## 1. Introduction

[2] A partially penetrating well is commonly situated in an aquifer that is relatively thick. *Hantush* [1962] presented a point source solution for the drawdown distribution around a partially penetrating well under constant flux pumping in an infinite confined aquifer. *Sternberg* [1973] provided a graphical solution for evaluating the total drawdown. *Strelsova-Adams* [1979] reported an analysis of the transient pressure response for a well with limited flow entry produced from an oil reservoir with a gas cap in a zone of low permeability and that with impermeable top and bottom boundaries. *Ruud and Kabala* [1997] developed a two-dimensional integrated well face flux (IWFF) model for computing the drawdown at the well face and around a fully or partially penetrating well with the wellbore storage situated in multilayer confined aquifers. For a partially penetrating well situated in a homogeneous isotropic aquifer, they found that the differences between the IWFF model and Hantush's model [*Hantush*, 1964] were insignificant for wellbore drawdowns but pronounced for the well face flux. Such differences may arise for a partially penetrating well situated in multilayer aquifers, especially if the screen is not located in the most conductive layer. *Cassiani and Kabala* [1998] developed a semianalytical solution to the mixed-type boundary value problem via the dual integral equations. The pumping and slug tests are performed on a partially penetrating well with wellbore storage, infinitesimal skin, and aquifer anisotropy. They stated that their solution is computationally more efficient than the corresponding finite difference solution. In addition, their solutions described accurately the point flux distribution along the well screen of a partially penetrating well.

[3] The objective of this study is to develop a closed form solution for a mathematical model describing the constant flux pumping test performed in a partially penetrating well with finite radius in a homogeneous (single zone) confined aquifer system. This closed form solution can be used to investigate the effects of screen length and location on the drawdown distribution and to produce type curves for the estimation of aquifer parameters with field drawdown data. On the basis of the mathematical model, the Laplace domain solution is derived using the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to the vertical coordinates. The modified Crump algorithm [*de Hoog et al.*, 1982; *Visual Numerics*, 1997] is adopted to invert the Laplace domain solution. The closed form solution is then obtained using the Bromwich integral method. A numerical approach, including a root search scheme, a numerical integration method, and the Shanks method [*Shanks*, 1955], is proposed to evaluate this solution.