Prediction of hydraulic fracture initiation pressure in a borehole based on a neural network model considering plastic critical distance

Prediction of the hydraulic fracture initiation pressure is essential for in-situ hydraulic fracturing design and stress measurement. The prediction models based on the theory of critical distance have been proofed to fit the abnormal initiation pressure caused by the bore size. However, the critical distance used by the previous models is not physics-based, which may result in errors for prediction. In addition, the laboratory determination of the critical distance neglected the boundary loading effect, causing an underestimating of the critical distance. This work aims to provide an efficient and accurate model for predicting the in-situ hydraulic fracture initiation pressure with consideration of a physic-based plastic critical distance. We first establish a universal analytical solution for stress distribution and plastic zone around a borehole in a cylindrical sample through ideal elastoplastic theory. Using the analytical solution, the plastic critical distance of shale rock is analyzed based on a hydraulic fracturing experiment, and compared with the one estimated by the previous methods. Then, a set of numerical simulation are carried out to build a data set of hydraulic fracture initiation pressure under different stresses, tensile strength, and ratio of plastic critical distance to borehole radius. Finally, the nonlinear relationship between these parameters is mapped by a deep neural network model. According to this study, the following conclusions are obtained: 1) The plastic critical distance increases as the loading stress increases. 2) The established neural network trained by numerical simulation results is plausible, meanwhile, with high precision and high efficiency. 3) Increase in stresses and tensile strength can strengthen the influence of critical plastic distance. 4) Kirsch's approximate stress solution can bring an error for determination of the critical distance in lab-scale experiments.