Development of unsteady-state Weymouth equations for gas volumetric flow rate in horizontal and inclined pipes

Calculations of Unsteady-State Gas volumetric flow rate in pipes occur more frequently in the design and operational analysis of natural gas systems. Most of the existing gas pipelines design procedures on Weymouth Equations are based on steady-state flow equations. Hence there is the need to develop equations capable of calculating the unsteady-state gas volumetric flow rate in horizontal and inclined pipes.This paper presents unsteady-state Weymouth Equations for flow of natural gas in long pipelines without neglecting any term in the momentum equation. The analytical solutions of the resulting differential equations are obtained in the form of Unsteady-State Weymouth equations.The equations give functional relationship between flow rate, inlet pressure and outlet pressure at any given time. The effect of pressure drop per segment on gas flow rate is presented.The new Weymouth Equations yield results close to steady-state flow and is able to account for the initial transience in gas volumetric flow rate.The equations considerably enhance gas pipeline design in terms of both ease of usage and accuracy. A simple computer program in FORTRAN is developed to handle these calculations.