Transient Flow in Natural Gas Pipelines Using Implicit Finite Difference Schemes

Abstract

Transmission o f natural gas through high pressure pipelines has been modeled by numerically solving the governing equations fo r one-dimensional compressible flow using implicit finite difference methods. In the first case the backward Euler method is consid ered using both standard first-order upwind and second-order centered differences fo r the spatial derivatives. The first-order upwind approximation, which is a one-sided approximation, is found to be unstable fo r CFL numbers less than 1, while the centered difference approximation is stable fo r any CFL number. In the second case a cell cen tered method is considered where flow values are calculated at the midpoint between grid points. This method is also stable fo r any CFL number. However, fo r a discontinuous change in inlet temperature, the method is observed to introduce unphysical oscillations in the temperature profile along the pipeline. A solution strategy where the hydraulic and thermal models are solved separately using different discretization techniques is sug gested. Such a solution strategy does not introduce unphysical oscillations fo r discontinu ous changes in inlet boundary conditions and is found to be stable fo r any CFL number. The one-dimensional flow model is validated using operational data from a high pressure natural gas pipeline.

An Efficiently Decoupled Implicit Method for Complex Natural Gas Pipeline Network Simulation

“…Their mathematical models can be found in much literature [12,23]. In this paper, the mathematical models of compressors and valves are presented as Equations (3) to (5) and Equations (6) to (7), respectively.…”

“…However, the mathematical model of unsteady simulation is a system of partial differential equations (PDEs) of mass conservation, momentum conservation, and energy conservation. The mathematical model is usually solved by numerical methods [6][7][8][9][10][11][12][13][14][15], and the frequently used numerical methods are method of characteristics (MOC), finite difference methods (FDM), and finite element methods (FEM). MOC firstly reduces PDEs to a family of ordinary differential equations (ODEs) along the characteristic curves, and the ODEs are then solved along the characteristic curves to obtain the flow and thermodynamic parameters.…”

“…Among these methods, the implicit finite difference method is one of the most widely applied methods because its time step is not restricted by the stability criterion [6,[17][18][19]. This means that the time step of the implicit finite difference method can be very large, which is very useful for simulating long-term transient flow in a natural gas pipeline.…”

Adaptive implicit finite difference method for natural gas pipeline transient flow

“…It has been widely studied since the 1960s, and different numerical methods have been proposed for solving the governing equations of transient gas flow in a pipeline. These methods can be summarized as follows: the characteristics method (Gutiérrez et al, 2002), implicit finite difference method (Helgaker et al, 2014), implicit finite volume method (Liang et al, 2013;Wang et al, 2011;Zhang, 2016), finite element method (Ebrahimzadeh et al, 2012), equivalent circuit method (Wang et al, 2014), state space model method (Alamian et al, 2012), reduced-order method (Behbahani-Nejad and Shekari, 2010). Among these methods, the implicit finite difference method is one of the most widely applied methods for transient natural gas simulation.…”

Mixed Integer Linear Programming Optimization of Gas Supply to a Local Market

“… 29 The work in the field of transient flow in pipelines has yielded new tools for solving this type of problem. 30 Some authors base their optimization on simulation. A tool is applied to simulate the system under different structural and operational parameters, that is, in many different scenarios until an “ideally” working network structure is found.…”