Flash Suspension Reduction of Ultra-fine Fe₂O₃ Powders and the Kinetic Analyzing

Abstract

In order to take the advantage of the large reaction surface of fine iron ore concentrates and expect a high reaction rate without sticking or agglomeration problems, a suspension gas-solid reaction system was designed to explore the feasibility of fast direct reduction of fine iron ore. In this study, upward gas flow was used to prolong the particles’ falling time. Pure silica particles were chosen as the dispersion agent. The Stokes gas-particle model with the relaxation time concept was applied to accurately model the falling process. Highly metallized porous iron particles over 90% of R_d (reduction degree) were obtained at 1273 K with 20.1 s of hydrogen reduction. The morphology evolution characteristics of the fine particles during reduction were investigated via SEM, and a conceptual diagram was formulated in this paper in order to well understand the relationship between the reduction condition and the structural evolution. The shrinking core model was introduced to analyzing the reduction kinetics in this experiment system, which indicates that the microstructure evolution of the particle during reduction can be influenced by temperature and the resistance of internal mass transfer cannot be ignored under this experiment condition especially in the later stage of reduction.

1. Introduction

This suspension gas-solid reduction method allows the direct use of concentrates which can bypass the pelletization or sintering processes, and fundamentally avoids the sticking/agglomeration problem promisingly. Owing to the great specific surface area and the fast gas-solid film mass transfer (k_d=140.6 m/s at 1273 K in this experiment condition, so the external diffusion resistance can be ignored), the reaction can be drastic. It was reported by H. Y. Sohn et al.¹⁾ that the reduction rate of fine concentrate particles by hydrogen above 1473 K took only a few seconds to be completed. Except for the large reduction rate, it can avoid the solid-solid contact during reduction thus solve the sticking problem existed in the fluidized bed or other direct reduction processes of iron ore concentrate.^2,3,4)

Themelis and Gauvin⁵⁾ derived a rate equation for reduction of iron oxide particles by hydrogen with particle sizes ranging from 70 to 42000 μm in diameter and indicated that the measured rates might contain mass transfer effects. F. Tsukihashi⁶⁾ investigated the kinetics and mechanism of reduction of molten iron oxide (wustite) with CO gas at high temperatures of 1723 K and 1873 K with a gas conveyed system, and he found that the oxide particles were melted and became spherical with reduced iron surrounded by liquid FeO during reduction. Also with the gas conveyed system, S. Hayashi^7,8) studied the reduction characteristics and mechanism of wustite during hydrogen reduction at 1723 K to 1823 K, moreover, he investigated the effect of gangue phase on the reduction behaviors. The reduction process was estimated to include an appreciable diffusion resistance under higher reducing potentials in his study. Still with the gas conveyed system, M. Ozawa⁹⁾ mainly studied the effect of vapor partial pressure on the iron oxide reduction. Y. K. Rao¹⁰⁾ has studied the rate of nucleation, the mode of growth of a metallic nucleus and their relationship to the reduction rate of wustite. Haitao Wang and H. Y. Sohn^1,11,12) introduced the nucleation and growth kinetics expression to describe the reduction rate of fine concentrate particles in the temperature range of 1423 K to 1673 K with hydrogen, and they thought that the overall reaction was rate controlled by the chemical reaction of individual particles and not affected by pore diffusion or external mass transfer.

Both S. Hayashi and H. T. Wang used the Stokes’ terminal velocity equation, and the former assuming that particles are falling at a constant velocity given at bed top. In this study, the falling progress was modeled more accurate with the introduction of relaxation time and end dropping speed. According to the previous studies, the absolutely reduction time could be shortened just to several seconds with hydrogen when the temperature is above 1573 K. However, the formation of liquid FeO phase could be a catastrophic problem for the refractory matters and block the way of normal production, and that is just the main problem for the well-known non-blast furnace process Hismelt^®. Therefore, this solid state particles reduction system was built to investigate the possibility of iron ore concentrate reduction at the temperature range of 873 K to 1373 K via the upward gas flow to prolong the reduction time. The gas-conveyed system is widely used in previous studies,^{1,5,6,7,8,9,11,12)} while the suspension reduction with upward gas flow is rarely studied. The counter current of gas and solid particles can enhance the mass transfer rate and increase the falling time of the particles, therefore, the reaction time can be prolonged to some extent and the facility size can be reduced. For the reaction kinetics, some researchers⁵⁾ found that the reaction resistance may include the mass transfer resistance except for the chemical reaction resistance when the experimental temperature is around 873 K–1273 K. For the aim of further studying the particle reduction kinetic in this temperature range, kinetic analysis was carried out in this work and provided more evidence for the existence of mass transfer or internal diffusion resistance. Finally, a comprehensive assessment on the feasibility and the possible improvement of this system are discussed as reference for the suspension flash iron reduction technology.

2. Experimental

2.1. Apparatus

The experimental setup is shown in Fig. 1. The drop tube reactor is made of heat-resistant steel with the effective height of 1.9 m and an inner diameter of 60 cm. The facility is heated by an electric resistance furnace with a maximum temperature of 1373 K. The reaction temperature control is achieved by a PID controller driven by a thermocouple constantly immersed in the drop tube. The reducing and shielding gas was piped from the bottom part into the reaction tube and the exhaust gas was piped out from the top part via an off gas tank. The off gas tank was used to prevent the sucking back of air. After dropping and reducing the iron particles fall into the cooling part of the reaction tube which is of atmosphere temperature out of the heating part. Then the reduction procedure is stopped immediately with the dropping of sample’s temperature. Finally open the ball valve and let the reduced sample flow into the sampling bottle with argon gas protected from oxidization.

Fig. 1.

Schematic diagram of the drop tube flash reduction apparatus.

The sample feeder attached on the top of the experimental apparatus is made of stainless steel. As shown in Fig. 2, it is made up of a storage cabin with a bell shaped distributor at the bottom and a rotating handle. Before adding the sample the outlet is keep upward and when rotate it downward the sample will flow down to the reaction tube. The feeding speed can be changed by adjusting the gap between the storage cabin and the bell shaped distributor. The feeding speed used in this experiment is about 10 grams per minute.

Fig. 2.

Picture of the sample feeder.

2.2. Materials

The pure Fe₂O₃ powders (99.5%) were grinded and screened into five particle grades: 10–30 μm, 30–38.5 μm, 38.5–53 μm, 53–74 μm, and 74–100 μm. Batches of 5 g Fe₂O₃ powders of the specific particle size and 35 g silica particles of particle size between 250–425 μm were mixed and feed into the reactor via the sample feeder. The silica particles here were used as the dispersing medium.

2.3. Experimental Procedure

The Fe₂O₃ powders were mixed with the silica particles and put into the sample feeder. Before the furnace rose to the pre-set temperature, the discharge port of the sample feeder was put upward. The argon gas was used as the shielding gas and when it reached the target temperature the gas flow was changed by H₂ or CO. To leave enough time for filling the reaction tube with reducing gas and heating it to the furnace temperature, then rotated the sample feeder with 180 degrees at the same time. The flash reduction procedure started then. The samples then fell to the cooling part of the tube. Then opened the ball valve and let the samples flow into the collector with argon gas filled. Finally, to sieve out the reduced Fe₂O₃ particles from the larger silica particles and prepared them for later tests.

2.4. Samples Analyzing and Parameters Definition

As the experimental samples are pure Fe₂O₃, the reduction degree R_d can be calculated as follow:   

$$R_{\text{d}}=\frac{m{T}_{\text{Fe}}+3/7\times m{T}_{\text{Fe}}-m}{3/7\times m{T}_{\text{Fe}}}\times 100\%$$(1)

Where m stands for the weight of the reduced sample, T_Fe stands for the weight percentage of total iron in the sample. The total iron content T_Fe was measured by the chemical analytical methods according to the national standards in China GB/T 6730.5-2007. The morphology of reduced samples was analyzed by a scanning electron microscope (SEM & EDS ZEISS EVO 18).

2.5. Determination of the Dropping Time

In the consideration of the gas-solid flow state, the concentration of Fe₂O₃ powders in the drop tube is very low and it makes little difference to the flow of reducing gas when the feeding speed is just 10 g/min. So the fine particles were considered to be isolated in the gas flow. Without supplement of reducing gas from the bottom the Fe₂O₃ particles fall in the still gas with the gravity. According to the theory of Stoke,¹³⁾ the accelerated velocity of the dropping particles was defined as below:   

$$\frac{d{u}_{\text{p}}}{dt}=-\frac{u_{\text{p}}}{{\tau }_{\text{V}}}f\text{(}Re\text{)}+\text{g}$$(2)

Where u_p is the falling velocity of particles, τ_V is the relaxation time of falling velocity (defined at followed passage), Re is the Reynolds number, g is the acceleration of gravity and t is time. The particle size is under 100 μm, and thus Re is small so it is proper to use Stokes resistance formula. Accordingly, it can be considered f(Re)=1.¹⁴⁾ From the state of t=0, u_p=0 the particles start to free fall. With the increase of falling velocity, the resistance item in Eq. (2) becomes larger and larger. When the resistance is equal to the gravity, the du_p/dt approaches zero, and the falling velocity is called the end falling velocity which is expressed by u_p,t:¹³⁾   

$$u_{\mathrm{p},\mathrm{t}}=\frac{{\tau }_{\mathrm{V}}\mathrm{g}}{f(Re)}$$(3)

The time of the particles from the beginning to fall to the falling speed reaching the end falling velocity is defined as the relaxation time τ_V:   

$${\tau }_{\text{V}}\text{=}\frac{{\rho }_{\text{p}}{D}^2}{18\mu }$$(4)

Where D is the diameter of particle, μ is the gas dynamic viscosity (Table 1), ρ_p is the particle density (Table 2). In this experiment, the particle density with different size was measured by the pycnometer method.

Table 1. The dynamic viscosity of H₂ and CO at different temperatures.

Temperature/K		873	1073	1273	1373
Viscosity	H2	173	187	220	242
10−7 Pa·s	CO	383	440	460	513

Table 2. The density of particles of different sizes.

Particle size/μm	10–30	30–38.5	38.5–53	53–74	74–100
Density/kg·m−3	4823.9	4685.5	4556.4	4372.6	3682.6

Substituting Eq. (4) into Eq. (3), then we can get Eq. (5) after rearranging:   

$$u_{\mathrm{p},\mathrm{t}}=\frac{{\rho }_{\mathrm{p}}{D}^{2}g}{18\mu }$$(5)

For the Stokes resistance the general solution of Eq. (2) is:   

$$u_{\text{p}}=\text{g}{\tau }_{\text{V}}\left[\text{1}-\text{exp}\left(-\frac{t}{{\tau }_{\text{V}}}\right)\right]=u_{\text{p,t}}\left[\text{1}-\text{exp}\left(-\frac{t}{{\tau }_{\text{V}}}\right)\right]$$(6)

The falling distance can be calculated by:   

$$s={\int }_0^t{u}_{\mathrm{p}}dt=u_{\mathrm{p},\mathrm{t}}\left\{t-{\tau }_{\mathrm{V}}\left[1-exp\left(-\frac{t}{{\tau }_{\mathrm{V}}}\right)\right]\right\}$$(7)

When piping into the reducing gas from the bottom of the reaction tube, the direction of the gas flow is opposite to the direction of gravity. Defining the gas velocity as u₀, then the falling process can be considered that the particles fall with the initial velocity u₀ in a still gas flow. The relaxation time is still the same as defined above. Then the dropping speed of particle changes into Eq. (8):   

$$u_{\text{p}}=(g{t}_{\mathrm{V}}-u_0)\left[1-exp\left(-\frac{t}{t_{\mathrm{V}}}\right)\right]$$(8)

The end dropping speed is:   

$$u_{\mathrm{p},\mathrm{t}}=\frac{{\rho }_{\mathrm{p}}{D}^{2}g}{18\mu }-u_0$$(9)

And the dropping distance is:   

$$s=u_{\mathrm{p},\mathrm{t}}\left\{t-{\tau }_{\mathrm{V}}\left[1-exp\left(-\frac{t}{{\tau }_{\mathrm{V}}}\right)\right]\right\}$$(10)

With above equations the residence time (falling time) of particles can be calculated, the results for particles of 30–38.5 μm are shown in Table 3.

Table 3. The residence time of particles with different reduction gas velocity (30–38.5 μm).

Temperature		Reduction gas velocity (NL/min)
		0	1	2	3	4	5
H2	873 K	8.8 s	9.6 s	10.5 s	11.5 s	12.9 s	14.6 s
	1073 K	9.5 s	10.6 s	12.1 s	13.9 s	16.4 s	20.1 s
	1273 K	11.1 s	13 s	15.7 s	20.1 s	27.1 s	42 s
	1373 K	12.3 s	14.8 s	18.8 s	25.9 s	–	–
CO	873 K	19.3 s	26.1 s	29.8 s	41.1 s	65.5 s	–
	1073 K	22.2 s	29.6 s	44.1 s	87.3 s	–	–
	1273 K	23.2 s	33.6 s	60.6 s	–	–	–
	1373 K	25.9 s	41.2 s	–	–	–	–

3. Results and Discussion

3.1. Suspension Reduction of Fe₂O₃ Particles with H₂ and CO

The cold test of the dropping state was firstly carried out via a one-to-one scale plexiglass tube. The experimental gas was N₂, and three different gas velocities were used in the test. As shown in Fig. 3 (left), the Fe₂O₃ particles distribute uniformly in the tube at room temperature. The gas velocities make great influence on the dropping speed of the particles as Fig. 3 (right) reflects, the arrows in the figure point out the forefront of the Fe₂O₃ dropping flow.

Fig. 3.

Dispersion state of the 30–38.5 μm Fe₂O₃ particles with different gas velocities at room temperature (left: bottom part; right: whole).

Figure 4 shows the reduction degree of Fe₂O₃ particles under different gas velocities. It is obvious that reduction temperature makes great influence on reduction degree regardless of the type of reducing gas.

Fig. 4.

Reduction degree of Fe₂O₃ particles versus gas velocity: (a) H₂; (b) CO.

According to the calculated residence time in Table 3, the reduction degrees of reduced Fe₂O₃ particles at different temperatures are plotted in Fig. 5. It is clear that the lowest temperature corresponds to the lowest reduction speed. With the increase of temperature from 873 K to 1073 K the hydrogen reduction speed accelerates quickly, 80% of R_d can be obtained with 14 seconds of reduction. But when the reduction temperature reaches 1273 K the hydrogen reduction rate gets a little lower than that of 1073 K. Moreover, with the temperature of 1373 K, the R_d merely increases with the residence time after 15 seconds of reduction.

Fig. 5.

Reduction degree of Fe₂O₃ particles versus residence time: (a) H₂; (b) CO.

With the reduction gas CO, the R_d increased apparently with the increase of reduction time at 1073 K and the top R_d is just about 40%. The lowest R_d at 1273 K and 1373 K was higher than the top R_d at 1073 K.

The surface morphology of Fe₂O₃ particle without reduction is shown in Fig. 6(a), grains with smooth and dense surface gather together to form a Fe₂O₃ particle. There are some new generated metallic iron crystals emerging on the particle surface together with some holes after hydrogen reduction as shown in Fig. 6(b). Then the particle becomes more and more porous with the increase of R_d as seen in Figs. 6(c) and 6(d). However, when used the CO as reducing gas, a lot of iron crystal nucleus emerged on the particle surface and no voids was found. This phenomenon can be well explained by the microstructure change theory of gaseous reduction:^15,16,17,18) when the decomposition rate of iron oxide is faster than the migration of iron ions, porous microstructures will show up as shown in Figs. 6(c), 6(d); when the decomposition of iron oxide is slower than the migration of iron ions, iron ions accumulate in the gas-solid reaction interface to produce a dense layer, what’s more, when the reduzate as CO₂ continuously generated at the interface of iron and oxide then the dense metallic layer will be broken and the fracture site will quickly evolve into new growing point of iron crystal nucleus or iron whiskers as shown in Fig. 6(e).

Fig. 6.

Surface morphology evolution of Fe₂O₃ particles with different reduction degrees and reduction gases: (a) original Fe₂O₃ particle; (b) R_d=41.9%, 1273 K, H₂; (c) R_d=78.4%, 1273 K, H₂; (d) R_d=91.07%, 1273 K, H₂; (e) R_d=52.55%, 1273 K, CO. with hydrogen (R_d=66.67%).

3.2. Effect of Particle Size on Reduction

Four kinds of Fe₂O₃ particles of different sizes were reduced with 0–3 NL/min hydrogen gas flow. The experimental results are plotted in Fig. 7. It can be seen that the smaller particle size corresponds to the lower reduction rate unexpectedly. This phenomenon also occurred in the study by Tsukihashi⁶⁾ and Haitao Wang.¹⁾ Haitao Wang suggested that for larger particles the cracks and holes was formed more readily during reduction, and the size of solid part between cracks was smaller. In addition, as the CaO or MgO contents can promote the gaseous reduction of wustite,^{7,19,20,21,22)} the contents of the main gangue materials CaO, MgO, and SiO₂ in iron oxide concentrate particles increase with particle size so he believe the major factor in this size dependence is the variation in the contents of the gangue materials in his study. Tsukihashi showed that the dispersion of small particles during falling down at high temperatures was difficult. If the particles did not disperse well in the reactor, the particles cannot contact well with the reducing gas, and the local concentration of water vapor or carbon dioxide became larger. But the dispersion situation is not clear in the reactor now, so all of these are possible reasons why larger particles have higher reduction rate below 1573 K. It is proved that the effect of particle size on the reduction rate was negligible after the temperature reached 1573 K.¹⁾

Fig. 7.

Reduction degree of Fe₂O₃ particles versus different particle sizes (1273 K).

3.3. Effect of Reduction Temperature

Reduction experiments were carried out at four temperatures: 873 K, 1073 K, 1273 K and 1373 K. The particle size of Fe₂O₃ was 30–38.5 μm. As shown in Fig. 4, for hydrogen reduction, the R_d is just around 30%–40% and increases very slowly with the increase of gas velocity at 873 K. When the temperature rises to 1073 K and 1273 K, the R_d goes up quickly with the increase of gas velocity. And the maximum reduction degree of 91.07% was obtained with 3 NL/min of reducing gas flow rate at 1273 K. When the reduction temperature rises to 1373 K, the R_d is higher than others with still gas flow but lower than those of 1073 K and 1273 K as the gas flow increases. The R_d maintains around 65% and hardly increases in the experiments at 1373 K.

The R_d in CO was small than that in H₂. The largest R_d was just about 50% with 1 NL/min CO at 1373 K. The rising of reduction temperature from 1073 K to 1273 K improved R_d a lot.

Concluded from the experimental results and the theory of microstructure evolvement of iron oxide particles gaseous reduction,^15,18) the reduction temperature has two contradictory effects on the reduction behaviors of the Fe₂O₃ particles: one is on the chemical reaction speed, normally the higher temperature corresponds to the higher reaction speed; the other is on the morphology evolution.

3.4. Structural Evaluation of Particles during Reduction

For the particles of size between 30–38.5 μm when the reduction temperature is 1273 K with hydrogen, the diffusion rate of the new generated iron is much smaller than its generating rate, namely, the reduction rate. So the porous structure caused by the removing of oxygen during reduction keeps steady without significantly change, and the reduction gas can go through the voids or channels easily to react with the iron oxide inside the particles as shown in Fig. 8 of 1273 K reduction. According to the cross section view, the voids are mostly interconnected, so the whole particle is highly metallized and shows a porous structure from outside to inside after reduction.

Fig. 8.

Cross section morphology of original and hydrogen reduced Fe₂O₃ particles at different temperatures with different R_d.

However, when the temperature is around 1373 K, it is certain that the reduction rate has increased with the increasing of temperature and that’s why the R_d at 1373 K with still gas flow is higher than others of lower temperatures as shown in Fig. 4(a). But to some extend the diffusion of iron cannot be ignored anymore, with the increasing of temperature the new generated iron can migrate more freely so the situation of chemical reaction speed versus iron ions migration rate start to change,¹⁶⁾ the newly generated iron gathers and connects to each other causing the closing up of voids as shown in Fig. 8 of 1373 K. The mark on the left shows the EDS map of “Fe” and the right hand side mark shows the EDS map of “O”. They help to indicate that due to the closing up of voids it makes difficulties for the reducing gas to diffuse into the center part of the particle, and left unreduced Fe_xO in the center with dense morphology. Some tiny parts of the particle with high surface energy can become softened or even melted below the melting point as a bulk, and that can be explained by the Taman temperature.^23,24) This effect subsequently increases the internal gas diffusion resistance and then reduces the reaction speed.

According to some other studies,^1,6,8) if the reduction temperature get higher continuously e.g. above 1573 K or more the particle firstly being reduced very quickly before the particle reaches the melting point. While short time later the iron phase almost totally melts and wraps the separated iron oxide phase (melting point of FeO is 1653 K). Finally, by the effect of surface tension the iron phase gathers into a metallic sphere in the center of the particle and the iron oxide phase is left outside exposed to the reducing gas as shown in Fig. 9. Thus, the new generated iron does not an obstacle for gas diffusion and the iron outside can be reduced quickly at high temperature. If a cooling part was designed at the bottom part to make the totally reduced micro liquid iron balls cooled down during dropping then the micro solid iron balls with high density can be produced.

Fig. 9.

Conceptual morphology evolution schematic of the Fe₂O₃ particles at different temperature ranges with hydrogen reduction.

3.5. Kinetics Analyzing

The shrinking core model is introduced in the kinetics analyzing of this suspension flash hydrogen reduction of Fe₂O₃ particles. This kinetics model is just used to simulate the reductions under the reduction temperature of 1373 K, when the particles have not start to melt. even at 1373 K the newly generated metallic iron became kind of soft and connected to each other to become barriers for internal gas diffusion, the particles could still be considered in solid state, and the reduction of the Fe₂O₃ particles can be divided into three procedures: the external gas diffusion, the internal gas diffusion and the chemical reaction, so it is proper to use the unreacted core model (shrinking core model) to simulate the reduction behaviors in this study. Accordingly, the relationship between R_d and reduction time when the reaction has reached the steady state is:   

$$\begin{array}{l}\frac{R}{3k_{\text{d}}}+\frac{r_0}{6D_{\text{eff}}}\left[\text{1}-\text{3(1}-R{\text{)}}^{2/3}+\text{2(1}-R\text{)}\right]\\ +\frac{K}{k_{+}\text{(1}+K\text{)}}\left[\text{1}-{\text{(1}-R\text{)}}^{1/3}\right]=\frac{C-C_{\text{equ}}}{r_0{d}_0}t\end{array}$$(11)

Here, R is reduction degree, %; k_d is the mass transfer coefficient of the gas phase boundary layer, m/s; r₀ is the particle’s radius, m; D_eff is the effective diffusion coefficient, m²/s; K is the equilibrium constant; k₊ is the positive reaction rate constant, m/s; C is the reducing gas concentration in the gas phase and the C_equ is the reducing gas concentration at equilibrium state, mol/m³; d₀ is the removable oxygen amount per unit volume, mol/m³.

In this experiment, the reducing gas was pure hydrogen, so the gas phase diffusion coefficient can be calculated according to the pneumodynamics theory as below:   

$$D_{{\text{H}}_2}=\frac{8.31\times {10}^{-6}{T}^{3/2}}{p{\sigma }_{{\text{H}}_2}^2\mathrm{\Omega }}\sqrt{\frac{1}{M_{{\text{H}}_2}}}=1.59\times {10}^{-3}{m}^2/s$$(12)

The k_d can be calculated with the equation below (d is the particle’s diameter):   

$$k_{\text{d}}=\frac{\text{(2}\text{.0}+\text{0}\text{.6}R{e}^{1/2}S{c}^{1/3}\text{)}D}{d}=140.6m/s$$(13)

The density of the Fe₂O₃ particles used in this experiment is 4685.5 kg/m³, and the d₀ is 8.78×10⁴ mol/m³. Above 843 K, the reduction of Fe₂O₃ is in this sequence: Fe₂O₃→Fe₃O₄→FeO→Fe, and during the whole reduction process FeO→Fe is the most difficult step, so the calculation of K and C_equ is just take this reaction into consideration: FeO+H₂=Fe+H₂O. The K and C−C_equ values at different temperatures are listed in Table 4. The concentration driving force varies with reduction degree as reaction time increases due to the formation of water vapor, and that effect is ignored in this model.

Table 4. K and C−C_equ values at different temperatures.

Temperature	873 K	1073 K	1273 K	1373 K
K	0.3476	0.5356	0.724	0.8076
C−Cequ mol/m3	3.589	3.949	4.01	3.953

Suppose that:   

$$A=\frac{r_0^2{d}_0}{6D_{\text{eff}}\text{(}C-C_{\mathrm{e}\mathrm{q}\mathrm{u}}\text{)}}$$(14)

  

$$B=\frac{K{r}_0{d}_0}{k_{+}\text{(1}+K\text{)(}C-C_{\text{equ}}\text{)}}$$(15)

  

$$F=1-{\text{(1}-R\text{)}}^{1/3}$$(16)

  

$$t_1=\frac{r_0{d}_{0}R}{3k_{\text{d}}\text{(}C-C_{\text{equ}}\text{)}}$$(17)

To take above equations into Eq. (11) then it changes to:   

$$\frac{t-t_1}{F}=A\text{(3}F-\text{2}{F}^2\text{)}+B$$(18)

Using the data in this experiment and set (t−t₁)/F as x-axis, (3F−2F²) as y-axis, then Fig. 10 can be plotted:

Fig. 10.

Relation between (t−t₁)/F and 3F−2F².

The D_eff and the k₊ can be obtained from the slope and intercept of the lines simulated by the plotted data, then the resistance of external diffusion, internal diffusion and reaction can be evaluated respectively by:   

$${\eta }_{\text{d}}=\frac{1}{k_{\text{d}}}$$(19)

  

$${\eta }_i=\frac{r_0\text{(}{r}_0-r_{\text{i}}\text{)}}{r_{\text{i}}{D}_{\text{eff}}}$$(20)

  

$${\eta }_c=\frac{K}{k_{+}\text{(}1+K\text{)}}\frac{r_0^2}{r_{\text{i}}^{\text{2}}}$$(21)

The value of 1/k_d in this experiment is very tiny, so the external diffusion resistance is negligible. To consider the whole reaction as several divisional stages, as Fig. 10 expresses, the slopes of the lines increase with the reaction progress, which indicates that the D_eff decreases while the η_i increases with the reaction progress. In other words, the internal diffusion resistance is negligible at initial stage and becomes more and more significant at later stage.^25,26) Simultaneously, the intercepts of the lines decrease with the reaction progress, which indicates that the k₊ increases while the η_c (reaction resistance) decreases with the reaction progress for each reduction temperatures. Moreover, the intercepts at initial stages generally declined with the increase of temperature, so it provides evidence that the reaction resistance generally declined with the increase of temperature.

Furthermore, to ignore the external diffusion resistance, and assume that the reaction rate is controlled by the chemical reaction and internal diffusion respectively, then Eq. (11) is simplified into the form of Eqs. (22) and (23):   

$$r_0{d}_0\text{[}1-{\text{(}1-R\text{)}}^{1/3}\text{]}=\frac{k_{+}\text{(}1+K\text{)}}{K}\text{(}C-C_{\text{equ}}\text{)}t$$(22)

  

$$r_0^2{d}_0\text{[}1-3{\text{(}1-R\text{)}}^{2/3}+2\text{(}1-R\text{)]}=\text{6}{D}_{\text{eff}}\text{(}C-C_{\mathrm{e}\mathrm{q}\mathrm{u}}\text{)}t$$(23)

To set 1−(1−R)^1/3 and [1−3(1−R)^2/3+2(1−R)] as the y-axis respectively, reduction time as the x-axis, then plotted with the experimental data as shown in Figs. 11 and 12.

Fig. 11.

Relationship between 1−(1−R)^1/3 and time in the reaction control model.

Fig. 12.

Relationship between [1−3(1−R)^2/3+2(1−R)] and time in the internal diffusion control model.

The liner fitting of the initial stage meets well with the experimental points in both models. The values of k₊ and D_eff can be evaluated by the slope of the linear fitting equations, and then the values of η_c and η_i can be calculated at the same time. Figure 13 shows the comparison of the internal diffusion and chemical reaction resistance under different reduction degrees. It is clear that the chemical reaction resistance and the internal diffusion resistance coexist in this experimental condition, and for each reduction temperature, the chemical reaction resistance is higher than the internal diffusion resistance at initial reduction stage while the latter surpasses the former at later reduction stage.

Fig. 13.

Comparison of the internal diffusion and chemical reaction resistance under different reduction degrees.

4. Conclusions

Introduction of upward gas flow in the suspension flash reduction system can truly prolong the residence time of particle, consequently, higher reduction degrees are likely to be obtained at lower temperature. The precise residence time of particles with different sizes at different temperatures was calculated by the Stokes gas solid dynamic theory with the relaxation time concept in this study.

The reduction rate decreased with the decrease of particle size below 1273 K in this experiment. That may cause by the difference of the cracks distribution density on the particle surface and the dispersion situation during falling down.

It is found that the microstructure evolution of the particles can affect the reduction behavior and the temperature makes great difference on the microstructure evolution. When the reduction temperature surpasses 1373 K, the voids emerging during reduction become kind of inclosed and that may cause the increase of the internal diffusion resistance and the decline of the final reduction rate.

The kinetics analyzing also manifests that the resistance of internal mass transfer becomes more and more significant with the increase of reduction temperature, and the chemical reaction resistance is higher than the internal diffusion resistance at initial reduction stage while the latter surpasses the former at later reduction stage.

Last but not the least, it is still not clear that the effect of water content on the reduction rate, and the online cooling of the product of high R_d should be taken into consideration as the agglomerating trend of ultra-fine particles at high temperature is very strong.

Acknowledgement

This work is supported by the National Natural Science Foundation of China (No.51234001) and the National Basic Research Program of China (973 Program, 2012CB720401).

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