Regime Identification, Dimensionless Numbers, and Parameter Sensitivity of Variable-Density Flow in Porous Media Based on Numerical Simulations

Variable-density flow and mass transport are important processes for a variety of groundwater problems. This study numerically investigated 2-D vertical unconfined aquifers with horizontal groundwater flow and vertical injection of dense solute from the top. In total, 189 numerical simulation cases were performed with various scenarios of boundary conditions and aquifer properties. Based on the simulation results, three end-member flow regimes were identified that are dominated by horizontal hydraulically driven flow, vertical hydraulically driven flow, and vertical density-driven flow, respectively. The regimes can be clearly distinguished by a set of three dimensionless numbers, which are the convective ratios M-x (the ratio of the total flux of the vertical density-driven flow to the total flux of the horizontal hydraulically driven flow) and M-z (the ratio of the total flux of the vertical density-driven flow to the total flux of the vertical hydraulically driven flow), and the modified Rayleigh number Ra-d (the ratio of the vertical density-driven force to the forces caused by dispersion and diffusion). The dimensionless numbers were applied to published numerical and physical experimental results for interpreting their flow behaviors and for classifying their flow regimes. Besides, the analysis of the parameter sensitivity indicated that the shifts among the end-member regimes are mainly controlled by dimensionless-number-related parameters including horizontal groundwater flow velocity, injection rate and concentration of solute, and anisotropy ratio of hydraulic conductivity. The regime shifts are not strongly affected by the unsaturated properties or heterogeneity of hydraulic conductivity within the parameter ranges investigated in this paper.