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<p>Accurate prediction of formation fracturing pressure is crucial for drilling safety and reservoir protection. In this study, a long short-term memory (LSTM) neural network model integrated with geomechanical constraints (Physical-LSTM) is proposed, which achieves deep coupling of data-driven approaches and physical laws through a physical constraint correction layer and a multi-objective loss function. Based on logging-while-drilling and drilling data from three wells in the Bohai Sea area, 15 key parameters were selected as the model inputs. The physical constraints include: the fracturing pressure must be greater than the pore pressure, less than the overburden pressure, and monotonically increasing with well depth. Bayesian optimization was employed to determine the weights of physical constraints and data fitting (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> = 0.8, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> = 0.6). The experimental results show that the Physical-LSTM model achieves a mean squared error (MSE) of only 0.0015, a mean absolute error (MAE) of 0.0261, a coefficient of determination (<i>R</i><sup>2</sup>) of 0.981, and a normalized Nash–Sutcliffe efficiency (NNSE) of 0.978 on the test set, which is significantly superior to the baseline models including LSTM, GRU, LightGBM, XGBoost, and RF. Compared with the traditional Eaton model, the Physical-LSTM not only maintains consistency in prediction trends but also substantially reduces prediction errors and eliminates physically unreasonable outliers. This study confirms that embedding physical constraints into machine learning models can significantly improve the accuracy, physical rationality, and engineering reliability of formation fracturing pressure prediction.</p>

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Physics-aware machine learning for fracture pressure prediction model

  • 期刊论文

  • 发表日期：

    2025年11月29日

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  • Xinru Li,
  • Fei Gao,
  • Jiahao Lan,
  • Zhongqiang Li,
  • Mengting Huang,
  • Jiayu Wang

摘要

Accurate prediction of formation fracturing pressure is crucial for drilling safety and reservoir protection. In this study, a long short-term memory (LSTM) neural network model integrated with geomechanical constraints (Physical-LSTM) is proposed, which achieves deep coupling of data-driven approaches and physical laws through a physical constraint correction layer and a multi-objective loss function. Based on logging-while-drilling and drilling data from three wells in the Bohai Sea area, 15 key parameters were selected as the model inputs. The physical constraints include: the fracturing pressure must be greater than the pore pressure, less than the overburden pressure, and monotonically increasing with well depth. Bayesian optimization was employed to determine the weights of physical constraints and data fitting ( \(\alpha\) α  = 0.8, \(\beta\) β  = 0.6). The experimental results show that the Physical-LSTM model achieves a mean squared error (MSE) of only 0.0015, a mean absolute error (MAE) of 0.0261, a coefficient of determination (R2) of 0.981, and a normalized Nash–Sutcliffe efficiency (NNSE) of 0.978 on the test set, which is significantly superior to the baseline models including LSTM, GRU, LightGBM, XGBoost, and RF. Compared with the traditional Eaton model, the Physical-LSTM not only maintains consistency in prediction trends but also substantially reduces prediction errors and eliminates physically unreasonable outliers. This study confirms that embedding physical constraints into machine learning models can significantly improve the accuracy, physical rationality, and engineering reliability of formation fracturing pressure prediction.