Mechanisms of reduction of dispersion in stable density-driven flows in heterogeneous porous media
Abstract
We analyze solute spreading in randomly heterogeneous porous media for a density-driven stable flow setting. We assess the longitudinal spread of saltwater injected into a column where a heterogeneous porous medium is initially fully saturated by freshwater. We derive the equations satisfied by section-averaged concentrations and their ensemble mean values so as to characterize the single realization and ensemble dispersive fluxes, respectively. To this end, we adopt a perturbation expansion approach. To overcome the problems associated to statistical and temporal non-stationarity, we decompose velocity and pressure in terms of a (statistically and temporally) stationary perturbation, associated to heterogeneity, plus a dynamic component that characterizes the additional effect of variable density. These perturbations are evaluated through appropriate closure equations, which are solved via semi-analytical and numerical approaches. Our formulations and results enable us to discriminate the relative impact on the density-driven solute displacement of the covariance of the permeability of the medium, the cross-covariance between permeability and concentration, and the cross-covariance between the dynamic and stationary velocities. Main findings of our study include the observation that the reduction of spreading and the ensuing contraction of spatially varying concentration profiles are due to a reorganization of the velocity field, as driven by the medium heterogeneity. We observe that heterogeneity of permeability favors a decrease of the velocity variance and of the spatial extent of velocity correlation, yielding a corresponding reduction of the strength of the dispersive flux.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2017
- Bibcode:
- 2017AGUFM.H31M..08R
- Keywords:
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- 0414 Biogeochemical cycles;
- processes;
- and modeling;
- BIOGEOSCIENCES;
- 1009 Geochemical modeling;
- GEOCHEMISTRY;
- 1830 Groundwater/surface water interaction;
- HYDROLOGY;
- 1831 Groundwater quality;
- HYDROLOGY