Variable‐density groundwater flow and solute transport in fractured rock: Applicability of the Tang et al. [1981] analytical solution

Abstract

The effect of fluid density variations on mixed convective (advective and density‐driven) transport in fractured rock is examined. Assuming a representative natural hydraulic gradient in a vertical fracture, breakthrough curves for variable‐density systems are shown to be significantly different from those with constant‐density conditions for even very small solute source concentrations (as low as approximately 2.3 g L−1 total dissolved solids, corresponding to 6.4% of seawater salinity). We compare analytical solutions with results of fully coupled numerical simulations of variable‐density groundwater flow and solute transport in fractured rock. Current analytical solutions for solute transport in fractured rock do not account for fluid density variations and therefore fail to predict variable‐density transport. Using a mixed convection ratio analysis, we determine the hydrogeologic conditions where variable‐density transport is important and hence when analytical solutions fail to predict variable‐density transport in fractured rock. We present a modified velocity term that includes a density‐driven flow component in a vertical fracture to account for fluid density variations. The modified velocity term is incorporated into the standard Tang et al. (1981) analytical solution. The original density‐invariant analytical solution is shown to be applicable near a solute source and at early time, while the velocity‐modified density‐variant solution gives very good results for long‐term and far‐field behavior. These results suggest that analytical solutions may still be useful for analyzing variable‐density transport in fractured rock. This study has implications for the analysis of dense plume transport in fractured rock where reliable long‐term predictions are important.