Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions

Hari, Sai Krishna Kanth; Sundar, Kaarthik; Srinivasan, Shriram; Zlotnik, Anatoly; Bent, Russell

doi:10.1109/tcst.2021.3071316

Cited by 16 publications

(3 citation statements)

References 32 publications

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“…As an aside, note that the nominal quantities are usually chosen to ensure that the non-dimensional variables have similar orders of magnitude. If the intent however is to have the transformed equations appear without the Euler and Mach numbers [15], [20], one can choose v 0 = a and ρ 0 = p 0 /a 2 to ensure that M = C = 1.…”

Section: Non-dimensionalization Of the Governing Equations For A Sing...mentioning

confidence: 99%

“…That mechanism enables modeling of any type of pressure or flow boundary condition at either end of a pipe, which is useful for representing valve actions in addition to compression in transient simulation. Alternatively, in the node-connecting representation [11], [15], compressors are associated with a pair of junctions and could be viewed as a pipe with zero length and prescribed pressure boost ratio. This representation simplifies the overall equations governing the flow of natural gas through networks of pipes and compressors in the context of steady-state modeling.…”

Section: Gas Flow Problem On a Networkmentioning

confidence: 99%

“…Such problems aim to minimize or maximize an objective function involving a cost or performance index subject to constraints that represent the physics of transient or steady-state natural gas flows. Examples include optimal network expansion [10]- [12], integrated gas-electric system operations [6], [13], [14], day-today operations of natural gas pipeline with [15] and without storage [16], [17], state and parameter estimation [18]- [21], and compressor power minimization [22], [23].…”

Section: Introductionmentioning

confidence: 99%

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

Srinivasan¹,

Sundar²,

Gyrya³

et al. 2022

Preprint

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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 indicate that the steadystate 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 [1]-[4]. 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.

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Section: Non-dimensionalization Of the Governing Equations For A Sing...mentioning

confidence: 99%

Section: Gas Flow Problem On a Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Srinivasan¹,

Sundar²,

Gyrya³

et al. 2022

Preprint

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Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography

Leppert,

Brehmer,

Boeker

et al. 2024

J of Separation Science

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A general method for the calculation of the flow and pressure of a gas in a network of cylindrical capillaries is presented. This method is used specifically for gas chromatographic systems in this work. With this approach, it is possible to easily calculate flow and pressures in complex gas chromatographic systems, like flow‐modulated or thermal‐modulated multidimensional gas chromatographic systems, or systems with multiple outlets at different pressures. A mathematic abstraction using graph theory is used to represent the system of capillaries. With this graph, the flow balance equations at the connections of the capillaries can easily be set up. Using a computer algebra system, the system of flow balance equations can be solved for the pressures at the connection points. For simple systems, this approach is presented, and calculated flows, pressures, and hold‐up times are compared with measured values. In addition, two complex systems (4‐Way‐Splitter, Deans Switch system) of capillaries are presented with calculations only. For these systems, certain conditions were formulated, that is, a certain difference in hold‐up times and a defined split ratio between different paths of these systems. Using a numeric non‐linear solver, configurations of these systems were found, that fulfill these conditions.

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Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations

Xue,

Xu,

Zhang

2024

J Syst Sci Complex

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Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions

Cited by 16 publications

References 32 publications

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

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

Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography

Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations

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