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

¹ Newton Energy Group, USA
² National University of Oil and Gas «Gubkin University», 119991, Leninsky pr., 65, Moscow,

^* Corresponding author: alexbeylin@yahoo.com

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.