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Highly Accurate Equations of State for Pure Fluids

Accurate knowledge of thermodynamic properties is essential for the design and optimization of any process in energy and process engineering. They also play an essential role in academic research. Nowadays, these properties are mainly calculated with the help of equations of state, which are usually generated based on experimentally determined property data (e.g. pressure, density, heat capacity, sound velocity, etc.). If such equations are available, they can be implemented in property software packages such as TREND [1], REFPROP [2] or CoolProp [3], allowing the user to calculate the required property data at any time and at (theoretically) arbitrary state points.

Equations of state vary widely in terms of their accuracy and the range of validity. Among the most accurate equations today are the so-called reference equations of state in the form of the Helmholtz energy, which ideally reproduce all available high-accuracy experimental data within their experimental uncertainties. Their range of validity usually extends over a wide temperature and pressure range of industrial interest. Due to the complexity of the equations and the consequent need for extensive, highly accurate experimental data sets of a wide variety of thermodynamic property data, there are only about 10 equations of state in this category in the literature. Already under the direction of Prof. Dr. Dr. e.h. W. Wagner, one of the main research topics of the Chair of Thermodynamics was the development of such equations. The measuring equipment available at the chair allows highly accurate measurements of property data, which were then used to fit reference equations of state. So far, these include the most important fluids in energy technology, such as water [4], deuterium oxide (heavy water) [5], carbon dioxide [6], the air components oxygen [7], nitrogen [8] and argon [9], or methane [10] and ethane [11] as main components of natural gases.

Especially in chemistry and process engineering, the substances used are often toxic, explosive, rapidly flammable, corrosive, etc. This complicates the experimental investigation of these substances, with the result that the experimental database is severely limited. Therefore, simpler cubic equations of state or semi-empirical models, such as those based on "Statistical Associating Fluid Theory", have been used in this field until now. However, the fitting methods, which have been strongly optimized in the last years, nowadays allow to develop Helmholtz equations of state also for many of these substances. These so-called equations of state for industrial applications are based on less accurate substance data and cover a smaller temperature and pressure range than reference equations of state. However, by using appropriate boundary conditions in the development of these equations, it is still possible to extrapolate beyond the range of validity and thus implement them in mixture models. For the research work on such mixture models, relevant pure equations are developed at the Chair of Thermodynamics. These include chemical components of flue gas scrubbing such as amines or glycols as hydrate formation inhibitors in water-containing mixtures. Furthermore, siloxanes are characterized as promising working fluids in Organic Rankin Cycle processes or new refrigerants (e.g. R1234ze or R1234yf). Furthermore, in the field of chemistry and process engineering, products and reactants for the production of vinyl chloride (e.g. chlorine, hydrogen chloride, vinyl chloride, 1,2-dichloroethane) are investigated.


References

[1] Span, R.; Beckmüller, R.; Hielscher, S.; Jäger, A.; Mickoleit, E.; Neumann, T.; Pohl, S.; Semrau, B.; Thol, M. TREND. Thermodynamic Reference and Engineering Data 5.0; Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum, 2020.

[2] Lemmon, E. W.; Bell, I. H.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0; National Institute of Standards and Technology, 2018.

[3] Bell, I. H.; Wronski, J.; Quoilin, S.; Lemort, V. Pure and Pseudo-Pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp. Ind. Eng. Chem. Res. 2014, 53 (6), 2498–2508. DOI: 10.1021/ie4033999.

[4] Wagner, W.; Pruss, A., J. Phys. Chem. Ref. Data 2002, 31 (2), 387–535. DOI: 10.1063/1.1461829.

[5] Herrig, S.; Thol, M.; Harvey, A. H.; Lemmon, E. W. A Reference Equation of State for Heavy Water. J. Phys. Chem. Ref. Data 2018, 47 (4), 043102. DOI: 10.1063/1.5053993.

[6] Span, R.; Wagner, W. A., J. Phys. Chem. Ref. Data 1996, 25 (6), 1509–1596. DOI: 10.1063/1.555991.

[7] Schmidt, R.; Wagner, W., Fluid Phase Equilib. 1985, 19 (3), 175–200. DOI: 10.1016/0378-3812(85)87016-3.

[8] Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W.; Yokozeki, A., J. Phys. Chem. Ref. Data 2000, 29 (6), 1361–1433. DOI: 10.1063/1.1349047.

[9] Tegeler, C.; Span, R.; Wagner, W., J. Phys. Chem. Ref. Data 1999, 28 (3), 779–850. DOI: 10.1063/1.556037.

[10] Setzmann, U.; Wagner, W., J. Phys. Chem. Ref. Data 1991, 20 (6), 1061–1155. DOI: 10.1063/1.555898.

[11] Bücker, D.; Wagner, W., J. Phys. Chem. Ref. Data 2006, 35 (1), 205–266. DOI: 10.1063/1.1859286.