Unsteady-State Natural-Gas Calculations in Complex Pipe Systems
Authors: Wylie E. Benjamin , Streeter Victor L. , Stoner Michael A. 
Published: December 2007

Introduction
In simulating transient flow in a natural gas pipeline, it is much more important to keep track of pipeline, it is much more important to keep track of the packing within the line than to note the exact instant when an imperceptible impulse caused by a step-size pressure change at one end of a pipe arrives at the other end. Inertia forces play a trivial role compared with wall friction forces and pressure drops. Many methods neglect the inertia pressure drops. Many methods neglect the inertia term completely and may handle the transient simulation for slow transients. The method proposed here retains the inertia term and in fact increases its value when it is very small compared with friction, but uses its proper value when sharp transients occur. The velocity transport term is neglected in all cases because of its lack of importance; this is demonstrated by a very severe transient case. By introducing the "inertia multiplier" it is shown that the time increment for the calculation may be greatly increased.The value of performing unsteady-state simulation in the design and operational analysis of natural gas systems is being recognized more and more each year by the industry. Needham and Blunt show the utility of compressor station placement by using an unsteady-state model in the design process. They show the relative merits of operating a system using maximum security or maximum economy as the control objective. Farmer and Mason use an unsteady-state simulation of their system to determine critical notification and operation times for accommodating the sudden large loads imposed on a system by gas-fired turbine electric generators. Because of the increasing emphasis on economics and regulatory control, studies like these are becoming the rule rather than the exception.The partial differential equations of motion and mass continuity, together with an equation of state, are generally treated numerically by an explicit or an implicit method. The implicit methods offer great advantages in that they can use time steps appropriate to the imposed boundary conditions. That is, for long-duration transients large time steps provide accurate, stable results and the number of computations are reduced accordingly. Conversely, for sharp, short-duration motions a shorter time step provides more detail on the phenomenon. As a disadvantage of implicit phenomenon. As a disadvantage of implicit procedures, large networks require a large computer procedures, large networks require a large computer storage capability to handle the problems since a simultaneous solution of the equations is necessary at each time step. Sparse matrix programming reduces the storage requirement, but a sizable block of storage is still necessary for many practical problems. Some implicit formulations have also problems. Some implicit formulations have also been known to produce erratic results during the imposition of some types of boundary conditions. The G. E. Simulator, CAP, as well as a few other reported programs, uses an implicit formulation.The explicit procedures avoid the difficulty of simultaneously solving a large matrix of equations and therefore can generally be used on smaller computers. However, without the introduction of an artificial constraint on the variables, these methods tend to be unstable unless the temporal and spatial step sizes are quite restricted. In most formulations the time step should not be greater than the reach length divided by the speed of sound in the fluid. Although this restriction is relaxed in some explicit procedures, the resulting constraints that must be procedures, the resulting constraints that must be imposed provide unnatural limits on the variables in some situations. The algorithms referred to as PIPETRAN and SATAN are two examples of PIPETRAN and SATAN are two examples of explicit methods.The method of characteristics is probably the most restrictive of all methods with respect to the time-step and distance relationship. In a complex network it is often necessary to adjust pipe lengths to satisfy the condition of a common time interval. In its favor, it is recognized that faithful simulation of transient behavior is virtually guaranteed if the method is properly applied. A recent development reported by Yow has effectively erased the drawbacks associated with the method of characteristics when dealing with a highly compressible medium such as natural gas.Recently there has emerged an additional finite-difference technique based upon classical variational methods of treatment of partial differential equations.
SPEJ
P. 35