A robust linear-pressure analog for the analysis of natural gas transportation networks

Abstract

Reliable analysis of transportation networks is crucial for design and planning purposes. A pipeline network system could range from simple to very sophisticated and complex arrangement: from a single pipe transporting fluid from a place to another or elaborated as an interconnected set of fluid networks for intra-state or international transportation. As the complexity of the network system grows, the solution for the network model complicates further. For a natural gas network system, the resulting set of fluid flow governing equations is highly non-linear. In such situations, the customary method employed for the solution of a set of non-linear equations is the multivariable Newton–Raphson method despite its potentially negative drawbacks. Newton–Raphson solution protocols demand a good initialization (i.e., a good initial “guess” of the actual solution) for satisfactory performance because convergence is only guaranteed to occur within a potentially narrow neighborhood around the solution vector. This prerequisite can become fairly restrictive for the solution of large gas network systems, where estimations of “good” initial gas load and nodal values across the domain can defy intuition. In addition, some Newton–Raphson formulations require pre-defining flow loops within a network system prior to attempting a solution, which proves to be a challenging task in an extensive network. We propose an alternate, simple yet elegant method to address the aforementioned problems. The proposed solution methodology retains most advantages of the Newton-nodal method while removing the need for initial guesses and eliminating the need for expensive Jacobian formulations and associated derivative calculations. The resulting linear-pressure analog model is robust, reliable and its execution and convergence is independent of user-defined initial guesses for nodal pressures and flow rates. This allows the simulation study of a steady-state gas network system to be efficiently and straight-forwardly conducted.