Calculation of natural gas isentropic exponent

Marić, Ivan; Galović, Antun; Šmuc, Tomislav

doi:10.1016/j.flowmeasinst.2004.11.003

Cited by 28 publications

(8 citation statements)

References 2 publications

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“…The constants a, b, c, d and e for some gases are shown in Table 1. The calculation of partial derivative of the AGA-8 compression factor with respect to the temperature at constant pressure (∂ Z /∂ T ) p as well as the calculation of first (∂Φ/∂ T ) and second derivatives (∂ 2 Φ/∂ T 2 ) of the fugacity coefficient with respect to the temperature is elaborated in [6]. Here we provide only the final equations, i.e.…”

Section: Methodsmentioning

confidence: 99%

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The Joule–Thomson effect in natural gas flow-rate measurements

Marić

2005

Flow Measurement and Instrumentation

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Section: Methodsmentioning

confidence: 99%

“…are calculated, where q m ( p, T, p) denotes the mass flow rate at the specified pressure p, temperature T and differential pressure p. Prior to computing the flow rate, the corresponding calculation of a natural gas density [3], viscosity (residual viscosity function) [11] and isentropic exponent [6] is performed. Fig.…”

Section: Flow-rate Errormentioning

confidence: 99%

The Joule–Thomson effect in natural gas flow-rate measurements

Marić

2005

Flow Measurement and Instrumentation

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“…Similar to the compressibility factor, the isentropic exponent has a complex dependence on temperature, pressure, and gas composition. The rigorous calculation of the isentropic exponent requires over 50 equations, most of which are nonlinear and several are implicitly defined [21]. Figure 3 shows that over typical natural gas pipeline operating conditions significant model error is introduced using the simplifiied Equation (12).…”

Section: Isentropic Exponentmentioning

confidence: 99%

Approximating Nonlinear Relationships for Optimal Operation of Natural Gas Transport Networks

Kazda

2018

Processes

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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.Processes 2018, 6, 198 2 of 31 constraints and physical equipment limitations. With an estimated 3-5% of all natural gas transported by transmission pipelines consumed by the compressor stations responsible for maintaining gas flow, substantial energy and cost savings can be realized through optimizing the FCMP. It has been estimated that at least a 20% reduction in compressor station fuel consumption can be obtained through global optimization of pipeline operation [2].The FCMP is a difficult optimization problem because real pipeline systems have complex network topographies, integer variables are required to represent the pipeline binary operating states (bi-directional flow, ON/OFF compressor units), and gas and compressor physics are governed by highly nonlinear equations. The FCMP is most appropriately modeled as a nonlinear program (NLP) or mixed-integer nonlinear program (MINLP), depending on whether bi-directional flow or ON/OFF compressor units are considered [3]. Given the complexity of the FCMP model, current algorithms can only solve simplified versions for networks large enough to have practical importance. With this, there are numerous simplifications of model parameters that are broadly accepted across FCMP literature because of the computational savings they provide. However, upon inspection of the error such simplifications introduce to the model, the ability for the model to provide a useful representation of the real system is brought into question.There has been virtually no previous work done on methods of approximating the nonlinear relationships inherent in...

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“…In the study, each thermodynamic property is a functional of natural gas pressure, temperature and specific gravity. These methods were developed by Farzaneh-Gord and Rahbari [14] and were previously presented in Farzaneh-Gord et al [24,25] and Marić [26][27][28].…”

Section: Introductionmentioning

confidence: 99%