Improved explainable multi-gene genetic programming correlations for predicting carbon dioxide solubility in various brines

Storing carbon dioxide (CO₂) in deep saline aquifers has gained significant attention as an effective approach to reducing greenhouse gas emissions. The success of carbon capture and storage (CCS) in deep saline aquifers relies on accurately assessing CO₂ solubility in brine under real operating conditions. Gaining detailed insight into CO₂ behavior in subsurface environments is essential for effectively implementing this method. In this study, we have made substantial efforts to compile a comprehensive dataset on CO₂ solubility in diverse aqueous electrolyte solutions of CaCl₂, NaCl, MgCl₂, Na₂SO₄, and KCl, encompassing a wide interval of operating conditions and widespread salt concentrations. To leverage this extensive dataset effectively, we applied a robust white-box machine learning technique, namely the multi-gene genetic programming (MGGP) to establish user-friendly explicit correlations for accurately predicting CO₂ solubility in numerous brines under subsurface conditions. Our evaluation revealed that the derived correlations provided significantly more precise predictions of CO₂ solubility. In this context, the MGGP-based correlations demonstrated trustworthy accuracy with total root mean square error (RMSE) values of only 0.0235, 0.0304, 0.0196, 0.0289, and 0.0313 for CaCl₂, NaCl, MgCl₂, Na₂SO₄, and KCl solutions, respectively. Additionally, the trend analysis showed that the proposed correlations effectively captured the behavior of CO₂ solubility across a wide range of operating pressures, temperatures, and solvent salinities, demonstrating their robustness and reliability. Furthermore, Shapley Additive Explanations (SHAP) provided useful insights into how different inputs contribute and interact, making the proposed correlations easier to understand and interpret. Lastly, the newly introduced MGGP-based correlations exhibit notable improvements in accuracy, user-friendliness, generalization, and explainability, ensuring superior performance across diverse subsurface conditions. These advancements mark a significant step forward in the cost-effective and precise estimation of CO₂ solubility in various brines, making the proposed correlations highly valuable for applications in carbon capture and storage, environmental impact assessment, petroleum geology, reservoir engineering, and other CO₂-related domains.