Modeling of Density-Dependent Flow based on the Thermodynamically Constrained Averaging Theory

The thermodynamically constrained averaging theory (TCAT) has been used to formulate general classes of porous medium models, including new models for density-dependent flow. The TCAT approach provides advantages that include a firm connection between the microscale, or pore scale, and the macroscale; a thermodynamically consistent basis; explicit inclusion of factors such as a diffusion that arises from gradients associated with pressure and activity and the ability to describe both high and low concentration displacement. The TCAT model is presented and closure relations for the TCAT model are postulated based on microscale averages and a parameter estimation is performed on a subset of the experimental data. Due to the sharpness of the fronts, an adaptive moving mesh technique was used to ensure grid independent solutions within the run time constraints. The optimized parameters are then used for forward simulations and compared to the set of experimental data not used for the parameter estimation.