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The general method of topological reduction for the network problems is presented on example of gas transport networks. The method is based on a contraction of series, parallel and tree-like subgraphs for the element equations of quadratic, power law and general monotone dependencies. The method allows to reduce significantly the complexity of the graph and to accelerate the solution procedure for stationary network problems. The method has been tested on a large set of realistic network scenarios. Possible extensions of the method have been described, including triangulated element equations, continuation of the equations at infinity, providing uniqueness of solution, a choice of Newtonian stabilizer for nearly degenerated systems. The method is applicable for various sectors in the field of energetics, including gas networks, water networks, electric networks, as well as for coupling of different sectors.
Pipeline transport is an efficient method for transporting fluids in energy supply and other technical applications. While natural gas is the classical example, the transport of hydrogen is becoming more and more important; both are transmitted under high pressure in a gaseous state. Also relevant is the transport of carbon dioxide, captured in the places of formation, transferred under high pressure in a liquid or supercritical state and pumped into underground reservoirs for storage. The transport of other fluids is also required in technical applications. Meanwhile, the transport equations for different fluids are essentially the same, and the simulation can be performed using the same methods. In this paper, the effect of control elements such as compressors, regulators and flaptraps on the stability of fluid transport simulations is studied. It is shown that modeling of these elements can lead to instabilities, both in stationary and dynamic simulations. Special regularization methods were developed to overcome these problems. Their functionality also for dynamic simulations is demonstrated for a number of numerical experiments.