Effect of Reservoir Compressive Stress on Rock Apparent Fracture Toughness in Hydraulic Fracturing

Hydraulic fracturing is the primary technology for extracting unconventional oil and gas resources. Rock apparent fracture toughness is the most critical parameter in hydraulic fracturing processes. Rock apparent fracture toughness exhibits characteristics distinct from those of metallic materials, particularly as field-estimated values of rock apparent fracture toughness in hydraulic fracturing exceed laboratory-measured values by 1–2 orders of magnitude. Existing interpretation models assume a constant stress distribution in the fracture process zone (FPZ), which contradicts the softening behavior of rock. To address this gap, and based on the assumption of a power-law softening stress distribution in the FPZ of quasi-brittle rock, we develop a mode I apparent fracture toughness model for rock under far-field tensile and compressive stress configurations. This model considers both the softening characteristics of rock and the fluid lag effect. A comparative analysis was conducted on the differences in rock apparent fracture toughness between far-field compressive stress and tensile stress configurations. The results reveal that the difference in configuration between far-field compressive stress and tensile stress constitutes the fundamental reason for the order-of-magnitude discrepancy between the rock apparent fracture toughness estimated from hydraulic fracturing field tests and that measured in laboratory experiments. The influence of the ratio of in situ stress to tensile strength, the ratio of FPZ length to fracture length, the ratio of fluid lag zone length to fracture length, and stress distribution within the FPZ on rock apparent fracture toughness was analyzed, and these factors are found to have decisive effects on the rock apparent fracture toughness. Additionally, the size effect on rock apparent fracture toughness was discussed. This research contributes to more precise hydraulic fracturing parameter design.