Modelling of Defluidization of ZrO₂/Fe Particles in High Temperature Gas Fluidization: Influence of Fe Contents

Abstract

The contents of Fe on the surface of iron ore fines had a great influence on the fluidization behavior during high temperature fluidized bed reduction, which would cause defluidization when exceeding a critical value. In this paper, simplistically, ZrO₂/Fe particles with different Fe contents on the surface were used as raw materials. Through modification of previous models, a quantitative relationship was established to predict the defluidization temperature of ZrO₂/Fe particles with different Fe contents, and the calculation results corresponded well with the experimental data obtained from the defluidization test. The model in this paper firstly explained the dependence of defluidization behavior on the contents of Fe in high temperature gas fluidization, and it could well predict the metallization degree of commercial iron ore fines when defluidization occurred during fluidized bed reduction. Therefore, the model could be used as a reference to select suitable operating conditions for treating fine iron oxide particles in high temperature gas fluidization processes, such as direction reduction and chemical looping.

1. Introduction

High temperature gas-solid fluidized bed is an ideal reactor in dealing with fine particles due to the high inter-phase mass transfer rate and heat transfer rate, and it has been widely used in direct reduction processes and chemical looping processes.¹⁾ Among those processes, fine iron oxide particles are always employed, such as acting as raw materials for the production of sponge iron in direct reduction processes, and acting as looping particles for the sequestration of CO₂ in chemical looping processes.^2,3) The high temperature gas fluidization of fine iron oxide particles exhibits high reactivity and productivity in those processes, while as the newly formed metallic iron precipitates on the surface of particles, deadly defluidization might occur, which would terminate the continuous production eventually and cause a great economic loss.⁴⁾ Therefore, it is important to understand the relationship between the newly formed metallic iron on the surface of particles and operating conditions in high temperature gas fluidization.

Former researches indicated that when the operating temperature exceeded the Tamman temperature of iron in high temperature gas fluidization, the newly formed metallic iron on the surface of fine particles would become active and sticky, which directly induced the agglomeration/defluidization of bed materials.^5,6,7) Guo et al.^8,9,10) proposed that the stickiness of iron was determined by the operation temperature, and the relation was positively correlative. Further, through thermo-mechanical analyses, they revealed that the viscosity and adhesion activity of fine particles were caused by surface softening at high temperatures. Thus, high stickiness induced by high operation temperature would accelerate the occurrence of defluidization. On the other hand, the iron morphology formed during fluidized bed reduction of iron ore fines could greatly affect the agglomeration behavior. Through quantitative comparisons using sticking index, Zhu et al.¹¹⁾ claimed that the long and strong iron whiskers were the most cohesive morphology than other ones. Apart from the stickiness and morphology of iron on the surface of fine particles, the Fe content also played a big role in the defluidization behavior in high temperature gas fluidization. Hayashi et al.^12,13) found that during fluidized bed reduction of iron ore fines, the metallization degree of products decreased with the increasing operating temperature when defluidization occurred. However, the detailed relationship is still unclear up to now. To well understand the defluidization behavior caused by iron, it is of vital importance to quantitatively associate the contents of Fe on the surface of particles with the defluidization behavior, which can be used to predict the defluidization point.

In this work, simplistically, ZrO₂/Fe particles with different Fe contents on the surface were used as raw materials. A mathematic model for inter-particle forces was established to quantitatively correlate the defluidization behavior of ZrO₂/Fe particles with the contents of Fe on the surface, by which the dependence of defluidization temperature on Fe contents was estimated. And the defluidization test experiments were conducted to verify the prediction results. Furthermore, the applicability of the model in direct reduction of commercial iron ore fines was also examined.

2. Experimental

2.1. Experimental Materials

The particle density of ZrO₂ is 5.85 g/cm³, which is close to that of iron oxides (Fe₂O₃, 5.24 g/cm³; Fe₃O₄, 5.18 g/cm³; FeO, 5.7 g/cm³). Therefore, ZrO₂ is suitable to be used as a substrate to iron oxide, and acts as the core of fine particles in high temperature gas fluidization. In the present work, spherical ZrO₂ powder (ZrO₂ content >99%) with a diameter of 100 μm was used, which was purchased from Aladdin-Reagent Company (Shanghai, China). Fe(NO₃)₃·9H₂O was employed as the iron source, which was mixed with ZrO₂ powders in different proportions. The mixtures were treated as the following steps: dissolved by pure water, dried evenly at 353 K, decomposed at 1073 K, and reduced in H₂ at 673 K. Eventually, a series of ZrO₂/Fe particles with different Fe contents are prepared, as shown in Fig. 1.

Fig. 1.

Characterizations of ZrO₂/Fe particles. (a) SEM photographs, (b) XRD patterns.

2.2. Defluidization Test

The experimental apparatus used in this study is the similar to our previous studies,^11,14,15) see Fig. 2. For defluidization test experiments, batches of 8 g ZrO₂/Fe particles were fluidized with N₂ in the hot zone of the furnace. The non-isothermal fluidization was carried out at a heated rate of 30 K/min in N₂ atmosphere. Point of bed defluidization was determined by the pressure drop profile and visual observation. The temperature where defluidization occurred was recorded as the defluidization temperature.⁸⁾

Fig. 2.

Experimental apparatus used for fluidized bed reduction.

2.3. Sample Characterization

The particle density was measured by pycnometer, and the particle diameter was determined by scanning electron microscope (SEM) and laser particle size analyzer. Minimum fluidization velocity (u_mf) was determined by plotting the bed pressure versus gas velocity.

3. Results and Discussion

3.1. Properties of ZrO₂/Fe Particles

As the important parameters of particle in gas-solid fluidization, the density, diameter, and u_mf of ZrO₂/Fe particles with different Fe contents were carefully measured. The density was determined by the pyknometer method, and the diameter was observed from the SEM photographs. The superficial gas velocity at which fluidization is initiated, called the minimum fluidization velocity u_mf, is an important property of particles and the fluidizing fluid, and it also appears in many of the relationships for predicting other properties of fluidized beds. The u_mf was obtained experimentally through the pressure drop vs. superficial velocity method. The variations of density, diameter, and u_mf with Fe contents are shown in Fig. 3. It indicated that those parameters increased regularly with increasing Fe content, which should be attributed to the homogeneous layers on the surface of ZrO₂/Fe particles. As is shown in Fig. 4, after decomposition and reduction of Fe(NO₃)₃·9H₂O, the morphology of Fe on the surface of ZrO₂ particles is porous, and it is worthwhile to note that some dendric structure appears as the content of Fe reaches 0.35. All the parameters (diameter, particle density, u_mf) would be used to calculate the inter-particle forces in high temperature gas fluidization.

Fig. 3.

Variation of diameter d_p (a), density (b), and u_mf (c) with different Fe contents.

Fig. 4.

Cross-sectional views of ZrO₂/Fe particles with different contents of Fe.

3.2. Fluidization Behavior of ZrO₂/Fe Particles

Figure 5 is obtained experimentally by plotting the fluidization state (fluidization or defluidization) of ZrO₂/Fe particles under different conditions, and it illustrates the fluidization phase diagram of ZrO₂/Fe particles with different Fe contents at 850–1200 K with the superficial gas velocity or the operating gas velocity of 0.1–0.45 m/s, which could clearly distinguish the fluidization behavior as fluidization or defluidization. The experimental results showed that the ZrO₂/Fe particles with a certain Fe content could fluidized stably under operation conditions below the characteristic curve, otherwise defluidization occurred. It also indicated that the operation region for stable fluidization reduced with increasing Fe content. With a given Fe content, high gas velocity and low temperature favored stable fluidization. However, the slope of the characteristic curves decreased with increasing Fe content, which suggested that temperature played a decisive role in the fluidization behavior of ZrO₂/Fe particles, especially with a high Fe content.

Fig. 5.

Fluidization phase diagram of ZrO₂/Fe particles in N₂, temperature: 850–1200 K, gas velocity: 0.1–0.45 m/s.

3.3. Establishment of Model for Inter-particle Forces

According to the previous studies,^7,8,9,10) if the cohesive force exceeded the segregation force, defluidization would occur. The collision force (F_collision) was the main segregation force, and the solid bridge force (F_cohesive) acted as the cohesive force in this study.

3.3.1. Variation of F_collision

F_collision between two ZrO₂/Fe particles in high temperature gas fluidization can be calculated from the following equation:¹⁵⁾   

$${\text{F}}_{\text{collision}}=0.166{\left(\frac{\pi {\rho }_p^3}{{\kappa }^2}\right)}^{0.2}{\text{V}}^{1.2}{\text{d}}_{\text{p}}^2$$(1)

where ρ_p is the particle density (kg/m³); d_p is the particle diameter (m); V is the relative collision velocity (m/s); κ is a function of Poisson’s ratio v and Young’s modulus E, see Eq. (2).   

$$\kappa =\frac{1-{\nu }^2}{\pi \text{E}}$$(2)

where ν is the Poisson’s ratio, ν=0.29; E is the Young’s modulus, E=2.07×10¹¹ Pa.

According to Xu et al.,¹⁶⁾ the relative collision velocity V can be calculated by:   

$$\text{V}=\xi \sqrt{{\text{u}}_{\text{g}}{\text{u}}_{\text{mfh}}}$$(3)

where ξ is a factor between 0 and 1. In this work, to compare the result of theoretical calculation with that of experimental research, the value of ξ is defined to be equal to the contents of Fe.

The minimal fluidization velocity u_mfh at high temperature can be estimated based on the minimal fluidization velocity u_mf at room temperature by the simplified Wen–Yu equation:   

$${\text{u}}_{\text{mfh}}=\frac{{\text{u}}_{\text{mf}}}{{\mu }_{\text{mfh}}}{\mu }_{\text{mf}}$$(4)

In Eq. (1), F_collision is determined by the particle density, particle diameter and relative collision velocity, which is strongly affected by the Fe content and superficial gas velocity. The influence of superficial gas velocity, Fe content, and temperature on F_collision is illustrated in Fig. 6. Figure 6(a) shows that F_collision increases with increasing superficial gas velocity and Fe content, which should be attributed to the increase of particle momentum, while Fig. 6(b) presents that it is rarely affected by temperature due to the fact that the value of u_mf varies little at different temperatures, see Eq. (4). Besides, it should be noted that F_collision of ZrO₂/Fe particles with different contents of Fe lay in a narrow range from 9×10⁻⁴ N to 1.8×10⁻³ N within the operating superficial gas velocities and temperatures. This was similar to the results reported by Lei et al.,¹⁵⁾ and the difference might be caused by the different particle properties. Furthermore, this indicated that the motion states of ZrO₂/Fe particles in high temperature gas fluidization were slightly affected by the variation of collision force.

Fig. 6.

Variation of F_collision with different superficial gas velocities. (a) Influence of Fe contents, T=900 K; (b) Influence of temperature, Fe=0.15.

3.3.2. Variation of F_cohesive

The cohesive force between two ZrO₂/Fe particles arises from surface viscosity, and the solid bridge force is determined by the plastic-viscous flow mechanism. Therefore, F_cohesive between two ZrO₂/Fe particles in high temperature gas fluidization can be calculated from the following equation:¹⁷⁾   

$${\text{F}}_{\text{cohesive}}=\pi \sigma x^2$$(5)

where σ is the tensile strength of a neck between two adhesive particles (Pa); x is the neck radius (m).

Based on the surface diffusion model,¹⁸⁾ the neck radius x can be calculated by:   

$$x={\left(\frac{56\gamma {\eta }^4}{\text{kT}}{\text{D}}_{\text{s}}{\alpha }^3\text{t}\right)}^{1/7}$$(6)

where α is the curvature radius, α=6.4×10⁻⁷ m; D_s is the surface diffusion coefficient (m²/s); T is the temperature (K); t is the time (s); γ is the surface tension, 1 N/m; η is the lattice constant, 2.87×10⁻⁷ m; k is the Boltzmann constant, k=1.47×10⁻¹² J/K.

The surface diffusivity of iron can be given as follows:   

$${\text{D}}_{\text{s}}={\text{D}}_0\text{exp}\left(-\frac{{\text{E}}_{\text{s}}}{\text{RT}}\right)$$(7)

where D₀ is the frequency factor, D₀=5.2 m²/s, T<1180 K; E_s is the activation energy of surface diffusion, E_s=2.21×10⁵ J/mol, T<1180 K.

The characteristic time t of sintering/agglomerating,¹⁹⁾ which should be sufficient to form a sinter neck of a size strong enough to overcome the disruption of bubble movement, can be expressed by:   

$$\text{t}=\frac{2}{3}\frac{{\text{D}}_{\text{b}}}{\left({\text{u}}_{\text{g}}-{\text{u}}_{\text{mfh}}\right)}$$(8)

where D_b is the diameter of the bubbles (m), see Eq. (9).   

$${\text{D}}_{\text{b}}=0.652{\left[{\text{S}}_0\left({\text{u}}_{\text{g}}-{\text{u}}_{\text{mfh}}\right)\right]}^{0.4}$$(9)

where S₀ is the cross-sectional area of bed, S₀=2.27×10⁻⁴ m².

According to Zhong et al.,²⁰⁾ the tensile strength σ is given by:   

$$\sigma =\frac{\text{At}}{{\mu }_{\text{s}}{\text{d}}_{\text{p}}}$$(10)

where A is a constant; t is the contact time of two particles (s); d_p is the diameter of particle (m); μ_s is the surface viscosity (Pa·s).

Solid surface viscosity μ_s can be expressed as follows:²¹⁾   

$${\mu }_{\text{s}}={\displaystyle \frac{4\beta \epsilon \text{W}}{\pi \left(1-\epsilon \right){\text{D}}_{\text{H}}^2{\displaystyle \frac{\partial \left(\text{f}{\displaystyle \frac{\mathrm{\Delta }\text{L}}{2{\text{L}}_0}}\right)}{\partial \text{t}}}}}$$(11)

where β is the correlation coefficient, β=0.4π; ε is the voidage of sample; D_H is the diameter of sample holder (m); W is the load on the sample (N); ΔL/L₀ is the sintering shrinkage.

The sticking/agglomerating of ZrO₂/Fe particles is similar to the initial stage of activated sintering process. The Fe layer on the surface of ZrO₂ particles acts as an activator in promoting sintering, and the sintering shrinkage ΔL/L₀ tracks to the sintering parameters as follows:²¹⁾   

$${\left(\frac{\mathrm{\Delta }\text{L}}{{\text{L}}_0}\right)}^3=\frac{{\text{CD}}_{\text{s}}\text{t}\delta }{{\text{Td}}_{\text{p}}^4}$$(12)

Where δ is the thickness of the Fe layer on the surface (m); d_p is the particle size of substrate, d_p=1×10⁻⁴ m; t is the sintering time (s); T is the temperature (K); D_s is the surface diffusion coefficient (m²/s); C is a constant.

According to Eqs. (10), (11) and (12), the tensile strength σ can be given by:   

$$\sigma =\frac{\text{C}{\left(\text{t}\cdot \delta \cdot {\text{D}}_{\text{s}}\right)}^{1/3}}{{\text{T}}^{1/3}{\text{d}}_{\text{p}}}$$(13)

As Mikami et al.¹⁷⁾ reported, σ was 20 MPa for iron particles with a diameter of 200 μm sintered at 1000 K. Thus, the σ under different sintering/agglomerating conditions could be obtained by a statistical regression method.

Figure 7(a) shows that F_cohesive increases sharply with increasing temperature, especially when the content of Fe is high, while it decreases slightly with increasing superficial gas velocity, see Fig. 7(b). It indicated that the cohesive force between two ZrO₂/Fe particles in high temperature gas fluidization depended on the Fe contents and temperature. On one hand, Fe contents had a great effect on the minimum fluidization velocity, see Fig. 3(c), which determined the sintering/agglomerating time as Eq. (8) indicated. And Eq. (10) showed that the neck growth between two ZrO₂/Fe particles was also directly related to the particle-particle contact time. On the other hand, temperature played a vital role in the diffusivity/activity of Fe on the surface (Eq. (10)) and the surface viscosity of particles (Eq. (11)). Besides, it was noteworthy that compared with the variation of F_collision, the change range of F_cohesive was much larger under the same operating conditions. This indicated that the motion states of ZrO₂/Fe particles in high temperature gas fluidization was dependent on the variation of cohesive force.

Fig. 7.

Variation of F_cohesive with different temperatures. (a) Influence of Fe content, u_g=0.3 m/s; (b) Influence of superficial gas velocity, Fe=0.15.

3.4. Validation of Model for Inter-particle Forces

Based on the force balance analyses, the critical point or defluidization point could be estimated by F_collision=F_cohesive. The solid line in Fig. 8 shows the defluidization temperature calculated from the model, which decreases with increasing Fe content, and it is consistent with the experimental result obtained from the defluidization test. The good coincidence between model and experiment indicated the clear physical meaning of established model and the correctness of estimated parameters. Specially, for comparison, the model built by Lei et al.¹⁵⁾ was also used to estimate the defluidization temperature of ZrO₂/Fe particles with different Fe contents, and obviously, the results obtained from Lei’s model deviated largely from the experimental measurements. The deviation of Lei’s model should be caused by overlooking the influence of Fe content on the inter-particle forces, and on the other hand, it reflected that the proposed model in this work was essential. Besides, through comparisons of defluidization temperatures at different superficial gas velocities, it showed that increasing superficial gas velocity could improve the defluidization temperature, while the effect weakened as the contents of Fe increased. This should be attributed to the dominant role of cohesive force in determining the motion states of ZrO₂/Fe particles in high temperature gas fluidization, which was mainly affected by the Fe contents and temperature, see Section 3.2.2.

Fig. 8.

Comparisons of theoretical and experimental results of defluidization temperature for different contents of Fe. (a) u_g=0.2 m/s, (b) u_g=0.4 m/s.

3.5. Application of Model

The reduction of iron oxides by H₂ beyond 843 K could be expressed as follows: Fe₂O₃→Fe₃O₄→FeO→Fe. The metallic iron was formed during the last step FeO→Fe, thus the quantitative relationship between Fe content and metallization degree could be obtained. In this way, the above model could be used to predict the metallization degree of products at different reduction temperatures when defluidization occurred. Three commercial iron ore fines were reduced in a laboratory fluidized bed by H₂ at 973 to 1123 K, and the particle properties are listed in Table 1. Although the melt was not formed in iron ore at 973–1123 K, the newly formed metallic iron became active and sticky when the reduction temperature exceeded the Tamman temperature of iron (about 903 K), which directly caused the agglomeration/defluidization of as-reduced iron ore fines. The theoretical and experimental results are illustrated in Fig. 9, and the solid line drawn from the model agreed well with the points obtained from the experiment. The metallization degree of iron ore fines was obtained when defluidization occurred, and the stable fluidization time decreased with increasing reduction temperature, indicating that higher temperature would induce shorter reduction time, thereby resulting in lower metallization degree. The differences between theoretical and experimental results might be caused by the reduction reaction and the nano/micro structures of newly formed metallic iron on the surface.²²⁾

Table 1. Properties of three commercial iron ore fines.

Location	Main composition	dp (μm)	umf (m/s)	ρp (kg/m3)	ρb (kg/m3)
Minas Gerais, Brazil	Fe2O3	112	0.022	4939	2209
Atacama Region, Chile	Fe3O4	98	0.016	4765	2741
Pilbara Region, Australia	Fe2O3	105	0.021	5017	2853

Fig. 9.

Comparisons of calculated results with experimental data at different temperatures, u_g=0.2 m/s.

4. Conclusions

In this work, a mathematic model was established to associate defluidization behavior of fine particles with the contents of Fe on the surface in high temperature gas fluidization. For a given content of Fe on the surface, the defluidization temperature of fine particles could be predicted. The prediction results showed that defluidization temperature decreased with increasing Fe content, and slightly increased with increasing superficial gas velocity, which were in good agreement with the experimental studies. Furthermore, the model showed a good applicability in predicting the defluidization point of commercial iron ore fines during high temperature gas-based fluidized bed reduction.

Acknowledgements

The authors gratefully acknowledge financial supports from the National Natural Science Foundation of China (Grant No. 21908227) and the Open Research Fund of State Key Laboratory of Multiphase Complex Systems (No. MPCS-2019-D-01).

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