烯烃制冷剂统计缔合流体理论状态方程参数优化

张钰婧; 田俊辉; 王晓坡

doi:10.7652/xjtuxb202509013

您当前的位置：

首页 >

文章列表页 >

烯烃制冷剂统计缔合流体理论状态方程参数优化

—————————————————————— | 更新时间：2025-09-11

- 烯烃制冷剂统计缔合流体理论状态方程参数优化
- Parameter Optimization of the Statistical Associating Fluid Theory Equation of State for Olefin Refrigerants
- 西安交通大学学报 2025年59卷第9期页码：132-141
- 作者机构：
  
  西安交通大学能源与动力工程学院， 710049，西安
- 作者简介：
  
  张钰婧（2000—），女，硕士生
  王晓坡，男，教授，博士生导师。
- 基金信息：
  
  国家重点研发计划资助项目(2022YFE0210200)
- DOI：10.7652/xjtuxb202509013
  中图分类号： TK121
- 收稿：2025-02-15，
  
  网络首发：2025-04-01，
  
  纸质出版：2025-09-10
- 稿件说明：
移动端阅览
张钰婧, 田俊辉, 王晓坡. 烯烃制冷剂统计缔合流体理论状态方程参数优化[J]. 西安交通大学学报, 2025,59(9):132-141.

ZHANG Yujing, TIAN Junhui, WANG Xiaopo. Parameter Optimization of the Statistical Associating Fluid Theory Equation of State for Olefin Refrigerants[J]. Journal of Xi’an Jiaotong University, 2025, 59(9): 132-141.
张钰婧, 田俊辉, 王晓坡. 烯烃制冷剂统计缔合流体理论状态方程参数优化[J]. 西安交通大学学报, 2025,59(9):132-141. DOI： 10.7652/xjtuxb202509013.

ZHANG Yujing, TIAN Junhui, WANG Xiaopo. Parameter Optimization of the Statistical Associating Fluid Theory Equation of State for Olefin Refrigerants[J]. Journal of Xi’an Jiaotong University, 2025, 59(9): 132-141. DOI： 10.7652/xjtuxb202509013.

摘要

为了精确标注带有极性特征的氢氟烯烃（HFOs）类制冷剂的热力学性质，通过引入显式极性项对原始基于可变范围米氏势的统计缔合流体理论（SAFT-VR-Mie）状态方程进行改进。以10种HFOs制冷剂为研究对象，基于饱和蒸气压、饱和液

相密度、饱和气相密度实验数据，通过非线性回归方法确定了改进方程的分子特征参数。利用改进方程计算了制冷剂的饱和蒸气压、饱和液相密度、饱和气相密度、蒸发焓、比定压热容、声速等热力学参数，计算值与实验数据的总体平均绝对偏差分别为0.48%、0.94%、0.06%、2.24%、3.78%和0.26%。以R1234yf和R1234ze（E）两种制冷剂为研究对象，比较了改进的SAFT-VR-Mie方程和原始SAFT-VR-Mie方程的计算精度。实验结果表明，除比定压热容外，改进方程对各热力学性质的预测精度均高于原始方程。应用改进方程对5种HFOs二元混合物的气液相平衡性质进行预测。结果表明，即使在不考虑二元交互参数（

=0）的情况下，改进的SAFT-VR-Mie方程对气液平衡的预测精度均高于Refprop软件计算结果。

Abstract

To accurately characterize the thermodynamic properties of hydrofluoroolefin (HFO) refrigerants with polar characteristics

this study enhances the original Statistical Associating Fluid Theory equation of state based on variable-range Mie potential (SAFT-VR-Mie) by incorporating an explicit polar term. Using experimental data of saturated vapor pressure

saturated liquid density

and saturated vapor density for ten HFO refrigerants

the molecular characteristic parameters of the modified equation through nonlinear regression are determined. The improved equation is employed to calculate various physical properties

including saturated vapor pressure

saturated liquid density

saturated vapor density

enthalpy of vaporization

isobaric heat capacity

and speed of sound. The overall average absolute deviations between calculated and experimental values are 0.48%

0.94%

0.06%

2.24%

3.78%

and 0.26%

respectively. A comparative analysis between the modified and original SAFT-VR-Mie equations is conducted for R1234yf and R1234ze(E) refrigerants. Results demonstrate that the modified equation achieves superior prediction accuracy for all thermodynamic properties except isobaric heat capacity. Furthermore

when applied to predict vapor-liquid equilibrium properties of five HFO binary mixtures

the modified SAFT-VR-Mie equation outperforms Refprop software calculations even without considering binary interaction parameters (

=0).

关键词

Keywords

references

ALBÀ C G , ALKHATIB I I I , LLOVELL F , et al . Hunting sustainable refrigerants fulfilling technical, environmental, safety and economic requirements [J ] . Renewable and Sustainable Energy Reviews , 2023 , 188 : 113806 .

CALM J M . The next generation of refrigerants-historical review, considerations, and outlook [J ] . International Journal of Refrigeration , 2008 , 31 ( 7 ): 1123 - 1133 .

CHAPMAN W G , GUBBINS K E , JACKSON G , et al . SAFT: equation-of-state solution model for associating fluids [J ] . Fluid Phase Equilibria , 1989 , 52 : 31 - 38 .

GROSS J , SADOWSKI G . Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules [J ] . Industrial & Engineering Chemistry Research , 2001 , 40 ( 4 ): 1244 - 1260 .

BLAS F J , VEGA L F . Thermodynamic behaviour of homonuclear and heteronuclear Lennard-Jones chains with association sites from simulation and theory [J ] . Molecular Physics , 1997 , 92 ( 1 ): 135 - 150 .

GIL-VILLEGAS A , GALINDO A , WHITEHEAD P J , et al . Statistical associating fluid theory for chain molecules with attractive potentials of variable range [J ] . The Journal of Chemical Physics , 1997 , 106 ( 10 ): 4168 - 4186 .

杨智 , 公茂琼 , 李会亚 , 等 . 基于不同的SAFT类状态方程研究甲烷的热物性 [J ] . 低温工程 , 2015 ( 3 ): 6 - 12 .

YANG Zhi , GONG Maoqiong , LI Huiya , et al . Thermophysical properties of methane studied by different SAFT-type equation of state [J ] . Cryogenics , 2015 ( 3 ): 6 - 12 .

康凯 , 李雪莉 , 杨树 , 等 . 状态方程参数化耦合制冷工质热导率性质预测模型 [J ] . 西安交通大学学报 , 2024 , 58 ( 4 ): 148 - 157 .

KANG Kai , LI Xueli , YANG Shu , et al . A prediction model of refrigerant thermal conductivity coupled with the standardized equation of the state parameterization scheme [J ] . Journal of Xi'an Jiaotong University , 2024 , 58 ( 4 ): 148 - 157 .

DUFAL S , LAFITTE T , GALINDO A , et al . Developing intermolecular-potential models for use with the SAFT-VR Mie equation of state [J ] . AIChE Journal , 2015 , 61 ( 9 ): 2891 - 2912 .

POLISHUK I , CHIKO A , CEA-KLAPP E , et al . Implementation of CP-PC-SAFT and CS-SAFT-VR-Mie for predicting thermodynamic properties of C 1 —C 3 halocarbon systems: I pure compounds and mixtures with nonassociating compounds [J ] . Industrial & Engineering Chemistry Research , 2021 , 60 ( 26 ): 9624 - 9636 .

毛元敬 , 杨智 , 莫松平 , 等 . C 6 ~C 10 烷醇的SAFT-VR Mie状态方程参数回归及其热物性研究 [J ] . 化工学报 , 2023 , 74 ( 3 ): 1033 - 1041 .

MAO Yuanjing , YANG Zhi , MO Songping , et al . Estimation of SAFT-VR Mie equation of state parameters and thermodynamic properties of C 6 —C 10 alcohols [J ] . CIESC Journal , 2023 , 74 ( 3 ): 1033 - 1041 .

GROSS J , VRABEC J . An equation-of-state contribution for polar components: dipolar molecules [J ] . AIChE Journal , 2006 , 52 ( 3 ): 1194 - 1204 .

ABED A M , AMEER S A A , ABDTAWFEEQ T H , et al . Effect of polarity on prediction of second order derivative thermodynamic properties of refrigerants [J ] . Fluid Phase Equilibria , 2023 , 565 : 113652 .

JOG P K , CHAPMAN W G . Application of Wertheim's thermodynamic perturbation theory to dipolar hard sphere chains [J ] . Molecular Physics , 1999 , 97 ( 3 ): 307 - 319 .

CRIPWELL J T , SCHWARZ C E , BURGER A J . SAFT-VR-Mie with an incorporated polar term for accurate holistic prediction of the thermodynamic properties of polar components [J ] . Fluid Phase Equilibria , 2018 , 455 : 24 - 42 .

JOG P K , SAUER S G , BLAESING J , et al . Application of dipolar chain theory to the phase behavior of polar fluids and mixtures [J ] . Industrial & Engineering Chemistry Research , 2001 , 40 ( 21 ): 4641 - 4648 .

PERDOMO F A , MILLÁN B M , ARAGÓN J L . Predicting the physical-chemical properties of biodiesel fuels assessing the molecular structure with the SAFT- γ group contribution approach [J ] . Energy , 2014 , 72 : 274 - 290 .

HURTER R M , CRIPWELL J T , BURGER A J . Expanding SAFT-γ Mie's application to dipolar species: 2-ketones, 3-ketones, and propanoate esters [J ] . Industrial & Engineering Chemistry Research , 2020 , 59 ( 16 ): 7993 - 8003 .

ASHRAFMANSOURI S S , RAEISSI S . Modeling gas solubility in ionic liquids with the SAFT-γ group contribution method [J ] . The Journal of Supercritical Fluids , 2012 , 63 : 81 - 91 .

LAFITTE T , APOSTOLAKOU A , AVENDAÑO C , et al . Accurate statistical associating fluid theory for chain molecules formed from Mie segments [J ] . The Journal of Chemical Physics , 2013 , 139 ( 15 ): 154504 .

SHAAHMADI F , SMITH S A , SCHWARZ C E , et al . Group-contribution SAFT equations of state: a review [J ] . Fluid Phase Equilibria , 2023 , 565 : 113674 .

LAFITTE T , PIÑEIRO M M , DARIDON J L , et al . A comprehensive description of chemical association effects on second derivative properties of alcohols through a SAFT-VR approach [J ] . The Journal of Physical Chemistry: B , 2007 , 111 ( 13 ): 3447 - 3461 .

GALLIERO G , LAFITTE T , BESSIERES D , et al . Thermodynamic properties of the Mien-6 fluid: a comparison between statistical associating fluid theory of variable range approach and molecular dynamics results [J ] . The Journal of Chemical Physics , 2007 , 127 ( 18 ): 184506 .

AL-SAIFI N M , HAMAD E Z , ENGLEZOS P . Prediction of vapor-liquid equilibrium in water-alcohol-hydrocarbon systems with the dipolar perturbed-chain SAFT equation of state [J ] . Fluid Phase Equilibria , 2008 , 271 ( 1/2 ): 82 - 93 .

LAGARIAS J C , REEDS J A , WRIGHT M H , et al . Convergence properties of the Nelder-Mead simplex method in low dimensions [J ] . SIAM Journal on Optimization , 1998 , 9 ( 1 ): 112 - 147 .

LEMMON E W , BELL I H , HUBER M L , et al . NIST standard reference database 23: reference fluid thermodynamic and transport properties-REFPROP, version 10.0, National Institute of Standards and Technology [EB/OL ] . [ 2024-08-01 ] . https://doi.org/10.18434/T4/1502528 https://doi.org/10.18434/T4/1502528 .

AKASAKA R , HUBER M L , SIMONI L D , et al . A Helmholtz energy equation of state for trans-1,1,1,4,4,4-hexafluoro-2-butene [R-1336mzz(E)] and an auxiliary extended corresponding states model for the transport properties [J ] . International Journal of Thermophysics , 2023 , 44 ( 4 ): 50 .

BROWN J S , FEDELE L , DI NICOLA G , et al . Compressed liquid density and vapor phase PvT measurements of cis-1,2,3,3,3-pentafluoroprop-1-ene (R1225ye(Z)) [J ] . Journal of Chemical & Engineering Data , 2015 , 60 ( 11 ): 3333 - 3340 .

DI NICOLA G , POLONARA F , SANTORI G . Saturated pressure measurements of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) [J ] . Journal of Chemical & Engineering Data , 2010 , 55 ( 1 ): 201 - 204 .

DI NICOLA G , BROWN J S , FEDELE L , et al . Saturated pressure measurements of trans-1,3,3,3-tetrafluoroprop-1-ene (R1234ze(E)) for reduced temperatures ranging from 0.58 to 0.92 [J ] . Journal of Chemical & Engineering Data , 2012 , 57 ( 8 ): 2197 - 2202 .

BROWN J S , DI NICOLA G , FEDELE L , et al . Saturated pressure measurements of 3,3,3-trifluoroprop-1-ene (R1243zf) for reduced temperatures ranging from 0.62 to 0.98 [J ] . Fluid Phase Equilibria , 2013 , 351 : 48 - 52 .

TANG Bo , YAO Xiaoyu , DONG Xueqiang , et al . Experimental investigation of saturated vapor pressure and critical parameter for R1234ze(Z) (cis-1,3,3,3-tetrafluoropropene) and R1336mzz(Z) (cis-1,1,1,4,4,4-hexafluoro-2-butene) [J ] . The Journal of Chemical Thermodynamics , 2024 , 189 : 107204 .

HIGASHI Y , SAKODA N , ISLAM M A , et al . Measurements of saturation pressures for trifluoroethene (R1123) and 3,3,3-trifluoropropene (R1243zf) [J ] . Journal of Chemical & Engineering Data , 2018 , 63 ( 2 ): 417 - 421 .

FEDELE L , DI NICOLA G , BROWN J S , et al . Measurements and correlations of cis-1,3,3,3-tetrafluoroprop-1-ene (R1234ze(Z)) saturation pressure [J ] . International Journal of Thermophysics , 2014 , 35 ( 1 ): 1 - 12 .

SAKODA N , HIGASHI Y , AKASAKA R . Measurements of PvT properties, vapor pressures, saturated densities, and critical parameters for trans-1,1,1,4,4,4-hexafluoro-2-butene (R1336mzz(E)) [J ] . Journal of Chemical & Engineering Data , 2021 , 66 ( 1 ): 734 - 739 .

FEDELE L , DI NICOLA G , BROWN J S , et al . Saturated pressure measurements of cis-pentafluoroprop-1-ene (R1225ye(Z)) [J ] . International Journal of Refrigeration , 2016 , 69 : 243 - 250 .

MONDÉJAR M E , MCLINDEN M O , LEMMON E W . Thermodynamic properties of trans-1-chloro-3,3,3-trifluoropropene (R1233zd(E)): vapor pressure, ( p, ρ, T ) behavior, and speed of sound measurements, and equation of state [J ] . Journal of Chemical & Engineering Data , 2015 , 60 ( 8 ): 2477 - 2489 .

BOBBO S , BET A , SCATTOLINI M , et al . Saturated pressure measurements of cis-1-chloro-2,3,3,3-tetrafluoropropene (R1224yd (Z)) saturation pressure [J ] . Journal of Chemical & Engineering Data , 2020 , 65 ( 9 ): 4263 - 4267 .

GAO Neng , JIANG Yunyun , WU Jie , et al . Measurements of the isobaric heat capacity of R1234yf in liquid phase at temperatures from 305 K to 355 K and pressures up to 5 MPa [J ] . Fluid Phase Equilibria , 2014 , 376 : 64 - 68 .

GAO Neng , CHEN Guangming , LI Rong , et al . Measurements of the isobaric heat capacity of pressurized liquid trans-1,3,3,3-tetrafluoropropene [R1234ze(E)] by scanning calorimetry [J ] . Journal of Thermal Analysis and Calorimetry , 2015 , 122 ( 3 ): 1469 - 1476 .

SHENG Bowen , ZHAO Yanxing , DONG Xueqiang , et al . The isobaric specific heat capacity and viscosity for 3,3,3-trifluoroprop-1-ene in liquid phase at temperatures from (230 to 293) K and pressures up to 8 MPa [J ] . The Journal of Chemical Thermodynamics , 2024 , 194 : 107277 .

LIU Yu , ZHAO Xiaoming . Measurement of the heat capacity of R1233zd(E) [J ] . International Journal of Refrigeration , 2018 , 86 : 127 - 132 .

KANO Y , KAYUKAWA Y , FUJII K , et al . Ideal-gas heat capacity for 2,3,3,3-tetrafluoropropene (HFO-1234yf) determined from speed-of-sound measurements [J ] . International Journal of Thermophysics , 2010 , 31 ( 11 ): 2051 - 2058 .

KANO Y , KAYUKAWA Y , FUJII K , et al . Ideal gas heat capacity derived from speed of sound measurements in the gaseous phase for trans-1,3,3,3-tetrafluoropropene [J ] . Journal of Chemical & Engineering Data , 2013 , 58 ( 11 ): 2966 - 2969 .

CHEN Hongyu , ZHANG Kai , YANG Zhen , et al . Experimental speed of sound for 3,3,3-trifluoropropene (R-1243zf) in gaseous phase measured with cylindrical resonator [J ] . Journal of Chemical & Engineering Data , 2021 , 66 ( 5 ): 2256 - 2263 .

PENG Xiayao , XU Liu , YANG Zhen , 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 .

KANO Y , KAYUKAWA Y , FUJITA Y . Dipole moment and heat capacity in the ideal gas state derived from relative permittivity and speed of sound measurements for HFO-1123 and HCFO-1224yd(Z) [J ] . International Journal of Refrigeration , 2020 , 118 : 354 - 364 .

LOZANO-MARTÍN D , RIPA D M , GAVIOSO R M . Speed of sound in gaseous cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) between 307 K and 420 K [J ] . International Journal of Refrigeration , 2019 , 100 : 37 - 47 .

KANO Y . Entropy, heat capacity, and thermal conductivity of trans-1,1,1,4,4,4-hexafluoro-2-butene [R1336mzz(E)] derived from the gaseous sound speed measurement [J ] . Journal of Chemical & Engineering Data , 2023 , 68 ( 3 ): 574 - 585 .

PENG Xiayao , LIU Hangtao , XU Liu , et al . Experimental speed of sound for trans-1-chloro-3,3,3-trifluoroprop-1-ene (R1233zd(E)) and trans-1,1,1,4,4,4-hexafluorobut-2-ene (R1336mzz(E)) in gaseous phase [J ] . The Journal of Chemical Thermodynamics , 2022 , 171 : 106808 .

GARRIDO J M , MEJÍA A , PIÑEIRO M M , et al . Interfacial tensions of industrial fluids from a molecular-based square gradient theory [J ] . AIChE Journal , 2016 , 62 ( 5 ): 1781 - 1794 .

MIYAMOTO H , NISHIDA M , SAITO T . Measurement of the vapour-liquid equilibrium properties of binary mixtures of the low-GWP refrigerants R1123 and R1234yf [J ] . The Journal of Chemical Thermodynamics , 2021 , 158 : 106456 .

YANG Zhiqiang , VALTZ A , COQUELET C , et al . Experimental measurement and modelling of vapor-liquid equilibrium for 3,3,3-trifluoropropene (R1243zf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) binary system [J ] . International Journal of Refrigeration , 2020 , 120 : 137 - 149 .

YANG Wei , HE Guogeng , ZHANG Zhihao , et al . Vapor-liquid equilibrium for the binary mixed refrigerant {R1234ze(E) + R1336mzz(E)} at temperatures from 283.15 K to 313.15 K [J ] . The Journal of Chemical Thermodynamics , 2023 , 185 : 107095 .

BOONAERT E , VALTZ A , BROCUS J , et al . Vapor-liquid equilibrium measurements for 5 binary mixtures involving HFO-1336mzz(E) at temperatures from 313 to 353 K and pressures up to 2.735 MPa [J ] . International Journal of Refrigeration , 2020 , 114 : 210 - 220 .

FEDELE L , LOMBARDO G , MENEGAZZO D , et al . Isothermal (vapour + liquid) equilibrium measurements and correlation of the binary mixture {3,3,3-trifluoropropene (HFO-1243zf)+2,3,3,3-tetrafluoropropene (HFO-1234yf)} at temperatures from 283.15 K to 323.15 K [J ] . International Journal of Thermophysics , 2023 , 44 ( 6 ): 83 .

ABBADI J E , COQUELET C , VALTZ A , et al . Experimental measurements and modelling of vapour-liquid equilibria for four mixtures of 2,3,3,3-tetrafluoropropene (R1234yf) with 1,1,1,2-tetrafluoroethane (R134a) or 1,1-difluoroethane (R152a) or trans-1-chloro-3,3,3-trifluoropropene (R1233zd(E)) or 2-chloro-3,3,3-trifluoropropene (R1233xf) [J ] . International Journal of Refrigeration , 2022 , 140 : 172 - 185 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

标准氢的状态方程研究

离子液体改性燃料的电流体动力学效应研究

张角凹坑气膜孔对双层壁气膜冷却特性的影响

融合物理信息与深度算子网络的变压器绕组热-流场快速计算方法

多工况下离心压气机叶轮-机匣一体联合设计优化