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.