Representative hydraulic conductivities in saturated groundwater flow

Abstract

Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective is to synthesize and to offer a critical appraisal of results related to the problem of finding representative hydraulic conductivities. By representative hydraulic conductivity we mean a parameter controlling the average behavior of groundwater flow within an aquifer at a given scale. Three related concepts are defined: effective hydraulic conductivity, which relates the ensemble averages of flux and head gradient; equivalent conductivity, which relates the spatial averages of flux and head gradient within a given volume of an aquifer; and interpreted conductivity, which is the one derived from interpretation of field data. Most theoretical results are related to effective conductivity, and their application to real world scenarios relies on ergodic assumptions. Fortunately, a number of results are available suggesting that conventional hydraulic test interpretations yield (interpreted) hydraulic conductivity values that can be closely linked to equivalent and/or effective hydraulic conductivities. Complex spatial distributions of geologic hydrofacies and flow conditions have a strong impact upon the existence and the actual values of representative parameters. Therefore it is not surprising that a large body of literature provides particular solutions for simplified boundary conditions and geological settings, which are, nevertheless, useful for many practical applications. Still, frequent observations of scale effects imply that efforts should be directed at characterizing well-connected stochastic random fields and at evaluating the corresponding representative hydraulic conductivities

Three-dimensional hydraulic conductivity upscaling in groundwater modeling

“…The need for upscaling stems from the fact that it is possible to characterize the spatial variability of hydraulic conductivity at very small scales, yet, it is prohibitive to perform numerical simulations at such scale, particularly in the context of sensitivity studies, inverse modeling or Monte-Carlo analyses, which require multiple runs of the computer codes. The reader is referred to many reviews about upscaling which are available (e.g., Wen and Gómez-Hernández, 1996;Renard and Marsily, 1997;Farmer, 2002;Sanchez-Vila et al, 2006).…”

Automatic estimation of aquifer parameters using long-term water supply pumping and injection records

“…Basically, these hydraulic parameters can be used to characterize the water-level variations at a monitoring location when operating a water-supply borehole; however, they cannot be considered as accurate estimates due to the limitation of the assumptions implied in the Theis (1935) solution. Instead, Harp and Vesselinov (2011) consider such estimates as interpreted hydraulic parameters (Sanchez-Vila et al 2006) and point out that these parameters should not be confused with effective or equivalent parameters.…”

Joint inference of groundwater–recharge and hydraulic–conductivity fields from head data using the ensemble Kalman filter

“…The estimation of hydraulic conductivity as a continuous field has been intensively investigated in the past (see the reviews of Sanchez-Vila et al, 2006;Vrugt et al, 2008;and recently Zhou et al, 2014). In these approaches discretization of the domain leads to a formal number of parameters to be estimated that is identical to the number of cells or grid points.…”