A deep learning framework for monotonic and physics-compliant CO2 trapping index forecasting

Abstract

The permanence and security of geological CO2 storage, a critical climate change mitigation strategy, hinges on a thorough understanding of subsurface trapping mechanisms. Predicting trapping efficiency traditionally relies on computationally-intensive numerical simulations, especially for complex, heterogeneous reservoirs. While data-driven deep learning models offer accelerated computation, they often act as “black boxes” with poor interpretability and no inherent adherence to physical laws. To address this, we present a physics-incorporated Deep Operator Network (DeepONet) for predicting two key density-driven trapping indexes: the Residual Trapping Index (RTI) and Solubility Trapping Index (STI). Our architecture enforces physical realism by encoding the laws of mass conservation and temporal monotonicity directly into a composite loss function and through architecturally guaranteed constraints, supported by advanced regularisation techniques. The model was trained and tested on a comprehensive dataset of over 11,000 samples compiled from global studies. Results demonstrated high predictive precision, with mean absolute errors of 0.0042 (RTI) and 0.0022 (STI), and R2 scores of 0.994 and 0.982, respectively. Crucially, the model maintained a 0% violation rate of the fundamental physical constraint (RTI+STI≤1) and preserved the expected monotonic behaviour of trapping over time. The close clustering of predicted and actual values, along with residuals centred around zero, confirms the model's robustness, reliability, and strong generalisation capability for predicting CO2 trapping across diverse geological conditions.