A linear-rate analog approach for the analysis of natural gas transportation networks

Modeling natural gas transportation networks poses a number of challenges due to the significant non-linearities associated to the governing equations. Pressure (nodal or p-) formulations and flow (nodal-loop or q-) formulations are the most commonly deployed approaches used to formulate gas flow network models. They treat nodal pressures and pipe branch flow rates as primary unknowns, respectively, and the Newton-Raphson method is the typical choice used to solve the resulting system of pipe network equations. The major disadvantage of Newton-Raphson methods is their tendency to hopelessly diverge when good initializations for the unknown pressure and flow variables are not available. In order to overcome this drawback, a linear-pressure analog approach, applicable to the p-formulation, was recently proposed to formulate an initial-guess-free solution protocol. However, solving the q-formulation rather than the p-formulation would be an alternate, practical, and desirable way to study gas flow in pipeline networks because the system of equations is predominantly linear-with the exception of the loop equations. Linear Theory and Hardy Cross methods have been used in the past solve such q-formulation. Unfortunately, these methods are not initial-guess-free and have been shown to become potentially unstable and thus inefficient because their convergence is also strongly associated with the availability of good initial guesses. This work proposes a linear-rate analog method capable of effectively solving the q-formulation. Through case studies, the proposed linear-rate analog method is shown to be a robust and initial-guess-free solution scheme to effectively model horizontal and inclined natural gas pipeline networks.