Evaluation of vapor-liquid equilibrium models for mixtures containing HFOs

doi:10.11949/0438-1157.20230386

Abstract

Abstract:

As the new environmentally friendly working fluid, HFOs have low global warming potential but are limited by their thermal performance and flammability. Mixtures containing HFOs can achieve complementary advantages and have good application prospects. Vapor-liquid equilibrium is the most basic thermodynamic property for the mixtures. To calculate the property of vapor-liquid equilibrium, the commonly-used PR equation of state, three mixing rules of vdW, HV and WS, and two activity coefficient models of NRTL and Wilson are selected to establish four theoretical models of PR-vdW, PR-HV-NRTL, PR-WS-NRTL and PR-WS-Wilson. Four sets of theoretical models were used to compare and evaluate the calculation performance of the vapor-liquid phase equilibrium of binary systems such as HFC+HFO, HC+HFO, and CO₂+HFO, and further analyzed the calculation effect and the ability to predict the phase equilibrium of the ternary system. The results indicate that the PR-vdW model has stable and good calculation performance for most mixtures. The PR-WS-NRTL and PR-WS-Wilson models have excellent calculation performance but cannot perform stalely enough for predicting the critical properties locus and the ternary vapor-liquid equilibrium. The PR-HV-NRTL model has good performance for predicting the ternary equilibrium.

Key words: HFO, vapor-liquid equilibrium, mixture, mixing rules, activity coefficient, critical properties locus

摘要：

HFO类新型环保工质具有很低的全球变暖潜能，但受限于热工性能且具有可燃性。含HFO的混合工质可实现优势互补，具有良好的应用前景。气液相平衡是混合物最基本的热力性质，其理论模型极为重要。选取PR状态方程，vdW、HV、WS三种混合规则和NRTL、Wilson两种活度系数模型，构建了PR-vdW、PR-HV-NRTL、PR-WS-NRTL和PR-WS-Wilson共4套理论模型，对HFC+HFO、HC+HFO、CO₂+HFO类二元体系气液相平衡的计算性能进行了比较和评价，并进一步分析了模型对含超临界组元体系的计算效果和对三元体系相平衡预测能力。结果表明PR-vdW模型计算性能稳定，对大多数体系计算性能优良；PR-WS-NRTL模型和PR-WS-Wilson模型性能优秀，但预测混合体系临界轨迹线和三元相平衡时稳定性不够好，PR-HV-NRTL模型预测三元相平衡时性能良好。

关键词: HFO, 汽液平衡, 混合物, 混合规则, 活度系数, 临界轨迹

CLC Number:

TK 121

Erqi WANG, Shuzhou PENG, Zhen YANG, Yuanyuan DUAN. Evaluation of vapor-liquid equilibrium models for mixtures containing HFOs[J]. CIESC Journal, 2023, 74(8): 3216-3225.

汪尔奇, 彭书舟, 杨震, 段远源. 含HFO混合体系气液相平衡的理论模型评价[J]. 化工学报, 2023, 74(8): 3216-3225.

Figures/Tables 10

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序号	二元体系	类型	ARD(p)/%
			沿等温线关联				温度无关关联
			PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson	PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson
HFC+HFO
1	R125+R1234yf^[19]	Z	0.60	0.59	0.57	0.56	0.71	0.71	0.69	0.69
2	R125+R1243zf^[20]	Z	0.20	0.19	0.19	0.19	0.21	0.20	0.20	0.20
3	R134+R1234ze(E)^[21]	A	0.20	0.21	0.20	0.20	0.23	0.21	0.21	0.21
4	R134+R1234ze(Z)^[22]	A	0.51	0.41	0.35	0.36	4.71	5.57	4.55	5.61
5	R134a+R1234yf^[19]	A	0.38	0.32	0.32	0.32	0.46	0.55	0.33	0.35
6	R134a+R1234ze(E)^[23]	Z	0.39	0.44	0.42	0.22	0.62	0.71	0.44	0.34
7	R134a+R1243zf^[24]	A	0.31	0.29	0.29	0.28	0.45	0.38	0.36	0.36
8	R134a+R1336mzz(E)^[25]	Z	0.54	0.35	0.32	0.34	0.58	0.46	0.42	0.54
9	R143a+R1234yf^[26]	Z	0.33	0.28	0.28	0.29	0.47	0.48	0.39	0.47
10	R152a+R1234yf^[27]	A	0.29	0.25	0.25	0.23	0.31	0.40	0.26	0.28
11	R152a+R1234ze(E)^[28]	Z	0.19	0.18	0.14	0.14	0.23	0.18	0.18	0.18
12	R152a+R1243zf^[29]	A	0.16	0.16	0.16	0.15	0.19	0.26	0.26	0.17
13	R152a+R1336mzz(E)^[25]	Z	0.76	0.29	0.28	0.27	0.78	0.46	0.39	0.61
14	R161+R1234yf^[30]	Z	0.23	0.21	0.21	0.20	0.28	0.34	0.22	0.29
15	R161+R1234ze(E)^[31]	Z	0.27	0.29	0.24	0.22	0.27	0.30	0.24	0.26
16	R161+R1336mzz(E)^[32]	Z	0.90	0.72	0.70	0.68	1.12	1.03	0.93	1.00
17	R227ea+R1234yf^[33]	Z	0.36	0.33	0.33	0.34	0.38	0.37	0.34	0.35
18	R227ea+R1336mzz(E)^[25]	Z	0.19	0.19	0.13	0.12	0.21	0.25	0.15	0.16
19	R23+R1234yf^[34]	Z	2.12	1.48	1.05	0.93	2.30	2.30	2.07	2.13
20	R245cb+R1234yf^[35]	Z	0.34	0.41	0.41	0.42	0.53	0.54	0.71	0.69
21	R32+R1234yf^[30]	Z	0.73	0.35	0.32	0.32	0.73	0.60	0.51	0.77
22	R32+R1234yf^[36]	C	1.16	1.07	0.40	0.42	1.36	1.33	0.74	0.96
23	R32+R1234ze(E)^[26]	Z	0.85	0.69	0.71	0.76	0.87	0.83	0.84	0.85
24	R32+R1234ze(E)^[37]	Z	0.65	0.38	0.40	0.40	0.67	0.43	0.43	0.46
25	R32+R1336mzz(E)^[32]	Z	1.09	1.02	0.94	0.94	1.14	1.15	1.10	1.11
HC+HFO
26	R170+R1234ze(E)^[38]	C	0.60	0.37	0.31	0.26	0.99	0.96	0.63	1.11
27	R290+R1234yf^[39]	A	0.18	0.15	0.13	0.11	0.25	0.50	0.16	0.86
28	R290+R1234ze(E)^[40]	A	0.38	0.31	0.25	0.23	0.39	0.60	0.30	0.96
29	R290+R1234ze(Z)^[41]	A	1.29	0.70	0.56	0.53	1.42	1.47	0.93	2.34
30	R290+R1243zf^[42]	A	0.41	0.23	0.21	0.18	0.44	0.56	0.29	0.87
31	R290+R1336mzz(E)^[28]	Z	0.55	0.25	0.18	0.30	0.60	0.76	0.30	0.91
32	R600+R1234yf^[43]	A	2.73	0.80	0.78	0.86	2.73	1.12	0.95	1.41
33	R600a+R1234yf^[44]	A	0.63	0.30	0.30	0.30	0.65	0.75	0.39	0.95
34	R600a+R1234ze(E)^[45]	A	0.48	0.21	0.19	0.16	0.55	0.52	0.19	0.95
35	R600a+R1234ze(Z)^[46]	A	0.72	0.42	0.39	0.39	0.75	1.13	0.64	1.57
CO₂+HFO
36	CO₂+R1234yf^[47]	C	1.11	0.91	0.52	0.52	1.12	1.44	0.90	0.96
37	CO₂+R1234yf^[48]	C	2.77	1.67	0.42	0.38	2.88	2.94	1.28	1.35
38	CO₂+R1234ze(E)^[49]	C	1.02	1.08	0.95	1.00	1.72	1.35	1.58	1.47
39	CO₂+R1243zf^[47]	C	0.76	0.64	0.30	0.28	1.19	0.74	0.52	0.47

序号	二元体系	类型	ARD(p)/%
			沿等温线关联				温度无关关联
			PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson	PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson
HFC+HFO
1	R125+R1234yf^[19]	Z	0.60	0.59	0.57	0.56	0.71	0.71	0.69	0.69
2	R125+R1243zf^[20]	Z	0.20	0.19	0.19	0.19	0.21	0.20	0.20	0.20
3	R134+R1234ze(E)^[21]	A	0.20	0.21	0.20	0.20	0.23	0.21	0.21	0.21
4	R134+R1234ze(Z)^[22]	A	0.51	0.41	0.35	0.36	4.71	5.57	4.55	5.61
5	R134a+R1234yf^[19]	A	0.38	0.32	0.32	0.32	0.46	0.55	0.33	0.35
6	R134a+R1234ze(E)^[23]	Z	0.39	0.44	0.42	0.22	0.62	0.71	0.44	0.34
7	R134a+R1243zf^[24]	A	0.31	0.29	0.29	0.28	0.45	0.38	0.36	0.36
8	R134a+R1336mzz(E)^[25]	Z	0.54	0.35	0.32	0.34	0.58	0.46	0.42	0.54
9	R143a+R1234yf^[26]	Z	0.33	0.28	0.28	0.29	0.47	0.48	0.39	0.47
10	R152a+R1234yf^[27]	A	0.29	0.25	0.25	0.23	0.31	0.40	0.26	0.28
11	R152a+R1234ze(E)^[28]	Z	0.19	0.18	0.14	0.14	0.23	0.18	0.18	0.18
12	R152a+R1243zf^[29]	A	0.16	0.16	0.16	0.15	0.19	0.26	0.26	0.17
13	R152a+R1336mzz(E)^[25]	Z	0.76	0.29	0.28	0.27	0.78	0.46	0.39	0.61
14	R161+R1234yf^[30]	Z	0.23	0.21	0.21	0.20	0.28	0.34	0.22	0.29
15	R161+R1234ze(E)^[31]	Z	0.27	0.29	0.24	0.22	0.27	0.30	0.24	0.26
16	R161+R1336mzz(E)^[32]	Z	0.90	0.72	0.70	0.68	1.12	1.03	0.93	1.00
17	R227ea+R1234yf^[33]	Z	0.36	0.33	0.33	0.34	0.38	0.37	0.34	0.35
18	R227ea+R1336mzz(E)^[25]	Z	0.19	0.19	0.13	0.12	0.21	0.25	0.15	0.16
19	R23+R1234yf^[34]	Z	2.12	1.48	1.05	0.93	2.30	2.30	2.07	2.13
20	R245cb+R1234yf^[35]	Z	0.34	0.41	0.41	0.42	0.53	0.54	0.71	0.69
21	R32+R1234yf^[30]	Z	0.73	0.35	0.32	0.32	0.73	0.60	0.51	0.77
22	R32+R1234yf^[36]	C	1.16	1.07	0.40	0.42	1.36	1.33	0.74	0.96
23	R32+R1234ze(E)^[26]	Z	0.85	0.69	0.71	0.76	0.87	0.83	0.84	0.85
24	R32+R1234ze(E)^[37]	Z	0.65	0.38	0.40	0.40	0.67	0.43	0.43	0.46
25	R32+R1336mzz(E)^[32]	Z	1.09	1.02	0.94	0.94	1.14	1.15	1.10	1.11
HC+HFO
26	R170+R1234ze(E)^[38]	C	0.60	0.37	0.31	0.26	0.99	0.96	0.63	1.11
27	R290+R1234yf^[39]	A	0.18	0.15	0.13	0.11	0.25	0.50	0.16	0.86
28	R290+R1234ze(E)^[40]	A	0.38	0.31	0.25	0.23	0.39	0.60	0.30	0.96
29	R290+R1234ze(Z)^[41]	A	1.29	0.70	0.56	0.53	1.42	1.47	0.93	2.34
30	R290+R1243zf^[42]	A	0.41	0.23	0.21	0.18	0.44	0.56	0.29	0.87
31	R290+R1336mzz(E)^[28]	Z	0.55	0.25	0.18	0.30	0.60	0.76	0.30	0.91
32	R600+R1234yf^[43]	A	2.73	0.80	0.78	0.86	2.73	1.12	0.95	1.41
33	R600a+R1234yf^[44]	A	0.63	0.30	0.30	0.30	0.65	0.75	0.39	0.95
34	R600a+R1234ze(E)^[45]	A	0.48	0.21	0.19	0.16	0.55	0.52	0.19	0.95
35	R600a+R1234ze(Z)^[46]	A	0.72	0.42	0.39	0.39	0.75	1.13	0.64	1.57
CO₂+HFO
36	CO₂+R1234yf^[47]	C	1.11	0.91	0.52	0.52	1.12	1.44	0.90	0.96
37	CO₂+R1234yf^[48]	C	2.77	1.67	0.42	0.38	2.88	2.94	1.28	1.35
38	CO₂+R1234ze(E)^[49]	C	1.02	1.08	0.95	1.00	1.72	1.35	1.58	1.47
39	CO₂+R1243zf^[47]	C	0.76	0.64	0.30	0.28	1.19	0.74	0.52	0.47

二元体系	ARD(p)/%
	沿等温线关联				温度无关关联
	PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson	PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson
HFC+HFO	0.551	0.444	0.385	0.372	0.792	0.801	0.678	0.762
HC+HFO	0.797	0.374	0.330	0.334	0.877	0.837	0.478	1.192
CO₂+HFO	1.414	1.074	0.549	0.546	1.729	1.616	1.070	1.061
全部体系	0.703	0.491	0.387	0.380	0.910	0.894	0.667	0.903

二元体系	ARD(p)/%
	沿等温线关联				温度无关关联
	PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson	PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson
HFC+HFO	0.551	0.444	0.385	0.372	0.792	0.801	0.678	0.762
HC+HFO	0.797	0.374	0.330	0.334	0.877	0.837	0.478	1.192
CO₂+HFO	1.414	1.074	0.549	0.546	1.729	1.616	1.070	1.061
全部体系	0.703	0.491	0.387	0.380	0.910	0.894	0.667	0.903

二元体系	实验中的超临界温度范围/K	ARD(p)/%（沿等温线关联）
二元体系	实验中的超临界温度范围/K	PR-vdW	PR-HV-NRTL	PR-WS-NRTL	PR-WS-Wilson
R32+R1234yf	353.13~358.15	2.67	2.67	0.36	0.38
R170+R1234ze(E)	308.04~347.52	0.52	0.42	0.37	0.30
CO₂+R1234yf	313.15	1.75	1.40	0.70	0.76
CO₂+R1234yf	308.20~353.15	3.43	2.02	0.42	0.42
CO₂+R1234ze(E)	313.15~343.15	1.19	1.26	1.13	1.20
CO₂+R1243zf	308.15~313.15	1.15	1.03	0.37	0.37
均值	—	1.79	1.47	0.56	0.57