 10.1023/A:1015568724369.