Friedrich-Alexander University (Erlangen, Germany)
We introduce a stationary model for gas ﬂow based on semilinear isothermal Euler equations in a non-cycled pipeline network. Especially the problem of the feasibility of a random load vector is analyzed. Feasibility in this context means the existence of a ﬂow vector meeting these loads, which satisﬁes the physical conservation laws with box constraints for the pressure.
An important aspect of the model is the support of compressor stations, which counteract the pressure loss caused by friction in the pipes. The network is assumed to have only one inﬂux node, all other nodes are eﬄux nodes.
With these assumptions, the set of feasible loads can be characterized analytically. In addition, we show the existence of optimal solutions for some optimization problems with probabilistic constraints. A numerical example based on real data completes this presentation.