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.

翻译：我们证明了气体混合物在网络上稳态流动的存在性结果。该模型基于等温欧拉方程的物理原理、流动与压力的耦合条件以及节点处流入流体的混合。状态方程基于天然气与氢气的理想气体状态方程的凸组合。我们分析了该模型的数学性质，从而能够证明解的存在性，特别针对树形网络及恰好含有一个环路的网络结构。数值算例验证了结果，并探讨了本方法对不同网络拓扑结构的适用性。