Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Journal Article · Tue Dec 27 00:00:00 EST 2022 · IEEE Transactions on Control of Network Systems

DOI:https://doi.org/10.1109/tcns.2022.3232524· OSTI ID:1969233

Srinivasan, Shriram ^[1]; Sundar, Kaarthik ^[1]; Gyrya, Vitaliy ^[1]; Zlotnik, Anatoly V. ^[1]

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

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

• 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: 1969233
• Report Number(s): LA-UR-22-21789
• Journal Information: IEEE Transactions on Control of Network Systems, Journal Name: IEEE Transactions on Control of Network Systems Journal Issue: 3 Vol. 10; ISSN 2325-5870
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Newton-Raphson
compressibility factor
computer science
mathematics
network flow equations
non-ideal gas
steady-state