A new prediction equation of compressed liquid isochoric heat capacity for pure fluids and mixtures

https://doi.org/10.1016/j.molliq.2021.117483Get rights and content

Highlights

  • A new prediction equation for compressed liquid cv was developed.

  • The new equation shows good agreement with cv experimental data for pure fluids and mixtures.

  • Prediction performance of new equation is significantly superior to other generalized models.

Abstract

In this paper, a new prediction equation for compressed liquid isochoric heat capacity (cv) was developed based on the corresponding states principle (CSP). By knowing acentric factor (ω), critical parameters (Tc, pc and vc) and ideal gas isochoric heat capacity (cv,0), the new equation could predict cv for pure fluids and mixtures (including polar and nonpolar fluids) at 0.25 < Tr < 1 and 0.5 < pr < 10. The overall average absolute relative deviation (AARD) of the new equation for 25 pure fluids and 10 mixtures are 2.21% and 1.62%, respectively. A comparison was conducted between the new equation and other models (PR EoS, Helmholtz energy EoSs, generalized equation (GE) of Zhong et al. [1] and corresponding states equation (CSE) of Sheng et al. [2]). The new equation significantly improves the prediction performance for the heat capacity of important fluids, such as halogenated hydrocarbons, carbon dioxide, water and so on, compared with the existing models. Although the prediction performance of the new equation is slightly worse than that of the Helmholtz energy EoS, the new equation has a simpler form and more powerful prediction performance than the Helmholtz energy EoS for mixtures.

Introduction

Isochoric heat capacity (cv) is one of the most important thermodynamic properties, which not only can be used to calculate key parameters in engineering application [1], such as internal enthalpy and entropy, but also provides a very useful check for calculations of the second derivative of the pressure with respect to temperature, which is essential to develop an accurate equation of state (EoS).

cv data are mainly obtained by the four approaches: experiments, theoretical calculation, molecular simulation and empirical equation. At present, experiments are still the most direct and reliable way. The National Institute of Standards and Technology [3], [4], Russian Academy of Sciences [5], Japanese National Defense Academy [6] and Chinese Academy of Sciences [7] have successively carried out cv research using adiabatic batch calorimeter. Nevertheless, experiments are not only time-consuming and expensive, but also can only obtain data at discrete points. In order to obtain the data corresponding to the required state points, it is necessary to use some mathematical methods such as interpolation or linear regression.

Theoretical calculation is a convenient and economical method to obtain cv data. With known ideal gas heat capacity (cv,0) and an accuracy EoS [8], cv can be derived by Eq. (1). So far, ideal gas heat capacity has been well studied, but an accurate EoS is hard to obtain. Zhong et al. [1] made a comparison between cv data of 17 refrigerants and values calculated by Peng-Robinson equation of state [9] (PR EoS) with the average absolute relative deviation (AARD) of 5.05%. He et al. [10] calculated the isobaric heat capacity (cp) based on the PR EoS and the Martin-Hou (MH) EoS. The AARD of 10 refrigerants is 12.85% for the PR EoS and 9.53% for the MH EoS.cv=cv,0-T0ρ2pT2ρdρρ2

Molecular simulation is becoming increasingly prevalent to calculate thermodynamic properties of fluids. Recently, diverse force field models [11], [12], [13], [14], [15], [16] have been developed. However, available force field models could not obtain accurate heat capacity data. Raabe and Maginn [15] predicted the liquid cp for R1234yf based on all-atom force field with a relative uncertainty of about 10%.

Empirical equations are favored by researchers and widely studied due to simple form and accurate prediction performance. The Helmholtz energy EoSs, a specific high-precision multi-parameters equation, are currently the most popular empirical equation. However, the establishment of Helmholtz energy EoSs needs a great deal of thermophysical properties data (including vapor pressure, density, speed of sound, heat capacity, etc.), Helmholtz energy EoSs are not available for fluids whose thermophysical properties data are scarce. In addition, the coefficients in Helmholtz energy EoSs are the result of the overall optimization of different thermophysical properties data, and the calculation accuracy of different thermophysical properties data is weighed during the optimization process. Therefore, the heat capacity data calculated by the Helmholtz energy EoSs is not necessarily optimal.

Establishing an empirical or semi-empirical equation that only applies to heat capacity can not only overcome the shortcomings of the Helmholtz energy EoSs, but also conveniently obtain high-precision heat capacity data. Table 1 summarized the empirical and semi-empirical equations of heat capacity in published literatures. Goodwin and Weber [17] developed an semi-empirical equation of cv for oxygen with density and temperature as arguments. The equation has at least five exponents and there remain eight arbitrary constants. The AARD is 0.47% for 151 data. Zhong et al. [1] developed a generalized equation (GE) based on PR EoS for the compressed liquid cv of pure refrigerants and mixtures. Six constant coefficients in the equation were obtained by regressing 1734 liquid experimental data of 17 refrigerants. The generalized equation shows good agreements with the experimental data and the AARD is 1.55%. Nevertheless, the use of reduced specific volume (vr) weakens the prediction ability of this equation due to the lack of sufficient high-precision vr data. In addition, this equation has large deviations in the prediction of cv for some important fluids such as carbon dioxide (CO2) and difluoromethane (R32). Recently, Sheng et al. [2] proposed a simple corresponding states equation (CSE) only depending on reduced temperature (Tr) to predict compressed liquid cv for 16 pure refrigerants and their mixtures. The equation includes two constant coefficients determined by regression of 1738 experimental data. The AARDs for 16 pure refrigerants and 9 mixed refrigerants are 1.82% and 3.69%, respectively. Nevertheless, the model has a poor prediction performance for small molecular fluids (nitrogen (N2), methane (R50), ethylene (R1150), etc.) and polar fluids (R32, CO2, water, etc.).

To sum up, some studies have been reported on the prediction model of liquid heat capacity. However, the existing models of cv in liquid phase still have obvious deficiencies. In this paper, a new generalized equation was developed based on the corresponding states principle (CSP). In order to overcome the shortcoming of the classical CSP, a new parameter (correction factor k for cv,0) was proposed. In the Section 2, the process of establishing new equation is introduced in detail. In the Section 3, the prediction performance of the new equation was discussed through comparison with experimental data and other models.

Section snippets

Data screening and optimization algorithm

The available cv data in compressed liquid states (ρ greater than 2ρc) were presented in Table 2. It is worth noting that the experimental data for propane (R290) of Kitajima et al. [18], R32 of Matsuguchi et al. [19] and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) of Yamaya et al. [20] have large deviation from other available experimental data [7], [8], [21], [22] in the same temperature and pressure range and from values calculated by Helmholtz energy EoSs [23], [24], [25]. Therefore, the

Comparison with experimental data of pure fluids

A comparison was carried out between the experimental cv data of 25 fluids and the prediction values of the new equation. Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9 present the distributions of deviation with the Tr for 25 fluids. Most data show good agreements with the calculated values, and the AARD and MARD for 25 fluids are displayed in Table 11. Totally 97% of the 2782 data points could be predicted within 10% deviation and 92% of the data points could be predicted with the deviations less

Conclusion

In this paper, a new generalized equation for cv in compressed liquid states was proposed based on the corresponding states principle (CSP). The new equation gives a good prediction performance for 25 pure fluids and 10 mixtures at 0.25 < Tr < 1 and 0.5 < pr < 10. In terms of comprehensive prediction performance, it is superior to existing generalized equations, such as PR EoS, CSE and GE. The overall average absolute relative deviation (AARD) of the new equation for pure fluids and mixtures

CRediT authorship contribution statement

Bowen Sheng: Methodology, Software, Validation, Writing – review & editing. Yanxing Zhao: Investigation, Writing – review & editing. Xueqiang Dong: Writing – review & editing, Funding acquisition. Haoran Lu: Supervision, Investigation. Wei Dai: Supervision, Investigation. Hao Guo: Supervision, Investigation. Maoqiong Gong: Supervision, Resources, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The authors would like to thank the support of the National Natural Science Foundation of China (No. 52036010) and Key Deployment Project of Centre for Ocean Mega-Research of Science, Chinese academy of science (COMS2020Q13).

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