International Pipeline Conference — Volume 2 ASM E 1996 APPLICATION OF HIGHER-ORDER TVD RESOLUTION FOR INVESTIGATION OF TRANSIENTS PROBLEMS IN NATURAL GAS PIPELINES Sarafa O. Ibraheem The Pennsylvania State University Petroleum & Natural Gas Engineering 204 Hosier Building University Park, Pennsylvania 16802, U.S.A. P: (814)863-0915 F: (814)863-1875 ibraheem @ pnge.psu.edu ABSTRACT A higher-order numerical procedure is applied to simulate typical transient phenomena in natural gas transportation. Reliable modeling and prediction of transients features in transmission pipelines are desirable for optimal control of gas deliverability, design and implementation of active controls, and modeling of operational behavior of network peripheral equipment (e.g., chokes, valves, compressors, etc.). As an alternative to the Method of Characteristics (MOC) that is widely used presently, a higher-order Total Variation Diminishing (TVD) method is used to model some transient problems. This, class of methods has the capability to capture fine-scale phenomena and provides a better resolution of frontal discontinuities. In this study, the TVD method is utilized in conjunction with upwind methods. Also, in order to ensure a stable time-stepping scheme over a wide range of Courant-Friedrich-Lewy (CFL) number, a special Runge-Kutta method is employed as the base solution algorithm to integrate the highly non-linear, hyperbolic equations which govern the transportation of natural gas in pipelines. The overall procedure is stable, robust and accurate when applied .3 solve practical problems with simulated pressure waves. NOMENCLATURE c = speed of sound d = pipe diameter E = inviscid flux F = wall friction force H = source terms / = friction factor M = molecular weight p = pressure Q = vector of conserved variables R = gas constant R" = residual at time n r = gradient Michael A. Adewumi The Pennsylvania State University Petroleum & Natural Gas Engineering 202 Hosier Building University Park, Pennsylvania 16802, U.S.A. P: (814)863-2816 F: (814)863-1875 M 2 A @ psuvm.psu.edu T = temperature r = time u = velocity x = coordinates Z = compressibility factor Greek a ,, <Xj, a 3, a 4 = Runge-Kutta coefficients 8 = difference operator p = density Subscripts i = indices k = Runge-Kutta stage w = wall Superscripts n - time level INTRODUCTION Natural gas is transported over thousands of m iles of pipelines that crisscross a wide variety of terrains and weather conditions. It is important to be able to predict die pressure surges that may be caused by either accidental and/or incidental occurrences for optimal design and safety purposes. Severe damage to pipelines and network peripheral facilities has been attributed to the effects o f pressure surges which are often analyzed by inadequate models. In fact, oscillatory transient pressures are known to build up to unusually large magnitude with many undesirable consequences. Several works that have attempted to solve this problem have been based either on graphical methods or on the Method of Characteristics (MOC). Both methods have tremendously improved our knowledge of transient phenomena but are now becoming inadequate in certain difficult situations. A large body of literature is devoted to MOC, including the work of Taylor et Copyright © 1996 by ASME IPC1996-1928 Downloaded from http://asmedigitalcollection.asme.org/IPC/proceedings-pdf/IPC1996/40214/1167/2506890/1167_1.pdf by guest on 18 November 2021