Steady-state non-isothermal flow model for natural gas transmission in pipes

In this article, we describe the work carried out for developing an accurate and fast numerical method that can efficiently integrate the mathematical model of natural gas flow in a pipeline under non-isothermal steady-state conditions. To do this, we transform the model equations in order to obtain a system of three explicit expressions for the spatial derivatives of gas velocity, pressure, and temperature, which can be easily integrated using any suitable numerical method. The proposed method enables us to determine the gas velocity, pressure, and temperature anywhere in the pipeline. Furthermore, we develop two procedures based on this method, one to calculate the flow rate and the other to experimentally determine the friction factor. We illustrate the performance of the proposed method using several numerical exercises and we compare the results with field measurements on a Spanish pipeline (provided by the company Enagas) and with those obtained using other methods.