A Graph-Enhanced DeepONet Approach for Real-Time Estimating Hydrogen-Enriched Natural Gas Flow under Variable Operations

Blending green hydrogen into natural gas presents a promising approach for renewable energy integration and fuel decarbonization. Accurate estimation of hydrogen fraction in hydrogen-enriched natural gas (HENG) pipeline networks is crucial for operational safety and efficiency, yet it remains challenging due to complex dynamics. While existing data-driven approaches adopt end-to-end architectures for HENG flow state estimation, their limited adaptability to varying operational conditions hinders practical applications. To this end, this study proposes a graph-enhanced DeepONet framework for the real-time estimation of HENG flow, especially hydrogen fractions. First, a dual-network architecture, called branch network and trunk network, is employed to characterize operational conditions and sparse sensor measurements to estimate the HENG state at targeted locations and time points. Second, a graph-enhance branch network is proposed to incorporate pipeline topology, improving the estimation accuracy in large-scale pipeline networks. Experimental results demonstrate that the proposed method achieves superior estimation accuracy for HCNG flow under varying operational conditions compared to conventional approaches.