变阱宽方阱链流体状态方程预测制冷剂的热力学性质

doi:10.11949/0438-1157.20250932

摘要/Abstract

摘要：

借助基于二阶微扰理论和PY2近似积分方程建立的变阱宽方阱链流体状态方程（SWCF-VR）和先前获得的18种制冷剂分子参数，预测了纯制冷剂及其二元混合物在饱和相区的热容、焦汤系数、声速等热力学性质，并比较了原始SAFT-VR（SW）、PC-SAFT等模型预测效果。结果表明，SWCF-VR模型可满意预测纯制冷剂的上述各热力学性质，但受二阶导数精度影响，对热容预测偏差较大。和同类模型相比，SWCF-VR在多数热力学性质的预测性能要优于SAFT-VR和PC-SAFT。对二元混合物，引入基于汽液平衡实验数据获得的二元交互参数后，可显著改善模型预测性能。本文结果将为制冷剂的设计、复配及制冷过程设计优化提供参考。

关键词: 状态方程, 热力学性质, 制冷剂, 相平衡

Abstract:

Thermodynamic properties such as heat capacity, Joule-Thomson coefficient, and speed of sound of pure refrigerants and binary mixtures in the saturated phase region were predicted using the equation of state for square-well chain fluid with variable range (SWCF-VR), which was established based on the second-order perturbation theory and Chiew's PY2 approximate integral equations and the molecular parameters of the 18 refrigerants previously obtained. The prediction results of the original SAFT-VR(SW), PC-SAFT and other models were also compared. The results show that the SWCF-VR model can satisfactorily predict the above thermodynamic properties of pure refrigerants, though deviations in heat capacity are relatively large due to the accuracy limitations of second-order derivatives. Compared with similar models, the SWCF-VR model demonstrates superior predictive accuracy for most thermodynamic properties over SAFT-VR and PC-SAFT. For binary mixtures, the introduction of binary interaction parameters obtained from vapor-liquid equilibrium (VLE) experimental data can significantly improve the predictive performance of the model. The findings of this study will provide valuable insights for the design and blending of refrigerants, as well as the optimization of refrigeration process design.

Key words: equation of state, thermodynamic properties, refrigerant, phase equilibria

中图分类号:

TQ 013.1

贾玉倩, 李佳书, 孙逸, 刘英杰, 叶青, 李进龙. 变阱宽方阱链流体状态方程预测制冷剂的热力学性质[J]. 化工学报, DOI: 10.11949/0438-1157.20250932.

Yuqian JIA, Jiashu LI, Yi SUN, Yingjie LIU, Qing YE, Jinlong LI. Predicting thermodynamic properties of refrigerants using an equation of state for square-well chain fluid with variable range[J]. CIESC Journal, DOI: 10.11949/0438-1157.20250932.

图/表 14

表 1 热力学性质关系式

Table 1 The thermodynamic property formulae.

Thermodynamic property	formulae
Isochoric heat capacity	$C v = C p i d e a l - R - R T 2 ∂ a r e s ∂ T * η + T ∂ 2 a r e s ∂ T * 2 η # 2$
Isobaric heat capacity	$C P = C v + T * η 2 ⋅ R ⋅ ∂ P * ∂ T * η 2 ∂ P * ∂ η T * # 3$
Speed of sound	$u = C p C v ⋅ ε k ⋅ R ⋅ ∂ P * ∂ η T * # 4$
Joule-Thomson coefficient	$μ J T = 1 ρ C p ⋅ T * η ⋅ ∂ P * ∂ T * η ∂ P * ∂ η T * - 1 # 5$
Residual enthalpy	$H r e s R T = - T * ∂ a r e s ∂ T * η + Z - 1 # 6$
partial derivative of $P $ with respect to $T $	$∂ P * ∂ T * η = η T * ∂ Z ∂ T * η + Z # 7$
partial derivative of $P *$ with respect to $η$	$∂ P * ∂ η T * = T * η ∂ Z ∂ η T * + Z # 8$

表 1 热力学性质关系式

Table 1 The thermodynamic property formulae.

Thermodynamic property	formulae
Isochoric heat capacity	$C v = C p i d e a l - R - R T 2 ∂ a r e s ∂ T * η + T ∂ 2 a r e s ∂ T * 2 η # 2$
Isobaric heat capacity	$C P = C v + T * η 2 ⋅ R ⋅ ∂ P * ∂ T * η 2 ∂ P * ∂ η T * # 3$
Speed of sound	$u = C p C v ⋅ ε k ⋅ R ⋅ ∂ P * ∂ η T * # 4$
Joule-Thomson coefficient	$μ J T = 1 ρ C p ⋅ T * η ⋅ ∂ P * ∂ T * η ∂ P * ∂ η T * - 1 # 5$
Residual enthalpy	$H r e s R T = - T * ∂ a r e s ∂ T * η + Z - 1 # 6$
partial derivative of $P $ with respect to $T $	$∂ P * ∂ T * η = η T * ∂ Z ∂ T * η + Z # 7$
partial derivative of $P *$ with respect to $η$	$∂ P * ∂ η T * = T * η ∂ Z ∂ η T * + Z # 8$

表 2 纯制冷剂的各种热力学性质预测值与实验值的总体平均偏差

Table 2 AARD and AAD of predicted thermodynamic properties from experimental values for pure refrigerants

System	T/K	AARD (%)/AAD
			Vapor				Liquid
		H_vap	C_v	C_p	$μ J T$ ^*	u	C_v	C_p	$μ J T$ ^*	u
Average		4.14	10.1	13.9	1.93	2.50	16.5	6.60	0.007	11.7
R11	245~425	2.79	7.65	9.71	1.78	1.35	9.92	5.16	0.005	5.65
R12	175~351	2.85	6.62	8.28	1.37	1.19	11.9	7.66	0.006	7.31
R13	145~295	5.16	11.0	15.7	1.90	2.50	16.7	11.2	0.017	11.8
R14	130~220	0.94	8.84	10.7	0.08	1.14	18.7	4.43	0.011	5.57
R21	230~430	4.52	9.16	13.0	1.71	2.18	20.0	7.22	0.006	13.0
R22	210~350	5.01	12.7	17.3	1.12	2.55	18.5	5.21	0.006	10.7
R23	140~280	4.47	22.2	25.2	7.28	3.36	28.7	6.77	0.005	18.9
R32	190~340	7.31	25.6	30.7	3.57	4.72	30.3	3.92	0.006	33.9
R113	270~430	2.52	4.13	5.45	0.90	1.38	6.5	5.70	0.003	7.3
R114	280~400	4.36	4.78	9.30	0.45	3.18	6.0	4.24	0.009	9.5
R116	198~282	4.90	7.10	12.6	0.47	3.20	9.1	7.16	0.012	8.1
R123	230~434	4.36	5.88	9.12	1.67	2.54	9.5	6.59	0.007	10.0
R125	180~320	2.90	7.27	9.83	1.46	1.77	14.6	5.56	0.004	5.7
R134a	200~350	4.43	9.92	15.1	2.32	3.04	17.9	8.37	0.004	7.75
R142b	195~390	3.95	8.36	12.3	2.69	2.19	13.5	8.98	0.007	8.77
R143a	190~330	6.80	12.3	18.3	2.36	4.06	16.3	6.13	0.010	15.57
R152a	205~340	2.89	9.63	12.9	2.75	2.23	21.2	8.04	0.003	11.36
R161	200~350	4.44	9.00	14.0	0.95	2.46	27.0	7.24	0.008	20.01

表 2 纯制冷剂的各种热力学性质预测值与实验值的总体平均偏差

Table 2 AARD and AAD of predicted thermodynamic properties from experimental values for pure refrigerants

System	T/K	AARD (%)/AAD
			Vapor				Liquid
		H_vap	C_v	C_p	$μ J T$ ^*	u	C_v	C_p	$μ J T$ ^*	u
Average		4.14	10.1	13.9	1.93	2.50	16.5	6.60	0.007	11.7
R11	245~425	2.79	7.65	9.71	1.78	1.35	9.92	5.16	0.005	5.65
R12	175~351	2.85	6.62	8.28	1.37	1.19	11.9	7.66	0.006	7.31
R13	145~295	5.16	11.0	15.7	1.90	2.50	16.7	11.2	0.017	11.8
R14	130~220	0.94	8.84	10.7	0.08	1.14	18.7	4.43	0.011	5.57
R21	230~430	4.52	9.16	13.0	1.71	2.18	20.0	7.22	0.006	13.0
R22	210~350	5.01	12.7	17.3	1.12	2.55	18.5	5.21	0.006	10.7
R23	140~280	4.47	22.2	25.2	7.28	3.36	28.7	6.77	0.005	18.9
R32	190~340	7.31	25.6	30.7	3.57	4.72	30.3	3.92	0.006	33.9
R113	270~430	2.52	4.13	5.45	0.90	1.38	6.5	5.70	0.003	7.3
R114	280~400	4.36	4.78	9.30	0.45	3.18	6.0	4.24	0.009	9.5
R116	198~282	4.90	7.10	12.6	0.47	3.20	9.1	7.16	0.012	8.1
R123	230~434	4.36	5.88	9.12	1.67	2.54	9.5	6.59	0.007	10.0
R125	180~320	2.90	7.27	9.83	1.46	1.77	14.6	5.56	0.004	5.7
R134a	200~350	4.43	9.92	15.1	2.32	3.04	17.9	8.37	0.004	7.75
R142b	195~390	3.95	8.36	12.3	2.69	2.19	13.5	8.98	0.007	8.77
R143a	190~330	6.80	12.3	18.3	2.36	4.06	16.3	6.13	0.010	15.57
R152a	205~340	2.89	9.63	12.9	2.75	2.23	21.2	8.04	0.003	11.36
R161	200~350	4.44	9.00	14.0	0.95	2.46	27.0	7.24	0.008	20.01

图 1 (a) 制冷剂的蒸发焓 (Hvap ) 实验值和理论值对比；(b) 不同状态方程预测制冷剂蒸发焓 (Hvap ) 的对比

Fig. 1 (a) Comparison of experimental and theoretical values for refrigerant enthalpy of vaporization; (b) Comparison of enthalpy of vaporization predictions for refrigerants using different equations of state (Points represent experimental values provided by the NIST REFPROP 9.1 database, and lines represent prediction curves)

图 2 (a) 制冷剂的饱和气体的等压热容 (CpV) 实验值和理论值对比；(b) 制冷剂的饱和液体的等压热容 (CpL) 实验值和理论值对比

Fig. 2 (a) Comparison of experimental and theoretical values for saturated vapor isobaric heat capacity of refrigerants; (b) Comparison of experimental and theoretical values for saturated liquid isobaric heat capacity of refrigerants (Points represent experimental values provided by the NIST REFPROP 9.1 database, and lines represent prediction curves of SWCF-VR)

图 3 (a) 制冷剂的饱和气体的等容热容 (CvV) 实验值和理论值对比；(b) 制冷剂的饱和液体的等容热容 (CvL) 实验值和理论值对比

Fig. 3 (a) Comparison of experimental and theoretical values for saturated vapor isochoric heat capacity of refrigerants; (b) Comparison of experimental and theoretical values for saturated liquid isochoric heat capacity of refrigerants (Points represent experimental values provided by the NIST REFPROP 9.1 database, and lines represent prediction curves of SWCF-VR)

图 4 (a) 不同状态方程预测R14的饱和气体等压热容 (CpV) 的结果；(b) 不同状态方程预测R14的饱和液体等压热容 (CpL) 的结果

Fig. 4 (a) Results of saturated vapor isobaric heat capacity predictions for R14 using different equations of state; (b) Results of saturated liquid isobaric heat capacity predictions for R14 using different equations of state (Points represent experimental values provided by the NIST REFPROP 9.1 database, and lines represent prediction curves)

图 5 (a) 饱和气体的声速 (uV) 预测曲线与实验值对比；(b) 饱和液体的声速 (uL) 预测曲线与实验值对比

Fig. 5 (a) Comparison of saturated vapor speed of sound prediction curves and experimental values; (b) Comparison of saturated liquid speed of sound prediction curves and experimental values (Points represent experimental values provided by the NIST REFPROP 9.1 database, and lines represent prediction curves of SWCF-VR)

图 6 (a) R14的饱和气体声速 (uV) 预测曲线对比；(b) R14的饱和液体声速 (uL) 预测曲线对比

Fig.6 (a) Comparison of saturated vapor speed of sound prediction curves for R14; (b) Comparison of saturated liquid speed of sound prediction curves for R14 (Points represent experimental values provided by the NIST REFPROP 9.1 database, and lines represent prediction curves)

图 7 (a) R14的饱和焦汤系数 (μJT ) 预测曲线对比；(b) R116的饱和焦汤系数 (μJT ) 预测曲线对比

Fig. 7 (a) Comparison of saturated Joule-Thomson coefficient prediction curves for R14; (b) Comparison of saturated Joule-Thomson coefficient prediction curves for R116 (Points represent experimental values provided by the NIST REFPROP 9.1 database, and lines represent prediction curves)

表 3 混合物制冷剂的各种热力学性质预测值与实验值的总体平均偏差

Table 3 AARD and AAD of predicted thermodynamic properties from experimental values for refrigerant mixture

System	T/K	P/bar	$κ i j$	AARD (%)/AAD
				y_pre^*	P_pre	Vapor				Liquid
				y_pre^*	P_pre	C_v	C_p	$μ J T$ ^*	u	C_v	C_p	$μ J T$ ^*	u
Average				0.0298	2.68	11.7	18.3	0.69	3.08	13.4	3.66	0.006	13.9
R123+R134a	250~300	0.97~7.02	0.0523	0.0264	4.65	6.65	8.33	1.64	0.72	14.2	8.53	0.004	6.54
R22+R12	343~350	18.7~34.4	0.0290	0.0255	0.75	16.4	30.0	0.27	5.50	11.9	1.85	0.002	21.6
R22+R123	320~350	1.92-34.42	0.0716	0.0248	0.66	10.6	14.8	0.43	1.62	10.6	3.29	0.008	4.23
R23+R116	200~250	1.64~14.74	0.0667	0.0978	9.00	14.5	18.7	0.86	2.24	16.1	6.27	0.005	13.3
R125+R134a	290~320	4.7~23.6	0.0071	0.0292	2.65	11.5	19.2	0.57	3.68	13.4	2.58	0.006	9.84
R143a+R152a	300~320	6.29~21.4	0	0.0146	0.36	14.2	22.7	0.72	5.21	14.7	2.21	0.006	21.7
R125+R143a	290-320	10.42~22.8	0	0.0089	1.80	14.1	25.4	0.56	5.86	13.0	1.75	0.014	21.5
R125+R161	290~320	7.35~23.6	0	0.0335	2.73	11.1	18.5	0.52	1.90	16.6	1.39	0.006	20.4
R11+R12	250~350	0.13~21.96	0.0124	0.0077	1.56	6.0	7.30	0.68	0.95	9.83	5.10	0.005	5.74

表 3 混合物制冷剂的各种热力学性质预测值与实验值的总体平均偏差

Table 3 AARD and AAD of predicted thermodynamic properties from experimental values for refrigerant mixture

System	T/K	P/bar	$κ i j$	AARD (%)/AAD
				y_pre^*	P_pre	Vapor				Liquid
				y_pre^*	P_pre	C_v	C_p	$μ J T$ ^*	u	C_v	C_p	$μ J T$ ^*	u
Average				0.0298	2.68	11.7	18.3	0.69	3.08	13.4	3.66	0.006	13.9
R123+R134a	250~300	0.97~7.02	0.0523	0.0264	4.65	6.65	8.33	1.64	0.72	14.2	8.53	0.004	6.54
R22+R12	343~350	18.7~34.4	0.0290	0.0255	0.75	16.4	30.0	0.27	5.50	11.9	1.85	0.002	21.6
R22+R123	320~350	1.92-34.42	0.0716	0.0248	0.66	10.6	14.8	0.43	1.62	10.6	3.29	0.008	4.23
R23+R116	200~250	1.64~14.74	0.0667	0.0978	9.00	14.5	18.7	0.86	2.24	16.1	6.27	0.005	13.3
R125+R134a	290~320	4.7~23.6	0.0071	0.0292	2.65	11.5	19.2	0.57	3.68	13.4	2.58	0.006	9.84
R143a+R152a	300~320	6.29~21.4	0	0.0146	0.36	14.2	22.7	0.72	5.21	14.7	2.21	0.006	21.7
R125+R143a	290-320	10.42~22.8	0	0.0089	1.80	14.1	25.4	0.56	5.86	13.0	1.75	0.014	21.5
R125+R161	290~320	7.35~23.6	0	0.0335	2.73	11.1	18.5	0.52	1.90	16.6	1.39	0.006	20.4
R11+R12	250~350	0.13~21.96	0.0124	0.0077	1.56	6.0	7.30	0.68	0.95	9.83	5.10	0.005	5.74

图 8(a) R22+R123体系的二元汽液平衡相图；(b) R143a+R152a体系的二元汽液平衡相图

Fig. 8(a) Vapor-liquid equilibrium (VLE) phase diagram for the R22 + R123 system (The solid line represents predictions with fitted binary interaction parameters, the dashed line denotes predictions without fitted binary interaction parameters, and the scattered points are experimental data); (b) Vapor-liquid equilibrium (VLE) phase diagram for the R143a + R152a system

图 9 R11+R12体系的混合液体声速 (uL) 与混合气体声速 (uV) 预测结果

Fig. 9 Predicted mixing saturated speed of sound for the R11+R12 (Solid lines represent liquid-phase results, while dashed lines represent vapor-phase results. The three lines correspond to temperatures of 250 K, 300 K, and 350 K, respectively)

图 10 R22+R123体系在320 K下的混合热容预测结果

Fig. 10 Predicted results of mixing saturated heat capacity for the R22 + R123 system at 320 K (The curves represent predicted values, while the scattered points denote experimental data. Cp is the isobaric heat capacity, Cv is the isochoric heat capacity, V denotes vapor phase, and L denotes liquid phase)

图 11(a) R22+R12体系在350 K下的混合焦汤系数 (μJT ) 预测结果；(b) R123+R134a体系在350 K下的混合焦汤系数(μJT ) 预测结果

Fig. 11(a) Predicted mixing saturated Joule-Thomson coefficient for the R22+R12 at 350 K; (b) Predicted mixing saturated Joule-Thomson coefficient for the R123+R134a at 350 K (Solid lines represent gas-phase results, while dashed lines represent liquid-phase results)

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