# Well Response in a Leaky Aquifer and Computational Interpretation of Pumping Tests

*by*Z. J. Kabala, Univ of California, Riverside, United States,

**Abstract:**An analytic solution is derived describing flow in a horizontal confined leaky aquifer of infinite extent around a fully penetrating well of negligible storage capacity. The differences between the new solution and the Hantush and Jacob [1955] solution are analyzed and demonstrated to be significant in the vicinity of the well for early times and/or for large leakage both for the transient and steady state cases. With growing leakage the new solution diverges from the Hantush-Jacob solution. For a confined aquifer the new solution reduces to the one given by Van Everdingen and Hurst [1949]. The new solution can be useful in interpreting the rapid single-borhole pumping tests. A proposed computational methodology for estimating aquifer parameters from pumping tests is based on the Newton-Raphson algorithm applied to a system of nonlinear equations, each describing the well response (or a piezometer response) at a different judiciously chosen time. The choice of the points on the well-response curve has to be such that the jacobian matrix in the Newton-Raphson scheme is well-conditioned. The number of nonlinear equations is equal to the number of unknown parameters. Starting with a reasonable estimate of the unknown parameters, the sequence produced by iterative solving of linearized equations converges to the solution of the system of nonlinear equations. The methodology is applied to synthetic well responses of a pumping test in a leaky aquifer, and is found to be robust.

**Subject Headings:**Pumping tests | Leakage | Aquifers | Wells (water) | Parameters (statistics) | Confined flow | Vehicles | Computing in civil engineering

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