When good statistical models of aquifer heterogeneity go right: The impact of aquifer permeability structures on 3D flow and transport

Natural gradient steady flow of mean velocity U takes place in heterogeneous aquifers of random logconductivity Y=lnK, characterized by the univariate PDF f(Y) and autocorrelation ρ_Y. Solute transport is analyzed through the Breakthrough Curve (BTC) at planes at distance x from the injection plane. The study examines the impact of permeability structures sharing same f(Y) and ρ_Y, but differing in higher order statistics (integral scales of variograms of Y classes) upon the numerical solution of flow and transport. Flow and transport are solved for 3D structures, rather than the 2D models adopted in most of previous works. We considered a few permeability structures, including the widely employed multi-Gaussian, the connected and disconnected fields introduced by Zinn and Harvey [2003] and a model characterized by equipartition of the correlation scale among Y values. We also consider the impact of statistical anisotropy of Y, the shape of ρ_Y and local diffusion. The main finding is that unlike 2D, the prediction of the BTC of ergodic plumes by numerical and analytical models for different structures is quite robust, displaying a seemingly universal behavior, and can be used with confidence in applications. However, as a prerequisite the basic parameters K_G (the geometric mean), σ_Y² (the logconductivity variance) and I (the horizontal integral scale of ρ_Y) have to be identified from field data. The results suggest that narrowing down the gap between the BTCs in applications can be achieved by obtaining K_ef (the effective conductivity) or U independently (e.g. by pumping tests), rather than attempting to characterize the permeability structure beyond f(Y) and ρ_Y.