Book Description

Abstract: Three-dimensional, field-scale (~ 100 m) convective mixing processes in heterogeneous porous media are examined. The focus is on fluid mixing rates and density-dependent macrodispersion, and the influence of small-scale (~ centimeters) instability development on large-scale variable-density flow and solute transport behavior. Dynamic adaptive mesh refinement methods (AMR) and a higher-order (solute advection term), mass-conservative Eulerian-Lagrangian discretization scheme for the solute transport equation are used to construct a new numerical code (DensTransAMR) that automatically adjusts to multiple scales of convective mixing processes by translating and adding/removing telescoping levels of progressively finer subgrids during a simulation. Because the flow and transport solutions for each subgrid are computed independently, field-scale simulations are broken into multiple smaller problems that can be modeled more efficiently and with finer detail. Two types of numerical experiments are performed: freshwater injection in a saltwater aquifer and dense fluid injection in a freshwater aquifer. Convective mixing rates are related to the geostatistical properties of the aquifer (variance and mean of the log permeability distribution, horizontal and vertical correlation scales), the fluid density difference, the magnitude of local small-scale dispersion, the effects of different permeability field realizations, the injection well size and orientation, hydraulic parameters such as injection rate and regional hydraulic gradient, and the spatial resolution. Convective mixing in heterogeneous porous media is shown to be more amenable to prediction than previously concluded. Computed three-dimensional fluid mixing rates are related to mathematical expressions for density-dependent macrodispersivity that are based on stochastic flow and solute transport theory and are a function of log permeability variance, the correlation scale, and a time-dependent parameter. Different instability patterns are generated when a different permeability field realization is used, the source location changes, or the mesh spacing is varied. However, long-term fluid mixing rates (i.e., after the mixing zone becomes large compared with the correlation scale) do not change if the fluid and macroscopic porous media properties (mean permeability, variance, and correlation lengths) remain constant. Porous media variability on scales smaller than the correlation lengths has an effect on the fluid mixing zone volume but does not affect long-term mixing rates.