Hydrogen-based direct reduction of industrial iron ore pellets: Statistically designed experiments and computational simulation

1.   Introduction

In the last decades, considerable efforts have been dedicated to understanding systems involving non-catalytic gas–solid reactions, which have many features similar to reactions catalyzed by porous solids [1]. The equating of these systems involves mass and heat transfer simultaneously to chemical reactions. Indeed, in non-catalytic reactions, transient structural changes occur in the solid phase as chemical reactions proceed, altering the physical properties of the gas–solid system [2]. These effects and other specific factors provide additional difficulties to mathematically describe the system.

The direct reduction (DR) process of iron ore is one of the most important applications of non-catalytic gas–solid reaction systems. It is an alternative route to the conventional blast furnace iron production process, without the smelting of iron ore and the use of coke. In fact, due to the lower availability of natural resources and deterioration in the quality of iron ore and coke, as well as the consequent increase in their costs, alternative processes have gained increasing interest [3]. For these reasons, the interest in DR of iron ore has grown significantly, being responsible for the global production of about 100 million tons of iron per year in recent years [4]. MIDREX (Midland-Ross Direct Iron Reduction) is the most widely used technology, contributing to around 80% of the total DR-based production.

Conversely, concerns about global warming have motivated the development of cleaner technologies in the manufacturing industries, aiming to reduce CO₂ emissions, since the iron and steel industry is one of the largest emitters of CO₂, representing about 7% of global anthropogenic emissions of carbon dioxide [5]. In order to achieve the goals of international treaties, such as the Paris Agreement and the European Green Deal, for drastically reducing CO₂ emissions by 55% until 2030, and achieving carbon neutrality by 2050 [6], considerable changes must be carried out in the iron and steel industries. One of the priorities conducted by a consortium of European steelmakers is the DR process using H₂ produced via electrolysis as the only reducing gas [7–8]. The use of H₂ makes the reduction process much more efficient [9–11] and results in zero CO₂ emissions. However, hydrogen production still demands high energy consumption, a challenge that still needs to be overcome.

In this context, the investigation of the main variables that affect the process is fundamental for a better understanding of the phenomena involved, allowing for an increase in productivity, product quality control, and optimal utilization of the hydrogen. For the DR process, the complexity increases due to the presence of consecutive reduction reactions and the structural transformations of the solid phase as the reactions proceed. Various studies reported in the literature adopt different levels of simplification, showing large discrepancies in results. These differences can be explained by the variety of experimental conditions considered in each study. The rate-controlling step (chemical, diffusive, intermediate) of the reduction process is not unique, as it may depend on a series of operational conditions, such as temperature, pressure, flow rate, gas composition, and parameters of the solid pellet, such as size, morphology, porosity, pore distribution, and mineralogical composition [12]. Despite this multiplicity of factors involved, experiments are commonly analyzed by varying only one factor at a time, while the others are kept unchanged. Consequently, interaction effects of important variables are neglected, and due to expenses with reagent, energy, and time in carrying out the experiments, studies are restricted to a relatively limited set of conditions.

At the pellet scale, the most relevant approaches developed for predicting the reaction of the solid reagent as a function of time are represented by the shrinking core model (SCM) and the grain model (GM). Due to the simplicity, many studies address the SCM to simulate the process. However, most recent investigations have pointed out erroneous conclusions in the application of this model to describe gas–solid reactions in porous solids, such as those used in the DR industrial process [13–15]. In a porous pellet, the chemical reaction and gas diffusion occur simultaneously, and the heterogeneous approach of the SCM is not appropriate. The GM, introduced by Szekely et al. [16], assumes that the pellet is composed of numerous grains surrounded by pores through which gases diffuse before reaching the reaction interface of the grain. The application of this microscale submodel results in more realistic results compared to the heterogeneous SCM, being more extensive to represent the non-catalytic gas–solid reactions [15–17].

The direct hematite reduction process with hydrogen consists of three reactions involving the solid compounds Fe₂O₃, Fe₃O₄, FeO, and Fe. The rate-controlling mechanism is determined not only by the chemical reactions, presenting steps with important diffusive limitations of the gas [18]. For this reason, the estimation of kinetic parameters reported in the literature, performed by model fitting from the Arrhenius equation, shows a large variability of values [12], which limits the general adoption of these parameters in process design. Furthermore, the mathematical modeling is restricted to the structural characteristics of the iron ore considered in each study, consisting of grains [19–20], powder [21–22], crystals [23], briquettes [24], sinters [25], and pellets [9,14,26–29]. In the case of iron ore pellets, publications applying the GM do not report the adopted grain size [9,14,27,29–30] and hinder the reproducibility of results and comparisons among performed simulations. The arbitrariness in adopting the pellet microstructure-dependent variables is also evident in studies that estimate both the kinetic parameters of the reduction reactions and the effective diffusivity that best fits the applied reduction process conditions [26,31–32]. In fact, these variables lump together the set of heterogeneous structural characteristics of the solid material involved and their transformations over time as reactions occur. The microstructural analyses of the reduction process along the reaction time presented by Ranzani da Costa et al. [33] and Patisson and Mirgaux [8] reveal considerable morphological changes, such as grain size and porosity of iron oxides, during the three reaction steps. Depending on the reduction temperature applied, the iron grains produced have different sizes and characteristics [8]. These considerations highlight the multi-scale approach required by the direct iron ore reduction process to obtain a more representative model. Thus, simulations carried out at the scale of an industrial reactor still need more comprehensive investigations at the pellet scale, especially concerning the direct reduction process with H₂, aimed at obtaining reliable predictions for the process as a whole.

The present study aims to investigate the direct reduction of industrial iron ore pellets using H₂, in laboratory scale-designed experiments. Subsequently, simulations are performed to evaluate the predictive capacity of the SCM and GM using the three consecutive reactions, and the effect of the process variables is statically evaluated.

2.   Materials and methods

2.1   Experimental procedure

Samples of industrially produced iron ore pellets used in all experiments were supplied by Vale Company. Table 1 shows the chemical composition of the pellets, which are mainly composed of hematite. A sample of the iron ore pellets was classified and dried in an oven to remove moisture. The values of mass, diameter, and porosity of the pellets were measured before and after the reduction process. The porosity was determined from the apparent density using a porosimeter (Automatica). Fig. S1 shows the porosity distribution based on 110 pellets.

Table  1.  Composition of the industrial iron ore pellet wt%

Fe2O3 (Fe*)	Al2O3	CaO	MgO	Mn	P	SiO2	TiO2	CL
96.1 (67.24)	0.53	1.00	0.06	0.082	0.024	1.72	0.09	0.29
Note: CL–calcination loss. *Percentage of elemental iron in the pellet.

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The reduction experiments with pure H₂ gas were carried out isothermally in a thermogravimetric analyzer (TGA) (STA 409, NETZSCH), as schematized in Fig 1. This apparatus consists of a furnace containing an alumina plate crucible and a carrier system comprising a tungsten rod to support the sample, which is connected to a precision balance (±0.001 g). Thus, the mass of the sample was monitored throughout the reaction time through a control system coupled to a computer. For each reduction experiment, the air contained in the furnace was initially removed through the evacuation system containing a vacuum pump, followed by the introduction of argon gas. Consecutively, the balance was tared and a single pellet was heated to the target temperature in argon gas at a flow rate of 150 mL/min. The inert gas was then switched with pure H₂ at a flow rate of 500 mL/min until a minimum reduction of 99% was achieved. Then, H₂ was replaced with argon flow until the sample was cooled to below 50°C. The overall conversion rate (X_global) of the experimental data from TGA is given by Eq. (1).

Fig. 1.  Schematic illustration of the thermogravimetric apparatus, highlighting the furnace on the right.

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where m₀ (g) is the initial mass of the pellet, m_t (g) is the mass of the pellet at time t (s), and m_∞ (g) is the final mass of the pellet. This equation corresponds to the mass loss of the oxygen removed in a given time in relation to the total mass of removable oxygen.

A response surface methodology based on the Doehlert experimental design [34] was applied to investigate the multivariate effects in the direct reduction process of a single pellet and to evaluate the effect of the process variables on the responses. This statistical method significantly reduces the number of experiments concerning the variables analyzed and has other advantages over other experimental designs, such as the possibility of extending the domain by adding new values of a variable or by adding another variable [35–36]. The diameter (d₀) and porosity (ε₀) of the pellets and reaction temperature (T) were studied respectively at five (10.5–16.5 mm), three (0.36–0.44), and seven (600–1200°C) levels of values, resulting in 13 experimental conditions (Table 2). In addition, two other repetitions of condition 1 (the central point of the design) were performed to determine the variability of the procedure. Multiple regression analysis was performed using the software Matlab R2017 for obtaining a second-order polynomial, according to Eq. (2) [35].

Table  2.  Doehlert experimental design for DR process and values of the experimental responses

Schematic representation	Exp.	Experimental value (${U}_{k}\;\mathrm{and}\;{U}_{k}'$)				Coded value (${Z}_{k}$ and ${Z}_{k}'$)				Response
		dp / mm ${U}_{1}'$ (U1)	T / °C ${U}_{2}'$ (U2)	ε0 ${U}_{3}'$ (U3)		${Z}_{1}'$ (Z1)	${Z}_{2}'$ (Z2)	${Z}_{3}'$ (Z3)		Y1 / min	Y2 / (N·mm −2)
	1	13.5 (13.6)	900 (905)	0.40 (0.40)		0.000 (0.0167)	0.000 (0.0144)	0.000 (0.0224)		18.4	2.33
	1'	13.5 (13.6)	900 (899)	0.40 (0.39)		0.000 (0.0367)	0.000 (−0.0029)	0.000 (−0.1387)		16.4	1.52
	1''	13.5 (13.6)	900 (898)	0.40 (0.39)		0.000 (0.0333)	0.000 (−0.0058)	0.000 (−0.1469)		16.8	1.66
	2	16.5 (16.5)	900 (901)	0.40 (0.39)		1.000 (1.0133)	0.000 (0.0029)	0.000 (−0.2244)		26.4	2.16
	3	15.0 (14.8)	1200 (1232)	0.40 (0.40)		0.500 (0.4333)	0.866 (0.9584)	0.000 (−0.0755)		10.4	0.30
	4	15.0 (14.7)	1000 (1001)	0.44 (0.44)		0.500 (0.3900)	0.289 (0.2916)	0.816 (0.8405)		14.0	0.91
	5	10.5 (10.5)	900 (904)	0.40 (0.41)		−1.000 (−1.0067)	0.000 (0.0115)	0.000 (0.1081)		10.0	1.69
	6	12.0 (11.6)	600 (597)	0.40 (0.39)		−0.500 (−0.6333)	−0.866 (−0.8747)	0.000 (−0.1040)		39.1	2.06
	7	12.0 (12.3)	800 (797)	0.36 (0.36)		−0.500 (−0.4000)	−0.289 (0.2973)	−0.816 (−0.7650)		21.1	2.32
	8	15.0 (15.2)	600 (595)	0.40 (0.40)		0.500 (0.5567)	−0.866 (−0.8804)	0.000 (0.0836)		75.5	2.82
	9	15.0 (15.0)	800 (795)	0.36 (0.36)		0.500 (0.4900)	−0.289 (−0.3031)	−0.816 (−0.7609)		27.3	2.66
	10	13.5 (13.8)	1100 (1108)	0.36 (0.35)		0.000 (0.0867)	0.577 (0.6004)	−0.816 (−0.9571)		10.3	0.63
	11	12.0 (11.7)	1200 (1190)	0.40 (0.39)		−0.500 (−0.6033)	0.866 (0.8371)	0.000 (−0.1122)		6.1	0.38
	12	12.0 (11.5)	1000 (1010)	0.44 (0.45)		−0.500 (−0.6567)	0.289 (0.3175)	0.816 (0.9996)		6.0	0.50
	13	13.5 (12.6)	700 (702)	0.44 (0.43)		0.000 (−0.2900)	−0.577 (−0.5716)	0.816 (0.5508)		27.7	2.43
	E1	10.5 (11.2)	800 (792)	0.36 (0.38)		−1.000 (−0.7767)	−0.289 (−0.3118)	−0.816 (−0.3101)		15.6	2.36
	E2	16.5 (16.6)	600 (597)	0.40 (0.41)		1.000 (1.0333)	−0.866 (−0.8747)	0.000 (0.1326)		88.5	1.70
Note: ${\mathit{U} }_{\mathit{k} }'\;{\rm and}\;{\mathit{U} }_{\mathit{k} }$ are nominal and measure experimental values, respectively; ${Z}_{k}'$ and ${Z}_{k}$ are the nominal and real coded values obtained from the experimental ${\mathit{U}}_{\mathit{k}}'$ and ${U}_{k}$, respectively, using the equation: ${Z}_{k}=({U}_{k}-{U}_{k}^{0})/{\Delta U}_{k})\times \delta$, where ${U}_{k}^{0}$ is the centered value, ${\Delta U}_{k}$ is the step value, $\delta$ is the maximum code value of each factor, and k represents the k-th value (k = 1, 2, 3) of each independent variable [34–36]. The Y1 and Y2 responses correspond respectively to the time reached for 90% reduction and the compressibility resistance (force per area) obtained by each reduced pellet. Exp. i.e. experiment.

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where a are the coefficients, Z_k corresponds to the codified values of the independent variables, and Y_i is the experimental response. Accordingly, two responses were measured: Y₁, the time required for a 90% reduction of hematite to iron; Y₂, the compressive resistance. For evaluating the mechanical strength of hematite and reduced pellets, compression tests were performed using the Precision Universal Tester (Shimadzu Autograph AGS-X 20 kN).

2.2   Mathematical modeling of the reduction process

The reduction of a single iron ore porous pellet involves the following steps:

(1) Mass transfer of gaseous reagents from the bulk of the gas phase to the pellet surface.

(2) Diffusion of gaseous reagents through the pores of the solid pellet.

(3) Adsorption of the gas on the internal surface of the particle pores.

(4) Chemical reaction between the adsorbed gas and the solids.

(5) Desorption of gaseous products from solid surfaces.

(6) Diffusion of the gaseous products through the pores of the solid pellet.

(7) Mass transfer of gaseous products from the surface of the pellet to the bulk flow.

The DR process involves three consecutive reduction reactions:

R1: $3{\mathrm{F}\mathrm{e}}_{2}{\mathrm{O}}_{3}+{\mathrm{H}}_{2}\rightleftharpoons 2{\mathrm{F}\mathrm{e}}_{3}{\mathrm{O}}_{4}+{\mathrm{H}}_{2}\mathrm{O}$.

R2: ${\mathrm{F}\mathrm{e}}_{3}{\mathrm{O}}_{4}+{\mathrm{H}}_{2}\rightleftharpoons 3\mathrm{F}\mathrm{e}\mathrm{O}+{\mathrm{H}}_{2}\mathrm{O}$.

R3: $\mathrm{F}\mathrm{e}\mathrm{O}+{\mathrm{H}}_{2}\rightleftharpoons \mathrm{F}\mathrm{e}+{\mathrm{H}}_{2}\mathrm{O}$.

Based on these phenomenological and reaction mechanisms described above, the pellet was considered to be made up of numerous grains. The main simplifications adopted are:

(1) Spherical pellet and grain;

(2) Temperature and pressure in and around the pellet are constant;

(3) H₂ and H₂O are considered ideal gases;

(4) First-order and reversible reactions;

(5) No change in the pellet diameter and no cracks formation in the pellet.

A 1D axial symmetric finite element method (FEM) discretized into 100 elements was developed in Comsol Multiphysics 4.3 software for modeling the pellet radius, applying a modified GM. Following the GM proposed by Valipour [29], the pellet consists of numerous grains and each grain follows the triple interface shrinking core model (SCM). This model is based on a combination of resistances provided by the gas film around each grain, diffusion, and the three consecutive reactions, generating a set of algebraic equations from the arrangement of resistances for each grain, as shown in Fig. S2. In the present study, intra- and inter-grain diffusions were considered in addition to porosity changes during the reactions. The governing equations for the gas and solid phases are shown in Eqs. (3)–(19). The global conversion of each solid is given by the integral of the local overall conversion of the grains (Eq. (18)). Additionally, the fractions indicated in Eq. (19) correspond proportionally to the contribution of each solid component to the total removal of oxygen in the overall conversion of hematite to iron.

Total mass balance equation for the gas phase:

Mass balance equations for the solid phase:

Reaction rate model:

where:

Initial conditions (t = 0):

Overall conversion of the pellet at each time:

The chemical reaction rate constants were calculated using the Arrhenius expression, applying the kinetic parameters presented by Valipour et al. [30], shown in Table 3. Additionally, the effective diffusivities of the reagent and product gases were determined for each experimental condition according to Eqs. (20)–(24) (Table 4) considering the characteristics of the solid (pellet size and porosity), and the temperature. The estimation of the gas–solid mass transfer coefficient was based on the correlation for the spherical pellet given by Eq. (25) (Table 4).

Table  3.  Kinetic parameters [30]: pre-exponential factor (k₀), apparent activation energy (E_a), and equilibrium constant (k_eq) for each reduction reactions with H₂

Reaction	k0 / (m·s−1)	Ea / (J·mol−1)	keq
R1	29.17	66989	$\mathrm{e}\mathrm{x}\mathrm{p}\left(-\dfrac{362.6}{T}+10.334\right)$
R2	15.56	75362.4	$\mathrm{e}\mathrm{x}\mathrm{p}\left(-\dfrac{7916.6}{T}+8.46\right)$
R3	2858.34	117230	$\mathrm{e}\mathrm{x}\mathrm{p}\left(-\dfrac{1586.9}{T}+0.9317\right)$

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Table  4.  Correlations used in the model

Correlation	Eq. No.
Knudsen diffusivity [37]: ${D}_{i}^{k}=\dfrac{4{K}_{0} }{3}\sqrt{\dfrac{8\bar{R}T}{\pi {M}_{i} } }$ (m2/s), i = H2, H2O	(20)
Binary molecular diffusion using Fuller-Schettler-Giddings correlation [38]: ${D}_{i,j}=\dfrac{ {10}^{-7}{T}^{\mathrm{1,75} }{\left(\dfrac{1}{ {M}_{i} }+\dfrac{1}{ {M}_{j} }\right)}^{1/2} }{P\left[{\left(\sum _{i}{\sigma }_{i}\right)}^{1/3}+{\left(\sum _{j}{\sigma }_{j}\right)}^{1/3}\right]}$ (m2/s), ${\sigma }_{ {\mathrm{H} }_{2} }=7.07\;\mathrm{c}{\mathrm{m} }^{3}/\mathrm{m}\mathrm{o}\mathrm{l}\;{\rm{and} }\;{\sigma }_{ {\mathrm{H} }_{2}\mathrm{O} }=12.7\;\mathrm{c}{\mathrm{m} }^{3}/\mathrm{m}\mathrm{o}\mathrm{l}$	(21)
Gas diffusivity in a gas mixture [39]: ${D}_{i}^{m}=(1-{y}_{i}){\left(\sum _{i\ne j}\dfrac{{y}_{j}}{{D}_{i,j}}\right)}^{-1}$ (m2/s), i, j = H2, H2O	(22)
Effective intraparticle diffusion [37]: ${D}_{i}=\dfrac{1}{\dfrac{1}{ {D}_{i}^{m} }+\dfrac{1}{ {D}_{i}^{k} } }$ (m2/s), i = H2, H2O	(23)
Effective diffusivity of the porous particle [40]: ${D}_{\mathrm{e}\mathrm{f}\mathrm{f},i}={\varepsilon }^{2}{D}_{i}$ (m2/s), i = H2, H2O	(24)
Gas–solid mass transfer coefficient [41]: $S h=\dfrac{ {k}_{\mathrm{g} }{d}_{\mathrm{p} } }{ {D}_{i} }=2+0.39{Re}_{\mathrm{p} }^{1/2}{S c}^{1/3}$	(25)

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The change in porosity was incorporated into the model during the three reduction reactions. Assuming that the diameter of the pellet and the grain did not change during the process, the relationship between the final (ε_s,f) and initial porosities (ε_s,0) of the solid is given by the molar balance in Eq. (26), from Szekely and Evans [37].

The molar densities of the solids used in this equation were calculated based on the mass densities reported by Akiyama et al. [42] in Table 5, taking into account the presence of approximately 3.8wt% of impurities contained in the industrially produced iron ore pellets used in this study.

Table  5.  Density of iron oxides

Solid	True mass density / (kg·m−3) [42]	Mass density / (kg·m−3) (present study)	Molar density / (mol·m−3) (present study)
Hematite (Fe2O3)	5210	5005	32500
Magnetite (Fe3O4)	5160	4957	22200
Wustite (FeO)	5460	5245	76000
Iron (Fe)	7860	7550	140800

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3.   Results and discussion

3.1   Experimental results

Figs. 2 and 3 compare the experimental results, according to the conditions of the Doehlert experimental design (Table 2), maintaining the temperature and pellet size approximately constant. The repetitions of the reduction experiment in condition 1 did not show significant deviations in the conversion profile over time. In all experiments, complete conversion was achieved. As expected, the reduction is considerably affected by the temperature and the pellet size. The higher the temperature and the smaller the pellet size, the faster is the pellet reduction. In fact, the increase in temperature considerably accelerates the process of reducing iron ore, since the kinetic rates and the gas diffusion increase with rising temperature. As shown in Fig. 2, the effect of pellet size is considerably larger at lower temperatures. At 600°C, increasing the pellet diameter from 11.6 to 15.2 mm leads to a 34 min increase in reduction time considering 90% conversion, while at 800°C, increasing the pellet from 11.2 mm to 15 mm, increases this same reduction time by 12 min, indicating that internal diffusion resistance is considerably smaller at this temperature. Fig. 3 shows that the effect of temperature on the reduction rate is more pronounced for larger pellet sizes. Regarding the porosity, the results showed no significant effects for the range of values studied (0.35 to 0.45).

Fig. 2.  Time–conversion profiles for different experimental conditions (a–e), showing the effect of diameter (d_p), according to Doehlert's matrix (in the upper left corner).

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Fig. 3.  Time–conversion profiles for different experimental conditions (a–e), showing the effect of temperature (T), according to Doehlert's matrix (in the upper left corner).

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Although higher temperatures accelerate the kinetic rate, some mechanical disadvantages occur at higher temperatures. While the loss of mass due to the removal of oxygen from iron oxides (around 28.6%) and porosity increase (around 86%) is common in all experiments, the volume of the pellet is considerably increased for samples processed above 1000°C (around 30%) (see Table S1). In these experiments, cracking was observed in the reduced pellets, as shown in Fig. 4, and consequently, the mechanical resistance of the produced iron solid is decreased. The greater fragility of the pellets can result in the consequent production of fines and dust, compromising the permeability of gases inside the shaft furnace [43].

Fig. 4.  Morphology of iron ore pellets under different conditions: (a) initial iron ore pellet; pellet reduced at (b) 600°C; (c) 700°C; (d) 800°C; (e) 900°C; (f) 1000°C; (g) 1100°C; (h) 1200°C.

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The occurrence of cracking has been the object of several studies and has been associated with changes in the atomic and grain scale of metal oxides, the rapid diffusion of the gas, and the considerable presence of impurities. According to these studies, the rearrangement of the crystalline lattice during the transformations of each solid phase as the reactions proceed causes tensions (lattice disturbance) that lead to the formation of cracks [44–45] since the hematite has a compacthexagonal structure, magnetite and wustite have face-centeredcubic crystal structures, and α-iron (pure iron up to 912°C) has a body-centered cubic crystal. Heidari et al. [46] revealed that the change in density from hematite (5.260 g/cm³) to magnetite (5.175 g/cm³) can cause microcracks due to the volume change. Additionally, Nyankson and Kolbeinsen [28] reported that the rapid diffusion of H₂, especially at higher temperatures, causes a rapid swelling due to the transformation of solid phases, mainly from hematite to magnetite. They observed the formation of more pronounced and wider cracks in pellets reduced with hydrogen compared to those processed with carbon monoxide. Mizutani et al. [47] also verified greater crack formation in pellets reduced with H₂ by comparing pellets reduced with 30vol%H₂–70vol%N₂ and 30vol%CO–70vol%N₂. In the case of CO-reduced pellets, crack formation occurs concentrically within the pellet, tending to follow the separation of the unreacted core, while in H₂-reduced pellets, cracks are more widespread throughout the pellet, showing different radial sizes that are seen from the surface to the center of the pellet. The results observed in our study in addition to these considerations from the literature indicate that the best structural and mineralogical characteristics of the pellets for the MIDREX process can be considerably different for the hydrogen-based reduction process. This is a relevant information for the further development of H₂-based DR processes.

Due to the difficulties in selecting exactly the desirable structural parameters of the industrial pellets, as well as setting the nominal temperature in the TGA, the real values of the evaluated variables show a slight deviation from the proposed experimental design. This was corrected by recoding these experimental values, as shown in Table 2. In addition, two extra experiments were added to improve the analysis. The repetition of the central condition (Exp. 1) shows a small error associated with the experimental procedure (standard deviation of 0.008).

Based on these values, the data obtained for the response of the time required for a 90% global fraction reduction (Y₁) was evaluated. The effect of the input variables on the response is shown in the Pareto charts (Fig. 5(a)) by analysis of variance (ANOVA) (F test with p < 0.05) and demonstrate considerable effects of pellet size (Z₁) and temperature (Z₂) on the process. Particularly, a strong interaction of these two variables (quadratic terms Z₁Z₂ and Z₂Z₂), indicates that the effect is temperature-dependent and that temperature and pellet size cannot be evaluated separately. In contrast, the effect of porosity on the three responses did not have a significant influence on the range of values studied. In fact, the porosity of industrial hematite pellets is considered relatively high and, therefore, the diffusive effect between different porosity values is negligible. Thiele’s modulus, here defined as ${\varPhi}^{2}=\dfrac{{k}_{n}{r}_{\mathrm{p}}}{{D}_{\mathrm{e}\mathrm{f}\mathrm{f}}}$ , is a quantitative measure of the ratio of diffusive to kinetic resistance. According to a study by Melchiori and Canu [15], three rate-controlling regimes can be defined by this parameter: diffusive regime (Ф² > 10³), intermediate regime (1 < Ф² < 10³, and kinetic regime (Ф² < 1). The calculated values for the three reactions applied in our study were considered low, in the order of 10⁻⁴ to 10⁻¹, indicating that the reaction rate is mostly controlled by chemical reactions than the transport of H₂ gas along with the pellet.

Fig. 5.  Standardized Pareto chart, considering all variables Z₁, Z₂ and Z₃: (a) for response Y₁ (time for 90% reduction, R² = 0.9848; (b) for response Y₂ (compressive resistance), R² = 0.8659.

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By removing the negligible effect of porosity (Z₃) from this analysis, the Y₁ response surface is shown in Fig. 6(a) and (b) (R² = 0.9492), considering a confidence level of 95%. The surface and contour plots reveal that, for some conditions, the same Y₁ response can be obtained using lower temperatures with smaller pellet sizes and higher temperatures with larger pellet sizes. Therefore, the analysis to determine the most favorable temperature and pellet size for the DR process must be carried out in addition to the reactor scale as decreasing the size of the pellets rises the resistance to flow in a packed bed.

Fig. 6.  Response surface plot (a) and contour plot (b) for Y₁ (time for 90% reduction) obtained by variation of Z₁ (d_p) and Z₂ (T); response surface plot (c) and contour plot (d) for Y₂ (compressive strength of pellets) obtained by variation of Z₂ (T) and Z₃ (ε₀). Equations determined by Doehlert design for the DR process: ${\boldsymbol{ {\boldsymbol{Y}}_{{\boldsymbol{1}}}'({\boldsymbol{Z}}_{\boldsymbol 1},{\boldsymbol{Z}}_{\boldsymbol 2})=\left(15.40\pm 3.56\right)+\left(11.38\pm 3.81\right) {\boldsymbol{Z}}_{\boldsymbol 1}-\left(26.97\pm 4.01\right){\boldsymbol{Z}}_{\boldsymbol 2}}}+$ ${\boldsymbol{ \left(2.76\pm 6.44\right){\boldsymbol{Z}}_{\boldsymbol 1}^{\boldsymbol 2}+(22.60\pm 6.49){\boldsymbol{Z}}_{\boldsymbol 2}^{\boldsymbol 2}{-({\boldsymbol{17.03}}{\boldsymbol{\pm}} {\boldsymbol{7.11}}){\boldsymbol Z}}_{\boldsymbol 1}{{\boldsymbol Z}}_{\boldsymbol 2}} }$ (R² = 0.9803). ${\boldsymbol {{\boldsymbol{Y}}_{2}' \left({\boldsymbol{Z}}_{1},{\boldsymbol{Z}}_{\boldsymbol 2}\right)=\left(1.86\pm 0.43\right)}}+{\boldsymbol{\left(0.16{\boldsymbol{Z}}_{1}\pm 0.46\right)-(1.29{\boldsymbol{Z}}_{2}\pm 0.49)-}}$${\boldsymbol {\left(0.14{\boldsymbol{Z}}_{1}^{2}\pm 0.78\right)+\left(0.28\pm 0.86\right){\boldsymbol{Z}}_{\boldsymbol 2}^{\boldsymbol 2}-{\left({\boldsymbol{0.71}}\pm {\boldsymbol{0.79}}\right)\boldsymbol{Z}}_{1}{\boldsymbol {Z}}_{\boldsymbol 2}} }$ (R² = 0.8431).

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Fig. 5(b) shows the Pareto chart using ANOVA (F test with p < 0.05) for the compressive resistance response (Y₂). The temperature has a significant negative effect on the compressive strength of pellets. Although not expressive, porosity exerts a larger effect on this response than pellet diameter. The increase in porosity decreases the mechanical strength of the pellets. Results of the compression test of hematite pellets (Y_{2, mean} = (17.79 ± 3.85) N/mm² or 2669 N/P; P represent pellet) indicated that there is a drastic loss of mechanical strength of the pellets compared to reduced pellets (Y_{2, mean} = (1.67 ± 0.83) N/mm²). The 86% increase in porosity during the reductive process can significantly affect the mechanical properties of the pellets, possibly due to solid and molecular arrangement changes.

The best conditions were found for the lowest temperature, i.e., porosities and diameters of 0.37 (Z₃ = −0.56) and 14.37 mm (Z₂ = 0.83), respectively. The Y₂ response surface graphs of temperature as a function of porosity and diameter in Fig. 6(c) and (d) shows a pronounced decrease in mechanical strength for temperatures above 900°C (Z₂ = 0). These observations reveal that although the increase in temperature favors the reduction kinetics, very high temperatures bring unwanted effects on the mechanical characteristics of the pellets.

3.2   Model results

During the reduction of the hematite pellet to iron, more porous solid products are formed. The measured initial and final porosities from the hematite pellets used in each reduction experiment, as well as the predicted porosities for each solid phase are shown in Table 6. As the volume change of the pellets between 595 to 905°C is small and can be disregarded, the calculated porosity of the iron formed in these experiments shows a good agreement with experimental results (mean absolute error of 0.01). At temperatures above 1000°C, the formation of cracks and the increase in volume affect the estimation of porosity.

Table  6.  Experimental and predicted porosities for each reduction experiment

Condition			Pellet porosity
Exp.	T / °C		Experimental			Predicted				Error
			ε0	εf		εM	εW	εFe		εFe − εf
8	595		0.40	0.71		0.42	0.49	0.72		−0.01
6	597		0.39	0.73		0.41	0.48	0.72		0.01
E2	597		0.41	0.71		0.42	0.49	0.72		−0.01
13	702		0.43	0.70		0.44	0.51	0.73		-0.03
E1	792		0.38	0.71		0.40	0.47	0.71		0.00
9	795		0.36	0.70		0.38	0.45	0.70		−0.01
7	797		0.36	0.71		0.38	0.45	0.70		0.01
1''	898		0.39	0.73		0.41	0.48	0.72		0.01
1'	899		0.39	0.74		0.41	0.48	0.72		0.02
2	901		0.39	0.74		0.40	0.48	0.72		0.02
5	904		0.41	0.74		0.42	0.49	0.72		0.01
1	905		0.40	0.74		0.42	0.49	0.72		0.01
4	1001		0.44	0.80		0.45	0.52	0.74		0.06
12	1010		0.45	0.78		0.46	0.53	0.74		0.03
10	1108		0.35	0.72		0.37	0.44	0.70		0.02
11	1190		0.39	0.80		0.41	0.48	0.72		0.08
3	1195		0.40	0.81		0.42	0.49	0.72		0.08
Mean			0.398	0.740		0.412	0.483	0.721		0.03*
Note: εM, εW, and εFe correspond to the predicted porosity of the magnetite, wustite, and iron, respectively. ε0 and εf corresponds to the experimental measurement of the initial and final porosity of the pellet, respectively. * The mean error was calculated by the module of the absolute errors from each experimental condition.

 | Show Table

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Fig. 7 shows a comparison between model predictions and experimental data, including predictions for each reaction conversion, under different conditions. The best fits were observed for the experiments carried out at temperatures around 800 and 900°C for the different sizes of pellets evaluated (10.5 to16.5 mm). At temperatures around 600 and 700°C, the model considerably overestimates the conversion for all pellet sizes studied, while the reverse occurs for simulations above 1000°C (only one pellet size is shown under this temperature). The occurrence of cracks in the pellets at temperatures above 1000°C was not considered in the model and, therefore, may have affected its prediction ability at such temperatures.

Fig. 7.  Predictions for overall conversion by GM compared to the experimental data. Cond. i.e. condition.

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These deviations between simulation and experimental results can be explained as follows. Firstly, the kinetic parameters, i.e., pre-exponential factor and apparent activation energy, adopted in the simulations are those estimated by Takenaka et al. [48] and corroborated by Valipour et al. [30], which were validated for temperatures between 800 and 900°C, and apparently cannot be extended to other temperatures. Secondly, the application of the GM requires a more detailed evaluation of the structural characteristics of the pellet, such as the size, geometry, and regularity of the grains, the distribution of pores and the presence of impurities. However, these properties may vary along the particle volume for industrially produced pellets and certainly change with the reduction process. For convenience, in this study, the grains were assumed to be spherical, with an average diameter of 12 μm in all simulations. For instance, the predictions made for temperatures around 600 and 700°C can be improved by assuming that the average grain size changes during the reduction process and with the temperature.

Some studies in the literature have reported significant structural changes in the grain scale as the reactions proceed. Ranzani da Costa et al. [33] described the morphological transformations during the reduction of small cubes of hematite through microstructural analyses. According to these authors, hematite and magnetite are initially composed of agglomerates of dense spherical grains (25 μm diameter). When the wustite appears, the grains break down into crystallites (2 μm diameter) and the solid becomes porous. Consecutively, wustite crystallites are reduced to iron and become porous due to the difference in molar volume between these two solid phases. In a follow-up study, Patisson and Mirgaux [8] show the micrographs of iron grains formed after reduction with H₂ at temperatures from 600 to 1200°C. They revealed that the morphology and sizes of iron grains were substantially different from the initial hematite grains for different temperatures.

Furthermore, Patisson and Mirgaux [8] have also reported that the optimal reduction temperature for the reduction process with hematite pellets and H₂ is between 800 and 900°C. Accordingly, Fig. 8 shows results for different pellet sizes at a temperature of 850°C, indicating that a 1 mm increase in pellet radius causes a 21% to 32% increase in time for a 90% reduction of the hematite. This illustrates the effect that the changes in structural characteristics of the pellet over time exert on the reduction process at this temperature.

Fig. 8.  Sensitivity analysis for the GM using different diameter sizes. Condition: T = 850 °C; ε₀ = 0.40.

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4.   Conclusions

By performing the described set of experiments based on a Doehlert experimental design, it was possible to statistically evaluate the effect of the process variables included in the study on the overall conversion of hematite to produce elemental iron by reacting with hydrogen gas.

The results showed that the temperature and the size of the pellet considerably affect the process, with a strong interaction between them, since the reduction rate is significantly accelerated at higher temperatures and smaller pellet sizes and, therefore, these variables cannot be considered independently. In contrast, the porosity did not show significant effects on the process for the domain considered in this study. During the reduction time, the porosity increases considerably, while the pellet volume remains practically constant between 600 and 1000°C. At these temperatures, the estimates of porosity after reduction, considering constant pellet size, were close to the experimental values. Above 1000°C, a considerable increase in pellet volume was observed, associated with the formation of cracks. Furthermore, compressibility tests showed a substantial decrease in mechanical strength of the reduced pellets compared to the hematite pellets. Accordingly, the reduction process is faster at higher temperatures, these structural modifications at higher temperatures impose a restriction of 900°C for the recommended maximum temperature in the reduction process. These findings indicate that the best structural and mineralogical characteristics of the pellets for the MIDREX process can be considerably different from the hydrogen reduction process and suggest modifications during the pelletizing process specifically designed for the CO₂-free steelmaking technology.

The fact that pellets reduced with H₂ do not present significant changes in volume can be an important simplification for the mathematical modeling of the process since only changes in porosity as a function of time must be considered. Simulations of the reduction process using kinetic parameters obtained from the literature resulted in good agreement with experiments for temperatures between 800 and 900°C. However, the structural changes observed in the pellets still need to be better clarified in order to describe the process by a rigorous approach. This experimental observation may be a key factor in the development of more generally applicable models of the direct reduction process.

Acknowledgements

The authors express their gratitude to Institute of Technological Research – IPT, Fundação de Amparo à Pesquisa do Estado de São Paulo, Brazil [Process 2019/05840-3] and Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil [Process 167470/2018-3].

Conflict of Interest

The authors declare no conflict of interest.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s12613-022-2487-3.

Nomenclature

Abbreviations
1D	One-dimensional space
ANOVA	Analysis of variance
CL	Calcination loss
DR	Direct reduction
E1	Extra reduction experiment 1
E2	Extra reduction experiment 2
FEM	Finite element method
GM	Grain model
MIDREX	Midland-ross direct iron reduction
SCM	Shrinking core model
TGA	Thermogravimetric analyzer
Symbols
a	Coefficients of the polynomial
An	Resistances due to chemical reactions n = 1, 2, 3, s/m
Bn	Resistances due to the diffusion of the reacted solid layer of n = 1 (magnetite), 2 (wustite), and 3 (iron), s/m
$C_{{\rm{eq}}n, {{\rm{H}}_2}}$	Equilibrium concentrations of H2 for each of reactions n = 1, 2, 3, mol/m3
CH, CM, CW, CFe	Concentration of hematite, magnetite, wustite, and iron, respectively, mol/m3
Ci	Concentration of specie i = H2 or H2O, mol/m3
Ci,bulk	Concentration bulk of specie i = H2 or H2O, mol/m3
dp, d0	Pellet initial diameter, mm
Deff, i	Effective diffusivity of i = H2 or H2O, m2/s
Di	Effective intraparticle diffusivity of i = H2 or H2O, m2/s
Di,j	Effective intraparticle diffusivity of i = H2 or H2O, m2/s
Dik	Knudsen diffusivity of i = H2 or H2O, m2/s
Dim	Molecular diffusivity of i = H2 or H2O, m2/s
F	Resistance of the gas film layer, s/m
K0	Effective Knudsen parameter, m
keq,n	Equilibrium constant of H2 for reactions n = 1, 2, 3, [-]
kg	Mass transfer coefficient through gaseous film, m/s
kn	Reaction rate constant for reaction n = 1, 2, 3, m/s
M	Molecular mass, g/mol
m0	Initial mass of the pellet, g
mt	Mass of the pellet at time t, g
m∞	Final mass of the pellet, g
N	Mol of the solid product formed by one mol of solid reagent
P	Pressure, Pa
$\bar{R}$	Gas constant, J·mol−1·K−1
R2	Coefficient of determination, [-]
r	Radial coordinate in the pellet, m
Re	Reynolds number
rg	Grain radius, m
rn	Radius of the reaction interface within each grain n = 1, 2, 3, m
rn,0	Initial radius of the reaction interface within each grain n = 1, 2, 3, m
Rn	Reaction rate for reactions n = 1, 2, 3 mol·m−3·s−1
rp	Pellet radius, m
Sc	Schmidt number, [-]
Sh	Sherwood number, [-]
T	Temperature, K or °C
t	Time, s
Uk	Measure experimental values for each factor k = 1, 2, 3, mm, °C, or [-]
$U_k'$	Nominal experimental values for each factor k = 1, 2, 3, mm, °C, or [-]
$U_{k}^{0}$	Centred experimental values for each factor k = 1, 2, 3, mm, °C, or [-]
vi	Stoichiometric coefficient
y	Mole fraction [-]
Yq	Response q, q = 1, 2, min or N/mm2
Xn	Fractional reduction for n = 1 (magnetite), 2 (wustite), and 3 (iron), [-]
xn	Local fractional reduction for n = 1 (magnetite), 2 (wustite), and 3 (iron), [-]
Xglobal	Global fractional reduction of the pellet, [-]
Zk	Real coded values for each factor k = 1, 2, 3, [-]
$Z_k'$	Nominal coded values for each factor k = 1, 2, 3, [-]
Greek symbols
δk	Maximum code value of each factor k = 1, 2, 3
ΔUk	Experimental step value, mm, °C, or [-]
ε	Pellet porosity, [-]
ε0, εs,0, εs	Initial porosity of the pellet, initial porosity and predicted porosity of the solids s = H, M, W, Fe, respectively, [-]
εM, εw, εFe	Porosity of the magnetite, wustite and iron, respectively, [-]
εf, εs,f	Final porosity of the pellet, predicted final porosity of the solids s = H, M, W, Fe, [-]
ρs,0	Initial true molar density of the s = H, M, W, Fe, mol/m3
ρs,f	Final true molar density of the s = H, M, W, Fe, mol/m3
σ	Diffusion volume of simple molecule, cm3/mol
Φ2	Thiele modulus, [-]
Note: [-] means the variables are dimensionless.