Fracture toughness evaluation of shale based on machine learning and micromechanical approach

The fracture toughness of shale is of great significance for quantitatively evaluating the fracturability of shale reservoirs. Therefore, machine learning and nanoindentation mechanics testing techniques are used to study rock mechanics’ micro fracture toughness characteristics and complete the scale upgrade. Statistical nanoindentation and deep nanoindentation mechanical experiments (indentation morphology method) were conducted on rock samples from the Longmaxi Formation, and SEM images of indentation points were simultaneously collected. Based on the verification that the indentation range of the sample can represent the overall mechanical properties, machine learning methods were used to upgrade the scale modeling and conduct analysis and discussion. The results indicate that the fracture toughness based on the fracture length method is closer to Type I (tensile) fracture toughness, while the fracture toughness based on the energy method is closer to Type II (shear) fracture toughness, approximately three times that of Type I. Load strength and indentation depth are the main reasons for the difference in results between the two testing methods. The K-means dynamic homogeneous clustering machine learning method and deconvolution method can identify three physical phases: organic matter/clay, intermediate substances (composite phases), and hard minerals. The average errors between the obtained shale elastic modulus and hardness using machine learning algorithms and the deconvolution results are 3.70 % and 2.44 %, respectively. Compared to Gaussian deconvolution, the K-means clustering method can clarify the boundaries of individual physical clusters more clearly, making it easier to quantify the properties of clusters and evaluate the coupling relationship between physical quantities through two-dimensional and three-dimensional clustering. In addition, deconvolution methods can collaborate with K-means to determine initial cluster centers, further improving the accuracy of mechanical parameter interpretation for microscopic phases. The combination of statistical nanoindentation technology, deconvolution, machine learning, and other methods is of great significance for revealing the mechanical properties of heterogeneous shale at the micro nano scale and upgrading the scale, expanding the application of machine learning in the field of petroleum engineering.