A new analytical equation is derived based on the continuity and momentum equations for gas flow in pipelines, without neglecting any terms in the momentum equation. The equation provides a functional relationship among inlet gas density, outlet gas density, gas mass flux, length, I. D., inclination, wall friction factor, and the isothermal sound speed in pipeline. It can handle any pipeline configuration, including horizontal, vertical and inclined pipelines. The new flow equation is presented, which is used for different cases of practical interest. Bottomhole pressure (BHP) calculations in flowing vertical gas wells and inclined long-distance gas pipeline design calculations are carried out to test the efficacy of this new flow equation. Excellent agreement between the predicted results and measured field data is obtained.
For steady-state natural gas flow through pipelines, there are several analytical equations, such as the Weymouth equation and the Panhandle equation which are derived by neglecting the kinetic energy term of the momentum equation. Recently, Tian and Adewumi [3] proposed an analytical equation for the calculation of steady-state flows in gas pipelines without neglecting the kinetic energy term in the momentum equation. Their analytical equation provides a fundamental relationship among the gas flow rate, the pressure at inlet, and pressure at outlet; and Newton-Raphson method was used to solve their implicit analytical equation. For the investigation of BHP calculation in flowing gas wells, previous investigators usually neglected the kinetic energy term in the energy equation (e. g. Sukkar and Cornell [4], Cullender and Smith [5], and Aziz [6]). In the present study, a rigorous, algebraic analytical equation for the analysis of steady-state flow in natural gas pipelines is derived from the steady-state continuity and momentum equations, without neglecting any terms in the momentum equation. This new equation provides a functional relationship among inlet gas density, outlet gas density, gas mass flux, length, I. D., inclination, wall friction factor, and the isothermal sound speed in the pipeline. Various forms of this flow equation are proposed for horizontal, vertical and inclined pipelines. The appropriate forms for different cases of practical interest suitable for both the Newton-Raphson method and the fixed-point algorithm are presented. Bottomhole pressure (BHP) calculations in gas wells and inclined long-distance gas pipeline design calculations are carried out to test the efficacy of this new algebraic analytical flow equation.
Analytical Equation for Horizontal Pipeline In this section, the analytical equation for the analysis of steady-state natural gas flow in horizontal pipelines is derived based on the continuity and momentum equations. The appropriate form of this equation is also presented, which is suitable for the fixed-point algorithm.
