低GWP制冷剂与润滑油混合物的相平衡关联与预测

doi:10.11949/0438-1157.20250592

化工学报 ›› 2025, Vol. 76 ›› Issue (11): 5828-5841.DOI: 10.11949/0438-1157.20250592

• 热力学 • 上一篇

低GWP制冷剂与润滑油混合物的相平衡关联与预测

王慧荣¹(), 孙玲玲¹, 戚文端², 胡熠暹², 邵艳坡², 杨智³, 赵延兴⁴()

^1.河南科技大学车辆与交通工程学院，河南洛阳 471003
^2.广东美的制冷设备有限公司，广东佛山 528311
^3.广东工业大学材料与能源学院，广东广州 510006
^4.中国科学院理化技术研究所，北京 100190

收稿日期:2025-06-03 修回日期:2025-08-04 出版日期:2025-11-25 发布日期:2025-12-19
通讯作者: 赵延兴
作者简介:王慧荣（1991—），女，博士，讲师，hrwang@haust.edu.cn
基金资助:
国家自然科学基金项目(52322602);国家自然科学基金项目(52036010)

Correlation and prediction of phase equilibria for mixtures of low-GWP refrigerants with lubricants

Huirong WANG¹(), Lingling SUN¹, Wenduan QI², Yixian HU², Yanpo SHAO², Zhi YANG³, Yanxing ZHAO⁴()

^1.College of Vehicle and Traffic Engineering, Henan University of Science and Technology, Luoyang 471003, Henan, China
^2.Guangdong Midea Refrigeration Equipment Co. , Ltd. , Foshan 528311, Guangdong, China
^3.College of Materials and Energy, Guangdong University of Technology, Guangzhou 510006, Guangdong, China
^4.Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China

Received:2025-06-03 Revised:2025-08-04 Online:2025-11-25 Published:2025-12-19
Contact: Yanxing ZHAO

摘要/Abstract

摘要：

制冷剂与润滑油所形成的混合物存在于制冷系统各部件中，其相平衡特性对热力循环及部件的设计优化具有重要意义。采用基于统计缔合流体理论的PC-SAFT状态方程，对R1234yf、R600a、R744等7种低GWP制冷剂与润滑油PEC4~PEC9的二元混合物气液相平衡进行计算，结果显示PC-SAFT模型与实验结果一致性较好，计算的平均压力偏差绝大部分在6%以内。同时，为进一步拓展模型对复杂多元混合物相平衡的预测性能，采用BP神经网络模型对PC-SAFT状态方程的二元交互参数进行训练，并将预测得到的二元交互参数用于缺乏实验数据的二元体系R1233zd（E）/PEC润滑油、多组分的复杂体系R744/POE润滑油和R290/POE润滑油的相平衡计算。采用神经网络模型预测得到的k_ij 对多组分复杂体系进行预测对比，平均压力偏差为8.99%，可用于实际工程计算。

关键词: 制冷剂, 润滑油, 相平衡, 混合物, PC-SAFT, BP神经网络

Abstract:

The mixture formed by refrigerants and lubricating oils is present in various components of the refrigeration system, and its phase equilibrium characteristics are of significant importance for the design optimization of thermodynamic cycles and components. Using the PC-SAFT state equation based on statistical associating fluid theory, the gas-liquid phase equilibrium of binary mixtures of seven low-GWP refrigerants such as R1234yf, R600a, R744, etc., with lubricating oils PEC4—PEC9 was calculated. The results show that the PC-SAFT model has good consistency with experimental results, and the average pressure deviation is mostly within 6%. Meanwhile, to further expand the model's predictive performance for complex multicomponent mixture phase equilibrium, a BP neural network model was used to train the binary interaction parameters of the PC-SAFT state equation, and the predicted binary interaction parameters were used for the phase equilibrium calculation of binary systems lacking experimental data, such as R1233zd(E)/PEC lubricating oil, multicomponent complex systems R744/POE lubricating oil, and R290/POE lubricating oil. The k_ij predicted by the neural network model was used to predict these complex multicomponent systems, with an average pressure deviation of 8.99%, indicating its applicability to practical engineering calculations.

Key words: refrigerant, lubricant oil, phase equilibria, mixtures, PC-SAFT, BP neural network

中图分类号:

TK 121

王慧荣, 孙玲玲, 戚文端, 胡熠暹, 邵艳坡, 杨智, 赵延兴. 低GWP制冷剂与润滑油混合物的相平衡关联与预测[J]. 化工学报, 2025, 76(11): 5828-5841.

Huirong WANG, Lingling SUN, Wenduan QI, Yixian HU, Yanpo SHAO, Zhi YANG, Yanxing ZHAO. Correlation and prediction of phase equilibria for mixtures of low-GWP refrigerants with lubricants[J]. CIESC Journal, 2025, 76(11): 5828-5841.

图/表 20

图1 BP神经网络的拓扑结构

Fig.1 Topology of BP neural network

表1 低GWP制冷剂与PECs润滑油的相平衡实验数据集

Table 1 Experimental data set on the phase equilibria of low-GWP refrigerants with PECs lubricants

制冷剂	润滑油	实验数据点数(等温组数)	温度/K	压力/MPa	文献
R1233zd(E)	PEC4	42 (6)	298~343	0.037~0.37	[7]
	PEC6	36 (6)	298~343	0.043~0.249	[7]
	PEC8	42 (6)	298~343	0.05~0.277	[7]
R1234yf	PEC4	63 (7)	293~348	0.066~2.071	[19]
	PEC5	63 (7)	293~348	0.079~2.087	[19]
	PEC6	63 (7)	293~348	0.075~2.079	[10]
	PEC7	63 (7)	293~348	0.078~2.04	[10]
	PEC8	63 (7)	293~348	0.083~2.088	[10]
	PEC9	49 (7)	293~348	0.179~1.689	[5]
R1234ze(E)	PEC4	56 (7)	293~353	0.054~1.81	[19]
	PEC5	72 (8)	283~353	0.045~1.80	[20]
	PEC6	56 (8)	283~353	0.05~1.795	[21]
	PEC7	64 (8)	283~353	0.054~1.897	[22]
	PEC8	56 (8)	283~353	0.06~1.86	[21]
	PEC9	56 (8)	283~353	0.059~1.856	[22]
R1243zf	PEC4	56 (8)	278~343	0.081~0.974	[23]
	PEC5	56 (8)	278~343	0.081~0.975	[23]
	PEC6	56 (8)	278~343	0.088~0.973	[6]
	PEC7	53 (8)	278~343	0.091~0.98	[24]
	PEC8	56 (8)	278~343	0.09~0.981	[6]
	PEC9	51 (8)	278~343	0.099~0.992	[24]
R600a	PEC4	49 (7)	293~348	0.054~1.013	[25]
	PEC5	49 (7)	293~348	0.070~1.031	[26]
	PEC6	49 (7)	293~348	0.048~0.995	[25]
	PEC7	49 (7)	293~348	0.056~0.967	[26]
	PEC8	49 (7)	293~348	0.047~0.994	[25]
	PEC9	49 (7)	293~348	0.089~0.989	[5]
RE170	PEC4	64 (8)	283~353	0.057~1.836	[27]
	PEC5	64 (8)	283~353	0.060~1.808	[27]
	PEC6	64 (8)	283~353	0.071~1.807	[28]
	PEC7	56 (7)	293~348	0.074~1.831	[29]
	PEC8	64 (8)	283~353	0.082~1.807	[28]
	PEC9	56 (7)	293~348	0.078~1.897	[29]
R744	PEC4	83 (8)	243~343	0.754~9.555	[4]
	PEC5	51 (7)	283~333	0.887~6.387	[30]
	PEC6	91 (8)	243~343	0.767~9.821	[31]
	PEC7	55 (8)	283~348	0.834~7.501	[32]
	PEC8	56 (5)	273~343	0.25~9.70	[33]
	PEC9	32 (7)	283~333	1.145~7.321	[32]

表2 制冷剂与PECs润滑油的相平衡实验扩充数据集

Table 2 Extended experimental data set for the phase equilibria of refrigerants with PECs lubricants

制冷剂	润滑油	文献	实验数据点数(等温组数)	温度/K	压力/MPa
R32	PEC5	[3]	28 (4)	303~363	0.007~1.795
	PEC9	[34]	28 (4)	303~363	0.203~1.937
R125	PEC5	[3]	30 (4)	303~363	0.073~1.897
	PEC9	[34]	28 (4)	303~363	0.093~2.104
R134a	PEC5	[3]	28 (4)	303~363	0.052~1.065
	PEC9	[34]	28 (4)	303~363	0.104~1.218
R143a	PEC5	[3]	28 (4)	303~363	0.088~1.843
	PEC9	[34]	28 (4)	303~363	0.135~1.974
R152a	PEC5	[3]	24 (4)	303~363	0.058~0.904
	PEC9	[34]	28 (4)	303~363	0.151~1.022

表3 制冷剂和PECs润滑油的PC-SAFT参数

Table 3 PC-SAFT parameters for refrigerants and PECs lubricants

流体	m	σ/Å	（ε/k）/K	MW/(g/mol)	μ/D	文献
R1233zdE	3.2449	3.3483	198.5	130.5	1.12	[36]
R1234yf	2.834	3.364	168.2	114.04	2.24	[14]
R1234zeE	3.294	3.165	171.2	114.04	1.13	[14]
R1243zf	2.544	3.457	178.242	96.05	2.43	本文^①
R600a	2.2616	3.7574	216.53	58.123	0	[15]
RE170	2.3071	3.2528	211.06	46.069	0	[15]
R744	2.5968	2.5503	151.24	44.01	0	[39]
R32	2.472	2.797	161.7	52.02	1.978	[35]
R125	3.147	3.12	153.7	120.02	1.563	[35]
R134a	3.262	3.002	162.1	102	2.058	[14]
R143a	2.516	3.268	160.184	84.04	2.34	本文^①
R152a	2.628	3.128	179.001	66.05	2.262	本文^①
PEC4	9.949	3.825	254.602	416.51	0	[12]
PEC5	10.533	3.972	261.81	472.61	0	[38]
PEC6	11.28	4.07	266.545	528.72	0	[12]
PEC7	12.104	4.141	269.99	584.83	0	[38]
PEC8	12.611	4.244	275.966	640.93	0	[12]
PEC9	12.893	4.364	284.83	697.05	0	[38]

表4 采用PC-SAFT计算的制冷剂与PECs二元混合物的压力偏差

Table 4 Pressure deviations of refrigerants with PECs binary mixtures calculated by PC-SAFT

工质	AARD(p)/%
工质	PEC4	PEC5	PEC6	PEC7	PEC8	PEC9	均值
R1233zdE	3.38	—	1.99	—	2.49	—	2.62
R1234yf	2.02	1.68	2.33	2.09	4.12	1.67	2.32
R1234zeE	1.48	1.95	2.11	2.6	2.74	3.27	2.36
R1243zf	3.54	4.28	4.59	4.76	5.15	5.18	4.58
R600a	0.69	1.15	1.86	1.59	2.84	3.69	1.97
RE170	3.56	3.02	4.49	3.54	5.92	4.39	4.15
R744	4.37	3.6	5.35	8.25	6.55	3.98	5.35
均值	2.72	2.61	3.24	3.80	4.26	3.70

图2 采用PC-SAFT模型计算的压力和实验值的比较

Fig.2 Comparison of calculated pressures with experimental values using the PC-SAFT model

图3 303.15 K下PC-SAFT计算制冷剂在不同PEC中的溶解度与实验值比较

Fig.3 Comparison of solubility of refrigerants in different PECs at 303.15 K with experimental values

图4 PC-SAFT计算的不同制冷剂在PEC5中的溶解度与实验值比较

Fig.4 Comparison of the solubility for different refrigerants in PEC5 with experimental values

图5 基于实验值回归得到PC-SAFT的二元交互参数

Fig.5 Regressed binary interaction parameters for PC-SAFT based on experimental values

表5 基于实验值线性回归得到的制冷剂与PECs二元混合物kij 的系数

Table 5 Coefficients of the linear regression obtained based on the experimental values of the refrigerant and PECs binary mixtures kij

工质	$k i j = α 1 + α 2 M W + α 3 T$			R²
工质	$α 1$	$α 2$	$α 3$	R²
R1233zdE	-0.03876	7.99×10^-5	2.59×10^-5	0.95618
R1234yf	-0.07829	1.38×10^-4	1.05×10^-4	0.99144
R1234zeE	-0.11221	1.80×10^-4	1.85×10^-4	0.99768
R1243zf	-0.0891	1.20×10^-4	8.07×10^-5	0.99686
R600a	0.03475	-2.65×10^-5	5.84×10^-6	0.52775
RE170	-0.04461	7.68×10^-5	7.57×10^-5	0.89349
R744	-0.04398	2.34×10^-4	1.32×10^-4	0.93748

表5 基于实验值线性回归得到的制冷剂与PECs二元混合物kij 的系数

Table 5 Coefficients of the linear regression obtained based on the experimental values of the refrigerant and PECs binary mixtures kij

工质	$k i j = α 1 + α 2 M W + α 3 T$			R²
工质	$α 1$	$α 2$	$α 3$	R²
R1233zdE	-0.03876	7.99×10^-5	2.59×10^-5	0.95618
R1234yf	-0.07829	1.38×10^-4	1.05×10^-4	0.99144
R1234zeE	-0.11221	1.80×10^-4	1.85×10^-4	0.99768
R1243zf	-0.0891	1.20×10^-4	8.07×10^-5	0.99686
R600a	0.03475	-2.65×10^-5	5.84×10^-6	0.52775
RE170	-0.04461	7.68×10^-5	7.57×10^-5	0.89349
R744	-0.04398	2.34×10^-4	1.32×10^-4	0.93748

图6 基于实验值线性回归得到的kij 与实验计算值的比较

Fig.6 Comparison of kij obtained from linear regression with experimental calculated values

图7 BP神经网络预测模型输入参数的Pearson相关性分析

Fig.7 Pearson correlation analysis of input parameters in BP neural network prediction model

图8 二元交互参数kij 的预测模型训练结果和实验值计算的比较

Fig.8 Comparison of the predicted model training results and the experimental values calculated for the kij

图9 基于BP预测模型计算的不同制冷剂在PEC中的溶解度与实验值比较

Fig.9 Comparison of the solubility in PEC calculated based on the BP prediction model for different refrigerants with experimental values

表6 基于不同二元交互参数的PC-SAFT方程计算的压力偏差比较

Table 6 Comparison of calculated pressure deviations based on the PC-SAFT equation with different binary interaction parameters

工质/润滑油	AARD(p) /% @303.15K
工质/润滑油	实验计算	线性回归	BP预测	实验计算	线性回归	BP预测
R1233zdE/PEC4	4.19	4.26	4.32	3.36	4.01	3.54
R600a/PEC6	2.71	4.24	3.02	1.86	3.42	2.11
R744/PEC8	9.02	9.58	9.12	5.94	8.44	6.42

表7 线性回归与BP预测得到的R1233zdE/PEC二元交互参数比较

Table 7 Comparison of R1233zdE / PEC binary interaction parameters obtained by linear regression and BP prediction

温度/K	PEC5
温度/K	线性回归	BP预测	线性回归	BP预测	线性回归	BP预测
298.15	0.00674	0.00554	0.01571	0.01629	0.02469	0.02096
303.15	0.00687	0.00623	0.01584	0.01748	0.02482	0.022
313.15	0.00713	0.00716	0.0161	0.01892	0.02508	0.02372
323.15	0.00739	0.00774	0.01636	0.01916	0.02534	0.02487
333.15	0.00765	0.00832	0.01662	0.01851	0.02559	0.02549
343.15	0.00791	0.00912	0.01688	0.01742	0.02585	0.02586

表8 本文采用的R290及多元POE润滑油的PC-SAFT参数

Table 8 PC-SAFT parameters of R290 and multivariate POE lubricant oils employed in this work

工质及润滑油	m	σ/Å	(ε/k)/K	MW/(g/mol)	文献
R290	2.002	3.6184	208.11	44.096	[15]
POE22	8.3216	4.677	321.08	540.6	[43]
POE68	11.1356	4.7572	301.87	760	[44]
POE75	7.0401	4.3303	270.4842	417.682	本文^①

图10 基于BP神经网络预测的kij 值和实验值计算的比较

Fig.10 Comparison of kij calculated based on BP neural network prediction and experimental values

图11 基于BP预测模型计算的制冷剂在POE中的溶解度与实验值比较

Fig.11 Comparison of the solubility of refrigerants in POE calculated based on the BP prediction model and experimental values

表9 基于不同二元交互参数的PC-SAFT方程计算的压力偏差比较

Table 9 Comparison of calculated pressure deviations based on the PC-SAFT equation with different binary interaction parameters

工质/润滑油	AARD(p) /% @Average
工质/润滑油	实验计算	线性回归	k_ij =0	BP预测
R744/POE68	5.91	11.66	—	7.14
R290/POE22	5.92	16.64	33.81	7.99
R290/POE75	2.14	28.76	44.15	11.83

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低GWP制冷剂与润滑油混合物的相平衡关联与预测

Correlation and prediction of phase equilibria for mixtures of low-GWP refrigerants with lubricants

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