Transverse Mixing in Heterogeneous Aquifers

Transverse mixing by local-scale dispersion plays a pivotal role in mixing-controlled reactions of continuously injected compounds and controls the length of steady-state plumes. In two-dimensional heterogeneous media, high-permeability inclusions cause a net enhancement of transverse mixing because the effect of reducing the transverse diffusion lengths in such inclusions prevails over the effect of reduced diffusion time. A simple scaling law for effective transverse mixing in two-dimensional domains could be derived by transferring the steady-state transport equation into streamline-coordinates. The net enhancement factor does not depend on scale. Closed-form expressions for effective mixing and its uncertainty could be derived for uniform-in-the-mean velocity in a multi-Gaussian log-conductivity field with isotropic, exponential covariance function. These expressions could be used to estimate the uncertainty of steady-state concentrations and reactive-plume lengths. The picture is more complex in three-dimensional domains where spatially variable orientation of anisotropy can lead to twisting streamlines. Macroscopically helical flow can lead to an enhancement of transverse mixing by about an order of magnitude more than the flow-focusing effects in two-dimensional flows.