Helmholtz energy equation of state for refrigerant hexafluoropropene (R1216)

LIU Huimin; MAN Jingru; SUN Xiaoyan; ZHAO Wenying; XIANG Shuguang

doi:10.11949/0438-1157.20260148

您当前的位置：

首页 >

文章列表页 >

Helmholtz energy equation of state for refrigerant hexafluoropropene (R1216)

Special Column\: Advances in Cryogenic Science and Technology\‌ | 更新时间：2026-09-16

- Helmholtz energy equation of state for refrigerant hexafluoropropene (R1216)
- CIESC Journal Vol. 77, Issue 8, Pages: 4407-4421(2026)
- 作者机构：
  
  青岛科技大学过程系统工程研究所，山东青岛 266044
- 作者简介：
- 基金信息：
- DOI：10.11949/0438-1157.20260148
  CLC： TB 61.2
- Received：30 January 2026，
  
  Revised：2026-04-27，
  
  Accepted：28 April 2026，
  
  Published：25 August 2026
- 稿件说明：
移动端阅览
刘慧敏, 满婧如, 孙晓岩, 赵文英, 项曙光. 制冷剂六氟丙烯（R1216）Helmholtz状态方程研究[J]. 化工学报, 2026, 77(8): 4407-4421

LIU Huimin, MAN Jingru, SUN Xiaoyan, ZHAO Wenying, XIANG Shuguang. Helmholtz energy equation of state for refrigerant hexafluoropropene (R1216)[J]. CIESC Journal, 2026, 77(8): 4407-4421
刘慧敏, 满婧如, 孙晓岩, 赵文英, 项曙光. 制冷剂六氟丙烯（R1216）Helmholtz状态方程研究[J]. 化工学报, 2026, 77(8): 4407-4421 DOI： 10.11949/0438-1157.20260148.

LIU Huimin, MAN Jingru, SUN Xiaoyan, ZHAO Wenying, XIANG Shuguang. Helmholtz energy equation of state for refrigerant hexafluoropropene (R1216)[J]. CIESC Journal, 2026, 77(8): 4407-4421 DOI： 10.11949/0438-1157.20260148.

摘要

基于制冷剂六氟丙烯（R1216）的蒸气压、饱和气液相密度、

pρT

数据、气相声速、理想气体比定压热容实验数据建立了R1216的Helmholtz状态方程，采用混合求解算法拟合方程参数。状态方程的适用范围为从三相点温度117.65 K至370 K，压力最高可达10 MPa。在此范围内，气液相密度、气相声速、理想气体比定压热容和饱和蒸气压平均绝对相对偏差（AARD）小于1.62%，饱和气液相密度的AARD分别为3.60%和0.62%。通过维里系数、压缩因子、热容、

pVT

关系、声速、相态识参数分别检验Helmholtz状态方程导出热力学性质外推行为的可靠性。结合实验数据质量评价与导出热力学性质的趋势，证明Helmholtz状态方程不仅在实验数据范围内物性计算结果准确且满足热力学约束，在远离三相点以及高温高压等极端条件下的热力学外推行为也是可靠的。

Abstract

A Helmholtz energy equation of state (EoS) for hexafluoropropene (R1216) was developed based on the experimental data of vapor pressu

saturated liquid and vapor densities

pρT

properties

vaporphase speed of sound

and ideal gas heat capacity at constant pressure. The model parameters were optimized using a hybrid solution algorithm. The applicable range of this EoS spans from the triplepoint temperature of 117.65 K to 370 K and the pressures up to 10 MPa. Within this range

the average absolute relative deviation (AARD) of gas-liquid phase density

gas-phase sound velocity

ideal gas isobaric heat capacity

and saturated vapor pressure is less than 1.62%; the AARDs for saturated gas-liquid phase density are 3.60% and 0.62%

respectively. The extrapolation behavior of the EoS was evaluated using derived thermodynamic properties

including Virial coefficients

the compressibility factor

capacities

pVT

relationships

the speed of sound

and the phase identification parameter. The Helmholtz EoS was evaluated by experimental data and the trends of derived thermodynamic properties. The results proved that the Helmholtz EoS can calculate thermodynamic properties accurately and satisfy thermodynamic constraints within the experimental data range

it also exhibits reliable thermodynamic extrapolation behavior under extreme conditions such as high temperature

high pressure

and the state far from the triple point.

关键词

Keywords

references

生态环境部对外合作与交流中心 . 蒙特利尔议定书(中文版) [EB/OL ] . 北京 : 生态环境部对外合作与交流中心 , 2016 [ 2026-04-27 ] . http://ozone.org.cn/zcwj_26905/gjgy/mtleydss/201610/t20161031_746817.html http://ozone.org.cn/zcwj_26905/gjgy/mtleydss/201610/t20161031_746817.html

Foreign Environmental Cooperation Center, Ministry of Ecology and Environment . Montreal Protocol on Substances that Deplete the Ozone Layer (Chinese Version) [EB/OL ] . Beijing : Foreign Environmental Cooperation Center , Ministry of Ecology and Environment, 2016 [ 2026-04-27 ] . http://ozone.org.cn/zcwj_26905/gjgy/mtleydss/201610/t20161031_746817.html http://ozone.org.cn/zcwj_26905/gjgy/mtleydss/201610/t20161031_746817.html .

ANSI/A SHRAE 34—2022 Designation and safety classification of refrigerants [S ] .

Armour K , Forster P , Storelvmo T , et al . The Earth's energy budget, climate feedbacks, and climate sensitivity [C ] //Masson-Delmotte V, Zhai P, Pirani A, et al. Climate Change 2021 : The Physical Science Basis. Contribution of Working Group Ⅰ to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change . Cambridge, United Kingdom : Cambridge University Press , 2021: 923 - 1054 .

Yang L X , Gong M Q , Guo H , et al . (Vapour+liquid) equilibrium data for the {1,1-difluoroethane (R152a)+1,1,1,3,3-pentafluoropropane (R245fa)} system at temperatures from (323.150 to 353.150)K [J ] . The Journal of Chemical Thermodynamics , 2015 , 91 : 414 - 419 .

Lv Z J , Yang Z , Zhang Y , et al . A comparative investigation on the flame inhibition characteristics and mechanism of 1,1,2,3,3,3-hexafluoro-1-propene (R1216) [J ] . Fuel , 2022 , 324 : 124652 .

李树凯 . 新型灭火介质(CF 3 CF https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411423&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411425&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411424&type= 3.00600004 0.72000003 2.822 CF 2 )的热分解、灭火及光解性能的研究 [D ] . 天津 : 河北工业大学 , 2023 .

Li S K . Study on the thermal decomposition, fire extinguishing and photolysis properties of a new fire extinguishing medium(CF 3 CF https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411403&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411420&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411404&type= 3.00600004 0.72000003 2.822 CF 2 ) [D ] . Tianjin : Hebei University of Technology , 2023 .

Subramoney S C , Nelson W M , Valtz A , et al . Pure component and binary vapor-liquid equilibrium + modeling for hexafluoropropylene and hexafluoropropylene oxide with toluene and hexafluoroethane [J ] . Journal of Chemical & Engineering Data , 2010 , 55 ( 1 ): 411 - 418 .

Lemmon E W , Akasaka R . An international standard formulation for 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) covering temperatures from the triple point temperature to 410 K and pressures up to 100 MPa [J ] . International Journal of Thermophysics , 2022 , 43 ( 8 ): 119 .

Akasaka R , Lemmon E W . An international standard formulation for trans -1-chloro-3,3,3-trifluoroprop-1-ene [R1233zd(E) ] covering temperatures from the triple-point temperature to 450 K and pressures up to 100 MPa [J ] . Journal of Physical and Chemical Reference Data , 2022 , 51 ( 2 ): 023101 .

Akasaka R , Lemmon E W . A Helmholtz energy equation of state for 3,3,3-trifluoroprop-1-ene (R-1243zf) [J ] . International Journal of Thermophysics , 2025 , 46 ( 2 ): 23 .

Bell I H . Superancillary equations for the multiparameter equations of state in REFPROP 10.0 [J ] . Journal of Physical and Chemical Reference Data , 2024 , 53 : 013102 .

Akasaka R . A reliable and useful method to determine the saturation state from Helmholtz energy equations of state [J ] . Journal of Thermal Science and Technology , 2008 , 3 ( 3 ): 442 - 451 .

Coquelet C , Ramjugernath D , Madani H , et al . Experimental measurement of vapor pressures and densities of pure hexafluoropropylene [J ] . Journal of Chemical & Engineering Data , 2010 , 55 ( 6 ): 2093 - 2099 .

Miller W T , Fainberg A H . Preferential replacement reactions of highly fluorinated alkyl halides <math id="M71"><mo stretchy="false">(</mo><mi mathvariant="normal">Ⅰ</mi><mo stretchy="false">)</mo></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411374&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118411396&type= 3.13266683 2.70933342 : Preparation of certain fluorinated allyl iodides [J ] . Journal of the American Chemical Society , 1957 , 79 ( 15 ): 4164 - 4169 .

Lemmon E W , Goodwin A R H . Critical properties and vapor pressure equation for alkanes C n H 2 n +2 : normal alkanes with n ≤36 and isomers for n =4 through n =9 [J ] . Journal of Physical and Chemical Reference Data , 2000 , 29 ( 1 ): 1 - 39 .

Gao K H , Wu J T , Lemmon E W . Equations of state for the thermodynamic properties of three hexane isomers: 3-methylpentane, 2,2-dimethylbutane, and 2,3-dimethylbutane [J ] . Journal of Physical and Chemical Reference Data , 2021 , 50 ( 3 ): 033103 .

Lemmon E W , Jacobsen R T . A new functional form and new fitting techniques for equations of state with application to pentafluoroethane (HFC-125) [J ] . Journal of Physical and Chemical Reference Data , 2005 , 34 ( 1 ): 69 - 108 .

Span R , Wagner W . On the extrapolation behavior of empirical equations of state [J ] . International Journal of Thermophysics , 1997 , 18 ( 6 ): 1415 - 1443 .

Lemmon E W , McLinden M O , Wagner W . Thermodynamic properties of propane(Ⅲ): A reference equation of state for temperatures from the melting line to 650 K and pressures up to 1000 MPa [J ] . Journal of Chemical & Engineering Data , 2009 , 54 ( 12 ): 3141 - 3180 .

Li X , Pang Q C , Liu J J , et al . Phase equilibrium for the binary mixture of 1,1,2,3,3,3-hexafluoro-1-propene (R1216) + propane (R290) at temperatures from 283.15 to 313.15 K [J ] . The Journal of Chemical Thermodynamics , 2022 , 167 : 106717 .

Hao Z A , He G G , Tian Q Q , et al . Vapor-liquid equilibrium data for binary mixture of 1,1,2,3,3,3-hexaflfluoro-1-propene (R1216) and trans-1,3,3,3-tetraflfluoropropene [R1234ze(E)] at temperatures from 275 to 315 K [J ] . The Journal of Chemical Thermodynamics , 2023 , 185 : 107117 .

李昌圣 , 冯耀声 , 吴兆立 . 六氟丙烯的蒸汽压 [J ] . 高校化学工程学报 , 1996 , 10 ( 1 ): 64 - 66 .

Li C S , Feng Y S , Wu Z L . Vapor pressure of hexafluoropropylene [J ] . Journal of Chemical Engineering of Chinese Universities , 1996 , 10 ( 1 ): 64 - 66 .

Whipple G H . Vapor-liquid equilibria of some fluorinated hydrocarbon systems [J ] . Industrial & Engineering Chemistry , 1952 , 44 ( 7 ): 1664 - 1667 .

冯国祥 , 刘洪来 , 胡英 . 二氟氯甲烷-全氟丙烯二元系中压汽液平衡的研究 [J ] . 华东化工学院学报 , 1986 , 12 ( 2 ): 225 - 232 .

Feng G X , Liu H L , Hu Y . Vapor-liquid equilibria of Freon 22 and hexafluropropylene binary system under moderate pressures [J ] . Journal of East China University of Science and Technology , 1986 , 12 ( 2 ): 225 - 232 .

Coquelet C , Valtz A , Naidoo P , et al . Isothermal vapor-liquid equilibrium data for the hexafluoropropylene (R1216) + propylene system at temperatures from (263.17 to 353.14)K [J ] . Journal of Chemical & Engineering Data , 2010 , 55 ( 4 ): 1636 - 1639 .

Subramoney S C , Valtz A , Coquelet C , et al . Vapor-liquid equilibrium measurements and modeling for the ethane (R-170) + 1,1,2,3,3,3-hexafluoro-1-propene (R-1216) binary system [J ] . Journal of Chemical & Engineering Data , 2012 , 57 ( 11 ): 2947 - 2955 .

Conradie F J , Crouse P L , Courtial X , et al . Isothermal vapor-liquid equilibrium data for the 1,1,2,2-tetrafluoroethene + 1,1,2,3,3,3-hexafluoroprop-1-ene binary system: measurement and modeling from (248 to 283)K [J ] . Journal of Chemical & Engineering Data , 2014 , 59 ( 1 ): 82 - 88 .

Nelson W M , Williams-Wynn M , Subramoney S C , et al . Isothermal vapor-liquid equilibrium data for the binary system 1,1,2,3,3,3-hexafluoro-1-propene (R1216) + 2,2,3-trifluoro-3-(trifluoromethyl)oxirane from (268.13 to 308.19)K [J ] . Journal of Chemical & Engineering Data , 2015 , 60 ( 3 ): 568 - 573 .

Hashemi H , Nelson W M , Babaee S , et al . Isothermal vapor-liquid equilibrium data for the binary systems consisting of 1,1,2,3,3,3-hexafluoro-1-propene and either methylcyclohexane, cyclohexane, n -hexane, 2-methyltetrahydrofuran, or 2,2,3,3,4,4,4-heptafluoro-1-butanol [J ] . Journal of Chemical & Engineering Data , 2019 , 64 ( 12 ): 5232 - 5237 .

Peng X Y , Xu L , Yang Z , et al . Gaseous speed of sound, ideal-gas heat capacity, and virial coefficients for cis -1,1,1,4,4,4-hexafluoro-2-butene [R1336mzz(Z) ] and cis -1,2,3,3,3-pentafluoroprop-1-ene [R1225ye(Z) ] [J ] . The Journal of Chemical Thermodynamics , 2023 , 184 : 107083 .

Zollweg J A , Mulholland G W . On the law of the rectilinear diameter [J ] . The Journal of Chemical Physics , 1972 , 57 ( 3 ): 1021 - 1025 .

Thol M , Rutkai G , Köster A , et al . Equation of state for the Lennard-Jones fluid [J ] . Journal of Physical and Chemical Reference Data , 2016 , 45 ( 2 ): 023101 .

Venkatarathnam G , Oellrich L R . Identification of the phase of a fluid using partial derivatives of pressure, volume, and temperature without reference to saturation properties: applications in phase equilibria calculations [J ] . Fluid Phase Equilibria , 2011 , 301 ( 2 ): 225 - 233 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Predicting thermodynamic properties of refrigerants using an equation of state for square-well chain fluid with variable range

Experimental and theoretical study on liquid viscosity of R1336mzz(E)

Research on the synthesis kinetics of 2-chloro-N-methylacetamide and reactor simulation

Regulating lithium dendritic evolution at interface by thermal management for ultrafast charging lithium-ion battery

An overview of digital twin systems for fuel cells

Related Author

JIA Yuqian

LI Jiashu

SUN Yi

LIU Yingjie

YE Qing

LI Jinlong

XU Chenyi

YE Gongran

Related Institution

School of Petrochemical Engineering, Changzhou University

Key Laboratory of Refrigeration and Cryogenic Technology of Zhejiang Province, Institute of Refrigeration and Cryogenics, Zhejiang University

State Key Laboratory of Fluorinated Greenhouse Gases Replacement and Control Treatment, Zhejiang Research Institute of Chemical Industry Co., Ltd.

School of Energy and Power Engineering, Xi'an Jiaotong University

School of Chemistry, Xi'an Jiaotong University

⁰