R290/R245fa汽液相平衡混合规则对比研究

doi:10.11949/0438-1157.20241420

摘要/Abstract

摘要：

R290/R245fa是一组适用于自动复叠喷射制冷循环的非共沸制冷剂，然而，现有文献中关于其实验数据稀缺，且各预测模型间存在显著偏差。为提升R290/R245fa混合工质汽液相平衡的计算精度，选取了PR方程，并结合VDW、WS、MHV1三种混合规则以及UNIFAC（Dortmund）活度系数模型，对该二元混合工质的汽液相平衡特性进行了评估。结果表明，在低压体系下，MHV1混合规则的计算精度优于WS和VDW混合规则。基于最优模型，考虑了氢键在氟代烃分子间的作用力对气液相组成的影响。通过修正活度系数模型中含氟基团的面积参数和体积参数，压力相对偏差降低至0.7937%，气相组分绝对偏差降低至0.0018。计算结果显示，修正后的模型与REFPROP 10.0模型的精度相当，其压力平均相对偏差为0.7051%，气相组分的绝对偏差则为0.0025。最后绘制了R290/R245fa混合工质在243.15~283.15 K温度范围内的相图。

关键词: 二元混合物, 活度系数, 汽液平衡, 碳氢化合物, 氢键

Abstract:

R290/R245fa constitutes a non-azeotropic refrigerant pair suitable for auto-cascade ejector refrigeration cycles. However, the scarcity of experimental data and significant discrepancies among prediction models pose challenges. To enhance the accuracy of vapor-liquid equilibrium (VLE) data calculations for the R290/R245fa binary mixture, this paper utilizes the Peng-Robinson (PR) equation in conjunction with three mixing rules: the van der Waals (VDW), Wong-Sandler (WS), and Modified Huron-Vidal first-order (MHV1) mixing rules. Additionally, it employs the UNIFAC (Dortmund) activity coefficient model to evaluate the VLE properties of the mixture. The results indicate that the MHV1 mixing rule exhibits superior computational accuracy for low-pressure systems compared to the WS and VDW mixing rules. Considering the impact of hydrogen bonding forces among fluorinated hydrocarbon molecules on the vapor-liquid phase composition, the optimal model modifies the area and volume parameters of fluorine-containing groups within the activity coefficient model. This modification reduces the average relative deviation of pressure to 0.7937% and lowers the absolute deviation of the vapor-phase component to 0.0018. The prediction results demonstrate that the accuracy of the modified model is comparable to that of REFPROP 10.0, with a relative deviation of pressure between the modified model and REFPROP 10.0 amounting to 0.7051%, and an absolute deviation of the vapor-phase component of 0.0025.Finally, utilizing the modified parameters, the phase diagram for the R290/R245fa mixed refrigerant is plotted within the temperature range of 243.15 K to 283.15 K.

Key words: binary mixtures, activity coefficient, vapor-liquid equilibria, hydrocarbon, hydrogen bond

中图分类号:

TK 123

丁昊, 王林, 刘豪. R290/R245fa汽液相平衡混合规则对比研究[J]. 化工学报, 2025, 76(S1): 9-16.

Hao DING, Lin WANG, Hao LIU. Comparative study on mixing rules of vapor-liquid equilibrium for R290/R245fa[J]. CIESC Journal, 2025, 76(S1): 9-16.

图/表 8

表1 Dort模型基团体积参数Rk 、表面积参数Qk 和交互作用参数［24］

Table 1 Dort model group volume parameter Rk， surface area parameter Qk， and interaction parameter［24］

序号	基团	R_k	Q_k	a_mn				b_mn
1	CH₃	0.6325	1.0608	0	0	342	342	0	0	-1.679	-1.679
2	CH₂	0.6325	0.7081	0	0	342	342	0	0	-1.679	-1.679
3	CF₃	1.284	1.266	-484.3	-484.3	0	0	2.467	2.467	0	0
4	CHF₂	1.284	1.098	-484.3	-484.3	0	0	2.467	2.467	0	0

表2 R290/R245fa三种模型汽液相平衡计算结果

Table 2 Calculation results of vapor-liquid phase equilibrium for R290/R245fa three models

温度/K	实验数据点数N_p	模型一计算压力p_cal	模型一气相组分y	模型二计算压力p_cal	模型二气相组分y	模型三计算压力p_cal	模型三气相组分y
298.18	16	AARD(p)	100ARD(y)	AARD(p)	100ARD(y)	AARD(p)	100ARD(y)
298.18	16	1.79%	0.4938	1.53%	1.18	1.25%	1.0940
313.22	16	AARD(p)	100ARD(y)	AARD(p)	100ARD(y)	AARD(p)	100ARD(y)
313.22	16	2.27%	0.7964	2.86%	1.22	2.03%	1.1064

表3 修正后基团体积Rk 参数及表面积参数Qk

Table 3 Revised group volume Rk parameter and surface area parameter Qk

主基团	序号	子基团	R_k	Q_k
CH₂	1	CH₃	0.6325	1.0608
CH₂	2	CH₂	0.6325	0.7081
CF₂	3	CF₃	1.5932	1.5330
CF₂	4	CHF₂	1.1623	1.4002

表4 R290/R245fa的修正结果与预测结果比较

Table 4 Comparison between the correction results and prediction results of R290/R245fa

温度/K	N_p	修正后计算压力p_cal	修正后气相组分y	REFPROP 10.0计算压力p_cal	REFPROP 10.0气相组分y
298.18	16	AARD(p)	100ARD(y)	AARD(p)	100ARD(y)
298.18	16	0.62%	0.1944	0.81%	0.2603
313.22	16	AARD(p)	100ARD(y)	AARD(p)	100ARD(y)
313.22	16	0.97%	0.1745	0.60%	0.2432

图1 修正后R290/R245fa的相对压力偏差

Fig.1 Revised relative pressure deviation of R290/R245fa

图2 修正后R290/R245fa气相组分偏差

Fig.2 Revised R290/R245fa vapor-phase component deviation

图3 修正后模型与REFPROP 10.0软件计算的p-x-y曲线

Fig.3 p-x-y curves calculated by revised model and REFPROP 10.0 software

图4 R290/R245fa混合工质p-x-y图

Fig.4 p-x-y diagram of R290/R245fa mixed refrigerants

参考文献 35

1	Li S Q, Wang L, Tan Y Y, et al. Zeotropic mixture ejector: Modeling approach, validation, and assessment based on composition ratio[J]. International Journal of Refrigeration, 2023, 156: 72-83.
2	黄鲤生, 谈莹莹, 王林, 等. 喷射增效自复叠制冷循环工质选择[J]. 低温与超导, 2021, 49(6): 49-56, 68.
	Huang L S, Tan Y Y, Wang L, et al. Selection of working fluids for the ejector enhanced auto-cascade refrigeration cycle[J]. Cryogenics & Superconductivity, 2021, 49(6): 49-56, 68.
3	李潼, 张华, 邱金友. R1234ze(E)/R32混合工质热泵系统性能的实验研究[J]. 制冷技术, 2018, 38(1): 32-36.
	Li T, Zhang H, Qiu J Y. Experimental study on performance of heat pump system with mixed refrigerant of R1234ze(E)/R32[J]. Chinese Journal of Refrigeration Technology, 2018, 38(1): 32-36.
4	穆德富, 陈日帅, 吴东, 等. 混合制冷剂R1234yf/R32热物性研究及分析[J]. 制冷技术, 2017, 37(2): 74-78.
	Mu D F, Chen R S, Wu D, et al. Study and analysis on thermophysical properties of mixture refrigerant R1234yf/R32[J]. Chinese Journal of Refrigeration Technology, 2017, 37(2): 74-78.
5	Perera U A, Sakoda N, Miyazaki T, et al. Measurements of saturation pressures for the novel refrigerant R1132(E)[J]. International Journal of Refrigeration, 2022, 135: 148-153.
6	Yadav S, Liu J, Kim S C. A comprehensive study on 21st-century refrigerants - R290 and R1234yf: a review[J]. International Journal of Heat and Mass Transfer, 2022, 182: 121947.
7	赵洋, 杨双, 蔡宁, 等. R290房间空调器安全与性能研究综述[J]. 制冷技术, 2023, 43(1): 81-86.
	Zhao Y, Yang S, Cai N, et al. Review of research on safety and performance of R290 room air conditioner[J]. Chinese Journal of Refrigeration Technology, 2023, 43(1): 81-86.
8	Giriprasath B S, Chandramohan R, Kumar R A, et al. Energy enhancement of air conditioner using R32 and R290 refrigerants[C]//AIP Conference Proceedings, Proceedings of The 14th Asia-Pacific Physics Conference. Kuching, Malaysia. AIP Publishing, 2021.
9	Seyf J Y, Shojaeian A. Vapor-liquid (azeotropic systems) and liquid-liquid equilibrium calculations using UNIFAC and NRTL-SAC activity coefficient models[J]. Fluid Phase Equilibria, 2019, 494: 33-44.
10	Seyf J Y, Nasiri L, Medi B. Development of the NRTL functional activity coefficient (NRTL-FAC) model using high quality and critically evaluated phase equilibria data. 2[J]. Fluid Phase Equilibria, 2024, 577: 113982.
11	Liu H D, Li X Y, Wang Y X, et al. Elements and chemical bonds contribution estimation of activity coefficients in nonideal liquid mixtures[J]. Processes, 2022, 10(10): 2141.
12	Koulocheris V, Koliva M, Louli V, et al. Modelling of pure refrigerant thermodynamic properties and vapor-liquid equilibrium of refrigerant mixtures with the UMR-PRU model[J]. Fluid Phase Equilibria, 2024, 580: 114052.
13	孙杨柳, 祁影霞, 张佳妮, 等. 基于COSMO-RS模型的制冷工质气液相平衡性质的模拟[J]. 制冷技术, 2017, 37(6): 26-28, 61.
	Sun Y L, Qi Y X, Zhang J N, et al. Simulation of vapor-liquid equilibrium properties of refrigerant based on COSMO-RS model[J]. Chinese Journal of Refrigeration Technology, 2017, 37(6): 26-28, 61.
14	Wang J Y, Sa T X, Zhu L Y. Vapor-liquid equilibrium predictions of refrigerant systems using COSMO based Gex-EoS methods[J]. Fluid Phase Equilibria, 2023, 563: 113584.
15	李树浩. HFO及其二元混合工质气液相平衡性质研究[D]. 北京: 清华大学, 2021.
	Li S H. Study on gas-liquid equilibrium properties of HFO and its binary mixture[D]. Beijing: Tsinghua University, 2021.
16	Peng S Z, Wang E Q, Li S H, et al. Vapor-liquid equilibrium measurements and models for the ternary mixtures of R1234yf + R32 + R125 and R1234yf + R32 + CO₂ [J]. International Journal of Refrigeration, 2023, 146: 225-236.
17	秦延斌, 张华, 吴银龙. R1234yf/R290/R134a系气液相平衡的模拟[J]. 制冷学报, 2017, 38(5): 29-40.
	Qin Y B, Zhang H, Wu Y L. Simulation on vapor liquid equilibria of R1234yf/R290/R134a ternary system[J]. Journal of Refrigeration, 2017, 38(5): 29-40.
18	Peng D Y, Robinson D B. A new two-constant equation of state[J]. Industrial & Engineering Chemistry Fundamentals, 1976, 15(1): 59-64.
19	Kwak T Y, Mansoori G A. van der Waals mixing rules for cubic equations of state. Applications for supercritical fluid extraction modelling[J]. Chemical Engineering Science, 1986, 41(5): 1303-1309.
20	胡芃, 高静轩, 陈龙祥, 等. PR方程结合vdW混合法则推算二元及三元HFC/HC混合工质汽液相平衡性质[J]. 化工学报, 2012, 63(2): 350-355.
	Hu P, Gao J X, Chen L X, et al. Prediction of vapor-liquid equilibria for binary and ternary HFC/HC mixtures using PR equation of state and vdW mixing rule[J]. CIESC Journal, 2012, 63(2): 350-355.
21	Wong D S H, Sandler S I. A theoretically correct mixing rule for cubic equations of state[J]. AIChE Journal, 1992, 38(5): 671-680.
22	Huron M J, Vidal J. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures[J]. Fluid Phase Equilibria, 1979, 3(4): 255-271.
23	Weidlich U, Gmehling J. A modified UNIFAC model. 1. Prediction of VLE, HE, and.gamma..infin[J]. Industrial & Engineering Chemistry Research, 1987, 26(7): 1372-1381.
24	Gmehling J, Li J D, Schiller M. A modified UNIFAC model. 2. Present parameter matrix and results for different thermodynamic properties[J]. Industrial & Engineering Chemistry Research, 1993, 32(1): 178-193.
25	Bobbo S, Camporese R, Scalabrin G. Isothermal vapour-liquid equilibrium measurements for the binary mixtures HFC-125+HFC-245fa and HC-290+HFC-245fa[J]. High Temperatures-High Pressures, 2000, 32(4): 441-447.
26	吴子睿, 孙瑞, 石凌峰, 等. CO₂混合工质的气液相平衡的混合规则对比与预测研究[J]. 化工学报, 2022, 73(4): 1483-1492.
	Wu Z R, Sun R, Shi L F, et al. A comparative and predictive study of the mixing rules for the vapor-liquid equilibria of CO₂-based mixtures[J]. CIESC Journal, 2022, 73(4): 1483-1492.
27	Chen C H, Su W, Xing L L, et al. A prediction model for the binary interaction parameter of PR-VDW to predict thermo-physical properties of CO₂ mixtures[J]. Fluid Phase Equilibria, 2023, 565: 113634.
28	Zhao Y X, Dong X Q, Zhong Q, et al. Modeling vapor liquid phase equilibrium for C _x H _y + C _x H _y F _z using Peng–Robinson and perturbed-chain SAFT[J]. Industrial & Engineering Chemistry Research, 2017, 56(25): 7384-7389.
29	Costa Cabral B J, Guedes R C, Pai-Panandiker R S, et al. Hydrogen bonding and the dipole moment of hydrofluorocarbons by density functional theory[J]. Physical Chemistry Chemical Physics, 2001, 3(19): 4200-4207.
30	Saha S, Rajput L, Joseph S, et al. IR spectroscopy as a probe for C—H⋯X hydrogen bonded supramolecular synthons[J]. CrystEngComm, 2015, 17(6): 1273-1290.
31	李懿伦, 袁耀锋, 叶克印. 全氟立方烷的笼状立体电子效应[J]. 大学化学, 2023, 38(11): 126-130.
	Li Y L, Yuan Y F, Ye K Y. Cage-type stereoelectronic effects of perfluorocubane[J]. University Chemistry, 2023, 38(11): 126-130.
32	Niksirat M, Aeenjan F, Khosharay S. Introducing hydrogen bonding contribution to the Patel-Teja thermal conductivity equation of state for hydrochlorofluorocarbons, hydrofluorocarbons and hydrofluoroolefins[J]. Journal of Molecular Liquids, 2022, 351: 118631.
33	Schmid B, Schedemann A, Gmehling J. Extension of the VTPR group contribution equation of state: group interaction parameters for additional 192 group combinations and typical results[J]. Industrial & Engineering Chemistry Research, 2014, 53(8): 3393-3405.
34	Schmid B, Gmehling J. Present status of the group contribution equation of state VTPR and typical applications for process development[J]. Fluid Phase Equilibria, 2016, 425: 443-450.
35	Bondi A. van der Waals volumes and radii[J]. The Journal of Physical Chemistry, 1964, 68(3): 441-451.

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