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

Dennis Delali Kwesi Wayo1, Sonny Irawan2, Lei Wang3

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|August 20, 2025
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Summary

This study introduces a hybrid model combining physics and machine learning to accurately predict proppant settling rate (PSR) in hydraulic fracturing. The new framework offers efficient and interpretable predictions for fracture design.

Keywords:
Computational geomechanicsFluid–solidHydraulic fracturingMachine learningProppant

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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.