Roughness-Dominated Hydraulic Fracture Propagation

Abstract:

Current understanding suggests that the energy to propagate a hydraulic fracture is defined by the viscous fluid pressure drop along the fracture channel, while the energy dissipation in the immediate vicinity of the fracture front (i.e. fracture toughness) is negligible. This status quo relies on the assumption of Poiseuille flow in the fracture, which transmissivity varies as cube of the aperture. We re-evaluate this assumption in the vicinity of the fracture tip, where the aperture roughness and/or branching of the fracture path may lead to very significant deviations from the cubic law. Existing relationships suggest rough fracture transmissivity power laws ~ w^r with 4.5 ≤ r ≤ 6, when aperture w is smaller than the roughness. Solving for the tip region of a steadily propagating hydraulic fracture with the “rough fracture” transmissivity, we are able to show (a) larger energy dissipation than predicted by the Poiseuille flow model; (b) localization of the fluid pressure drop into the low-transmissivity, rough tip region; and (c) emergence of potentially preeminent “toughness-dominated” fracture propagation regime where most of the energy is dissipated at the tip and can be described in the context of classical fracture mechanics by invoking the effective fracture toughness dependent upon the details of the pressure drop in the rough tip. We establish that the ratio of the roughness scale w_c to the viscous aperture scale w_μ = μVE / σ₀², controls the pressure drop localization. (Here V - propagation speed, μ - fluid viscosity, E - rock modulus, and σ₀ - in-situ stress). For a range of industrial fracturing fluids (from slick-water to linear gels) and treatment conditions, w_c/w_μ is large, suggesting a fully-localized pressure drop and energy dissipation. The latter is adequately described by the effective toughness - a function of the propagation velocity, confining stress and material parameters, which estimated values are much larger than the “dry” rock fracture toughness measured in the lab. Using the effective, velocity-dependent fracture toughness to predict the evolution of a penny-shape fracture, we are able to show how/when the classical viscosity-dominated and toughness-dominated solutions based upon the Poiseuille law and the “dry”, laboratory fracture toughness values, respectively, may become inadequate.