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A mathematical model is presented for a constant-head test performed in a partially penetrating well with a finite-thickness skin. The model uses a no-flow boundary condition for the casing and a constant-head boundary condition for the screen to represent the partially penetrating well. The Laplace-domain solutions for the dimensionless flow rate at the wellbore and the hydraulic heads in the skin and formation zones are derived using the Laplace and finite Fourier cosine transforms. The solutions of hydraulic heads have been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the pressure head and flow rate at the interface of the skin zone and undisturbed formation. In addition, an efficient algorithm for evaluating those solutions is also presented. The dimensionless flow rates obtained from new solutions have been shown to be better than those of Novakowski's solutions, especially when the penetration ratio is large.

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SUMMARYA mathematical model describing the constant pumping is developed for a partially penetrating well in a heterogeneous aquifer system. The Laplace-domain solution for the model is derived by applying the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to vertical co-ordinates. This solution is used to produce the curves of dimensionless drawdown versus dimensionless time to investigate the influences of the patch zone and well partial penetration on the drawdown distributions. The results show that the dimensionless drawdown depends on the hydraulic properties of the patch and formation zones. The effect of a partially penetrating well on the drawdown with a negative patch zone is larger than that with a positive patch zone. For a single-zone aquifer case, neglecting the effect of a well radius will give significant error in estimating dimensionless drawdown, especially when dimensionless distance is small. The dimensionless drawdown curves for cases with and without considering the well radius approach the Hantush equation (Advances in Hydroscience. Academic Press: New York, 1964) at large time and/or large distance away from a test well.