Abstract
Summary
Transient flow of natural gas in pipelines is simulated without neglecting the inertia term. The governing equations constitute a nonhomogeneous hyperbolic set of first-order quasilinear partial differential equations. The first-order, three-point, explicit Godunov scheme and the second-order, five-point, total variation diminishing (TVD) scheme are used to solve this set of equations. Two examples are simulated. The first is the propagation of a slow transient, with 24-hour cycle, in a 45-mile long, 8-in. inside diameter (ID) transmission pipeline, while the second is propagation of a fast transient in a 24-in., 300-ft long pipe. Comparisons between the predicted results and the measured data are fairly good and appear to be better than the predictions reported in the literature. This suggests that the mathematical model presented in the present study, which includes the inertia term in the momentum equation, is more realistic and the numerical schemes used are more robust.
Introduction
Design and cost-effective operation of a gas transmission pipeline requires accounting for its response under transient loads. Actual operations invariably encounter transient states. The loss of a compressor, the addition or loss of supply or sale points, replacement of equipment, and variable demand are a few of the initiators of line transients.
Under isothermal conditions, the continuity and momentum equations, together with the equation of state, constitute the governing equations describing transient flow in natural gas pipelines. The assumptions usually made include isothermal flow, applicability of steady-state friction, and negligible wall expansion or contraction under pressure loads.
In simulating transient flow of single-phase natural gas in pipelines, many previous investigators neglected the inertia term in the momentum equation. This renders the resulting set of partial differential equations linear. Numerical methods previously used to solve this system of linear partial differential equations include the method of characteristics (MOC) and a variety of explicit and implicit finite difference schemes. Neglecting the inertia term in the momentum equation will result in loss of accuracy of the simulation results. To compensate for completely neglecting the inertia term in the momentum equation, Yow introduced the concept of "inertia multiplier" to partially account for the effect of the inertia term in the momentum equation. Wylie et al. simulated transients in natural gas pipelines in accordance with the concept of "inertia multiplier." Rachford and Dupont demonstrated that calculations based on the concept of "inertia multiplier" sometimes will yield very misleading results. In the present study, the inertia term in the momentum equation is included. The governing equations, together with an equation of state, constitute a hyperbolic set of first-order quasilinear partial differential equations. However, the numerical solution of this set of nonhomogeneous quasilinear hyperbolic partial differential equations is not trivial. Appropriate numerical algorithms for handling this problem are presented and field examples are analyzed using the model.