Combined Deep Learning and Optimization for Hydrogen-Solubility Prediction in Aqueous Systems Appropriate for Underground Hydrogen Storage Reservoirs

The widespread use of fossil fuels drives greenhouse gas emissions, prompting the need for cleaner energy alternatives like hydrogen. Underground hydrogen storage (UHS) is a promising solution, but measuring the hydrogen (H₂) solubility in brine is complex and costly. Machine learning can provide accurate and reliable predictions of H₂ solubility by analyzing diverse input variables, surpassing traditional methods. This advancement is crucial for improving UHS, making it a viable component of the sustainable energy infrastructure. Given its importance, this study utilized convolutional neural network (CNN) and long–short-term memory (LSTM) deep learning algorithms in combination with growth optimization (GO) and grey wolf optimization (GWO) algorithms to predict H₂ solubility. A total of 1078 data points were collected from laboratory results, including the variables temperature (T), pressure (P), salinity (S), and salt type (ST). After removing 97 data points, which were identified as outliers and duplicates, the remaining 981 data points were divided into training and testing sets using the best separation ratio selected based on sensitivity analysis. Standalone and hybrid forms of deep learning algorithms were then applied to the training data to develop predictive models with optimized control parameters for both deep learning and optimization algorithms. Among the developed models, CNN-GO has the lowest root-mean-square error (RMSE, train: 0.00006 mole fraction and test: 0.00021 mole fraction) compared to other hybrid and standalone deep learning models. The application of scoring and regression error characteristic (REC) curve analysis showed that this model generated the best prediction performance. Shapley additive explanation analysis indicated that P was the most important factor influencing H₂ solubility, followed by S, T, and ST, in that order. Partial dependency analysis for the CNN-GO model revealed its ability to capture complex nonlinear relationships between input features and the target variable.