On the Existence of Steady-State Solutions to the Equations Governing Fluid Flow in Networks

Journal Article · Fri Apr 26 00:00:00 EDT 2024 · IEEE Control Systems Letters

DOI:https://doi.org/10.1109/lcsys.2024.3394317· OSTI ID:2477796

Srinivasan, Shriram ^[1]; Panda, Nishant ^[1]; Sundar, Kaarthik ^[1]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

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. Further, 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2477796
• Report Number(s): LA-UR--23-30213
• Journal Information: IEEE Control Systems Letters, Journal Name: IEEE Control Systems Letters Vol. 8; ISSN 2475-1456
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

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Energy Sciences
Mathematics