# 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Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system.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:

- 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:

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

- Sponsoring Org.:
- USDOE Office of Electricity Delivery and Energy Reliability (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:
- Journal Article: 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.

```
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. doi:10.1016/j.physd.2017.09.002.

```
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.
doi:10.1016/j.physd.2017.09.002.
```

```
@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}

}