A number of new results for pressure transient behavior of hydraulically fractured wells are presented. The fracture is considered to be fully penetrating with the well located at its center, and to be of dimensionless conductivity FD. The solutions are obtained in the Laplace transform domain, and so may be easily combined with wellbore storage. For the case of an infinite conductivity fracture (FD → ∞), it is shown that the exact solution (exhibiting early time linear flow in the formation and late time radial flow) may be written in terms of so-called Painlevé functions; this representation is much more convenient than the Mathieu function solution given in the literature, because the Painlevé function may be easily computed as the solution to a (non-linear) ordinary differential equation. In the case of a low conductivity fracture (FD → 0) the fracture may considered to be infinite in length; in this limit it is shown that the exact solution (exhibiting early time linear flow in the fracture, intermediate time bilinear flow and late time radial flow) may be written in closed form in terms of elementary functions. It is observed that the early time part of this solution is valid even in the case of a high conductivity fracture. By use of the method of matched asymptotics, the above solutions are combined to obtain a new Laplace domain solution which works well for all values of FD and for all times. The solution compares well with numerical results given in the literature, exhibits all known flow regimes, and may be coded very efficiently on a computer.

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