Abstract
Cubic equations of state have thus far yielded poor predictions of the thermodynamic properties of quantum fluids such as hydrogen, helium and deuterium at low temperatures. Furthermore, the shape of the optimal α functions of helium and hydrogen have been shown to not decay monotonically as for other fluids. In this work, we derive temperature-dependent quantum corrections for the covolume parameter of cubic equations of state by mapping them onto the excluded volumes predicted by quantum-corrected Mie potentials. Subsequent regression of the Twu α function recovers a near classical behavior with a monotonic decay for most of the temperature range. The quantum corrections result in a significantly better accuracy, especially for caloric properties. While the average deviation of the isochoric heat capacity of liquid hydrogen at saturation exceeds 80% with the present state-of-the-art, the average deviation is 4% with quantum corrections. Average deviations for the saturation pressure are well below 1% for all four fluids. Using Péneloux volume shifts gives average errors in saturation densities that are below 2% for helium and about 1% for hydrogen, deuterium and neon. Parameters are presented for two cubic equations of state: Peng–Robinson and Soave–Redlich–Kwong. The quantum-corrected cubic equations of state are also able to reproduce the vapor-liquid equilibrium of binary mixtures of quantum fluids, and they are the first cubic equations of state that are able to accurately model the vapor-liquid equilibrium of the helium–neon mixture. Similar to the quantum-corrected Mie potentials that were used to develop the covolume corrections, an interaction parameter for the covolume is needed to represent the helium–hydrogen mixture to a high accuracy. The quantum-corrected cubic equation of state paves the way for technological applications of quantum fluids that require models with both high accuracy and computational speed.
Highlights
Since the first cubic equation of state (EoS) was introduced by van der Waals [1] more than 100 years ago, cubic EoS have remained the preferred choice when computational speed in combination with a reasonable accuracy is needed
Neon and hydrogen have been touted as promising refrigerants with the potential to significantly improve the energy efficiency of the hydrogen liquefaction process [12,13]
Eq (18) is plotted together with the increase in the effective diameter from the first and the second order corrected Mie potentials with parameters for hydrogen, deuterium, neon and helium in Fig. 3, where the curves are from Eq (18) and the circles are from the quantum-corrected Mie potentials
Summary
Since the first cubic equation of state (EoS) was introduced by van der Waals [1] more than 100 years ago, cubic EoS have remained the preferred choice when computational speed in combination with a reasonable accuracy is needed. The shortcomings of cubic EoS for describing fluids that exhibit quantum effects has for long been known In his celebrated work that formed the basis for the SRK EoS [4], Soave pointed out that less accurate results were obtained for mixtures with hydrogen. Le Guennec et al [24] showed that the α function of hydrogen and helium did not exhibit a monotonic decay with temperature, and did not follow the consistency criteria derived for other fluids. The reason for this behavior has remained unexplained, it has been linked to their acentric factors being negative [6]. The VLE of all examined fluid mixtures are reproduced to a high accuracy without the need for advanced mixing rules [28]
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