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

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.