On the effective hydraulic conductivity and macrodispersivity for density-dependent groundwater flow

In this paper, semi-analytical expressions of the effective hydraulic conductivity ( $K^{E})$ and macrodispersivity ( $\alpha ^{E})$ for 3D steady-state density-dependent groundwater flow are derived using a stationary spectral method. Based on the derived expressions, we present the dependence of $K^{E}$ and $\alpha ^{E}$ on the density of fluid under different dispersivity and spatial correlation scale of hydraulic conductivity. The results show that the horizontal $K^{E}$ and $\alpha ^{E}$ are not affected by density-induced flow. However, due to gravitational instability of the fluid induced by density contrasts, both vertical $K^{E}$ and $\alpha ^{E}$ are found to be reduced slightly when the density factor ( $\gamma $ ) is less than 0.01, whereas significant decreases occur when $\gamma $ exceeds 0.01. Of note, the variation of $K^{E}$ and $\alpha ^{E}$ is more significant when local dispersivity is small and the correlation scale of hydraulic conductivity is large.