Modelling Hydraulic Fracturing with a Point-Based Approximation for the Maximum Principal Stress Criterion

Accurate simulation of the propagation of hydraulic fractures under in situ stress conditions in three dimensions (3D) is critical for the enhanced design and optimization of hydraulic fracturing in various engineering applications, such as shale gas/oil production and geothermal utilization. To model fracture propagation for geotechnical applications numerically, a maximum principal stress criterion (MPS-criterion) with a weighted average approximation is conventionally applied. However, it is found that the weighted average approximation is inappropriate for hydraulic fracturing under in situ stress conditions, where the presence of both hydraulic pressure and in situ stress can lead to sharp changes of the stress field in the vicinity of the fracture tips. When both hydraulic pressure and in situ stress are considered, the simulated results with the weighted average approximation are inaccurate and are sensitive to the radius of the computational area. In this paper, we present numerical tests to identify this limitation of the weighted average approximation and propose a novel point-based approximation for the MPS-criterion. The performance of the MPS-criterion with the point-based approximation for hydraulic fracturing under in situ stress conditions is confirmed by a numerical test. It can be seen that, compared to the traditional weighted average approximation, the MPS-criterion with the point-based approximation is more stable and accurate for modelling hydraulic fracturing under in situ stress conditions.