Influence of Reducing Gas Composition on Disintegration Behavior of Iron Ore Agglomerates

Abstract

H₂ injection through the shaft into blast furnace (BF) is a potential option for a further reduction of CO₂ emission from BF. H₂ promotes reduction reaction of burden materials, but its influence on their reduction disintegration behavior remains unknown in detail. This study has investigated the influence on the iron ore sinter, self-fluxed and acid pellets and specified essential factors governing the reduction disintegration behavior.

Mass ratios of particles below 3 mm in size were measured as an index for reduction disintegration (RDI) after the reduction of burden samples applying the gas mixtures of CO–H₂–CO₂–N₂ at 823 K. The reduced samples were observed by an optical-microscope and an electron probe micro-analyzer for evaluation of reaction mode. Further, using the measurement results, stress, strain energy and crack area generated during reduction were calculated and formation mechanism of cracks was examined.

RDI value of self-fluxed pellet increased under higher H₂ condition (40%N₂-20%H₂-10%CO-30%CO₂) and reached to 26 mass%. Such an increase was larger than expected from the standard RDI measure without H₂. Sample observation revealed a fact that reaction mode governed RDI value, that is, disintegration worsened under the reduction with non-topochemical mode. The fact was explained by the calculation as an influence of crack formation and propagation. In a case of reduction with topochemical reaction, cracks generated in a concentric fashion. Meanwhile, reduction with non-topochemical reaction tended to generate cracks in radial direction, which causes pellet chipping and further degradation. Calculated crack areas showed good correlation with RDI values. The Crack area of non-toochemical reaction was more than double than that of topochemical reaction. This result indicates that disintegration does not much progress when crack area is less than the certain limit value, but it proceeds drastically when it exceeded the limit value.

1. Introduction

The Japanese steel industry is known to have important issues related to the CO₂ emission and the quality of iron ore. In general, approximately 16% of CO₂ is emitted from the steel industry in Japan,¹⁾ and within that amount, about 70% of CO₂ is emitted from ironmaking process due to a large amount utilization of coke as reducing agents.²⁾ However, it is well known that Japanese steel industry has been introducing and developing the energy-saving technologies, the energy efficiency is resulting in the highest level in the world, thus further reduction of CO₂ is difficult.³⁾ In order to trying further reduction of CO₂ emission, the development of H₂ utilization technology for the blast furnace has been promoted.^{4,5,6,7,8,9,10,11,12,13)} Although large numbers of studies of reduction disintegration of sinter with CO reduction were reported,^14,15,16,17) there is a few reports about reduction disintegration behavior associated with the H₂ reduction.^12,18,19,20)

The second problem is a decrease of Fe contents and an increase of SiO₂ contents of iron ore.^20,21,22) This causes increase of slag volume of sinter, resulting in increasing in the reducing agent ratio of the BF.²³⁾ In contrast, Fe contents of pellet is higher as compared with the fine ore and stable, since their raw material is iron ore concentrates produced by a beneficiation process at the mining site. Therefore, it is possible to reduce the slag amount using more pellet to BF. However, it has been a few reports about the reduction disintegration behavior of the pellets. In order to increase a using amount of the pellets, it is necessary to investigate their reduction disintegration behavior and mechanism in detail.

The main factor of reduction disintegration is the crack generating by volume expansion with reduction from hematite to magnetite.¹⁴⁾ It is also known that mineralogical type of hematite is closely related to reduction disintegration behavior. For example, whereas porphyric hematite suppresses the crack generating, skeletal rhombohedral hematite causes a further crack generation and a crack propagation.¹⁵⁾ In addition, Haruna et al.¹⁶⁾ mentioned that reduction with non-topochemical reaction mode of porphyric hematite causes further disintegration.

Recently, the reduction disintegration behavior under H₂ atmosphere is reported. Murakami et al.^9,10,11) investigated the disintegration behavior of sinter under mix gas CO–CO₂–H₂–H₂O–N₂. In the case of addition of small amount of H2, the RDI value increased, whereas more increase in the H₂ concentration to 12% led to a decrease of RDI values. In contrast, Takeuchi et al.¹²⁾ pointed out that influence of H₂ gas on reduction disintegration behavior is slightly difference from Murakami’s conclusion. According to his report, the RDI value increased due to the increase in the H₂ concentration, but the influence of the H₂ concentration on the RDI valuye decreases in the range of the H₂ concentration of 3.8 to 6.8 vol%. Thus, there is some unclearness in the influence of H₂ on reduction disintegration. In clearly, diffusion coefficient of H₂ gas is approximately five times as high as that of CO gas,²⁴⁾ it is presumed that reaction mode with H₂ gas reduction is difference from that with CO gas. However, reaction modes in the case of addition of H₂ gas have been un-clarified, also the relationship and mechanism between reduction disintegration and reaction mode was not evaluated quantitatively.

In this study, therefore, the prediction model of reduction disintegration behavior by quantifying crack generation was examined through examination of the relationship between reaction mode and gas composition for clarifying the mechanism of reduction disintegration behavior of sinter and pellet in high H₂ condition.

2. Experimental

The samples used in this study were iron ore sinter, self-fluxed pellet and acid pellet, which were used in an actual plant and had the compositions listed in Table 1. These were sieved to grain size range between 10.0 and 15.0 mm. Samples with the total weight of 500 g ±1 g were randomly picked up and charged in the electrical furnace shown in Fig. 1.

Table 1. Chemical composition, JIS-RDI and JIS-RI values of samples.

Sample	T.Fe (mass%)	FeO (mass%)	SiO2 (mass%)	Al2O3 (mass%)	CaO (mass%)	MgO (mass%)	C/S (–)	JIS-RDI (mass%)	JIS-RI (mass%)
Sinter	58.01	6.08	5.23	1.82	9.36	0.93	1.79	34.3	62.6
Pellet A	65.93	0.66	2.36	0.54	2.62	0.01	1.11	2.1	55.7
Pellet B	65.57	1.29	2.63	0.78	2.04	0.09	0.78	3.4	71.9

Fig. 1.

Schematic of apparatus of reduction experiment.

Although reduction temperature of ISO4696-2 is fixed at 823 K, in this study, it was varied between 723 and 923 K. The samples were first heated in a N₂ gas stream with a flow rate of 15 NL/min and kept for 10 min. Subsequently, the gas was changed to a gas mixture listed Table 2 with the same flow rate and the reduction was carried out for 10, 20 and 30 min. After the reduction, the gas was changed to N₂ again, and the reduced samples were cooled down below 373 K. Then, the reduction degree was calculated from weight change during reduction.

Table 2. Reducing gas composition applied in this study.

Case	Gas composition (vol.%)
	H2	CO	CO2	N2
1	0	30	0	70
2	0	30	30	40
3	10	20	0	70
4	10	20	30	40
5	20	10	0	70
6	20	10	30	40
7	30	0	0	70
8	30	0	30	40

Disintegration tests were also conducted for the reduced samples on the basis of ISO4696-2 using a tumbling drum with an inner diameter of 130 mm at a rotation speed of 30 rpm for 30 min. Then, the sample was sieved using a 3 mm mesh to determine the weight of sample larger than 3 mm in particle size. RDI values were calculated using the following equation:   

$$\text{RDI}=\left(1-\frac{W1}{W0}\right)\times 100$$(1)

where W0 is a weight of the sample after the reduction experiment, and W1 is a weight of particles larger than 3 mm.

Quantification of reaction mode during reduction was attempted. A method for measuring the radial direction of the O/Fe [mol/mol] distribution of reduction after the sample by EPMA has been reported for a target the reduction from wȕstite to metallic iron at 900°C or above.^25,26,27) The value of O/Fe for hematite and magnetite are relatively close values, it becomes necessary to measure more precisely the value of O/Fe to apply this method for the reduction from hematite to magnetite of interest in this study. Therefore, high resolution analysis was adopted to quantify the gangue components. Specifically, O, Fe, Si, Ca, Al, Mg in samples after reduction were measured at each 20 mm square by EPMA.

Then, the molar concentration distribution of each component was calculated by Eq. (2), a molar concentration distribution of O that binds Fe, Si, Ca, Al or Mg by Eq. (3), O/Fe by Eq. (4). Here, since it was estimated that hematite is in the area with 3/2 of O/Fe, magnetite is in the area with 4/3, distribution of volume fraction of magnetite was derived by Eq. (5).   

$$n_A=\frac{W_A}{M_A}$$(2)

  

$$n_{O-A}=n_A\times \frac{i\times M_O}{M_{AOi}}$$(3)

  

$$\frac{\text{O}}{\text{Fe}}=\frac{n_{O-Fe}}{n_{Fe}}=\frac{\left\{n_O-\left(n_{O-Si}+n_{O-Al}+n_{O-Ca}+n_{O-Mg}\right)\right\}}{n_{Fe}}$$(4)

  

$$X_M=-\frac{1}{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.-\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\frac{\text{O}}{\text{Fe}}+\frac{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.-\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$(5)

where n_O−X is the molar number of oxygen binding X, n_X is the molar number of X, M_X is the molar mass of X, i is a number of binding oxygen and W_X is a mass fraction of X measured by EPMA, X_M is a volume fraction of magnetite.

3. Results

3.1. Influence of Gas Composition on RDI

Figure 2 shows the relationships between H₂/(H₂+CO) and RDI. RDI of pellet in CO reduction based on ISO4694-1 is the lowest compared with those of other cases, it was confirmed that pellets were hard to disintegrate in CO reduction as reported in previous studies.¹⁵⁾ RDI in H₂ reduction were higher than that in CO reduction in all burden materials. Furthermore, RDI values in mixed gas of H₂–CO reduction were always higher than the weight average of RDI in CO and H₂ reduction. RDI reached 26 mass% when self-fluxed pellet was reduced in a CO–CO₂–H₂ atmosphere. The increase is approximately five times as high as the standard RDI test (without H₂).

Fig. 2.

Influence of H₂/(H₂+CO) ratio on RDI value with different CO₂ concentrations at 773 K.

Figure 3 shows the relationship between RDI and reduction degree (R.D.). The R.D. values of sinter ranged from 3% to 7%. The R.D. values of pellet were higher than those of sinter, and ranged from 5% to 14%. Test conditions showing high RDI were confirmed at the same reduction degree in case with both for sinter and pellets. These results mean that H₂ reduction causes further disintegration even if its reduction degree is the same as CO reduction.

Fig. 3.

Relationship between RDI value and reduction degree (R.D.).

3.2. Crack Formation and Reaction Mode during Reduction

Figure 4 shows the cross-sectional images of sinter, pellet A and pellet B. Cracks were generated by reduction in each case. Reaction mode and crack propagation trend of sinter in CO reduction shows similar to that in H₂ reduction. However, crack formations and reaction modes of pellet A and pellet B were different between the cases of CO and H₂ reduction. In the case of CO reduction, reduction tended to progress with topochemical reaction, and cracks were formed in a concentric fashion. In contrast, H₂ reduction led to non-topochemical reaction and formation of radial cracks. In addition, increasing CO₂ changed the reaction mode from topochemically to non-topochemically. From the viewpoints of relationships between RDI and reaction mode, non-topochemically reduction tended to cause the further disintegration. This tendency was consistent with Haruna’s report.¹⁶⁾ In general, it is known that the reaction rate of H₂ reduction is higher than that of CO reduction, but the effect of the diffusion coefficient increase is greater than that of reaction rate,²⁴⁾ so the reaction mode tended to be nontopochemical (homogeneous reaction) . On the other hand, in the case of CO₂ increase, it is presumed that the chemical reaction rate decreased and the reaction rate becomes relatively rate-determining of reduction.²⁸⁾ Therefore, it appears that reaction tended to progress with non-topochemical reaction by increasing the un-reacted gas which penetrated to center part of pellets with high H₂ and CO₂ condition.

Fig. 4.

Microstructure of samples reduced at 773 K for 1.8 ks.

Figure 5 shows an example of the EPMA elemental mapping. Low O contents at surface parts of Case 1 as CO reduction shows that the reduction progressed topochemically. On the other hand, O content distribution of Case 7 shows non-topochemical reaction since H₂ reduction progressed uniformly. Figure 6 shows the radial O/Fe distribution of samples after reduction. In Case 1, minerals at surface parts and center parts were identified as magnetite and hematite, respectively. Hematite and magnetite were formed at intermediate parts, defying as the reaction zone. On the other hand, each sample at case7 showed non-topochemical reaction, and their reaction zone thickness are similar to the pellet radius. On the contrary, non-uniform distribution was observed in the sinter sample after CO reduction. The reason can be assumed as follows:

Fig. 5.

EPMA elemental mappings of pellet B. (a) Case 1: Reduced with 30%CO-70%N₂, (b) Case 7: Reduced with 30%H2-70%N₂.

Fig. 6.

Examples of radial O/Fe distribution of samples.

(i) Reduction of sinter comparably progresses non-uniformly since it has large and non-uniform pores as shown in Fig. 5.

(ii) Sinter contains calcium ferrite phases and therefore O/Fe calculated by Eqs. (2), (3), (4) cannot be directly applied.

From the above, it was considered that quantitatively evaluation of reaction mode by EPMA element mapping becomes possible only in the case of pellet.

4. Discussion

4.1. Basic Concept of Crack Area

It is known that the stress generates by volume expansion during reduction from hematite to magnetite, resulting in a generation of strain energy and, as a result, crack generation at the reaction interface becomes one of the factors of reduction disintegration.¹⁴⁾ However, quantitative evaluation on the stress, strain energy and an amount of cracks were not sufficiently made so far. In this study, therefore, reduction disintegration mechanism was tried to examine by quantitative evaluation of stress, strain energy and crack area during reduction. For the ceramics, stress model around the particles in an isotropic medium is well established, especially for particle-dispersed composite material.^29,30,31) Because the expansion coefficients of the two phases are generally different, stresses are set up with in and around the particles as the body cools down from the fabrication temperature. Weyl²⁹⁾ and Selsin³⁰⁾ have shown the stress generated in the boundary, σ is expressed by Eq. (6):   

$$\sigma =\frac{\mathrm{\Delta }CLE}{\frac{\left(1+{\nu }_c\right)}{2E_c}+\frac{\left(1-2{\nu }_n\right)}{E_n}}$$(6)

where σ is stress, ΔCLE is difference of coefficient of linear expansion, ν is poisson’s ratio, E is young modulus, n is nuclear material (particle in composite material) and c is circumnuclear material (matrix). As shown in Eq. (6), stress generated at the boundary is found to not depend on the size of the nuclear.

According to Davidge et al.,³¹⁾ the total strain energy generated in the nuclear and circumnuclear material represented by Eq. (7) when the diameter of the spherical particles is R.   

$$Ut={\sigma }^2\pi {R_n}^3\left[\frac{\left(1+{\nu }_c\right)}{E_c}+\frac{2\left(1-2{\nu }_n\right)}{E_n}\right]$$(7)

Where R is diameter and Ut is strain energy. Unlike the stress, strain energy seems to be dependent on the diameter of the nuclear material.

When the cracks are generated in the coexist area of nuclear and circumnuclear material, the total strain energy is converted to the energy creating a new surface, that is surface energy, γ. Crack area, Ac generated during the conversion of the energy is expressed by Eq. (8).   

$$Ac=\frac{Ut}{2{\gamma }_c}=\frac{{\sigma }^2\pi {R_n}^3}{2{\gamma }_c}\left[\frac{\left(1+{\nu }_c\right)}{E_c}+\frac{2\left(1-2{\nu }_n\right)}{E_n}\right]$$(8)

Iron ore sinter and pellets can be also regarded as composite materials consisting of hematite and magnetite, and therefore the stress model can be applicable. On the other hand, diameter of nuclear material (particle in composite material) changes during reduction. Details how to apply these equations for iron ore sinter and pellet will be explained in the following sections.

Young’ modulus, E, poisson’s ratio, ν and effective surface energy, γ of hematite and magnetite at each temperature were taken from the references^32,33,34,35) and listed in Table 3. γ is expressed by the Griffith’s fracture criterion,³⁶⁾ as shown in Eq. (9). In general, it is known that temperature dependency of E of oxide material is high, but it has been reported that the E do not change greatly with an temperature increase in the temperature range from 400 degrees C to 700 degrees C³⁴⁾   

$$\gamma =\frac{{K_{IC}}^2}{2E}$$(9)

where K_IC is fracture toughness and E is young modulus.

Table 3. Physical properties of hematite (Fe₂O₃) and magnetite (Fe₃O₄).

°C	Hematite (Fe2O3)				Magnetite (Fe3O4)				ΔCLE32) [–]
	Young modulus E [GPa]33)	Poisson ratio ν [–]34)	Fracture toughness KIC [MPa·m1/2]35)	Effective surface energy γ [N/m]	Young modulus E [GPa]33)	Poisson ratio ν [–]34)	Fracture toughness KIC [MPa·m1/2]35)	Effective surface energy γ [N/m]
400	144	0.28	1.93	16.54	119	0.33	1.83	12.87	0.0123
500	142	0.28	1.90	17.23	124	0.33	1.91	12.69	0.0196
550	140	0.28	1.87	17.09	123	0.33	1.89	12.51	0.0296
600	138	0.28	1.84	16.95	122	0.33	1.88	12.33	0.0282
700	133	0.28	1.78	16.67	120	0.33	1.85	11.89	0.0244

It is assumed that the young’s modulus and the fracture toughness are proportional, high temperature fracture toughness were calculated from a high-temperature Young’s modulus.

On the other hand, the temperature dependence of the Poisson’s ratio of hematite and magnetite has not been reported. However, the influence of Poisson’s ratio of the porous material has on its rigidity is known as small,³⁸⁾ utilizing the literature value at room temperature³³⁾ in this study.

4.2. Estimation of Crack Area with Reduction

4.2.1. Crack Generation Mechanism and Estimation of Crack Area with Topochemical Reaction

In case of reduction with topochemical reaction mode, it was observed that cracks generate with reduction progressed in a concentric fashion as shown Fig. 3. Figure 7 shows the microstructure in CO reduction, showing topochemical reaction. At the interface between hematite of initial phase and magnetite produced after reduction from hematite changes to magnetite, at this moment, the diameter of nuclear of hematite decreases. From this observation results, we propose the pattern diagram of crack generation process with topochemical reaction as shown Fig. 8. The formation reaction of magnetite from the homogeneous hematite is treated as well as the general un-reacted nuclear model.^38,39) Here, on the basis of the above-mentioned Davidge’s Eq. (6), stress generated at the boundary of hematite and magnetite with topochemical reaction, σ_topo is expressed by Eq. (10) when magnetite is treated as the circumnuclear and hematite is treated as the nuclear.   

$${\sigma }_{topo}=\frac{\mathrm{\Delta }CLE}{\frac{\left(1+{\nu }_M\right)}{2E_M}+\frac{\left(1-2{\nu }_H\right)}{E_H}}$$(10)

where M is magnetite and H is hematite.

Fig. 7.

Microstructure of sample after reduction showing topochemical reaction (Pellet B, Case 1). H; hematite, M; magnetite, P; pore, C; crack.

Fig. 8.

Pattern diagram of crack generation process in the case of topochemical reaction.

As the diameter of hematite is R_H, the strain energy and the generated crack area are expressed by Eqs. (7) and (8) as well as the calculation of stress.   

$$U{t}_{topo}={{\sigma }_{topo}}^2\pi {R_H}^3\left[\frac{\left(1+{\nu }_M\right)}{E_M}+\frac{2\left(1-2{\nu }_H\right)}{E_H}\right]$$(11)

  

$$A{c}_{topo}=\frac{U{t}_{topo}}{2{\gamma }_M}=\frac{{{\sigma }_{topo}}^2\pi {R_H}^3}{2{\gamma }_M}\left[\frac{\left(1+{\nu }_M\right)}{E_M}+\frac{2\left(1-2{\nu }_H\right)}{E_H}\right]$$(12)

Here, in case of topochemical reaction, diameter of hematite, R_H changes with progress of the reduction. Then, the crack areas with topochemical reaction in changing R_H were derived by following methods. First, volume fraction of magnetite, X_M and initial volume, V were calculated by Eqs. (13) and (14).   

$$X_M=1-\frac{{R_H}^3}{{R_P}^3}$$(13)

  

$$V=\frac{4\pi {R_P}^3}{3}$$(14)

Next, crack area with topochemical, Ac_topo was derived as shown in Eq. (15) by substitution of each Eqs. (13) and (14) for Eq. (12).   

$$A{c}_{topo}=\frac{3{\sigma }^2{V}_P\left(1-X_M\right)}{8{\gamma }_M}\left[\frac{\left(1+{\nu }_M\right)}{E_M}{X}_M+\frac{2\left(1-2{\nu }_H\right)}{E_H}\right]$$(15)

Finally, Eq. (15) was divided by Eq. (13), and integrated with respect to X_M to derive the total crack area, At_topo (Eq. (16)), which generated with topochemically reduction in changing R_H.   

$$\begin{array}{l}A{t}_{topo}={\int }_0^{X_M}\frac{A{c}_{topo}}{V_P}d{X}_M\\ \hspace{1em}\hspace{1em}\hspace{0.5em}=\frac{3{\sigma }^2}{8{\gamma }_M}[-\frac{\left(1+{\nu }_M\right)}{3E_M}{X_M}^3+\frac{1}{2}\left\{\frac{\left(1+{\nu }_M\right)}{E_M}-\frac{2\left(1-2{\nu }_H\right)}{E_H}\right\}\\ \hspace{1em}\hspace{1em}\hspace{0.5em}{X_M}^2+\frac{2\left(1-2{\nu }_H\right)}{E_H}{X}_M]\end{array}$$(16)

At_topo is hold physical properties such as poisson’s ratio, ν, young modulus, E and surface energy, γ. Volume fraction of Magnetite, X_M is a variable that changes with progress of reduction. In this way, it was possible to quantitatively derive the crack area with topochemical reaction, which was not evaluated quantitatively so far.

4.2.2. Crack Generation Mechanism and Estimation of Crack Area with Non-topochemical Reaction

Grain model is known as a typical reaction model described non-topochemical reaction.^40,41) In grain model, the sinter and pellet are composed of aggregation of dense hematite fine particles, it was described that the constituting all particles are locally reduced with topochemical reaction. However, from the microstructure with H₂ reduction, showing non-topochemical reaction (Fig. 9), appearance in which cracks are generated in a radial pattern due to the precipitation of magnetite from hematite surrounding pore, was observed in the early reduction period. Furthermore, it was observed that the crack propagation progressed with magnetite growth in the later period.

Fig. 9.

Microstructure of pellet sample after reduction showing non-topochemical reaction (Pellet A, Case7). H; hematite, M; magnetite, P; pore, C; crack.

From these observation results, it was assumed that magnetite generated from the porous hematite grew spherically, as shown in Fig. 10. Nuclear particles of magnetite are regarded to be large number in the porous Hematite, the diameter R_M is changed by the progressing reduction. Based on this assumption, stress, strain energy and crack area with non-topochemical reaction were estimated as follows: First, on the basis of the above-mentioned Davidge’s Eq. (6), stress generated at the boundary of Hematite and Magnetite with non-topochemical reaction, σ_n–topo is expressed by Eq. (17).   

$${\sigma }_{\text{n}-topo}=\frac{\mathrm{\Delta }{C}_{LE}}{\frac{\left(1+{\nu }_H\right)}{2E_H}+\frac{\left(1-2{\nu }_M\right)}{E_M}}$$(17)

Unlike the topochemical reaction, nuclear is treated as magnetite and circumnuclear is treated as hematite. In the same way, strain energy, Ut_n–topo and crack area, Ac_n–topo, which generated boundary of hematite and magnetite per one particle were calculated using Eqs. (18) and (19).   

$$U{t}_{n-topo}={{\sigma }_{\text{n}-topo}}^2\pi {R_M}^3\left[\frac{\left(1+{\nu }_H\right)}{E_H}+\frac{2\left(1-2{\nu }_M\right)}{E_M}\right]$$(18)

  

$$A{c}_{n-topo}=\frac{{{\sigma }_{\text{n}-topo}}^2\pi {R_M}^3}{2{\gamma }_H}\left[\frac{\left(1+{\nu }_H\right)}{E_H}+\frac{2\left(1-2{\nu }_M\right)}{E_M}\right]$$(19)

Fig. 10.

Pattern diagram of crack generation process in the case of non-topochemical reaction.

As described above, there are many nuclear of magnetite in porous hematite. The number, N, of the nuclear particles of magnetite is represented by Eq. (20).   

$$N=\frac{3X_M}{4\pi {R_M}^3}$$(20)

Total crack area, At_n–topo was derived by Eq. (21) to multiply crack area per one particle, Ac_n–topo and number of magnetite N, and to integrate with respect to X_M.   

$$\begin{array}{l}A{t}_{n-topo}={\int }_0^{X_M}A{c}_{n-topo}N\cdot d{X}_M\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}=\frac{3{\sigma }^2}{16{\gamma }_H}\left[\frac{\left(1+{\nu }_H\right)}{E_H}+\frac{2\left(1-2{\nu }_M\right)}{E_M}\right]{X_M}^2\end{array}$$(21)

At_n–topo is hold physical properties such as poisson’s ratio,ν, young modulus, E and surface energy, γ and volume fraction of magnetite, X_M. In this way, it was possible to quantitatively derive the crack area with non-topochemical reaction like topochemical reaction.

4.3. Verification of Reduction Disintegration Behavior by Application of Estimation of Crack Area

Figure 11 shows the examples of total crack area, which were calculated by substitution physical properties, such as poisson’s ratio,ν, young modulus, E and surface energy, γ and volume fraction of magnetite, X_M in Eqs. (16) and (21), and tests results of RDI value during reduction with topochemical (Case1) and non-topochemical reaction (Case7). Increasing volume fraction X_M, which equivalents to reduction degree, increasing total crack area, At. When X_M =1, the total crack area of non-toochemical reaction was more than double than that of topochemical reaction, the tendencies of calculation and test results matched well. In these results, it suggests that crack area increased dramatically in latter stage of reduction with non-topochemical reaction. Furthermore, generated cracks became the reaction interfaces, causing pellet chipping and further degradation.

Fig. 11.

Comparison of calculation results on the total crack area.

However, reduction of pellets usually progress with an intermediate range between topochemical and non-topochemical. To quantitatively evaluate the reaction modes in intermediate range, measurement results of EPMA were analyzed by following methods. Figure 12 shows the example of the radial magnetite distribution after reduction.

Fig. 12.

Example of evaluation of RMI using radius magnetite distribution from EPMA.

Here, when attention is paid to the angle of the graph in Fig. 12, in the topochemical reaction θ = 90 degree, in the non-topochemical reaction become θ = 0 degree. Therefore, the slope of the graph, RMI (Reaction Mode Index), is defined as an index for quantitatively representing the reaction mode. It was assumed that the total crack area with intermediate range, At_int. comes into existence of a weighted average between crack area of topochemical and non-topochemical reaction, At_int. is expressed by Eq. (22) as a function of RMI.   

$$\begin{array}{l}A{t}_{int.}=si{n}^2\theta \times A{t}_{topo}+co{s}^2\theta \times A{t}_{n.topo}\\ \hspace{1em}\hspace{1em} =\frac{RM{I}^2}{1+RM{I}^2}A{t}_{topo}+\frac{1}{1+RM{I}^2}A{t}_{n.topo}\end{array}$$(22)

θ is then angle of the radius magnetite distribution from EPMA analysis data. RMI (Reduction Mode Index) is the slope of the radius magnetite distribution.

Figure 13 shows the relationships between composition on reduction gas and RMI. RMI in CO reduction was higher value than that in other cases. It mean that the reduction progressed the reaction mode close to topochemical reaction by CO reduction. On the other hand, H₂ reduction tended to lower RMI values, and namely progressed in the reaction mode close to non-topochemical reaction. RMI of reduction with gas mixture of CO–H₂ became less than a weighted average value between CO and H₂ reduction. In addition, increasing CO contents tended to degrease RMI.

Fig. 13.

Relationship between gas composition and RMI.

Figure 14 shows the relationships between the RDI and crack area. RDI values increased with high total crack area, At and rose sharply in more than certain limit value of At. This limit value was same regardless of pellet brand. It was assumed that disintegration does not much progress when crack area under the value. Meanwhile over the value, it was presumed that the crack links each other and disintegration progress drastically. It suggests that it is important to keep the crack area under the value for inhibition of reduction disintegration under high H₂ atmosphere. And finally, we found the possibility to predict the fine generation caused by reduction disintegration in actual blast furnace under high H₂ atmosphere using this model.

Fig. 14.

Relationship between calculated total crack area and RDI value.

5. Conclusion

The reduction disintegration behavior of sinter and pellet in reduction with high H₂ concentration was investigated and the degree of disintegration was related to Reaction Mode Index (RMI), which was defined using EPMA data. Following conclusions were obtained:

(1) Reduction disintegration significantly depends on the reaction mode, which is strongly affected by reducing gas composition. Reduction with topochemical reaction tended to inhibit reduction disintegration. On the other hand, the reduction with non-topochemical reaction mode was dominant factor of further disintegration.

(2) Derivation patterns of crack area with topochemical reaction, non-topochemical reaction and intermediate range between both of them were developed. The crack areas show good correlation to RDI value. RDI value rapidly increases when the total crack area exceeds a certain threshold value.

Nomenclature

σ: Stress [N/m²]

ΔCLE: Difference of liner expansion ratio [–]

ν: Poisson’s ratio [–]

E: Young’s modulus [Pa]

K_IC: Fracture toughness

γ : Surface energy [N/m]

X: Volume fraction [–]

Ac: Crack area [m²]

At: Total crack area per unit volume [m²/m³]

n: Morality [mol%]

W: Mass fraction [mass%]

M: Mass number [–]

n: Nuclear material

c: Circumnuclear material

h: hematite

m: magnetite

topo: topochemical

n.topo: non-topochemical

Int.: Intermediate range between topochemical and non-topochemical

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