An infinite- or finite-conductivity vertical fracture intersecting a well produced at a constant rate within a closed system is considered. Fracture is modeled as a vertical slab with lengthwise variation in the fracture geometric properties. The long-time inflow performance is obtained from a finite-element solutions of pseudosteady-state diffusivity equation, which considers fixed flux over all reservoir region.

The first part of this paper examines the behavior of an infinite-conductivity fracture. Comparisons of well productivity calculated with transient and pseudosteady-state solutions show a good agreement. Computations for anisotropic reservoirs were made to examine the effects of reservoir permeability anisotropy and fracture length on the late-time pressure response. It is demonstrated that well productivity is heavily dependent on the fracture orientation and main flow pattern. The second part investigates the effects of fracture permeability on the pressure response of a finite-conductivity fracture. The fracture conductivity is a decreasing function of distance from wellbore.

The new fracture model and solution technique provides more realistic description for fracture geometry and long-time pressure response with a minimum computational effort.

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