Introduction

Climate change and energy shortage represent an urgent and potentially irreversible threat to human society. China’s energy utilization efficiency is far lower than the Europe and other developed countries [1], and China needs to further reduce carbon dioxide emissions per unit of gross domestic product [2]. High-purity hydrogen is in great demand at hydrogenation process and fuel cell to meet the increasingly stringent requirements of environmental requirements in China [3, 4]. Chemical-looping hydrogen generation (CLHG) is developed from both chemical-looping combustion (CLC) and hydrogen production by the steam–iron process. CLHG produces high-purity hydrogen while achieving low-cost inherent CO2 separation [5]. In addition, low NOX [6] and low dioxin [7] are realized by avoiding direct contact between fuel and gaseous oxygen for CLHG.

The reduction of iron-based oxygen carriers is the key part of the entire cycle. Steam–iron process only occurred between steam and either Fe or FeO. And the hydrogen production potential positively correlates with the reduction degree of the iron oxides. So the study on deep reduction of iron oxides necessitates an improved understanding of reduction mechanisms and determination of the kinetic parameters for reduction processes [8–10]. Synthesis gas from biomass pyrolysis or coal gasification and refinery gas can be used as fuel gases in the CLC process [11]. Although the concentration of H2 in hydrogen-containing gas is about 5–20% in the low-temperature pyrolysis or other conventional technology with the goal of producing bio-char or bio-oil, the hydrogen-rich gas through high reaction temperature, high heating rate and the catalyst has attracted more and more attentions [12–14]. The concentration gradient of H2 in this work (10–40%) was chosen on the basis of generalized hydrogen-containing gas and hydrogen-rich gas. By CLHG, low-grade hydrogen-containing gases can be converted into high-value pure hydrogen.

Actually adding some inert supports or poly-metallic structure would improve or inhibit the reactivity and stability over cycling [15–17]. This could be because the compound in inert support may catalyze the reduction reaction, or the compound in inert support may react with Fe2O3. Luo et al. [18] investigated the performance of three iron-based oxygen carriers (pure Fe2O3, synthetic Fe2O3/MgAl2O4 and iron ore) in reduction process using methane as fuel. They found that iron-based mixed oxygen carrier particles were potential to be used in methane chemical-looping process, but the reactivity of the iron ore needs to be increased. Hua et al. [19] found Fe2O3/Al2O3 showed better reactivity and higher activation energy than pure Fe2O3 by comparing the reduction mechanism and kinetics of pure Fe2O3 and Fe2O3/Al2O3. It is clear that the reduction kinetics and mechanism of pure Fe2O3 are fundamental and essential to understand the reduction behavior of various iron-based oxygen carriers.

Although the reduction of iron-based oxygen carrier by CO and H2–CO mixtures has been extensively studied [19–21], the study on reduction kinetics of iron-based oxygen carrier by H2 at different concentrations is relatively limited. Lin et al. [22] studied the two-stage reduction of iron oxide by hydrogen and proposed a unimolecular model for Fe2O3 → Fe3O4 and a 2D nucleation model for Fe3O4 → Fe. Sastri et al. [23] proposed the reduction of Fe2O3 by hydrogen proceeded by a consecutive two-step mechanism via Fe3O4. Moon et al. [24] investigated the reduction behavior of hematite by H2 and H2–CO mixtures. The reduction is controlled by the chemical reaction at oxide/metal interface initially, mixed controlled in the transition phase and followed by the diffusion control toward the end of the reduction. Zhou et al. [25] used the Johnson–Mehl–Avrami kinetic model to study the reduction of hematite to Fe by pure hydrogen at 873–1073 K. Bonalde et al. [26] studied the reduction kinetics of hematite pellets by H2–CO mixture. They proposed that the chemical reaction and internal gas diffusion are competing processes during the first stage of the reduction and that internal gas diffusion is the controlling step at the last stage of the process. Pineau et al. [27] proposed that the reduction of Fe2O3 → Fe3O4 by H2 is characterized by an apparent activation energy of 76 kJ mol−1. The apparent activation energy of Fe3O4 → Fe is 88 and 39 kJ mol−1 for temperatures lower and higher than 693 K, respectively. In summary, in a reaction with CO and H2, the reduction of Fe2O3 is usually described as a two-step mechanism, i.e., Fe2O3 → Fe3O4 → Fe or Fe2O3 → FeO → Fe [28].

The reduction behavior and mechanism of iron-based oxygen carriers are still not well understood, and there has been considerable disagreement in kinetic data mentioned above. This study aims to explore the mechanism reactions between pure Fe2O3 and H2 with the assistance of X-ray diffraction analysis. Moreover, most works before were only successful in obtaining independent equations for specific reducing condition. This study aims to develop a theoretical rate equation for specific concentration gradient of H2.

Experimental

Preparation of iron-based oxygen carrier

Pure Fe2O3 powder (analytical reagent, Sinopharm Chemical Reagent Co., Ltd., China) was calcined at 1473 K for 24 h and was sieved to a uniform size of 100–200 μm.

Experiment procedure

Kinetic data were obtained in a thermogravimetric analyzer (TA-STD 600, TA Instruments Inc., USA) under isothermal conditions. The gas flow of reducing gases was controlled by an external mass flow controller and was diluted by N2 before being introduced into the TG. Iron-based oxygen carrier particles (40 mg) were placed in an aluminum oxide crucible and then heated from ambient temperature to designed temperatures (973–1173 K) under N2 atmosphere. 10–40% H2 balanced by N2 was introduced to TG. The volume flow of the H2/N2 mixtures was 100 mL min−1. The reaction finished when mass losing rate dropped to nearly 0.01 mg s−1.

The iron-based oxygen carriers with mass ratios of 0.97, 0.90 and 0.89 described in Fig. 1 are reduction products of initial Fe2O3. To understand the transformation of iron oxides in the reduction process, the mass of sample was shown on the TG in real time, and the reactant gases were converted from reducing gases to inert gas when the mass ratios reached the objective ones of 0.97, 0.90 and 0.89, respectively.

Fig. 1
figure 1

XRD patterns of iron-based oxygen carrier with specific at 1173 K: (a) initial iron-based oxygen carrier; (b–d) iron-based oxygen carriers with mass ratios of 0.97, 0.90 and 0.89

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The phase structure of the iron oxides was identified with X-ray diffraction (XRD, D8 Advance, Bruker Inc., Germany) with the use of Cu Kα1 (40 kV, 40 mA, λ = 0.15406 nm). The samples were scanned at a rate of 6° min−1 from 2θ = 20°–90°. The qualitative phase analysis was solved by the XRD analysis software Jade (v9.3, Materials Data, Inc., USA).

Kinetic model

In general, the kinetic model of a gas–solid reaction can be expressed as follows:

$$\frac{{{\text{d}}X}}{{{\text{d}}t}} = kf(X)$$
(1)

The integral of Eq. (1) was obtained as follows:

$$g(X) = \int_{0}^{X} {\frac{{{\text{d}}X}}{f(X)} = kt}$$
(2)

where dX/dt is the solid conversion rate; X is the solid conversion; t is the reaction time, s; and k is the reaction rate constant which satisfies the Arrhenius law:

$$k = k_{0} {\text{e}}^{{ - \frac{{{\text{E}}_{\text{a}} }}{{\text{RT}}}}}$$
(3)

which can also be written as:

$$\ln k = \ln k_{0} + \left( { - \frac{{E_{\text{a}} }}{R}} \right)\frac{1}{T}$$
(4)

where k 0 is the pre-exponential factor; E a is the activation energy, kJ mol−1; R is the ideal gas constant, 8.314 J mol−1 K−1; T is the absolute temperature, K. The activation energy and pre-exponential factor can be calculated by plotting ln k − 1/T.

The models, which typically interpret the reaction mechanism for the solid–gas reaction of iron oxides, are commonly categorized as reaction order (F), geometrical contraction (R), diffusion (D), and nucleation (Avrami–Erofe’ev, AE). The expressions of f(X) and g(X) of the kinetic models are listed in Table 1.

Table 1 Rate and integral expressions for common gas–solid reactions [29, 30]
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Hancock and Sharp developed a simplified solution to improve the efficiency of the screening reaction model. The expression is as follows:

$$X(t) = 1 - {\text{e}}^{{ - {\text{at}}^{{\text{n}}}}}$$
(5)

which can be written as:

$$\ln ( - \ln (1 - X(t))) = \ln a + n\ln t$$
(6)

where a is a constant that partially depends on the nucleation frequency of nuclei formation and the rate of crystalline growth; n is a constant associated with the geometric shape of particles. Slope n can be used as a diagnostic tool by plotting ln(ln(1 − X)) − ln t to preliminarily screen all types of kinetic mechanisms in Table 1. Those kinetic mechanisms whose n are approximate to the slope n are regarded as the candidate mechanisms.

The Hancock–Sharp method, which is based on the nucleation and nuclei growth model, is commonly used at the solid conversion ranging from 0.15 to 0.5. Selecting the best fit model by plotting X − t over a full-scale range is preferable. That is, the kinetic expressions of the candidate models are utilized to match the experimental data in the form of X − t profiles, and models with the smallest residual sum of squares (RSS) and Akaike information criterion with correction (AICC) are selected among the candidate mechanisms mentioned above [31]. The parameter estimation program was solved using multivariable least-squares regression in MATLAB (R2015b, Mathworks Inc., USA).

Results and discussion

Characteristics of iron-based oxygen carriers

The initial iron-based oxygen carrier was pure Fe2O3, and the X-ray diffraction pattern of this oxygen carrier is shown in Fig. 1a. In theory, the Fe2O3 → Fe3O4 will loss 3.34% mass of pure Fe2O3; the Fe2O3 → FeO will loss 10% mass of pure Fe2O3. The mass ratios 0.966 and 0.90 are associated with mass loss of producing Fe3O4 and FeO, respectively. The iron-based oxygen carrier with a mass ratios of 0.97 consists of Fe3O4, FeO and Fe2O3 and devoid of Fe as in Fig. 1b. The existence of FeO indicated that the Fe2O3 → Fe3O4 and Fe3O4 → FeO both conducted in the mass loss stage from 1 to 0.97. The iron-based oxygen carrier with a mass ratios of 0.90 consists of mainly FeO and slightly Fe3O4 and devoid of Fe2O3 and Fe as in Fig. 1c. This indicated that FeO → Fe did not conduct in the mass loss stage from 1 to 0.90. The iron-based oxygen carrier with a mass ratios of 0.89 consists of FeO and Fe and devoid of Fe2O3 and Fe3O4 as in Fig. 1d. This indicated that Fe2O3 → Fe3O4 and Fe3O4 → FeO did not conduct in the mass loss stage from 0.90 to 0.70. The results illustrated that Fe2O3 → Fe3O4 and Fe3O4 → FeO proceeded simultaneously. But Fe2O3 → FeO and FeO → Fe proceeded independently because there is no Fe coexisted with Fe2O3 or Fe3O4.

Reduction performance and reduction kinetics of iron oxides

The reduction performance of Fe2O3 reduced by 40% H2 at different temperatures is shown in Fig. 2. Figure 2 shows that the reaction rates of mass loss increase significantly with temperature in each step. It is also seen that the mass loss at the first stage of the reduction (m(t)/m 0 = 1–0.9) was fast, and then, the reduction slowed in the middle of the reduction (m(t)/m 0 = 0.9–0.8). At the last stage of the reduction (m(t)/m 0 = 0.8–0.7), the mass loss became slower than other before. On the basis of the phase analysis with different mass ratios, two intermediate reactions (Fe2O3 → FeO and FeO → Fe) were relatively independent at 973–1173 K; thus, the mass loss may proceed according to the following reactions:

$${\text{Fe}}_{2} {\text{O}}_{3} + {\text{H}}_{2} = 2{\text{FeO}} + {\text{H}}_{2} {\text{O}}$$
(7)
$${\text{FeO}} + {\text{H}}_{2} = {\text{Fe}} + {\text{H}}_{2} {\text{O}}.$$
(8)
Fig. 2
figure 2

Mass changing curve of reduction with 40% H2

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On the basis of the stoichiometry of the reduction of Fe2O3, the mass changes of Eqs. 7 and 8 correspond to 10 and 20% of the initial sample. Thus, the solid conversion for each step can be defined as follows:

$$X_{\text{i}} (t) = \frac{{(m_{{{\text{i}},0}} - m(t))}}{{m_{0} \times X_{\text{i}}^{*} }}\quad (i = 1,2),$$
(9)

where m i,o is the initial mass of iron-based oxygen carriers in the step i, mg; m(t) is the mass of iron-based oxygen carriers at time t, mg; m 0 is the initial mass of iron-based oxygen carriers, mg; and X i * is the solid conversion of step i in theory, with X 1 * = 0.1, X 2 * = 0.2.

Figure 3 indicates the X − t of the two steps is calculated by Eq. (9). The reaction rate of Fe2O3 → FeO grew at the beginning and declined at the end. The process of FeO → Fe can be divided into two stages. The reaction rate FeO → Fe was relatively fast at the first stage (X 2 = 0–0.4) and become slow at the last stage (X 2 = 0.4–1).

Fig. 3
figure 3

X − t plots of two steps at different temperatures with 40% H2: a Fe2O3 → FeO, b FeO → Fe

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To determine the reaction mechanism of each step, the Hancock and Sharp method was applied. The ln(ln(1 − X)) − ln t plots and corresponding n values are illustrated in Fig. 4. The slopes for Fe2O3 → FeO are in the range of 2 ± 0.1. These results indicate that this step is isokinetic within the temperature range 973–1173 K; that is, the mechanism is the same for various H2 concentrations and different temperatures. As for FeO → Fe, the plots of ln(ln(1 − X)) − ln t consisted of two stages. The slopes of first section are in the range of 1.10 ± 0.1, whereas those of the second section increase with temperature. The reaction mechanism of Fe2O3 → FeO can be described by the nucleation and growth model AE2 (i.e., Avrami–Erofe’ev equation). The n values of the first section of FeO → Fe are in the range of 1.0–1.2, which identify F0 (n = 1.24), F1 (n = 1), R2 (n = 1.11) and R3 (n = 1.07) as the substantive kinetic models. Figure 5 shows the comparison between the experimental data and the model predictions of the four substantive models, with 40% H2 at 1173 K. The regression statistics of the four models are listed in Table 2.

Fig. 4
figure 4

Plots of the Hancock and Sharp method for two steps with 40% H2: a Fe2O3 → FeO, b FeO → Fe

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Fig. 5
figure 5

Comparison between the experimental data of the X − t and model predictions with 40% H2 at 1173 K for FeO → Fe

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Table 2 Statistical analyses of the candidate models for the X − t
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The results of the X − t fitting show that R2 exhibits the smallest RSS and AICC than other models. The fitting results indicate that R2 is the most suitable mechanism for the first section of FeO → Fe.

The comparisons of the experimental data with the calculation results from AE2 and R2 are shown in Fig. 6. For Fe2O3 → FeO, the AE2 model predicts the experimental data very well. As for FeO → Fe, the first section is controlled by a phase-boundary reaction. Then, the chemical reaction and oxygen diffusion are competing processes during the transition stage, and oxygen diffusion is the controlling step at the last stage.

Fig. 6
figure 6

Comparison of experimental data with calculation results with 40% H2: a Fe2O3 → FeO, b first section of FeO → Fe

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Figure 7 presents the schematic description of two steps. The crystalline grains of Fe3O4 proceed with nucleation and growth on the surface of Fe2O3 particle. Before all Fe2O3 transforms into Fe3O4, the crystalline grains of FeO appear on the surface of iron-based oxygen carrier particle. Then, crystalline grains of FeO grow and the particle becomes pure FeO. The first section of FeO → Fe is controlled by geometrical contraction models. The geometrical contraction models in Table 1 are form of the classic shrinking core model with the phase-boundary reaction control of different geometries. The R2 model represents 2D growth/shrinkage. At the last stage of FeO → Fe, the rate is controlled by oxygen diffusion, that is, the transport of oxygen to the active interface [32].

Fig. 7
figure 7

Scheme of nuclei growth model and geometrical contracting model and nucleation applicable to iron oxides crystallite

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The rate equation for Fe2O3 → FeO is given as:

$$( - \ln (1 - X))^{1/2} = kt$$
(10)

The reaction rate k at different temperatures and CO concentrations can be obtained by Eq. (10). The activation energy together with the pre-exponential factor is obtained from the Arrhenius equation. The resulting activation energy was determined from the slope of the lines in Fig. 8, whereas the values of the intercept are the pre-exponential factor. The activation energy of Fe2O3 → FeO was estimated to be 36.74 ± 1.09 kJ mol−1. The value of k 0 increased with increasing H2 concentration in the same step. As shown in Fig. 9, a significant linear correlation can be observed between the pre-exponential factors and the H2 concentrations. Combining the equations in Fig. 9, the reaction rates constant derived from the Arrhenius equation for Fe2O3 → FeO can be estimated as follows:

$$k_{1} \left( {{\text{s}}^{ - 1} } \right) = 0.0172y_{{{\text{H}}_{2} }} {\text{e}}^{{ - \frac{4418.95}{{\text{T}}}}}$$
(11)

where k 1 is the chemical reaction rate for Fe2O3 → FeO; yH2 is the H2 concentration.

Fig. 8
figure 8

Arrhenius plots of Fe2O3 → FeO

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Fig. 9
figure 9

Effect of H2 concentration on the reaction rate constant for Fe2O3 → FeO

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The reaction rate equation for Fe2O3 → FeO is as follows:

$$\frac{{{\text{d}}X_{1} }}{{{\text{d}}t}} = k_{1} f\left( X \right) = 0.0172y_{{{\text{H}}_{2} }} {\text{e}}^{{ - \frac{4418.95}{{\text{T}}}}} \times 2 \times \left( {1 - X_{1} } \right) \times [ - \ln \left( {1 - X} \right)]^{1/2}$$
(12)

where dX 1/dt is the chemical reaction rate for Fe2O3 → FeO; X 1 is the solid conversion for Fe2O3 → FeO.

Conclusions

XRD patterns illustrate that Fe2O3 → Fe3O4 and Fe3O4 → FeO proceed simultaneously. The reduction of Fe2O3 by H2 is a two-step process, i.e., Fe2O3 → FeO and FeO → Fe. The Fe2O3 → FeO is controlled by 2D nucleation and growth model, and its activation energy is estimated to be 36.74 ± 1.09 kJ mol−1. A theoretical rate equation is developed to predict the reaction rate in the process of Fe2O3 → FeO with 10–40% H2. As for FeO → Fe, the kinetic mechanisms varied between three reaction stages: the first stage is controlled by 2D phase-boundary model; chemical reaction and oxygen diffusion are competing processes during the transition stage; then, oxygen diffusion is the controlling step at the last stage of the process. The study on reduction mechanism and kinetics of pure Fe2O3 by hydrogen is essential for the exploration on deep reduction for CLHG and provides fundamental data for the evaluation and selection of iron-based oxygen carriers.