Prediction of particle settling velocity during hydraulic fracturing using machine learning

Abstract

Prediction of particle settling velocity with high accuracy is crucial in the evaluation of proppant transport and placement during hydraulic fracturing, where high settling velocities may negatively impact the placement of proppants and fracture conductivity. Highly nonlinear relationships in settling behavior depend on a set of associated factors, such as particle size, density difference, and rheological properties of the fluid. Established empirical and semiempirical equations and correlations are intended only for specific fluids and have limited conditions. Therefore, this study investigates the use of machine learning approaches for predicting particle settling velocity in hydraulic fracturing. A literature-based dataset was gathered from more than 20 published papers, which included different fluid systems such as Newtonian, power law, viscoplastic, and viscoelastic fluids. 1341 clean and preprocessed datapoints were gained at the end. The input features were particle diameter, particle density, fluid density, consistency index, and flow behavior. In addition, density ratio and density difference were computed as well. Exploratory analysis showed the nonlinearity and heterogeneity of the compiled dataset, which supported the suitable use of nonlinear machine learning models. Several regression algorithm-based models were developed and tested. The train-test split of the data was 80/20%, respectively. 5-fold cross-validation and hyperparameter tuning processes were included in the development of the model. CatBoost achieved the best performance among the other models, reaching the superior outcome metrics for the test R2 = 0.9169, RMSE = 0.0232, and MAE = 0.0132. According to the feature importance analysis, particle diameter was identified as the most influential input variable, followed by the consistency index, which proved the crucial role of the particle size and rheological properties in settling behavior. Moreover, the best model was compared to the selected literature models of the rheology-based subset. In the Newtonian system, classical correlations were highly competitive and slightly better than CatBoost. In the power law fluid, CatBoost showed greater results than the Shah et al. (2007) correlation. In general, the results indicate that machine learning models, especially CatBoost, provide predictive tools for settling velocity of particles in hydraulic fracturing.