Estimating transmissivity from single‐well pumping tests in heterogeneous aquifers

Abstract

Although aquifers are naturally heterogeneous, the interpretation of pumping tests is commonly performed under the assumption of aquifer homogeneity. This yields interpreted hydraulic parameters averaged over a domain of uncertain extent which disguises their relation to the underlying heterogeneity. In this study, we numerically investigate the sensitivity of the transient drawdown at the pumping well, to nonuniform distributions of transmissivity in confined aquifers. Frechet kernels and their time derivative are used to estimate two spatially averaged transmissivities, denoted the equivalent and interpreted transmissivity, T eq and T in , respectively, for the case of single-well pumping tests. Interrelating T eq and T in is achieved by modeling T in in terms of a distance dependent, radially heterogeneous field. In weakly heterogeneous aquifers, T eq approximates T PW , the local transmissivity at the pumped well. With increasing degree of heterogeneity, T eq deviates from T PW as pumping propagates. T in starts at T PW , approaching the spatial geometric mean of transmissivity during late pumping times. Limits of the proposed spatial weighting functions are investigated by treating the interpreted storativity, S est , as an indicator for flow connectivity. It is shown numerically that the spatial weights for T eq and T in agree well to the underlying heterogeneity if S est < 1. Finally, implications for applying the concepts of T eq and T in to heterogeneous domains, and, for real world applications are discussed. It is found that time-dependent spatial averages of T in agree well with estimates of the interpreted transmissivity from the Continuous-Derivation method.

Policy Targeting to Reduce Economic Damages From Land Subsidence

“…However, the Theis equation also requires the assumption of homogeneous transmissivity and storativity across space, which rarely holds in practice. Even so, the Theis equation is often used as an approximation in pumping tests applied to heterogeneous aquifers because of its analytical tractability (Pechstein et al, ). With this caveat, we allow these parameters to vary by model cell in the simulation to capture spatial differences in groundwater movement.…”

What We Talk About When We Talk About Uncertainty. Toward a Unified, Data-Driven Framework for Uncertainty Characterization in Hydrogeology

“…This workflow, known as point estimation in inference, is based on a (regularized) data fitting or optimization approach which tries to identify a unique solution to the inverse problem. Typical examples in hydrogeology are goodness-of-fit criteria, i.e., the task of finding a single set of parameters such that the distance between predictions and observations is minimized (Indelman et al, 1996;Sánchez-Vila et al, 1999;Firmani et al, 2006;Schneider and Attinger, 2008;Riva et al, 2009;Copty et al, 2011;Pechstein et al, 2016;Zech et al, 2016). Even when pointestimators are not applied during calibration and a probabilistic sampling of the parameter distribution is advised instead, often the analysis is performed again, by deriving single solutions through, e.g., averaging (Neuman, 2014).…”

On the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells in unconfined aquifers

“…With significant advances in directional drilling technology over the last 20 years, the interest in horizontal and/or slant wells has been reignited. Until now, flow to horizontal and/or slant wells has been investigated in various aspects, including flow in confined aquifers (Cleveland, 1994;Zhan, 1999;Zhan et al, 2001;Kompani-Zare et al, 2005), unconfined aquifers (Huang et al, 2011(Huang et al, , 2016Rushton and Brassington, 2013;Zhan and Zlotnik, 2002;Mohamed and Published by Copernicus Publications on behalf of the European Geosciences Union. 1252 X.…”