Effect of Coke Breeze Distribution on Coke Combustion Rate of the Quasi-particle

Abstract

Coke combustion rate in an iron ore sintering process is one of the most important factors for quality and productivity of sintering iron ore.

In order to improve coke combustion efficiency, a new granulation method was developed. In the new granulation method, coke and limestone are segregated to the particle’s surface. The purpose of this study is to investigate the effect of coke distribution in the quasi-particle on coke combustion rate.

Four kinds of samples, which have different coke distributions, were prepared. The samples consist of interior part and exterior part.

Combustion experiments were carried out under air atmosphere at 1073 K, 1223 K, 1373 K and 1523 K. From the results, coke combustion rates were improved when added coke were segregated to sample’s surface. At higher experimental temperature, the combustion rates become faster. The results were analyzed by using unreacted-core model with one reaction interface.

From the kinetic analysis, it was found that the coke distribution of the quasi-particle had effects on not the interfacial reaction rate but the oxygen diffusion. In other words, oxygen diffusion in the quasi-particle become faster when added coke was segregated to the quasi-particle’s surface. This is one of the main reasons that coke combustion rate in quasi-particle made from new granulation method was improved.

1. Introduction

It is becoming more severe to make sintering iron ore because of remarkable rise of the raw materials price, environmental regulation and inferior in quality of raw materials. Therefore, it is necessary to improve a method of making sintering iron ore. In the sintering process, coke combustion rate is one of the most important factors for quality and productivity of sintering ore.

In order to improve coke combustion efficiency, new granulation method was developed.^1,2,3) Figure 1 shows new granulation method. In this method, coke and limestone are coating to the quasi-particle’s surface.

Fig. 1.

Ordinary granulation method and coating granulation method.

It is thought that this coating method can be improve combustion of coke and high quality and productivity of sintering iron ore can be accomplished.

The purpose of this study is to investigate the effect of coke distribution in the quasi-particle on coke combustion rate.

2. Experiment Sample and Procedure

As simulant quasi-particle, the experiment samples were prepared using alumina powder and coke powder. For simplification of experimental condition, alumina powder was prepared as the substitute of iron ore. It can make to ignore the effects of melt formation, reduction and re-oxidation of iron ore on the coke combustion. Based on previous study,⁴⁾ volume ratio of alumina and coke set 61:39 substituting for hematite by alumina of the same volume as the weight ratio of hematite and cokes was 80:20. Coke powder, particle diameter was −125 μm, and alumina powder, particle diameter was −250 μm, were well mixed as given mass ratios shown in Table 1. 4 kinds of samples, which have different coke distributions, were prepared. Figure 2 shows Over-all view of raw materials and sample. The samples consist of interior part and exterior part. After the alumina and coke powders were well mixed, the mixture was pressed into tablet shape of 10 mm in the diameter by stainless dies. This tablet was interior part and the height of tablet was 10 mm and void ratio was 35%. After that, interior part was coated with exterior part and pressed into tablet shape of 15 mm in the diameter. The height of sample tablet was 15 mm and void ratio was 35%. The coke mixing ratio of exterior part was varied from 33 vol% to 55 vol%.

Table 1. Mixing ratio of samples.

	Interior part		Exterior part
	Coke (vol%)	Alumina (vol%)	Coke (vol%)	Alumina (vol%)
Type1 (55 vol%Coke)	0	100	55	45
Type2 (46 vol%Coke)	22	78	46	54
Type3 (39 vol%Coke)	39	61	39	61
Type4 (33 vol%Coke)	52	48	33	67

Fig. 2.

Over-all view of raw materials and sample.

Measurement of sample weight loss during coke combustion was carried out by thermobalance in this study as shown in Fig. 3. The sample was put into platinum basket. The vertical electric resistance furnace was used in order to make isothermal heating condition. The isothermal zone was heated up to 1073 K, 1223 K, 1373 K and 1523 K. Before combustion experiment, heat treatment was carried out at each given temperature under N₂ atmosphere in order to remove water and volatile matter from sample. After that, an inside of a reaction tube was changed to air atmosphere and air flow rate was 4 Nl/min. When the weigth loss of sample was not observed, the experiment was terminated. And, it was thought that coke ash did not influence the weight loss of sample because the amount of coke in every sample is the same.

Fig. 3.

Schematic diagram of the experimental device.

3. Result

Definition of reaction ratio in this study is removal ratio of fixed carbon from the sample. Carbon combustion reaction can be described as following chemical reaction, if CO gas formation would be ignored.   

$$\text{C}(s)+{\text{O}}_{\text{2}}(g)={\text{CO}}_{\text{2}}(g)$$(1)

In combustion experiment, sample weight loss was considered as decrease amount of fixed carbon. Therefore, a reaction ratio at a reaction time could describe as Eq. (2).   

$$F=\frac{\mathrm{\Delta }{w}_t}{W}$$(2)

Fractional reaction curves at 1073 K, 1223 K, 1373 K and 1523 K are shown in Figs. 4, 5, 6 and 7. From these figures, coke combustion rates were faster when added coke were segregated to sample’s surface. However, combustion rate of Type4 was almost same with that of Type3. It was thought that the diffusive resistance of oxygen of Type4 was the same with that of Type3 because the difference of alumina quantity in exterior part between Type3 and Type4 was small. At higher experimental temperature, the combustion rates became faster.

Fig. 4.

Fractional reaction curves of coke combustion at 1073 K.

Fig. 5.

Fractional reaction curves of coke combustion at 1223 K.

Fig. 6.

Fractional reaction curves of coke combustion at 1373 K.

Fig. 7.

Fractional reaction curves of coke combustion at 1523 K.

4. Kinetic Analysis

4.1. Analysis Method

From fractional reaction curves obtained from combustion experiment, combustion reaction rate constant was determined by using the unreacted-core model.⁵⁾ The combustion reaction has 5 process.

I. O₂ transport from the gas phase to the particle surface through gas film.   

$$-{\dot{n}}_{g\cdot {\text{O}}_{\text{2}}}=4\pi r_0^2{k}_f\left(C_{{\text{O}}_{\text{2}}}^{}-C_{{\text{O}}_{\text{2}}\cdot s}^{}\right)$$(3)

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

$$-{\dot{n}}_{d\cdot {\text{O}}_2}={(D_{{\text{O}}_{\text{2}}})}_{eff}\frac{4\pi r_0{r}_i}{r_0-r_i}\left(C_{{\text{O}}_2\cdot s}^{}-C_{{\text{O}}_2\cdot i}^{}\right)$$(4)

III. Combustion reaction at reaction interface.   

$$-\dot{R}=4\pi r_i^2{k}_c\left(C_{{\text{O}}_{\text{2}}\cdot i}-\frac{C_{{\text{CO}}_{\text{2}}\cdot i}^{}}{K}\right)$$(5)

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

$${\dot{n}}_{d\cdot {\text{CO}}_{\text{2}}}={(D_{{\text{CO}}_{\text{2}}})}_{eff}\frac{4\pi r_0{r}_i}{r_0-r_i}\left(C_{{\text{CO}}_{\text{2}}\cdot i}^{}-C_{{\text{CO}}_{\text{2}}\cdot s}^{}\right)$$(6)

V. CO₂ transport from the particle surface to the gas phase through gas film.   

$${\dot{n}}_{g\cdot {\text{CO}}_{\text{2}}}=4\pi r_0^2{k}_f\left(C_{{\text{CO}}_{\text{2}}\cdot s}^{}-C_{{\text{CO}}_{\text{2}}}^{}\right)$$(7)

Overall rate equation could be described by quasi-steady state analysis method as follow.   

$$-\dot{n}=\frac{4\pi r_0^2\left(\frac{K}{1+K}\right)\left(C_{{\text{O}}_{\text{2}}}^{}-C_{{\text{CO}}_{\text{2}}}\right)}{\frac{1}{k_f}+\frac{1}{D_e}\cdot \frac{r_0\left(r_o-r_i\right)}{r_i}+\frac{1}{k_c}\cdot \frac{K}{1+K}{\left(\frac{r_0}{r_i}\right)}^2}$$(8)

  

$$\frac{1}{D_e}=\frac{K}{1+K}\left(\frac{1}{{(D_{{\text{O}}_{\text{2}}})}_{eff}}+\frac{1}{K{(D_{{\text{CO}}_{\text{2}}})}_{eff}}\right)$$(9)

Equation (8) could be expressed as the following equation, if it could be assumed that the combustion reaction of coke is irreversible reaction and the equilibrium constant K is infinite.   

$$-\dot{n}=\frac{4\pi r_0^2{C}_{{\text{O}}_{\text{2}}}}{\frac{1}{k_f}+\frac{1}{D_e}\cdot \frac{r_0\left(r_0-r_i\right)}{r_i}+\frac{1}{k_c}\cdot {\left(\frac{r_0}{r_i}\right)}^2}$$(10)

And $\dot{n}$ could be replaced with the following equation.   

$$-\dot{n}=-\frac{d}{dt}\left(\frac{4}{3}\pi r_i^3{\rho }_{\text{C}m}\right) =-4\pi r_i^2{\rho }_{\text{C}m}\cdot \frac{d{r}_i}{dt}$$(11)

The reaction ratio F is expressed as Eq. (12)   

$$F=1-{\left(\frac{r_i}{r_0}\right)}^3$$(12)

When Eqs. (10), (11) and (12) was combined and integrate under the boundary conditions are r=r₀ at t=0 and r=r_i at t=t, Eq. (13) is obtained.   

$$\begin{array}{l}t=\frac{{\rho }_{\text{C}m}{r}_0}{C_{{\text{O}}_{\text{2}}}}\cdot \\ \left[\frac{F}{3k_f}+\frac{d_r}{16D_e}\left\{3-3{\left(1-F\right)}^{\frac{2}{3}}+2F\right\}+\frac{1}{k_C}\left\{1-{\left(1-F\right)}^{\frac{1}{3}}\right\}\right]\end{array}$$(13)

Gas film mass transfer coefficient k_f could be calculated from Ranz-Marshall’s equation.⁶⁾ The value of effective diffusion coefficient in the alumina layer D_e and interfacial reaction rate coefficient of coke k_C were obtained by parameter fitting using the non-linear least-squares method to the fractional reaction curves.

4.2. Analysis Result

Effective diffusion coefficient in the alumina layer D_e and interfacial reaction rate coefficient of coke k_C could be refered to the following equation with Arrhenius’s equation.   

$$k_C=A_{(k_C)}exp\left(-\frac{E_a{\hspace{0.17em}}_{(k_C)}}{RT}\right)$$(14)

  

$$D_e=A_{(D_e)}exp\left(-\frac{E_{a(D_e)}}{RT}\right)$$(15)

Equations (13) and (14) could be transformed into the follow.   

$$ln{k}_C=-\frac{E_{a(k_C)}}{R}\cdot \frac{1}{T}+ln{A}_{(k_C)}$$(16)

  

$$ln{D}_e=-\frac{E_{a(D_e)}}{R}\cdot \frac{1}{T}+ln{A}_{(D_e)}$$(17)

Figure 8 shows Arrhenius plot of k_c. The values of k_c are almost the same in all samples.

Fig. 8.

Temperature dependence of reaction rate constants k_c.

The temperature dependence of k_c was expressed by Eq. (18)   

$$kc=5.03\times {10}^{-2}exp\left(-\frac{7.63\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[m/s]}$$(18)

Figure 9 shows Arrhenius plot of D_e in this study. The temperature dependence of D_e was expressed by Eqs. (19), (20), (21), (22) of every Type.

Fig. 9.

Temperature dependence of effective diffusivities D_e.

・Type1 (55 vol%Coke)   

$$D_{e(55vol\%Coke)}=5.74\times {10}^{-4}exp\left(-\frac{15.3\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[}{m}^2\text{/s]}$$(19)

・Type2 (46 vol%Coke)   

$$D_{e(46vol\%Coke)}=1.12\times {10}^{-3}exp\left(-\frac{27.4\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[}{m}^2\text{/s]}$$(20)

・Type3 (39 vol%Coke)   

$$D_{e(39vol\%Coke)}=3.56\times {10}^{-4}exp\left(-\frac{23.0\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[}{m}^2\text{/s]}$$(21)

・Type4 (33 vol%Coke)   

$$D_{e(33vol\%Coke)}=2.11\times {10}^{-4}exp\left(-\frac{18.9\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[}{m}^2\text{/s]}$$(22)

The value of D_e became lager in the order of Type1>Type2>Type3≒Type4.

Generally, effective diffusion coefficient (D_e), porosity (ε) and tortuosity factor (τ) had the following relation.   

$$D_e=D_{{\mathrm{O}}_2}\cdot \epsilon \cdot \frac{1}{\tau }\hspace{1em}\hspace{1em}\text{[}{m}^2\text{/s]}$$

In previous study,⁴⁾ τ became constant when porosity was more than 0.6 and τ increased rapidly when porosity was less than 0.6.

In this experiment, porosity in exterior part was 0.71 in Type1, 0.65 in Type2, 0.60 in Type3 and 0.57 in Type4. It was thought D_e of Type2 was larger than that of Type3 because of the influence of tortuosity factor. However, it is not so clear about the influence factor to D_e when the coke distribution is changed, therefore detailed analysis is a future problem.

From the kinetic analysis, it was found that the coke distribution of the quasi-particle had effects on not the interfacial reaction rate but the oxygen diffusion. In other words, oxygen diffusion in the quasi-particle is faster when added coke was segregated to the quasi-particle’s surface. This could be one of the main reasons that coke combustion rate in quasi-particle made from new granulation method improved.

5. Sintering Simulation Model

5.1. Simulation Method

The coating method was simulated with this study result, referring to Ohno’s model.⁷⁾ Distribution of the coke in quasi-particles is different between the ordinary model and the coating model. The ordinary model had S′-type, C-type and P-type. Furthermore in this study, new quasi-particles coke segregated to the surface were definded as C′-type and P′-type as showing Fig. 10.

Fig. 10.

Classification of quasi-particle.

From analysis result at 4-2, the following things were understood in combustion of coke.

I. Interfacial reaction rate coefficient of coke k_C does not have effect of Coke distribution.

II. Effective diffusion coefficient D_e depends on coke distribution.

Combustion reaction rate in quasi-particle is expressed by Eqs. (23) and (24)   

$$r_{Quasi-particle}^{*}=4\pi r_{Quasi-particle}^2{k}^{\prime }{C}_{{\text{O}}_{\text{2}}}$$(23)

  

$$k^{\prime }=1/\left(\frac{1}{k_f}+\frac{r_0(r_0-r_i)}{D_e{r}_i}+\frac{r_0^2}{k_c{r}_i^2}\right)$$(24)

k_C and D_e of ordinary and coating model is shown as follows.

I. Interfacial reaction rate coefficient of coke k_C of ordinary and coating model   

$$kc=5.03\times {10}^{-2}exp\left(-\frac{7.63\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[m/s]}$$

II. Effective diffusion coefficient D_e

・Ordinary model   

$$D_{e(39vol\%Coke)}=3.56\times {10}^{-4}exp\left(-\frac{23.0\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[}{m}^2\text{/s]}$$

・Coating model   

$$D_{e(55vol\%Coke)}=5.74\times {10}^{-4}exp\left(-\frac{15.3\times {10}^3}{RT}\right)\hspace{1em}\hspace{1em}\text{[}{m}^2\text{/s]}$$

In this study, coating model was simulated using result of Type1 (55 vol%Coke) because coke are coating to the quasi-particle’s surface in coating granulation method, and ordinary model using result of Type3 (39 vol%Coke). It was assumed that the quasi-particles of coating model had not C-type and P-type but C′-type and P′-type.

5.2. Calculation Conditions

Table 2 shows common calculation conditions for all cases based on practical sintering process. The particle size of hematite was setted 2.5 mm and 0.25 mm, and it assumed that 2.5 mm was nuclear particle and 0.25 mm was adhering fine ore in quasi-particle.

Table 2. Common calculation conditions.

・Sinter bed
Bed depth	700 mm
Porosity of sinter bed	35%
・Composition of raw materials
Hematite	84.2 mass%
Lime stone (CaCO3)	8.7 mass%
Moisture	7.1 mass%
Coke	3.8 mass% (Additionally)
・Diameter of raw materials
Hematite	2.5 mm, 0.25 mm
Coke [S′-type]	1.5, 1.25, 0.75, 0.375 mm
Coke [C,C′,P,P′-type]	0.125 mm
Lime stone (CaCO3)	2.0 mm
・Others
Initial temperature	298 K
Ignition temperature	1573 K
Ignition time	60 s
Gas flow rate (outlet)	0.38 m/s
Calculation cell	5 mm
Time step	0.001 s

Table 3 shows existing state of coke in quasi-particle of sintering bed for calculation using the date of the sinter pot test as reference. Case1 is ordinary model and Case2 is coating model.

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

	Type of quasi-particle (mass%Coke)
	S′-type	C-type	P-type	C′-type	P′-type
Quasi-particle’s diameter (mm)	1.5	3.4	2.0	3.4	2.0
	1.25
	0.75
	0.375
	[in the same mass ratio]
Case1	24	47.5	28.5	0	0
Case2	24	0	0	47.5	28.5

5.3. Calculation Results

Visualized calculation results of heat distribution in Case 1 and Case2 were shown in Fig. 11. It could be simulated that combustion zone was advanced with time in Case1 and Case2. In this study, when temperature at 700 mm of sintering bed was not rised, the sintering reaction was terminated.

Fig. 11.

Simulation result of temperature distribution.

Termination time of sintering reaction in Case1 was 2714 s and that in Case2 was 2630 s. Sintering reaction rate in coating model was faster than ordinary model, because coke combustion rate in quasi-particle of coating model was faster than that of ordinary model. The highest arrival temperature in sintering bed of Case1 was 1815 K, and Case2 was 1627 K. The highest arrival temperature of coating model was lower than that of ordinary model.

Figures 12 and 13 show temperature and combustion rate of coke at 1500 s in Case1 and Case2, respectively. The maximum coke combustion rate of S′-type, C′-type and P′-type in Case2 was improved more than that of Case1. However, width of the combustion zone (1473 K–1673 K) of Case2 was smaller than that of Case1. Width of the combustion zone was affected by coke combustion rate.⁸⁾ Coke combustion rate was faster, width of the combustion zone was smaller. Therefore, width of the combustion zone of Case2 was smaller because coke combustion rate of P′-type and C′-type was faster than that of P-type and C-type. High temperature retention time of Case2 decreased than Case1 because of the reduction of width of combustion zone in Case2. The decrease of high temperature retention time and highest arrival temperature of Case2 caused reducing the quantity of heat storage. However, the useless combustion of coke could be prevented in Case2.

Fig. 12.

Simulation result of temperature distribution at 1500 s (Case1).

Fig. 13.

Simulation result of temperature distribution at 1500 s (Case2).

Therefore, productivity of sintering iron ore could improve because sintering time was reduced by using the coating method.

6. Conclusions

In order to understand the effect of coke distribution on coke combustion rate of the quasi-particle, combustion experiments were carried out when coke powder distribution in sample was changed, and following conclusions were obtained.

(1) Coke combustion rates in the quasi-particle are improved when added coke are segregated to sample’s surface. At higher experimental temperature, the combustion rates of coke become faster.

(2) The coke distribution of the quasi-particle have effects on not the interfacial reaction rate but the oxygen diffusion.

(3) Oxygen diffusion in the quasi-particle become faster when added coke is segregated to the quasi-particle’s surface.

(4) Sintering rate of coating method is faster than that of ordinary method because combustion of coke in quasi-particle using coating method is faster. However, the decrease of high temperature retention time and highest arrival temperature by using coating method caused reducing the quantity of heat storage.

(5) Productivity of sintering iron ore could improve because sintering time was reduced by using the coating method.

Nomenclature

A(_kc,De): Frequency factor (m/s)

C_O2,CO2: O₂ or CO₂ concentration in gas phase (mol/m³)

C_O2,CO2･i: O₂ or CO₂ concentration at reaction interface (mol/m³)

C_O2,CO2･s: O₂ or CO₂ concentration at particle surface (mol/m³)

D_e: Effective diffusion coefficient in Al₂O₃ powder layer (m²/s)

(D_O2,CO2)_eff: Effective diffusion coefficient of O₂ or CO₂ in Al₂O₃ powder layer (m²/s)

E_a(kc,De): Activation energy (J/mol)

F: Reaction ratio (−)

K: Equilibrium constant (−)

k_C: Interfacial chemical reaction rate coefficient (m/s)

k_f: Mass transfer coefficient in gas film (m/s)

r₀: Initial radius (m)

r_i: Radius of non-reaction nucleus (m)

r_{Quasi-particle}: Distance from center of particle to reaction interface of quasi-particle (m)

r*_{Quasi-particle}: Reaction rate per one particle of quasi-particle (mol/s)

Δw_t: Sample weight change (kg)

W : Fixed carbon in sample (kg)

τ: Tortuosity factor (–)

ρ_Cm: Carbon concentration in sample (mol/m³)

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