Comparison study on the accuracy and efficiency of the four forms of hydraulic equation of a natural gas pipeline based on linearized solution

• Four forms of hydraulic equations have the same numerical accuracy but different efficiency.
• Different solving processes of linearized equation parameters and non-basic variables lead to the efficiency differences.
• The equation with density and velocity being the basic variables is the most efficient hydraulic equation.

Linearization technique is an efficient and fast method for the natural gas pipeline simulation. In order to determine the optimal selection of basic variables which have advantages on both the accuracy and efficiency for linearization method, the present paper systematically researched on the four forms of hydraulic equations according to various selections of the basic variables for solving the hydraulic equations: pressure and mass flux combination (F1(p,m)), pressure and velocity combination (F2(p,w)), density and mass flux combination (F3(ρ,m)), density and velocity combination (F4(ρ,w)), and the efficiency as well as the accuracy is compared based on their linearizations. Through analyzing the numerical results, it can be concluded that F4(ρ,w) is the most efficient and easiest form to implement on a computer for solving hydraulic equations as natural gas simulation is based on linearization technique, while the calculation using F1(p,m) turns out to be the slowest one.