Analysis of a model of a natural gas pipeline—a transfer function approach

A framework for natural gas pipelines is developed in a context similar to the theory of electric transmission lines. The system of semi-linear partial differential equations describing the time-dependent flow of natural gas is linearized around the steady-state flow. Additional approximations lead to a constant coefficient linear system that is equivalent to an electrical circuit that is analytically solvable and admits an ABCD matrix representation of input and output. The sinusoidal steady-state operation of natural gas pipelines is analysed including the distortion of waves. It is shown that the timing of the propagation of phases and other events is accurately represented in the approximation. The quantitative accuracy for flux and gas density of the approximation depending on different operating scenarios and depending on the frequency of the disturbances is documented.