The threshold pressure gradient, which is associated with non-Darcy flow in low permeability tight gas formation, is defined as the level of pressure gradient that has to be attained to enable the fluid to overcome the viscous forces and start to flow. With low velocity and non-Darcy flow, the fluid flow boundary is controlled by the threshold pressure gradient and can extend outward continuously, while the fluid beyond this boundary cannot flow.
This paper presents analytical solutions to the pressure transient equations of a uniform-flux hydraulically fractured gas well in tight gas formation with threshold pressure gradient. These solutions are obtained by using Green's functions method with numerical approximations. A method to determine the location of the moving boundary front is also presented.
This paper concludes that the pseudopressure equalpotential surfaces for a fully penetrating vertical uniform-flux hydraulically fractured gas well are a family of ellipse, whose focuses are the two endpoints of the hydraulic fracture. This paper also concludes that both pressure transient distance in the direction perpendicular to the fracture and pseudopressure drop at the wellbore are approximately linear functions of the square root of producing time. Finally, the solution procedure proposed in this paper is a fast tool to evaluate a hydraulically fractured gas well performance in tight gas formation.