Analysis Of Transient Gas Flow Through Pipelines

Abstract This study consists of a theoretical examination of transient gas flow through a pipeline containing a compressor. The system considered is comprised of a line of length Ll + L2 with a compressor located at point L1. The differential equations describing flow through such a system are stated. Since these equations are non-linear, approximate closed form solutions are presented which are sufficiently accurate under specified conditions. These solutions permit the evaluation of pressure and gravimetric flow rate distributions during steady flow, and transient flow for large values of time, where the transient is initiated by a change in consumer demand or the compressor cutting in or both. The solutions obtained are used to describe behavior during periods of semi-steady flow to determine the time interval required in going from one steady state to another and to formulate a compressor optimal control procedure. Introduction The concept of storage capacity of natural gas transmission lines has been known for many years [1,2]. However, the use of this reserve in handling consumption peaks was initially confined to the steady state or packing effect [3]. Within the last 15 years the development of computer modeling of various transient phenomena has resulted in the re-examination of gas transmission. This re-examination showed that changes in demand resulted in pressure and flow rate perturbances of long duration. Since the differential equations describing transient flow in such systems are nonlinear, they have been attacked by numerical methods for a variety of situations [4,5,6,7,8,9]. These methods are not only costly and time consuming, but the results are difficult to use when one tries to extend them to other solutions. To circumvent these difficulties, approximate closed form solutions have been obtained [10,16] which provide flexibility at the expense of accuracy. These studies contain initial indications that the perturbances in pressure and flow rate distribution can be significant and of long duration. For example, it has been observed that the transient time required for flow to change from one steady state to another may be of the order of tens of hours for lines which are 300 km in length. It is felt that in large diameter long lines such as are being proposed to carry gas from Alaska and the Arctic Islands to Canadian and United States markets, the transient behavior will become of greater significance and economic concern. Since such lines will require a number of compressors along trek length, the coupling of large storage capacity with transient behavior due to variation of supply, demand and the cutting in and out of compressors will result in further and more detailed study of the behavior of such systems. For example, the design and optimal use of compressor installations will require a thorough knowledge of the parameters and transient response patterns for such systems under a variety of operating conditions. It was therefore decided, in this investigation, to extend the results of previous studies to cover some aspects of such systems [10–16].