Analytical solution of linearized equations for transient gas flows in gas pipelines

Alexandr Beylin,Mikhail Sukharev,N.N Novitsky,V.V Tarasevich,E Todini,V.R Chupin,E Khaltar,M Negnevitsky,L.B Korelstein,C Sarica,S.A Miedema,M.G Sukharev,B Serttter,V.A Stennikov

doi:10.1051/e3sconf/202021901001

Abstract

We consider the new class of high precision simplified linear models of transient high-pressure gas flows along linear sections of pipelines. Representatives of this class are obtained from different initial models defined by partial differential equations. The new models are based on the exact solution of the Klein-Gordon equation, which appears as a result of piecewise linear approximation of nonlinear models in the form of Charny’s equations [1–4] or piecewise constant approximation in models that describe deviations of pressure and mass flow rates from their values in the basic stationary mode [10–13, 16–17]. The new class of models has significant advantages over nonlinear simplified models in optimization problems of large-scale networks, reducing the calculation time by more than two orders of magnitude. They are also free from errors of the approximate inverse Laplace transform or dimensionality reduction techniques traditionally applied in such situations.

Highlights

The emergence of cheap gas significantly changes its role in the energy sector of developed countries
Simplified lumped models of unsteady gas motion have emerged as a tool to speed up computations over partial differential equations (PDE) models
It is difficult to estimate the error of such models, some specific examples of calculations look good in comparison with exact solutions for PDE obtained by classical numerical methods

Summary

Introduction

The emergence of cheap gas significantly changes its role in the energy sector of developed countries. In addition to the traditional technological reasons [1], variations of gas flow in high-pressure pipelines have systemic reasons as well. They relate fluctuations in the gas supply market and the growing frequency of connection and disconnection of gas-consuming electric generators, which compensate for the intermittent production of wind and solar-based energy. In this regard, the need for analysis, control, and optimization of gas flows in highpressure gas pipelines with complex structure increases significantly. It takes into account the non-isothermal nature of the processes and describes numerical experiments

A brief overview of lumped parameter models

Nonlinear simplified models

Linear simplified models

Linearization methods leading to the Klein-Gordon equation