Improved Homogeneous–Heterogeneous Kinetic Mechanism Using a Langmuir–Hinshelwood-Based Microkinetic
Model for High-Pressure Oxidative Coupling of Methane
Item Type Article
Authors Yu, Yuhang;Lundin, Sean-Thomas B.;Obata, Keisuke;Sarathy, Mani;Takanabe, Kazuhiro
Citation Yu, Y., Lundin, S.-T. B., Obata, K., Sarathy, S. M., & Takanabe, K. (2023). Improved Homogeneous–Heterogeneous Kinetic Mechanism Using a Langmuir–Hinshelwood-Based Microkinetic Model for High-Pressure Oxidative Coupling of Methane.
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DOI 10.1021/acs.iecr.2c04678
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Improved Homogeneous−Heterogeneous Kinetic Mechanism Using a Langmuir−Hinshelwood-Based Microkinetic Model for
High‑Pressure Oxidative Coupling of Methane
Yuhang Yu, Sean-Thomas B. Lundin, Keisuke Obata, S. Mani Sarathy, and Kazuhiro Takanabe *
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sı Supporting InformationABSTRACT: A comprehensive microkinetic mechanism for the oxidative coupling of methane (OCM) was developed by using the model La2O3−CeO2 catalyst at industrially relevant conditions up to 0.9 MPa and a gas hourly space velocity (GHSV) of∼650,000 h−1. A Langmuir−Hinshelwood (LH)-based surface mechanism was coupled with gas-phase reactions (KAM 1-GS mechanism). The developed model was verified against low-pressure experimental results that minimized reaction exotherms. The improved LH mechanism, dividing the adsorption steps and surface reactions, provides flexible temperature and pressure dependencies to reproduce the experimental results across broad pressure
conditions (0.010−0.80 MPa CH4). Specifically, the adsorption constant of C2H4 was found 20 times larger than that of C2H6
due to the π-electron-related high affinity of C2H4to the surface. Additionally, high-pressure conditions were well described by considering the non-isothermal behavior from OCM reactions and heat dissipation from the reactor. The rate of production (ROP) results indicated that the enhanced unselective gas-phase reaction at high pressures caused the loss of C2−3yield.
1. INTRODUCTION
Due to concerns about the depletion of petroleum resources, increasing demand for chemical products, and environmental protection, significant attention is being drawn to the utilization of methane.1 Conversion of methane into high- value-added commodities (e.g., ethylene, ethane, propane, etc.) is performed either directly (single-step transformation) or indirectly (multistep transformation through synthesis gas).
The indirect route is more practical at present, but the direct way has greater advantages in saving energy due to a reduction in the number of processes involved.2 As one of the most promising direct routes, oxidative coupling of methane (OCM) is well known for its high per-pass yield of CH4to C2hydrocarbons, up to 22−25%.3,4
In addition to the potential industrial relevance of OCM, the complex coupling between homogeneous and heterogeneous reactions is of great academic interest.3,5 Arutyunov and Krylov’s review paper provides a good summary of the recent developments in OCM6 and the corresponding mechanistic analysis. The desired OCM products mainly form from the recombination of free methyl radicals in the gas phase (2CH3•
⇌C2H6), which was proven by the experiments of Campbell and Lunsford.7 For establishing an economic OCM process, catalysts with high activity and selectivity toward producing methyl radicals are necessary.8The surface would also oxidize methyl radicals to CO2and CO (COx) and H2O through the CH3O intermediate, which resembles the gas-phase radical quenching pathway.9 Simultaneously, produced C2H6 can be dehydrogenated on the surface to produce C2H4,10which can
be further oxidized to COx.11 The modeling of the reaction network should contain the combination of gas-phase and surface reactions, constituting a complex homogeneous−
heterogeneous reaction network.
Microkinetic analysis is an effective technique to analyze complex reaction networks and elucidate important mecha- nistic information. Valuable insights into a reaction network can be attained by simple models, such as our simplified pseudo-first-order model, to estimate the ratios between rate constants among different pathways.12,13 A well-formulated microkinetic model includes information on pre-exponential factors and activation energies of each elementary step, which reflect the chemical properties of reactants, intermediates, and products, such as bond strength and activity and affinity of the catalyst surface. The resultant reaction mechanism would provide critical information into rate-limiting steps and areas of interest for catalyst development. A sophisticated homoge- neous−heterogeneous reaction network utilizing combustion radical chemistry was reported by Mims et al., where the consequence of the ethylene product was the focus of the study.14 Aparicio et al. implemented an early microkinetic analysis on OCM reactions and observed the significance of
Received: December 30, 2022 Revised: March 14, 2023 Accepted: March 21, 2023
© XXXX The Authors. Published by American Chemical Society
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catalytic oxidation of C2 products on the final selectivity distribution.15Su et al. improved the microkinetic model with additional surface chemical steps and used Brønsted−Evans−
Polanyi relationships16,17between the activation energies and reaction enthalpies to fit a thermodynamically consistent set of surface kinetic expressions.18 The Brønsted−Evans−Polanyi relationships are analogous to similar gas-phase reactions,19 and the microkinetic model and the corresponding thermody- namic methodology were later verified with experimental data.3,20 Sun et al. advanced efforts to create a more useful microkinetic model by introducing catalyst descriptors to give the parameters more physical meaning.21They also provided a detailed pathway of deep oxidation of methyl radical on the catalyst surface. Thereafter, Thybaut et al. added a new pathway for the oxidation of ethylene on the catalyst surface, wherein ethylene molecules can be captured and directly oxidized by a surface oxygen species.22 Kechagiopoulos et al.
further extended the reaction network and investigated the influence of mass transport limitations in their reactor model.23 Later, Karakaya et al. utilized the same reaction network to explore the kinetic behavior under non-isothermal conditions, which captured the significant temperature rise within the catalyst bed associated with the high exothermicity of OCM under low pressure.24,25 Recently, various reported gas-phase mechanisms were compared to better describe the gas-phase experiments in the presence of CH4 and O2 to utilize in the OCM microkinetic study.26 The findings in the gas-phase mechanism were introduced in the microkinetic study on the La2O3−CeO2 catalyst with a reported surface mechanism under low pressure (total 101 kPa).27
Most of the previously proposed surface elementary reactions are based on equivalent gas-phase reactions, with the hydrocarbon reacting directly from the gas phase onto an adsorbed oxygen species (e.g., CH4+ O* ⇌CH3•+ OH*).
Yet, chemisorptions of hydrocarbons (CH4, C2H4, C2H6, etc.) have been observed on metal and metal oxide surfaces,28−30 with higher polarizability (CH4 < C2H6< C2H4), leading to stronger adsorption for unsaturated hydrocarbons.29 C2H4 shows a much stronger interaction with surfaces than CH4
because of the π-electrons in its unsaturated bond, leading to faster combustion.31 Additionally, CO2 and CO exhibit competitive adsorption with hydrocarbons on catalytic surfaces, which further influences the oxidation of hydro- carbons.32 The pseudo-first-order nature of the hydrocarbon activation steps resembles Eley−Rideal (ER) mechanisms, i.e., adsorption steps happening at an equal rate (or the same adsorption constants) among the different hydrocarbons even when the Langmuir−Hinshelwood (LH) mechanism is assumed. ER mechanisms are extremely rare compared to LH mechanisms,33,34and almost all thermal surface-catalyzed reactions can be described using the LH mechanism.34Baxter and Hu proposed that the LH mechanism is generally more accurate for most catalytic reactions of heterogeneous catalysis.35 Despite this, most OCM kinetic models have used several ER-like steps in their mechanisms to simplify the calculation, especially for C2 and C3, which results in ambiguous descriptions of each step, mixing chemisorption steps and surface reaction steps.
The La2O3-based catalyst is known to show both high activity and yield. Song et al. tested various amounts of Sr on La2O3 and reported that the La−Sr−O catalyst achieved a maximum C2yield of 20% at 923 K, showing the advantages of using La2O3-based catalysts.36The superior performance of a
nanofiber La2O3-CeO2catalyst was demonstrated by Noon et al., achieving a maximum C2+yield of 22% at a CH4/O2feed ratio of 4, a temperature of 793 K, and a total molar flow rate of 0.0112 mol gcat−1s−1.37The La2O3−CeO2catalyst was also found to be coke-tolerant, which is beneficial for industrial application. The doping of CeO2into La2O3can improve the catalytic performance as well as the stability in the presence of CO2and H2O.27
Industrial processes are typically beneficial at elevated pressures to increase productivity and reduce capital costs,38 so understanding OCM at higher pressures is an important goal of kinetic modeling. This study aims to improve the kinetic mechanism to describe catalytic behavior under various conditions using the La2O3−CeO2 catalyst, which was obtained from the industry, specifically by introducing explicit adsorption terms for all relevant hydrocarbons. Equilibrium adsorption constants were analyzed to prove the importance of adding adsorption steps for hydrocarbons. All parameters were rationally optimized according to the bond enthalpies and experimentally reported values. The model was first validated using low-pressure experiments diluted with inert gas (Ar) to minimize the contributions of exothermicity from the reaction.
For experimental data at higher reaction pressures from 101 to 901 kPa, the temperature deviations between the catalyst bed and the furnace set point were predicted using the established kinetic model. The difference in rates and selectivities was effectively explained by introducing a heat transfer model, which enables the prediction of temperature profiles and the heat transfer coefficient of the reactor used in this study. Both elevated temperature and pressure accelerate the total reaction rates, enhancing the productivity per reactor volume almost proportional to the reaction pressure. To understand high- pressure OCM reactions better, a quantitative comparison of the rate of production (ROP) for surface and gas-phase pathways was performed between low and high pressures. The oxidation of hydrocarbons to CO in the gas phase contributed more prominently as the pressure increased, which is one of the main reasons for the C2yield loss at high pressures.
2. EXPERIMENTAL METHODS
2.1. Catalyst. The nanofiber La2O3−CeO2 catalyst39 is a promising catalyst for industrial application because of its high activity and coke tolerance.24 The La2O3−CeO2 nanofiber catalyst used in this study was provided by Japan Vilene Company, Ltd. The key parameters of the catalyst and the reactor are summarized in Table 1.
2.2. Experimental Reactor.Experimental catalytic meas- urements were performed in a vertical fixed-bed flow reactor using a quartz tube with an inner diameter of 2.5 mm. The catalyst was fixed by quartz wool with quartz rods (2.0 mm outer diameter) on the lower and upper portions to reduce dead space. The temperature profile in the axial direction of the electric furnace was measured, and the catalyst was placed in the center of the highest temperature zone with a K-type thermocouple placed directly outside of the reactor. The temperature was controlled by an Omron controller (Omron, E5CC). CH4 (>99.999%) and O2 (>99.999%) were used as reactants, while Ar (>99.9999%) was used as a diluent in lower partial pressure measurements. Mass flow controllers (Alicat, MC-series) were used to control the flow of reactants. The pressure was controlled using a backpressure regulator and measured at the front of the catalyst bed. The pressure drop through the catalyst bed was measured to be ca. 15 kPa at low
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pressure and up to ca. 100 kPa at the highest pressure tested.
Before gas analysis, water vapor was removed from the exit gas using an ice box (0 °C) condenser. For low-pressure experiments, the effluent gas was measured by a micro gas chromatograph (2-Module Micro GC Fusion, INFICON) with an Rt-Molsieve 5A capillary column (0.25 mm, 10 m, Backflush 1.0 μL) and an Rt-Q-bond capillary column (0.25 mm, 3 m) equipped with a thermal conductivity detector (TCD) for all components. For high-pressure experiments, the effluent gas was measured by a gas chromatograph (GC-2014, SHIMADZU) with a Shincarbon column equipped with a flame ionization detector (FID) for CH4, C2H2, C2H4, C2H6, C3H6, C3H8, and C4H8and a TCD for CO, CO2, H2, and O2. 2.3. Characterization. The Brunauer−Emmett−Teller (BET) method (Micromeritics, 3 Flex) was used to measure the surface area of catalysts as received and after calcination using liquid N2 as the coolant (Table 1). The catalysts were pretreated under vacuum at 573 K for around 3 h to remove any adsorbates before measurement.
Scanning electron microscopy (SEM) images were acquired using a Horiba S-4700 with a 3 kV operating voltage and a working distance of 12 mm (Figure S1). Energy-dispersive X- ray spectroscopy (EDS) was used to conduct compositional analysis. The composition was determined to be 93 wt % La and 7 wt % Ce using a 20 kV accelerating voltage.
2.4. Stability and Activity Tests.Stability measurements were performed on the La2O3−CeO2catalyst at 101 kPa and 1073 K using a total molar flow rate of 7.36×10−5mol s−1 with a CH4/O2feed ratio of 6, both before and after exposure to high-pressure conditions up to 901 kPa (Figure S1).Figure S1a,bshows the SEM images of fresh and spent La2O3−CeO2 catalyst samples tested under low partial pressure (total 101 kPa including balance gas) conditions. The nanofiber size and appearance remain similar between the two samples, suggesting no significant structural changes due to exposure to OCM conditions.Figure S1cshows that the conversion and selectivity were stable for the 24 h test at low partial pressure conditions, suggesting that the data at various conditions collected over time are reliable for kinetic fittings.
A total of 102 data points for low partial pressures were used to fit the kinetic equations using a wide range of conditions (Table 2). Data were obtained for CH4partial pressures of 2,
4, 6, 10, and 20 kPa at each O2partial pressure of 0.2, 0.4, 1.0, and 2.0 kPa, respectively. Of these, 34 points with a CH4/O2
ratio from 3 to 100 were repeated every 50 K from 973 to 1073 K. For model validation at higher pressures, a series of 18 data points were taken using undiluted CH4/O2feed ratios of 6 and 10, an inlet reactor temperature of 1023 K, and pressures of 101 to 901 kPa.
3. MICROKINETIC MODELING METHODS
3.1. Reactor Model. The reactor model employed was a standard one-dimensional (1D) plug flow reactor model using CHEMKIN-PRO 17.0 software, with mass transport equations detailed elsewhere.40 Catalyst pellets in OCM have been shown to have irreducible mass transportation limitations, with differences between interstitial and intraparticle phases, which would require a two-dimensional (2D) model.41However, the La2O3−CeO2 catalyst used in this model was fabricated as a nanofiber without pelletization. The combination of nanofibers and a high bed porosity of 94% was considered sufficient to ignore the intraparticle phase, so a 1D model was assumed to be sufficient. The Thiele modulus and effectiveness are calculated as 0.0372 and 0.9995, respectively, based on the catalyst properties and reaction rates. The calculation steps are listed in the Supporting Information (SI). The values quantitatively show that the mass transportation limitation does not affect so much for the current reactor. The reactor and catalyst parameters are summarized in Table 1.
3.2. Gas-Phase Reaction.The KAM1-GS mechanism was adopted as the gas-phase mechanism in this paper, which includes the AramcoMech,42Alkylaromatics,43PAH,44and 1- GS45mechanisms. The combined mechanism, including a total of 3379 gas-phase reactions with 574 species, was validated by Park, Wang and co-workers46,47using experimental data from the literature. Additionally, 100 gas-phase reactions as well as rate parameters are listed in Table S2 in sequence from the highest one based on the rate of production (ROP) analysis discussed inFigure 6, which would help readers to choose the number of reactions to simplify the gas-phase mechanism according to their needs.
3.3. Surface Reaction. The surface mechanism included 28 elementary catalytic reactions, representing the primary catalytic reactions in OCM up to the C3products (Table 3).
The oxidation reactions of OCM start from the adsorption of O2 and CH4 on the catalyst surface to produce O* surface species. The ultimate products are COx, with the obtained Table 1. Key Parameters of the La2O3−CeO2Catalyst and
the Reactor
catalyst parameters
weight at low/high pressure (mg) 9.0/9.0
density (kg m−3) 6570.6
content of Ce (%) 7.0
BET surface area (m2gcat−1
)
as-received at 25°C 18.0
calcined 2 h at 800°C 16.9
calcined 2 h at 1000°C 9.54
reactor parameters
bed length (mm) 4.5
inner diameter (mm) 2.5
outer diameter (mm) 4.0
bed porosity 0.94
bed density (kg m−3) 407.4
pressure for low (kPa) 101.0
pressure for high (kPa) 101.0−901.0
surface area per length (m) 20.0
Table 2. Experimental Conditions Used for Model Development
low-partial-pressure condition
CH4molar fraction (%) 1.98−19.8
O2molar fraction (%) 0.198−1.98
CH4/O2feed ratio 3.0−100.0
setup temperature (K) 973.0−1073.0
bed pressure (kPa) 101.0
total molar flow rate (mol gcat−1s−1) 0.0165 high-pressure condition
CH4molar fraction (%) 85.74/90.9
O2molar fraction (%) 14.26/9.09
CH4/O2feed ratio 6.0/10.0
setup temperature (K) 1023.0
bed pressure (kPa) 101.0−901.0
total molar flow rate (mol gcat−1s−1) 0.0022−0.0198
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product distribution as a result of kinetic limitations, not thermodynamics. The catalytic reactions include two pathways to form COx: primary COx formation from CH4, and secondary COx formation from C2 and C3. The system was developed assuming an LH mechanism for all components, meaning the reactants were adsorbed on the catalyst surface, reacted as two adsorbed species, and then desorbed.
3.4. Parameter Justification. The reaction rate coef- ficients for both the surface and gas phase were expressed in the Arrhenius form as follows
=
k AT exp( E RTa/ ) (1)
which consists of a pre-exponential factor,A, activation energy, Ea, the universal gas constant, R, the reaction temperature,T, and a temperature dependence factor, β. Both forward and reverse reactions use this expression, andβwas set to zero for
all surface reactions. For adsorption steps, the forward reactions were assumed to be nonactivated, so the activation energies were set to zero. The expression for the adsorption reaction rate,kads,f, was given as follows40
=
k S RT
M
n 2
ads,f 0
(2) whereS0is the initial sticking probability or the probability of a molecule chemisorbing to the surface, Γ is the active site density,nis the reaction order of the surface species, andMis the molar mass.
Due to the large number of parameters that must be solved in the mechanism (Table 3), several relationships and simplifying assumptions were used to reduce the number of independent variables. Pre-exponential factors involving the interaction between the two adsorbed surface species were Table 3. LH-Based Surface Mechanism with Optimized Kinetic Data
no. reactiona Afin cm, mol, s Eaf (kJ mol−1) Abin cm, mol, s Eab(kJ mol−1)
1 O2+ *2 F2O 0.396b 0.0 1.75×1019 81.2
2 H O2 +*FH O2 0.521b 0.0 2.10×1013 54.2
3 2OH*FH O2 * +O 2.25×1019 171 2.17×1019 108
4 CH3• +O*FCH O3 2.54×10−5b 0.0 1.24×1013 283
5 CH4+*FCH4 2.87×10−2b 0.0 1.49×1013 77.2
6 CH4* + *O FCH3* +OH 1.75×1019 112.5 1.75×1019 87.5
7 CH3* FCH3• + 1.24×1013 118 1.50×10−6b 0.0
8 C H2 6+ FC2H6 0.297b 0.0 4.20×1013 80.1
9 C H2 6* + *O FC H2 5* +OH 1.75×1019 104.5 1.75×1019 95.4
10 C H2 5* FC H2 5• + 1.24×1013 118 1.50×10−6b 0.0
11 C H2 4+* FC H2 4 0.198b 0.0 1.77×1013 99.4
12 C H2 4* + *O FC H2 3* +OH 1.75×1019 126 1.75×1019 74.3 13 C H2 5* + *O FC H2 4* +OH 1.40×1019 0.0 1.40×1019 209 14 C H2 3* + *O FC H O2 3 * + 1.75×1019 45.4 1.75×1019 98.0 15 C H O2 3 * + *O FCH O2 * +CHO 1.75×1019 0.0 1.75×1019 420 16 C H3 6+O*FC H O3 6 1.63×10−3b 0.0 1.24×1013 212 17 C H O3 6 * + *O FC H O3 5 * +OH 1.75×1019 108 1.75×1019 92.2 18 C H O3 5 * + *O FC H O2 3 * +CH O2 1.75×1019 151 1.75×1019 187
19 C H3 8+*FC H3 8 1.64×10−6b 0.0 1.24×1013 142
20 C H3 8* + *O FC H3 7* +OH 1.24×1019 101 1.75×1019 98.7 21 C H3 7* + *O FC H3 6* +OH 1.24×1019 11.7 1.75×1019 188
22 C H3 6*FC H3 6+ 1.24×1013 122 1.64×10−6b 0.0
23 CH O3 * + *O FCH O2 * +OH 1.72×1019 6.60 1.69×1019 193
24 CH O2 * + *O FCHO* +OH 1.69×1019 28.3 1.75×1019 172
25 CHO* + *O FCO* +OH 1.75×1019 41.2 1.81×1019 159
26 CO* + *O FCO2* + 1.94×1023 80.0 1.39×1019 417
27 CO+*FCO 1.40×10−4b 0.0 1.24×1013 35.7
28 CO2+*FCO2 9.78×10−3b 0.0 1.24×1013 131
aThe species followed with an asterisk “∗” means the corresponding adsorbed surface species, while a stand-alone "∗" means a surface site.
bIndicates an initial sticking probability. The active site density is 1.29×10−9mol cm−2. Units:A, cm2mol−1s−1for reaction 1b, 3f+b, 6f+b, 9f+b, 12f+b, 13f+b, 14f+b, 15f+b, 17f+b, 18f+b, 20f+b, 21f+b, 23f+b, 24f+b, 25f+b, 26f+b; s−1for reaction 2b, 4b, 5b, 7f, 8b, 10f, 11b, 16b, 19b, 22f, 27b, 28b.
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estimated by transition-state theory,21 while those involving the adsorption of gas-phase species onto the surface were described by initial sticking probabilities usingeq 2. The orders of magnitude of both these pre-exponential factors and the active site density agree well with the literature.21,48 Specifically, the pre-exponential factors were around 1019for the reactions of two surface species and 1013for the desorption steps. Several exceptions were fitted according to temperature dependency, such as forward reaction 26. The initial sticking probability of the methyl radical on several metal oxide catalysts is around 10−4−10−8, according to Tong and Lunsford.9 Other initial sticking probabilities range from 10−4 to 1.0, of which the orders of magnitude are similar to Sun’s work.21 The active site density was calculated to be around 10−9mol cm−2for the La2O3−CeO2catalyst.
In addition to assuming that the adsorption steps were nonactivated, the number of independent activation energy variables was reduced further using thermodynamic relation- ships between the reaction enthalpies, similar to the work of Su et al.18 The reaction enthalpies were calculated from the formation enthalpy of all species. Reactions 11 and 12 are taken as examples. Except for the adsorption steps, each reaction enthalpy is directly related to the difference between the sum of the products’ formation enthalpies and the sum of the reactants’ formation enthalpies, e.g.,
= *+ * * *
H12 HfC H HfOH HfC H HfO
2 3 2 4 (3)
where ΔHfrepresents the formation enthalpy. For adsorption steps, the formation enthalpy is
= *=
H11 HfC H EC HCS
2 4 2 4 (4)
whereΔHfCd2Hd4
−*is the formation enthalpy of the bond between a molecule and an active site, which is equal to the negative of the chemisorption energyECd2Hd4
CS . Then, the formation enthalpy of the surface species can be obtained from the formation enthalpies of the corresponding gas-phase species and the corresponding bond, e.g.,
= +
* *
HfC H HfC H HfC H
2 4 2 4 2 4 (5)
Using this method, some formation enthalpies can be obtained from reaction enthalpies.
The enthalpies of gas-phase species, such asΔHfCd2Hd4, were taken from the previously built databases mentioned inSection 3.2. The enthalpies of reactions 9, 12, and 20 were obtained directly from reaction 6 through the C−H bond energy of hydrocarbon, e.g.,
= +
H12 H6 (QH C H QH CH)
2 3 3 (6)
where the C−H bond energies of methaneQH−CHd3, ethylene QH−Cd2Hd3, ethane QH−Cd2Hd5, and propane QH−Cd3Hd7 are 438.9, 465.3, 423.0, and 416.5 kJ mol−1, respectively.49
Most activation energies were calculated by assuming a Brønsted−Evans−Polanyi relationship, which assumes a linear relationship between the activation energy and the reaction enthalpy for heterogeneous catalysts.17 Elementary reactions with similar properties were classified as individual groups. The description and important parameters of the four reaction families are as follows
(a) Hydrogen abstraction by the surface reaction: reactions 6, 9, 12, 13, 17, 20−21, and 23−25 withα1= 0.550and E01= 100.5.21
(b) Recombination of hydroxyls: reaction 3 withα2= 0.6551 andE02= 130.2.48
(c) C−C cleavage on the surface: reactions 15 and 18 with α3= 0.9752andE03= 185.7.48
(d) Adsorption and oxidation without the Brønsted−
Evans−Polanyi relationship: reactions 14 and 26.
For example, the corresponding activation energies of the third group can be calculated as follows
= + =
Eafi E03 3 H ii( 15, 18) (7)
=
Eabi Eafi Hi (8)
where α3 and E03 represent the Brønsted−Evans−Polanyi coefficient and the intrinsic activation barrier of the third family, respectively;EaifandEaibare the activation energies of the forward and backward reactions; and i represents the corresponding surface reaction number. For the reactions that are not described by the Brønsted−Evans−Polanyi relationship (group d), the activation energies of their forward reaction were optimized.
To obtain activation energies, the forward activation energies of reactions 6, 14, and 26 and some of the chemisorption energies were optimized as parameters to minimize the residual of the criteria function. The detailed optimization model is described in Section 3.5. Initial value ranges, used to optimize the molar heats of chemisorption, | Ecs|, were obtained from the literature to keep the optimization program within a reasonable range. Measured values were not found for the La2O3−CeO2catalyst, so the optimization model inputs were the approximate ranges, assuming similarity to other oxides. The value ranges are summarized in Table S1.
Values used included 60−73 kJ mol−1for CO,53 60−180 kJ mol−1for CO2,54below 300 kJ mol−1for O2,5521.8−65.8 kJ mol−1 for H2O,56 and 124.4−166.8 kJ mol−1 for C2H4.30 Additionally, CH4< C2H6< C2H4was used as a constraint for the corresponding desorption energies based on their polar- izability.29
3.5. Optimization Model.Low-partial pressure conditions were fit using an isothermal model, and then high-partial pressure conditions were fit by adding a simple heat transfer effect to account for the exothermicity.
3.5.1. Low Partial Pressure. While it is typical for kinetic fitting to be performed on low conversion data to maintain an isothermal environment, the kinetic fitting for OCM requires higher conversions to capture the behavior of secondary reactions involving the products. However, the low partial pressure and thin reactor diameter were assumed to have sufficient heat transfer to treat the kinetic data as isothermal for fitting. First, the parameters were adjusted manually to obtain good initial values. Then, a particle swarm optimization algorithm,57 written in Python, was employed to refine the values using the following criteria function
=
=
G(var) E w E min
i n
i T
Ei i 1
low
(9)
=
Eij f x( ; ) Y
ij i ij (10)
=
wEi Ei2 (11)
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wherenlowis the total number of observations in low-pressure conditions;Eiis the error matrix of theith observation,q×1;
Eijrepresents thejth response from theith observation (0 <j≤ q);qis the number of responses retrieved from the model;wEdi
is the weight matrix corresponding to the responses, q × q, which can be either the full matrix (the inverse of the error covariance matrix,σEdi
−2, was used here) or its diagonal matrix
estimated from the residual of the initial fitting;58Yijis thejth response of theith observation; andβis the parameter vector.
After the optimization, the developed model reasonably reproduced the conversion and the selectivities obtained experimentally (Figure S2).
3.5.2. High Partial Pressure. The stability tests on the catalyst indicated that operation under high-pressure con- ditions resulted in a catalyst activity reduction of about half, as Figure 1.Low-pressure experimental (a) C2selectivity and (b) COxselectivity versus CH4conversion of data at 1023 K, CH4of 2−20 kPa, O2of 0.2−2 kPa, a total pressure of 101 kPa, CH4/O2ratios of 3−100, Ar dilution, and a total molar flow rate of 0.0165 mol gcat−1
s−1. (c) Change of CH4pressures at constant O2pressure and (d) change of O2pressures at constant CH4pressure under the same other conditions as low pressure.
High-pressure experimental (e) C2selectivity and (f) COxselectivity versus total pressures at 1023 K, CH4/O2ratios of 3−100 with O2depleted under total pressures of 101−901 kPa without Ar dilution, and total molar flow rates of 0.0022−0.0198 mol gcat−1
s−1to keep the same residence time.
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shown inFigure S1d. Thus, our calculations assumed that the active site density was half for the high-pressure conditions.
Unlike low-partial pressure conditions, high-pressure con- ditions cannot be assumed to be isothermal due to the high exothermicity of the OCM reactions. The high partial pressures of the reactants contribute to fast reaction rates that cause a significant temperature increase in the catalyst bed until the reaction heat and the heat dissipation become balanced. The temperature of the catalyst bed becomes significantly higher than the surroundings, so the predictions from the kinetic model will not agree with the experimental data if the model assumes an isothermal condition. To solve this, heat transfer was added to the model, where a heat transfer coefficient (ht) was optimized to minimize the following criteria function
=
=
G h( ) E w E min
i n
i T
Ei i h t
1
high
t
(12) wherenhighis the total number of observations in high-pressure conditions. The heat loss (Qloss) is as follows
=
Qloss Sh Tt( T0) (13)
where Sis the contact area between the catalyst bed and the surroundings,Tis the temperature in the catalyst bed, andT0 is the set furnace temperature. A parametric study was performed with a step size of 1 W m−2K−1, and the simplified model was sufficient to validate the high-pressure conditions.
Under some high-activity conditions, the O2 conversion reached 100% early in the catalyst bed and caused the simulation to fail due to the difficulty of calculating the O2 mole fraction close to zero. For solutions that failed to converge, the total reactor length (4.5 mm) was split into two sub-reactors to solve this issue. The first sub-reactor modeled both gas-phase and surface reactions until the O2was depleted, while the second sub-reactor only included gas-phase reactions without considering O2in the model. The length of the first sub-reactor (catalyst bed) was reduced until the model converged, and the second sub-reactor (gas phase only) was given an excess length. This technique allowed for the product distribution change based on gas-phase reactions after O2
depletion, but it had limited influence on the mole fraction of gases from the outlet of the first sub-reactor.
3.6. Definition of Conversion and Selectivity. The conversions of O2 (χOd2) and CH4 (χCHd4) were calculated as follows
=n /(n + n )
O O consumed O consumed O
2 2 2 2 (14)
= n /(n +n )
CH carbon carbon CH
4 4 (15)
where nOd2‑consumed is the oxygen consumed during the OCM reaction and ncarbon is the effective molar amount of total carbon products in the outlet, defined as follows
= + + +
+ + + +
+
n n n n n
n n n n
n n
1.5 2 1.5
0.5 1.5 2
1.5
O consumed CO CO C H C H
C H C H C H C H
C H H
2 2 2 2 2 4
2 6 3 6 3 8 4 8
4 10 2 (16)
= + + + +
+ + + +
n n n n n n
n n n n
2( )
3( ) 4( )
carbon CO CO C H C H C H
C H C H C H C H
2 2 2 2 4 2 6
3 6 3 8 4 8 4 10 (17)
where nxis the reactor outlet concentration of species x(i.e., CO, CO2, CH4, O2, C2, C3, or C4). Each product selectivity was calculated as follows
= ×
S i
n
C n
C carbon
i
i
(18) where i= 2, 3, or 4 based on the number of carbons in the corresponding product (e.g., i = 3 for C3H6), and nCdi is the molar amount of the corresponding product in the outlet.
4. RESULTS AND DISCUSSION
4.1. Experimental Data at Various Reaction Pres- sures.The La2O3−CeO2catalyst was very active for OCM. At 1023 K, a CH4feed of 20 kPa, O2of 2 kPa, 101 kPa diluted with Ar, and an O2conversion of 83.9%, the CH4conversion rate reached 357μmol gcat−1s−1. A high total molar flow rate of 0.0165 mol gcat−1
s−1, as well as low partial pressures of the reactants, was used to minimize the reaction heat. The reactants were diluted with Ar to lower their partial pressures to decrease the total reaction rates. A wide range of CH4
conversion was realized by varying the CH4/O2ratio from 3 to 100. The different ratios were distinguished by different colors, as presented in Figure 1a,b, including C2H4, C2H6, CO, and CO2selectivities and O2conversion. The O2 conversion was controlled to be not depleted. Because of the limited reaction rates and reaction heating rates, the conditions were regarded as isothermal and used for the fit of the kinetic model. The changes in CH4 conversion and C2 selectivity as functions of CH4and O2pressures are shown inFigure 1c,d, respectively.
High-pressure conditions were operated at total pressures of 101−901 kPa without dilution, a CH4/O2ratio of 6, 1023 K with O2 depleted, as shown in Figure 1e,f, including C2H4, C2H6, CO, and CO2 selectivities and CH4 conversion. With the increasing total pressures from 101 to 901 kPa, C2 selectivity decreased while the selectivity of COx increased.
This might be because of the increased unselective reaction rates at high pressures due to the rise of both temperature and partial pressure.
4.2. Hydrocarbon Adsorption Steps. The surface mechanism and the kinetic parameters are shown inTable 3, where the adsorption steps were introduced into the hydrogen abstraction reactions of hydrocarbons (e.g., CH4, C2H4, C2H6, and C3) to replace the corresponding Eley−Rideal reactions.
Table 4 shows the ratios of the adsorption equilibrium constants of C2H6,Kads,Cd2Hd6, and C2H4, Kads,Cd2Hd4, over that of CH4,Kads,CHd4, at varying temperatures as well as the adsorption equilibrium constants of CH4, which were calculated from Table 3. The adsorption equilibrium constants of C2H4 and
Table 4. Ratios of Adsorption Equilibrium Constants of C2H6and C2H4over CH4at Varying Temperatures as well as the Adsorption Equilibrium Constants of CH4
temperature (K) Kads,CHd4(m3mol−1) Kads,Cd2Hd6/Kads,CHd4 Kads,Cd2Hd4/Kads,CHd4
973 5.91×10−4 3.84 68.28
1023 3.80×10−4 3.77 59.71
1073 2.55×10−4 3.71 52.87
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C2H6 can be calculated from that of CH4 and the corresponding ratios in Table 4. The relevant adsorption constants are 2.55 ×10−4, 1.35 ×10−2, and 9.46×10−4m3 mol−1at 1073 K for CH4, C2H4, and C2H6, respectively. The concentrations of CH4, C2H4, and C2H6 are 81.0 mol m−3, 0.479 mol m−3, and 0.982 mol m−3 under a pressure of 901 kPa and an O2 conversion of 20%, respectively. Thus, the values of Ki*Piof CH4, C2H4, and C2H6are 2.02×10−2, 6.47
×10−3, and 9.29×10−4, respectively, where that of CH4is the most significant because of its high partial pressure of around
733 kPa. Although the coverage is small, these adsorption equilibrium ratios relative to CH4cause a drastic loss of C2 products. The species with a larger adsorption equilibrium constant is more prone to adsorb, which will be followed by C−H bond activation reflecting the respective C−H bond strength. The loss of C2selectivity originates from the faster transformation of C2H4 relative to that of CH4 according to their large adsorption constant ratio (>50).
Their ratios are all larger than 1, indicating the preferential adsorption of C2products over CH4, which would lead to the Figure 2. Comparison of (a), (b) C2H4 and (c), (d) C2H6 selectivities and (e), (f) CH4 conversion between Eley−Rideal and Langmuir−
Hinshelwood mechanisms under 101 kPa, 973−1073 K, CH42−20 kPa, O20.2−2 kPa, a CH4/O2ratio of 3−100, and a molar flow rate of 0.0165 mol gcat−1
s−1.
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