Model Development for Brittleness Index Estimation and Depth Determination in Hydraulic Fracturing Operations in Shale Gas Reservoirs Using Machine Learning Algorithms

Summary Accurate estimation of the brittleness index (BI) is critical for optimizing hydraulic fracturing operations in shale gas reservoirs, as it directly influences fracture propagation and gas recovery efficiency. The BI quantifies the resistance of rock to fracturing, a key factor in determining the optimal depth for fracture stimulation. Prior methods of estimating BI, such as empirical correlations and other utilized machine learning (ML) techniques, often suffer from limited accuracy and generalizability, particularly in complex geological formations like the Fuling shale gas field. To address these limitations, ML techniques have gained prominence due to their ability to capture complex, nonlinear relationships within large data sets, improving predictive accuracy. In this study, we propose a novel approach that utilizes a hybrid group method of data handling based on discrete differential evolution (GMDH-DDE) to predict the BI. The GMDH-DDE model was compared with the group method of data handling (GMDH), random forest (RF), and multilayer perceptron (MLP). The results demonstrate that GMDH-DDE significantly outperforms these models, achieving a coefficient of determination (R2) of 0.9984, a root mean square error (RMSE) of 0.2895, and a mean absolute error (MAE) of 0.02543 to unseen data. The GMDH model ranked second in BI estimation, achieving an R2 of 0.9805, RMSE of 0.4635, and MAE of 0.04224. It was followed by the RF model, with an R2 of 0.9599, RMSE of 0.6034, and MAE of 0.0997. The MLP model, however, had the lowest performance, with an R2 of 0.9263, RMSE of 0.9566, and MAE of 0.1256. Additionally, the GMDH-DDE model demonstrates superior computational efficiency, requiring only 1.12 seconds. This is a significant advantage over other methods, with GMDH taking 4.82 seconds, RF requiring 11.23 seconds, and MLP taking 27.45 seconds. These findings highlight the potential of GMDH-DDE in providing accurate and computationally efficient BI estimations. The improved accuracy and efficiency of BI estimation by GMDH-DDE are expected to contribute to more effective and cost-efficient hydraulic fracturing operations, ultimately enhancing the economic viability of shale gas reservoirs.