Variable-density Flow In Porous Media Research Articles

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

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.

A consistent velocity approximation for variable-density flow and transport in porous media

Summary Using a finite-volume nodal-based code, we introduce a new consistent numerical scheme for approximating the seepage velocity in variable-density flow in porous media. It has been known from previous works that the lack of consistency in the numerical approximation for the seepage velocity can severely compromise the accuracy of numerical solutions of salt-transport in porous media. This paper provides a detailed description of the code needed for the new consistent velocity approximation, including numerical approximations and algorithm implementations. The new scheme is tested against two challenging benchmark cases in the field: the hydrostatic test and the salt-pool problem. Results obtained with the newly proposed consistent scheme show the best agreement with the benchmark experiments achieved so far. When an inconsistent approximation is used instead, the accuracy of the numerical results is greatly degraded. The current work confirms that using a consistent velocity approximation is essential for maintaining accuracy in numerical simulations of variable-density flow, especially in cases with high salt mass fraction, when the system of governing equations is strongly coupled.

Variable-density flow in porous media

Steady-state distributions of water potential and salt concentration in coastal aquifers are typically modelled by the Henry problem, which consists of a fully coupled system of flow and transport equations. Coupling arises from the dependence of water density on salt concentration. The physical behaviour of the system is fully described by two dimensionless groups: (i) the coupling parameter . The proposed perturbation approach is applicable to a wide range of variable-density flows in porous media, including seawater intrusion into coastal aquifers and temperature or pressure-driven density flows in deep aquifers.