Steady State Blended Gas Flow on Networks: Existence and Uniqueness of Solutions

TL;DR

This paper proves the existence and uniqueness of steady state gas flow solutions on networks, considering gas mixtures like natural gas and hydrogen, with numerical examples demonstrating applicability.

Contribution

It introduces a mathematical model for steady gas flow on networks with mixed gases and proves solution existence for specific network topologies.

Findings

Existence of solutions for tree-shaped networks.

Existence of solutions for networks with one cycle.

Numerical examples validate the theoretical results.

Abstract

We prove an existence result for the steady state flow of gas mixtures on networks. The basis of the model are the physical principles of the isothermal Euler equation, coupling conditions for the flow and pressure, and the mixing of incoming flow at nodes. The state equation is based on a convex combination of the ideal gas equations of state for natural gas and hydrogen. We analyze mathematical properties of the model allowing us to prove the existence of solutions in particular for tree-shaped networks and networks with exactly one cycle. Numerical examples illustrate the results and explore the applicability of our approach to different network topologies.