Modelling compressors, resistors and valves in finite element simulation of gas transmission networks

Abstract

In previous papers, the authors introduced a new formulation of the flow equations, involving friction and gravity effects, in gas transportation networks. They also proposed finite element methods combined with Newton-like algorithms for numerical solution. The main goal of the present paper is to include into the above formulation the usual devices existing in a gas transmission network other than pipelines, namely, compressors, pressure control valves (PCV), flow control valves (FCV) and resistors. One of the main novelties of this paper is that, unlike many related ones, all of the above devices are modelled as nodes instead of edges of the graph which makes numerical solution simpler and computationally cheaper. This is the case, for instance, in the frequent situation where there are many valves in the network but only a few of them are working in each specific simulation scenario. Instead of introducing one edge per valve in the graph, we only consider that, at specific time intervals, some valves are acting which leads to simple modifications in the discrete system which are made dynamically and locally. An interesting feature of the full discrete model is that mass conservation is exactly preserved which is a very important issue, particularly for long time simulations.