Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.; Chertkov, Michael

doi:10.1016/j.physd.2017.09.002

Title: Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

Abstract

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme is unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.

Authors:

Dyachenko, Sergey A. ^[1];

^[2]; Korotkevich, Alexander O. ^[3];

^[4]

Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Mathematics
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of New Mexico, Albuquerque, NM (United States). Dept. of Mathematics & Statistics; L. D. Landau Inst. for Theoretical Physics, Moscow (Russia)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Energy System Center, Skoltech, Moscow (Russia)

Publication Date:: Tue Sep 19 00:00:00 EDT 2017

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Electricity (OE); USDOE Advanced Research Projects Agency - Energy (ARPA-E)

OSTI Identifier:: 1394973

Report Number(s):: LA-UR-16-29073
Journal ID: ISSN 0167-2789

Grant/Contract Number:: AC52-06NA25396; AR0000673

Resource Type:: Accepted Manuscript

Journal Name:: Physica. D, Nonlinear Phenomena

Additional Journal Information:: Journal Volume: 361; Journal ID: ISSN 0167-2789

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Computer Science; Energy Sciences; Mathematics; Natural Gas; Computational Methods

Citation Formats


                    Dyachenko, Sergey A., Zlotnik, Anatoly, Korotkevich, Alexander O., and Chertkov, Michael. Operator splitting method for simulation of dynamic flows in natural gas pipeline networks.  United States: N. p., 2017. 
Web.  doi:10.1016/j.physd.2017.09.002.

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                    Dyachenko, Sergey A., Zlotnik, Anatoly, Korotkevich, Alexander O., & Chertkov, Michael. Operator splitting method for simulation of dynamic flows in natural gas pipeline networks.  United States.  https://doi.org/10.1016/j.physd.2017.09.002

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                    Dyachenko, Sergey A., Zlotnik, Anatoly, Korotkevich, Alexander O., and Chertkov, Michael. Tue .  
"Operator splitting method for simulation of dynamic flows in natural gas pipeline networks".  United States.  https://doi.org/10.1016/j.physd.2017.09.002.  https://www.osti.gov/servlets/purl/1394973.

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@article{osti_1394973,

  title        = {Operator splitting method for simulation of dynamic flows in natural gas pipeline networks},

  author       = {Dyachenko, Sergey A. and Zlotnik, Anatoly and Korotkevich, Alexander O. and Chertkov, Michael},

  abstractNote = {Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme is unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.},

  doi          = {10.1016/j.physd.2017.09.002},

  journal      = {Physica. D, Nonlinear Phenomena},

  number       = ,

  volume       = 361,

  place        = {United States},

  year         = {Tue Sep 19 00:00:00 EDT 2017},

  month        = {Tue Sep 19 00:00:00 EDT 2017}

}

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Works referenced in this record:

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Modelling and optimization of supply chains on complex networks
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Title: Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

Abstract

Citation Formats

Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation journal, August 1984

A new model for gas flow in pipe networks journal, July 2009

An implicit method for transient gas flows in pipe networks journal, October 1994

Optimal control of transient flow in natural gas networks conference, December 2015

Transient modeling of non-isothermal, dispersed two-phase flow in natural gas pipelines journal, February 2010

Coupling Conditions for Networked Systems of Euler Equations journal, January 2008

Modelling and optimization of supply chains on complex networks journal, January 2006

Cascading of fluctuations in interdependent energy infrastructures: Gas-grid coupling journal, December 2015

Coupling conditions for gas networks governed by the isothermal Euler equations journal, January 2006

Multiscale modeling for gas flow in pipe networks journal, August 2007

A new model for gas flow in pipe networks journal, July 2009

Unsteady and transient flow of compressible fluids in pipelines—a review of theoretical and some experimental studies journal, March 1987

Simulation of transients in natural gas pipelines using hybrid TVD schemes journal, February 2000

Coupling Conditions for Networked Systems of Euler Equations journal, January 2008

Simulation of transient gas flows in networks journal, January 1984

On the Construction and Comparison of Difference Schemes journal, September 1968

Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation journal, August 1984

An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds journal, May 1996

Transient modeling of non-isothermal, dispersed two-phase flow in natural gas pipelines journal, February 2010

Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
journal, August 1984

A new model for gas flow in pipe networks
journal, July 2009

An implicit method for transient gas flows in pipe networks
journal, October 1994

Optimal control of transient flow in natural gas networks
conference, December 2015

Transient modeling of non-isothermal, dispersed two-phase flow in natural gas pipelines
journal, February 2010

Coupling Conditions for Networked Systems of Euler Equations
journal, January 2008

Modelling and optimization of supply chains on complex networks
journal, January 2006

Cascading of fluctuations in interdependent energy infrastructures: Gas-grid coupling
journal, December 2015

Coupling conditions for gas networks governed by the isothermal Euler equations
journal, January 2006

Multiscale modeling for gas flow in pipe networks
journal, August 2007

A new model for gas flow in pipe networks
journal, July 2009

Unsteady and transient flow of compressible fluids in pipelines—a review of theoretical and some experimental studies
journal, March 1987

Simulation of transients in natural gas pipelines using hybrid TVD schemes
journal, February 2000

Coupling Conditions for Networked Systems of Euler Equations
journal, January 2008

Simulation of transient gas flows in networks
journal, January 1984

On the Construction and Comparison of Difference Schemes
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Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
journal, August 1984

An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
journal, May 1996

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journal, February 2010