Thermokinetic Characteristics of Coal Combustion under High Temperatures and Oxygen–Limited Atmospheres

Figures & data

Table 1. Proximate analyzes of the two coal samples (wt.%)

Sample	Rank	Moisture	Ash	Volatile	Fixed Carbon
Coal A	Gas coal	2.45	8.85	33.42	55.28
Coal B	Meager-lean coal	0.74	10.49	15.61	73.16

Figure 1. TG and DTG curves for the two coal samples under various oxygen concentrations (5 K/min).

Figure 2. DSC curves for the two coal samples under various oxygen concentrations (5 K/min).

Table 2. Temperatures and the scopes for the coal combustion stage of the two coal samples under 5 K/min heating rate

Coal sample	Temperature (K)	CO2 (vol.%)
		5	9	13	17	21
Coal A	T1	581.37	576.52	575.55	573.73	571.07
	T2	907.48	868.53	848.61	836.03	827.10
	ΔT	326.11	292.01	273.06	262.3	256.03
Coal B	T1	637.43	630.90	629.53	620.92	615.30
	T2	958.93	906.74	884.87	870.91	859.94
	ΔT	321.50	275.84	255.34	249.99	244.64

Figure 3. Relationship between the quantity of heat release and mass for the two coal samples.

Figure 4. Ratio of the peak width at half the maximum of the DSC curves.

Figure 5. Ratio of the peak width at half the maximum of the DTG curves.

Table 3. Commonly used kinetic mode (Hu et al. 2008)

No.	Name	Mode	G(α)
1	Parabola principle	One-dimensional diffusion	α^2
2	Valensi equation	Two-dimensional diffusion	α + (1 − α)ln(1 − α)
3–4	Jander equation	Two-dimensional diffusion, n = 1/2 and 2, respectively.	[1 − (1 − α)^1/2]^n
5–6	Jander equation	Three-dimensional diffusion, n = 1/2 and 2, respectively.	[1 − (1 − α)^1/3]^n
7	G-B equation	Three-dimensional diffusion	1 − 2α/3 − (1 − α)^2/3
8	Anti-Jander equation	Three-dimensional diffusion	[(1 + α)^1/3 − 1]^2
9	Z–L–Tequation	Three-dimensional diffusion	[(1 − α)^−1/3 − 1]^2
10–15	A–E equation	Random nucleation and subsequent growth, n = 1/4, 1/3, 2/5, 1/2, 2/3, and 3/4, respectively.	[−ln(1 − α)]^n
16	Mample principle	Random nucleation and subsequent growth.	−ln(1 − α)
17–20	A–E equation	Random nucleation and subsequent growth, n = 3/2, 2, 3, and 4, respectively.	[−ln(1 − α)]^n
21–26	Power function principle	n = 1/4, 1/3, 1/2, 1, 3/2, and 2, respectively.	a^n
27	Reaction order	n = 1/4	1 − (1 − α)^1/4
28	Contractive sphere	n = 1/3	1 − (1 − α)^1/3
29	Contractive sphere	n = 3	3[1 − (1 − α)^1/3]
30	Contractive cylinder	n = 1/2	1 − (1 − α)^1/2
31	Contractive cylinder	n = 2	2[1 − (1 − α)^1/2]

Note:G–B, Z–L–T, and A–E, are the abbreviations of Ginstling–Brounshtein, Zhuralev–Lesokin–Tempelman, and Avrami–Erofeev, respectively.

Table 4. Kinetic modes under various oxygen concentrations for the two coal samples

Coal sample	CO2 (vol. %)	Kinetic modes
		No.	Name	Mode	G(α)
Coal A	21	16	Mample principle	Random nucleation and subsequent growth	−ln(1 − α)
	17	16	Mample principle	Random nucleation and subsequent growth	−ln(1 − α)
	13	27	Reaction order	n = 1/4	1 − (1 − α)^1/4
	9	27	Reaction order	n = 1/4	1 − (1 − α)^1/4
	5	28	Contractive sphere	n = 1/3	1 − (1 − α)^1/3
Coal B	21	15	A–E equation	n = 3/4	[−ln(1 − α)]^3/4
	17	15	A–E equation	n = 3/4	[−ln(1 − α)]^3/4
	13	15	A–E equation	n = 3/4	[−ln(1 − α)]^3/4
	9	27	Reaction order	n = 1/4	1 − (1 − α)^1/4
	5	28	Contractive sphere	n = 1/3	1 − (1 − α)^1/3

Figure 6. Determination of kinetic mode for coal A by Popescu and Málek methods.

Figure 6. (Continued).

Figure 7. E_a vs. α for the two coal samples under various oxygen concentrations.

Table 5. Kinetic compensation effects under various oxygen concentrations for the two coal samples

Coal sample	CO2 (vol. %)	Kinetic compensation effect	r^2
Coal A	21	lnA = 0.15476Ea – 2.00548	0.996
	17	lnA = 0.1567Ea–2.45456	0.994
	13	lnA = 0.16285Ea–4.81377	0.998
	9	lnA = 0.16471Ea–5.24113	0.997
	5	lnA = 0.16708Ea–5.54194	0.997
Coal B	21	lnA = 0.15705Ea – 3.05031	0.998
	17	lnA = 0.15566Ea–3.13311	0.998
	13	lnA = 0.15503Ea–3.32386	0.998
	9	lnA = 0.1429Ea–4.3573	0.999
	5	lnA = 0.14807Ea–5.0228	0.999

Table

A	Pre–exponential factor, min^–1	T	Temperature, K
a, b	Compensation parameters	T0.5	Temperature at 0.5 conversion, K
CO2	Oxygen concentration, vol.%	T1	Ignition temperature, K
DSC	Differential scanning calorimetry, mW/mg	T2	Burnout temperature, K
DTG	First–order differential of TG, %/min	ΔT	Temperature scope of coal combustion, K
Ea	Apparent activation energy, kJ/mol	Ti,Tj	Selected temperatures, K
f(α), G(α)	Differential and integral types of mechanistic function, $f(\alpha )={\left[\mathrm{d}G(\alpha )/\mathrm{d}\alpha \right]}^{-1}$	TG	Thermogravimetry, mg
k	Reaction rate, min^−1	t	Time, min
m1	Mass at ignition temperature, mg	y(α)	Custom function
m2	Mass at burnout temperature, mg
mx	Mass at a certain temperature, mg	Greek symbol
Q	Quantity of heat release, J/g	α		Conversion
R	Gas constant, 8.314 × 10^−3 kJ/(mol·K)	αi,αj		Conversions corresponding to TiandTj
r	Fitting degree	β		Heating rate, K/min

Hu, R. Z., S. L. Gao, F. Q. Zhao, Q. Z. Shi, T. L. Zhang, and J. J. Zhang. 2008. Thermal analysis kinetics. Beijing, China: Science Press. (In Chinese).

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