On the Existence of Steady States for Blended Gas Flow with Non-Constant Compressibility Factor on Networks

TL;DR

This paper proves the existence of steady states in hydrogen-natural gas pipeline networks with composition-dependent compressibility factors, using mathematical analysis and numerical examples to explore different models' effects.

Contribution

It introduces a mathematical proof for steady states in complex gas flow models with non-constant compressibility factors on networks.

Findings

Existence of steady states proven for broad class of models

Numerical examples demonstrate impact of compressibility models

Analysis overcomes discontinuous composition dependence

Abstract

In this paper, we study hydrogen-natural gas mixtures transported through pipeline networks. The flow is modeled by the isothermal Euler equations with a pressure law involving a non-constant, composition-dependent compressibility factor. For a broad class of such compressibility models, we prove the existence of steady-state solutions on networks containing compressor stations. The analysis is based on an implicit representation of the pressure profiles and a continuity argument that overcomes the discontinuous dependence of the gas composition on the flow direction. Numerical examples illustrate the influence of different compressibility models on the resulting states.