Influence of density contrasts on the solute transport through a horizontal fracture
Résumé
Contaminant transport in heterogeneous fractured aquifers occurs mostly through the networks of intersecting fractures. Solute transport through individual fractures is often studied considering a continuous inflow of solute. Here we investigate the spreading of a finite amount of solute entering a fracture of constant aperture and with no significant wall roughness. When solute buoyancy is negligible, the dispersion process eventually leads to the well-known asymptotic Taylor-Aris[1] dispersion regime, in which the solute progresses along the fracture at the average fluid velocity, according to a one-dimensional longitudinal advection-dispersion process. We address more realistic configurations for which the solute-induced density contrasts within the fluid play a role on solute transport, in particular at small and moderate times. Flow and transport are simulated using a mathematical description based on the Boussinesq approximation and a numerical scheme based on a finite element analysis. This enables complete characterization of the process, in particular at moderate times for which existing analytical models are not valid. Dispersion is characterized both in terms of longitudinal spreading and by computing the time evolution of the dilution index. The asymptotic Taylor-Aris effective dispersion coefficient is reached eventually, but vertical density currents, which are significant at short and moderate times, are responsible for a systematic retardation of the asymptotic mean solute position with respect to the frame moving at the mean fluid velocity, as well as for a time shift in the establishment of the asymptotic dispersion regime [2]. These delays are characterized as functions of non-dimensional numbers. In accordance with a long-existing prediction and depending on the Péclet number, the asymptotic spreading is measured to be either larger or smaller than what it would be in the absence of buoyancy effects [2]. Breakthrough curves, measured at distances larger than the typical distance needed to reach the asymptotic dispersion regime, are impacted accordingly. Additionally, as density effects affect the distribution of the solute in the fracture thickness, the solute transfer between the fracture and the rock matrix is impacted. Fracture-matrix transfer predictions are often based on a “perfect transverse mixing” assumption. We study the effect of the vertically-heterogeneous solute distribution and of density contrasts on this exchange, by coupling the description of transport in the fracture and that of the transverse solute diffusion in the matrix. Our findings suggest that, under certain conditions, density/buoyancy effects may have to be taken into consideration when interpreting field measurements of solute transport in fractured media, even in the absence of significant fracture wall roughness. [1] Taylor, G.I. , 1953. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A219(1137), 186-203 [2] Bouquain, J., Méheust, Y., Davy, P., Horizontal pre-asymptotic solute transport in a plane fracture with significant density contrasts, Journal of Contaminant Hydrology (2010), doi: 10.1016/j.jconhyd.2010.08.002