CIESC Journal ›› 2019, Vol. 70 ›› Issue (8): 3058-3070.DOI: 10.11949/0438-1157.20190184
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Cong ZHANG(),Jinbo JIANG,Xudong PENG(),Wenjing ZHAO,Jiyun LI
Received:
2019-03-04
Revised:
2019-05-22
Online:
2019-08-05
Published:
2019-08-05
Contact:
Xudong PENG
通讯作者:
彭旭东
作者简介:
章聪(1995—),男,硕士研究生,<email>zc_derek@163.com</email>
基金资助:
CLC Number:
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.
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.
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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 |
VS4 | 100.0 | 216.58~1000.0 | 0.94825 | 2006 | |
热导率 | TC1 | 800.0 | 216.58~2000.0 | 0.50567 | 1990 |
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 |
VS4 | 100.0 | 216.58~1000.0 | 0.94825 | 2006 | |
热导率 | TC1 | 800.0 | 216.58~2000.0 | 0.50567 | 1990 |
T /K | p/kPa | ρe/ (kg/m3) | ρc/ (kg/m3) | AE/% | T/K | p/kPa | ρe/ (kg/m3) | ρc/ (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 |
Table 2 Condition point and corresponding density values with large relative error of CO2 at near critical point
T /K | p/kPa | ρe/ (kg/m3) | ρc/ (kg/m3) | AE/% | T/K | p/kPa | ρe/ (kg/m3) | ρc/ (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 |
T/K | p/kPa | μe/(μPa·s) | μc/(μPa·s) | AE/% | T/K | p/kPa | μe/(μPa·s) | μc/(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 |
Table 3 Condition point and corresponding viscosity values with large relative error of CO2 at near critical point
T/K | p/kPa | μe/(μPa·s) | μc/(μPa·s) | AE/% | T/K | p/kPa | μe/(μPa·s) | μc/(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 |
T/K | p/kPa | λe/ (mW/(m·K)) | λc/ (mW/(m·K)) | AE/% | T/K | p /kPa | λe/ (mW/(m·K)) | λc/ (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 |
Table 4 Condition point and corresponding thermal conductivity values with large relative error of CO2
T/K | p/kPa | λe/ (mW/(m·K)) | λc/ (mW/(m·K)) | AE/% | T/K | p /kPa | λe/ (mW/(m·K)) | λc/ (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 |
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*) | 隐藏层神经元个数m |
---|---|---|---|
密度预测模型 | logsig | tansig | 9 |
黏度预测模型 | tansig | tansig | 9 |
热导率预测模型 | logsig | purelin | 6 |
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*) | 隐藏层神经元个数m |
---|---|---|---|
密度预测模型 | logsig | tansig | 9 |
黏度预测模型 | tansig | tansig | 9 |
热导率预测模型 | logsig | purelin | 6 |
CO2 物性 | i | |||||
---|---|---|---|---|---|---|
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 | — |
Table 7 Fitted physical property model coefficients of CO2 at critical point based on ANN
CO2 物性 | i | |||||
---|---|---|---|---|---|---|
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 | — |
物性 | 平均相对误差 AEav /% | 最大相对误差 AEmax /% | 相对误差10%内占比 /% | |||
---|---|---|---|---|---|---|
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 |
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 AEav /% | 最大相对误差 AEmax /% | 相对误差10%内占比 /% | |||
---|---|---|---|---|---|---|
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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