  We formulate a steady-state network flow problem for non-ideal gas that
relates injection rates and nodal pressures in the network to flows in pipes.
For this problem, we present and prove a theorem on uniqueness of generalized
solution for a broad class of non-ideal pressure-density relations that satisfy
a monotonicity property. Further, we develop a Newton-Raphson algorithm for
numerical solution of the steady-state problem, which is made possible by a
systematic non-dimensionalization of the equations. The developed algorithm has
been extensively tested on benchmark instances and shown to converge robustly
to a generalized solution. Previous results indicate that the steady-state
network flow equations for an ideal gas are difficult to solve by the
Newton-Raphson method because of its extreme sensitivity to the initial guess.
In contrast, we find that non-dimensionalization of the steady-state problem is
key to robust convergence of the Newton-Raphson method. We identify criteria
based on the uniqueness of solutions under which the existence of a
non-physical generalized solution found by a non-linear solver implies
non-existence of a physical solution, i.e., infeasibility of the problem.
Finally, we compare pressure and flow solutions based on ideal and non-ideal
equations of state to demonstrate the need to apply the latter in practice. The
solver developed in this article is open-source and is made available for both
the academic and research communities as well as the industry.
