A Kinetic Model for Catalytic N-Butane Oxidative Dehydrogenation under Oxygen-Free Reaction Conditions in a Fluidized CREC Riser Simulator

Abstract

This study considers the development of a kinetic model for the n-butane oxidative dehydrogenation (ODH) to C₄-olefins using a VO_x/MgO−γAl₂O₃ catalyst. The prepared catalyst contained 5 wt% V on an MgO modified γAl₂O₃ support. The developed catalyst exhibited both weak and medium acid sites, as revealed by NH₃-temperature-programmed desorption. TPR/TPO analyses also indicated that 73% of the loaded VO_x was reducible. Kinetic experiments were conducted in a fluidized CREC Riser Simulator at temperatures ranging from 475–550 °C and residence times of 5–20 s. An optimal C₄-olefin selectivity of 86% was achieved at 500 °C and 10 s, with this selectivity then decreasing at higher temperatures and longer residence times. The kinetic model developed involved a Langmuir–Hinshelwood-type of kinetics that incorporated cracking, oxydehydrogenation, and complete oxidation reactions. Model parameters were determined by fitting experimental data with kinetic parameters established with narrow 95% confidence intervals and low cross-correlation.

1. Introduction

The production of C₄-olefins through the oxidative dehydrogenation (ODH) of n-butane is a potentially important industrial process. C₄-olefins are in high demand due to being used to make petrochemical products like plastics, rubber, and resins [1,2,3]. Traditionally, olefins have been produced through fluid catalytic cracking (FCC), steam cracking, and the catalytic dehydrogenation of light paraffins. In FCC, olefins are a side product, while in steam cracking and in the dehydrogenation of paraffins, olefins are obtained directly [4,5,6]. These conventional processes face the following significant challenges: (a) a significant amount of thermal energy is required due to the endothermic reactions involved, (b) product separation is costly, and (c) catalysts are deactivated by coke, leading to frequent plant shutdowns [7,8,9,10].

The ODH process offers, instead, a more efficient alternative to produce C₃ and C₄-olefins with high selectivity. The overall ODH reaction is exothermic and can therefore, be conducted at lower temperatures. In addition, coke formation is limited. Consequently, the life of the catalyst can be extended significantly [11,12]. However, achieving high olefin selectivity is challenging, given the non-negligible amounts of complete oxidation products such as carbon dioxide. Thus, ODH requires efficient catalysts that limit complete n-butane oxidation [13,14]. These catalysts should supply solid-phase oxygen without having oxygen in the gas phase (gas-phase oxygen-free conditions), boosting, in this manner, olefin selectivity. In this way, metal oxide-based catalysts can function both as catalysts and as solid-phase oxygen providers, with their lattice oxygen favoring ODH olefin selectivity [15,16].

The ODH that converts n-butane into C₄-olefins is described in Figure 1. It involves a partial oxidation step where C₄-olefins are produced. However, several phenomena compete with this desirable reaction: (a) complete oxidation, during which both n-butane and formed C₄-olefins are converted into carbon oxides (CO₂ and CO); (b) the formation of coke, which may lead to catalyst deactivation;(c) a combined ODH and cracking, during which small amounts of unwanted lighter hydrocarbons, such as CH₄, C₂H₄,C₂H₆, C₃H₆ and C₃H_8, are formed [17,18,19]. One should mention that these unwanted lighter hydrocarbons and coke can be further oxidized to form carbon oxides.

Thus, successful ODH requires the development of effective catalysts to improve the desired ODH reaction while minimizing unwanted side effects, such as cracking, coke formation, and complete hydrocarbon species oxidation.

Vanadium oxide-based catalysts are among the metal/support ODH catalysts that have been examined in previous research [20,21,22,23]. Furthermore, a series of magnesium oxide-modified vanadium oxide-based catalysts for alkane ODH has also been recently considered by our research group. These catalysts were characterized using BET, TPD/TPR, MH3-TPD, XRD, FTIR, LRS, and XPS. In particular, XPS analysis showed that the dominant catalyst oxidation species on the MgO-γAl₂O₃ catalyst are likely a blend of the V⁺⁴ and V⁺⁵ species [24].

The kinetics of the oxidative dehydrogenation (ODH) of n-butane to produce olefins have only been studied in a few works. A modified Mars van Krevelen (MK) mechanism was proposed by Grabowski et al. (2006) [25]. This work, which was developed in a fixed bed reactor under anaerobic conditions, suggests that alkane oxidation occurs through a reaction with the lattice oxygen of the metal oxide catalysts. In this kinetic model, it is assumed that the lattice oxygen of the catalyst is responsible for olefin formation while the surface oxygen of the catalyst contributes to the complete oxidation of hydrocarbons into carbon oxides.

Rubio and colleagues (2003) proposed an updated redox model for n-butane ODH. The reaction experiments were performed under anaerobic conditions in a fluidized bed reactor. This model distinguishes between the strongly bounded lattice oxygen and the loosely bounded oxygen of the catalyst studied [26]. This research suggests that the strongly bounded lattice oxygen is more selective towards olefin formation and the loosely bounded oxygen is better for producing carbon oxides. These researchers also considered that ODH is influenced by the oxidation state of the catalyst, with the oxygen species readily reacting with the fed alkanes and the olefin produced contributing to the formation of CO_x products.

The possible implementation of ODH under gas-phase oxygen-free conditions in risers and downer reactors presents new and valuable technological opportunities. These advantages have been demonstrated by our research team for both ethane and propane ODH under gas-phase oxygen-free conditions in a mini-fluidized CREC Riser Simulator [27,28]. The data obtained in this study have led to phenomenological-based kinetics with estimated parameters displaying narrow 95% confidence intervals [15,27,28,29]. Given these encouraging results, and the high prospects of implementing ODH on the industrial scale, research for N-butane ODH employing a VO_x support on an MgO-γAl₂O₃ catalyst, under gas-phase oxygen-free conditions, has been recently developed [24]. This study included an assessment of catalyst synthesis, catalyst characterization, and catalyst performance. Furthermore, based on these positive outcomes, a kinetics and reaction network is established in this article that involves the catalyst lattice oxygen and dominant product species, such as butane, butenes, CO_x and coke, as well as their changes with reaction time. The reported rate equations are highly valuable, given that they can assist in the ODH catalytic reactor development and process scale-up.

2. Results and Discussion

2.1. Catalyst Characterization

Table 1. Summary of Characterization Results for Supports and Catalysts.

Sample	SBET (m2/g)	Dpore (Å)	H2 Uptake (cm3 STP/g)	Reducible V (%)	NH3 Uptake (cm3 STP/g)	Kdes (mmole/gcat.min)	Edes (KJ/mole)
γAl2O3	208	109	-	-	6.03	1.117 ± 0.78	74.43 ± 2.54
5 wt%V/γAl2O3	177	105	9.22	3.02	8.22	1.151 ± 0.89	69.32 ± 2.12
MgO−γAl2O3 (1:1)	152	164	-	-	4.34	1.615 ± 0.71	48.17 ± 2.14
5 wt% V/MgO−γAl2O3	198	89	12.42	3.63	5.56	1.165 ± 0.96	76.97 ± 2.02

reports catalyst characterization results. In this respect, the H₂-TPR analysis of the 5 wt% V/MgO−γAl₂O₃ (1:1) BODH catalyst reveals a distinct peak in the 475–485 °C range, showing controlled oxygen release. In addition, H₂-TPR displays a higher rate of hydrogen consumption. Thus, on this basis, one can consider that a greater amount of oxygen is available in the 5 wt% V/MgO−γAl₂O₃ (1:1). This explains the catalyst’s ability to assist in producing highly selective C₄-olefins. A more detailed description of catalyst properties can be found in Bin Sulayman et al. [24].

Furthermore, results obtained from NH₃-TPD indicate that the 5 wt.%V/γAl₂O₃ catalyst has a higher acidity than the 5 wt.% V/MgO−γAl₂O₃ with MgO. This reduction in acidity can be attributed to the role of the MgO in moderating alumina acidity as well as blocking the acid sites within γAl₂O₃.

The results in Table 1 show the changes on the γ-alumina surface area when adding vanadium and magnesium. In that case, the 208 m²/g for γ-alumina support decreases to 177 m²/g and 152 m²/g for added vanadium and added magnesium, respectively. This reduction in surface area is attributed to the blockage of micropores in the γ-alumina, as the vanadium and magnesium particles can fill or obstruct the tiny support pores. Furthermore, when vanadium and magnesium are added together, it is observed that the vanadium and magnesium phases help each other to achieve a better-added oxide dispersion, leading, as a result, to an average pore size similar to the one for γ-alumina, with mild differences in specific surface area.

2.2. Oxidative Dehydrogenation of N-Butane in the CREC Riser Simulator

Figure 2 illustrates the influence of both reaction time and temperature on N-butane conversion. The data reported are the average values for four of the six consecutive n-butane injections in the CREC Riser Simulator. Typical standard deviations for repeat runs were in the ±7.16–9.56% range, with carbon balances closing in the 95% range, as documented in the upcoming

Table 2. Product Distribution Obtained from Sequential Injections of n-Butane in Oxidative Dehydrogenation Experiments Using the 5 wt%V/MgO-γAl₂O₃ Catalyst at 10 s and Various Reaction Temperatures.

Temperature (°C)	Injection	Selectivity (%)								X.C4H10 (%)	Y.C4H8 (%)
		CO	CH4	CO2	C2H4	C2H6	C3H6	C3H8	C4H8
475	1	6.10	1.63	8.56	3.05	1.30	13.55	2.02	63.80	22.56	14.40
	2	3.57	1.90	7.56	3.45	1.53	13.53	1.96	66.48	18.65	12.40
	3	2.52	2.01	7.21	3.98	1.69	13.84	1.81	66.94	17.70	11.85
	4	2.22	1.97	6.79	3.92	1.78	14.57	1.65	67.11	17.22	11.55
	5	1.98	1.90	6.32	3.84	1.94	15.23	1.53	67.27	17.15	11.54
	6	1.95	1.85	5.66	3.85	2.03	15.02	1.43	68.21	17.03	11.61
500	1	6.35	0.32	10.62	1.30	0.07	5.31	0.64	75.39	32.96	24.85
	2	2.24	0.41	7.22	1.36	0.07	5.57	0.55	84.58	27.51	22.72
	3	1.56	0.46	6.07	1.69	0.10	6.01	0.38	85.73	26.06	21.82
	4	1.42	0.52	4.62	1.91	0.10	6.06	0.32	86.84	26.10	22.20
	5	1.28	0.51	4.00	1.92	0.10	5.97	0.31	86.91	26.05	22.38
	6	1.15	0.49	3.55	1.90	0.11	5.76	0.29	87.14	25.76	22.34
525	1	7.19	0.37	12.03	1.80	0.08	6.88	0.72	70.92	33.51	23.77
	2	2.75	0.50	8.87	1.67	0.09	9.05	0.68	76.38	29.06	22.20
	3	2.02	0.59	7.82	2.18	0.12	9.36	0.50	77.41	28.47	22.04
	4	1.90	0.70	6.20	2.57	0.13	10.10	0.43	77.97	27.69	21.59
	5	1.77	0.71	5.56	2.66	0.15	10.50	0.43	78.22	27.35	21.39
	6	1.63	0.70	5.03	2.70	0.16	10.68	0.41	78.69	27.85	21.92
550	1	7.61	0.33	14.38	1.99	0.07	10.34	0.66	64.62	37.36	24.14
	2	3.28	0.47	9.36	2.53	0.08	11.95	0.64	71.69	32.79	23.51
	3	2.42	0.57	8.74	2.70	0.12	12.53	0.48	72.43	31.17	22.58
	4	2.14	0.66	7.64	2.81	0.12	12.98	0.40	73.24	30.84	22.59
	5	1.93	0.68	6.37	3.03	0.14	13.55	0.41	73.89	30.21	22.32
	6	1.83	0.68	5.31	3.23	0.16	13.95	0.41	74.44	29.65	22.07

. The results obtained for the first and second injections were neglected from further analysis, given that they tended to yield lower olefin selectivities. This behaviour was assigned to the catalyst-surface-adsorbed oxygen, available for ODH, following catalyst regeneration. One should note, in this respect, that the stability of the average n-butane conversion values for the four successive n-butane injections allowed one to neglect catalyst deactivation, an important kinetic model assumption.

Figure 2 reports that both temperature and reaction time have positive effects on n-butane conversion, which rises from 9% at 475 °C in 5 s to 37% at 550 °C and 20 s. Thus, longer contact times and higher temperatures are desirable properties for promising ODH, given that these conditions lead to more effective lattice oxygen utilization.

Figure 3 shows the influence of temperature and reaction time on product selectivity. The data reported here correspond again to the average values for data collected from four of the six n-butane consecutive injections. In the data reported in Table 2, one can see that there is a narrow range of selectivity variations, which allows one to disregard catalyst deactivation effects during successive runs.

Figure 3 reports that longer reaction times lead to a decrease in C₄-olefin selectivity while simultaneously increasing CO_x production. Thus, on this basis, shorter contact times (e.g., 10 s), which favorably facilitate ODH in downer or riser units, are preferred. Furthermore, in Figure 3, one can observe that 500 °C provides an optimum selectivity, reaching 90% butene selectivity, at 10 s. This behaviour can be assigned to the difference in magnitude between pre-exponential factors and energies of activation for ODH and CO_x formation. As a result, one can conclude that the kinetic constant values reflect the significant influence of temperature and contact time on reaction selectivity, favoring butene formation at specific optimal conditions.

Table 2 reports the various chemical species selectivities and butane conversions obtained for one complete run at 10 s reaction time and 500 °C, 525 °C, and 550 °C. Every run was developed using six consecutive injections, with catalyst regeneration being conducted after every run. All runs, as with the ones reported in Table 2, were repeated three times. One can observe that, for injections 3–6, reproducible butane conversions and C₂, C₃, C₄ olefin selectivities were obtained. All this points to the adequate and stable performance of the 5 wt%V/MgO-γAl₂O₃ catalyst. It has to be mentioned that only injection 1 and 2 yielded some extra butane conversion, likely due to the butane reaction with the catalyst labile oxygen, and, as a result, they were not used in the kinetic model analysis.

One should note, as shown in Table 2, that carbon-containing products other than C₄-olefins were also detected. These were CO, CO₂, CH₄, C₂H₄, C₂H₆, C₃H₆, and C₃H₈. In particular, the percentage yields of the CH₄, C₂H₄, C₂H₆, C₃H₆, and C₃H₈ species were below 2% (Table 2), and, as a result, their corresponding formation and consumption rates, as shown in Figure 1, are disregarded in the upcoming kinetics analysis.

Furthermore, the possible influence of thermal cracking in the ODH kinetics was also deemed negligible. This was the case given that, under the most extreme conditions, thermal cracking (temperature: 550 °C, reaction time: 20 s) was found to contribute no more than 2% to n-butane conversion.

Finally, experiments developed in the CREC Riser Simulator also allowed one to ascertain that the C₄-Olefin/H₂ ratio significantly surpassed the value of 1 while falling consistently in the 3.09–3.99 range. This supports the hypothesized oxidative dehydrogenation of n-butane, via catalytic ODH. Further information about this matter can be found in a previous study [24].

2.3. Kinetic Parameters Estimation

The kinetics of ODH can be based on the reaction network described in Figure 1 using a number of sound simplifications, as described in Section 2.2, with an effectiveness factor of 1; this gives an estimated Thiele Modulus lower than 1.

On this basis, the rate of N-butane consumption can be expressed as follows:

$$\begin{array}{l}{\displaystyle \frac{{\mathrm{dp}}_{\mathrm{C}4\mathrm{H}10}}{\mathrm{dt}}}=-{\displaystyle \frac{{\mathrm{W}}_{\mathrm{c}}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{R}}}}\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=-{\displaystyle \frac{{\mathrm{W}}_{\mathrm{c}}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{R}}}}{\displaystyle \frac{\left({\mathrm{k}}_1+{\mathrm{k}}_2\right){\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}10}}{\left(1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{p}}_{\mathrm{COX}}\right)}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times \exp -\mathsf{\lambda }\left({\mathrm{X}}_{\mathrm{C}4\mathrm{H}10}\right)\end{array}$$

(1)

Furthermore, the rate of butene formation can be described as:

$$\begin{array}{l}{\displaystyle \frac{{\mathrm{dp}}_{\mathrm{C}4\mathrm{H}8}}{\mathrm{dt}}}=-{\displaystyle \frac{{\mathrm{W}}_{\mathrm{c}}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{R}}}}\left({\mathrm{r}}_1-{\mathrm{r}}_3\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}={\displaystyle \frac{{\mathrm{W}}_{\mathrm{c}}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{R}}}}{\displaystyle \frac{\left({\mathrm{k}}_1{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}10}-{\mathrm{k}}_3{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}8}\right)}{\left(1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{p}}_{\mathrm{COX}}\right)}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times \exp -\mathsf{\lambda }\left({\mathrm{X}}_{\mathrm{C}4\mathrm{H}10 }\right)\end{array}$$

(2)

Finally, the rate of CO_X formation can be expressed as follows:

$$\begin{array}{l}{\displaystyle \frac{{\mathrm{dp}}_{\mathrm{COX}}}{\mathrm{dt}}}=-{\displaystyle \frac{{\mathrm{W}}_{\mathrm{c}}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{R}}}}\left(4{\mathrm{r}}_2+4{\mathrm{r}}_3\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}={\displaystyle \frac{4{\mathrm{W}}_{\mathrm{c}}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{R}}}}{\displaystyle \frac{\left({\mathrm{k}}_2{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{k}}_3{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}8}\right)}{\left(1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{p}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{p}}_{\mathrm{COX}}\right)}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times \exp -\mathsf{\lambda }\left({\mathrm{X}}_{\mathrm{C}4\mathrm{H}10 }\right)\end{array}$$

(3)

with V_R (cm³) representing the volume of the reactor, W_c (g) standing for the weight of the catalyst, pi (atm) denoting the partial pressure of the “i” species, R (cm³ atm mol⁻¹K⁻¹) being the universal gas constant, T (k) representing the reactor temperature, and t (sec) denoting the reaction time.

Regarding Equations (1) to (3), and due to the absence of activity decay after the second n-butane injection, the λ decay parameter was set to zero for the analyses of the third, fourth, fifth, and sixth injections.

2.4. Adsorption Constants

Equations (1)–(3) include adsorption constants. These parameters may display strong correlations, and, as a result, one must be careful when selecting the approach to be adopted for their numerical derivations.

To address this issue, adsorption studies were developed in the mini-fluidized CREC Riser Simulator, with adsorption constants for the various chemical species on the γ-alumina support being determined using the following equations:

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{i}}^{\mathrm{A}}}{{\mathrm{V}}_{\mathrm{m}}}}={\displaystyle \frac{{\mathrm{K}}_{\mathrm{i}}{\mathrm{p}}_{\mathrm{i}}}{1+{\mathrm{K}}_{\mathrm{i}}{\mathrm{p}}_{\mathrm{i}}}}$$

(4)

$${\mathrm{K}}_{\mathrm{i}}={\mathrm{K}}_{\mathrm{i}}^0\exp \left[{\displaystyle \frac{-\Delta {\mathrm{H}}_{\mathrm{i}}}{\mathrm{R}}}\left({\displaystyle \frac{1}{\mathrm{T}}}-{\displaystyle \frac{1}{{\mathrm{T}}_{\mathrm{m}}}}\right)\right]$$

(5)

with “${\mathrm{V}}_{\mathrm{i}}^{\mathrm{A}}$” referring to the volume of the species that is adsorbed on the surface, V_m representing the volume of monolayer, K_i denoting the species adsorption constant (atm⁻¹), p_i standing for the species’ partial pressure (atm), ${\mathrm{K}}_{\mathrm{i}}^0$ being the pre-exponential factor of the adsorption constant (atm), −ΔH representing the heat of adsorption (kJ/mole), and T_m, being the selected median temperature.

On this basis, the adsorption parameters were calculated using a regression fitting process conducted by using a Nonlinear ModelFit built function in Wolfram Mathematica [24].

Table 3. Adsorption Parameters of Different Species. Tm = 515 °C.

Parameter (atm−1)	Estimated Value with 95% Confidence Spans	Parameter (KJmol−1)	Estimated Value with 95% Confidence Spans
${\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}^0$	0.83 ± 0.03	$-\Delta {\mathrm{H}}_{\mathrm{C}4\mathrm{H}10}$	31.2 ± 0.72
${\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}^0$	0.41 ± 0.012	$-\Delta {\mathrm{H}}_{\mathrm{C}4\mathrm{H}8}$	60.8 ± 1.20
${\mathrm{K}}_{\mathrm{COX}}^0$	0.50 ± 0.018	$-\Delta {\mathrm{H}}_{\mathrm{COX}}$	54.0 ± 1.05

reports the adsorption constants and heats of adsorption for the dominant species involved in the ODH butane conversion. The narrow 95% confidence spans show the limited parameter variation and, as a result, their potential phenomenological value.

2.5. Intrinsic Kinetic Parameters

The estimation of the six parameters (${\mathrm{k}}_1^{*0}={\mathrm{k}}_1^0{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}^0$, ${\mathrm{k}}_2^{*0}$ = ${\mathrm{k}}_1^0{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}^0, {\mathrm{k}}_3^{*0}={\mathrm{k}}_3^0{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}^0$, E₁, E₂, and E₃) was conducted using nonlinear least-squares regression. The MATLAB function “lsqnonlin” was employed for this regression analysis. The numerical integration of the differential system, described in Equations (1)–(3), and the determination of the 95% confidence intervals for each estimated parameter were performed using the MATLAB functions “ode45” and “nlparci”, respectively. It was assumed that all reaction rate constants and activation energies had to lead to positive values during optimization.

The six kinetic parameters were estimated using a Trust Region Reflective Method, which minimized the objective function, as described in Equation (6):

$$\mathrm{SSQ}=\sqrt{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{p}}_{\mathrm{i},\mathrm{experimental}}-{\mathrm{p}}_{\mathrm{i},\mathrm{theoretical}}\right)}^2}$$

(6)

With this end in mind, various partial pressures of “i” components (n-butane, butene and CO_x species) obtained both experimentally, and predicted via the kinetic model, were considered in parameter regression using Equation (6). The lowest sum of squares (SSQ), as per Equation (6), was used for determining correlation coefficients (R₂) and achieving model discrimination.

Table 4. Summary of Intrinsic Kinetic Parameters, with 95% Confidence Intervals (CIs), for the Proposed Kinetic Model when Using the 5 wt% V/MgO−γAl₂O₃ Catalyst.

Parameters	Value	95% CI	Correlation Matrix
			${\mathrm{k}}_1^{*0}$	${\mathrm{k}}_2^{*0}$	${\mathrm{k}}_3^{*0}$	E1	E2	E3
${\mathrm{k}}_1^{*0}$	2.64 × 10−5	±2.66 × 10−7	1
${\mathrm{k}}_2^{*0}$	4.87 × 10−7	±4.97 × 10−9	−0.41	1
${\mathrm{k}}_3^{*0}$	2.23 × 10−7	±4.57 × 10−9	0.40	−0.88	1
E1	89	±8.92	−0.19	−0.25	0.23	1
E2	42	±4.87	−0.36	0.86	−0.79	−0.28	1
E3	44	±5.34	−0.39	0.86	−0.89	−0.21	0.75	1
m	576
DOF	570

reports the six estimated parameters, along with their corresponding 95% confidence intervals (CIs), when using a 5 wt% V/MgO−γAl₂O₃ catalyst.

As reported in Table 4, a high DOF (degrees of freedom) was used in this analysis to adequately calculate the six model parameters. The degree of freedom (DOF) was 570 and accounted for 576 experimental data points, minus the six kinetic constants that were numerically regressed. This was the case, given that every experimental condition considered included the third to sixth butane consecutive injections (excluding the first and second ones), with runs being repeated three times. The catalyst was regenerated after every complete run.

Table 4 shows that the estimated parameters were defined with reduced and desirable 95% confidence intervals. The other important information that can be seen in Table 4 is the low degree of cross-correlation between parameters (smaller than 1), with all reported cross-correlation coefficients being below 0.89.

When analyzing the activation energies reported in Table 4, several noteworthy observations emerged: (a) firstly, the BODH (Equation (1)) exhibits a favorable butene selectivity, given the large 2.64 × 10⁻⁵ mol.gcat⁻¹.s⁻¹ frequency factor; (b) conversely, despite the relatively high activation energy of 42 kJmol⁻¹, the transformation of N-butane to CO_x (Equations (1) and (3)) is constrained by a very low-frequency factor; (c) lastly, the Equation (2) reaction, which involves the CO_x obtained from the C₄-olefins, is substantially limited due to the combination of a 44 kJmol⁻¹ activation energy and a small 2.32 × 10⁻⁷ mol.gcat⁻¹.s⁻¹ frequency factor. These findings are consistent with n-butane ODH kinetics, which confirm a triangular reaction network.

Furthermore, the high reaction rate constants for the formation of C₄-olefins from N-butane through ODH point toward a highly selective C₄-olefins process. Additionally, the very low kinetic constant required for complete C₄-olefin oxidation can be explained given the expected role of magnesium oxide. Magnesium oxide reduces surface acidity, which inhibits C₄-olefin re-adsorption and thus contributes to high C₄-olefin selectivity.

To gain further insight into the accuracy of the proposed kinetic model, and that of the estimated parameters, the reactant and product partial pressure model predictions were compared with the experimental data. Figure 4a–d illustrate these comparisons. It is noteworthy to mention that the model predictions align closely with the experimental data, thus validating the proposed BODH reaction model, within the limits of experimental error.

Furthermore, the analysis presented in Figure 5 shows that the data do not exhibit any clear clustering patterns, suggesting that there are no significant external factors influencing the observed conversion changes. Additionally, the cross-correlation matrix, as shown in Table 4, reveals that the estimated parameters are weakly correlated. This further validates the reliability of our proposed kinetic model. Overall, these findings demonstrate that both the established adsorption and the kinetic parameters, along with the developed model, predict BODH reaction rates within the range of the operating conditions studied.

In this study, we compared the activation energies of BODH, obtained using different supported VO_x catalysts, with values reported in the technical literature. Our findings, presented in

Table 5. Comparison of Activation Energies for Main BODH Product Formation.

Catalysts	Activation Energies of Formation (KJ/mole)			Reference
	C4-Olefins	Carbon Oxides
VOx/MgO−γAl2O3	89	42 a	44 b	Present Study
VOx/CeO2−γAl2O3	90.2	105.5 a	81 b	[30]
V2O5/Al/Mg	88.6	37.4 a	45.4 b	[31]
VOx/Al2O3	70.2	65 a	81.3 b	[32]

^a Formation from N-butane. ^b Formation from C₄-olefins.

, demonstrate that the 5 wt%V/MgO−γAl₂O₃ fluidizable catalyst exhibits a similar activation energy to other catalysts used for the formation of C₄-olefins from N-butane (Step 1). Additionally, our research indicates that the 5 wt%V/MgO−γAl₂O₃ catalyst has the lowest activation energy for C₄-olefins oxidation compared to those reported in the literature (Equation (3)). Thus, these results confirm that the C₄-olefins selectivity is enhanced by a severe constrained placed on C₄-olefins in regard to being further C₄-olefin oxidation into carbon oxides.

Furthermore, the 5 wt%V/MgO−γAl₂O₃ fluidizable catalyst that was developed exhibited minimal coke formation (<0.02 wt %), as demonstrated in Table 5. This is a remarkable feature. This finding supports the conclusion that the λ decay parameter can be considered negligible in this case, as highlighted in this study. This beneficial characteristic of the 5 wt%V/MgO−γAl₂O₃ catalyst is a significant feature that is not present in other vanadium-supported catalysts for BODH [12,30,33,34,35].

In summary, the catalytic experiments conducted in this study, using a 5 wt%V/MgO−γAl₂O₃ fluidizable catalyst, in the CREC Riser Simulator provide a strong corroboration of the value of a phenomenologically based kinetic model. This BODH kinetics has the significant advantage of facilitating the development of a BODH process that employs a twin circulating fluidized bed configuration consisting of a BODH reactor and a dense fluidized bed catalyst regenerator [15]. The integrated BODH fluidized bed process is projected to achieve a 26% conversion of n-butane with a valuable 87% selectivity towards C₄-olefins. Thus, this makes the ODH a promising avenue to explore further in regard to the production of olefins and, in particular, butenes.

3. Experimental Methods

3.1. Catalyst Synthesis and Characterization

The catalyst employed in this study, consisting of a 5 wt%V/MgO−γAl₂O₃, was prepared using a wet saturation impregnation technique. The γAl₂O₃ support (SASOL, Sasolburg, South Africa, Catalox SSCa 5/200) underwent modification with magnesium, and the vanadium loading was achieved using an ammonium metavanadate (NH₄VO₃; Sigma–Aldrich, Saint Louis, MO, USA, 99%) precursor. Various characterization techniques, including BET surface area analysis, X-ray diffraction (XRD), H₂-temperature-programmed reduction (H₂-TPR), NH₃-temperature-programmed desorption (TPD), pyridine Fourier transform infrared spectroscopy (FTIR), laser Raman spectroscopy (LRS), and X-ray photoelectron spectroscopy (XPS), were used to characterize the catalyst. The detailed syntheses and characterization procedures for the catalyst, used in oxidative dehydrogenation (ODH), can be found in a recent publication by Bin Sulayman et al. [24].

3.2. Oxidative Dehydrogenation of N-Butane Using Catalyst Lattice Oxygen

The BODH experiments were conducted by using a 5 wt% V/MgO−γAl₂O₃ catalys, in the CREC Riser Simulator, which is a bench-scale mini-fluidized bed reactor. The reactor operates under batch conditions and is designed to evaluate catalysts and conduct kinetics relevant for circulating fluidized beds, such is the case of risers and downers [36]. An overview of the operating procedures and system configurations was previously described by de Lasa [36]. Additional details regarding the CREC Riser Simulator unit are provided in Appendix A.

In the experiments of this study, six consecutive injections of butane were introduced into the CREC Riser Simulator without having the catalyst regenerated between injections. The runs were conducted at temperatures ranging from 475 °C to 550 °C and contact times varying from 5 to 20 s. Each run utilized 0.7 g of catalyst and 4 mL butane injections while maintaining a constant catalyst-to-feed weight ratio. The degree of catalyst reduction was monitored by comparing its initial oxygen content with its oxygen content after each injection. Instantaneous conversion rates and selectivities to primary products were calculated following every injection. To ensure result reproducibility, all thermal and catalytic experiments were repeated three times.

The analyses of reactor effluents and the methods used to calculate n-butane conversion and product selectivities were detailed in recent publications [24]. Carbon mass balances, accounting for all carbon-containing products (carbon monoxide, methane, carbon dioxide, ethylene, ethane, propylene, propane, and carbon deposited over the ODH catalyst), exceeded 95% in all cases [24].

4. Kinetic Modeling Methods

The oxidative dehydrogenation of n-butane involves a complex parallel-series reaction network. This reaction network can be simplified as follows: (a) the conversion of n-butane to C₄-olefins, (b) the undesired formation of CO_x from n-butane, and (c) the secondary combustion of C₄-olefins to CO_x. In these reactions, the catalyst lattice oxygen serves as the sole source of oxygen:

○

ODH of n-butane to C₄ olefins:

$${ \mathrm{nC}}_4{\mathrm{H}}_{10}+-\mathrm{O}-\stackrel{{\mathrm{VO}}_{\mathrm{X}}/\mathrm{MgO}-{\mathsf{\gamma }\mathrm{Al}}_2{\mathrm{O}}_3 }{\to }{\mathrm{C}}_4-\mathrm{Olefins} +{ \mathrm{H}}_2\mathrm{O}$$

(7)

○

Complete oxidation of n-butane:

$${\mathrm{nC}}_4{\mathrm{H}}_{10}+\left(5+4\mathrm{x}\right)-\mathrm{O}-\stackrel{{\mathrm{VO}}_{\mathrm{X}}/\mathrm{MgO}-{\mathsf{\gamma }\mathrm{Al}}_2{\mathrm{O}}_3 }{\to }{\mathrm{CO}}_{\mathrm{X}}+5{ \mathrm{H}}_2\mathrm{O}$$

(8)

○

Complete oxidation of C₄ olefins:

$${\mathrm{C}}_4-\mathrm{olefins}+\left(4+4\mathrm{x}\right)-\mathrm{O}-\stackrel{{\mathrm{VO}}_{\mathrm{X}}/\mathrm{MgO}-{\mathsf{\gamma }\mathrm{Al}}_2{\mathrm{O}}_3 }{\to }4{ \mathrm{CO}}_{\mathrm{X}}+4{ \mathrm{H}}_2\mathrm{O}$$

(9)

with −O− representing oxygen species on the vanadium oxide lattice.

Reactions as described via Equations (7) and (8) are considered as primary reactions, while a reaction as reported with Equation (9) is considered to be a secondary reaction step. These three reactions steps play a crucial role in determining the selectivity of C₄-Olefins. Based on this, we propose a triangular parallel-series reaction network for the BODH process.

The proposed reaction network suggests that n-butane reacts with the lattice oxygen of the catalyst, leading to the production of both C₄-olefins and CO_x. The associated rate constants for these reactions are denoted as k₁ and k₂, respectively. Additionally, C₄-Olefins can undergo further combustion to form CO_x, with the associated rate constant being designated as k₃.

4.1. Development of the Kinetic Model

In the n-butane oxidative dehydrogenation (BODH) study conducted and discussed in this work, in the absence of gas-phase oxygen, two types of oxygen species can be considered: (a) surface oxygen, or weakly adsorbed oxygen, and (b) lattice oxygen. The surface oxygen facilitates the combustion of n-butane and C₄-Olefins to produce CO_x, while the lattice oxygen plays a key role in providing a controlled release of oxygen, which is crucial for high C₄-Olefins formation.

According to the Langmuir–Hinshelwood mechanism, n-butane, C₄-Olefins, and CO_x are adsorbed at equilibrium on a catalyst surface. Therefore, the surface reaction step is deemed to be the rate-controlling step, in contrast to the species adsorption and desorption steps. According to this mechanism, there are two types of sites: (a) Site1-[V₂O₅-O-], where lattice sites are in an oxidized state, (b) Site 1-[V₂O₅^R], where there are reduced lattice oxygen sites and surface oxygen vacancies, and (c) Site 2-[S], which are the support sites.

Based on this, the following elementary steps can be considered as follows:

• Adsorption of n-butane, on Site-2:

  C₄H₁₀ (g) + [S](s) ←⎯⎯→ C₄H₁₀ − [S](s).

  (10)
• Reaction between adsorbed n-butane in Site 2 and lattice oxygen in Site1-[V₂O₅⁰] with C₄-olefin formation:

  C₄H₁₀ − [S](s) + [V₂O₅-O] (s) → C₄H₈ − [S](s) + H₂O(g) + [V₂O₅^R](s).

  (11)
• Desorption of C₄-olefin formed in Site 2:

  C₄H₈ − [S](s) ←⎯⎯→ C₄H₈ (g) + [S](s).

  (12)
• Reaction between adsorbed n-butane in Site 2 and lattice oxygen [V₂O₅⁰] in Site 1 with formation of CO_x:

  C₄H₁₀ − [S](s) + (5 + 4x) [V₂O₅-O-](s) → 4CO_x(g) + 5H₂O(g) + (5 + 4x) [V₂O₅^R](s) + [S](s)

  (13)
• Reaction between adsorbed butene in Site 2 and lattice oxygen [V₂O₅⁰] in Site 1 with formation of CO_x.

  C₄H₈ − [S](s) + (4 + 4x) [V₂O₅-O-] (s) → 4CO_x(g) + 4H₂O(g) + (4 + 4x) [V₂O₅^R](s) + [S](s).

  (14)
• Site 1 reoxidation with gas-phase oxygen during catalyst regeneration:

  [V₂O₅^R] (s) +0.5 O₂ (g) → [V₂ O₅-O-](s).

  (15)

Thus, on this basis, and as described with Equations (7)–(9), it follows that:

r₁ = k₁θ_C4H10(1 − β)

(16)

r₂ = k₂θ_C4H10(1 − β)

(17)

r₃ = k₃θ_C4H8(1 − β)

(18)

where k_i is the reaction rate constant (mol/gcat.s), r_i stands as the reaction rate (mol/gcat.s), θ_i denotes the surface coverage of the adsorbed species “i”, and β represents the reduced vanadium site fractions. Furthermore, γ + β= 1 represents the reduced and oxidized vanadium site fractions, and θ_C4H10 + θ_C4H8 + θ_COx + θ_v = 1 stand for the support-site fractions.

Therefore, the θ_i the support site fractions can be defined as follows:

$${\mathsf{\theta }}_{\mathrm{C}4\mathrm{H}10}={\displaystyle \frac{{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{C}}_{\mathrm{C}4\mathrm{H}10}}{1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{C}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{C}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{C}}_{\mathrm{COX}}}}$$

(19)

$${\mathsf{\theta }}_{\mathrm{C}4\mathrm{H}8}={\displaystyle \frac{{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{C}}_{\mathrm{C}4\mathrm{H}8}}{1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{C}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{C}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{C}}_{\mathrm{COX}}}}$$

(20)

with K_i representing the adsorption constant in cm³/mol and C_i denoting the concentration of species “i” in mol/cm³.

In order to account for the consumption of the lattice oxygen during BODH reactions, the proposed kinetic model incorporated a time-dependent oxidation extent variable. This extent variable was calculated by comparing the remaining oxygen content of the catalyst after the run to the initial oxygen content of the catalyst before the BODH run. As expected, the degree of catalyst oxidation decreased over successive reaction cycles, requiring reoxidation after a certain number of cycles. In our study, a total of six injections were introduced into the reactor without the reoxidation of the catalyst, given that, beyond this point, a decrease in C₄-olefin selectivity and an increase in cracking products were observed. This change in selectivity can be attributed to the depletion of surface oxygen under these conditions. Thus, catalyst regeneration was performed after six cycles, corresponding to 1/6 of the total catalyst mass flow in a continuous n-butane ODH unit.

To represent the $\mathsf{\phi }$ catalytic activity, a decay function based on the converted n-butane was reported to be suitable for gas-phase free oxygen BODH [15], as follows:

$$\mathsf{\phi }=\exp \left[-\mathsf{\lambda }\left({\mathrm{X}}_{\mathrm{C}4\mathrm{H}10}\right)\right]$$

(21)

where φ is the degree of oxidation of the catalyst, X is the n-butane conversion, and λ is a decay constant. This function has the benefit of accounting for the effects of reaction parameters (concentration, temperature, and reaction time) based on the extent of the oxidation of the catalyst.

According to Equations (16)–(18), β can be linked to φ as:

$$\left(1-\mathsf{\beta }\right)=\mathsf{\phi }$$

(22)

A substitution of Equations (19)–(22) into (16)–(18), can be used to express reaction rates in terms of the partial pressures of different species, as follows:

$${\mathrm{r}}_1={\displaystyle \frac{{\mathrm{k}}_1{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}10}}{\left(1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{P}}_{\mathrm{COX}}\right)}}\times \exp -\mathsf{\lambda }\left({\mathrm{X}}_{\mathrm{C}4\mathrm{H}10 }\right)$$

(23)

$${\mathrm{r}}_2={\displaystyle \frac{{\mathrm{k}}_2{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}10}}{\left(1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{P}}_{\mathrm{COX}}\right)}}\times \exp -\mathsf{\lambda }\left({\mathrm{X}}_{\mathrm{C}4\mathrm{H}10 }\right)$$

(24)

$${\mathrm{r}}_3={\displaystyle \frac{{\mathrm{k}}_3{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}8}}{\left(1+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}10}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}10}+{\mathrm{K}}_{\mathrm{C}4\mathrm{H}8}{\mathrm{P}}_{\mathrm{C}4\mathrm{H}8}+{\mathrm{K}}_{\mathrm{COX}}{\mathrm{P}}_{\mathrm{COX}}\right)}}\times \exp -\mathsf{\lambda }\left({\mathrm{X}}_{\mathrm{C}4\mathrm{H}10 }\right)$$

(25)

This was the case, given the fact that the effects of coke formation on BODH were negligible (<0.02 wt%), thereby excluding any possibility that they could cause catalyst deactivation.

4.2. Kinetic Modeling in the Riser Simulator Reactor

BODH reactions are performed in a well-mixed mini-fluidized batch reactor designated as the CREC Riser Simulator [37]. Equation (26) can be used to describe the rates at which these reactions have been studied at the Chemical Reactor Engineering Centre labs at Western University, as follows:

$${\mathsf{\eta }\mathrm{r}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{R}}}{{\mathrm{W}}_{\mathrm{C}}}} {\displaystyle \frac{\mathrm{d}\left(\frac{{\mathrm{p}}_{\mathrm{i}}}{\mathrm{RT}}\right)}{\mathrm{dt}}}$$

(26)

with V_R being the volume of the reactor (cm³), W_c standing for the catalyst weight (g), p_i representing the partial pressure of a species “i” (atm), R denoting the universal gas constant, T being the temperature of the reactor (K), t standing for the reaction time, and η being the catalyst effectiveness factor.

In the case of an effectiveness factor of 1, the following Equation (27) can be used to determine the reaction rate:

$${\mathrm{r}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{R}}}{{\mathrm{W}}_{\mathrm{C}}}}{\displaystyle \frac{\mathrm{d}\left(\frac{{\mathrm{p}}_{\mathrm{i}}}{\mathrm{RT}}\right)}{\mathrm{dt}}}$$

(27)

As a result, the general rate of reaction for each chemical species can be calculated as follows:

$${\displaystyle \frac{{\mathrm{dp}}_{\mathrm{i}}}{\mathrm{dt}}}={\displaystyle \frac{{\mathrm{W}}_{\mathrm{c}}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{R}}}}{\mathrm{r}}_{\mathrm{i}}$$

(28)

Equations (23)–(25) and (28) can be further employed to derive Equations (1)–(3), already reported in Section 2.3 of the present study.

5. Conclusions

(a)

A reaction kinetics for n-butane ODH, using a 5 wt%V/MgO−γAl₂O₃ (1:1) fluidizable catalyst within an oxygen-free atmosphere, can be successfully established using data obtained from a fluidized bed CREC Riser Simulator.

(b)

The adsorption and intrinsic kinetic parameters from the postulated Langmuir–Hinshelwood rate model can be determined separately via independent adsorption and reaction experiments.

(c)

The evaluated intrinsic kinetic parameters for n-butane ODH (k₁⁰, k₂⁰, k₃⁰, E₁, E₂, and E₃) can be successfully determined using a large degree of freedom (DOF) data set, with satisfactorily reduced 95% confidence intervals and low kinetic parameter cross-correlation.

(d)

The derived n-butane ODH kinetics provides a good estimation of n-butane conversions and butene selectivities at various temperatures and contact times. In particular, the postulated kinetics accurately predicts the n-butane conversions, ranging from 25% to 27%, and C₄-olefins selectivities, ranging from 84% to 87%, at 10 s with negligible coke formation.

(e)

The derived n-butane ODH kinetics provides an excellent tool for riser and downer reactor industrial scale simulations, given that it was derived under operating conditions (temperature, reaction time, partial pressures, catalyst/n-butane weight ratios) close to the ones anticipated for large scale riser and downer units.