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 nonlinear system is known to have a unique solution (when one exists), the absence of a definite result on the 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 for any fluid whose equation of state is a scaled monomial, a unique solution exists for such nonlinear systems if the term solution is interpreted in terms of potentials and flows rather than pressures and flows. However, for gases following the CNGA equation of state, while the question of existence remains open, we construct an alternative system that always has a unique solution and show that the solution to this system is a good approximant of the true solution. 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, our result enables correct diagnosis of algorithmic failure, problem stiffness, and non-convergence in computational algorithms.

翻译：摘要：管网基础设施中由节点势能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组成部分。尽管已知非线性系统在解存在时具有唯一性，但解存在性判定依据的缺失制约了计算算法的发展——因无法区分算法失效与解不存在的情形。本文证明：对于状态方程为缩放单项式的任意流体，若将"解"的概念从压力-流量关系扩展为势能-流量关系，则该类非线性系统必然存在唯一解。然而，对于遵循CNGA状态方程的气体，虽解存在性问题尚未解决，我们构建了一个始终存在唯一解的替代系统，并证明该系统的解能良好逼近真实解。天然气网络流动的存在性结论同样适用于其他流体管网，如给水管网或碳捕集与封存中的二氧化碳输送管网。尤为重要的是，本研究成果能够为计算算法中的算法失效、问题刚性与不收敛现象提供准确的诊断依据。