The 2D steady hydraulic head field surrounding a pumping well in a finite heterogeneous confined aquifer

We present a second-order analytic solution [in terms of a heterogeneous lo g-transmissivity Y(r) = ln T(r)] for the hydraulic head field in a finite 2 D confined heterogeneous aquifer under steady radial flow conditions assumi ng fixed head boundary conditions at the well and at a circular exterior bo undary. 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 functio n techniques, leads us to postulate a more general form of the head for arb itrarily large-variance fields and may be used to obtain moment relations b etween the log-transmissivity and head under convergent flow conditions whe n 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 In T covariance. Finally, we look at the effect of parameter variations on the mean head beh avior and present numerical simulations verifying the second-order mean hea d expressions.