Gas pipeline flow that changes with time: Why are partial differential equation a good model?

What is it about?

Gas pipeline systems are operated with high pressure and small Mach numbers. A mathematical model for the flow is given by partial differential equations. In this paper we present a number of transient and stationary analytical solutions of this model. They are used to discuss and clarify why a PDE model is necessary to handle certain dynamic situations in the operation of gas transportation networks. We show that adequate numerical discretizations can capture the dynamical behavior sufficiently accurate. We also present examples that show that in certain cases an optimization approach that is based on multi-period optimization of steady states does not lead to approximations that converge to the optimal state.

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Photo by ThisisEngineering RAEng on Unsplash

Photo by ThisisEngineering RAEng on Unsplash

Why is it important?

The operation of gas pipeline systems is an important part of the energy infrastructur: Think for example for a gas powered electricity plant that should be started up quickly in the case that not sufficient energy from renewable source is available. In such a situation the flow changes rapidly with time, therefore for the simulation and control mathematical models are necessary, that can capture this situation. In the paper, we point out that hyberbolic partial differential equations should be used to model situations like this, whereas a quasi-static approach, where supposedly at each moment there is a steady state, does not provide accurate results.

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