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 \emph{solution} is interpreted in terms of \emph{potentials} and flows rather than \emph{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：由节点/接点势能驱动的管道基础设施网络中流体流动的稳态解，是系统设计与运行中多种决策支持工具的关键组成部分。尽管已知该非线性系统在解存在时具有唯一解，但由于缺乏关于解存在性的明确结论，算法的开发受到了阻碍——我们无法区分是算法失败还是解本身不存在。本文证明，若将术语“解”理解为基于“势能”与流量（而非“压力”与流量），则此类非线性系统存在唯一解。天然气网络流动的存在性结论同样适用于其他流体网络，例如供水管网或碳捕集与封存中输送二氧化碳的网络。尤为重要的是，通过完整回答解的存在性问题，我们的结论能够正确诊断计算算法中的算法失效、病态问题及不收敛现象。