Kinetic Mechanism Development for the Direct Reduction of Single Hematite Pellets in H2/CO Atmospheres

Increasing interest in the direct reduction process of iron ore has revived investigations on gaseous and heterogeneous iron oxides’ kinetics. Despite extensive studies on the reduction of iron oxides with pure hydrogen or syngas, the development of a generic reduction mechanism for iron oxides is still lacking. The conventional shrinking core model hardly distinguishes between transport and reaction processes, leading to biases or even errors in the kinetic models. In the present study, a porous solid model, which solves mass balances of the individual gas‐phase species and solid ones assuming spherical symmetry, is used for developing a heterogeneous kinetic mechanism accounting for different iron oxidation stages (Fe2O3, Fe3O4, FeO). It also accounts for carbon accumulation and cementite formation to model the carburization phenomena when using carbon‐containing reducing agents like syngas. The proposed generic mechanism successfully reproduces 49 experimental data sets from the literature for single iron oxide pellets’ isothermal reduction with syngas of varying hydrogen content up to pure hydrogen without any adjustment of its parameters. The model predictions are in excellent agreement with the experimental data. Finally, the carburization kinetics are explained, and the factors (e.g., temperature, hydrogen content) affecting the carbon deposition are analyzed.

DOI: 10.1002/srin.202200043 Increasing interest in the direct reduction process of iron ore has revived investigations on gaseous and heterogeneous iron oxides' kinetics. Despite extensive studies on the reduction of iron oxides with pure hydrogen or syngas, the development of a generic reduction mechanism for iron oxides is still lacking. The conventional shrinking core model hardly distinguishes between transport and reaction processes, leading to biases or even errors in the kinetic models. In the present study, a porous solid model, which solves mass balances of the individual gas-phase species and solid ones assuming spherical symmetry, is used for developing a heterogeneous kinetic mechanism accounting for different iron oxidation stages (Fe 2 O 3 , Fe 3 O 4 , FeO). It also accounts for carbon accumulation and cementite formation to model the carburization phenomena when using carbon-containing reducing agents like syngas. The proposed generic mechanism successfully reproduces 49 experimental data sets from the literature for single iron oxide pellets' isothermal reduction with syngas of varying hydrogen content up to pure hydrogen without any adjustment of its parameters. The model predictions are in excellent agreement with the experimental data. Finally, the carburization kinetics are explained, and the factors (e.g., temperature, hydrogen content) affecting the carbon deposition are analyzed.
Hai-bin et al. [9] investigated the controlling steps of the iron oxide reduction kinetics with H 2 /CO-mixtures and concluded that the process is initially interfacial chemical reaction controlled and later shifts to a diffusion-controlled or mixed regime. Mousa et al. [10] studied the isothermal reduction of iron oxide with simulated original and reformed coke oven gas in the temperature range from 973 to 1253 K. They mentioned the cracking of CH 4 into carbon and H 2 at temperature above 973 K. Furthermore, carbon deposition was observed at the later reduction stage with an increase in CH 4 content. Towhidi and Szekely [11] researched the effect of carbon deposition on the reduction kinetics of commercial-grade hematite pellets with CO, H 2 , and N 2 . Their results show that, below 1173 K and with H 2 /CO-mixtures, the reduction process is accompanied by the carbon deposition process, and this carbon deposition is proportional to the CO content in the reducing gas. Xu et al. [12] showed that active Fe is a catalyst for carbon deposition reactions while diffusion is not a rate-controlling factor for CO decomposition.
Considering the previous works, the absence of a generic mathematical model which can reproduce the iron ore pellet reduction process for a wide range of experimental operating conditions becomes apparent. Most of the models perform satisfactorily in a narrow window of experimental conditions. To the best of the authors' knowledge, the number of available mathematical models gets even lower when it comes to predicting the reduction process with complex carbon deposition.
In this work, we propose a generic kinetic mechanism for the direct reduction process of a single hematite (Fe 2 O 3 ) spherical pellet in a shaft reactor using H 2 /CO as reducing gases. The concept of a porous solid pellet model has been considered, which defines mass fluxes of the reactant gases and pellet properties along the reduction process. The variation of the pellet porosity with time and the film resistance has been considered to make the model more robust. With the usual three-step heterogeneous iron oxide reduction reactions (Fe 2 O 3 !Fe 3 O 4 !FeO!Fe), chemical kinetics of carburization is also considered. The scheme has been designed for atmospheric pressure operation and at a temperature range from 873 to 1507 K. This kinetic mechanism has been validated against comprehensive sets of available literature data. So the main goals of the present work can be summarized as 1) reproducing comprehensive sets of available experimental data from the literature to prove the robustness of the present model, 2) investigating the difference of using H 2 , CO, and H 2 /CO mixtures for the reduction process concerning the reduction kinetics and the associated chemical reactions, and 3) explaining the carburization kinetics and analyzing the probable factors (e.g., temperature, hydrogen content in the mixture) affecting the carbon deposition.

Modeling Framework
The porous solid pellet model is adopted in this work as the basis for predicting the kinetic mechanism of the heterogeneous gaseous iron oxide reduction process. As in the reduction process, the chemical reactions and the gaseous diffusion occur simultaneously inside the pellet, the conventional shrinking core model is not an appropriate choice to investigate the chemical kinetics.
The porous solid pellet model discretizes and solves gaseous and solid species variables along the radius of a spherical geometry. The model determines the evolution of the gas and solid species and can handle multiphase chemistry. The chemical source term and species transport through diffusion evolve with time. The basic equations are as follows In the following, the index i will be used for gaseous species and j for any solid species. The variables ε, C, D eff , ρ, X, M, and s ⋅ are respec-  (1) and (2), the properties P j X j ¼ 1 and the density ρ j , of the pure substance, is considered constant. After transformations, we obtain a set of equations comprising the temporal derivatives of each gas species, of each solid species, and of the pellet porosity.
These equations are discretized along the pellet radius for a certain number of spatial points. A system of ordinary differential equations (ODEs) will be generated by this process. The detailed mathematical expressions and derivations of our model are discussed in another article. [13] This article gives further insights into the solution of the gas species concentrations and solid mole fractions along the pellet radius, assuming spherical symmetry.

Reaction Schemes
The gaseous reduction of hematite (Fe 2 O 3 ) is a complex temperature-dependent process. Iron ore reduction undergoes the following sequence.
Depending on the reducing gas concentration, temperature, and extent of reaction, the solid can be found in any of those states mentioned earlier. The chemical formula FeO is a simplified representation of wüstite. Reduction carried out at a temperature lower than 843 K will bypass the FeO (wüstite) from the sequence, as wüstite is unstable at this zone. [14] However, DR of iron ore pellets is usually performed at a higher temperature, involving wüstite. The time of completion of the last reduction states (FeO!Fe) is the slowest of all. [15] The proposed kinetic scheme consists of 14 reactions, all of which are first-order reaction. Among them, 13 are heterogeneous and one is a homogeneous reaction (reaction 19). The chemical source term (s ⋅ ) mentioned in 2.1 considers the solid species mole fractions and the gas species concentrations. The reduction chemistry of iron oxide to iron with pure hydrogen can be described with the following steps.
Equation (7) is exothermic in nature, whereas Equation (8) and (9) are endothermic. This could indicate why the reduction of iron ore consisting of Fe 2 O 3 is usually faster than the one with only Fe 3 O 4 . [14] Reduction with CO and C follows similar three-step reactions as the reduction with hydrogen.
FeO ðsÞ þ C ðsÞ ! Fe ðsÞ þ CO ðgÞ (15) Now, considering the stoichiometry associated with these reactions, the theoretical weight loss in each of the states is shown in Table 1. This clearly shows that the maximum weight loss or removal of oxygen happens at the last stage.
The reduction in the presence of carbon monoxide is relatively complex as it is accompanied by the carbon deposition and the formation of intermediate carbides.
It should be noted that Equation (7)-(15) results in a weight loss for the sample while Equation (16) and (17) cause a net weight gain. Equation (16) is known as the Boudouard reaction [16] and plays a crucial role in iron oxide reduction. Carbon monoxide tends to decompose into carbon dioxide at a certain low temperature and deposit carbon. Equation (16) and (17) are responsible for carbon deposition when H 2 /CO mixtures are used as reducing gases. Which reactions among these two will dominate in the carbon deposition process depends on the H 2 concentration. [17] A detailed discussion will follow in the last part of this article. But from a naked eye perspective, it is understandable that adding H 2 will push the equilibrium of reaction 17 toward the right. This will produce more deposited carbon. However, it is not wise to come to a decision barely from the chemical reactions, as other factors like temperature play a huge role. The carbon produced at low temperatures has a twofold effect: 1) reducing the iron oxide as an indirect reduction process as given by Equation (13)- (15), where carbon reduces the iron oxides to iron. However, this reduction with carbon is relatively slow [18] and 2) depositing as soot might have negative aftereffects, as will be seen later.
A lot of experimental studies in the literature [10][11][12]19] mentioned the presence of cementite through carburization. Therefore, Equation (18) The iron oxide reduction process and the carbide formation take place simultaneously, as the cementite is present in partially reduced samples. [19] Investigating the solid species evolution with time in our model also shows similar insights.
A detailed reduction mechanism including methane submechanism will be published in due course. Under practical conditions, the water-gas shift reaction (CO (g) þ H 2 O (g) ↔ H 2(g) þ CO 2(g) ) could be an interesting possibility while using H 2 /CO mixtures. In an actual shaft reactor, as the pellets will be in an atmosphere containing these product gases (H 2 O, CO 2 ), this has important consequences on the required reduction time. However, for lab-scale experiments where insignificant amounts of product gases are available, this reaction has almost no effects. Hence, it is not included in our current reaction scheme.

Thermodynamics of Carbon Deposition and Cementite Formation
The range of gas compositions and temperatures over which carbon deposition is expected depends on the thermodynamic of that system. Therefore, a thermodynamic analysis of carbon deposition and cementite formation serves as an initial screening for a proposed kinetics reaction scheme. From thermodynamic considerations, the reduction with hydrogen should always be done at the highest possible operating temperature due to the expansion of the stable iron regime. However, the scenario with CO reduction is different; as the temperature decreases, iron's stability regime increases and the reducing gas utilization decreases. However, due to economic and kinetic limitations, an optimal operating temperature needs to be maintained for a better reduction degree. A Baur-Glässner diagram for the Fe-O-C-H system has been illustrated in Figure 1. It shows the Table 1. Iron ore reduction states and associated theoretical weight loss.

Reaction states
Weight loss Equation no.
FeO!Fe 22.28% (9), (12), (15)  thermodynamically most stable iron phases under variation of CO or H 2 content in CO/CO 2 or in H 2 /H 2 O atmospheres and the temperature. Carbon deposition mainly takes place at the surface of the pellet and under certain conditions (reducing gas concentrations, the total pressure in the reactor, residence time, and temperatures). However initially, carbon could also deposit inside the pellet, and as time progresses, a dense layer of soot will prevent further deposition inside. Eventually, the deposition rate is high enough to influence the overall conversion degree. This carbon layer hinders the availability of the reducing gas inside the pellet resulting in an incomplete reduction and a weight gain of the sample. [11] It can be seen in Figure 1 that the Boudouard reaction line crosses the wüstite reduction reaction line at 971 K. So on the left side area of this line, CO will be converted to CO 2 , and carbon will start to deposit. It was also reported in DR experiments [19] that carbon deposition started significantly at 973 K and below. As the reduction progresses, the carbon deposition continues to form on the surface, creating a layer, which eventually hinders the diffusion of reductant inside the pellet. This deposition process will go on until 1273 K; afterward, regardless of the gas composition, there could be practically no further carbon deposition found on the pellet surface. [11] Cementite is relatively stable in a temperature range of 973 and 1123 K. [12,19] After 1223 K the cementite fraction in the sample will start to decompose. [19]

Parameters Estimation
The model employs a certain number of parameters that are detailed in the following subsections. Among these parameters, some are unknown and need to be estimated. To this end, the least square method has been employed. Starting from an initial set of parameters, the system of ODEs is solved and the global conversion degrees obtained from the model are compared to the experimental data. The parameters are then fit to minimize the sum of the squares of the deviations. To avoid overfitting issues, the number of parameters to fit is kept as low as possible. A unique set of chemical parameters is used for all experiments. An additional unknown parameter, the tortuosity, is related to the intrinsic properties of the pellets and was also kept constant when several experiments utilize the same pellet. More details are given in the following.

Activation Energies and Rate Constants
Despite having numerous studies on the kinetic parameters and their use in scaling up reactors, reliable kinetic parameters are not yet available. Gas-solid reaction kinetics is inherently complex compared with homogeneous reaction kinetics as they can rarely be explained by a single n th order algebraic equation over the entire reaction range. The geometrical considerations are one of the most critical experimental factors that introduce considerable deviations [20] in the measured frequency factor (A) and activation energy (E a ) for a particular reaction. Therefore, considering the usual energy barrier model of homogeneous chemical reactions is not suitable. Instead the apparent activation energy is used. The Arrhenius relation is used to calculate the rate constants (k) of the reduction reactions.
From the literature, it can be seen that the variation in E a is wide. Spreitzer et al. [21] summarized the apparent activation energy proposed by different research groups. They showed that the range of apparent energy varies from 30 to 246 kJ mol À1 for Fe 2 O 3 ! Fe 3 O 4 . For the reaction states of Fe 3 O 4 ! FeO, the values are in the range between 33 and 47 kJ mol À1 . Moreover, for the most important states of the reduction process, FeO ! Fe, it varies from 11 to 85 kJ mol À1 . This value depends on material characteristics, gas compositions, operating temperature, grain size, material impurities, and the types of the experiments.
The determination of the kinetic parameters of the mechanism presented in Section 2.2 has been achieved sequentially. For example, experiments utilizing pure hydrogen involve only the three reduction reactions (Equation (7)-(9)). The kinetic parameters of these three reactions were determined on this reduced set of experiments. Similarly, experiments utilizing only carbon monoxide have supported the optimization of the chemical parameters of the reactions that do not involve hydrogen. Finally, the remaining reactions (Equation (17) and (20)) were fit based on syngas cases. One simplification has been made; though the reduction from magnetite to wüstite and from wüstite to iron is by nature reversible, it is not possible from the current available experimental setups to calculate separately the reverse reaction rates from the forward rates. The reverse reactions simply slow down the forward ones, so that both forward and backwards rates are lumped in apparent forward rates. A similar issue arises while trying to fit the individual step of the reduction as every step takes place simultaneously and this is coupled with transport effects. For these reasons, the choice was made to only fit forward rates for the reduction and to employ a common activation energy for a same reducing agent. After optimization, the activation energies found for the reduction with H 2 and CO for all the three reduction steps in this work are 75 and 65 kJ mol À1 , respectively.

Porosity
The porosity affects the reduction process considerably. Most of the previous works either considered it as constant or modeled it using linear correlations with too many empirical coefficients. However, considering empirical coefficients for each solid oxides, which also change for different pellet types (fired pellet, nonfired pellet, sintered) makes the model overfitted. In this work, the initial porosity is taken from the corresponding author and later discretized and solved along the radius of the pellet.
In this way, our model considers the porosity variation with the time and along the radius without prior assumptions.

Effective Diffusivity
The bulk diffusivity of each gaseous species is calculated using Cantera [22] to obtain the mixture-averaged diffusion coefficients (D coeff ) [m 2 s À1 ] relating the molar diffusive fluxes to gradients in the species mole fractions. As the diffusion of gaseous species through porous solid depends on the porosity, the tortuosity, and the pore size distribution, [23] the effective diffusivity (D eff ) is calculated by the following equation where, ε and τ represent the pellet's porosity and tortuosity, respectively. Some of the researchers also include Knudsen diffusivity to calculate the effective diffusivity. [7] Molecular and Knudsen diffusion usually coexist and it is essential to consider both effects, when the pores in the porous materials are in the nanometer range. However, as the pores in the industrial pellets are not very fine and reduction operations are carried out at atmospheric pressure, the Knudsen diffusion term is not considered here. [24] As the morphology of pellet sample varies from one research group to another, the tortuosity values of the pellets for different research groups are not comparable. For a pellet sample of similar initial porosity used by a research group, the tortuosity values are the same. (e.g., Bonlade et al. [25] in Table 2 carried out three experiments with a pellet porosity of ε ¼ 22%; as the values of the initial porosity used by the group are the same, the tortuosity factor values are kept identical; here, τ % 6.3). There are certain analytical expressions (e.g., Bruggeman correlation) relating the porosity to the tortuosity factor to describe transport in porous media. This type of correlation often includes arbitrary indices that need to be fitted. So, to avoid such unwanted complexity, the tortuosity factor is directly optimized to fit the experimental data.

Mass Transfer Coefficient
Many mathematical models made a simplified assumption of neglecting external mass transfer. The general claim is that when the gas flow rate is greater than 1 Nl/min, external mass transfer is not a rate-limiting factor anymore. However, Kazemi et al. [26] show that the gas flow rate has specific effects on the overall conversion degree. In this work, the mass transfer coefficient (k coeff ) is also considered for the gas film resistance and optimized for each experimental case.

Literature Experimental Data Sets
Several experimental data from different research groups have been considered to validate the proposed generic mechanism. The literature data considered here focus on the reduction of spherical hematite pellets, and the reducing gases are H 2 and CO at atmospheric pressure, eventually in the presence of other gas species (He, CO 2 , CH 4 ). A summary of the isothermal experimental data sets is listed in Table 2. The traditional experimental setup for studying the kinetics of gaseous reduction of iron ore is the thermogravimetric analyzer (TGA). Though the similar term "TGA" has been used when referring to the experimental process by almost all the research groups, the techniques of starting the reduction process are quite different. In a usual TGA setup, the sample is heated in inert atmosphere to the desired reduction temperature. Then the inert gas is switched to the reducing gas to start the reduction process. This process involves a comparatively longer time to reach the desired reduction temperature, and the uncertainty of initial gas composition can affect the overall reduction process. The group of Kazemi et al. [26] introduced a new type of TGA setup with a cooling chamber on top of the reaction tube. The sample can be moved up and down to introduce it into the reaction chamber to start the reduction process or to retract it to the cooling chamber to stop it immediately. The TGA setup can also differ in terms of reducing gas introduction. For example, the group Beheshti et al. [27] used a concentric walled crucible where the reducing gases are heated through their way to the down while passing in between the walls. In this technique, the opening of the inlet port at the bottom of the concentric crucible is large enough not to build up any pressure. While passing through the concentric wall these gases will also be heated uniformly. Other research groups like Mousa et al. [10] used a system consisting of a vertical Tammann furnace with a layer of alumina ball at the bottom to get a uniform flow of reducing gas. All the research groups considered here generally used industrial pellets for the experiments. There are some uncertainties in the data listed here, for example, data from Beheshti et al. [27] show quite a bit of irregularity in the trend. Some data from Towhidi et al. [11] demand further discussions.

Results and Discussions
In order to better understand the chemical and the transport processes of a hematite pellet reduced in a gaseous environment, the present model has been validated against the literature data listed in Table 2. The global conversion degree (F) is the main validation criterion for the model and is defined as where mðtÞ is the instantaneous weight of the solid during the reduction process. The parameters m 0 and m f represent the initial weight of the pellet and the theoretical weight after complete reduction.

Reduction Behavior of Hematite with Pure H 2 or Pure CO
The reduction behaviors of hematite in pure H 2 , diluted H 2 , or pure CO atmospheres are shown in Figure 2.
Except at 878 K, where experimental data at a later stage are missing, all cases with pure H 2 (Figure 2a,b) show a conversion degree (F) of hematite higher than 98% at the end. From Figure 2a, it is visible that, with increasing temperatures, the rate of conversion degree dF dt À Á also increases. Another observation is that a higher porosity of the sample contributes to a higher conversion degree. Overall, the model is well responsive to the temperature variation or the pellet porosity. The cases involving hydrogen diluted in helium (Figure 2c) are also well rendered by the simulations. The dilution of hydrogen logically slows down the reduction process. For example, the full conversion Kazemi et al. [26] 0 Towhidi et al. [11] Pure is obtained at about 3000 s at 1073 K in the diluted case, while it was 1300 s for a pellet featuring almost similar porosity in the pure hydrogen case. Based on these results, the choice of the transport modeling and of the partial order of 1 with respect to hydrogen seems adapted.
The reduction with pure carbon monoxide in Figure 2d shows different profiles. The hematite sample is clearly visible to be converted to the highest degrees at shorter retention times with pure H 2 . At 1507 K, the experimental results with pure CO show complete conversion while the present model reaches a maximum below the complete conversion. The iron ore reduction modeling at high (above 1300 K) temperature is relatively an uncharted territory. This very high process temperature might involve additional chemical pathways, cracking, or swelling of the sample not considered here. Most importantly, the DR processes are usually carried out approximately at a temperature range of 1073-1373 K. [30] In Figure 2d, two examples illustrate the direct reduction at these intermediate temperatures (1173 and 1266 K). The conversion degree reaches a plateau below 1, whose value depends on the temperature. In these cases, the pellet can be totally converted, but the presence of carbon, mainly in cementite form, accounts for additional weight, not considered in the theoretical weight after the complete reduction that appears in the conversion degree term. Furthermore, at temperatures below 1059 K, the hematite reduction (weight loss) and carbon deposition (weight gain) are competing processes, which explain the shape of the curves and render the problem more complex. Considering this, deviations from the experiments while modeling carbon deposition phenomena are to be expected.

Reduction Behavior of Hematite with Syngas (H 2 /CO)
The reduction with syngas (H 2 þ CO) is not as straightforward as with H 2 , rather associated with other submechanisms (like carbon deposition, Fe 3 C formation, gasification reactions, etc.), which make it difficult to establish a model for a wide range of experimental conditions. Figure 3 shows the conversion degree (F) against the retention time for various gas compositions (r ¼ H 2 :CO molar ratio). From these two graphs, it is evident that with increasing H 2 content, the conversion degree of the sample also increases but does not reach 100% conversion like the reduction with H 2 in Figure 2a,b. This is due to the carburization of reduced iron into cementite (Fe 3 C) in the later stage of reduction. In Figure 3b, the model shows some disagreements with the data because the experimental setup used by the author could not produce consistent data and the uncertainties in those data are quite high. Figure 4 illustrates the sensitivity of the operating temperature on the total conversion degree. With increasing operating temperatures, the rate of conversion dF dt À Á , as well as the final conversion degree also increased.
An interesting trait is that, similar to the reduction with CO, when the reducing temperatures are lower than 1059 K, the Figure 2. Reduction behavior of hematite pellet using pure H 2 or diluted H 2 (40% Helium) or pure CO as reducing gas versus time. Dashed lines and symbols represent the current model simulation and the experimental data from the literature, respectively. Literature data considered are a) Kazemi et al., [28] b,d) Towhidi et al., [11] and c) Patisson et al. [29] ε represents the pellet porosity, and the pellet characteristics are given in Table 2.
www.advancedsciencenews.com l www.steel-research.de steel research int. 2022, 93, 2200043 reduction proceeds to a certain maximum conversion degree and then the conversion curve starts to go down. This negative slope in the conversion degree curve represents a net weight gain of the pellet. This is due to the mass of carbon depositing that overcomes the mass of iron oxide that reduces. Extreme cases of carbon deposition are experienced with r ¼ 0.33. Our model reproduces those traits quite well. Surprisingly, the experimental test case at 973 K in Figure 4c reaches a higher final conversion degree than the case at 1059 K. There might be a bias in these specific experimental data, as it contradicts all other observations. Based on that, the difference at 973 K between the simulated result and experimental data at the end is well justified.

Effects of Varying Reducing Gas Composition
In the steel-making community, a growing interest has been observed in reducing iron ore using pure hydrogen. Several key factors must be investigated while transitioning the Figure 3. Influence of the gas composition on the reduction behavior of hematite pellet using syngas (H 2 /CO) versus time. Dashed lines and symbols represent the current model simulation and the experimental data from the literature, respectively. Literature data considered are a) Kazemi et al. [26] and b) Beheshti et al. [27] . ε and r represent the pellet porosity and H 2 :CO ratio and the pellet characteristics are given in Table 2.  data (a, b, and c) are taken from Towhidi et al. [11] ε and r represent the pellet porosity and H 2 :CO ratio, and the pellet characteristics are given in Table 2.
www.advancedsciencenews.com l www.steel-research.de steel research int. 2022, 93, 2200043 steelmaking process towards hydrogen. Those are chemical kinetics, thermodynamics, or heat transfer effects. Regarding the chemical kinetics on the reduction of iron ore using H 2 , CO, and syngas, at a constant temperature, Figure 5a (here at T ¼ 1173 K) clearly shows that the kinetics of H 2 is the fastest, then followed by syngas, and then CO. To investigate which reactions play a major role, a sensitivity analysis has been done; the analyses were performed at a conversion degree of 55% to serve as an example. The sensitivity coefficient (S n ) for the n th reaction in the reaction scheme is calculated as follows.
Here, F t and F Sens t represent the global conversion degree (F) at a particular time t and the global conversion degree achieved at the same time, when the reaction rate (k n ) of the n th reaction is increased or decreased by a certain amount. In our case, we tested the sensitivity by increasing and decreasing the reaction rates by 10%.
The reduction with pure H 2 involves only three reactions, and as it could be expected, FeO!Fe reaction is the most dominating reaction. The two other reaction rates are not rate limiting in the process and have therefore a limited impact on the conversion degree. For the reduction with CO, as we can see clearly from Figure 5c, no reaction overpasses the others. The sensitivity of the Boudouard reaction (carbon deposition) is of the same magnitude as the reduction step FeO ! Fe with CO, but with the opposite sign. The main reactions that reduce the oxides are challenged parallelly by the carbon deposition, characterized by a final conversion degree much lower than 1. The syngas sensitivity analysis in Figure 5d clearly indicates that the FeO þ H 2 !FeþH 2 O and FeO þ CO!FeþCO 2 reactions are the major reactions. Cementite formation reactions show quite a minor sensitivity, in accordance with the low amount of carbon that the final conversion seems to indicate. This figure also shows that at this temperature and syngas composition rich in hydrogen, the process is mostly dominated by the reduction. Figure 6a tackles the impact of the gas composition and temperature on the conversion rates. The initial conversion rates at a given H 2 /CO ratio divided by the conversion rates with pure CO at a certain temperature T are shown in Figure 6, where each line corresponds to a different temperature of reference.
From the kinetic point of view, the conversion rates using 100% hydrogen is up to 7 times faster than the conversion rates using CO. This is also experimentally reported by several researchers. [23,25] It is well known that hydrogen always acts as a better reducing agent: it is more reactive with the oxides and diffuses faster than CO. [9] However, the present study allows for a quantification of these phenomena. The gas composition has a more limited impact at lower temperatures. As the reduction of iron oxide with H 2 is thermodynamically not favored at lower temperature (□À973 K and ΔÀ1059 K) the values of the rate (H2/CO) :rate COT in Figure 6a do not vary much with the increase in H 2 content in the reducing gas. A key aspect is that the increase is not linear. The increase is limited between the H 2 : CO gas ratio of 25:75 and 75:25 but rises near pure hydrogen conditions (Figure 6a). This rise might be explained by the Figure 5. Sensitivity analysis of chemical reactions in the reduction process with H 2 , CO, and syngas; all at T ¼ 1173 K. a) Comparison of the reduction behavior using pure H 2 , pure CO, and syngas. The experimental data are taken from Bonlade et al. [25] A horizontal dashed-doted line (-.-) at 55% conversion indicates where the sensitivity analysis has been performed. b,c,d) Sensitivity analysis at 55% conversion degree with H 2 , CO, and syngas, respectively. complete absence of carbon deposition in pure hydrogen cases, which would enable the transport of the reducing agent to the oxide sites, in addition to the better diffusivity and reactivity of hydrogen. Another considerable effect of varying gas compositions on the reduction behaviour of iron oxide is the evolution of the pellet porosity across the radius. Figure 6b illustrates the structural changes during the reduction process, more specifically the porosity for various gas compositions at the half time of the reduction process at 973 K. The initial porosity of the pellet for all these three cases is 15.8%. The case with pure hydrogen is easier to apprehend. The process is governed by the step-wise reduction of hematite to iron, and the absolute density of iron is greater than the one of the oxides. As the pellet volume is kept constant and the reduction starts from the surface, the porosity is maximum near the surface and lower toward the core of the pellet. At the end of the complete conversion, the porosity reaches up to 60%. This goes in line with the experimental investigation of Towhidi et al., [11] who concluded that the pellet porosity increases considerably during the reduction process. They measured an initial pellet porosity of 15.8% and a porosity after reduction using H 2 of about 61.0%. The profiles of the syngas and CO cases are different. The porosity increase due to the reduction is counterbalanced by the carbon that deposites, especially on the surface. The two chosen cases illustrate extreme carbon deposition cases. The porosity approaches zero, which stops the diffusion inside the pellet. At this point, the only process going on is carbon depositing on the surface as it does not require internal transport. In real experiments, the layer of carbon is growing with time. Our model only considers constant pellet size, but it was sufficient to reproduce these cases with important carbon deposition.

Carbon Deposition and Cementite Formation
In DR processes, hematite reduction reactions occur simultaneously with the carburization reactions. [11] However, at a certain stage, the rate of carburization reactions (carbon deposition and cementite formation reactions) exceeds the rate of reduction reactions. From that point onward, the pellet gains weight due to cementite formation and the carbon deposition. At which stage and to what extent, the carburization reactions will outplay the reduction reactions depend on several experimental conditions. Before going further with the chemistry of the carburization process, a schematic illustration of the process is presented in Figure 7 to investigate these phenomena.
The process starts with the reduction of the hematite with reducing gas. As the reduced iron appears on the pellet's surface, it starts to react with the available carbon/-CO/-CH 4 to form the cementite (Fe 3 C). This carbon is produced through the Boudouard reaction. As the formation of the cementite grows on the surface, the reduction process slows down. With time, the surface of the pellet will be saturated with cementite. At this stage, the carbon produced by the Boudouard reaction will start to deposit on top of the cementite layer. This dense layer will prevent the reducing gas from diffusing through the pellet and eventually stop the reduction process. From then, the pellet  starts to gain weight due to soot formation. Carbon deposition is mainly controlled by the temperature, pressure, CO concentration, and nature of the solid surface. [11] After reproducing a large number of experimental data, our model gives us enough confidence to use it as a tool to analyze the data regarding carburization. In Figure 8a, the rate of carbon formation along the time for several temperatures using 50:50 H 2 :CO gas composition is calculated. The highest initial carbon formation rate is observed at 878 K, and as the operating temperature increases, this rate decreases. At 1173 K, negligible amounts of carbon form in the system. Another important aspect: the rate of carbon formation increases until a certain time for all the operating temperatures. Then, the carbon formation rate becomes almost steady. This nature of carbon formation can be explained like this.
1) Carbon is formed through the Boudouard reaction and Equation (17). Hence, the lower the operating temperature, the higher the rate of carbon formation. 2) The rate of carbon formation is initially lower because the available carbon in the system will be consumed for a certain time through a) reducing the iron oxide and b) converting the reduced iron to cementite. 3) As the pellet surface is saturated with Fe 3 C, the carbon formation rate becomes steady. From this point, carbon formed in the system will start to deposit on the pellet's surface.
Another observation in Figure 8a is that the time required to stabilize the rate of carbon formation varies for different temperatures. The lower the operating temperature, the longer it will take to reach a steady formation of carbon. This is due to the slower reduction of iron oxide at lower temperatures so that the formation of the cementite and saturation of the surface takes a longer time. An important factor affecting carbon deposition is the concentration of H 2 in the H 2 /CO mixtures. [17] In Figure 8b, the effect of the gas composition on carbon deposition is presented. The rate of carbon deposition in this figure is calculated at around 50 min. It is due to the observation from Figure 8a, where the carbon formation rate stabilizes on an average after 50 min. Hydrogen presence in the reducing gas mixture promotes carbon deposition. However, when the H 2 percentage in the reducing gas mixture is higher than 50%, the carbon deposition reduces drastically. These findings were also experimentally reported by Turkdogan et al. [17] The reason could be that at low H 2 :CO ratios, the carbon deposition is obtained not only from the Boudouard reaction, but also because of Equation (17), CO (g) þ H 2(g) ¼ C (s) þ H 2 O (g) . At higher H 2 content, the contribution of the Boudouard reaction becomes limited, and as H 2 is participating more in the reduction, more H 2 O is produced, which pushes the equilibrium of Equation (17) Figure 8. Simulated model analysis of a) rate of carbon formation along the reduction process for H 2 :CO ¼ 50:50 and b) effects of gas composition and temperature on the rate of carbon deposition in H 2 /CO mixtures at around 50 min. from right to left. The formation of cementite can be directly correlated with the amount of carbon deposition. A qualitative analysis of Fe, FeO, Fe 3 C, and C will shed more light on the discussion. In Figure 9, a comparative quantitative analysis between 973 and 1059 K temperature for different reducing gas mixtures is shown for a 55% reduced sample. If we compare these two figures, we can clearly see that, more reduced iron is available for all the gas mixtures at higher temperature as higher temperature promotes faster reduction reactions. The amount of cementite formed at 1059 K is lower than the temperature of 973 K for all the gas compositions. The deposited carbon at the temperature of 973 K is clearly higher than the temperature of 1059 K. Increasing H 2 content in the reducing gas mixture affects the growth of the cementite and carbon deposition in a positive way up to a certain degree. The highest amount of cementite formation is calculated using H 2 :CO ¼ 25:75 for both temperatures.

Conclusion
A kinetic model has been proposed which is sufficiently generic to successfully predict the direct reduction process of a single hematite spherical pellet for a wide range of conditions like the porosity, the temperature, the pellet size, or the gas compositions with high accuracy. The kinetic mechanism is supported by a reduction model that includes the variation of porosity with time and the consideration of mass transfer limitations in the gas phase. On this basis, the kinetic model also shows maturity in predicting complex carbon deposition phenomena. The differences between the reduction using CO, syngas, and H 2 are discussed in light of thermodynamics and chemical kinetics. At the end, the carburization kinetics is explained schematically. Sensitivity of temperature and gas compositions on carbon deposition and cementite formation are discussed. Our calculated results to explain the carburization process are aligned with the thermodynamic considerations and comforted by similar trends and results reported in the literature. This better understanding will help to support the development of DR processes with flexible reducing agent compositions, up to pure hydrogen.