A Novel Method of Kinetic Analysis and Its Application to Pulverized Coal Combustion under Different Oxygen Concentrations
Abstract
:1. Introduction
2. Methodology
2.1. DIM Method
2.2. Experimental Results
3. The DIM Method Application and Discussion
4. Validation
5. Conclusions
- A formula combining differential and integral was deduced through an analytical approach, which can offset the defects of a single differential or integral method.
- In the application of the DIM method of pulverized coal combustion under different O2 concentrations (3%, 5%, 10%, 15%, and 21%), E, A, and O2 concentration exponent n were calculated as 258,164 J/mol, 6.660 × 1017 s−1, and 3.326, respectively, and the mechanism function was determined as the Avrami-Erofeev equation. Subsequently, the kinetic model was obtained.
- The experimental TG curve with a 7% O2 concentration was compared with four calculated curves generated by DIM, Wang, Achar, and Coats-Redfern methods, respectively. The DIM method showed a good accuracy with 1.26% average deviation.
Author Contributions
Funding
Conflicts of Interest
References
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Proximate Analysis (w%) | Ultimate Analysis (w%) | |||||||
---|---|---|---|---|---|---|---|---|
Mad | Aad | Vad | FCad | Cad | Had | Nad | Sad | Oad |
4.81 | 16.97 | 24.51 | 53.71 | 62.56 | 2.62 | 0.9 | 0.41 | 11.73 |
Number | Model | ||
---|---|---|---|
1 | Parabolic law | ||
2 | Valensi equation | ||
3 | Jander equation | ||
4 | Jander equation | ||
5 | Jander equation | ||
6 | Jander equation | ||
7 | G-B equation | ||
8 | Inverse Jander equation | ||
9 | Z-L-T equation | ||
10 | Avrami-Erofeev equation | ||
11 | Avrami-Erofeev equation | ||
12 | Avrami-Erofeev equation | ||
13 | Avrami-Erofeev equation | ||
14 | Avrami-Erofeev equation | ||
15 | Avrami-Erofeev equation | ||
16 | Avrami-Erofeev equation | ||
17 | Avrami-Erofeev equation | ||
18 | Avrami-Erofeev equation | ||
19 | Avrami-Erofeev equation | ||
20 | First order | ||
21 | P-T equation | ||
22 | Mampel power law | ||
23 | Mampel power law | ||
24 | Mampel power law | ||
25 | Mampel power law | 1 | |
26 | Mampel power law | ||
27 | Mampel power law | ||
28 | Reaction order | ||
29 | Contracting sphere | ||
30 | Contracting sphere | ||
31 | Contracting cylinder | ||
32 | Contracting cylinder | ||
33 | Reaction order | ||
34 | Reaction order | ||
35 | Reaction order | ||
36 | Second order | ||
37 | Reaction order | ||
38 | Two-third order | ||
39 | Exponent law | ||
40 | Exponent law | ||
41 | Third order |
No. | E1 (Equation (11)) (J/mol) | E2 (Equation (13)) (J/mol) | △E = E1 − E2 (J/mol) | |△E/E1| | |△E/E2| |
---|---|---|---|---|---|
1 | 61,074.64 | 34,272.76 | 26,801.89 | 0.4388 | 0.7820 |
2 | 67,418.23 | 39,282.32 | 28,135.91 | 0.4173 | 0.7162 |
3 | 10,758.32 | 3345.33 | 7412.99 | 0.6890 | 2.2159 |
4 | 73,246.34 | 45,688.96 | 27,557.38 | 0.3762 | 0.6032 |
5 | 12,279.78 | 5360.19 | 6919.59 | 0.5635 | 1.2909 |
6 | 79,332.19 | 53,748.39 | 25,583.80 | 0.3225 | 0.4760 |
7 | 7,0951.68 | 42,817.59 | 28,134.09 | 0.3965 | 0.6571 |
8 | 56,576.77 | 31,257.31 | 25,319.46 | 0.4475 | 0.8100 |
9 | 121,550.68 | 152,645.18 | −31,094.50 | 0.2558 | 0.2037 |
10 | 3251.61 | 1488.91 | 1762.69 | 0.5421 | 1.1839 |
11 | 7692.94 | 5574.96 | 2117.99 | 0.2753 | 0.3799 |
12 | 11,248.84 | 8843.79 | 2405.05 | 0.2138 | 0.2719 |
13 | 16,578.12 | 13,747.04 | 2831.08 | 0.1708 | 0.2059 |
14 | 25,457.47 | 21,919.13 | 3538.34 | 0.1390 | 0.1614 |
15 | 29,905.46 | 54,607.46 | −2,4702.00 | 0.8260 | 0.4524 |
16 | 69,879.17 | 62,779.55 | 7099.62 | 0.1016 | 0.1131 |
17 | 96,525.54 | 87,295.80 | 9229.74 | 0.0956 | 0.1057 |
18 | 149,818.28 | 136,328.31 | 13,489.97 | 0.0900 | 0.0990 |
19 | 203,111.02 | 185,360.81 | 17,750.21 | 0.0874 | 0.0958 |
20 | 43,224.49 | 38,263.29 | 4961.19 | 0.1148 | 0.1297 |
21 | - | 99,773.33 | - | - | - |
22 | −1,180.59 | −5138.97 | 3958.38 | 3.3529 | 0.7703 |
23 | 1783.35 | −3262.22 | 5045.57 | 2.8293 | 1.5467 |
24 | 7712.07 | 491.28 | 7220.79 | 0.9363 | 14.6979 |
25 | 25,499.04 | 11,751.77 | 13,747.27 | 0.5391 | 1.1698 |
26 | 43,282.68 | 23,012.27 | 20,270.42 | 0.4683 | 0.8809 |
27 | 61,074.64 | 34,272.76 | 26,801.89 | 0.4388 | 0.7820 |
28 | 36,431.95 | 24,366.94 | 12,065.00 | 0.3312 | 0.4951 |
29 | 34,627.81 | 21,489.59 | 13,138.22 | 0.3794 | 0.6114 |
30 | 34,627.81 | 21,489.59 | 13,138.22 | 0.3794 | 0.6114 |
31 | 31,584.89 | 17,459.87 | 14,125.01 | 0.4472 | 0.8090 |
32 | 31,584.89 | 17,459.87 | 14,125.01 | 0.4472 | 0.8090 |
33 | 19,113.89 | 7222.95 | 11,890.94 | 0.6221 | 1.6463 |
34 | 15,430.78 | 4848.13 | 10,582.65 | 0.6858 | 2.1828 |
35 | 12,870.07 | 3261.72 | 9608.36 | 0.7466 | 2.9458 |
36 | 53,276.11 | 137,575.97 | −84,299.86 | 1.5823 | 0.6128 |
37 | 88,876.66 | 160,096.95 | −71,220.29 | 0.8013 | 0.4449 |
38 | 21,599.77 | 63,403.38 | −41,803.61 | 1.9354 | 0.6593 |
39 | - | −167,150.70 | - | - | - |
40 | - | −167,150.70 | - | - | - |
41 | 116,645.42 | 285,921.15 | −169,275.73 | 1.4512 | 0.5920 |
No. | Achar | C-R | ||||
---|---|---|---|---|---|---|
E(J/mol) | A(s−1) | R2 | E(J/mol) | A(s−1) | R2 | |
1 | 27,036.20 | 6.64 × 10−4 | 0.1246 | 64,006.40 | 1.74 | 0.8560 |
2 | 45,189.28 | 1.29 × 10−2 | 0.3375 | 70,286.46 | 3.52 | 0.8787 |
3 | 643.80 | 7.71 × 10−5 | 2.38 × 10−4 | 9439.80 | 4.70 × 10−4 | 0.6541 |
4 | 67,295.67 | 5.03 × 10−1 | 0.6425 | 76,091.67 | 6.19 | 0.8997 |
5 | 10,514.86 | 4.42 × 10−4 | 0.07516 | 10,974.36 | 6.09 × 10−4 | 0.7347 |
6 | 81,770.40 | 3.98 | 0.7818 | 82,229.91 | 1.03 × 101 | 0.9165 |
7 | 58,959.17 | 4.34 × 10−2 | 0.5337 | 73,785.82 | 1.68 | 0.8915 |
8 | 20,581.27 | 1.82 × 10−5 | 0.07567 | 59,482.26 | 6.77 × 10−2 | 0.8436 |
9 | 150,204.08 | 3.07 × 106 | 0.9567 | 127,852.36 | 1.34 × 105 | 0.9415 |
10 | 14,669.16 | 1.91 × 10−3 | 0.1912 | 1358.77 | 4.30 × 10−5 | 0.1610 |
11 | 19,381.24 | 4.97 × 10−3 | 0.2962 | 6070.86 | 3.75 × 10−4 | 0.6956 |
12 | 23,150.91 | 1.02 × 10−2 | 0.3785 | 9840.53 | 1.04 × 10−3 | 0.8091 |
13 | 28,805.42 | 2.85 × 10−2 | 0.4900 | 15,495.03 | 3.67 × 10−3 | 0.8713 |
14 | 38,229.58 | 1.45 × 10−1 | 0.6342 | 24,919.20 | 2.25 × 10−2 | 0.9076 |
15 | 42,941.67 | 5.68 × 10−1 | 0.6682 | 29,631.29 | 5.24 × 10−2 | 0.9163 |
16 | 85,350.45 | 2.67 × 102 | 0.8938 | 72,040.06 | 5.33 × 101 | 0.9405 |
17 | 113,622.97 | 1.99 × 104 | 0.9294 | 100,312.58 | 4.15 × 103 | 0.9448 |
18 | 170,168.00 | 9.35 × 107 | 0.9527 | 156,857.62 | 2.03 × 107 | 0.9485 |
19 | 226,713.04 | 3.90 × 1011 | 0.9590 | 213,402.65 | 8.62 × 1010 | 0.9502 |
20 | 57,077.93 | 3.19 | 0.7976 | 43,767.55 | 5.79 × 10−1 | 0.9301 |
21 | 18,685.98 | 3.97 × 10−2 | 0.3348 | - | - | - |
22 | −40,149.71 | 3.86 × 10−8 | 0.3194 | −3179.50 | −4.03 × 10−5 | 0.3664 |
23 | −36,950.38 | 7.41 × 10−8 | 0.2810 | 19.83 | 3.62 × 10−7 | 1.46 × 10−5 |
24 | −30,551.72 | 2.31 × 10−7 | 0.2051 | 6418.48 | 2.43 × 10−4 | 0.4396 |
25 | −11,355.75 | 4.14 × 10−6 | 0.0309 | 25,614.45 | 8.70 × 10−3 | 0.7814 |
26 | 7840.22 | 5.56 × 10−5 | 0.0133 | 44,810.43 | 1.36 × 10−1 | 0.8354 |
27 | 27,036.20 | 6.64 × 10−4 | 0.1246 | 64,006.40 | 1.74 | 0.8560 |
28 | 39,969.51 | 2.69 × 10−2 | 0.5600 | 36,577.09 | 2.89 × 10−2 | 0.8970 |
29 | 34,266.70 | 1.16 × 10−2 | 0.4468 | 34,726.21 | 2.52 × 10−2 | 0.8833 |
30 | 34,266.70 | 3.48 × 10−2 | 0.4468 | 34,726.21 | 7.57 × 10−2 | 0.8833 |
31 | 22,861.09 | 1.81 × 10−3 | 0.2127 | 31,657.09 | 1.86 × 10−2 | 0.8557 |
32 | 22,861.09 | 3.63 × 10−3 | 0.2127 | 31,657.09 | 3.71 × 10−2 | 0.8557 |
33 | −79,789.43 | 1.07 × 10−11 | 0.3612 | 19,246.64 | 3.40 × 10−3 | 0.6704 |
34 | −148,223.11 | 2.09 × 10−17 | 0.4943 | 15,525.15 | 1.84 × 10−3 | 0.5838 |
35 | −216,656.80 | 3.61 × 10−23 | 0.5546 | 12,918.33 | 1.15 × 10−3 | 0.5093 |
36 | 125,511.61 | 2.46 × 106 | 0.9071 | 55,656.19 | 1.81 × 102 | 0.6242 |
37 | 125,511.61 | 2.46 × 106 | 0.9071 | 94,048.13 | 2.46 × 104 | 0.8625 |
38 | 91,294.77 | 1.40 × 103 | 0.9205 | 21,439.35 | 7.97 × 10−2 | 0.5146 |
39 | −49,747.69 | 5.15 × 10−8 | 0.4305 | - | - | - |
40 | −49,747.69 | 1.03 × 10−7 | 0.4305 | - | - | - |
41 | 193,945.29 | 3.79 × 1012 | 0.8546 | 124,089.88 | 3.12 × 108 | 0.6658 |
Method | Average Deviation () |
---|---|
DIM | 1.26 |
Wang | 9.58 |
Achar | 4.05 |
Coats-Redfern | 3.01 |
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Gou, X.; Zhang, Q.; Liu, Y.; Wang, Z.; Zou, M.; Zhao, X. A Novel Method of Kinetic Analysis and Its Application to Pulverized Coal Combustion under Different Oxygen Concentrations. Energies 2018, 11, 1799. https://doi.org/10.3390/en11071799
Gou X, Zhang Q, Liu Y, Wang Z, Zou M, Zhao X. A Novel Method of Kinetic Analysis and Its Application to Pulverized Coal Combustion under Different Oxygen Concentrations. Energies. 2018; 11(7):1799. https://doi.org/10.3390/en11071799
Chicago/Turabian StyleGou, Xiang, Qiyan Zhang, Yingfan Liu, Zifang Wang, Mulin Zou, and Xuan Zhao. 2018. "A Novel Method of Kinetic Analysis and Its Application to Pulverized Coal Combustion under Different Oxygen Concentrations" Energies 11, no. 7: 1799. https://doi.org/10.3390/en11071799