It has been long established from well testing concepts that an elliptical flow pattern exists in hydraulically-fractured wells producing from low permeability (<0.01 md) and ultra-low (<0.001 md) formations (often referred to as "tight gas" or "shale gas" sands). Conceptually, the elliptical flow period is a transitional flow regime that occurs between the end of bilinear and/or formation linear flow and the onset of pseudo-radial flow. In a practical sense, the elliptical flow regime can (and does) dominate the well performance for very low permeability reservoir systems.

Elliptical flow (as with pseudo-radial flow) represents a time period when the reservoir properties begin to dominate the reservoir performance. Moreover, the duration of the elliptical flow period may last for many months, perhaps even years, depending on the reservoir and hydraulic fracture properties. Consequently, understanding the elliptical flow period and its impact on well performance is critical for the optimal development of a tight gas sand reservoir.

This paper presents a series of decline type-curves for a system consisting of a hydraulic fracture at the center of an elliptical reservoir. The curves are generated from the pressure solution obtained using an analytical method. The curves are generated for different values of the fracture conductivity and as a function of the elliptical boundary characteristic parameter (ξ0).

For the low permeability cases where the elliptical flow period dominates, the elliptical boundary characteristic parameter (ξ0) is a useful parameter for establishing the optimum well spacing and the optimal design for the drainage aspect ratio. We note that the ξ0-parameter essentially reduces the optimization process for tight gas reservoirs to a single parameter that should yield the optimum configuration for drainage and production performance. Obviously the fracture conductivity is also a major factor, as is the reservoir permeability and the fracture half-length — but the ξ0-para-meter is the key to recovery and performance in systems dominated by elliptical flow behavior.

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