Physics-Informed Graph Connected Element Model for Reservoir Connectivity Identification and Production Forecasting in CO2-EOR

Abstract This paper aims to develop a hybrid modeling framework that integrates the Connected Element Method (CEM), Graph Neural Networks (GNNs), and Physics-Informed Neural Networks (PINNs) to enhance reservoir connectivity identification and production forecasting in CO2-EOR operations. The framework addresses the limitations of traditional and purely data-driven models by ensuring physical consistency and improving predictive accuracy. The methodology incorporates three key components: (1) preprocessing reservoir data using CEM to extract physical parameters like transmissibility and connected pore volume, forming a graph representation of the reservoir; (2) employing GNNs with self-attention mechanisms to capture dynamic inter-well connectivity and heterogeneity; and (3) embedding material balance equations within PINNs to ensure that predictions adhere to fundamental physical laws. The framework is implemented using Python's TensorFlow library and validated using a reservoir model. The proposed PINN-GCEM framework demonstrated significant improvements in both accuracy and efficiency compared to LSTM and PINN-RPM models. PINN-GCEM achieved faster convergence and lower residual errors due to the integration of CEM preprocessing and GNNs, which effectively captured inter-well connectivity and reservoir heterogeneity. Validation results showed that PINN-GCEM's predictions closely matched actual production data, maintaining long-term stability and outperforming PINN-RPM, especially in capturing complex physical behaviors. Additionally, transmissibility predictions from PINN-GCEM were consistent with CEM history-matched results, highlighting its reliability for reconstructing connectivity fields. These findings demonstrate the framework's potential for optimizing CO2 injection strategies and production forecasting in real-time applications. This study introduces a novel combination of CEM, GNNs, and PINNs, providing a robust and physically consistent approach to reservoir modeling. By addressing the limitations of traditional and data-driven methods, the proposed framework offers an efficient and accurate solution for complex reservoir systems, contributing valuable insights to CO2-EOR optimization and reservoir engineering practices.