Evaluation of the Elliptical Flow Period for Hydraulically-Fractured Wells in Tight Gas Sands -- Theoretical Aspects and Practical Considerations Conference Paper uri icon


  • Abstract 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 (x0). For the low permeability cases where the elliptical flow period dominates, the elliptical boundary characteristic parameter (x0) is a useful parameter for establishing the optimum well spacing and the optimal design for the drainage aspect ratio. We note that the x0-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 x0-parameter is the key to recovery and performance in systems dominated by elliptical flow behavior. Introduction Elliptical flow has long been considered as a transitional flow pattern that occurs between linear and pseudoradial flow in the traditional well test analysis of fractured wells.1 Elliptical flow also occurs also in circular anisotropic reservoirs. The study of elliptical flow has a considerable history in the petroleum engineering literature2–10 (as well as other disciplines --- e.g., water resources and physics).  Prats2, 3 studied the effect of vertical fracture on the reservoir behavior for incompressible and compressible fluid cases. Prats proposed the representation of a fracture with an equivalent effective well radius (this was a convenience of the times (early 1960's)). Kuchuk6 developed the analytical solution for the transient elliptical flow problem resulting from an infinite conductivity fracture producing from an elliptical, or an anisotropic-radial reservoir. The behavior of composite, elliptically-shaped reservoirs has also been studied by Obut, and Ertekin5 and Stanislav et al6,7 --- assuming a variety of boundary conditions. Perhaps the most "analytical" treatment of the problem was provided by Riley8 who developed an analytical solution for the case of a vertical well with a finite conductivity vertical fracture in an infinite-acting reservoir system. In addition to attempts to obtain analytical solutions for the elliptical flow problem, there are numerous studies which consider numerical modeling of the elliptical flow problem. Hale9 applied type curve solutions (dimensionless plots) derived from numerical simulation of the elliptical problem as a mechanism to interpret well tests in tight gas reservoirs. Liao10 developed a general numerical model for the elliptical flow case which is capable of accounting for the simultaneous effects of wellbore storage and fracture face skin effects on the behavior of pressure transient tests.

name of conference

  • SPE Hydraulic Fracturing Technology Conference

published proceedings

  • All Days

author list (cited authors)

  • Blasingame, T. A., Amini, S., & Rushing, J

complete list of authors

  • Blasingame, Thomas Alwin||Amini, Shahram||Rushing, Jay

publication date

  • January 1, 2007 11:11 AM


  • SPE  Publisher