Mechanistic investigation of methane steam reforming over Ce-promoted Ni/SBA-15 catalyst

Abstract

Methane steam reforming experiments were carried out at atmospheric pressure for temperatures between 873 and 1073 K and by varying the partial pressure of methane and steam to achieve S:C between 0.5 and 2.5. Mechanistic considerations for Methane steam reforming (MSR) were derived on the basis of Langmuir–Hinshelwood and Eley–Rideal reaction mechanisms based on single- and dual-site associative and dissociative adsorption of one or both reactants. However, discrimination of these models on statistical and thermodynamic grounds revealed that the model representing a single-site dissociative adsorption of methane and steam most adequately explained the data. However, the product formation rates from these experiments were reasonably captured by power-law model. The parameter estimates from the power-law model revealed an order of 0.94 with respect to methane and −0.16 for steam with activation energy of 49.8 kJ mol⁻¹ for MSR. The negative order with respect to steam for methane consumption was likely due to steam inhibition.

Introduction

Methane steam reforming (MSR) is the most important, well-established and economical route which currently accounts to 48 % of the global hydrogen production [1, 2]. Hydrogen or syngas produced via MSR (cf. reaction 1) over Ni-based catalysts is employed in the manufacturing of methanol, ammonia and the Fischer–Tropsch synthesis of hydrocarbons.

$$ {\text{CH}}_{ 4} + {\text{ H}}_{ 2} {\text{O}} \rightleftharpoons {\text{CO }} + {\text{ 3H}}_{ 2} \quad \Delta H_{298}^{0} \; = 20 5. 8\;{\text{kJ}}\;{\text{mol}}^{ - 1}, $$

(1)

$$ {\text{CO}} + {\text{ H}}_{ 2} {\text{O}} \rightleftharpoons {\text{CO}}_{ 2} \, + {\text{ H}}_{ 2} \quad \Delta H_{298}^{0} \; = - 41{\text{ kJ}}\;{\text{mol}}^{ - 1}. $$

(2)

Carbon deposition via hydrocarbon dehydrogenation or CO dissociation (the Boudouard reaction) is a deleterious competing reaction. The performance of the catalyst is typically governed by the particular mechanism on the catalyst [3]. The identification of the sequence of elementary steps in the reaction has been the subject of many investigations and has been corroborated through the application of formal Langmuir–Hinshelwood (LH) and Eley–Rideal (ER) mechanistic formulations [4–11]. In the past decades, several investigations were carried out to explore the mechanism of the MSR and to develop kinetic models for this such complex process. One such kinetic expression to explain the MSR mechanism was proposed by Xu and Froment [12]. Their experiments were carried out over Ni/MgAl₂O₄ spinel catalyst, and they claimed that the adsorption of CO and subsequent formation of CO₂ on the active sites were the rate-determining steps (RDS). The kinetic models of MSR in the previous study, conducted by Xu and Froment, was implemented by Wang et al. [13] to develop the most effective kinetic models for MSR. One of the major claims of that study was the significant enhancement of operating temperatures on the carbon deposition as well as the role of the excess steam in the carbon gasification process. In another study conducted by Bradford and Vannice [14] with Ni supported on either MgO or TiO₂, the surface decomposition of CH₄ (to CH_x, 0 < x < 4) and formation CH_xO were found to be the rate-controlling steps. The support also seemed to serve as a sink for surface hydroxyl species which facilitates CH_xO formation (reaction between adsorbed CH_x and surface OH) at the metal-support interface. They suggested that CO₂ participation was via the reverse WGS reaction and proposed a kinetic model which was insensitive to the value of x. Significantly, the associated mechanism also appeared to be useful for the description of the steam reforming reaction over the same catalyst system.

Berman et al. [15] employed 2 % Ru/4.8 % MnO/α-Al₂O₃ catalyst and observed a decrease in methane consumption with an increase in S:C (steam-to-carbon) and reported that the RDS was the bonding of nascent oxygen species on the active Ru sites and gasification of adsorbed carbon by this intermediate to form adsorbed CO on those sites. Furthermore, an important proposition of the reaction mechanism indicates that the steam molecules were adsorbed on the support active sites and subsequently dissociate on nearby metal sites into adsorbed hydrogen and hydroxyl species, suggesting that some of the reaction intermediates were support related which was analogous to the claims made by Bradford and Vannice [14]. A similar negative influence of steam partial pressure for MSR reactions over Ni/YSZ (yttria-stabilized zirconia) were observed by Dicks et al. [16]. However, Wei and Iglesia [17] claimed that the concentration of steam was kinetically irrelevant with respect to MSR rate based on their experiments conducted over Ni/MgO catalyst. Hence, the only rate-determining step is the methane dissociation on the metal sites (C–H bond activation). This view was reflected by Zeppieri et al. [17] based on their investigation of MSR over BaRh_xZr_(1−x)O₃ catalyst (5 wt.% Rh). The studies by Wei and Iglesia [17] and Zeppieri et al. [18] involved alkalis, Mg and Ba, respectively, which purportedly enhance steam adsorption and in turn spill-over to metal sites [19]. Therefore, the elemental composition of the MSR catalyst is significant from the stand point of methane conversion [20]. In these investigations, methane reforming inhibition by carbon deposition was inevitable [21].

In view of the foregoing literature evidence, there is a need to procure a catalyst for MSR which would be highly active, ensures desired product selectivity and is reasonably stable during the course of the reaction. In a previous study [22], we employed artificial neural network (ANN) analysis of MSR data covering two decades of investigations from different research groups. The ANN input matrix included catalyst design variables, viz Ni loading, support type, for example, SBA-15, SiO₂, α-Al₂O₃ and γ-Al₂O₃; promoters—B, Mo, Zr, Ce, catalyst reduction temperature using H₂ as well as reactor operating variables such as S:C ratio $W_{{{\text{cat}}}} /F_{{{\text{CH}}_{4} }}$, reforming temperature and pressure to determine the overall product yield and conversion [21]. Results from the ANN model were taken further for empirical verification and the experimental outcomes suggested that a catalyst with composition 1 wt.% Ce/10 wt.% Ni/SBA-15 may be most suitable for the methane reforming reaction [22]. Therefore, methane consumption rates over 1 wt.% Ce/10 wt.% Ni/SBA-15 was used to evaluate the intrinsic kinetics for MSR employing empirical power-law modelling which elucidated approximately 1st (0.94) order with respect to methane and a negative (−0.16) order dependency on steam [22]. Further, in this study, we have used the methane consumption data from experiments carried out in our previous study [22] and evaluated in terms of the formal LH and ER models to determine MSR mechanism over 1 wt.% Ce/10 wt.% Ni/SBA-15. In this investigation, the mechanistic models were proposed using reaction pathways that are defined by the most abundant reactive intermediates (MARI) which are converted into products through surface reaction over the one or more catalyst active sites [6, 23–25]. Nevertheless, mechanistic model based on single-site dissociative adsorption of methane and steam adequately captured the rate behaviour on the Ce/Ni/SBA-15 catalyst.

Experimental

Support and catalyst preparation

The SBA-15 support was synthesized as detailed by Zhao et al. [26], a mixture of HCl and tri-block copolymer (EO₂₀-PO₇₀-EO₂₀) (Pluronic P123) (chemicals used in this study were procured from Sigma-Aldrich, unless otherwise specified) was stirred continuously at 308 K until the copolymer was dissolved completely. Tetraethyl orthosilicate was added to the mixture, and the stirring was continued for another 20 h, at 308 K; later the mixture was held at 373 K for 48 h. Upon filtration, the solid obtained was calcined at 773 K for 6 h, to remove the template resulting in pristine white SBA-15 which was pelletised at six ton pressure followed by size reduction and pre-treatment at 1073 K for 6 h. Aqueous solutions of Ni(NO₃)₂·6H₂O and Ce(NO₃)₃·6H₂O were used as precursors for Ni and Ce, respectively. The catalysts 1 wt.% Ce/10 wt.% Ni/SBA-15 was prepared via wet impregnation of SBA-15 support using Ni and Ce precursors. After impregnation, the wet solid samples were dried at 375 K for 24 h followed by calcination in air at 1123 K for 6 h to obtain the oxide catalysts.

Catalysts characterization

Multi-point BET surface area, pore volume and diameter of both fresh and used catalysts were measured via N₂ physisorption at 77 K using Quantachrome Autosorb unit, and the samples were held at 573 K for 3 h before analysis. Powder X-ray diffraction (XRD) pattern of the calcined catalyst was obtained on X’pert Pro multipurpose X-ray diffraction (MPD) system using Cu Kα radiation (λ = 0.154 nm) operated at 40 mA and 45 kV. NH₃-, CO₂-temperature-programmed desorption (TPD) and pulse H₂-chemisorption were conducted employing Micromeritics Autochem 2910. The calcined catalysts were reduced in situ with H₂ at 1073 K for 2 h at a heating rate of 10 K min⁻¹ and then cooled to 383 K under flowing N₂, followed by pulse injection of 10 % H₂/N₂. The solid sample was cooled to 323 K after reduction for NH₃- and CO₂-TPD followed by passage of 10 % NH₃/N₂ and 10 % CO₂/He, respectively, and subsequent desorption of the relevant probe gas at heating rates of 10, 15, 20 and 30 K min⁻¹.

Catalysts activity evaluation and reaction metrics

The catalyst activity test was conducted in a stainless steel fixed bed reactor operated under atmospheric pressure with an internal diameter of 10 mm using 0.25 g of catalyst (with particle size 140–200 µm) supported on quartz wool. Distilled and deionised water was fed in specific quantities from a small reservoir via Gilson Minipuls 3M 312 peristaltic pump by passage through a steam generator and mixer maintained at 453 K to form S:C feed mixture with ratios varying from 0.5:1 to 2.5:1. This mixture was further diluted in Ar and supplied as feed stream (at a fixed gas-hourly space velocity, GHSV = 2.5 × 10⁴ h⁻¹) downwards from the top end of the reactor. These conditions ensured negligible external and internal transport intrusions in the collection of subsequent rate data. Runs were carried out in the range 873–1073 K. Prior to each activity test, the catalyst was reduced in a stream of 50 % H₂/Ar flowing at 55 mL min⁻¹ for 2 h at 1073 K. Moisture was removed by passing the gas over a steam trap maintained at 275 K, and the dry gas composition was analysed by gas chromatography on a Shimadzu GC-8A equipped with a thermal conductivity detector.

The catalyst performance was evaluated in terms of CH₄ conversion $(X_{{{\text{CH}}_{ 4} }} )$, consumption rate $(r_{{{\text{CH}}_{ 4} }} )$, product selectivity (S_i, i = H₂, CO and CO₂) and product yield (Y _i) that are calculated as shown in Eqs. 3–8.

$$ X_{{{\text{CH}}_{ 4} }} = \frac{{F_{{{\text{CH}}_{ 4} }}^{\text{In}} - F_{{{\text{CH}}_{ 4} }}^{\text{Out}} }}{{F_{{{\text{CH}}_{ 4} }}^{\text{In}} }}, $$

(3)

$$ r_{{{\text{CH}}_{ 4} }} { = }\frac{{F_{\text{CH4}}^{\text{In}} - F_{\text{CH4}}^{\text{Out}} }}{{M_{\text{SA}} \times W_{\text{catalyst}} }}, $$

(4)

$$ {\text{S}}_{\text{i}} = \frac{{r_{i} }}{{\sum\limits_{{{\text{i = H}}_{ 2} , {\text{CO,CO}}_{ 2} }} {r_{i} } }}, $$

(5)

$$ Y_{{{\text{H}}_{2} }} \; = \;\frac{{ 2 {\text{F}}_{{{\text{H}}_{2} }}^{\text{out}} }}{{3({\text{F}}_{{{\text{CH}}_{ 4} }}^{\text{in}} + {\text{F}}_{{{\text{CH}}_{2} {\text{O}}}}^{\text{in}} )}} \times 100, $$

(6)

$$ Y_{\text{CO}} \; = \;\frac{{2F_{{CO_{2} }}^{\text{out}} }}{{\left( {F_{{{\text{CH}}_{ 4} }}^{in} + F_{{{\text{H}}_{2} {\text{O}}}}^{in} } \right)}} \times 100, $$

(7)

$$ Y_{{{\text{CO}}_{ 2} }} \; = \;\frac{{3F_{{{\text{CO}}_{ 2} }}^{\text{Out}} }}{{\left( {F_{{{\text{CH}}_{ 4} }}^{\text{in}} + F_{{{\text{H}}_{ 2} {\text{O}}}}^{\text{in}} } \right)}} \times 100, $$

(8)

where F stands for molar flow rate (mol s⁻¹), w_catalyst is the catalyst weight (g) used in the reaction, M_SA is the active metal surface area (m² g ⁻¹_catalyst ) and ${\text{r}}_{{{\text{CH}}_{ 4} }}$ is the specific activity for methane consumption (mol m⁻² s⁻¹)

Results and discussion

Catalyst characterization

The physiochemical properties of calcined support, unpromoted and promoted catalysts are presented in Table 1; BET surface area, pore volume and pore size of calcined catalysts had smaller values than the support as a result of pore blockage by Ni metal particles. A similar trend was observed between unpromoted and promoted SBA-15 supported catalysts.

Table 1 Physiochemical properties of support, unpromoted and promoted catalysts

The Ni metal dispersion and specific metal surface area for SBA-15-supported catalysts were found to be low due to the increased metal particle size resulting from a high ratio of metal deposition in the abundant mesopores to the metal deposition on surface of SBA-15 structure [27].

Figure 1a, b shows the NH₃- and CO₂-TPD profiles of Ce/Ni/SBA-15 catalyst. Ce promotion resulted in decreasing the acid-to-basic sites concentration of Ni/SBA-15 catalyst by 12 % while Ni loading of the bare support lead to significant increase of 171 %. The SBA-15 support has weak Lewis acid (465–690 K) and basic sites (365–430 K), which is in agreement with other studies [28, 29]. The activation and deactivation kinetics corresponding to the catalyst property used in this study was discussed in detail in our previous work [22]

Fig. 1

TCD signals for a NH₃-TPD and b CO₂-TPD on calcined 1 wt.% Ce/10 wt.% Ni/SBA-15

Figure 2 shows small-angle X-ray diffractogram of synthesized SBA-15 after removal of template at 773 K for 6 h; distinctive three peaks which can be indexed as (1 0 0) (1 1 0) and (2 0 0) between 2θ angle of 0.9° to 1.7° validate the p 6 mm hexagonal symmetry of the mesopores, while the same X-ray diffractogram enlarged by an order of 20 shows small but sharp peaks between 2° and 3.5° associated to (2 1 0) (3 0 0) (2 2 0) and (3 1 0) indicating the abundance of these mesopores [26].

Fig. 2

Template removed small-angle XRD diffractogram of SBA-15

Effect of reactant partial pressure on product distribution

It is worth mentioning that Kinetic and mechanism investigations may be carried out by employing mole fraction or partial pressure of reactants for ideal gas mixtures [3]. Methane steam reforming and products formation rates were obtained from MSR runs carried out at temperatures between 873 and 1073 K by varying $P_{{{\text{CH}}_{ 4} }}$ between 9.1 and 45.6 kPa and $P_{{{\text{H}}_{ 2} {\text{O}}}}$ between 11.4 and 57.0 kPa, which corresponds to S:C of 0.5:1–2.5:1 and free from any transport limitations [21]. Figure 3 shows a representative transient profiles of these feed composition for methane partial pressure $(P_{{{\text{CH}}_{ 4} }} )$ 11.41 kPa and steam partial pressure $(P_{{{\text{H}}_{ 2} {\text{O}}}} )$ 22.82 kPa (i.e., S:C = 2:1) at a temperature of 1073 K. Figure 3 displays methane conversion levels reaching constancy very early during reforming, which indicates steady-state condition. However, CO initially peaked before levelling off, while CO₂ showed a steady increase with time to plateau after 3 h time-on-stream. In similarity with the methane conversion profiles, H₂ formation rates exhibited quick steady state and thereafter remained invariant with time.

Fig. 3

Transient dry composition profiles of methane steam reforming and H₂, CO and CO₂ for S:C = 2:1 at 1073 K

Figures 4, 5 and 6 show the product selectivity, ratio and yield, respectively, as a function of $P_{{{\text{CH}}_{ 4} }}$ and $P_{{{\text{H}}_{ 2} {\text{O}}}}$ at 1073 K. Figure 4a, b, clearly indicates that the change in partial pressure of methane or steam does not affect H₂ selectivity significantly. However, CO selectivity decreased with increasing $P_{{{\text{H}}_{ 2} {\text{O}}}}$ (cf. Fig. 4b) or with decreasing (cf. Fig. 4a) and conversely a corresponding increase was observed in CO₂ selectivity. Maximum CO selectivity (Fig. 4a, b) and yield (Fig. 6a, b) were observed only when P _CH4 = P _H2O; this behaviour substantiates that increasing steam partial pressure results in more CO converted to CO2 via water–gas shift (WGS) reaction (cf. Eq. 2). Furthermore, this fact was reflected in product ratios (cf. Fig. 5a, b). Increasing partial pressure of steam resulted in H₂:CO increase while H₂:CO₂ and CO:CO₂ decreased. Both H₂ and CO₂ were produced during WGS reaction; H₂ production rates were in order of magnitude higher in comparison to CO₂ rates. The yield profiles (cf. Fig. 6a, b) were similar to selectivity profiles with the exception of H₂ yield.

Fig. 4

a Selectivity of products at 1073 K as function of $P_{{\text{CH}_{4} }}$ $(P_{{\text{H}_{2} \text{O}}} { = }\; 2 2. 8 2\; {\text{ kPa)}}$, b selectivity of products at 1073 K as function of $P_{{\text{H}_{2}\text{O}}}$ $(P_{{\text{CH}_{4} }} = 2 2. 8 2\; {\text{ kPa)}}$

Fig. 5

a Ratio of products at 1073 K as function of $P_{{\text{CH}_{4}}}$ $(P_{{\text{H}_{2} \text{O}}} = 2 2. 8 2\; {\text{ kPa)}}$, b ratio of products at 1073 K as function of $P_{{\text{H}_{2} \text{O}}}$ $(P_{{\text{CH}_{4} }} = 2 2. 8 2\; {\text{ kPa)}}$

Fig. 6

a Product yields at 1073 K as function of $P_{{\text{CH}_{4} }}$ $(P_{{\text{H}_{2} \text{O}}} = 2 2. 8 2\; {\text{ kPa)}}$, b Product yields at 1073 K as function of $P_{{\text{H}_{2}\text{O}}}$ $(P_{{\text{CH}_{4} }} { = }\; 2 2. 8 2\; {\text{ kPa)}}$

Maximum H₂ yield was observed only when $P_{{{\text{H}}_{ 2} {\text{O}}}} \; = \;P_{{{\text{CH}}_{ 4} }}$ ; yield was measured on the basis of net production of H₂ from total amount of H₂O available in the feed composition. Although an increase in steam partial pressure contributes to a corresponding increase in H₂ in the feed. This resulted in a fractional H₂ increase in the products, which subsequently reflected as a significant decrease in H₂ yield. These observations evidently indicate a significant quantity of H₂ was produced via reforming, and a very small fraction was produced via WGS reaction.

Mechanistic considerations

Kinetic rate expressions with Langmuir–Hinshelwood (LH) and Eley–Rideal (ER) approach were considered. Mechanistic models were proposed on the basis of single- and dual-site Langmuir–Hinshelwood mechanisms. Employing Eley–Rideal models which admit the possibility of one reactant remaining in gas phase while the other is adsorbed on the active site were explored. Both the approaches involved associative and dissociative adsorption of the reactants [17, 19, 30].

Langmuir–Hinshelwood mechanisms

These elementary reaction steps proposed here are routed on the assumption that methane and steam are associatively adsorbed on a single or an identical site (X represents active site):

$$ \begin{array}{*{20}l} {{\text{CH}}_{ 4} {\text{ + X}} \leftrightarrow {\text{CH}}_{ 4} - {\text{X}}} \hfill \\ {{\text{H}}_{ 2} {\text{O + X}} \leftrightarrow {\text{H}}_{ 2} {\text{O}} - {\text{X}}} \hfill \\ {{\text{CH}}_{ 4} - {\text{X + H}}_{2} {\text{O}} - {\text{X}} \to {\text{CHO}} - {\text{X}} + 2{\text{H}}_{2} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CHO}} - {\text{X}} + {\text{X}} \leftrightarrow {\text{CO}} - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CO}} - {\text{X}} + {\text{H}}_{ 2} {\text{O}} - X \to {\text{CO}}_{ 2} - X + {\text{H}}_{ 2} - {\text{X}}} \hfill \\ {{\text{CO}} - {\text{X}} \leftrightarrow {\text{CO}} + {\text{X}}} \hfill \\ {{\text{CO}}_{ 2} - {\text{X}} \leftrightarrow {\text{CO}}_{ 2} + {\text{X}}} \hfill \\ {2{\text{H}} - {\text{X}} \leftrightarrow {\text{H}}_{ 2} - {\text{X}} + {\text{X}}} \hfill \\ {{\text{H}}_{ 2} - {\text{X}} \leftrightarrow {\text{H}}_{ 2} + {\text{X}}} \hfill \\ \end{array}. $$

These elementary reaction steps proposed here are based on the assumption that dissociative adsorption of methane and steam takes place on a single or an identical site:

$$ \begin{array}{*{20}l} {{\text{CH}}_{ 4} + 2{\text{X}} \leftrightarrow {\text{CH}}_{ 3} - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CH}}_{ 3} - {\text{X}} + {\text{X}} \leftrightarrow {\text{CH}}_{ 2} - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CH}}_{ 2} - {\text{X}} + {\text{X}} \leftrightarrow {\text{CH}} - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{H}}_{ 2} {\text{O}} + 2{\text{X}} \leftrightarrow {\text{OH}} - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{OH}} - {\text{X}} + {\text{X}} \leftrightarrow O - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CH}} - {\text{X}} + {\text{O}} - {\text{X}} \leftrightarrow {\text{CHO}} - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CHO}} - {\text{X}} + {\text{X}} \leftrightarrow {\text{CO}} - {\text{X}} + H - {\text{X}}} \hfill \\ {{\text{CHO}} - {\text{X}} + {\text{O}} - {\text{X}} \leftrightarrow {\text{CO}}_{ 2} - {\text{X}} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CO}} - X \leftrightarrow {\text{CO}} + {\text{X}}} \hfill \\ {{\text{CO}}_{ 2} - X \leftrightarrow {\text{CO}}_{ 2} + {\text{X}}} \hfill \\ { 2 {\text{H}} - {\text{X}} \leftrightarrow {\text{H}}_{ 2} - {\text{X}} + {\text{X}}} \hfill \\ {{\text{H}}_{ 2} - {\text{X}} \leftrightarrow {\text{H}}_{ 2} + {\text{X}}} \hfill \\ \end{array}. $$

The elementary reaction steps proposed below are based on the assumption that preferential associative adsorption of methane and steam on dual or different active sites (X₁ and X₂) available on the catalyst surface:

$$ \begin{array}{*{20}l} {{\text{CH}}_{4} + {\text{X}}_{1} \leftrightarrow {\text{CH}}_{4} - {\text{X}}_{1} } \hfill \\ {{\text{H}}_{2} {\text{O}} + {\text{X}}_{2} \leftrightarrow {\text{H}}_{2} {\text{O}} - {\text{X}}_{2} } \hfill \\ {{\text{CH}}_{4} - {\text{X}}_{1} + {\text{H}}_{2} {\text{O}} - {\text{X}}_{2} \to {\text{CHO}} - {\text{X}}_{1} + 2{\text{H}}_{2} + {\text{H}} - {\text{X}}} \hfill \\ {{\text{CHO}} - {\text{X}}_{1} + {\text{X}}_{2} \leftrightarrow {\text{CO}} - {\text{X}}_{1} + {\text{H}} - {\text{X}}_{{22}} } \hfill \\ {{\text{CO}} - {\text{X}}_{1} \; + {\text{H}}_{2} {\text{O}} - {\text{X}}_{2} \to {\text{CO}}_{2} - {\text{X}}_{1} \; + {\text{H}}_{2} - {\text{X}}_{2} } \hfill \\ {{\text{CO}} - {\text{X}}_{1} \leftrightarrow {\text{CO}} + {\text{X}}_{1} } \hfill \\ {{\text{CO}}_{2} - {\text{X}}_{1} \leftrightarrow {\text{CO}}_{2} + {\text{X}}_{1} } \hfill \\ {2{\text{H}} - {\text{X}}_{2} \leftrightarrow {\text{H}}_{2} - {\text{X}}_{2} + {\text{X}}_{2} } \hfill \\ {{\text{H}}_{2} - {\text{X}}_{2} \leftrightarrow {\text{H}}_{2} + {\text{X}}_{2} } \hfill \\ \end{array}.$$

The elementary reaction steps proposed below are based on the assumption that preferential dissociative adsorption of methane and steam on dual or different active sites (X ₁ and X ₂) available on the catalyst surface:

$$ \text{CH}_{4} + 2\text{X}_{1} \leftrightarrow \text{CH}_{3} - X_{1} + \text{H} -\text{X}_{1} $$

$$ \text{CH}_{3} - \text{X}_{1} + X_{1} \leftrightarrow \text{CH}_{2} - \text{X}_{1} + \text{H} - \text{X}_{1} $$

$$ \text{H}_{2} \text{O} + 2\text{X}_{2} \leftrightarrow \text{OH} - \text{X}_{2} + \text{H} - \text{X}_{2} $$

$$ \text{OH} - \text{X}_{2} + \text{X}_{1} \leftrightarrow \text{O} - \text{X}_{1} + \text{H} - \text{X}_{2} $$

$$ \text{CH}_{2} - \text{X}_{1} + \text{O} - \text{X}_{1} \leftrightarrow \text{CHO} - \text{X}_{1} + \text{H} - \text{X}_{1} $$

$$ \text{CHO} - X_{1} + \text{X}_{1} \leftrightarrow \text{CO} - \text{X}_{1} + \text{H} - \text{X}_{1} $$

$$ \text{CHO} - \text{X}_{1} + \text{O} - \text{X}_{1} \leftrightarrow \text{CO}_{2} - X_{1} + \text{H} - \text{X}_{1} $$

$$ \text{CO} - \text{X}_{1} \leftrightarrow \text{CO} + \text{X}_{1} $$

$$ \text{CO}_{2} - \text{X}_{1} \leftrightarrow \text{CO}_{2} + \text{X}_{1} $$

$$ 2\text{H} - \text{X}_{1} \leftrightarrow \text{H}_{2} - \text{X}_{1} + \text{X}_{1} $$

$$ 2\text{H} - \text{X}_{2} \leftrightarrow \text{H}_{2} - \text{X}_{2} + \text{X}_{2} $$

$$ \text{H}_{2} - \text{X}_{1} \leftrightarrow \text{H}_{2} + \text{X}_{1} $$

$$ \text{H}_{2} - \text{X}_{2} \leftrightarrow \text{H}_{2} + \text{X}_{2}. $$

Eley–Rideal mechanism

Associative molecular adsorption of methane with steam in the gas phase was assumed for these elementary reaction steps:

$$ \text{CH}_{4} + \text{X} \leftrightarrow \text{CH}_{4} - \text{X}_{1} $$

$$ \text{CH}_{4} - \text{X} + \text{X} \leftrightarrow \text{CH}_{2} - \text{X} + \text{H}_{2} - \text{X} $$

$$ \text{CH}_{2} - \text{X} + \text{H}_{2} \text{O} \to \text{CH}_{2} \text{O} - \text{X} + \text{H}_{2} $$

$$ \text{CH}_{2} \text{O} - \text{X} + \text{X} \leftrightarrow \text{CHO} - \text{X} + \text{H} - \text{X} $$

$$ \text{CHO} - \text{X} + \text{X} \leftrightarrow \text{CO} - \text{X} + \text{H} - \text{X} $$

$$ \text{CO} - \text{X} + \text{H}_{2} \text{O} \to \text{CO}_{2} - \text{X} + \text{H}_{2} $$

$$ \text{CO}_{2} - \text{X} \leftrightarrow \text{CO}_{2} + \text{X} $$

$$ \text{CO} - \text{X} \leftrightarrow \text{CO} + \text{X} $$

$$ 2\text{H} - \text{X} \leftrightarrow \text{H}_{2} - \text{X} + \text{X} $$

$$ \text{H}_{2} - \text{X} \leftrightarrow \text{H}_{2} + \text{X} $$

Dissociative molecular adsorption of methane with steam in the gas phase was assumed for these elementary reaction steps.

$$ \text{CH}_{4} + 2\text{X} \leftrightarrow \text{CH}_{2} - \text{X} + \text{H}_{2} - \text{X} $$

$$ \text{CH}_{2} - \text{X} + \text{H}_{2} \text{O} \to \text{CH}_{2} \text{O} - \text{X} + \text{H}_{2} $$

$$ \text{CH}_{2} \text{O} - \text{X} + \text{X} \to \text{CHO} - \text{X} + \text{H} - \text{X} $$

$$ \text{CHO} - \text{X} + \text{X} \to \text{CO} - \text{X} + \text{H} - \text{X} $$

$$ \text{CO} - \text{X} + \text{H}_{2} \text{O} \to \text{CO}_{2} - \text{X} + \text{H}_{2} $$

$$ \text{CO}_{2} - \text{X} \leftrightarrow \text{CO}_{2} + \text{X} $$

$$ \text{CO} - \text{X} \leftrightarrow \text{CO} + \text{X} $$

$$ 2\text{H} - \text{X} \leftrightarrow \text{H}_{2} - \text{X} + \text{X} $$

$$ \text{H}_{2} - \text{X} \leftrightarrow \text{H}_{2} + \text{X}. $$

By applying quasi-steady-state approximation and integrating the concept of most abundant reactive intermediate (MARI) [6, 23–25], a range of rate expressions were derived for those mechanisms laid out earlier which are summarized in Table 2 (where $P_{{{\text{CH}}_{ 4} }}$ partial pressure of methane,$P_{{{\text{H}}_{ 2} {\text{O}}}}$ partial pressure of steam, $K_{{{\text{CH}}_{ 4} }}$: methane adsorption constant, $K_{{{\text{H}}_{ 2} {\text{O}}}}$: steam adsorption constant,: $k_{\text{rxn}}$ methane steam reforming constant). Illustrations of rate expression derivations are shown in Appendix A.

Table 2 Langmuir–Hinshelwood (LH) and Eley–Rideal (ER) rate models

Further, a nonlinear regression was carried out (using POLMATH 6.0 with Levenberg–Marquardt algorithm for approximating the objective function) with the models from Table 2 using methane steam reforming data (cf. Fig. 7a, b) [22] to evaluate the estimates,$K_{{{\text{CH}}_{ 4} }}$ $K_{{{\text{H}}_{ 2} {\text{O}}}}$ and $k_{\text{rxn}}.$ The results from this exercise are provided in Table 3. Two criteria were used for model selection. The models were considered for further analysis if R ² > 0.9 for any model across the temperature range and an apparent trend for all the estimates with respect to temperature. From Table 3, it is evident that only models 3 and 7 pass these constraints and are therefore subjected to further scrutiny.

Fig. 7

a Specific CH₄ consumption rates as function of $P_{{CH_{4} }}$ $(P_{{H_{2} O}} { = }\; 2 2. 8 2 {\text{ kPa)}}$, b Specific CH₄ consumption rates as function of $P_{{H_{2} O}}$ $(P_{{CH_{4} }} { = }\; 2 2. 8 2 {\text{ kPa)}}$

Table 3 Estimates of mechanistic models for methane steam reforming data

Even though these models are statistically significant, they should also have some thermodynamic relevance. Langmuir–Hinshelwood models can be assessed from the stand point of thermodynamic significance with the aid of Eq. 9 [31]:

$$ 10 \le - \Delta S \le 12.2 - 0.0014\;\Delta H, $$

(9)

$$ {\text{where}}\,\Delta S\; = \,{\text{change in entropy }}\left( {{\text{J mol}}^{ - 1} {\text{K}}^{ - 1} } \right) \text{and} $$

$$ \Delta H\; = \,{\text{change in enthalpy }}\left( {{\text{J mol}}^{ - 1} } \right). $$

Models 3 and 7 represent Langmuir–Hinshelwood rate expressions; therefore, the criterion depicted by Eq. 9 can be employed to evaluate the thermodynamic implication. However, the change in entropies and enthalpies can be abstracted by Eq. 10:

$$ K = - \frac{\Delta H}{RT} + \frac{\Delta S}{R}, $$

(10)

where K = adsorption constant (for methane or steam),

R = ideal gas constant and

T = temperature (K).

The estimated thermodynamic parameters, $\Delta H$ and $\Delta S$, for methane and steam are listed in Table 4. Apparently, model 3 failed to satisfy the thermodynamic criterion, while model 7 provides a meaningful explanation of the data. In particular, the activation energy of 50.76 kJ mol⁻¹ for model 7 from Table 5 which is in close vicinity to the value obtained from macroscopic power-law (E _A = 49.8 kJ mol⁻¹) analysis [22]. The order on methane and steam obtained through power-law model were 0.94 and −0.16, respectively, where the negative order on steam clearly indicates that steam competes for the active sites which are the precursor for methane decomposition [22], and Model 7 representing a single-site was consistent with this finding (Fig. 8).

Table 4 Verification of models using change in entropies and enthalpies for methane and steam

Table 5 Arrhenius parameters for models 3 and 7

Fig. 8

Comparison between model 7 (best model) data and the experimental data

Moreover, X-ray diffractogram of used catalysts from MSR runs carried out at 873 and 973 K (Fig. 9) shows small but distinct peaks at 2θ = 37.2°, 43.2° and 62.8° relative to NiO. While diffractogram corresponding to a catalyst from reaction conducted at 1073 K does not show any peaks for NiO, it is identical to the reduced catalyst pattern. Moreover, this phenomenon indicates the possible involvement of support active sites responsible for the formation of some reaction intermediate species through the adsorption followed by the dissociation of steam molecules on nearby metal active sites which was analogues to claims reported in the literature [13, 14]. Laosiripojana et al. found steam inhibition for MSR initiating around S:C = 1.5–2 with an order on steam partial pressure of −0.4 [32]. Various other studies also claimed a negative order on steam for MSR [15, 16, 33–36]. Therefore, methane steam reforming over Ce-promoted Ni/SBA-15 catalyst appears to proceed via a single-site dissociative adsorption of methane and steam mechanism which is reported by other researchers [12, 32, 37].

Fig. 9

X-ray diffractogram of spent (S:C = 2) at 873–1073 K and reduced catalysts

Conclusions

The kinetic analysis of reaction rate data for methane steam reforming over Ce-promoted Ni/SBA catalyst has been carried out. The Langmuir–Hinshelwood model involving single-site and dissociative adsorption of both methane and steam was adequate in explaining the variability in the experimental data while satisfying statistical significance and thermodynamic constraints. Furthermore, the model was consistent with the evidence of negative order with respect to steam for methane consumption from our previous work. The methane consumption rates tend to drop with increase in S:C (S:C > 1). Hence, for the catalyst used in this study, optimum methane conversion and minimum CO₂ formation could be achieved during MSR when the S:C = 1. The presence of NiO peaks observed in the diffractograms from spent catalyst XRD is consistent with the dissociation of steam molecule during the reaction. Therefore, MSR over 1 wt.% Ce/10 wt.% Ni/SBA-15 catalyst is effectively captured by a Langmuir–Hinshelwood model representing a single-site dissociative adsorption of methane and steam.

Appendix A

• 1. Langmuir–Hinshelwood model for single-site dissociative adsorption of both CH₄ and H₂O molecules. For dissociative adsorption of methane and steam on single site:,

  $$ \theta {\text{CH}}_{ 2} \theta {\text{H}}_{ 2} \; = \;K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} \theta_{X}^{2}, $$
  $$ \theta_{\text{OH}} \theta_{\text{H}} \; = \;K_{{{\text{H}}_{ 2} {\text{O}}}} P_{{{\text{H}}_{ 2} {\text{O}}}} \theta_{X}^{2}, $$

  where θ_i and θ_X are the fraction of active sites occupied by intermediate species i and unoccupied active sites, respectively. The variables on the left hand side of the above expressions can be modified by replacing $\theta_{{{\text{CH}}_{ 2} }} = \theta_{{{\text{H}}_{ 2} }}$ and $\theta_{\text{OH}} = \theta_{\text{H}}$ since these species are formed due to the dissociation of methane and steam, respectively. Therefore,

  $$ \theta_{{{\text{CH}}_{ 2} }} \; = \;\theta_{X} \sqrt {K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} }, $$
  $$ \theta_{\text{H}} \; = \;\theta_{X} \sqrt {K_{{{\text{H}}_{ 2} {\text{O}}}} P_{{{\text{H}}_{ 2} {\text{O}}}} }, $$

  and the site balance for X suggests

  $$ 1 = \,\theta_{X} + \theta_{{{\text{CH}}_{ 2} }} + \theta_{H} + \sum\limits_{{i \ne_{{{\text{CH}}_{ 2} }} }} {\theta_{i} }; $$

  hence, if $\theta_{{{\text{CH}}_{ 2} }}$ and $\theta_{\text{H}}$ are most abundant reactive intermediates, the site balance is reduced to

  $$ 1 = \,\theta_{X} + \theta_{{{\text{CH}}_{ 2} }} + \theta_{\text{H}} ,\,{\text{since}}\,\sum\limits_{{i \ne_{{{\text{CH}}_{ 2} }} }} {\theta_{i} } \approx 0; $$

  substituting $\theta_{{{\text{CH}}_{ 2} }}$ and $\theta_{\text{H}}$ in the above site balance, we get

  $$ 1 = \,\theta_{X} + \theta_{X} \sqrt {K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} } + \theta_{X} \sqrt {K_{{{\text{H}}_{ 2} {\text{O}}}} P_{{{\text{H}}_{ 2} {\text{O}}}} }, $$
  $$ \theta_{X} = \,\frac{1}{{1 + \sqrt {K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} + \sqrt {K_{{{\text{H}}_{ 2} {\text{O}}}} P_{{{\text{H}}_{ 2} {\text{O}}}} } } }}. $$

  Assuming the surface reaction of most abundant reactive intermediates as the rate-determining step,

  $$ r = k\theta_{{{\text{CH}}_{ 2} }} \theta_{\text{OH}}, $$
  $$ r = k(\theta_{X} \sqrt {K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} } )(\theta_{X} \sqrt {K_{{{\text{H}}_{ 2} {\text{O}}}} P_{{{\text{H}}_{ 2} {\text{O}}}} } ). $$
  $$ r = \frac{{k_{rxn} \sqrt {P_{{{\text{CH}}_{ 4} }} P_{{{\text{H}}_{ 2} {\text{O}}}} } }}{{\left( {1 + \sqrt {K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} } + \sqrt {K_{{{\text{H}}_{ 2} {\text{O}}}} P_{{{\text{H}}_{ 2} {\text{O}}}} } } \right)^{2} }}, $$

  where $k_{rxn} \; = \sqrt {K_{{{\text{CH}}_{ 4} }} K_{{{\text{H}}_{ 2} {\text{O}}}} }.$

• 2. Eley–Rideal model for associative molecular adsorption of CH₄ with H₂O in gas phase. Since methane is adsorbed associatively on the site X while steam is unabsorbed,

$$ \theta_{{{\text{CH}}_{ 4} }} = \;K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} \theta_{X}; $$

site balance for X suggests

$$ 1 = \,\theta_{X} + \theta_{{{\text{CH}}_{ 4} }}, $$

$$ 1 = \,\theta_{X} + K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} \theta_{X}, $$

$$ \,\theta_{X} = \;\frac{1}{{1 + K_{{{\text{CH}}_{ 4} }} P_{{{\text{CH}}_{ 4} }} }}. $$

Assuming the bimolecular reaction between methane which is adsorbed on the surface and unabsorbed steam in gas phase as the rate-determining step,

$$ r = \,k\theta_{{{\text{CH}}_{ 4} }} + P_{{{\text{H}}_{ 2} {\text{O}}}}, $$

$$ r = \,k(K_{{{\text{CH}}_{ 4} }} + P_{{{\text{CH}}_{ 4} }} \theta_{X} )P_{{{\text{H}}_{{_{ 2} }} {\text{o}}}}, $$

$$ r = \,\frac{{k_{\text{rxn}} P_{{{\text{CH}}_{ 4} }} P_{{{\text{H}}_{{_{ 2} }} {\text{o}}}} }}{{1 + K_{{{\text{CH}}_{ 4} }} + P_{{{\text{CH}}_{ 4} }} }}, $$

where $k_{rxn} = \;k\;K_{{CH_{4} }}.$