Cohesive-zone effects in hydraulic fracture propagation

Abstract

Hydraulic fracture presents an interesting case of crack elasticity and fracture propagation non-linearly coupled to fluid flow. Hydraulic fracture (HF) is often modeled using the Linear Elastic Fracture Mechanics (LEFM), which assumes that the damaged zone associated with the rock breakage near the advancing fracture front is small compared to the lengthscales of other physical processes acting during propagation. The latter include dissipation in viscous fluid flow in the fracture channel, of which the fluid lag - a region adjacent to the fracture tip filled with fracturing fluid volatiles and/or infiltrated formation pore fluid - is the extreme manifestation. In this study we address the validity of the LEFM approach to hydraulic fracturing by constructing the solution for the near tip region of a cohesive fracture driven by Newtonian fluid in an impermeable linear-elastic rock. We show that the near HF tip solution has an intricate structure supported by a number of nested lengthscales on which different dissipation processes are realized. This structure is bookended by the solid ‘c’ or fluid lag ‘o’ process zone immediately near the tip and by the viscosity ‘m’ asymptote away from the tip, while the LEFM ‘k’ asymptote may emerge at intermediate distances within the c/o to m transition. Realization of the k asymptote, and, therefore, the viability of the LEFM in HF, depends on two parameters: the cohesive-to-fluid-lag fracture energy ratio Gc/Go and the cohesive-to-in-situ stress ratio σc/σo. For representative values of the former, we show that the LEFM-behavior emerges only when the cohesive stress is large compared to the in situ confining. Since σc ∼ few MPa for most rocks, it follows that the LEFM may only be applicable to laboratory hydraulic fracture conducted under low confining stress, and, conversely, is not applicable to the field hydraulic fracturing characterized by larger values of σo. We further use an approximate “equation of motion” approach based on the continuation of the tip solution onto the entire fracture to solve for the propagation of a penny-shaped HF driven by a point source fluid injection and quantify the prominence of the non-LEFM effects.