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It introduces a dual physical constraint mechanism based on the Arps decline equation and Darcy’s law, plus a dynamic weighting strategy tuned to production stages. Results reach R2=0.85 with full histories and R2=0.83 with limited data, improving conventional static approaches by 5.7% for Duvernay shale while remaining robust under data scarcity.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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is EUR prediction challenging in shale gas development?","Question",{"text":62,"@type":63},"EUR prediction is difficult because shale reservoirs show strong geological heterogeneity and EUR depends on complex nonlinear relationships between multiple sources of geological and production data.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is the core idea of the proposed hybrid modeling framework?",{"text":67,"@type":63},"The framework combines static geological parameters with dynamic production data using a hybrid machine learning approach to improve EUR prediction accuracy.",{"name":69,"@type":60,"acceptedAnswer":70},"How do physical constraints improve the model?",{"text":71,"@type":63},"Physical constraints are incorporated through a dual mechanism using the Arps decline equation and Darcy’s law, guiding the learning process toward physically consistent decline and flow 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 Article   \nApplication of Dynamic-Static Neural Network Model Integrating Physical Constraints in EUR Prediction of Shale Gas Wells  \nYe Li, Zhiyang Pi, * Gang Hui, * Zhangxin Chen, Jing Li, Ke Zhang, Chenqi Ge, Penghu Bao, Yujie Zhang, and Fei Gu  \n Cite This: ACS Omega 2025, 10, 59947−59962  \nRead Online  \n\n|  |  |  |  |\n| --- | --- | --- | --- |\n| ACCESS   | Metrics & More |  |  Article Recommendations |\n\nABSTRACT: Accurate estimation of estimated ultimate recovery (EUR) is critical for shale reservoir development but remains challenging due to the complex interplay of geological and production factors. This paper presents a hybrid machine learning framework that combines static geological parameters with dynamic production data to enhance EUR prediction. Key innovations include a dual physical constraint mechanism incorporating the Arps decline equation and Darcy’s law, and a dynamic weighting strategy that adaptively balances static and dynamic feature contributions based on production stage. The model achieves an R2 of 0.85 for wells with complete production history and 0.83 for those with limited data􀀁a 5.7% improvement over conventional static methods in the Duvernay shale. Notably, using only 20 months of production data combined with static parameters, the model attains high prediction accuracy (R2 = 0.83), demonstrating strong performance even under data scarcity. This approach provides a reliable tool for EUR prediction in marginal or undeveloped oil fields, supporting informed investment decisions and optimized development.  \n1. INTRODUCTION  \nEUR (Estimated Ultimate Recovery) prediction in shale gas development plays a decisive role in the economic evaluation, development plan optimization, and risk management. 1 Traditional prediction methods rely on empirical formulasand numerical simulations, which struggle to effectively address the strong heterogeneity of shale reservoirs and the complex nonlinear relationships among multisource data. Machine learning technologies integrate geological parameters, engineering data, and dynamic production history, utilizing algorithms such as Random Forest and XGBoost to uncover key feature correlations. Combined with interpretable tools like SHAP values to quantify the contribution of each factor to EUR, these methods significantly enhance prediction accuracy. Typical cases demonstrate that machine learning algorithms exhibit significant advantages in EUR prediction. Among these, the Random Forest (RF) model, with its strong generalization capabilities and ability to handle high-dimensional data, has performed exceptionally well in EUR predictions for multiple shale basins such as Bakken,.2,3 Research indicates that RF effectively reduces overfitting risks and improves prediction accuracy by constructing an ensemble of decision trees, resulting in lower root-mean-square error (RMSE) values.4 The CatBoost algorithm outperforms XGBoost and LightGBMin handling categorical features and reducing overfitting due to its symmetric decision tree structure and gradient boosting mechanism.5 Support Vector Machines (SVM) and Artificial  \nNeural Networks (ANN) also have their own unique features: SVM excels in small sample scenarios by constructing an optimal hyperplane,6,7 while ANN is more suitable for simulating nonlinear relationships in large-scale data sets through its multilayer network structure,.8,9 In terms of data integration, multisource data integration significantly improves prediction accuracy, feature importance assessment methods based on Shapley values can effectively identify key features,10 and imbalanced data set issues can be mitigated through methods such as resampling and ensemble learning. In terms of model optimization, hyperparameter optimization, 11, 12 crossvalidation, 13 and model interpretability methods14 collectively enhance the predi","cbCaihTklGwHuEYJ","https://ap.wps.com/l/cbCaihTklGwHuEYJ","pdf",9519067,16,"English","# ABSTRACT\n# 1. INTRODUCTION\n## EUR prediction challenges in shale gas\n## Machine learning approaches and algorithms\n## Data integration and model optimization","[{\"question\":\"Why is EUR prediction challenging in shale gas development?\",\"answer\":\"EUR prediction is difficult because shale reservoirs show strong geological heterogeneity and EUR depends on complex nonlinear relationships between multiple sources of geological and production data.\"},{\"question\":\"What is the core idea of the proposed hybrid modeling framework?\",\"answer\":\"The framework combines static geological parameters with dynamic production data using a hybrid machine learning approach to improve EUR prediction accuracy.\"},{\"question\":\"How do physical constraints improve the model?\",\"answer\":\"Physical constraints are incorporated through a dual mechanism using the Arps decline equation and Darcy’s law, guiding the learning process toward physically consistent decline and flow behavior.\"}]","Application of Dynamic-Static Neural Network Model Integrating Physical Constraints in EUR Prediction of Shale Gas Wells | PDF",1790700649]