Kinetic study of the methane dry (CO₂) reforming reaction over the Ce_0.70La_0.20Ni_0.10O_2−δ catalyst

Abstract

The kinetic behaviour of the Ce_0.70La_0.20Ni_0.10O_2−δ catalyst during the methane dry reforming reaction was investigated in a fixed bed reactor in the temperature range of 923–1023 K with the partial pressure of CH₄ and CO₂ ranging between 5 and 50 kPa. The experimental data were fitted using the empirical power-law rate equation and Langmuir–Hinshelwood kinetic models proposed in literature for the Ni–La₂O₃ catalytic system and based on two-step single- and dual-site mechanisms. The obtained fitting results, after statistical and thermodynamic discrimination, showed that the mechanism of the dry reforming reaction over the Ce_0.70La_0.20Ni_0.10O_2−δ catalyst could be successfully described by the two-step dual-site mechanism. The activation energies for the CH₄ consumption from the power law and Langmuir–Hinshelwood models were estimated to be 91.5 and 136.9 kJ mol⁻¹, respectively. The lower activation energies for the CO₂ consumption (70.2 and 100.6 kJ mol⁻¹ from both models) suggested that the CO₂ activation should faster than CH₄. The basic nature of the Ce–La–O sites catalyzed the CO₂ conversion to oxy-carbonate, decreasing the CO₂ activation energy compared to that of CH₄.

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1. Introduction

The “Paris Agreement” signed by 195 countries under the United Nations Framework Convention on Climate Change (UNFCC) aims to reduce greenhouse gas emissions, limiting the earth to a 2 °C temperature rise.¹ This ambitious perspective involves, as an energetic strategy, the conversion of the current energetic vector from petroleum to an H₂-based energetic vector, which is widely considered an efficient and clean energy source.^2,3 Indeed, as an energy carrier, hydrogen allows decarbonisation in many sectors like transport, industries, space heating and storage for intermittent renewable energy.⁴ In this context, methane dry reforming (CH₄ + CO₂ → 2H₂ + 2CO, ΔH₂₉₈ = 260.5 kJ mol⁻¹) can be considered as a dual global warming addressing technology as it consumes and/or mitigates two greenhouse gases (CO₂ and CH₄), producing synthesis gas (CO and H₂) with an H₂/CO molar ratio closer to unity. This is adequate for the production of valuable synthetic liquid fuels and oxygenated chemicals via oxo- and Fischer–Tropsch synthesis processes.^5,6

Natural gas with a high CO₂ content yet very abundant in nature^7,8 and biogas produced by the anaerobic digestion of biomass^9,10 can represent significant sources of CO₂ and CH₄. Despite these advantages, methane dry reforming is not yet regarded as an industrially mature process. The main limitation lies in catalyst deactivation occurring as a result of the large amount of carbon deposition due to the high reaction temperature.^11,12

Generally, two types of supported catalysts have been applied for the dry reforming reaction: noble metal (Pt, Pd, Rh, Ru, Ir, etc.)-based and transition metal (Ni, Co, Fe, etc.)-based catalysts. Although noble metals have been found to be less sensitive to coke deposition,^13–16 Ni-based catalysts have been largely studied because of its abundance and low cost. However, a propensity for deactivation can be observed that normally takes place due to the sintering, cooking and phase transformation of the active metal during the reaction.^17,18

Different strategies have been adopted to increase the resistance to coke deposition in Ni-based catalysts:¹⁹ modification by promoters (structural and chemical);²⁰ selection of suitable supports (CeO₂, MgO, La₂O₃, CeO₂–ZrO₂, TiO₂) able to promote coke gasification by CO₂ activation;^21,22 the investigation of novel Ni-structures such as core–shell, core-tube and mesoporous framework.^23–25 In addition, it has been evidenced that a fine-tuning and intensification of the interactions between Ni and support can induce better anti-coke and anti-sintering performance of the catalysts.^26,27

The effect of interactions between the active metal and support, as a result of the formation of a solid solution, on the catalysts' performance during dry reforming reaction has been widely evaluated in literature. Excellent activity and stability have been reported by Hu for the NiO–MgO (or CoO–MgO) solid solution;²⁸ the carbon deposition is inhibited by the isolation effect of small nickel particles formed on the catalytic surface coupled with the surface basicity of MgO. Sadykov et al. showed that a strong interaction of Ni with Ce–Zr–O oxide, as a support in the reduced state, induces a high activity and coking stability of the developed catalyst.²⁹ Jang et al. attributed the excellent activity of the MgO-promoted Ni/Ce_0.8Zr_0.2O₂ sample (equilibrium CH₄ and CO₂ conversion for 200 h without carbon deposition) to the high strength of the interactions between the components.³⁰ Makri et al. pointed out that the metal oxide interface in the Ni/Ce_0.8Pr_0.2O₂ catalyst plays an important role in reducing coke formation under dry reforming conditions.³¹

The catalytic Ni/La–Ce–O_x mixed oxide system has been widely studied by our research group and successfully applied to reforming reactions.^32,33 In particular, the selected Ce_0.70La_0.20Ni_0.10O_2−δ catalyst under appropriate pre-treatment (reduction at 1023 K) exhibited promising activity and stability during the dry reforming reaction.³⁴ The absence of carbon deposition and stable performance (CH_4,conversion = 73%; CO_2,conversion = 83%) for 50 h on stream at a gas hourly space velocity (GHSV) of 26 400 h⁻¹, were observed. In addition, a negligible amount (0.12–0.20%) was deposited at increasing GHSV (52 800–105 600 h⁻¹) after H₂ pre-reduction of the catalyst at 1023 K. From the characterizations of the catalyst, a complex structure has been highlighted that includes: i) a strong metal support interaction (SMSI) evidenced by the suppression of CO and H₂ chemisorption; ii) the presence of oxygen vacancy defects induced by the partial incorporation of Ni²⁺ in the Ce–La–O_x support with partial exsolution of Ni²⁺ and/or La³⁺ ions from bulk to surface; iii) the bi-functional role of the support, where CeO₂ coupled with La₂O₃ are involved in CO₂ adsorption and coke gasification. All of these features seemed to be responsible for the observed catalytic performance.

Kinetics and mechanistic studies over Ni catalysts have been widely reported in literature, as summarized in some recent reviews.^35,36 In the presence of La₂O₃ as a support, the proposed mechanisms include the presence of a single- or dual-active site, where the dissociation of methane on Ni particles and carbon gasification by adsorbed CO₂ on the support sites are the rate-determining steps.^37,38

In the current study, kinetic measurements over the Ce_0.70La_0.20Ni_0.10O_2−δ catalyst were performed. The dependency of the reactant consumption rate and product formation rate on the temperature (923–1023 K) and the reactant partial pressure (5–50 kPa) were evaluated. The results were fitted into a power-law model and the cited Langmuir–Hinshelwood models proposed in literature for the two-step single- and dual-site adsorption mechanisms.

To the best of our knowledge, the intrinsic kinetics of the CeO₂–La₂O₃ mixed oxide-supported Ni catalyst for the dry reforming reaction have not been investigated in detail. The purpose of this study is to combine the characterizations and performance test results from previous investigations with the present kinetics data to propose a plausible kinetics model for the reaction.³⁴

2. Experimental

2.1 Catalyst preparation

The catalyst, Ce_0.70La_0.20Ni_0.10O_2−δ (3.66 wt% Ni), was prepared by combustion synthesis as previously reported.^33,34 The metal precursors of cerium ammonium nitrate ((NH₄)₂Ce(NO₃)₆·6H₂O), nickel nitrate (Ni(NO₃)₂·6H₂O), and lanthanum nitrate (La(NO₃)₃·6H₂O) with oxalyldihydrazide as fuel (C₂H₆N₄O₂, all reagents from Aldrich) were dissolved in a minimum amount of H₂O. The mixture was then transferred into an oven furnace heated at 623 K to allow water evaporation, promoting the combustion reaction. A huge amount of fumes were produced and a few seconds after ignition, a fragile foam was formed that easily crumbled into powder. The obtained sample, heated at 873 K in air to burn off the carbonaceous residues, was tableted, ground and sieved to obtain particles with the required size.

2.2 Kinetic evaluations

Kinetic studies under different conditions were carried out in a continuous-flow quartz reactor (i.d. = 6 mm) placed in an electric oven. The selection of experimental conditions (reported below) was such that the effect of the external/internal mass and heat transfer could be considered negligible. Weighted amounts of the catalyst (0.011–0.044 g) diluted with quartz of the same size (dilution 1 : 5) were loaded in the middle part of the reactor and supported on quartz wool. The reaction temperature was measured/controlled by two k-thermocouples. One of the thermocouples was placed inside a thermowell and centered in the catalyst bed; the other was located at the outlet of the catalytic bed. The catalyst activation before the catalytic tests was carried out in situ by treatment with a 25% H₂/N₂ flow (80 ml min⁻¹) at 1023 K for 2 h, and then the temperature was maintained and/or dropped to the desired reaction temperature. The feed was controlled by mass flow controllers, and the products were analyzed with the help of a gas chromatograph (Agilent 6890 Plus) equipped with FID and TCD detectors. Kinetic measurements were performed in the temperature range of 923–1023 K, employing dilute CH₄ : CO₂ : N₂ = 1 : 1 : 3 feeds. The partial pressure dependencies were evaluated by maintaining the pressure of one reactant at 20 kPa and varying the pressure of the other reactant between 5 to 50 kPa. N₂, as the balance gas, was adjusted to maintain the overall pressure constant (101.32 kPa). The gas hourly space velocity was controlled at 1.2 × 10⁶ h⁻¹ using 0.022 g of the catalyst and appropriate feed flows to obtain significantly lower conversion (<15%) than those defined by thermodynamic equilibrium, and the reaction was controlled by kinetics. For each reactant stream and reaction temperature, the kinetic data were collected after the catalyst was stabilized for about 2 h. The reaction rates, based on the reactant consumption and product formation, were calculated by the following equations:where F_i,in (mol min⁻¹) is the volume flow rate of the reagent gas, F_i,out (mol min⁻¹) is the volume flow rate of the component i in the outflow gas, Conv._i is the reagent conversion and W_cat. (g) is the weight of the catalyst.³⁹

2.3 Diagnostic tests for mass and heat transfer limitations

In order to evaluate the appropriate experimental conditions under which the effect of the external and internal mass transfer limitations on the methane dry reforming reaction can be considered negligible, preliminary reforming tests were performed by changing the total flow rate and catalyst particle size. The inter-particle limitation tests were performed at a GHSV of 1.2 × 10⁶ h⁻¹ (reaction conditions: feed composition 20/20/60 vol%; reaction temperature = 923–1023 K, pressure = 101.32 kPa), and showed an invariant rate for flow rates above 200 ml min⁻¹. This indicated that no external limitations existed under those conditions, as shown in Fig. 1a.

Fig. 1 Effect of volumetric feed flow rate (a) and catalyst particle size (b) on the methane consumption during dry reforming at constant GHSV = 1.2 × 10⁶ h⁻¹.

At a selected flow rate of 200 ml min⁻¹, the absence of the intra-particle limitations was verified by using different average sizes of the catalyst particles (0.180–0.444 mm). As evidenced in Fig. 1b, the reaction rate results were almost invariant with particle sizes ranging between 0.254 to 0.444 mm. This suggests that the internal mass transfer limitations can be considered negligible. In summary, the mass transfer limitations and diffusion rate-controlling regime were fully excluded for the conditions selected to perform the catalytic tests, i.e., a flow rate of 200 ml min⁻¹ and average particle size of 0.254 mm.

To further investigate the heat and mass transfer limitations for the reaction over the studied catalyst, suitable diagnostic criteria have been also applied. The effect of intra-/interphase heat transfer limitations on the intrinsic kinetics of the reaction was ruled out using the Mears and Anderson criteria, respectively, represented by the following notations:^40,41

where ΔH is the reaction enthalpy (260 kJ mol⁻¹), rate_exp is the highest reaction rate (R_CO2 = 2.07 × 10⁻⁴ mol g⁻¹ s⁻¹), d_p is the catalyst particle diameter (254 × 10⁻⁶ m), E_a is the experimentally derived activation energy (70.17 kJ mol⁻¹), h is the heat transfer coefficient between the gas phase and the catalyst surface (908 W m² K), λ_eff is the catalyst thermal conductivity (11.71 W m K), R is the universal gas constant and T is the reaction temperature (1023 K). The derived values of 2.4 × 10⁻² and 4.6 × 10⁻⁴ suggest that the diagnostic criteria are satisfied; thus, the heat transfer effect was not significant. In addition, the effects of the external mass transfer and intra-phase diffusion were checked by application of the Mears and Weisz–Prater criteria, respectively, that can be defined as follows:⁴²where ρ_s is the catalyst particle density (assumed spherical, 2500 kg m⁻³), n is the reaction order (0.31), p_CO2 is the partial pressure of CO₂ at the external surface (20 kPa), k_c is the mass transfer coefficient (0.206 m s⁻¹). Also, in this case, the derived values of 0.18 and 8.4 × 10⁻², respectively, confirm a negligible influence of the mass transfer on the reaction rate.

3. Results

3.1 Kinetic evaluations

Apparent activation energy. The effect of the temperature on the reaction rate was investigated in the temperature range 873–1023 K, employing a feed mixture consisting of CH₄ : CO₂ : N₂ = 20 : 20 : 60 vol% under a pressure of 101.32 kPa. The results, in the form of an Arrhenius plot, are depicted in Fig. 2. The apparent activation energies estimated for the CH₄ and CO₂ consumption, as well as H₂ and CO formation, are presented in Table 1 and compared with analogous data from Ni-based catalysts derived from literature. As evident, the apparent activation energy can reach very different values over the different catalytic systems applied to the reaction. The support of the Ni catalysts can significantly influence the activation energy by altering the rate-controlling step in the reaction sequence.^45,49 Bradford and Vannice pointed out that the activation energies for the reforming reaction, carried out with Ni catalysts supported on different supports, were typically included in the range 30–100 kJ mol⁻¹. Conversely, high values of up to 160 kJ mol⁻¹ have been obtained for some classes of catalysts.⁵⁰

Fig. 2 Influence of the reaction temperature on the CH₄ and CO₂ consumption rate, as well as the H₂ and CO formation rate derived at 101.32 kPa, CH₄ : CO₂ : N₂ = 1 : 1 : 3 and GHSV = 1.2 × 10⁶ h⁻¹.

Table 1 Comparison of apparent activation energy (E_a, kJ mol⁻¹) over Ni-based catalysts

Catalyst	Temperature (K)	Reagent compositions (kPa)			E a (CH4)	E a (CO2)	E a (CO)	E a (H2)	Ref.
		CH4	CO2	N2
Ce0.70La0.20Ni0.10O2−δ	873–1023	20	20	60	70.5	71.0	78.3	80.4	This work
Ni/La2O3	773–973				68.0	77.0			38
Ni° from 20 LaNi-SBA(10)	813–893	50	50	—	64.7	57.8	63.7	82.7	47
Ni/CaO–Al2O3	893–963	50	50		106.7	98.8	103.0	147.4	44
Ni15CeMgAl	773–873	20	20	60	65.5	62.2	40.8	61.3	39
13.5Ni–2K/10CeO2–Al2O3	873–1073	20	20	60	46.1	46.2	47.4	54.0	45
1Ce5Ni3Mg/Al	613–673	25	25	50	21.7	23.9			48
Ni–Co/Al–Mg–O	923–1023	62	62	186	69.4	25.9	61.8	85.1	46
Ni/γAl2O3	773–973	25	25	50	50.9	56.1	80.5		43

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In the current investigation with the Ce_0.70La_0.20Ni_0.10O_2−δ catalyst, the activation energies for CH₄ and CO₂ consumption were very close and comparable with analogous data reported by Sierra-Gallego et al. for the Ni/La₂O₃ catalytic system.³⁸ The apparent activation energies for hydrogen and CO were greater than those for CH₄ and CO₂, suggesting that the rate-determining step for CO and H₂ formation are different from those for CH₄ and CO₂ consumption. In addition, the activation energy for H₂ production was higher than that for the formation of CO. This could be related to the parallel occurrence of the reverse water gas shift reaction (RWSR) that influences the reaction mechanism.⁴⁵

Effect of reactant partial pressures on dry reforming rate. The influence of the partial pressure of CH₄ and CO₂ on the reforming rate was evaluated at a pressure of 101.32 kPa in the temperature range of 923–1023 K. The effect of the CH₄ partial pressure on the consumption rate of CH₄ was evaluated at a constant CO₂ partial pressure of 20 kPa as the CH₄ partial pressure was increased from 5 to 50 kPa. The results evaluated at the different temperatures are depicted in Fig. 3a.

Fig. 3 Effect of variation of partial pressure of CH₄ (a) and CO₂ (b) at constant p_CO2 and p_CH4, respectively, on the reaction rate over the Ce_0.70La_0.30Ni_0.10O_2−δ catalyst in the temperature range of 923–1023 K.

As evident, the rate of methane consumption was noticeably influenced by the CH₄ partial pressure over the whole experimental range of 5–30 kPa. A further increase of the CH₄ partial pressure up to 30 kPa induced a less significant effect in the consumption rate. This behavior was observed at high reaction temperatures (973–1023 K). At 923 K, the reforming rate was sensitively affected by the low partial pressures of CH₄ (≤20 kPa), remaining almost unchanged with further increase of the CH₄ partial pressure.

The effect of the variation of the CO₂ partial pressure on the rate of the methane consumption is depicted in Fig. 3b. It can be see that the methane consumption rate increased with increasing CO₂ partial pressure in the range of 5–20 kPa, remaining almost constant at higher partial pressures (20–50 kPa). The relatively constant reaction rate, recorded at all investigated reaction temperatures, can be ascribed to a limitation of the thermodynamic equilibrium of the limiting reactant CH₄ (p_CH4 = 20 kPa).

In addition, the effect of the CO₂ partial pressure appeared less significant in the tests carried out at a lower temperature (923 K) in relation to analogous tests at higher temperatures (973–1023 K).

A comparison of Fig. 3a and b suggests that the CH₄ consumption rate was more sensitive to the CO₂ partial pressure than the CH₄ partial pressure at low CH₄ and CO₂ partial pressures, respectively. From these results, a stronger CO₂ adsorption on the catalyst surface can be derived than CH₄ adsorption due to the strong interaction of the CO₂ molecule with the basic surface of the mixed Ni–La–CeO_x oxides, as previous envisaged.³² The presence of the Ce₂O₃ support from the pre-reduction step of the catalyst can enhance CO₂ adsorption by forming the strong ionic oxide Ce₂O₂CO₃. The sequential dissociation of the carbonate species into CO₂ and further to CO and O generates oxygen species able to react with carbon deposits at the Ni–Ce₂O₂CO₃ interface.⁵¹ Similarly, CO₂ can adsorb onto La₂O₃ (present on the surface) to form La–oxycarbonates, which in turn react with the carbon formed from CH₄ activation at the metal–La interface, cleaning the surface of the catalyst from carbon accumulation. This scavenging effect of the carbonate species on carbon from Ni has been proven to be responsible for the stability evidenced by the Ni/La₂O₃, Rh/La₂O₃ and Rh/La₂O₃–SiO₂ catalysts.^{37,44,52–54} Finally, the presence of oxygen vacancies on CeO₂–La₂O₃ in solid solution can promote the dissociation of adsorbed CO₂, generating lattice oxygen that reacts with the carbon atom. This can play a fundamental role in the stability of the doped Ni–CeO₂ catalytic system.³¹ Results of the previous investigation with the Ce_0.70La_0.20Ni_0.10O_2−δ catalyst, under analogous experimental conditions after 50 h of reaction, showed the absence of carbon deposition.³⁴

Effect of reactant partial pressures on product formation rates. The formation rates of H₂ and CO as a function of the partial pressure of the reactants are depicted in Fig. 4. The rate of H₂ formation for constant CO₂ partial pressure increases linearly by increasing the CH₄ partial pressure in the range 5–20 kPa. A more limited increase at higher CH₄ partial pressure was recorded, as shown in Fig. 4a. This suggests that the dry reforming and RWGS reactions rates become lower in the presence of a limited CO₂ amount. This is supported by the experiments conducted at constant CH₄ partial pressure. Depicted in Fig. 4b, the increase in the CO₂ partial pressure up to the stoichiometric value (20 kPa) involves a noticeable increase in the H₂ formation rates that become invariant at higher partial pressures of CO₂. The equilibrium that is established between H₂ produced by reforming and consumed by RWGS results responsible of the observed trend. The dependence of the CO formation rate on the partial pressures of CH₄ and CO₂, is depicted in Fig. 4c and d, respectively.

Fig. 4 Effect of the alteration of CH₄ partial pressure (a and c) and CO₂ (b and d) at constant p_CO2 and p_CH4, respectively, on the H₂ and CO formation rates.

A quasi-linear dependence of the CO formation rate on the CH₄ partial pressure ranging between 5 to 20 kPa can be observed. Conversely, a light decrease in the CO formation rate at a high partial pressure of CH₄ (Fig. 4c) was observed. This could be due to the effect of side reactions such as RWGS, that limit the CO formation when CO₂ is the limiting reagent. This is supported by the observation of Fig. 4d: the CO formation increases progressively by increasing the partial pressure of CO₂. The observed trend agrees well with those reported by other authors such as Osazuwa et al. with the SmCoO₃ perovskite catalyst,⁵⁵ Nandini et al. who evaluated the catalytic activity of a Ni–K/CeO₂–Al₂O₃ sample,⁴⁵ and Fan et al. who applied a bimetallic Ni–Co/MgO–ZrO₂ catalyst to the dry reforming reaction.²⁰

Effect of product partial pressures on dry formation rates. The effect of H₂ in the feed on the dry reforming rate was investigated in the range of 5–20 kPa at a constant CH₄ and CO₂ partial pressure of 10 kPa and reaction temperature of 1023 K. The results depicted in Fig. 5a show that the increase in the H₂ partial pressure induced a light inhibition of the methane consumption rate, while exerting a positive effect on the CO₂ consumption rate and CO production rate. This behavior, attributable to the occurrence of the reverse water gas shift reaction, shows that the Ni–H produced on the surface can reach an equilibrium state with the hydrogen product from the dry reforming reaction.⁴⁴

Fig. 5 Influence of H₂ (a) and CO addition (b) to the feed mixture (T = 1023 K, p_CH4 = p_CO2 = 10 kPa) on the reaction rates.

The effect of the increased CO partial pressure from 1 to 3 kPa in the feed stream on the reaction rates is evidenced in Fig. 5b. The reforming rates were slightly influenced by the CO partial pressure. A decrease in the reforming rate was observed for p_CO (up to 2 kPa) that remained almost constant with further increases in the CO partial pressure. Taking in consideration that the CH₄ dissociation and CO adsorption occurred on the Ni active sites, the inhibition effect of CO on the reaction rate was due to the competitive adsorption of CO on active sites that limited the adsorption/dissociation of CH₄ for which the reforming rate decreased. The invariant CH₄ consumption rate observed at high CO partial pressure can suggest a limited CO adsorption on the Ni active sites.

3.2 Kinetic modeling

Power law model. The obtained kinetic data, including the reaction rates and partial pressures of the reactants (CH₄ and CO₂), were first fitted into the empirical power law model. This provides a rough estimation of the reaction parameters even though it does not account for the reaction mechanisms. The empirical power law model for the dry reforming reaction is given in the following equation:where r_i represents the consumption rates of CH₄ and CO₂, as well as the formation rates of H₂ and CO; A represents the pre-exponential factor, E_a is the activation energy; R is the universal gas constant; p_CH4 and p_CO2 are the partial pressures of CH₄ and CO₂, respectively, with m and n as the related reaction orders; and T is the absolute reaction temperature.

The SOLVER function, available in Excel spreadsheets, was employed to evaluate the kinetic parameters from the nonlinear power law model.^56,57 The goodness of fit was determined by the coefficient of determination (R²). The estimated values of the kinetic parameters, as well as the corresponding R², Rmsd (residual sum of square) and σ (standard deviation) values are summarized in Table 2. It can be seen that the reaction rates for the reactants and products were satisfactorily predicted with R² ≥ 0.95.

Table 2 Estimation of kinetics parameters from the power law model

Reaction species	Kinetics parameters
	m	n	A (mol g^−1 s^−1) kPa^−(m+n)	E a (kJ mol^−1)	R ^2	Rmsd (mol g^−1 s^−1)	σ (mol g^−1 s^−1)
Rmsd: root mean square deviation; σ: standard deviation.
CH4	0.50	0.20	0.66	91.50	0.97	8.6 × 10^−6	4.7 × 10^−5
CO2	0.29	0.31	0.10	70.17	0.97	9.9 × 10^−6	6.0 × 10^−5
H2	0.54	0.15	5.62	105.41	0.95	1.7 × 10^−5	1.0 × 10^−4
CO	0.26	0.28	0.53	78.52	0.96	1.8 × 10^−5	7.8 × 10^−5

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Activation energies of approximately 91.5 kJ mol⁻¹ and 70.17 kJ mol⁻¹ were derived for CH₄ and CO₂ consumption, respectively, as evidenced in Table 2. The activation energy of the CH₄ consumption was higher than that of the CO₂ consumption. This indicates that the CH₄ activation is more temperature-sensitive than that of CO₂.

The lower CO₂ activation energy related to the methane activation energy implied furthermore that the rate of CO₂ consumption was faster than that for CH₄. Thus, the CO₂ conversion was higher than the CH₄ conversion.⁵⁸

The reaction orders obtained for the CH₄ consumption (m = 0.50; n = 0.20) indicate that the CH₄ partial pressure significantly influences the methane reforming. In addition, the CO₂ consumption is influenced by the CO₂ partial pressure (m = 0.29; n = 0.31).

The activation energies of H₂ (105.41 kJ mol⁻¹) and CO (78.52 kJ mol⁻¹) are comparable to that of CH₄ and CO₂, respectively. Therefore, it can be derived that the H₂ formation was predominantly influenced by CH₄, while the CO formation was primarily influenced by CO₂. Furthermore, both values were higher than those for the CH₄ and CO₂ consumption. This suggests, as previously observed, that the rate-determining steps for the H₂ and CO formation are different from those for the reagent consumption.

The activation energy for H₂ production, noticeably higher than that CO, is a clear indication of the influence of the RWGS reaction on the H₂ formation. A comparison of the experimental rates for CH₄ and CO₂ consumption, as well as for the H₂ and CO formation with those predicted by the power law model, are given in Fig. 6. A good agreement between the predicted and experimental values emerged.

Fig. 6 Statistical fit of the postulated power law model showing the comparison of the rate predicted by the model to the experimental rate.

The derived kinetic parameters are very similar to the reported values by Bradford and Vannice⁴⁹ and Ayodele et al. for the reaction carried out with Ni/MgO and Co/La₂O₃,⁶⁰ respectively, as evidenced in Table 3. Its results are noticeably higher than the activation energy reported by Takano et al. over a traditional Ni/Al₂O₃ (cordierite) catalyst.⁵⁹ Although the different supports have different influences on the activity of the metallic phase, this could be ascribed to the high interaction occurring between Ni and the La–CeO_x support.

Table 3 Activation energy from the power law reported in the literature

Catalyst	Temperature (K)	Partial pressure (kPa)	E CH4 (kJ mol^−1)	E CO2 (kJ mol^−1)	E CO (kJ mol^−1)	E H2 (kJ mol^−1)	Ref.
10.1Ni/MgO	673–823	5–53	92.10	87.9	87.90	146.51	49
1.22Ni/TiO2	673–823	"	108.8	87.9	96.28	133.95	"
Co/La2O3	923–1023	5–50	96.44	72.22	69.71	101.50	60
Ni/Al2O3	850–1000	17–51	76.0				59
5Ni/CeO2–SiO2-c	703–733	20–40	154.7				61
5Ni/CeO2–SiO2-p	"	"	97.3				"
4.7Ni/ZnO	863–883	4.5–11	110.7	118.4			62
4.8Ni–4.3MgO/ZnO	743–763	"	97.4	106.3			"

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Indeed, Bradford and Vannice pointed out that with the Ni–TiO₂ catalyst, the SMSI induced a noticeable value of the activation energy (108 kJ mol⁻¹) that increased to 171.6 kJ mol⁻¹ after 18 h of stream.⁴⁹ In this case, the migration of TiO_x on the Ni surface may increase the activation barrier for methane dissociation. Recently, Yan et al. showed that the close metal–support interface between Ni and CeO₂ in the Ni–CeO₂–SiO₂ catalyst led to a substantial decrease in the activation energy from 154.7 kJ mol⁻¹ (Ni–CeO₂–SiO₂ sample C) to 97.3 kJ mol⁻¹ with the sample in the absence of interactions (Ni–CeO₂–SiO₂ sample P).⁶¹ Analogous evidence emerged from the study reported by Singha et al., where the methane activation energy of the Ni/ZnO catalyst decreased significantly from 110.7 kJ mol⁻¹ to 97.4 kJ mol⁻¹ by the addition of MgO in the catalyst formulation, inducing high Ni dispersion and metal–support interactions.⁶² Therefore, other models may be more appropriate than the power law. In the following section, the Langmuir–Hinshelwood mechanism models proposed in the literature for the Ni–La₂O₃ catalytic system (and as previously mentioned) were applied to evaluate the kinetic mechanism of the current sample.

Langmuir–Hinshelwood models. Many studies related to the kinetics of methane reforming with CO₂ are generally based on mechanistic steps that include: i) the dissociation/activation of CH₄ and CO₂; ii) adsorption of elemental and intermediate species on active sites; iii) formation of products via surface reactions; iv) desorption of product species.⁶³ The fundamental study carried out by L. M. Aparicio showed that there is not a single rate-determining step (RDS) in the reaction.⁶⁴ Therefore, in most cases, the CH₄ and CO₂ dissociation or activation are considered to be the RDS.

Based on DRIFT (diffuse reflectance infrared Fourier transform) and SSITKA (steady-state isotopic transient kinetic analysis) studies, Verykios and co-workers proposed a mechanistic sequence for the Ni/La₂O₃ catalytic system where CH₄ cracking is a slow step, while the CH₄ adsorption is at equilibrium.^65–67 The strong interaction occurring between CO₂ and La₂O₃ that leads to the formation of the La₂O₂CO₃ species, can be considered a fast step at equilibrium. Conversely, the reaction between this formed species with Ni particles at the Ni/La₂O₂CO₃ interface oxygenated species becomes a slow step.³⁷

This mechanistic step can be synthetically represented by the following reactions:

H₂ + 2–S ↔ 2H–S(equilibrium) (12)

In addition, the simultaneous occurrence of RGSR includes the sequence of the following reaction steps:

CO₂ + S ↔ S–CO₂(equilibrium) (13)

S–CO₂ + H–S → S–CO + OH–S(slow) (14)

S–OH + H–S ↔ 2S–H₂O(equilibrium). (15)

On this basis, the authors derived the following rate expression for the methane consumption:where K₁ is the adsorption equilibrium constant for CH₄; k₂ is the rate constant of methane cracking on the metallic surface; K₃ is the adsorption equilibrium constant of the reaction between CO₂ and La₂O₃; k₄ is the rate constant of the reaction between the oxycarbonate species and carbon deposited on the Ni surface.

Sierra-Gallego et al. studied the kinetic behaviour of the Ni/La₂O₃ catalyst obtained from the reduction of LaNiO₃ perovskite structure.³⁸ From XPS (X-ray photoelectron spectroscopy) after the catalytic tests, the authors derived that the Ni particles were partially covered by the La₂O₂CO₃ species due to the migration of La₂O₃ over the metal particles. From this evidence, the authors developed a rate reaction equation including, for the first time, the presence of two active sites on the catalyst surface: metallic nickel particles and the La₂O₃ metal support. Assuming a negligible H₂ and CO surface coverage, the proposed dual active-site mechanism involves the following steps:

where S₁ represents the metallic active site (Ni°) and S₂ is the La₂O₃ support as the active site. The related rate model assumes the following form:The current catalytic system can be envisaged as a Ni-solid solution with ceria–lanthana in which the presence of anionic vacancies can help the abstraction of H species from CH₄. The sequential decomposition of the CH₃ intermediate into C, that could substitute steps 9/17 in previous models and is described as:occurs very fast. The reversible CO₂ adsorption on the support surface can happen on both La₂O₃ and Ce₂O₃, generating carbonate species at the boundary of Ni particles. The subsequent reaction with adsorbed carbon generates CO, restoring the active sites.

The presence of oxygen vacancies (□) on the ceria–lanthana support contributes to the CO₂ adsorption/dissociation step:

CO₂ + □ → CO + O_lattice

Diffusion of the generated lattice oxygen towards the Ni surface exerts a promoting effect in the cleaning steps (carbon oxidation to CO) of the surface sites envisaged in the reaction sequences.

On this basis, the kinetic models proposed by Verykios's group (model 1) and Sierra-Gallego et al. (model 2) were applied to fit the experimental data obtained from this study over the Ce_0.70La _0.20Ni_0.10O_2−δ catalyst. The parameters of both models were estimated using the nonlinear regression method with the ANEMONA.XLS tools, an Excel template previously developed and successfully tested with some kinetic models applied in literature for the dry reforming reaction.⁶⁸

The summary of the kinetic parameters estimated from the two Langmuir–Hinshelwood rate expressions are summarized in Table 4. As evident, both models gave fitting regression coefficients (R²) greater than 0.90, which can be considered to be a good fitting. Thus, the models are statistically significant.

Table 4 Langmuir–Hinshelwood kinetic models parameters

Model no.	Temperature (K)	Kinetic constant
		K 1 (kPa^−1)	k 2 (mol g^−1 s^−1)	K 3 (kPa^−1)	k 4 (mol g^−1 s^−1)	R ^2	Rmsd (mol g^−1 s^−1)	σ (mol g^−1 s^−1)
Rmsd: root mean square deviation. σ: standard deviation, (values in parenthesis are the standard deviation for the kinetic constants).
1	1023	0.0323 (1.8 × 10^−2)	0.00036 (1.5 × 10^−4)	0.0037 (3.5 × 10^−1)	0.00815 (7.0 × 10^−2)	0.97	2.3 × 10^−5	2.6 × 10^−3
	973	0.0250 (1.3 × 10^−2)	0.00025 (9.4 × 10^−5)	0.0080 (1.0 × 10^−1)	0.00267 (3.4 × 10^−1)	0.96	3.0 × 10^−6	7.5 × 10^−6
	923	0.0811 (5.4 × 10^−2)	0.00005 (1.8 × 10^−5)	0.0100 (3.0 × 10^−2)	0.00299 (8.1 × 10^−3)	0.91	7.9 × 10^−6	1.8 × 10^−5
2	1023	0.0285 (2.7 × 10^−2)	0.00040 (3.2 × 10^−5)	0.0069 (2.5 × 10^−2)	0.0043 (1.4 × 10^−3)	0.97	1.5 × 10^−5	8.7 × 10^−4
	973	0.0466 (5.4 × 10^−2)	0.00019 (1.8 × 10^−4)	0.0100 (9.0 × 10^−2)	0.0024 (1.1 × 10^−3)	0.93	1.4 × 10^−5	2.8 × 10^−4
	923	0.0679 (7.7 × 10^−2)	0.00007 (5.6 × 10^−5)	0.0181 (3.2 × 10^−1)	0.0012 (8.2 × 10^−4)	0.92	2.4 × 10^−6	4.8 × 10^−6

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In order to evaluate the related thermodynamic relevance, the models were further screened by application of the criteria designed to evaluate the adsorption equilibrium constants obtained in a Langmuirian rate expression, defined by the following equation:⁶⁹

10 ≤ −ΔS ≤ 12.2 − 0.0014ΔH (20)

where ΔS and ΔH are the changes in entropy and enthalpy, respectively. However, the change in the entropies and enthalpies have been estimated using the Van't Hoff expression:where K_i is the adsorption constant (K₁ for CH₄ or K₃ for CO₂). The derived thermodynamic parameters for CH₄ and CO₂ and the related evaluations are synthesized in Table 5. As evident, model 2 emerges as the best kinetic model that represents the mechanism of the reaction: it satisfies the thermodynamic criterion, the R² values (0.98 and 0.99) are considerably higher than the corresponding values derived for model 1 (0.58 and 0.89) that failed to satisfy the thermodynamic criteria.

Table 5 Models screening using change in entropies and enthalpies for CH₄ and CO₂

Reagent	Model no.	ΔH (kJ mol^−1)	ΔS (kJ mol^−1 K)	R ^2	Criteria (eqn (20))
CH4	1	−74.04	−102.92	0.58	10 ≤ 102.92 ≤ 115.85 (yes)
	2	−68.84	−97.87	0.98	10 ≤ 97.87 ≤ 108.58 (yes)
CO2	1	−77.25	−121.20	0.89	10 ≤ 121.20 ≤ 120.35 (no)
	2	−76.49	−117.21	0.99	10 ≤ 117.21 ≤ 119.30 (yes)

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The temperature dependence of the reaction rate parameters derived from model 2 is shown in the following equations obtained from the Arrhenius plots (depicted in Fig. 7) of the K₁, k₂, K₃ and k₄ constants:

K₁ = 7.82 × 10⁻⁶ exp(8280/T) (22)

k₂ = 4.80 × 10³  exp(−16 470/T) (23)

K₃ = 7.54 × 10⁻⁷  exp(9200/T) (24)

k₄ = 6.32 × 10²  exp(−12 110/T). (25)

The adsorption equilibrium constants K₁ and K₃ increase with decreasing reaction temperature, as expected since the CH₄ and CO₂ adsorptions are exothermal processes. The reaction rate constants k₂ and k₄ follow an opposite trend. It is interesting to note that the k₄ values are noticeably higher than the k₂ rate constants related to the methane cracking. From this, it is possible to derive that the catalysts kinetically inhibited the carbon deposition in accordance with analogous observations reported by other authors.^20,39

Fig. 7 Effect of the temperature on the adsorption (K₁ and K₃) and reaction constants (k₂ and k₄) for the Langmuir–Hinshelwood kinetic model (model 2).

The absence of the carbon deposition observed in all experimental tests suggests that the catalyst stabilizes CH_x decomposition and CO disproportion that is likely the mechanism for carbon deposition during the dry reforming reaction.⁴⁹ The ability to activate the C–H bond cleavage requires the electron pair donation from CH₄ to the unfilled d-orbital of nickel. The high d-electron density of the Ni atoms, as previously revealed by XPS studies, inhibits this process.³⁴ Similarly, the evidenced suppression of CO chemisorptions shown by this catalytic system may increase the activation barrier for CO dissociation.

The activation energies related to CH₄ and CO₂ were 136.9 and 100.6 kJ mol⁻¹, respectively, which are higher than the corresponding values derived with the power law rate expression. This is reasonable considering that the Langmuir–Hinshelwood rate expression takes into account the adsorption/desorption enthalpies. Thus, the predicted values are expected to be higher than the power law expression.⁷⁰

The parity plot showing the comparison between the experimental and predicted CH₄ reaction rates is shown in Fig. 8. The kinetic model shows a good fit with the experimental data with a correlation coefficient of R² = 0.97.

Fig. 8 Statistical fit of the postulated model 2 comparing the rate predicted by the model to the experimental rate.

Conclusions

The kinetics of methane dry reforming over the Ce_0.70La_0.20Ni_0.10O_2-δ catalyst has been evaluated at CH₄ and CO₂ partial pressures ranging between 5 to 50 kPa at 923, 973 and 1023 K. The reaction mechanism was proposed on the basis of literature and experimental observations.

The experimental data were fitted into the power law and Langmuir–Hinshelwood kinetics expression considering a dual-step with single-(Ni°) and dual-active sites (La₂O₃ support), respectively, for the reaction. The discrimination between the two models, statistically and thermodynamically, was evidenced as the reaction mechanism of the dry reforming reaction over the Ce_0.70La_0.20Ni_0.10O_2−δ catalyst. It can be described by a dual molecular adsorption of both CH₄ and CO₂ on metallic nickel and support (La₂O₃), respectively, with surface reactions as the rate-determining steps. The reaction between CO₂ and support generates the La₂O₂CO₃ species, and is able to react with carbon at the metal–carbon interface to produce CO and clean up the metallic surface.

The high value of the kinetic constant k₄ (reaction between carbonate species and carbon deposited) compared with k₂ (methane cracking) suggests that the catalyst kinetically inhibits the excess of carbon deposition.

Conflicts of interest

There are no conflicts to declare.

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