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. 2021 Apr 22;6(17):11436–11446. doi: 10.1021/acsomega.1c00443

Kinetic Modeling of CO2 and H2O Gasification Reactions for Metallurgical Coke Using a Distributed Activation Energy Model

Yui Numazawa †,*, Yuki Hara †, Yoshiya Matsukawa †, Yohsuke Matsushita †, Hideyuki Aoki †, Takahiro Shishido ‡, Noriyuki Okuyama ‡
PMCID: PMC8153985  PMID: 34056299

Abstract

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A distributed activation energy model (DAEM) was applied to the kinetic analysis of CO2 and H2O gasification reactions for pulverized metallurgical coke. The results of the scanning electron microscopy observations and CO2 gas adsorption suggested that the gasification reaction occurs at the particle surface. Therefore, a grain model was employed as a gasification reaction model. The reaction rates of CO2 and H2O gasification were evaluated based on the DAEM. The activation energy changed as the reaction progressed and hardly depended on the particle size. The activation energies were 200–260 kJ/mol in CO2 gasification and 220–290 kJ/mol in H2O gasification. The frequency factor of H2O gasification was approximately 10 times larger than that of CO2 gasification, regardless of the progress of the reaction. At the same activation energy level, the frequency factor showed a higher value with a decrease in the particle size. This result was consistent with the theory of the grain model and indicated that the gasification reaction of the pulverized coke with a micrometer scale occurs on the surface of the coke particle. Furthermore, the value predicted by the DAEM was in good agreement with the experimental one.

1. Introduction

Metallurgical coke is the reducing agent for iron ore and gets converted to CO or CO2 by various gasification reactions. In addition, it acts as a spacer in a blast furnace, and hence, its strength is important. The iron-making industry emits a large amount of CO2 gas—a major greenhouse gas. Therefore, many countries are trying to supply H2 gas into a blast furnace in an effort to reduce the production of CO and/or CO2 gases. As part of this endeavor, Japan has started a national project “COURSE50 (CO2 Ultimate Reduction System for Cool Earth 50)”. The aim of this is to reduce the CO2 gas emission from a blast furnace by approximately 30% by 2050 using H2 gas converted from coke oven gas (COG). However, H2O gas is generated by the oxidation of H2 gas, and the gas atmosphere in the furnace is different from that of conventional furnaces. Therefore, any change in the gas atmosphere would affect coke gasification.

Coke gasification is the reaction to convert solid fuels into a heat source and a reducing agent such as H2 or CO gases. Hence, the reactivity of coke is a very important property. Although the coke reactivity index (CRI) expresses the apparent reaction rate of a coke lump and is affected by gas diffusion, the CRI has been widely used as a parameter for evaluating gasification reactivity.1−6 Pusz and Buszko focused on the difference between the mean maximum and minimum reflectances, the CRI.4 They showed that the crystallinity greatly affected the reactivity.4 Morga et al. analyzed several cokes produced at 1223 K by Raman spectroscopy and suggested that the CRI of the coke produced under these conditions can be predicted based on the half-width of the G and D2 bands.5,6 These studies also showed that the reactivity of coke gasification and carbon crystallinity are closely related. Also, the crystal structure of carbon changed by gasification and thermal treatment.7−9 Moreover, carbon matrices with various reactivities would exist in coke.

To evaluate the intrinsic reaction rate, thermogravimetric analysis (TGA) is widely used for the kinetic analysis of coal and biomass gasification. Roberts et al. investigated the intrinsic reaction rate of the gasification reaction of coal char by measuring the reaction rate of gasification with various reactant gases.10−13 Specifically, they calculated the reaction rate per unit surface area by measuring the surface area by the Brunauer–Emmett–Teller (BET) method; they also evaluated the effect of ambient pressure on the reaction rate of coal char gasification.10 In addition, they calculated the adsorption rate of CO2 gas from the reaction rate measured by TGA based on the Langmuir–Hinshelwood mechanism and reported that the adsorption rate almost corresponded to that obtained by CO2 gas adsorption based on the BET method at an ambient pressure of <30 atm.11 Following this study, both competition and inhibition between reactant gases were examined based on the Langmuir–Hinshelwood mechanism under a mixed atmosphere of CO2 and H2O.13 These investigations indicated that the data accuracy obtained from TGA is sufficient to discuss on the basis of the reaction mechanism. Thus, to evaluate reactivity of coke gasification accurately, it is necessary to measure the reaction rate under the condition that the effect of gas diffusion was removed and to employ the model that considers spatial distribution of reactivity.

To analyze the reaction rate of coke gasification taking into consideration the spatial distribution of reactivity, the distributed activation energy model (DAEM),14 which is often used for the release of volatile matter from coal,15−17 can be used because the change in carbon crystallinity by gasification and the spatial distribution of reactivity in coke cannot be neglected. The DAEM is a reaction model that expresses the distribution of activation energy when many different reactions, such as pyrolysis and oxidation of heavy oils,18,19 occur simultaneously. For metallurgical coke, although it is considered that CO2 gasification of coke proceeds as a single reaction, coke contains carbon matrices with various states, as mentioned above, and each matrix could have different reactivities. Xu et al. applied the DAEM to only CO2 gasification of metallurgical coke20 and showed that the predicted value of the DAEM almost corresponded to the experimental one. In this previous study, they focused on only CO2 gasification and assumed that the activation energy has a Gaussian distribution. When the DAEM is used, the distribution of activation energy should be fitted in general.21−23 De Caprariis et al. demonstrated that the prediction accuracy of the reaction rate determined with the double Gaussian distribution is greater than that obtained with a single Gaussian distribution.22 In addition, Wang et al. showed that the values calculated from the DAEM with the triple Gaussian distribution were in good agreement with the experimental values.23 These studies show that the prediction accuracy can be improved by increasing the number of Gaussian distributions. However, Miura proposed the method based on the DAEM without a Gaussian distribution, in which the Arrhenius parameters were calculated using the DAEM without assuming any distribution function24 and by utilizing the experimental results obtained under different heating rates; the calculated value corresponded to the experimental one.24,25 Maki et al. investigated the pyrolysis of coals with different properties and discussed the ratio of volatile matter present in the coal samples by applying the method to the experimental result.26 In other studies for the pyrolysis of biomass and low-rank coal, the conversion predicted from the method proposed by Wang et al. was in good agreement with the experimental one.27−29

In this study, we investigated not only CO2 gasification but also H2O gasification using thermogravimetry (TG) for metallurgical cokes pulverized to micrometers in order to remove the effect of pore diffusion. Xu et al. focused on only CO2 gasification and assumed the Gaussian distribution as the distribution of activation energy.20 In contrast, the novelty of this study is to apply the distributed activation energy model (DAEM) to the coke gasification reaction and to determine activation energies and frequency factors of CO2 gasification and H2O gasification of coke by using the method proposed by Miura and Maki,24,25 in which the distribution of activation energy was not assumed as the Gaussian distribution. The reaction model for kinetic analysis was selected based on the results of gas adsorption and scanning electron microscopy (SEM). In addition, the reaction rate measured by TG was analyzed using the method proposed by Miura and Maki24,25 that uses the DAEM. In addition, changes in the activation energy and frequency factor as the reaction progressed were evaluated. The reaction rate was analytically calculated using the obtained Arrhenius parameters, and the validity of the analysis was evaluated by comparing the result obtained with the experimental values.

2. Experimental Section

2.1. Sample Preparation and Analysis of Sample Properties

2.1.1. Preparation of the Sample

Metallurgical coke produced in a coke oven was used as the sample. The properties of the sample—obtained by proximate analysis (JIS M 8812), ultimate analysis (JIS M 8819, JIS M 8813 (O)), and ash composition analysis—are listed in Table 1. The coke sample was pulverized and sieved based on JIS Z 8801. The aperture sizes were set to 32–53 μm (Coke S), 75–100 μm (Coke M), and 125–150 μm (Coke L). To evaluate the accuracy of sieving, the particle size distributions of the samples were measured with a laser diffraction particle size analyzer (Microtrac HRA, NIKKISO). Figure 1 shows the particle size distribution of the samples. The refractive indices of the solvent and the sample were set to 1.33 and 1.51, respectively, which were those of water and glass, respectively. The measurement time and the number of measurements were 30 s and 2, respectively. As shown in Figure 1, all samples showed unimodal particle size distributions, and the volume median diameter followed the order Coke L, Coke M, and Coke S. Hence, the particle size distribution was different for different samples, and the average diameter followed the order Coke L, Coke M, and Coke S.

Table 1. Properties of the Coke Sample.
proximate analysis [wt % d.b.] ash composition [wt %]
volatile matter 0.8 SiO2 6.32
fixed carbon 87.0 Al2O3 3.87
ash 12.2 TiO2 0.18
ultimate analysis   Fe2O3 0.73
C 85.8 CaO 0.29
H <0.01 MgO 0.12
N 1.16 K2O 0.17
S 0.50 SO3 0.10
Oa 0.39    
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a

By difference values that are not measured.

Figure 1.

Figure 1

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Particle size distributions of Coke S, Coke M, and Coke L.

2.1.2. Observation of the Surface of Coke Samples Using SEM

To evaluate the surface structure of coke samples, the sample surface was observed by SEM (S-4800, Hitachi High-Technologies, Inc.). The acceleration voltage was set to 3.0–5.0 kV.

2.1.3. Measurement of the Pore Surface Area and Pore Size Distribution Based on the Gas Adsorption Method

To quantitatively evaluate the surface structure of the particles in the coke samples, their specific surface area and pore size distributions were measured using an automatic specific surface area/pore size distribution measurement instrument (AS1-MP, Quantachrome Instruments). The specific surface area was estimated based on the BET method.30 The pore size distribution was obtained by fitting the adsorption isotherm curve calculated by density functional theory (DFT) to the experimentally obtained curve. The calculated adsorption isotherm curve was obtained by assuming a slit pore. Both the fitting based on the non-local density functional theory (NLDFT) method and the one based on the Monte Carlo models were conducted, and the fitting errors of the two methods were compared. Herein, the pore size distribution by the NLDFT method was used because it produces a smaller error than the Monte Carlo model.

2.2. Gasification Experiments

Gasification experiments of CO2 and H2O were conducted using a thermogravimetry analyzer (STA 449 F1 Jupiter, NETZSCH) and one (TG/DTA-2000SA, Bruker AXS K.K.) equipped with a steam generator (HC9700, NETZSCH, Japan), respectively. The reaction rate of gasification was calculated by measuring the weight loss. Before the gasification experiment, 1.00 ± 0.05 mg of the coke sample was measured and placed in an alumina crucible. To avoid the stacking of coke particles, they were dispersed in the crucible. Next, the crucible was placed on the sample carrier of the thermogravimetry analyzer. The furnace temperature was increased under a nonactive atmosphere. The heating rate was set to 5, 10, or 15 K/min because the gasification experiment under elevated temperature requires at least three runs with different heating rates.31 The furnace temperature profile is shown in Figure 2. The heating rate is 10 K/min. The flow rate of the inert gas was set to 200 mL/min, and the furnace temperature was increased from room temperature to 473 K under an inert atmosphere. The inert gas was nitrogen in the case of CO2 gasification and argon in the case of H2O gasification. After 15 min, the reactant gas was flowed into the furnace, and the furnace temperature was increased to 1773 K (the yellow region in Figure 2). At this time, the total flow rate was not changed, and the concentration of the reactant gas was set to 15 vol %. The reactant gases were CO2 gas in the CO2 gasification experiment and H2O gas in the H2O gasification experiment. When the furnace temperature reached 1773 K, the gasification experiment was finalized by flowing only the inert gas into the furnace. The conversion, X, can be obtained using eq 1

2.2. 1

where m0 is the initial weight of carbon and mt is the weight of carbon at the elapsed time of t.

Figure 2.

Figure 2

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Temperature profile in the case of 10 K/min. The reactant gas was introduced at 473 K, and the gasification reaction proceeded to 1773 K.

2.3. Kinetic Analysis Based on the Distributed Activation Energy Model

The activation energy and frequency factor of the gasification reaction were determined based on the DAEM.14 At each conversion, ln(a/T2) was plotted for the inverse of temperature, and both the activation energy, Ea, and frequency factor, k0, were calculated from eq 2 that Miura24 proposed.

2.3. 2

Here, a is the heating rate, f(X) is the equation of the reaction model, R is the gas constant, and T is the sample temperature. Note that f(X) is expressed in the grain model by eq 3.

2.3. 3

To investigate the validity of the obtained Arrhenius parameters, the reaction rate was analytically calculated by assigning the activation energy and frequency factor obtained from the above method to eq 4, and the obtained value was compared with the experimental values.

2.3. 4

In eq 4, the assigned activation energy and the frequency factor are the values obtained at the conversion of X. The activation energy and frequency factor values at each conversion were obtained by linear interpolation between discrete points because the values calculated by fitting were discontinuous. The calculated value of the conversion was defined using eq 5

2.3. 5

where n is the time step and the time increment Δt was set to 0.1 s. The calculated value did not change when the time increment was set to under 0.1 s.

3. Results and Discussion

3.1. Difference in the Physical Structure between Coke Samples

To select the reaction model, the external surface of the coke samples was qualitatively evaluated. Figure 3 shows the SEM images of Coke S and Coke L before the reaction (X = 0). As can be seen in the low-magnification images shown in Figure 3a,c, the external surface of the particle had hardly any microscale pores; as a result, the surface was smooth. This is because the pores that existed inside the coke samples were eliminated by pulverization. The higher-magnification images (Figure 3b,d) show that although the external surface was rough and fine particles attached to the external surface, micrometer-scale pores were not observed. Therefore, the gasification reaction is expected to occur on the external surface of the coke sample.

Figure 3.

Figure 3

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SEM images of (a,b) Coke S and (c,d) Coke L with (a,c) low and (b,d) high magnification before reaction (X = 0).

Pores smaller than macropores of size 0.1–1000 μm could not be distinguished in the SEM images. To quantitatively evaluate the smaller pores, the pore size distributions of Coke S and Coke L before the reaction were obtained by the gas adsorption method (Figure 4). Each sample had pores smaller than 1.4 nm with a cumulative pore volume of 2.0 × 10–9–3.2 × 10–9 m3/g. The total volume of the sample is calculated to be 1 × 10–6 m3/g by assuming that the bulk density of the coke sample is 1000 kg/m3. From this result, the volume fraction of the pores of size <1.4 nm in the coke sample is calculated to be approximately 0.001 vol %, and thus, there were hardly any pores in the coke samples. Table 2 shows the specific surface areas of Coke S and Coke L before the reaction. The specific surface area of Coke S was larger than that of Coke L because the former had smaller particles than the latter. This result is similar to the trend shown in the SEM images and the pore size distribution. Therefore, it can be suggested that the reaction model in which the reaction occurs on the sample surface is suitable for the gasification reaction of metallurgical coke pulverized to a micrometer scale. In this study, the grain model was employed as the reaction model for kinetics analysis.

Figure 4.

Figure 4

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Pore size distributions of (a) Coke S and (b) Coke L before reaction.

Table 2. Specific Surface Areas of Coke S and Coke L before Reaction.

sample specific surface area [m2/g]
Coke S 9.01
Coke L 8.50
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3.2. Difference in Gasification Reactivity According to Particle Size and Reactant Gas

Figure 5 shows changes in the conversion and reaction rate as the reaction progresses. For each reactant gas, the reaction time decreased with an increase in the heating rate. When the time elapsed was the same, the reaction temperature was high when the heating rate was high. Thus, the reaction rate of gasification increased with the heating rate when the time elapsed was the same, and the reaction time became shorter with an increase in the heating rate. The reaction time tended to decrease with an increase in the particle size of the sample. This tendency was particularly remarkable for CO2 gasification. As shown in Figure 5b, the reaction rates are almost equal regardless of the particle size when the reaction temperature was below 1300 K. However, at 1300–1500 K, the reaction rate increased with a decrease in the particle size. This result is consistent with that obtained from the SEM images, the pore size distribution, and the specific surface area. Especially, the specific surface area increased with a decrease in the particle size as shown in Table 2, and then, the reaction rate was proportional to the specific surface area. This result suggested that the reaction occurred at the external surface of the particle, and the effect of nanosized pores on the reaction rate was small. In addition, when the reaction temperature was over 1500 K, the reaction rate monotonically decreased in each case because the reaction surface area of the sample decreases as the reaction progresses. In addition, in the case of H2O gasification, the reaction rate increased with a decrease in the particle size at 1250–1400 K. As these results show, the reaction rate depended on the particle size at the middle stage of the reaction, and thus, the reaction time decreased with decreasing particle size. Moreover, a comparison of the reaction time between CO2 gasification and H2O gasification showed that the reaction time for H2O gasification was approximately 1.3 times shorter than that of CO2 gasification. This tendency is common1,2,32,33 and is probably caused by the difference in the reactivity of the reactant gas.

Figure 5.

Figure 5

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Change in (a) conversion and (b) reaction rates of Coke S, Coke M, and Coke L at heating rates of 5, 10, and 15 K/min for CO2 gasification and H2O gasification.

3.3. Evaluation of Arrhenius Parameters Obtained from the DAEM

Figure 6 shows the relationship between ln(a/T2) and the inverse of temperature for determining the activation energy and frequency factor by the method proposed by Miura and Maki.25 In this figure, to calculate the distribution of the activation energy with high accuracy, the values are plotted with an increment of 0.025 in the conversion range between 0.1 and 0.9. At each conversion, the three different heating rates had a negative relationship; Honaker et al. also reported a similar result.24,25

Figure 6.

Figure 6

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Relationship between ln(a/T2) and 1/T at each conversion for CO2 gasification and H2O gasification of (a) Coke S, (b) Coke M, and (c) Coke L.

Figure 7 shows the activation energy and the frequency factor calculated based on the conversion. The grain model was employed as the reaction model used for fitting by the DAEM. For each reactant gas, the activation energy first decreased and then increased with the reaction. The frequency factor also showed a similar behavior. As shown in Figure 7b, the activation energy of Coke M was minimum at a conversion of 0.3; the frequency factor also showed a similar trend, perhaps owing to the compensation effect.34 Compared with the reactant gases, the activation energy of CO2 gasification was 200–260 kJ/mol (Figure 7a) and was equivalent to that reported in previous studies.35 In contrast, the activation energy of H2O gasification was 220–290 kJ/mol, which was higher than that of the CO2 gasification reaction. Although this is different from the general trend,10,36,37 a previous study10 also reported a similar trend. Similar to the activation energy, the frequency factor of the H2O gasification reaction seemed to be higher than that of the CO2 gasification reaction. To compare the frequency factor at the same activation energy, the change in the frequency factor for the activation energy is plotted in Figure 8. For each gasification reaction, the activation energy and the frequency factor have a positive correlation owing to the compensation effect.34 For each particle size, the frequency factor of the H2O gasification reaction was always approximately 10 times larger than that of the CO2 gasification reaction. In this study, the reaction rate of H2O gasification was larger than that of CO2 gasification because of the difference in the frequency factor. It seems that the activation energy and the frequency factor hardly depend on the particle size in each gasification reaction (Figure 7). However, when the activation energy was the same, the frequency factor increased with a decrease in the particle size (Figure 8). This tendency did not change by changing the reactant gas. In a previous study,38,39 the frequency factor of CO2 gasification of a high ash coal char was larger with a smaller particle. The reaction rate also increased with a decrease in the particle size, and thus, this result was similar to our results. Moreover, the frequency factor calculated using the grain model, kg, is inversely proportional to the initial particle size, as shown in eq 8.

3.3. 8

Figure 7.

Figure 7

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Change in the activation energy and the frequency factor for (a) CO2 gasification and (b) H2O gasification.

Figure 8.

Figure 8

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Relationship between the frequency factor and the activation energy for (a) CO2 gasification and (b) H2O gasification.

Thus, the frequency factor could express the reaction model. This result suggested that the gasification reaction of the coke pulverized into micrometer particles is a surface reaction.

3.4. Evaluation of the Validity of the Analysis

Figures 9 and 10 show the conversion and reaction rate calculated using the DAEM with the experimental values. In the CO2 gasification reaction, the calculated values correspond to the experimental values, and the prediction accuracy would be almost equivalent regardless of the heating rate and particle size (Figure 9). At a reaction temperature of 1400–1600 K, the calculated reaction rate of each particle size slightly overestimated the experimental value. This is because the accuracy of fitting decreased around 1400 K owing to the change in the slope of the experimental reaction rate. In addition, in the H2O gasification reaction, the calculated value overestimated the experimental value at 1300–1500 K. In this temperature range, the difference between the calculated and experimental values for H2O gasification was larger than that for CO2 gasification. This is because the slope of the measured reaction rate in H2O gasification changed around 1300 K, similar to CO2 gasification, and this change was larger than that of the CO2 gasification reaction. Thus, the accuracy of fitting in H2O gasification was lower than that in CO2 gasification. However, the calculated values of H2O gasification and CO2 gasification were similar to the experimental values obtained at reaction temperatures below 1300 K or over 1500 K. Therefore, the reaction rate calculated from the DAEM expressed the experimental value, suggesting that the analysis performed in this study is almost valid.

Figure 9.

Figure 9

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Comparison of (a) conversion and (b) reaction rate of Coke S, Coke M, and Coke L between the experimental and calculated results at heating rates of 5, 10, and 15 K/min for CO2 gasification.

Figure 10.

Figure 10

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Comparison of (a) conversion and (b) reaction rate of Coke S, Coke M, and Coke L between the experimental and calculated results at heating rates of 5, 10, and 15 K/min for H2O gasification.

4. Conclusions

Gasification experiments of CO2 gas or H2O gas for coke pulverized to the micrometer scale were conducted, and kinetic parameters were determined based on the distributed activation energy model (DAEM).

To select the reaction model, the surface of the coke sample was evaluated by scanning electron microscopy (SEM) and gas adsorption. The SEM images showed that there were hardly any micrometer-scale pores on the sample surface. In contrast, the gas adsorption results showed that Coke S and Coke L have pores of size <1.4 nm. However, the cumulative volume of the small pores was approximately 0.001 vol %. Moreover, the specific surface area was larger with a decrease in the particle size. The reaction time decreased with the particle size for each reactant gas as well. These results suggest that the reaction occurs on the surface, and thus, the grain model was employed as a reaction model.

For the kinetic parameters, the activation energy of each gasification changed with the reaction and was hardly dependent on the particle size. The activation energy was 200–260 kJ/mol for CO2 gasification and 220–290 kJ/mol for H2O gasification. At the same activation energy, the frequency factor increased with the particle size, suggesting that the gasification of coke pulverized to a microscale size occurs on the particle surface.

In the comparison of the value predicted by the DAEM with the experimental one, the calculated and the experimental values corresponded well, and thus, it was confirmed that the analysis in this study is almost valid. As a future work, the kinetic parameters will be applied to large-scale simulation of coke degradation based on computational fluid dynamics40 and contribute to improve the prediction accuracy of the numerical simulation.

Acknowledgments

This work was carried out as a part of the research activities “CO2 Ultimate Reduction System for Cool Earth 50 (COURSE50)”.

Glossary

Abbreviations

BET

Brunauer–Emmett–Teller

COG

coke oven gas

CRI

coke reactivity index

CSR

coke strength after reaction

DAEM

distributed activation energy model

DFT

density functional theory

SEM

scanning electron microscopy

TG

thermogravimetry

XRD

X-ray diffraction

Financial support from the New Energy and Industrial Technology Development Organization (NEDO) is gratefully acknowledged. This work was also supported by the Japan Society for the Promotion of Science, grant no. 19J20961.

The authors declare no competing financial interest.

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