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Machine learning-based models for predicting gas breakthrough pressure of porous media with low/ultra-low permeability

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Gas breakthrough pressure is a significant parameter for the gas exploration and safety evaluation of engineering barrier systems in the carbon dioxide storage, remediation of contaminated sites, and deep geological repository for disposal of high-level nuclear waste, etc. Test for determining gas breakthrough pressure is very difficult and time-consuming, due to the low/ultra-low conductivity of the specimen. It is also difficult to get a comprehensive and high-precision model based on limited results obtained through individual experiments, as the measurements of gas breakthrough pressure were influenced by many factors. In this study, a collected database was built that covered a lot of former test data, and then, two models were developed by the random forest (RF) algorithm and multiexpression programming (MEP) method. The MEP model constructed with explicit expressions for the gas breakthrough pressure overcame the drawbacks of common “black box” models. Meanwhile, five significant indicators were selected from ten common features using the permutation importance algorithm. The RF model was interpreted by the Shapley value and the PDP/ICE plots, while the MEP model was analyzed through the proposed explicit expression, showing strong consistence with that in former studies. Finally, robustness analysis was conducted, and stability of the proposed two models was verified.

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All data will be made available on reasonable request.


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The financial supports from the National Natural Science Foundation of China (42030714 and 42172298) and the National Key R&D Program of China (2019YFC1509900) are greatly acknowledged.

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Authors and Affiliations



Wei-Min Ye: conceptualization, validation, formal analysis, investigation, data curation, writing—review and editing, project administration, and funding acquisition. Cen Gao: methodology, writing—original draft, supervision, software, validation, formal analysis, investigation, resources, and visualization. Pu-Huai Lu: data collection, methodology, and writing—review and editing. Zhang-Rong Liu: writing—review and editing. Qiong Wang: writing—review and editing. Yong-Gui Chen: writing—review and editing.

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Correspondence to Wei-Min Ye.

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• Two machine learning-based models were established for prediction of gas breakthrough pressures.

• Five features were extracted as final indictors based on the permutation importance.

• Shapley value and PDP/ICE plots were introduced to show the interpretability and prediction trend of the RF model.

• The RF model has a high accuracy in predicting the gas breakthrough pressure.

• The MEP model is more convincible with the explicit prediction formula.

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Gao, C., Lu, PH., Ye, WM. et al. Machine learning-based models for predicting gas breakthrough pressure of porous media with low/ultra-low permeability. Environ Sci Pollut Res 30, 35872–35890 (2023).

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