Key Takeaways & Executive Findings
- •• Developed a nonlinear hydraulic fracture propagation criterion that incorporates the fracture process zone (FPZ) using the cohesive zone model (CZM). • Derived an analytical model for FPZ length and established a relationship between FPZ length and breakdown pressure. • The criterion accurately predicts breakdown pressure in deep reservoirs, overcoming limitations of linear elastic fracture mechanics (LEFM). • Revealed that fracture propagation initiates when apparent stress intensity reaches apparent fracture toughness or in-situ stress intensity reaches in-situ fracture toughness.
Abstract
The linear elastic hydraulic fracture criterion is not applicable to deep reservoirs when nonlinear behavior is present over an extensive zone at the fracture tip. This study aims to develop a criterion for nonlinear hydraulic fracture considering the fracture process zone (FPZ) and seeks to reveal the causes of nonlinearity during fracture propagation in deep reservoirs. A closing stress profile considering the in-situ stress was established by using the cohesive zone model (CZM) to describe the FPZ at the fracture tip. An analytical model for the FPZ length was derived, while the criterion for nonlinear fracture propagation was proposed. The FPZ fully developed and the fracture began to propagate when the apparent stress intensity at the fracture tip reached the apparent fracture toughness or when the in-situ stress intensity reached the in-situ fracture toughness. The proposed criterion can clearly determine the length of the FPZ, accurately predict the breakdown pressure during fracturing operations, and establish a relationship between these two parameters. It addresses the inherent limitations of conventional linear elastic fracture mechanics (LEFM), which often underestimates fracture toughness and neglects the effects of the FPZ. This research is expected to enhance the fracturing design in deep reservoirs.
1. Introduction
As exploration and development technologies advance, oil and gas exploration has increasingly targeted deep reservoirs over the past few decades (>4500 m) [1–3]. Medium and deep reservoirs have contributed to 30% of the newly discovered hydrocarbon reserves. Currently, deep reservoirs account for 34.3% of global oil reserves and 59.5% of natural gas reserves. However, these reservoirs remain underexplored due to their unsatisfactory physical properties and often require hydraulic fracturing for effective industrial exploration [4–6]. In deep or ultra-deep reservoirs, the rock fracture mechanism transitions from quasi-brittle to plastic or ductile, and the nonlinear fracture process zone at the hydraulic fracture tip dominates the extension and propagation of the fracture.
Conventional LEFM criteria have demonstrated limitations in addressing fracture problems within such reservoirs. The LEFM criterion assumes that the stress field at the fracture tip exhibits linear singularity but neglects the nonlinear fracture behavior at the fracture tip that arises under high-stress conditions. Consequently, fracture toughness values predicted using LEFM criteria are underestimated, resulting in an underestimation of reservoir breakdown pressures [7–10]. Given that existing LEFM criteria fail to adequately describe the nonlinear fracture behavior at the fracture tip, it is urgent to develop fracture propagation criteria that take into account nonlinear fracture behavior. This would enable a better characterization of the strengthening effect of in-situ stress on fracture toughness and provide deeper insights into the nonlinear mechanism governing fracture propagation.
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Senlin Luo, Guangqing Zhang, Yansen Ling, Jinmiao Tan, Renyi Qiu, Bin Sun (2025). A nonlinear hydraulic fracture propagation criterion considering the fracture process zone. SinoTechIntel Verified Research. https://doi.org/10.1016/j.ijmst.2025.09.007
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Frequently Asked Questions
What is the fracture process zone (FPZ) in hydraulic fracturing?
The fracture process zone refers to the region where progressive rock damage occurs at the fracture tip, accompanied by the accumulation of numerous microcracks. It is the primary site of energy dissipation, used to overcome rock cohesive stress, generate new microcracks, and counteract friction between particles.
Why is the linear elastic fracture mechanics (LEFM) criterion inadequate for deep reservoirs?
LEFM assumes a linear singular stress field at the fracture tip and neglects nonlinear fracture behavior that occurs under high-stress conditions in deep reservoirs. This leads to underestimation of fracture toughness and breakdown pressure, making it unsuitable for deep or ultra-deep reservoirs where rock behavior becomes plastic or ductile.
How does the proposed nonlinear criterion improve fracture propagation prediction?
The proposed criterion incorporates the fracture process zone using a cohesive zone model, derives an analytical model for FPZ length, and establishes a relationship between FPZ length and breakdown pressure. It accurately predicts breakdown pressure and accounts for the strengthening effect of in-situ stress on fracture toughness, overcoming LEFM limitations.
What are the key conditions for fracture propagation according to the proposed criterion?
Fracture propagation occurs when the apparent stress intensity at the fracture tip reaches the apparent fracture toughness, or when the in-situ stress intensity reaches the in-situ fracture toughness. At this point, the FPZ is fully developed and the fracture begins to propagate.
What is the significance of this research for hydraulic fracturing design?
This research provides a more accurate criterion for predicting breakdown pressure and understanding nonlinear fracture behavior in deep reservoirs. It enhances fracturing design by enabling better characterization of fracture toughness and the effects of the FPZ, leading to more effective stimulation treatments.
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