Steady State Gas Flow in Pipeline Networks: Existence and Uniqueness of Solution

Agegnehu Atena, Wondimu Tekalign, Tilahun Muche
2020 Journal of Applied Mathematics and Physics  
In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real gas flow network that includes pipelines, compressors, and the connectors. The pipelines and compressors are represented as edges of the graph and the interconnecting points are represented as nodes of the graph representing the network. We show that a unique solution of such a
more » ... ion of such a system exists. We use monotonicity property of a mapping to proof uniqueness, and the contraction mapping theorem is used to prove existence.
doi:10.4236/jamp.2020.86087 fatcat:wx4rleq5e5dfdh7uzix7fnl37a