Temperature Distribution Estimation in a Dwight–Lloyd Sinter Machine Based on the Combustion Rate of Charcoal Quasi-Particles

Abstract

The coke combustion rate in an iron ore sintering process is one of the most important determining factors of quality and productivity. Biomass carbon material is considered to be a coke substitute with a lower CO₂ emission in the sintering process. The purpose of this study was to investigate the combustion rate of a biomass carbon material and to use a sintering simulation model to calculate its temperature profile. The samples were prepared using alumina powder and woody biomass powder. To simplify the experimental conditions, alumina powder, which cannot be reduced, was prepared as a substitute of iron ore. Combustion experiments were carried out in the open at 1073 K~1523 K. The results show that the combustion rates of the biomass carbon material were higher than that of coke. The results were analyzed using an unreacted core model with one reaction interface. The kinetic analysis found that the k_c of charcoal was higher than that of coke. It is believed that the larger surface area of charcoal may affect its combustion rate. The analysis of the sintering simulation results shows that the high temperature range of charcoal was smaller than that of coke because of charcoal’s low fixed carbon content and density.

1. Introduction

CO₂ emission from Japan’s industrial sector is much higher than that from other sectors. In 2017, it accounted for approximately 37.2% of the total emission. In the industrial sector, the iron and steel-making industry accounts for approximately 39.4% of energy consumption. The steel industry emits approximately 13% of the CO₂ in Japan [1]. The demands of global environmental conservation require a greenhouse gas reduction. Currently, approximately 80 million tons of pig iron are produced by blast furnace annually in Japan. Coal and coke are used as reducing materials and heat sources, respectively, and a large amount of CO₂ is emitted in the iron-making process. Therefore, the development of innovative technologies is required to reduce the CO₂ emission.

Trees absorb carbon dioxide during photosynthesis. When wood from forests is burned as fuel, carbon dioxide is generated. If the forest is renewed after tree cutting, the carbon dioxide will be absorbed by the trees again during the growth process. Thus, the use of wood for energy is carbon neutral. Therefore, using wood instead of fossil fuels makes it possible to reduce carbon dioxide emissions and contribute to the prevention of global warming [2].

It is increasingly difficult to prepare a sintering iron ore due to the high price of raw materials, environmental regulations and inferior quality raw materials. Limited work [3,4,5,6] has been conducted to investigate the application of biomass in the sintering process to replace coke breeze, with this work mainly focused on its environmental impacts and low substitution rates. Therefore, it is necessary to improve the sintering iron ore method. In the sintering process, the coke combustion rate is one of the most important determining factors of quality and productivity.

However, little research has been conducted on the combustion behavior of biomass carbon material quasi-particles during the sintering process. The purpose of this study was to investigate the combustion rate of a biomass carbon material and use a sintering simulation model to calculate its temperature profile.

2. Experimental Sample and Procedure

To simulate the test particles, the samples were prepared using alumina powder and woody biomass powder. The woody biomass powder used in this study was commercial mangrove charcoal, which is normally used for barbecues. To simplify the experimental conditions, alumina powder was prepared as a substitute for iron ore. Alumina eliminated the effects of melt formation, reduction and re-oxidation of iron ore during coke combustion. Charcoal powder with a particle diameter of −125 μm and 125~250 μm was used in this experiment. The particle size of iron ore was to simulate the adhere powder layer, but not the coke particle. Coke powder with the same particle diameter was used to compare the results. Alumina powder with a particle diameter of −250 μm was prepared to match the particle size of the iron ore. The analysis of the results of prepared carbon material are listed in

Table 1. Properties of carbon materials.

	Ash (mass %)	V.M. (mass %)	Fix.C. (mass %)	Specific Surface Area (m2/g)
Charcoal (−125 μm)	1.84	29.2	69.0	61.0
Charcoal (125~250 μm)				28.5
Coke (−125 μm)	10.1	1.71	88.2	2.59
Coke (125~250 μm)				0.92

. Compared with coke, charcoal has a lower ash ratio and higher volatile matter content and therefore charcoal has a lower fixed carbon. The surface area of charcoal is higher than that of coke. This was also observed by an SEM, as shown in Figure 1. Figure 2 shows the overall view of raw materials and samples. After the alumina and coke powders were mixed, 0.5 mass % flour was mixed as a binder. The flour was just used to enable keeping the tablet shape until it was inserted to the platinum basket. It was thought that the effect of the flour could be negligible, because flour evaporates at a lower temperature—600 K—than the experimental temperature in this study. Then, the mixture was pressed into 10 mm diameter tablets by stainless dies. The height of the tablet was 10 mm with a void ratio of 35%. The void ratio was decided from the information on the tablet volume and the true density of the sample mixture. Each true density of the sample materials was measured by pycnometer. The weight ratio of coke in each sample was fixed at 20 mass %. To ensure that the volume ratio of the samples was the same as the hematite and alumina samples, 22.1 mass % coke with 77.9 mass % alumina and 20.8 mass % charcoal with 79.2 mass % alumina was also prepared.

The measurement of the sample weight loss during coke combustion was done by the thermobalance shown in Figure 3. The sample was placed in a platinum basket. A vertical electric resistance furnace was used to do isothermal heating. The isothermal zone was heated up to 1073 K, 1223 K, 1373 K and 1523 K. Before the combustion experiment, heat treatment of the samples was carried out at each of the given temperatures in a N₂ atmosphere for 30 mins to remove water, Volatile matter (V.M.) and the binder from the samples. Then, air was passed through the reaction tube. The air flow rate was 4 NL/min. When a weight change in the sample was not observed, the experiment was terminated. It was hypothesized that coke ash did not influence the weight loss of the sample because the amount of coke in every sample stayed the same.

3. Results

The reaction ratio in the study was defined as the removal ratio of fixed carbon from the sample. A carbon combustion reaction can be described using the following chemical reaction, if CO gas formation is ignored:

$$C\left(s\right)+O_2\left(g\right)={\mathrm{CO}}_2\left(g\right)$$

(1)

In the combustion experiment, the sample weight loss was attributed to the decrease in the amount of fixed carbon. Therefore, the reaction ratio (F) at a reaction time can be described by Equation (2):

$$F=\frac{\Delta w_t}{W}$$

(2)

Fractional reaction curves at 1073 K are shown in Figure 4. The figure shows that combustion rates of charcoal were quicker than those of coke. This tendency was also observed at 1223 K, 1373 K and 1523 K.

To verify the reaction mechanism of the combustion reaction, samples with a reaction ratio of 50% were also prepared under 1073 K and 1523 K and cross-sectional and microscopic observations were made. Figure 5 and Figure 6 show the cross-sectional observation and the microstructure at the reaction interfaces of each sample. It was clear that the combustion reaction was a topochemical reaction.

4. Kinetic Analysis

4.1. Unreacted Core Model for Coke

From the fractional reaction curves obtained from the combustion experiment, the combustion reaction rate constant was determined using the unreacted core model [7]. The combustion reaction has five processes [8].

1.

O₂ transport from the gas phase to the particle surface through the gas film:

$$-{\dot{n}}_{g\cdot O_2}=4\pi r_0^2{k}_f\left(C_{O_2}-C_{O_2\cdot s}\right)$$

(3)

2.

O₂ transport from the particle surface to the reaction interface through the alumina powder layer after coke combustion:

$$-{\dot{n}}_{d\cdot O_2}={(D_{O_2})}_{eff}\frac{4\pi r_0{r}_i}{r_0-r_i}\left(C_{O_2\cdot s}-C_{O_2\cdot i}\right)$$

(4)

3.

The combustion reaction at the reaction interface:

$$-\dot{R}=4\pi r_i^2{k}_c\left(C_{O_2\cdot i}-\frac{C_{{\mathrm{CO}}_2\cdot i}}{K}\right)$$

(5)

4.

CO₂ transport from the reaction interface to the particle surface through the alumina powder layer after coke combustion:

$${\dot{n}}_{d\cdot {\mathrm{CO}}_2}={(D_{{\mathrm{CO}}_2})}_{eff}\frac{4\pi r_0{r}_i}{r_0-r_i}\left(C_{{\mathrm{CO}}_2\cdot i}-C_{{\mathrm{CO}}_2\cdot s}\right)$$

(6)

5.

CO₂ transport from the particle surface to the gas phase through the gas film:

$${\dot{n}}_{g\cdot {\mathrm{CO}}_2}=4\pi r_0^2{k}_f\left(C_{{\mathrm{CO}}_2\cdot s}-C_{{\mathrm{CO}}_2}\right)$$

(7)

The overall rate equation can be described by the quasi-steady state analysis method below:

$$-\dot{n}=\frac{4\pi r_0^2\left(\frac{K}{1+K}\right)\left(C_{O_2}-C_{{\mathrm{CO}}_2}\right)}{\frac{1}{k_f}+\frac{1}{D_e}\cdot \frac{r_0\left(r_o-r_i\right)}{r_i}+\frac{1}{k_c}\cdot \frac{K}{1+K}{\left(\frac{r_0}{r_i}\right)}^2}$$

(8)

$$\frac{1}{D_e}=\frac{K}{1+K}\left(\frac{1}{{(D_{O_2})}_{eff}}+\frac{1}{K{(D_{{\mathrm{CO}}_2})}_{eff}}\right)$$

(9)

Equation (8) can be expressed by the following equation, assuming that the combustion reaction of coke was an irreversible reaction and the equilibrium constant K infinite:

$$-\dot{n}=\frac{4\pi r_0^2{C}_{O_2}}{\frac{1}{k_f}+\frac{1}{D_e}\cdot \frac{r_0\left(r_0-r_i\right)}{r_i}+\frac{1}{k_c}\cdot {\left(\frac{r_0}{r_i}\right)}^2}$$

(10)

$\dot{n}$ can be replaced by the following equation:

$$-\dot{n}=-\frac{d}{dt}\left(\frac{4}{3}\pi r_i^3{\rho }_{Cm}\right)=-4\pi r_i^2{\rho }_{Cm}\cdot \frac{d{r}_i}{dt}$$

(11)

The reaction ratio F is expressed by Equation (12):

$$F=1-{\left(\frac{r_i}{r_0}\right)}^3$$

(12)

When Equations (10)–(12) are combined and integrated under boundary conditions; r = r₀ at t = 0 and r = r_i at t = t, Equation(13) is obtained:

$$t=\frac{{\rho }_{Cm}{r}_0}{C_{O_2}}\cdot \left[\frac{F}{3k_f}+\frac{d_r}{16D_e}\left\{3-3{\left(1-F\right)}^{\frac{2}{3}}+2F\right\}+\frac{1}{k_C}\left\{1-{\left(1-F\right)}^{\frac{1}{3}}\right\}\right]$$

(13)

The gas film mass transfer coefficient, k_f, can be calculated from Ranz–Marshall’s Equation [9]. The value of the effective diffusion coefficient in the alumina layer, D_e, and the interfacial reaction rate coefficient of coke, k_C, was obtained by parameter-fitting using the nonlinear least-squares method to the fractional reaction curves.

D_e, and k_C can be expressed by substituting the coefficients in Arrhenius’ equation as shown:

$$k_C=A_{\left(k_C\right)}exp\left(-\frac{E_a{}_{\left(k_C\right)}}{RT}\right)$$

(14)

$$D_e=A_{\left(D_e\right)}exp\left(-\frac{E_{a\left(D_e\right)}}{RT}\right)$$

(15)

Equations (13) and (14) can be transformed into the following equations:

$$ln{k}_C=-\frac{E_{a\left(k_C\right)}}{R}\cdot \frac{1}{T}+ln{A}_{\left(k_C\right)}$$

(16)

$$ln{D}_e=-\frac{E_{a\left(D_e\right)}}{R}\cdot \frac{1}{T}+ln{A}_{\left(D_e\right)}$$

(17)

Figure 7 shows the Arrhenius plot of k_c. The values of k_c are at the same level in all samples.

The temperature dependence of k_c is expressed as

Coke	(−125 μm)	kc = 6.02 × 10−2 exp(−9.32 × 103/RT)	(m/s)
	(125~250 µm)	kc = 4.51 × 10−2 exp(−5.12 × 103/RT)	(m/s)

Figure 7. Temperature dependence of the reaction rate constants k_c.

Figure 7. Temperature dependence of the reaction rate constants k_c.

Figure 8 shows the Arrhenius plot of D_e. The temperature dependence of D_e can be expressed as

Coke	(−125 μm)	De = 1.79 × 10−3 exp(−36.4 × 103/RT)	(m/s)
	(125~250 µm)	De = 3.06 × 10−3 exp(−36.6 × 103/RT)	(m/s)

Figure 8. Temperature dependence of the effective diffusivities D_e.

Figure 8. Temperature dependence of the effective diffusivities D_e.

4.2. Chemical Reaction Control Step for Charcoal

Because the surface area of charcoal is larger than that of coke, when a combustion reaction takes place, the reaction area of charcoal will also be larger. Moreover, due to the low ash ratio in the charcoal, the O₂ transportation rate in the alumina layer will be large. Therefore, the reaction is based on the chemical reaction control step.

For the charcoal samples, the chemical reaction control step can be used in the analysis method shown below:

The combustion reaction at the reaction interface can be expressed by Equation (5).

The combustion rate can be expressed as

$$-\dot{n}=\frac{4\pi r_0^2\left(\frac{K}{1+K}\right)\left(C_{O_2}-\raisebox{1ex}{$C_{C{O}_2}$}\!\left/ \!\raisebox{-1ex}{$K$}\right.\right)}{\frac{1}{k_c}\cdot \frac{K}{1+K}{\left(\frac{r_0}{r_i}\right)}^2}$$

(18)

Under boundary conditions, r = r₀ at t = 0 and r = r_i at t = t, and this gives Equation (19):

$$\left[1-{\left(1-F\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right]=\frac{C_{O_2}}{\rho c_m{r}_0}{k}_{c}t$$

(19)

Based on the reaction curves obtained by the experiments, k_c was determined using the unreacted core model [3].

k_C can be substituted in Arrhenius’ equation as shown by Equation (14) which also can be transformed as Equation (16).

Figure 9 shows the Arrhenius plot of k_c.

The temperature dependence of k_c can be expressed as

Coke	(−125 μm)	kc = ${8.24\times 10}^{-3}\exp \left({-10.6\times 10}^3/RT\right)$	(m/s)
	(125~250 µm)	kc = ${8.54\times 10}^{-3}\exp \left({-10.3\times 10}^3/RT\right)$	(m/s)

Figure 9. Temperature dependence of the reaction rate constants k_c.

Figure 9. Temperature dependence of the reaction rate constants k_c.

5. Sintering Simulation Model

5.1. Simulation Method

The simulation condition was based on the study results using Ohno’s model [10]. The model has S’-type, C-type and P-type quasi-particles as shown in Figure 10. The S’ type was calculated using Hottel’s equation [11,12,13], while the C and P types were calculated based the results obtained in this study.

Our mathematical model is based on the Dwight–Lloyd sinter machine and the calculation range is from the ignition point on the pallet to the discharge of the sinter ore.

The numerical analysis was based on the control volume method shown in Figure 11. The control volume method is obtained by dividing the analysis target region into equal minute portions. Various basic equations, representing phenomena, such as the continuous and energy conservation equations, govern the inside of the analysis target area and are relational equations to be established in each control volume. Assuming that these control volumes are in a sufficiently small area, there would not be a large error even if the changes in various quantities inside the control volumes were linear or approximated to be constant values. In other words, changes in various quantities in a certain control volume can be represented using values at a representative point in the control volume adjacent to the representative point. In our mathematical model, the sintering material layer was divided into minute control volumes in one dimension, the basic governing equations were discretized, and each difference approximation equation was solved using an explicit method.

In the model used, the temperature distribution was estimated considering the combustion of carbonaceous materials, the decomposition reaction of CaCO₃, the evaporation and condensation of water, and the formation and solidification of calcium ferrite melt according to Ohno’s model [10].

D_e depends on coke distribution.

The combustion reaction rate of the quasi-particles is expressed by Equations (20) and (21):

$$r_{Quasi-particle}^{*}=4\pi r_{Quasi-particle}^2{k}^{\prime }{C}_{O_2}$$

(20)

$$k^{\prime }=1/\left(\frac{1}{k_f}+\frac{r_0\left(r_0-r_i\right)}{D_e{r}_i}+\frac{r_0^2}{k_c{r}_i^2}\right)$$

(21)

In this equation, D_e has a value of 10⁸ because the resistance of the diffusion can be ignored.

The material balance is calculated using Equation (22):

$$\frac{{{\rho }_{i\cdot x}|}_{t+\Delta t}-{{\rho }_{i\cdot x}|}_t}{\Delta t}=-\frac{{\left({\rho }_{Z+\Delta Z}{u}_i\right)|}_{Z+\Delta Z}-{\left({\rho }_Z{u}_{i-1}\right)|}_Z}{\Delta Z}+r_{i,x}^{*}$$

(22)

The material balance equations of N₂, O₂, CO₂ and H₂ respectively, can be expressed as follows:

$$\frac{\partial \left({\rho }_{N_2}u\right)}{\partial Z}=-\frac{\partial {\rho }_{N_2}}{\partial t}$$

(23)

$$\frac{\partial \left({\rho }_{O_2}u\right)}{\partial Z}=-\frac{\partial {\rho }_{O_2}}{\partial t}-r_{Coke}^{*}$$

(24)

$$\frac{\partial \left({\rho }_{C{O}_2}u\right)}{\partial Z}=-\frac{\partial {\rho }_{C{O}_2}}{\partial t}+r_{Coke}^{*}+r_{CaC{O}_3}^{*}$$

(25)

$$\frac{\partial \left({\rho }_{H_{2}O}u\right)}{\partial Z}=-\frac{\partial {\rho }_{H_{2}O}}{\partial t}+r_{H_{2}O}^{*}$$

(26)

Because convection did not occur in the solid phase, the thermal budget of the phase considering heat transfer and reaction heat can be represented as

$$\begin{gathered} {\rho }_s{C}_{P\cdot s}\frac{\partial T_s}{\partial t}-\frac{6\left(1-{\epsilon }_a\right)}{\dot{d}}h\left(T_g-T_s\right)+H_{Coke}\left(r_{Coke}^{*}{n}_{Coke}+r_{Quasi-paritcle}^{*}{n}_{Quasi-particle}\right) \\ +H_{CaC{O}_3}{r}_{CaC{O}_3}^{*}{n}_{CaC{O}_3}+H_{H_{2}O\cdot V}{r}_{H_{2}O\cdot V}^{*}+H_{CF\cdot G}{r}_{CF\cdot G}^{*}+H_{CF\cdot S}{r}_{CF\cdot S}^{*}=k\frac{{\partial }^2{T}_s}{\partial Z^2} \end{gathered}$$

(27)

The thermal budget of the gas phase factoring the heat transfer and combustion reaction heat can be expressed as

$${\rho }_g{C}_{P\cdot g}\frac{\partial T_g}{\partial t}-\frac{6\left(1-{\epsilon }_a\right)}{\dot{d}}h\left(T_s-T_g\right)+C_{P\cdot g}\frac{\partial {\rho }_{g}u{T}_g}{\partial Z}=k\frac{{\partial }^2{T}_g}{\partial Z^2}$$

(28)

The particles were charged in the control volume. Therefore, the pressure loss of the fluid also needed to be considered. The pressure loss of a laminar-turbulent transition area can be represented by Ergun’s equation as shown:

$$\frac{\Delta P}{\Delta Z}=\frac{150{(1-{\epsilon }_a)}^2}{{(\phi d)}^2{\epsilon }_a{}^3}\cdot \frac{{\mu }_g}{{\rho }_g}U+1.75\frac{1-{\epsilon }_a}{\phi d{\epsilon }_a{}^3}{U}^2$$

(29)

5.2. Calculation Conditions

Table 2. Common calculation conditions.

▪Sinter Bed
Bed depth	450 mm
Porosity of sinter bed	35%
▪Composition of Raw materials
Hematite	85.0 mass %
Lime (CaO)	10.0 mass %
Moisture	5.0 mass %
Coke, Charcoal	4.0 mass % (additionally)
Charcoal	5.1 mass % (additionally)
▪Diameter of Raw Materials
Hematite	2.5 mm:0.25 mm ≈ 88.6:11.4
Lime (CaO)	2.0 mm
▪Others
Initial temperature	298 K
Ignition temperature	1573 K
Ignition time	90 s
Gas flow rate (outlet)	0.6 m/s
Calculation cell	5 mm
Time step	0.001 s
Courant number	0.2

lists the common calculation conditions for the sintering process. The composition of raw materials was set to simplify the calculation condition. The influence of MgO was not considered in this study. The particle size of hematite was set to 2.5 mm and 0.25 mm. It was assumed that 2.5 mm and 0.25 mm were the sizes of the nuclear particle and the adhering fine ores, respectively, in the quasi-particle. The 5.1 mass % charcoal calculation was compared with the 4 mass % coke calculation when the fixed carbon content is the same which means that the combustion heat of coke and charcoal during this process is the same. However, in this study, the effect of V.M. was not discussed. As a thought, the gas generated when V.M. is heated may improve the permeability and affect the temperature profile in the same way as a gas fuel injection, mentioned by Oyama [14]. Further research is needed to clarify this factor.

Table 3. Existing state of the coke quasi-particles in the sinter bed.

Existing State of Coke (%)			Total	Amount of Coke and Charcoal in Sinter Bed (%)
S’-Type	C-Type	P-Type
40.0	30.0	30.0	100	4.0, 5.1

lists the state of the coke quasi-particles in the sinter bed for calculation using the date of the sinter pot test based on Hida’s study [15].

5.3. Calculation Results

Figure 12 and Figure 13 show the temperature profiles of the cases of coke and charcoal at a depth of 20 cm and 40 cm, respectively. The basic case was 4 mass% coke mixing condition. It was compared with cases of 4 mass % and 5.1 mass % charcoal mixing conditions. The influence of particle size is not apparent. Compared with the results for coke, charcoal has a lower temperature profile and a shorter holding time at a high temperature. This is thought to be due to the low fixed carbon content and the density of charcoal which leads to the presence of unreacted charcoal. As a result, the temperature of charcoal in all the sinter cakes was lower than that of coke.

However, when the amount of charcoal was 5.1 mass %, the holding times at a high temperature of both kinds of carbon material were at the same level. The highest temperature of charcoal was higher than that of coke. The rate of the temperature increase of charcoal was also faster than that of coke. This is because the combustion rate of charcoal is higher than that of coke, i.e., if the fixed carbon content of charcoal is equivalent to that of coke, the temperature profile of the same level can be obtained. Therefore, the sintering simulation results of this study show that there are probabilities that charcoal can replace coke in the sintering process.

6. Conclusions

The study aimed to understand the combustion rate of a biomass carbon material using a sintering model to calculate its temperature profile. The following conclusions were made:

• Compared with coke, the reaction curves of charcoal combustion show that the combustion reaction of charcoal is faster.
• The interfacial chemical reaction rate coefficient of charcoal for the experimental data was calculated as follows:

Coke	(−125 μm)	kc = ${8.24\times 10}^{-3}\exp \left({-10.6\times 10}^3/RT\right)$	(m/s)
	(125~250 µm)	kc = ${8.54\times 10}^{-3}\exp \left({-10.3\times 10}^3/RT\right)$	(m/s)

• Calculations using the rate equation obtained in the sintering simulation model found that the high temperature range of charcoal is smaller than that of coke due to charcoal’s low fixed carbon content and density.
• If the fixed carbon content of charcoal is the same as that of coke, which means that the combustion heat of carbon materials is the same, a temperature profile of the same level can be obtained.
• The sintering simulation results suggest that there are probabilities that biomass carbon materials can replace coke in the sintering process.