Pressure-gradient singularity and production enhancement for hydraulically fractured wells

When a hydraulic fracture is modelled as a slit, the flow of the reservoir fluid towards the fracture develops a pressure-gradient singularity at the sharp fracture tips for both steady and transient flows. This pressure-gradient singularity also creates a flux-density singularity of the same type at the fracture tips. We study this pressure-gradient/flux singularity and its role in the production enhancement for hydraulically fractured wells in detail for the stabilized flow regime. Analytical solutions for slit, rectangular and elliptical shape fractures in the limit of infinite dimensionless fracture conductivity are used to analyse the flow physics. Our analyses reveal the exact mathematical nature of the pressure-gradient tip singularity and its regularization by the elliptical geometry. We show that this pressure-gradient tip singularity causes the flow from the region ahead of the fracture tip to converge and focus at the fracture tip. This flow pattern concentrates the production to the region near the fracture tip and increases the flux along the entire fracture surface. The singularity in the reservoir pressure-gradient is inherent for all fractures with sharp ends in both steady and transient flows regardless of the fracture conductivity. Our results establish pressure-gradient tip singularity as a universal and primary mechanism for enhanced productivity from hydraulically fractured wells. The large suction forces at the fracture tips induce the fluid to flow from an ultra-low permeability reservoir into a hydraulic fracture.