Apparent fracture toughness for LEFM applications in hydraulic fracture modeling

Abstract

Linear Elastic Fracture Mechanics (LEFM) is a widely applied theory to numerically simulate hydraulic fracture initiation and propagation in the subsurface. However, LEFM with the typical fracture toughness measured from unconfined laboratory tests does not apply to hydraulic fracturing applications under subsurface conditions because the fracture toughness is affected by the confining stress and fluid lag at the fracture tip. Thus, the apparent fracture toughness was proposed by Rubin (1993) to consider the contributions of fluid lag and confining stress.The main objective of this study is to validate the applicability of LEFM with the apparent fracture toughness in simulating hydraulic fracture under subsurface conditions. We utilized the finite element models to compare the near-tip stress state between the LEFM approach and the cohesive zone model (CZM), which considers the effect of confining stress and fluid lag. In addition, we compared the analytical solutions of fracture energy between LEFM and CZM. This study showed that the near-tip stress state of CZM outside the fluid lag and cohesive zone is comparable to the stress field predicted by LEFM with the apparent fracture toughness. However, LEFM with the fracture toughness measured from standard unconfined laboratory tests underestimates the near-tip stress state of fractures under confining stress. This study also revealed that the fracture energy of fluid-driven fractures calculated by CZM is identical to the fracture energy estimated from the approach of LEFM with the apparent fracture toughness. Thus, this study demonstrated that LEFM with the apparent fracture toughness is an appropriate and accurate method to simulate hydraulic fracture propagation in the subsurface.