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Modeling Vapor Liquid Phase Equilibrium for CxHy + CxHyFz Using PR And PCSAFT Yanxing Zhao, Xueqiang Dong, Quan Zhong, Haiyang Zhang, Huiya Li, Jun Shen, and Maoqiong Gong Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 01 Jun 2017 Downloaded from http://pubs.acs.org on June 6, 2017
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Modeling Vapor Liquid Phase Equilibrium for CxHy + CxHyFz Using PR And PCSAFT Yanxing Zhao†,‡, Xueqiang Dong*,†, Quan Zhong†,‡, Haiyang Zhang§, Huiya Li†, Jun Shen†, Maoqiong Gong*,† †
Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese
Academy of Sciences, P. O. Box 2711, Beijing 100190, China ‡
University of Chinese Academy of Sciences, Beijing 100039, China
§
Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P. O. Box 2711,
Beijing 100190, China
*
Corresponding author. Tel. /fax: +86 10 82543736
Email address:
[email protected] (X. D.) *
Corresponding author. Tel. /fax: +86 10 82543728
Email address:
[email protected] (M. G.)
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ABSTRACT Modeling the vapor liquid phase equilibrium of mixed refrigerants is the essential precondition for the calculation of refrigeration system. In this work, the study on 48 pure substances and 58 binary systems consisting of CxHy and CxHyFz was performed. Both PR and PCSAFT were investigated. The relationship between the parameters in PR and PCSAFT was exhibited. Strong linear function of the volume parameter mσ3 in PCSAFT with covolume parameter b in PR were found, as well as the energy parameter mε2 in PCSAFT with energy parameter a/b in PR. This correlated characteristic provides an idea for regressing pure substance parameters and a criterion whether the regressed parameters are reasonable or not. Besides, the interaction parameters in PR-VDW and PCSAFT show consistent tendency, and both are limited to a very narrow range. The simple predictive method was proposed by using the average value 0.146 for PR-VDW and 0.093 for PCSAFT. The internal correlated behaviours result that the PCSAFT equation is no better than PR equation on the VLE description of CxHy + CxHyFz systems. Key words: Hydrocarbon; Hydrofluorocarbons; PR; PCSAFT; Vapor liquid equilibrium 1.
INTRODUCTION Due to the environmental protection requirements, the mixed refrigerants consisting of
hydrocarbons (HC) and hydrofluorocarbons (HFC) attract growing attention. Mixtures of this type have two superiorities as promising refrigerants. On the one hand, the HCs are natural refrigerants with zero ozone depleting potential (ODP) and low global warming potential (GWP, generally below 201). Moreover, they have excellent intermiscibility with inexpensive mineral lubricants and good thermodynamic properties such as high heat transfer properties and good coefficient of thermal conductivity. However, the HCs refrigerants are highly flammable and explosive which limits its application. Besides, the volumetric refrigerating capacity of HCs refrigerants is low, which means a larger compressor is required. Comparing to HCs, the HFCs have lower flammability, higher volumetric refrigerating capacity, but bigger GWP value and worse intermiscibility with mineral oils. Thus, the HCs and the HFCs can complement each other perfectly. On the other hand, most of the HC + HFC systems can form positive azeotropes. The refrigeration systems with azeotropic mixtures can achieve higher volumetric refrigerating capacity, which would dramatically reduce the refrigerant charge and the potential risk of explosion. The potential refrigeration performance of these mixtures can be estimated by their thermodynamic parameters. Vapor liquid equilibrium (VLE) data is one of the most important fundamental parameters. Since the Peng-Robinson2 (PR) equation of state is still one of the most widely used models in engineering field. Many studies have been done to correlate or predict the VLE of HFC + HC systems based on PR EoS. In Zhang’s3 and Hu’s4 work, the binary interaction parameters in PR-VDW were determined by summing the contribution coefficient of each pure component times its contribution. Successful VLE reproduction can
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be done for refrigerant mixtures. Hou5 and Elvassore6 developed the group contribution method for - CxHyFz (x ∈ [1, 2, 3], y, z ∈ [0, 1, 2, 3, 4]) group, and good VLE prediction were achieved with limited substances. With more experimental VLE data published, the UNIFAC model showed its limitation7. Meanwhile, the theoretically derived PCSAFT 8 EoS has been successfully applied to many complex systems. This model is given predictive ability usually by setting the interaction parameter to zero. However, one significant drawback of PCSAFT is that the pure component parameters obtained from pure substance p-ρ-T data are frequently inadequate for modeling mixture behavior9. This work aims at modeling vapor liquid phase equilibrium for CxHy + CxHyFz (x ∈ [1, 2, 3], y, z ∈ [0, 1, 2, 3, 4]) mixed refrigerants using PR and PCSAFT EoS. The CxHy includes alkanes, alkenes and cycloalkanes. The CxHyFz includes hydrofluorocarbons and hydrofluoroolefins. The relationship between the parameters in PR and PCSAFT for both pure substances and mixtures were found. 2.
THERMODYNAMIC MODEL
2.1. PR-VDW The semiempirical PR cubic equation of state, with simple form and acceptable precision, has been successfully used in the field of chemical industry since it was proposed. It is used in the original form as: p=
a = 0.457235
RT a − . v − b ( v + c1b )( v + c2 b )
(1)
2 R 2Tc2 1 + (0.37464 + 1.54226ω − 0.26992ω 2 )(1 − T / Tc ) , pc
(2)
RTc , pc
(3)
and b = 0.077796
where p is the pressure, Pa; v is the mole volume, m3·mol-1; T is the temperature, K; R is the gas constant, 8.31441 J·mol-1·K-1, c1 = 1 − 2 , c2 = 1 + 2 , pc and Tc are the critical pressure and temperature, respectively, and ω is the acentric factor. The VDW10 mixing rule is employed to establish the relationship between the mixed energy parameters am and pure substance parameter ai, as well as the covolume parameters bm and bi. The geometric mean rule is used for the cross energy parameter and the arithmetic mean rule is used for the cross covolume parameter.
am = ∑∑ xi x j aij , aij = aii a jj (1 − kij ),
(4)
bm = ∑∑ xi x j bij , bij = (bii + b jj ) / 2.
(5)
i
j
i
j
2.2. PCSAFT
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The theoretically derived PCSAFT8 EoS is based on the molecular model suggested by Chen11
∞ 3ε u(r ) = −ε 0
r
