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.