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A. Guadagnini and D. M. Tartakovsky, "Stochastic analysis of groundwater pumping from bounded, randomly heterogeneous aquifers", in Geological Society of America Special Papers, No. 348, Eds. D. Zhang and C.L. Winter (Symposium on theory, modeling, and field investigation in hydrogelogy in honor of Shlomo P. Neuman's 60th Birthday) , (Tucson, October 17, 1998), pp. 73-79, 2000

Abstract

We analyze, both analytically and numerically, steady-state pumping from a single well in the presence of a background flow in a bounded domain. It is assumed that one can infer meaningful statistical information about hydraulic conductivity, such as its ensemble mean, variance, and covariance, from available data, Our numerical finite-element analysis consists of directly evaluating the Green's function for the mean field and subsequently solving (conditional) nonlocal moments equations. We start by treating hydraulic conductivity as a two-dimensional, statistically homogeneous random field. For this case, we present a novel analytical formulation of the nonlocal head estimates. Numerical finite element results of the mean field are in excellent agreement with those obtained analytically and by unconditional Monte Carlo simulations. On the basis of numerical results we notice that the head estimator in the vicinity of the well is subject to great uncertainty as its variance peaks at the well location. Conditioning plays an important role in such cases. In field applications, conductivity data (used in our conditioning) are often available at well sites. Hence, we further consider the effect of conditioning precisely at the well location. We solve moment equations by our nonlocal finite element methodology and find that the conditioning at the well dramatically decreases head variance. The agreement with the conditional Monte Carlo simulations is excellent.

BibTeX Entry

@inproceedings{guadagnini-2000-stochastic,
author = {A. Guadagnini and D. M. Tartakovsky},
title = {Stochastic analysis of groundwater pumping from bounded, randomly heterogeneous aquifers},
year = {2000},
booktitle = {Geological {S}ociety of {A}merica Special Papers, {N}o. 348, {E}ds. {D. Z}hang and {C.L. W}inter ({S}ymposium on theory, modeling, and field investigation in hydrogelogy in honor of {S}hlomo {P}. {N}euman's 60th {B}irthday) },
address = {Tucson, October 17, 1998},
pages = {73-79}
}