### Cite Details

M. Riva, A. Guadagnini, S. P. Neuman and D. M. Tartakovsky, "Three-dimensional steady state flow to a well in a randomly
heterogeneous aquifer", in *IAHS Publication
No. 265,
Eds. F. Stauffer,
W. Kinzelbach, K. Kovar,
E. Hoen
(ModelCARE'99)
*, (Zurich, Switzerland, September 20-23, 1999), pp. 131-136, 2000

### Abstract

We consider three-dimensional steady state flow towards a
well that fully penetrates a randomly heterogeneous aquifer
confined between horizontal no-flow boundaries, and bounded
laterally by a cylindrical, deterministically prescribed
constant head boundary. The well is represented by a line sink
that produces water at a deterministically prescribed constant
rate *Q* for unit aquifer thickness. The log
hydraulic conductivity, *Y = ln K*, of the aquifer is
multivariate Gaussian, statistically homogeneous with a Gaussian
spatial autocorrelation function. We develop an analytical
solution for the variance of hydraulic head as a function of
dimensionless vertical and horizontal locations within the
aquifer, variance
σ_{Y}^{2} of
*Y* and dimensionless ratios between the
principal spatial correlation scales. Our analysis is based on
the non-local theory first proposed for steady state and
transient flows in bounded, randomly heterogeneous media by
Neuman and Orr (1993), Neuman et al. (1996), Guadagnini and Neuman
(1999a,b) and Tartakovsky and Neuman (1998, 1999). In particular,
we develop and solve analytically recursive closure
approximations of the governing non-local moment equations to
second order in σ_{Y}
by means of an appropriate
Green's function. We evaluate our analytical solutions by means
of Gaussian quadratures for the special case of the isotropic *Y*
field.

### BibTeX Entry

@inproceedings{riva-2000-three,

author = {M. Riva and A. Guadagnini and S. P. Neuman and D. M. Tartakovsky},

title = {Three-dimensional steady state flow to a well in a randomly
heterogeneous aquifer},

year = {2000},

booktitle = {{IAHS P}ublication
{N}o. 265,
{E}ds. {F. S}tauffer,
{W. K}inzelbach, {K. K}ovar,
{E. H}oen
({M}odel{CARE}'99)
},

address = {Zurich, Switzerland, September 20-23, 1999},

pages = {131-136}

}