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

Abstract

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 ρY. 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 ρY, 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 ρY 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 KG (the geometric mean), σY2 (the logconductivity variance) and I (the horizontal integral scale of ρY) 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 Kef (the effective conductivity) or U independently (e.g. by pumping tests), rather than attempting to characterize the permeability structure beyond f(Y) and ρY.