Natural gas enters the pipeline from a supply source, and then is transported to one or more delivery points. One of the most important collections of components in this system is the compressor station located about every 60 miles along the pipeline. The compressor station overcomes the gas pressure drop in the pipe. Consequently, detailed mathematical modeling of compressor stations is critical for optimizing and understanding the ability of the gas pipeline system to deliver natural gas to the end-user. The dynamic behavior of the gas flow within a compressor station is described by nonlinear partial differential equations that describe pipe flow together with nonlinear algebraic equations that describe the quasi-steady flow through the compressors and other components. The set of equations describing pipe flow, compressor performance and throughput, and the equations that describe the performance and operation of the compressor driver must be solved simultaneously to obtain a realistic representation of the overall compressor station performance. Most of the investigations that have been completed for compressor stations utilize isothermal solutions for pipe flow. In the present work, the pipe flow is treated as a nonisothermal unsteady one-dimensional compressible flow. This is accomplished by treating the compressibility factor as a function of pressure and temperature, and the friction factor as a function of Reynolds number. The solution method is the fully implicit finite difference method, which provides solution stability, even for relatively large time steps. The algorithm for solving the nonlinear finite difference equations of pipe flow is based on the Newton-Raphson Method. The compressors within the compressor station are modeled using centrifugal compressor map-based polynomial equations. This modeling technique permits the designation of different models of compressors in the compressor station. The method can be easily extended to include other types of compressors. The paper demonstrates the impact of varying boundary conditions on compressor station components, and shows how this detailed compressor station model can be used to determine compressor speed, power requirement, engine fuel consumption, and head for each compressor with respect to time.


Mathematical modeling is one of the most cost-effective tools that can be used to aid in design, operation, and optimization studies. The systems under consideration actually operate in an unsteady nature, and although much effort has been and continues to be spent on unsteady mathematical models, many over-simplifications are introduced that bring into question the simulation results. Several investigators tried to simulate unsteady condition for pipeline and some of them focused in compressor station modeling. Botros et al. [1,2] and Botros [3] presented a dynamic compressor station simulation that consists of nonlinear partial differential equations describing the pipe flow together with nonlinear algebraic equations describing the quasi-steady flow through various valves, constrictions, and compressors. This model included mathematical descriptions of the control system, which consists of mixed algebraic and ordinary differential equations with some controller limits.

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