The steady-state solution of fluid flow in pipeline infrastructure networks driven by junction/node potentials is a crucial ingredient in various decision support tools for system design and operation. While the non-linear system is known to have a unique solution (when one exists), the absence of a definite result on existence of solutions hobbles the development of computational algorithms, for it is not possible to distinguish between algorithm failure and non-existence of a solution. In this letter we show that a unique solution exists for such non-linear systems if the term solution is interpreted in terms of potentials and flows rather than pressures and flows. The existence result for flow of natural gas in networks also applies to other fluid flow networks such as water distribution networks or networks that transport carbon dioxide in carbon capture and sequestration. Most importantly, by giving a complete answer to the question of existence of solutions, our result enables correct diagnosis of algorithmic failure, problem stiffness and non-convergence in computational algorithms.

翻译：管道基础设施网络中由节点/结电势驱动的流体流动稳态解是系统设计与运行中各类决策支持工具的关键要素。尽管已知该非线性系统在解存在时具有唯一性，但解存在性判定结果的缺失阻碍了计算算法的发展——因为无法区分算法失效与解不存在这两种情况。本文证明：若将“解”的概念从“压力-流量”重新诠释为“势-流量”关系，此类非线性系统必然存在唯一解。天然气网络流动的存在性结论同样适用于配水管网及碳捕集与封存系统中的二氧化碳输送网络。更重要的是，通过完整回答解的存在性问题，该成果为计算算法中算法故障、问题刚性与不收敛现象的正确诊断提供了理论依据。