Master's Thesis

Abstract

In this thesis, we study transient (time-dependent) gas flow in natural gas networks with a focus on passive gas networks. We compare different algorithms to approximate flow and pressure values in a gas network. A gas network consists of pipelines that deliver gas from suppliers to consumers. The gas flow in a pipe can be described by the Euler Equations which are a set of nonlinear partial differential equations. We use the so-called friction-dominated model to simplify the gas flow equations and apply an implicit box scheme to derive a suitable discretization. We compare different linearization methods to solve the resulting nonlinear system of equations. We introduce six known mixed-integer formulations for piecewise linear functions and describe how to use these formulations to approximate the nonlinear functions in the gas flow model. Further, we develop an iterative method, to solve the pipe flow system. We call the method “iterative velocity approximation”, and it is based on a linearization of the momentum equation. We linearize the equation by fixing the absolute gas flow velocity. We show convergence on single pipes. We evaluate and compare the performance of generic nonlinear solvers, the piecewise linear approximations and the iterative velocity approximation on nine different networks.

Publication
Fast Approximation of Equations of transient Gasflow
Andre Weltsch
Junior Software-Engineer at Immobilienscout24