A Comprehensive Study on Thermophysical Properties of Carbon Dioxide through the Cubic-Plus-Association and Crossover Cubic-Plus-Association Equations of State

Abstract

The applications of carbon dioxide in heat pump and refrigeration systems are based on a good understanding of its thermophysical properties. Equations of state (EoSs) are largely used to describe the thermophysical behaviors of fluids and can usually give satisfactory results at conditions far from the critical region. However, in the vicinity of the critical point, the long-wavelength of density fluctuations induce an asymptotic singular behavior of fluids, which cannot be described properly by the classical mean-field based EoS. The use of the renormalization group (RG) method with EoSs can correct this nonanalytical behavior near the critical point and not affect the classical behavior far away from the critical region. In this work, an RG method is applied to the Cubic-Plus-Association (CPA) EoS to build a crossover equation. A comprehensive study on thermophysical properties of carbon dioxide, containing vapor−liquid phase equilibrium (VLE) of pure carbon dioxide and its binary mixtures with n-decane and water, compressed density, derivative properties, and transport properties, is performed using this crossover CPA (c-CPA) and the original CPA EoSs to analyze the effects of the RG method on these properties. Our results show that the RG approach can improve the EoS's performances on VLE, compressed density, and some derivative properties such as isobaric heat capacity, while there is no remarkable influence observed on the calculation of transport properties.

Modeling Thermophysical Properties of Carbon Dioxide: Performance Comparison and Assessment

“…Usually, the classical equations, developed within the framework of the mean-field theory, almost all cannot completely describe the singular asymptotic behavior of fluids in the vicinity of the critical point caused by the critical fluctuations. Efforts to incorporate the critical fluctuations into the classical model have been made recently; e.g., Kiselev's crossover method based on the renormalization group theory is an effective way [55][56][57]. However, the accuracy of the conventional models for predictions in the RACP still needs to be greatly improved because of the limitations of their algorithm.…”

Quantification of Dipolar Contribution and Modeling of Green Polar Fluids with the Polar Cubic-Plus-Association Equation of State

“…For the polar CPA (PCPA) EoS, the residual Helmholtz energy of the fluid is considered as a combination of different interaction contributions, which can be given as follows: where A res is the residual molar Helmholtz energy. A SRK and A assoc represent the contributions from the van der Waals and hydrogen bond interactions, respectively, and the details of these two terms can be found in literature. , A dd is the contribution from the dipole–dipole interaction, and in this work, a dipolar term proposed by Jog and Chapman , is implemented. Then, the Padé approximate form for the dipolar term from Rushbrooke et al is adopted: where the second- and third-order terms A 2 dd and A 3 dd are given by where R is the universal gas constant, T is the temperature, V is the molar volume, N A is Avogadro’s constant, k is the Boltzmann constant, n c is the number of components, x is the molar fraction of each component, x p is the fraction of dipole moment in each molecule, μ is the dipole moment, and d is the segment diameter of the molecule.…”