PRESSURE BEHAVIOR OF UNIFORM-FLUX HYDRAULICALLY FRACTURED WELLS IN LOW-PERMEABILITY RESERVOIRS WITH THRESHOLD PRESSURE GRADIENT

Abstract

The threshold pressure gradient, which is associated with non-Darcy flow in low-permeability reservoirs, is defined as the level of pressure gradient that must 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 uniform-flux hydraulically fractured wells in low-permeability reservoirs with a threshold pressure gradient. These solutions are obtained by using the 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 equipotential surfaces of a fully penetrating vertical uniform-flux hydraulically fractured well are a family of ellipses, whose focuses are the two end points of the hydraulic fracture. The paper also concludes that both the pressure transient equivalent radius and pressure drop at the wellbore are linear functions of the square root of producing time. It is known that the radius of investigation of conventional reservoirs is independent of flow rate, but this study concludes that the pressure transient equivalent radius is a function of flow rate. When threshold pressure gradient is equal to zero, the proposed formula to calculate the pressure transient equivalent radius almost reduces to the formula to calculate radius of investigation of conventional reservoirs in the literature. Finally, the solution procedure proposed in this paper is a fast tool to evaluate hydraulically fractured well performance in low-permeability reservoirs.