Abstract
The thermodynamic behaviour of fluids can be accurately described by equations of state (EoS) in terms of the Helmholtz energy, with temperature and density as independent variables. The known properties in dynamic simulations of power or refrigeration cycles are usually different from temperature and density. Partial derivatives of state properties with respect to the known properties of the simulation have to be transformed into partial derivatives with respect to the independent variables of the EoS. This transformation is demonstrated step by step for the single-phase region, along the saturation line and within the two-phase region.
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Acknowledgements
The authors would like to thank Eric W. Lemmon for answering an abundance of questions and for providing a modified version of RefProp (Lemmon et al. 2010) capable of outputting additional intermediate results. The comments by Ian H. Bell and an anonymous reviewer are also much appreciated. This work was funded by the Federal Ministry of Education and Research of Germany (GeoEn II, Grant 03G0767A) and the Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (Qualification of geothermal technology - integration of subsurface and surface systems, Grant 0325217).
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Thorade, M., Saadat, A. Partial derivatives of thermodynamic state properties for dynamic simulation. Environ Earth Sci 70, 3497–3503 (2013). https://doi.org/10.1007/s12665-013-2394-z
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DOI: https://doi.org/10.1007/s12665-013-2394-z