Natural Gas Pipeline Transients

Methods for accurate calculation of transients in long, natural gas pipelines depend primarily upon the handling of the transients within the piping element, since boundary conditions at compressor stations or other controls are assumed to be without inertia effects. An improved characteristics method is outlined which uses an integrated friction term so that it conforms exactly with the steady-state formulation when transients are ignored. Since the characteristics method requires a computing time period equal to the length of reach divided by the period equal to the length of reach divided by the isothermal pulse-wave speed, it may increase the time of computations when small reaches are involved. By using an implicit finite-difference method for the small reaches and then combining with the characteristics method for the longer reaches, considerable computing time may be saved. The characteristics method, together with the implicit method, is presented and an example is given using the characteristics method alone, and the combined method. Introduction The design of most natural gas transmission lines and distribution systems is based upon steady-state calculations. Similarly the operation of the system is generally based on the same type of calculations and upon the operator's experience. As the gas industry becomes more and more concerned with the identification of the reliability of a system and with optimum means of operation of a system, unsteady flow calculations are becoming more significant and necessary. The objective of this presentation is to outline a reliable, economical means of computing transients in natural gas systems. Many types of transient flow conditions are possible in a system, depending mainly upon its possible in a system, depending mainly upon its geometry and upon the cause of the transient. The unsteady flow can be of very extended duration as in starting up a long transmission system; its duration may be of the order of 1 day as in the supply to industrial, commercial and residential areas, or, it may be short term, perhaps 1 hour, in the case of an unexpected mechanical failure or power shutdown. Ideally, when one is looking for a power shutdown. Ideally, when one is looking for a method of performing unsteady flow calculations, the method should be detailed enough to produce accurate results for the rapid transient, yet not so comprehensive that the computation of the slow transient is so time consuming that it is uneconomical. Probably the best known method for the computation of unsteady flow in the gas industry is the algorithm identified as PIPETRAN. Details of the method are not generally available in the literature, but its use is widely recognized. An explicit solution of the partial differential equations is used and certain empirical restraints have been added to aid in achieving stability. Other algorithms have been developed using an explicit solution. Wilkinson et al. linearized the differential equations and introduced transfer functions to obtain a solution. Stoners used the method of characteristics in the solution of the equations and produced excellent results, including experimental confirmation of the method. If a disadvantage exists in the characteristics method solution, it is only one of costly computation for a slow transient in a complicated system. For stability in the solution the time increment cannot exceed the reach length divided by the isothermal wave speed. An implicit finite-difference representation of the equations has not been attempted in any practical applications as it requires the solution of a set of nonlinear simultaneous equations. This latter approach, however, offers the advantage of guaranteed stability for a large time step. The time increment selected in this approach is not related to the length of reach but depends only upon yielding an accurate representation of the boundary condition. This study unites the characteristics method with the implicit representation of the equations into a combined solution. SPEJ P. 357