The 2D Steady Hydraulic Head Field Surrounding a Pumping Well in a Finite Heterogeneous Confined Aquifer |
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| Authors: | Carl L Axness and Jesus Carrera |
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| Institution: | (1) Sandia National Laboratories, P. O. Box 5800, Albuquerque, New Mexico, 87185;(2) Technical University of Catalonia, Barcelona, Spain |
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| Abstract: | We present a second-order analytic solution in terms of a heterogeneous log-transmissivity Y(r) = ln T(r)] for the hydraulic head field in a finite 2D confined heterogeneous aquifer under steady radial flow conditions assuming fixed head boundary conditions at the well and at a circular exterior boundary. The solution may be used to obtain the gradient used in calculation of solute transport to a well in a heterogeneous transmissivity field. The solution, obtained using perturbation methods coupled with Green's function techniques, leads us to postulate a more general form of the head for arbitrarily large-variance fields and may be used to obtain moment relations between the log-transmissivity and head under convergent flow conditions when Y(r) is expressed as a random space function. We present expressions for the mean head field when the log-transmissivity is Gaussian and conditioned on the transmissivity value at the well for an arbitrary ln T covariance. Finally, we look at the effect of parameter variations on the mean head behavior and present numerical simulations verifying the second-order mean head expressions. |
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| Keywords: | Stochastic Green's functions perturbation methods conditioning nonstationary nonergodic |
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