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<p>This study provides an in-depth analysis of time series forecasting methods to predict the time-dependent deformation trend (also known as creep) of salt rock under varying confining pressure conditions. Creep deformation assessment is essential for designing and operating underground storage facilities for nuclear waste, hydrogen energy, or radioactive materials. Salt rocks, known for their mechanical properties like low porosity, low permeability, high ductility, and exceptional creep and self-healing capacities, were examined using multi-stage triaxial creep data. After resampling, axial strain datasets were recorded at 5–10&#xa0;sec intervals under confining pressure levels ranging from 5 to 35&#xa0;MPa over 5.8–21&#xa0;days. Initial analyses, including Seasonal-Trend Decomposition and Granger causality tests, revealed minimal seasonality and causality between axial strain and temperature data. Further statistical tests, such as the Automated Dickey–Fuller test, confirmed the stationarity of the data with <i>p</i>-values less than 0.05, and wavelet coherence plot analysis indicated repeating trends. A suite of deep neural network (DNN) models—Neural Basis Expansion Analysis for Time Series (N-BEATS), Temporal Convolutional Networks (TCN), Recurrent Neural Networks, and Transformers—were utilized and compared against statistical baseline models. Predictive performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE in %), and Symmetric Mean Absolute Percentage Error (SMAPE in %). Results demonstrated that N-BEATS and TCN models outperformed others, with RMSE values of(0.3325–1.257) and 0.540–1.352, MAE from 0.287–0.961 and 0.472–1.177, MAPE from 1.45–4.54 and 2.85–6.28, and SMAPE from 1.46–4.62 and 2.88–6.03 across various stress levels, respectively. DNN models, particularly N-BEATS and TCN, showed a 15% improvement in accuracy over traditional analytical models, effectively capturing complex temporal dependencies and patterns. This research significantly advances time series forecasting in geosciences, offering crucial insights for the safe and efficient management of underground storage in rock salt formations.</p>

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Salt rock creep deformation forecasting using deep neural networks and analytical models for subsurface energy storage applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月3日

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  • Pradeep Kumar Shukla,
  • Tanujit Chakraborty,
  • Mustafa Sari,
  • Joel Sarout,
  • Partha Pratim Mandal

摘要

This study provides an in-depth analysis of time series forecasting methods to predict the time-dependent deformation trend (also known as creep) of salt rock under varying confining pressure conditions. Creep deformation assessment is essential for designing and operating underground storage facilities for nuclear waste, hydrogen energy, or radioactive materials. Salt rocks, known for their mechanical properties like low porosity, low permeability, high ductility, and exceptional creep and self-healing capacities, were examined using multi-stage triaxial creep data. After resampling, axial strain datasets were recorded at 5–10 sec intervals under confining pressure levels ranging from 5 to 35 MPa over 5.8–21 days. Initial analyses, including Seasonal-Trend Decomposition and Granger causality tests, revealed minimal seasonality and causality between axial strain and temperature data. Further statistical tests, such as the Automated Dickey–Fuller test, confirmed the stationarity of the data with p-values less than 0.05, and wavelet coherence plot analysis indicated repeating trends. A suite of deep neural network (DNN) models—Neural Basis Expansion Analysis for Time Series (N-BEATS), Temporal Convolutional Networks (TCN), Recurrent Neural Networks, and Transformers—were utilized and compared against statistical baseline models. Predictive performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE in %), and Symmetric Mean Absolute Percentage Error (SMAPE in %). Results demonstrated that N-BEATS and TCN models outperformed others, with RMSE values of(0.3325–1.257) and 0.540–1.352, MAE from 0.287–0.961 and 0.472–1.177, MAPE from 1.45–4.54 and 2.85–6.28, and SMAPE from 1.46–4.62 and 2.88–6.03 across various stress levels, respectively. DNN models, particularly N-BEATS and TCN, showed a 15% improvement in accuracy over traditional analytical models, effectively capturing complex temporal dependencies and patterns. This research significantly advances time series forecasting in geosciences, offering crucial insights for the safe and efficient management of underground storage in rock salt formations.