The Productivity of a Well Completed With a Vertical Penny-Shaped Fracture

Summary In this work, we present a simple polynomial relationship for the effective well radius of a well completed with a vertical, infinite-conductivity, penny-shaped hydraulic fracture as a function of fracture diameter. It is based on an analytical solution for steady-state, single-phase flow to a circular, constant-pressure surface in an infinite porous medium. This solution is extended to a vertical, penny-shaped fracture in the center of a plane circular reservoir. The effective well radius increases with increasing fracture diameter to approximately 0.2 times the fracture diameter for a fracture diameter equal to the reservoir thickness. As a rule of thumb, the productivity of a well with an infinite-conductivity, penny-shaped fracture exceeds the openhole productivity for fracture diameters larger than one-third of the reservoir thickness. The productivity of a well with a fracture diameter equal to the reservoir thickness is approximately twice the openhole productivity. The adverse effect of fracture conductivity can be estimated by a simple formula that relates fracture efficiency to the productivity index of a well with an infinite-conductivity fracture and to the ratio of the flow capacity of the fracture to that of the reservoir.