To adapt the presented approach to model the flow of hydrogen-natural gas mixtures in energy networks, several modifications and considerations need to be made. Since hydrogen and natural gas have different thermodynamic properties, including different equations of state and energy conversion characteristics, the pH formulation would need to account for these differences.
One approach would be to extend the pH formulation to include separate state variables and equations for hydrogen and natural gas components in the network. This would involve defining specific Hamiltonians, effort variables, and coupling conditions for each gas type to accurately represent their thermodynamic behavior and interactions within the network.
Additionally, the boundary conditions and external inputs in the pH formulation would need to be tailored to reflect the properties of hydrogen-natural gas mixtures, such as varying compositions, pressures, and temperatures. By incorporating the specific thermodynamic properties of hydrogen and natural gas into the pH framework, the model can simulate the flow dynamics and energy transport in networks with mixed gas components effectively.