Abstract

Simulation of a gas network on a computer gives rise to the solution of a set of non linear equations. This set has to be repeatedly approximated by linear equations which can be solved. This linearisation process is often done in an unpredictable manner which leads to failures. This process will be enlightened in a graphical way that is simple understood. Moreover Nodal and Loop methods will be put in perspective.

1 Introduction

In the last 20 years many computer programs for dynamic and stationary gas network simulation were made. I found some common mistakes in American and German programs. Some people thought it had to do with the inter connected nature of a network. So when some thing happens in Alabama there may be a strange effect in New York. What I found was that the modelling of basic things like pipes was some times wrong. It was modelled so accurately and sophisticated that at the start of a solution process when variables are far from being in accordance with equations, the process felt down. In the next sections I will give an overview of the equations involved, the solution methods and an exposer around linearisation technics. Furthermore examples where things go wrong and connection with existing literature.

A Network eauations

We consider a network with only pressure nodes, flow nodes and legs. A pressure node is a node where the pressure is given and the in or out going flow has to be calculated. A flow node is a node where the in or out going flow is given (for instance 0) and the pressure has to be calculated. A network with morethen 1 pressure node is called a stressed network. In a non stressed tree network all flows are easy to determine by addition starting at flow nodes with only one pipe. After that all pressures can be calculated starting at the pressure node. However, as soon as the network is stressed or there are loops in the network this procedure does not hold. Define a fixed DP path as a path where the difference between first and last node is fixed. If the first and last node are the same it is a loop otherwise it is a path between two fixed pressure nodes. Select a fixed DP path and a pipe in it. Repeat this step considering only paths with no selected pipes until no path can be found anymore. Without the selected pipes the remaining network consist of one or more tree networks. Give the selected pipe flows a certain value and calculate all flows and pressure drops. Now in a selected path the sum of the pressure drops should be equal to the fixed pressure drop. With the loop method the selected pipe flows are corrected until all path pressure drops equal there fixed pressure drop.

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