Analytical solution and mechanisms of fluid production from hydraulically fractured wells with finite fracture conductivity

A comprehensive study of the physical mechanisms of fluid production from a well intersected by a narrow elliptically shaped vertical fracture with finite fracture conductivity is carried out using a newly obtained analytical solution. The flow pattern, flux density distribution along the fracture surface, and fluid production rate are analyzed systematically with respect to finite fracture conductivity. The simplicity of the new analytical solution reveals many physical insights not attainable from existing analytical or numerical solutions. It is shown that the nearly singular pressure gradient developed at the fracture tip induces the reservoir flow to converge to and focus at the tip region, promoting flux density along the entire fracture surface and enhancing the production rate. It is established that the flow in the reservoir is a superposition of two basic flows, a confocal elliptical flow responsible for the fluid production, and a redistributive nonproducing flow induced by a finite fracture conductivity that draws fluids out of the fracture from the part near the tip and redeposits them back to the part of the fracture close to the wellbore. An explicit analytical formula for the fluid production rate is also derived that exhibits a simple dependency on the dimensionless fracture conductivity.