<p>The initiation of fractures in hydraulic fracturing depends on the relative magnitude of the Mode-I stress intensity factor (K<sub>I</sub>) and the fracture toughness (K<sub>IC</sub>) of the reservoir. Laboratory-measured K<sub>IC</sub> values are often overlooked in hydraulic fracturing design due to their lower magnitudes, which may lead to challenges in the execution of fracturing operations. However, these parameters reach a threshold under in situ stresses where they significantly influence the fracture initiation and propagation. Estimating the K<sub>I</sub>–K<sub>IC</sub> relationship at field scale is complex due to the need for sophisticated field testing and intricate analytical methodologies. This study investigates the scaling effects of K<sub>I</sub> on hydraulic fracture initiation in the Middle Bakken Formation through geomechanical characterization-driven numerical simulations using the Finite Element Method (FEM). The studied section had high brittleness due to higher quartz and carbonate content, making it well suited for hydraulic fracturing. The numerical simulation K<sub>I</sub> matched well with analytical models, showing an increasing trend with injection pressure and fracture length while fracture initiation pressure (FIP) decreased with distance from the borehole. The most accurate field scale K<sub>IC</sub> results were obtained for 30–40&#xa0;mm crack sizes, with errors within 15% of analytical solutions. The simulated FIP had a good agreement with Diagnostic Fracture Injection Test (DFIT) showing only 0.6% difference. FIP aligned well with flaw-based analytical models, whereas tensile strength-based models significantly overestimated it. These findings provide a practical framework for field-scale FIP calibration under K<sub>I</sub>–K<sub>IC</sub> condition in the Middle Bakken Formation, improving fracture-initiation prediction accuracy and supporting more efficient and reliable hydraulic fracturing design.</p>

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Numerical Investigation of Stress Intensity Factor Scaling in Hydraulic Fracture Initiation: A Case Study from the Middle Bakken Formation

  • Atif Ismail,
  • Saman Azadbakht

摘要

The initiation of fractures in hydraulic fracturing depends on the relative magnitude of the Mode-I stress intensity factor (KI) and the fracture toughness (KIC) of the reservoir. Laboratory-measured KIC values are often overlooked in hydraulic fracturing design due to their lower magnitudes, which may lead to challenges in the execution of fracturing operations. However, these parameters reach a threshold under in situ stresses where they significantly influence the fracture initiation and propagation. Estimating the KI–KIC relationship at field scale is complex due to the need for sophisticated field testing and intricate analytical methodologies. This study investigates the scaling effects of KI on hydraulic fracture initiation in the Middle Bakken Formation through geomechanical characterization-driven numerical simulations using the Finite Element Method (FEM). The studied section had high brittleness due to higher quartz and carbonate content, making it well suited for hydraulic fracturing. The numerical simulation KI matched well with analytical models, showing an increasing trend with injection pressure and fracture length while fracture initiation pressure (FIP) decreased with distance from the borehole. The most accurate field scale KIC results were obtained for 30–40 mm crack sizes, with errors within 15% of analytical solutions. The simulated FIP had a good agreement with Diagnostic Fracture Injection Test (DFIT) showing only 0.6% difference. FIP aligned well with flaw-based analytical models, whereas tensile strength-based models significantly overestimated it. These findings provide a practical framework for field-scale FIP calibration under KI–KIC condition in the Middle Bakken Formation, improving fracture-initiation prediction accuracy and supporting more efficient and reliable hydraulic fracturing design.