3.2.1. Combustion Characteristics of Anthracite and Coke

In order to better characterize the combustion process of anthracite and coke powder for sintering, this study conducted a TG-DTG analysis on the two fuels by means of thermogravimetric experiments at the same heating rate. It can be seen from Figure 4 that the combustion interval of anthracite and coke powder is concentrated in a certain region, and there is only one section of weightlessness. Because the volatile content of anthracite and coke powder is low, most of the reaction weight loss can be considered as the result of fixed carbon combustion. However, the volatile content of anthracite is 6.94%, which is significantly higher than that of coke powder. Therefore, the combustion interval of anthracite is obviously smaller than that of coke powder.

**Figure 4.** Thermogravimetric curves of anthracite and coke.

Combined with Equations (2) and (3), the combustion characteristic parameters of anthracite and coke powder for sintering can be obtained. As shown in Table 4, the average combustion rate, ignition stability *C* value and combustion characteristic index *S* value of anthracite were higher than that of coke powder, while the combustion time was lower than that of coke powder. Therefore, anthracite has a better combustion performance than coke powder. This is because the volatile content of coke powder and the strength of hydroxyl absorption peak are low, which directly leads to the ignition temperature of anthracite being lower than that of coke powder, resulting in significant differences in the combustion performance of the two. Therefore, the coal coke mixed fuel used in sintering raw materials will have multi-stage weightless reactions during the combustion process.

**Table 4.** Combustion characteristics of anthracite and coke powder.


#### 3.2.2. Combustion Characteristics of MBF and QPF

Figure 5 shows the conversion (α) and the reaction rate (dα/d*t*) of MBF and QPF at different heating rates. The improving trend of the reaction rates gradually slows down as the heating rate increases and all the reaction curves have a common feature that the weight loss reaction of the two samples is divided into two parts, which is because that the different combustion characteristics of anthracite and coke divide the whole combustion process into two reaction zones. The first reaction zone is mainly the combustion reaction of anthracite, which occurs in the temperature range of about 400–600 ◦C. The second reaction zone is the combustion of coke breeze, and the temperature range of this reaction is about 550–950 ◦C. Because of the difference in the amount of anthracite and coke powder added, the rate of change peak of the latter is significantly higher than that of the former.

As shown in Table 5, when the heating rate (β) is increased from 5 ◦C/min to 20 ◦C/min, *T*i, *T*j, *T*p-1 and *T*p-2 all increase, and the conversion rate and reaction rate curves are shifted to the high-temperature region, which indicates that the amount of heat transferred from the surrounding environment to the inside of the sample per unit time increases. The increase of the heat will greatly improve the combustion rate of the fuel but also shortens the reaction time (*t*) of samples at the same temperature, so the phenomenon of the curve's movement to the high-temperature area will occur. By comparing the *T*p-2 and *T*<sup>j</sup> values of MBF in Table 5 at 5 ◦C/min with the *T*<sup>p</sup> and *T*<sup>j</sup> values in Table 4, it can be seen that the maximum reaction rate and the corresponding temperature at the end reaction of the coke powder in the mixed fuel are significantly lower than the corresponding temperature when the coke powder is burned alone. This indicates that the combustion of anthracite before coke powder provides heat for the latter's oxidation, thus speeding up the reaction process of coke powder. Therefore, when the sintering site adopts anthracite to partially replace coke powder, the migration speed of combustion zone will be accelerated and the sintering efficiency will be improved.

**Figure 5.** Fractional conversion and reaction rate-conversion curves of MBF and QPF at different heating rates.


**Table 5.** Combustion characteristic parameters of MBF and QPF at different heating rates.

It can be seen that the QPF flammability index, combustion characteristic index and combustion reaction time are significantly higher than MBF, while the average burning rate of both is about the same. This indicates that the quasi-particle structure extends the reaction time of fuel combustion, but it does not inhibit the burning rate and in fact, improves the combustion performance. It is probable that the inert particles around the fuel reduce the loss of heat generated by the combustion reaction. At the same time, as the combustion reaction progresses, the particle size of the fuel gradually shrinks, so that a "regenerator" is formed around the wrapped fuel. The specific schematic diagram is shown in Figure 6. This is also the reason for the heat storage in the combustion zone during sintering.

**Figure 6.** Thermal storage of quasi-particle sintering.

#### *3.3. Combustion Kinetic Parameters*

The relationship between the conversion rates and reaction rates of the two kinds of fuel at different heating rates is shown in Figure 7. The whole combustion reaction process is divided into two stages. The earlier stage is mainly anthracite combustion, while the latter stage is mainly composed of coke-powder combustion. The trend of the curves describing the two combustion stages is roughly the same. The rate in the initial stage of the reaction increases rapidly with an increase in the conversion rate and then decreases rapidly after reaching a certain peak value. The combustion reaction of anthracite and coke breeze follow the law of non-uniform reaction. Therefore, the combustion reaction of the fuel in the low-temperature condition is in the "chemical-controlled zone", where the combustion rate is greatly affected by the temperature, and the reaction rate increases with an increase of temperature; As the reaction proceeds, the ash content on the fuel surface gradually increases and adheres to the particle surface, which limits the diffusion of gas to the solid boundary layer and the desorption of gaseous reaction products from the solid surface to a certain extent, then greatly slows down the rate of late combustion reactions. After the peak, the reaction enters the "diffusion-controlled zone". Because of the dependence of reaction rate on the diffusion rate of the gas, the burning rate of the fuel decreases as the conversion rate increases.

**Figure 7.** Combustion rates of MBF, QPF and fitting curves of double parallel reaction volume model (DVM) and double parallel random pore model (DRPM).

Table 6 lists the kinetic parameters and correlation coefficient *R*<sup>2</sup> of MBF and QPF calculated according to Equations (14) and (15). It can be seen from the data that the correlation coefficients of the two samples calculated by the DVM model are all ≤ 0.9993, and the correlation coefficients calculated by DRPM are all ≥ 0.9994. Whether it is MBF or QPF, the correlation coefficient of the data calculated by the latter is slightly higher than by the former. Table 7 lists the *RMSEs* of conversion and combustion rates calculated according to Equations (16) and (17). The results show that the *RMSEs* of conversion and combustion rate calculated by DRPM model at different heating rates are less than 0.8 and 0.01, respectively, which are far less than the *RMSEs* of the conversion rate and combustion rate calculated by the DVM model. Therefore, the combustion behavior of the MBF and QPF follows the combustion law of the double parallel reaction random pore model.

To further verify the reliability of the data calculated by the DRPM model, the corresponding kinetic parameters in Table 6 were brought into Equation (15), and the resulting conversion curves were compared with the experimental curves. As shown in Figure 8, α<sup>1</sup> and α<sup>2</sup> increase with temperature at different heating rates, representing the conversion curves of anthracite and coke powder. The remaining curves are experimental and calculated results of MBF and QPF. It can be seen from the figure that they have a high degree of fit. The experimental results are equivalent to the sum of the anthracite combustion conversion rate and the coke powder combustion conversion rate.

It can be seen from Table 6 that the activation energy of the MBF calculated by DRPM is slightly lower than that of QPF. In order to better reflect the height of barriers, Equation (18) was introduced to calculate the apparent activation energy of samples,

$$E\_a = c\_1 E\_1 + c\_2 E\_2 \tag{18}$$

where *<sup>E</sup>*<sup>α</sup> is the apparent activation energy of samples in kJ·mol<sup>−</sup>1, *<sup>c</sup>*<sup>1</sup> is the proportion of the anthracite combustion reaction to the total response, *E*<sup>1</sup> is the activation energy of the anthracite combustion reaction in kJ·mol<sup>−</sup>1, *<sup>c</sup>*<sup>2</sup> is the proportion of the coke combustion reaction to the total response, and *<sup>E</sup>*<sup>2</sup> is the activation energy of the coke combustion reaction in kJ·mol<sup>−</sup>1.

The calculation results are shown in Figure 9.




**Table 7.** Deviation between the experimental and calculated curves.

**Figure 8.** Comparison the correlation between experimental data and calculation results of MBF and QPF at different heating rates.

**Figure 9.** Comparison the apparent activation energy of MBF and QPF calculated by DRPM.

At different heating rates, the apparent activation energy of QPF is significantly higher than that of MBF, and the difference between them is maintained between 13.62 and 14.53 kJ·mol<sup>−</sup>1, which does not change with the increase of the heating rate. This indicates that the difference in apparent activation energy between QPF and MPF is the reaction energy barrier provided by the diffusion resistance during the combustion reaction. The inert particles in the quasi-particle structure hinder the contact of the active part on the fuel particles with the air, thereby improving the reaction energy barrier of internal fuel. Compared with the conventional simple fuel particle structure, an increased number of particles in the quasi-particle structure increase the tortuosity of the internal pores, which greatly reduces the diffusion coefficient of the gas in the heterogeneous reaction and then increases the diffusion resistance of anthracite and coke powder combustion and the activation degree of the diffusion control reaction. However, by comparing the combustion performance parameters of QPF and MBF, it can be seen that the quasi-granular structure can produce a certain heat storage effect on the fuel during the combustion reaction process, which not only improves the combustion performance of the fuel but also increases its combustion rate, thus reducing the adverse effect of diffusion on fuel combustion.

#### *3.4. Kinetic Analysis of Quasi-Particle Fuel Combustion*

In order to clarify the coupling effect between the redox reaction of iron oxide and the combustion of fuel in the sintering mixture, we carried out SDM in the thermal analysis experiments at different heating rates, as shown in Figure 10. The increase of heating rate accelerates the reaction speed of each reaction in the sintering process and the weight variation of SDM increases with the increase of heating rate. Since the reaction is complicated in the sintering process, a reaction overlap is highly likely to occur. In order to better distinguish the redox reaction and explore the reasons for the change of sample weight, we carried out experiments using a DTA analysis under different heating rates and found that the second derivative of the DTA curve obtained the hidden information of the peak structure in the overlapping region. The results of the analysis are shown in Figure 11.

**Figure 10.** Fractional conversion and reaction rate-conversion curves of the sintered mixture at different heating rates.

˄ ˅ ˄ ˅ As can be seen from the figure, SDM exhibits a small change in exothermic → endotherm → exothermic below 500 ◦C. The volatile first undergoes combustion and exothermic reaction, which provides a reducing atmosphere for Fe2O3 in the sample and a small amount of CO is sufficient to completely reduce Fe2O3 to Fe3O4. Due to the continuous renewal of the reaction gas, the reducing atmosphere is replaced by an oxidizing atmosphere. The Fe3O4 produced by the reduction is oxidized and the experimental curve shows a slight exothermic weight gain,

$$\text{Volatile} + (\text{x}/2 + y + z/2)\text{O}\_2 \to \text{xCO} + y\text{CO}\_2 + z\text{H}\_2\text{O} \tag{19}$$

$$\text{2Fe}\_2\text{O}\_3 + \text{CO} = 2\text{Fe}\_3\text{O}\_4 + \text{CO}\_2 \tag{20}$$

$$2\text{Fe}\_3\text{O}\_4 + 1/2\text{O}\_2 = 3\text{Fe}\_2\text{O}\_3\tag{21}$$

˄ ˅ ˄ ˅ The reactions can be regarded as a series of reactions at this stage. Among them, CO and Fe3O4 are both the product of the former reaction and the reactant of the latter reaction. This indicates that the increase of the latter reaction rate will promote the previous reaction, and the slowing of the previous reaction rate will inhibit the latter reaction, thus forming a significant coupling relationship.

**Figure 11.** Differential thermal analysis curves of the sintered mixture at different heating rates. (**a**) 5 ◦C/min, (**b**) 10 ◦C/min, (**c**) 15 ◦C/min, (**d**) 20 ◦C/min.

Above 500 ◦C, anthracite and coke breeze burn, and the exothermic is intense, which may mask the reduction reaction of Fe2O3. However, the DTA curve shows a significant reduction of the endothermic peak in the 550–630 ◦C range. This is because this stage is the combustion interval between anthracite and coke breeze and the oxidative exothermic is replaced by the reduced endotherm. However, due to the large weight loss caused by the combustion and reduction reactions, a weight gain phenomenon is not obvious at this stage. The coupling phenomenon of each reaction in the sintering mixture is very obvious and is complicated.
