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Article

Approximating Nonlinear Relationships for Optimal Operation of Natural Gas Transport Networks

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Department of Chemical Engineering, Queen’s University, 19 Division Street, Kington, ON K7L 3N6, Canada
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Author to whom correspondence should be addressed.
Processes 2018, 6(10), 198; https://doi.org/10.3390/pr6100198
Received: 4 September 2018 / Revised: 13 October 2018 / Accepted: 15 October 2018 / Published: 18 October 2018
(This article belongs to the Special Issue Modeling and Simulation of Energy Systems)
The compressor fuel cost minimization problem (FCMP) for natural gas pipelines is a relevant problem because of the substantial energy consumption of compressor stations transporting the large global demand for natural gas. The common method for modeling the FCMP is to assume key modeling parameters such as the friction factor, compressibility factor, isentropic exponent, and compressor efficiency to be constants, and their nonlinear relationships to the system operating conditions are ignored. Previous work has avoided the complexity associated with the nonlinear relationships inherent in the FCMP to avoid unreasonably long solution times for practical transportation systems. In this paper, a mixed-integer linear programming (MILP) based method is introduced to generate piecewise-linear functions that approximate the previously ignored nonlinear relationships. The MILP determines the optimal break-points and orientation of the linear segments so that approximation error is minimized. A novel FCMP model that includes the piecewise-linear approximations is applied in a case study on three simple gas networks. The case study shows that the novel FCMP model captures the nonlinear relationships with a high degree of accuracy and only marginally increases solution time compared to the common simplified FCMP model. The common simplified model is found to produce solutions with high error and infeasibility when applied on a rigorous simulation. View Full-Text
Keywords: fuel cost minimization problem; FCMP; piecewise-linear function generation; linearization; natural gas transportation; compressor modeling; compressibility factor; isentropic exponent; friction factor fuel cost minimization problem; FCMP; piecewise-linear function generation; linearization; natural gas transportation; compressor modeling; compressibility factor; isentropic exponent; friction factor
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MDPI and ACS Style

Kazda, K.; Li, X. Approximating Nonlinear Relationships for Optimal Operation of Natural Gas Transport Networks. Processes 2018, 6, 198. https://doi.org/10.3390/pr6100198

AMA Style

Kazda K, Li X. Approximating Nonlinear Relationships for Optimal Operation of Natural Gas Transport Networks. Processes. 2018; 6(10):198. https://doi.org/10.3390/pr6100198

Chicago/Turabian Style

Kazda, Kody, and Xiang Li. 2018. "Approximating Nonlinear Relationships for Optimal Operation of Natural Gas Transport Networks" Processes 6, no. 10: 198. https://doi.org/10.3390/pr6100198

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