  The critical role of gas fired-plants to compensate renewable generation has
increased the operational variability in natural gas networks (GN). Towards
developing more reliable and efficient computational tools for GN monitoring,
control, and planning, this work considers the task of solving the nonlinear
equations governing steady-state flows and pressures in GNs. It is first shown
that if the gas flow equations are feasible, they enjoy a unique solution. To
the best of our knowledge, this is the first result proving uniqueness of the
steady-state gas flow solution over the entire feasible domain of gas
injections. To find this solution, we put forth a mixed-integer second-order
cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow
equations. This relaxation is provably exact under specific network topologies.
Unlike existing alternatives, the devised solver does not need proper
initialization or knowing the gas flow directions beforehand, and can handle
gas networks with compressors. Numerical tests on tree and meshed networks with
random gas injections indicate that the relaxation is exact even when the
derived conditions are not met.
