Machine learning-enhanced fully coupled fluid-solid interaction models for proppant dynamics in hydraulic fractures.

Area of Science:

• Petroleum Engineering
• Computational Fluid Dynamics
• Machine Learning

Background:

• Accurate prediction of proppant settling rate (PSR) is crucial for optimizing hydraulic fracturing and ensuring effective proppant transport.
• Traditional methods like Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations are computationally expensive and time-consuming.
• Developing efficient and interpretable models for PSR prediction is essential for real-time decision support in fracture design.

Purpose of the Study:

• To develop a hybrid modeling framework integrating symbolic physics-based derivations, parametric simulations, and ensemble machine learning for predicting proppant settling rate (PSR).
• To validate the physics consistency and performance of the proposed framework against traditional methods.
• To provide an interpretable, accurate, and computationally efficient alternative to full-scale CFD-DEM simulations for proppant transport analysis.

Main Methods:

• Formulated symbolic expressions for PSR using Stokes' law, drag equations, and pressure-gradient dynamics.
• Generated synthetic symbolic and CFD-informed datasets covering realistic physical parameter ranges (proppant density, fluid viscosity, particle diameter, strain, pressure gradient).
• Trained stacked ensemble regressors (Random Forest, Extra Trees, Gradient Boosting, XGBoost, SVR) with a RidgeCV meta-learner on the combined datasets.

Main Results:

• The physics-based symbolic model achieved high accuracy (R² = 0.9934, RMSE = 0.0436).
• CFD simulations provided complementary data, yielding R² = 0.9941 and RMSE = 0.2033.
• The hybrid ensemble model demonstrated superior performance with R² = 0.9970 and RMSE = 0.1801, outperforming individual models.
• Parametric studies showed significant reductions in settling velocity and depth influenced by strain and pressure gradients.

Conclusions:

• The hybrid modeling framework provides an accurate, interpretable, and computationally efficient method for predicting proppant settling rate (PSR).
• This approach eliminates the need for extensive CFD-DEM simulations, facilitating faster decision-making in hydraulic fracturing.
• The framework is highly suitable for multiscale fracture design and real-time proppant transport analysis.