Transient Flow to Finite Well in Unconfined Aquifer

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Abstract
The problem of a nonsteady radial flow toward a finite well in an unconfined aquifer is solved by a form of the Galerkin method. The equations are reduced to a set of coupled nonlinear ordinary differential equations in the time-dependent Galerkin coefficients, with a constraint equation due to the nonlinear well bore boundary condition. These are solved numerically by the Adams method for a range of forcing. An eight term approximation proves sufficient to yield good results for the trial functions used. Where comparison is possible, there is good agreement with other results and other solution methods. Response of the flow system depends strongly on the parameters characterizing the aquifer. Time to maximum drawdown at the well is very sensitive to production rate and well radius. A similarity transformation for this problem, with a singularity at r = O, has frequently appeared. Retransformation to remove the singularity yields a more thorough understanding of the range of validity of the solution.

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