A Dynamic Linear Flow Model of a Gas Distribution System
Authors: Yingling A.E. , Raphael D.L. , Slater G.E. 
Published: December 2007

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Abstract
This paper is an extension of an earlier paper, "The Application of Linear Flow Models paper, "The Application of Linear Flow Models to Natural Gas Distribution Systems", which was concerned with the development of a static linear flow model and its application to the Pennsylvania Gas Co.'s distribution network. Pennsylvania Gas Co.'s distribution network. The same network is modeled in this paper by means of a dynamic linear flow model; Unlike the static model that is applicable only over a single period of time such as a day, the dynamic linear flow model is capable of depicting the day-today operations of a complex distribution system over larger periods of time such as a month or year. Like the static model, the dynamic model is a valuable tool in studying both the direct and indirect effects of some alteration in the system. Examples of alterations within a gas distribution system include a new underground gas storage field, a severed pipeline or a reduced gas contract.
The development of a dynamic linear flow model is largely a matter of collecting a sequential set of static linear flow models, analyzing the behavior of the technical coefficients over time, and then developing suitable methods for predicting these coefficients as a function of time. However, the model is incomplete and of little use to management and engineering until it is applied to the future. This paper presents a stage-wise forecast of the future based upon the technical coefficients over a previous time period. In addition to the model building process and the actual field application, an impact study is performed to exhibit the type of information performed to exhibit the type of information available from a dynamic linear flow model.

Introduction
A deterministic operations research model, the linear flow model, was applied to a gas distribution network in a previous paper. In general, the model can be applied to any complex flow system where homogeneous flow units enter, travel within the flow system according to some process, and then eventually leave. A "static" process, and then eventually leave. A "static" linear flow model is concerned with the characteristics of this flow over a single period of time. The model portrays the flow period of time. The model portrays the flow system as a group of interrelated sectors, with each sector having a physical counterpart in the real-world situation. In a gas distribution system, the flow units (scf) enter the network from various sources (contract gas, gas from underground storage, gas produced by the distribution company itself, etc.), travel through pipelines and compressor stations, and finally are consumed by those served by the system, lost into the atmosphere, or stored for later use.