近临界区CO2物性预测模型对比与修正

doi:10.11949/0438-1157.20190184

摘要/Abstract

摘要：

超临界二氧化碳（SCO₂）布雷顿循环系统是未来极具潜力的发电能量转换系统，CO₂物性表征模型对布雷顿循环系统中动力设备转轴密封和轴承性能的预测精度影响显著。在总结权威文献中不同温度和压力下CO₂物性实验测试数据的基础上，对比分析了经典物性查询软件REFPROP软件中CO₂密度、黏度和热导率预测模型的预测精度，获得了预测精度最高的物性预测模型及对应临界点附近误差较大的区域，采用人工神经网络算法获得了近临界区预测精度更高的CO₂物性预测模型。结果表明：REFPROP软件中的FEK模型、VS1模型和TC1模型分别对CO₂的密度、黏度和热导率具有最高的预测精度，不过其在近临界区的物性预测最大和平均误差仍分别达到40%和8%以上，利用神经网络算法所获得的CO₂物性预测模型可使近临界点区的物性预测最大和平均误差分别降至30%和4%以下。

关键词: 二氧化碳, REFPROP软件, 物性表征模型, 神经网络, 近临界区

Abstract:

The supercritical carbon dioxide (SCO₂) Brayton cycle system is a promising power generation energy conversion system in the future. The CO₂ physical property characterization model has a significant impact on the prediction accuracy of the power equipment shaft seal and bearing performance in the Brayton cycle system. On the basis of summarizing the experimental data of CO₂ physical properties under different temperatures and pressures in authoritative literature, the prediction accuracy of CO₂ density, viscosity and thermal conductivity prediction model in the classical physical property query software REFPROP software is compared and analyzed, and the physical prediction model with the highest prediction accuracy is obtained. The artificial neural network algorithm is used to obtain the prediction model of CO₂ physical property with higher precision in near critical region. The results show that the FEK model, VS1 model and TC1 model in REFPROP software have the highest prediction accuracy for CO₂ density, viscosity and thermal conductivity, respectively, but the maximum and average error predictions in the near critical region are still more than 40% and 8%, the CO₂ physical property prediction model obtained by the neural network algorithm can reduce the maximum and average error prediction of the near critical point area to 30% and 4%, respectively.

Key words: carbon dioxide, REFPROP software, physical property characterization model, neural network, near critical region

中图分类号:

TH 117.2

章聪, 江锦波, 彭旭东, 赵文静, 李纪云. 近临界区CO₂物性预测模型对比与修正[J]. 化工学报, 2019, 70(8): 3058-3070.

Cong ZHANG, Jinbo JIANG, Xudong PENG, Wenjing ZHAO, Jiyun LI. Comparison and correction of CO₂ properties model in critical region[J]. CIESC Journal, 2019, 70(8): 3058-3070.

图/表 16

图1 CO2物性模型与压力、温度之间的耦合关系

Fig.1 Coupling relationship between physical property model of CO2 and pressure and temperature

图2 CO2密度实测值与模型计算值的对比

Fig.2 Comparison between experimental values and calculated values of CO2 density

图3 CO2黏度实验值与模型计算值的对比

Fig.3 Comparison between experimental values and calculated values of CO2 viscosity

图4 CO2热导率实验值与计算值的对比

Fig.4 Comparison between experimental values and calculated values of CO2 thermal conductivity

表1 REFPROP软件CO2物性模型对比

Table 1 Comparison of CO2 physical properties models in REFPROP

CO₂ 物性	REFPROP模型	最大适用压力/MPa	温度适用范围/K	近临界区域相关系数R	提出年份
密度	FEQ	800.0	216.59~2000.0	0.95536	1996
	FEK	800.0	216.59~1100.0	0.95721	2007
	BWR	40.0	216.58~440.1	0.94394	1987
	FES	100.0	216.59~600.0	0.95490	2003
黏度	VS1	800.0	216.59~2000.0	0.94871	1998
黏度	VS4	100.0	216.58~1000.0	0.94825	2006
热导率	TC1	800.0	216.58~2000.0	0.50567	1990

图5 不同温度和压力下的CO2物性实测值及模型计算值相对误差

Fig.5 Experimental physical properties and corresponding relative error of calculated values of CO2 at different p and T

表2 近临界区CO2密度计算值误差较大的工况点及对应密度值

Table 2 Condition point and corresponding density values with large relative error of CO2 at near critical point

T /K	p/kPa	ρ_e/ (kg/m³)	ρ_c/ (kg/m³)	AE/%	T/K	p/kPa	ρ_e/ (kg/m³)	ρ_c/ (kg/m³)	AE/%
304.25	7408.60	379.91	544.55	43.34	304.25	7420.30	442.18	562.96	27.32
304.25	7405.30	374.69	535.69	42.97	304.65	7483.50	424.85	536.29	26.23
304.25	7412.30	388.11	551.81	42.18	304.23	7366.33	482.80	358.89	25.66
304.25	7416.00	402.05	557.52	38.67	304.27	7386.59	502.70	379.48	24.51
304.35	7428.20	392.50	544.01	38.60	304.26	7386.59	502.70	382.30	23.95
304.25	7417.70	411.13	559.79	36.16	308.15	7500.00	358.00	273.00	23.74
304.35	7418.70	373.83	508.89	36.13	304.95	7529.50	416.73	509.42	22.24
304.35	7432.70	407.35	552.04	35.52	304.31	7386.59	469.70	370.38	21.15
304.25	7419.00	416.37	561.42	34.84	304.95	7533.70	429.97	520.18	20.98
304.25	7419.30	422.83	561.78	32.86	304.95	7537.90	444.12	528.84	19.08
304.20	7366.33	532.90	363.52	31.78	304.33	7406.86	508.40	414.00	18.57
304.24	7376.46	532.90	369.73	30.62	304.37	7406.86	479.26	392.21	18.16
304.65	7475.30	398.34	514.33	29.12	304.95	7540.20	455.09	532.91	17.10
304.65	7480.00	412.43	528.54	28.15	304.16	7380.62	504.68	423.03	16.18
307.00	7399.08	213.93	273.86	28.02	304.95	7513.10	385.19	446.49	15.91

表3 近临界区CO2黏度计算值误差较大的工况点及对应黏度值

Table 3 Condition point and corresponding viscosity values with large relative error of CO2 at near critical point

T/K	p/kPa	μ_e/(μPa·s)	μ_c/(μPa·s)	AE/%	T/K	p/kPa	μ_e/(μPa·s)	μ_c/(μPa·s)	AE/%
304.25	7408.60	27.55	39.65	43.90	304.25	7420.30	32.93	41.14	24.91
304.25	7412.30	28.12	40.22	43.02	304.65	7485.70	31.87	39.30	23.34
304.35	7428.20	28.40	39.61	39.47	304.37	7406.86	36.04	27.67	23.22
304.35	7418.70	27.13	37.05	36.57	304.95	7529.50	30.00	36.86	22.89
304.35	7432.70	29.61	40.24	35.89	304.65	7467.40	27.61	33.76	22.28
304.20	7366.33	40.03	26.09	34.82	307.75	7995.56	42.30	33.09	21.77
304.25	7419.00	30.61	41.01	33.96	304.95	7533.70	30.99	37.69	21.64
305.35	7558.85	42.50	28.57	32.79	304.95	7522.50	28.87	34.87	20.79
304.25	7419.30	31.11	41.04	31.92	304.95	7537.90	32.10	38.36	19.49
304.65	7475.30	28.72	37.35	30.03	304.25	7420.70	34.48	41.18	19.44
304.23	7366.33	36.74	25.85	29.63	307.75	8058.38	45.40	36.68	19.21
304.65	7480.00	29.80	38.41	28.90	304.65	7489.40	33.55	39.76	18.53
304.25	7419.80	32.00	41.09	28.40	304.95	7540.20	32.89	38.67	17.58
304.35	7436.20	31.87	40.65	27.52	305.35	7535.54	32.30	26.86	16.83
304.65	7483.5	30.852	38.989	26.37	304.25	7420.80	35.46	41.19	16.15

表4 近临界区CO2热导率计算值误差较大的工况点及对应热导率值

Table 4 Condition point and corresponding thermal conductivity values with large relative error of CO2

T/K	p/kPa	λ_e/ (mW/(m·K))	λ_c/ (mW/(m·K))	AE/%	T/K	p /kPa	λ_e/ (mW/(m·K))	λ_c/ (mW/(m·K))	AE/%
304.39	7421.55	125.16	240.43	92.10	304.35	7412.23	146.09	208.28	42.57
304.36	7416.38	133.53	253.66	89.97	304.37	7409.29	226.04	134.82	40.35
304.38	7421.45	115.95	207.84	79.25	304.35	7405.95	217.66	132.62	39.07
304.40	7421.85	136.88	244.85	78.88	304.36	7406.96	213.48	132.09	38.12
304.35	7407.36	334.87	141.32	57.80	304.35	7409.90	246.97	157.52	36.22
304.35	7407.26	322.31	141.71	56.03	304.35	7409.70	246.97	158.79	35.70
304.35	7407.67	322.31	143.31	55.54	304.41	7421.85	153.62	203.36	32.38
304.35	7406.96	301.38	137.92	54.24	304.37	7412.03	209.29	152.93	26.93
304.35	7407.87	313.94	144.70	53.91	304.36	7407.16	171.62	128.06	25.38
304.37	7411.32	309.75	147.24	52.47	304.37	7408.07	166.60	128.51	22.86
304.35	7408.28	301.38	146.44	51.41	305.28	7548.41	134.37	107.48	20.01
304.35	7408.18	297.20	145.70	50.98	304.38	7413.95	197.99	158.64	19.88
304.35	7412.03	146.92	217.77	48.22	304.37	7407.06	149.02	123.47	17.14
305.20	7547.70	238.59	127.20	46.69	304.37	7406.86	141.90	122.78	13.47
304.35	7408.88	276.27	152.63	44.75	305.29	7588.43	109.67	120.69	10.05

图6 人工神经网络结构图

Fig.6 Artificial neural network structure

表6 CO2拟合物性模型的传递函数及神经元个数

Table 6 Transfer function and neurons number of CO2 fitted physical property models

CO₂物性模型

隐藏层传递函数

g(p^*, T^*)

输出层传递函数

f(p^*, T^*)

表7 基于神经网络的近临界区CO2拟合物性模型系数

Table 7 Fitted physical property model coefficients of CO2 at critical point based on ANN

CO₂ 物性	i	$w 1, i 1$	$w 2, i 1$	$b i 1$	$w i, 1 2$	$b i 2$
密度	1	-572.529	214.906	-79.968	0.966	-13.351
	2	-2.324	2.755	2.967	-10.763	—
	3	60.386	-158.569	-77.113	23.150	—
	4	-135.533	25.237	-30.575	-0.929	—
	5	-39.418	-419.105	-184.927	-0.602	—
	6	-15.035	32.165	11.590	-0.942	—
	7	-66.029	174.221	84.738	22.221	—
	8	-332.675	239.779	-7.965	-0.446	—
	9	30.406	27.444	43.399	1.326	—
黏度	1	-62.456	18.295	-8.561	14.012	0.044
	2	2.366	22.768	4.137	-9.818	—
	3	2.893	88.865	21.973	0.466	—
	4	-45.189	73.230	22.725	0.532	—
	5	80.073	-108.726	-34.601	0.382	—
	6	2.669	25.374	4.582	9.468	—
	7	1.192	-1.270	-0.318	1.513	—
	8	-68.184	19.930	-9.392	-13.906	—
	9	11.116	-19.621	-5.947	0.714	—
热导率	1	48.443	57.263	-83.375	-4.447	-1.653
	2	59.400	40.667	-77.210	4.419	—
	3	176.335	-142.068	1.555	-26.882	—
	4	177.240	-143.144	1.828	27.048	—
	5	7.515	-3.207	12.705	0.797	—
	6	93.796	-95.549	-2.409	-0.232	—

表7 基于神经网络的近临界区CO2拟合物性模型系数

Table 7 Fitted physical property model coefficients of CO2 at critical point based on ANN

CO₂ 物性	i	$w 1, i 1$	$w 2, i 1$	$b i 1$	$w i, 1 2$	$b i 2$
密度	1	-572.529	214.906	-79.968	0.966	-13.351
	2	-2.324	2.755	2.967	-10.763	—
	3	60.386	-158.569	-77.113	23.150	—
	4	-135.533	25.237	-30.575	-0.929	—
	5	-39.418	-419.105	-184.927	-0.602	—
	6	-15.035	32.165	11.590	-0.942	—
	7	-66.029	174.221	84.738	22.221	—
	8	-332.675	239.779	-7.965	-0.446	—
	9	30.406	27.444	43.399	1.326	—
黏度	1	-62.456	18.295	-8.561	14.012	0.044
	2	2.366	22.768	4.137	-9.818	—
	3	2.893	88.865	21.973	0.466	—
	4	-45.189	73.230	22.725	0.532	—
	5	80.073	-108.726	-34.601	0.382	—
	6	2.669	25.374	4.582	9.468	—
	7	1.192	-1.270	-0.318	1.513	—
	8	-68.184	19.930	-9.392	-13.906	—
	9	11.116	-19.621	-5.947	0.714	—
热导率	1	48.443	57.263	-83.375	-4.447	-1.653
	2	59.400	40.667	-77.210	4.419	—
	3	176.335	-142.068	1.555	-26.882	—
	4	177.240	-143.144	1.828	27.048	—
	5	7.515	-3.207	12.705	0.797	—
	6	93.796	-95.549	-2.409	-0.232	—

图7 人工神经网络拟合模型与REFPROP软件FEK模型密度计算值及相对误差

Fig.7 Density and corresponding relative error calculated by ANN fitted model and FEK model on REFPROP software

图8 人工神经网络拟合模型与REFPROP软件VS1模型黏度计算值及相对误差

Fig.8 Viscosity and corresponding relative error calculated by ANN fitted model and VS1 model on REFPROP software

图9 人工神经网络拟合模型与REFPROP软件TC1模型热导率计算值及相对误差

Fig.9 Thermal conductivity and corresponding relative error calculated by ANN fitted model and TC1 model on REFPROP software

表8 ANN拟合模型和REFPROP物性模型对应的物性计算值相对误差

Table 8 Relative error of calculated physical property values obtained by ANN fitted model and REFPROP software

物性	平均相对误差 AE_av /%		最大相对误差 AE_max /%		相对误差10%内占比 /%
物性	REFPROP	ANN	REFPROP	ANN	REFPROP	ANN
密度	8.32	3.84	43.34	27.19	69.79	91.06
黏度	9.60	3.86	43.90	29.09	65.09	91.51
热导率	26.52	3.61	92.10	22.14	34.41	93.55

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近临界区CO₂物性预测模型对比与修正

Comparison and correction of CO₂ properties model in critical region

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