Oxidative Coupling of Methane for Ethylene Production: Reviewing Kinetic Modelling Approaches, Thermodynamics and Catalysts

: Ethylene production via oxidative coupling of methane (OCM) represents an interesting route for natural gas upscaling, being the focus of intensive research worldwide. Here, OCM developments are analysed in terms of kinetic mechanisms and respective applications in chemical reactor models, discussing current challenges and directions for further developments. Furthermore, some thermodynamic aspects of the OCM reactions are also revised, providing achievable oleﬁns yields in a wide range of operational reaction conditions. Finally, OCM catalysts are reviewed in terms of respective catalytic performances and thermal stability, providing an executive summary for future studies on OCM economic feasibility.


Introduction
The oxidative coupling of methane (OCM) represents an interesting alternative process for producing ethylene, typically manufactured in steam-crackers from naphtha [1,2]. Here, OCM developments are critically revised in terms of kinetic mechanisms and respective applications towards chemical reactor modelling and design, discussing current challenges and directions for further research. Furthermore, thermodynamic aspects of the OCM reactions are also discussed, providing achievable olefins yields in a wide range of reaction conditions. Finally, OCM catalysts are revised in terms of the respective catalytic performances and thermal stability, providing an executive summary for future studies on OCM economic feasibility.
This work is organised as follows: Section 2 presents a bibliometric analysis of OCM scientific publications and patents, highlighting geographic, chronological and topic distributions; Section 3 revises OCM reaction and kinetic models, critically analysing chemical reactor modelling approaches; Section 4 summarises thermodynamic aspects of the OCM reactions and presents original calculations for extents of reaction, focusing on presenting maximum ethylene yields in a wide range of temperatures, pressures and feed compositions; Section 5 discusses OCM catalysts, summarising their performances and main features; Section 6 briefly discusses sustainability aspects of the OCM reactions; and, finally, Section 7 presents the main conclusions and opportunities for future work.  Comparison between the chronological distribution of search results using the keyword set (a) (oxidative, methane and coupling) and the prices of WTI crude oil (in USD per barrel) [3] and Henry Hub natural gas (in USD per million BTU) [4]; and the production of U.S. shale gas (in billion ft 3 per day) [5].
Even though it might be expected that higher oil prices could encourage the development of cheaper alternative processes to the conventional cracking of ethane and/or heavier hydrocarbons to produce ethylene, the relationship between WTI crude oil prices and search results does not seem obvious. Instead, it is the price of natural gas that seems to more pronouncedly affect the efforts dedicated to OCM development, in combination with the increased production of shale gas, as previously mentioned.
The above relationship also makes sense when the geographical distribution of search results is considered, as shown in Figure 3, which illustrates how the U.S. appears to dominate the interest in the OCM technology, concentrating the highest number of search results obtained for keyword sets (a) and (b). Figure 3 further illustrates the rank of search results up to the ninth country position, which embraces 73 and 66% of the total number of search results for keywords in sets (a) and (b), respectively, from which the U.S., China, Germany, Japan and Russia represent the five countries that have dedicated the most effort towards the development of OCM technologies. Comparison between the chronological distribution of search results using the keyword set (a) (oxidative, methane and coupling) and the prices of WTI crude oil (in USD per barrel) [3] and Henry Hub natural gas (in USD per million BTU) [4]; and the production of U.S. shale gas (in billion ft 3 per day) [5].
The total number of patents, equal to 284 and 154 for keyword sets (a) and (b), respectively, also supports the previously suggested lack of maturity of the OCM technology, when compared to the numbers of patents filed on established industrial processes in the same period, as suggested by the number of results found while using the search words 'hydrocarbon cracking' and 'methane reforming', which resulted in 8442 and 2326 documents, respectively.
Based on the obtained data, the American companies Siluria Technologies Inc. and Lummus Technology (the latter having recently taken ownership of the former) have so far been the leaders in protecting their OCM developments, presenting a total of 30 patents during the last decade, followed by the Saudi Arabian Sabic Global Technologies, the Chinese Sinopec and the related China Petroleum & Chemical Corporation, the German Linde Group, and the Dutch Shell ( Figure 5). Whereas the leadership on OCM intellectual property protection from American companies can be easily associated with the country's largest worldwide production of natural gas, oil and natural gas liquids (NGL) (which includes ethane, liquified petroleum gas, LPG, and naphtha separated The total number of patents, equal to 284 and 154 for keyword sets (a) and (b), respectively, also supports the previously suggested lack of maturity of the OCM technology, when compared to the numbers of patents filed on established industrial processes in the same period, as suggested by the number of results found while using the search words 'hydrocarbon cracking' and 'methane reforming', which resulted in 8442 and 2326 documents, respectively.
Based on the obtained data, the American companies Siluria Technologies Inc. and Lummus Technology (the latter having recently taken ownership of the former) have so far been the leaders in protecting their OCM developments, presenting a total of 30 patents during the last decade, followed by the Saudi Arabian Sabic Global Technologies, the Chinese Sinopec and the related China Petroleum & Chemical Corporation, the German Linde Group, and the Dutch Shell ( Figure 5). Whereas the leadership on OCM intellectual property protection from American companies can be easily associated with the country's . Filed patent distribution per assignee between 2010 and 2020, from the search using the 'Derwent Innovations Index' database from the "Web of Science" platform and keyword set (b). For clarity, assignees with fewer than 5 filed patents were omitted. Numbers represent 69% of the total number of searched patents.

What Are OCM Scientific Publications and Patents about?
One of the main aims of the present review is the evaluation of the distribution of topics discussed in the published materials, in order to identify areas that have been receiving significant attention or have been seemingly overlooked by the technical communities. Thus, an extracted sample of the scientific papers (containing 120 papers published between 2016 and 2020) and patents (containing 121 deposits filed between 2010 and 2020) obtained from the search using keyword set (b) (ethylene, methane, oxidative, coupling) was evaluated in relation to the main focus of analysis.

What Are OCM Scientific Publications and Patents about?
One of the main aims of the present review is the evaluation of the distribution of topics discussed in the published materials, in order to identify areas that have been receiving significant attention or have been seemingly overlooked by the technical communities. Thus, an extracted sample of the scientific papers (containing 120 papers published between 2016 and 2020) and patents (containing 121 deposits filed between 2010 and 2020) obtained from the search using keyword set (b) (ethylene, methane, oxidative, coupling) was evaluated in relation to the main focus of analysis.
Among the main identified subjects, the development of new catalysts for the OCM reaction seems to constitute the focus of most scientific publications, representing the subject of almost half of the assessed papers, as illustrated in Figure 6, which presents the obtained distribution of topics for scientific publications. In contrast, the remaining subjects have received less attention, with only 20% of mentioned subjects focusing on the mathematical description of the OCM process.
Processes 2021, 9, x FOR PEER REVIEW 6 of 51 compositions (including different oxidants or levels of inert dilution) [67,89], and experimental studies performed to optimise reactor performance through the investigation of the impact of reaction operational conditions on the ethylene yields [16,22,73,90]. Among the main identified subjects, the development of new catalysts for the OCM reaction seems to constitute the focus of most scientific publications, representing the subject of almost half of the assessed papers, as illustrated in Figure 6, which presents the obtained distribution of topics for scientific publications. In contrast, the remaining subjects have received less attention, with only 20% of mentioned subjects focusing on the mathematical description of the OCM process. From the extracted sample of filed patents, a different focus was identified, as illustrated in Figure 7, which presents the topic distribution among the main four identified subject streams. In this case, nearly half of the subjects were related to process flow diagrams, translating ideas of actual OCM process implementations, whereas only 27.8% of the mentioned topics described innovations in catalyst development. In addition, a significant part of the filed patents (almost 20%) proposes the use of OCM to produce other final products, rather than ethylene, such as ethylene oxide, liquid fuels, synthesis gas, poly-alpha-olefins, propylene, propanal, ethylbenzene, among others, therefore illustrating attempts to integrate OCM reactions with other processes. Finally, a smaller number of patents (2.4%) describes alternative processes for methane coupling, involving non-oxidative routes. From the extracted sample of filed patents, a different focus was identified, as illustrated in Figure 7, which presents the topic distribution among the main four identified subject streams. In this case, nearly half of the subjects were related to process flow diagrams, translating ideas of actual OCM process implementations, whereas only 27.8% of the mentioned topics described innovations in catalyst development. In addition, a significant part of the filed patents (almost 20%) proposes the use of OCM to produce other final products, rather than ethylene, such as ethylene oxide, liquid fuels, synthesis gas, poly-alpha-olefins, propylene, propanal, ethylbenzene, among others, therefore illustrating attempts to integrate OCM reactions with other processes. Finally, a smaller number of patents (2.4%) describes alternative processes for methane coupling, involving non-oxidative routes.
Processes 2021, 9, x FOR PEER REVIEW 6 of 51 compositions (including different oxidants or levels of inert dilution) [67,89], and experimental studies performed to optimise reactor performance through the investigation of the impact of reaction operational conditions on the ethylene yields [16,22,73,90]. Among the main identified subjects, the development of new catalysts for the OCM reaction seems to constitute the focus of most scientific publications, representing the subject of almost half of the assessed papers, as illustrated in Figure 6, which presents the obtained distribution of topics for scientific publications. In contrast, the remaining subjects have received less attention, with only 20% of mentioned subjects focusing on the mathematical description of the OCM process. From the extracted sample of filed patents, a different focus was identified, as illustrated in Figure 7, which presents the topic distribution among the main four identified subject streams. In this case, nearly half of the subjects were related to process flow diagrams, translating ideas of actual OCM process implementations, whereas only 27.8% of the mentioned topics described innovations in catalyst development. In addition, a significant part of the filed patents (almost 20%) proposes the use of OCM to produce other final products, rather than ethylene, such as ethylene oxide, liquid fuels, synthesis gas, poly-alpha-olefins, propylene, propanal, ethylbenzene, among others, therefore illustrating attempts to integrate OCM reactions with other processes. Finally, a smaller number of patents (2.4%) describes alternative processes for methane coupling, involving non-oxidative routes.  Among the filed patents related to process flow diagrams focused on ethylene production, five sub-streams of subjects could be identified, as illustrated in Figure 8. These sub-streams included: (1) downstream separation, involving analyses of pressure swing adsorption units or absorption towers, in addition to the conventional cryogenic distillation for separating CH4 and olefins; (2) reactor development, involving analyses of fluidized bed reactors and special configurations for packed-bed reactors, including distinct catalyst bed configurations, specific distribution of catalytic layers, dilution of the catalytic bed with inert solids and the use of multi-stage adiabatic reactors; (3) OCM process flow diagrams, dealing with analyses of process design alternatives, including recycling and the use of distinct separation systems for purification of the OCM output reactor stream; (4) feeding systems and feed compositions, involving analyses of alternatives for mixing of reactants, spatial positioning of feed streams in the reactor vessel, investigation of different reactant feed compositions, and addition of water, CO2, CO and chlorine radical precursors in the conventional CH4 and O2 feed streams; and, finally, (5) energy recovery, focusing on process ideas for utilising the heat produced in the OCM reactor for either adjusting the reactor feed mixture temperature and/or producing steam vapour. The analysis of topic distribution among scientific publications and patents interestingly suggests the distinct perspectives of the scientific community and industrial sector, in which the former seems to be concentrating efforts on the development of improved catalysts, while the latter seems to be trying to find solutions for engineering problems related to process implementation, in terms of downstream separation and reactor design. Therefore, this analysis provides some evidence for the need for further scientific studies concerning engineering aspects of the overall process implementation.

OCM Reactions and Kinetic Models
The oxidative coupling of methane (OCM) involves the conversion of methane mainly into ethane in the presence of oxygen and a suitable heterogeneous catalyst at high temperatures (reaction 1, Table 1).

Reaction
No. The analysis of topic distribution among scientific publications and patents interestingly suggests the distinct perspectives of the scientific community and industrial sector, in which the former seems to be concentrating efforts on the development of improved catalysts, while the latter seems to be trying to find solutions for engineering problems related to process implementation, in terms of downstream separation and reactor design. Therefore, this analysis provides some evidence for the need for further scientific studies concerning engineering aspects of the overall process implementation.

OCM Reactions and Kinetic Models
The oxidative coupling of methane (OCM) involves the conversion of methane mainly into ethane in the presence of oxygen and a suitable heterogeneous catalyst at high temperatures (reaction 1, Table 1). Table 1. Possible global reactions involved in the OCM reaction mechanism [91,92].

Reaction
No.

Reaction
No. 2 11 Ethane can be dehydrogenated to ethene via catalytic heterogeneous or thermal gasphase oxidation (reactions 2 and 3). Partial and complete methane oxidation reactions are the main competitive pathways leading to CO and CO 2 (reactions 4-6). Consecutive reactions account for CO conversion to CO 2 (reaction 7), and ethene oxidation to CO (reaction 8). Moreover, the water-gas shift reaction (in both directions, reactions 9 and 10) and ethene steam reforming (reaction 11) have also been reported as important pathways [92].
The actual fundamental steps of the reaction mechanism described in Table 1 can be very complex, and both catalyst surface and gas-phase reactions must be taken into account to describe the overall kinetics through a model that can remain valid within a wide range of reaction conditions, enabling the more involved industrial reactor design [18,[92][93][94]. It has been discussed that current kinetic models are not able to fully describe available experimental datasets, indicating that models proposed so far may be incomplete [29,95]. In spite of that, pioneering developments on OCM catalytic kinetic models made use of experiments performed in operational regions where gas-phase reactions could be minimised and thus neglected [92]. Similarly, gas-phase reaction kinetics have initially been investigated in the absence of catalysts [96,97].

Kinetics in the Absence of Catalyst
One of the pioneering studies regarding the OCM gas-phase reaction network in the absence of a heterogeneous catalyst was described by Zanthoff and Baerns [98]. These authors compiled a model involving a set of 164 elementary free-radical reactions and used kinetic constants obtained from the combustion literature. Later, dedicated experimental measurements, regression, sensitivity and parameter contribution analyses allowed for the reduction in the reaction network to 33 elementary free-radical reactions (reactions 1-33, Table 2), in accordance with a study that investigated OCM gas-phase reactions at atmospheric pressure, between 600 and 850 • C, using methane to oxygen feed ratios between 4 and 10 with different inert dilution levels, and spatial times between 0.1 and 1.9 m 3 ·s·mol −1 [96]. Table 2. Gas-phase reaction mechanism, as proposed by Chen et al. [96] for describing OCM reactions in the absence of catalysts and at atmospheric pressure.

Reaction
No.

Reaction
No.
a M denotes any other molecular species from the system. However, the reaction network described in Table 2 was not suitable for describing experimental observations at higher pressure conditions up to nearly 1000 kPa [97], leading to the development of a modified and expanded reaction network where some of the reactions from Table 2 were removed and additional steps were included. The modifications accounted for the effect of pressure and the production of propane and propene, resulting in a system of 38 elementary free-radical reactions [97]. For instance, reactions No 11,16,20,25 and 30 from Table 2 were not present in the updated model, which presented reactions No 1-6 summarised in Table 3 instead, in addition to reactions No 7-10, which involved the formation of propane and propene. Table 3. Additional gas-phase reaction steps (in respect to Table 2), as proposed by Chen at al. [97], for describing OCM reactions in the absence of catalysts and under pressures up to 1000 kPa.

Reaction
No.

Reaction
No.
The effect of pressure on the reaction rates involving unimolecular reactions was accounted for using Equation (1), where C M represents the weighted sum of the concentration of all molecular species and k u , k and k ∞ are reaction rate constants. Thus, at low pressure conditions, the reaction order was increased by one due to the influence of C M , while this effect was less important at higher pressure conditions.
According to a contribution analysis performed with the model developed at atmospheric pressure, when the importance of a given reaction step for the consumption or production rate of a given species could be assessed, the methyl radical production originates mainly from hydrogen abstraction from methane by radicals (reaction steps No 2, 4 and 5, Table 2), whereas the initiation step involving molecular oxygen does not play an important role [96]. Moreover, the consumption of methyl radicals is mostly driven by reactions that result in the CO precursors CH 3 O • and CH 2 O (reaction steps No 6-8, Table 2) and return to methane (reactions No 2, 12 and 19, Table 2). This would be the main reason for unselective oxidation, as the reaction leading to ethane production (No 9, Table 2) would account for only 33% of the methyl radical consumption.
The updated kinetic model for the OCM gas-phase reaction system comprised thirteen differential equations, one for each molecule j , and assumed that the reactor behaviour could be described by a plug-flow model at steady state, Equation (2), where temperature and pressure gradients could be neglected. In Equation (2), F j is the molar flow rate of compound j, d t is the reactor inner diameter, v ij is the stoichiometric coefficient of compound j at reaction i, and r i is the reaction rate of reaction i, described according to Equation (3). In Equation (3), k i and k -i are the rate constants of the forward and backward reaction, respectively, C j is the molar concentration of the species j and α ij represents the stoichiometric factor of the reactants. Radical concentrations were defined with the help of the quasi steady-state approximation [96].
The reaction network used to describe the OCM kinetics in the absence of catalyst was later modified and expanded from 38 [97] to 39 [99] reaction steps, although these modifications would not significantly change previous model interpretations. Modified reaction steps (reactions 7, 9 and 10 in Table 3) were re-written considering the presence of a collision partner, M, while the additional included step further accounted for the formation of ethyl radicals from ethane, Equation (4).
These pioneering studies contributed to the understanding of the effects of operational variables on achievable values of conversions and products distribution. For instance, CH 4 conversions have been shown to reach up to approximately 33%, depending on the O 2 feed composition ( Figure 9). However, higher spatial times can lead to a reduction in ethene and ethane selectivities, while CO and CO 2 productions can increase considerably, Figure 10a. The linear effect of temperature, in turn, has also been shown to be positive for increasing CH 4 and O 2 conversions and CO and CO 2 selectivities, whereas ethene and ethane selectivities are reduced (Figure 10b).
Higher pressures were reported to promote CH 4 and O 2 conversions, as shown in Figure 11a, while its effect on selectivities of carbonaceous products was less pronounced and depended on O 2 conversion, Figure 11b. These results suggest that C2 yields might be increased at higher pressures, as higher methane conversions can be achieved while keeping C2 selectivity nearly constant, at least for conditions of high oxygen conversions. A similar effect of pressure was reported by Ekstrom et al. [100] and Beck et al. [101], who showed the beneficial effect of pressure for C2 and C3 yields in the presence of catalyst up to 10 bar. be positive for increasing CH4 and O2 conversions and CO and CO2 selectivities, whereas ethene and ethane selectivities are reduced ( Figure 10b). Figure 9. Effect of spatial time on experimental CH4 conversion for different feed compositions at atmospheric pressure and in the absence of catalyst [96,97]. The maximum temperature across the reactor ranged between 790 and 826 °C at the analysed conditions. Spatial time is defined as the ratio between the reactor volume and the inlet molar flow rate of CH4. Higher pressures were reported to promote CH4 and O2 conversions, as shown in Figure 11a, while its effect on selectivities of carbonaceous products was less pronounced and depended on O2 conversion, Figure 11b. These results suggest that C2 yields might be increased at higher pressures, as higher methane conversions can be achieved while keeping C2 selectivity nearly constant, at least for conditions of high oxygen conversions. A similar effect of pressure was reported by Ekstrom et al. [100] and Beck et al. [101], who showed the beneficial effect of pressure for C2 and C3 yields in the presence of catalyst up to 10 bar.  [96,97]. The maximum temperature across the reactor ranged between 790 and 826 • C at the analysed conditions. Spatial time is defined as the ratio between the reactor volume and the inlet molar flow rate of CH 4 .
Processes 2021, 9, x FOR PEER REVIEW 11 of 51 be positive for increasing CH4 and O2 conversions and CO and CO2 selectivities, whereas ethene and ethane selectivities are reduced ( Figure 10b). Figure 9. Effect of spatial time on experimental CH4 conversion for different feed compositions at atmospheric pressure and in the absence of catalyst [96,97]. The maximum temperature across the reactor ranged between 790 and 826 °C at the analysed conditions. Spatial time is defined as the ratio between the reactor volume and the inlet molar flow rate of CH4. Higher pressures were reported to promote CH4 and O2 conversions, as shown in Figure 11a, while its effect on selectivities of carbonaceous products was less pronounced and depended on O2 conversion, Figure 11b. These results suggest that C2 yields might be increased at higher pressures, as higher methane conversions can be achieved while keeping C2 selectivity nearly constant, at least for conditions of high oxygen conversions. A similar effect of pressure was reported by Ekstrom et al. [100] and Beck et al. [101], who showed the beneficial effect of pressure for C2 and C3 yields in the presence of catalyst up to 10 bar.

Kinetics in the Presence of Catalyst
In the presence of catalyst, and assuming that gas-phase reactions are not significant (as suggested by experiments performed in the absence of catalyst), a one-dimensional, pseudo-homogeneous plug-flow model embracing 10 reaction steps, as presented in Table 4, was able to fairly well describe experimental data obtained over a La 2 O 3 /CaO catalyst in a catalytic packed-bed reactor [92]. The model was built using experimental data acquired under pressure between 1 and 1.3 atm, maximum axial reactor temperature between 700 and 955 • C, inlet CH 4 /O 2 molar ratio between 5 and 10, CH 4 conversion between 1 and 32% and O 2 conversion between 15-100%. The whole model contained 52 parameters which were estimated with a total of 135 experiments. According to the authors, the main drawback of this model lies in the assumption that gas-phase reactions are negligible, limiting its application to reactors with small gas-phase volumes.

Kinetics in the Presence of Catalyst
In the presence of catalyst, and assuming that gas-phase reactions are not significant (as suggested by experiments performed in the absence of catalyst), a one-dimensional, pseudo-homogeneous plug-flow model embracing 10 reaction steps, as presented in Table 4, was able to fairly well describe experimental data obtained over a La2O3/CaO catalyst in a catalytic packed-bed reactor [92]. The model was built using experimental data acquired under pressure between 1 and 1.3 atm, maximum axial reactor temperature between 700 and 955 °C, inlet CH4/O2 molar ratio between 5 and 10, CH4 conversion between 1 and 32% and O2 conversion between 15-100%. The whole model contained 52 parameters which were estimated with a total of 135 experiments. According to the authors, the main drawback of this model lies in the assumption that gas-phase reactions are negligible, limiting its application to reactors with small gas-phase volumes.

Reaction Reaction Rate Equation
p i is the partial pressure of compound j; k i denotes the specific reaction rate constant for reaction i, which is related to temperature by the Arrhenius equation; K i represents the equilibrium adsorption constants, and m i and n i are parameters related to the order of the reaction i with respect to the compound j. Figure 12 shows the effect of spatial time on CH 4 and O 2 conversions, and main carbon containing products yields, at 700 and 830 • C, over a La 2 O 3 /CaO catalyst [92]. No further increase in the CH 4 conversion with spatial time was observed when O 2 was completely consumed. Moreover, ethane yield behaviour supported the hypothesis that ethane is a primary product, as evidenced by the observation of a smooth maximum as a function of spatial time (Figure 12b). Ethene is also suggested as an intermediate compound, as its yield is levelled off. Finally, CO and CO 2 were also assumed to be primary products. CO yield goes through a maximum at higher temperatures, indicating its likely conversion to CO 2 , Figure 12c. The catalytic conversion of CO into CO 2 was also supported by experiments performed with CO and O 2 in the feed only, over a Li/MgO catalyst [102]. ethane is a primary product, as evidenced by the observation of a smooth maximum as a function of spatial time (Figure 12b). Ethene is also suggested as an intermediate compound, as its yield is levelled off. Finally, CO and CO2 were also assumed to be primary products. CO yield goes through a maximum at higher temperatures, indicating its likely conversion to CO2, Figure 12c. The catalytic conversion of CO into CO2 was also supported by experiments performed with CO and O2 in the feed only, over a Li/MgO catalyst [102]. Based on kinetic parameter estimates, the increase in C2 selectivity with reaction temperature has been rationalised as being due to the higher activation energy for ethane formation, when compared to activation energies for CO and CO2 formations from CH4 [92]. However, the positive effect of temperature on C2 selectivity has also been reported as being due to the decrease in the rate of formation of carbon oxides from the decomposition of methyl peroxy radicals (such as CH3OO • ) at the catalyst surface, which would be less favoured at higher temperatures [103]. Based on kinetic parameter estimates, the increase in C2 selectivity with reaction temperature has been rationalised as being due to the higher activation energy for ethane formation, when compared to activation energies for CO and CO 2 formations from CH 4 [92]. However, the positive effect of temperature on C2 selectivity has also been reported as being due to the decrease in the rate of formation of carbon oxides from the decomposition of methyl peroxy radicals (such as CH 3 OO • ) at the catalyst surface, which would be less favoured at higher temperatures [103].
Furthermore, steam-reforming reactions of CH 4 and C 2 H 6 were ruled out by experiments performed using only methane and water, and ethane and water as feed over the La 2 O 3 /CaO catalyst. Even at high temperatures (tested between 800 and 880 • C) and spatial times, methane conversion was negligible, whereas ethane was converted mainly into ethene, indicating its conversion to ethene via dehydrogenation. Conversely, a feed comprising only ethene and water produced mainly CO and CO 2 , suggesting that ethene might be converted by steam reforming (Table 4, reaction 8) and implying the importance of water-gas shift reactions in the mechanism (Table 4, reaction 9-10). The rate of C2 formation was observed to increase linearly with the methane partial pressure, whereas it passed through a maximum as a function of the O 2 partial pressure. On the other hand, increasing both CH 4 and O 2 partial pressures caused a positive linear effect on the rate of CO x formation [92].
Moreover, experiments performed with the co-feeding of CH 4 , O 2 and CO 2 showed that the increase in the CO 2 partial pressure (whereas keeping CH 4 and O 2 partial pressures constant) in the feed was harmful to C2 formation rates over a La 2 O 3 /CaO catalyst, as shown in Figure 13a [92]. A similar effect from the co-feeding of CH 4 , O 2 and CO 2 was also reported over a Li/MgO catalyst [102]. The authors further verified that the reaction of CH 4 with CO 2 to CO could be promoted at OCM reaction conditions, by performing reactions using only CH 4 and CO 2 as feed (the importance of gas-phase methane dry reform was ruled out based on experiments performed in the absence of the catalyst). The effect of CO 2 was evaluated while keeping the partial pressures of CH 4 and O 2 and total pressure constant, by using helium as balance gas [102]. Thus, the CO 2 effect was not related to total pressure or methane partial pressure effects. In line with results from previous studies [92,93], the increase in the CO 2 partial pressure resulted in lower methane conversions, as shown in Figure 13b, and lower formation rates of C2 and COx products (not shown).
form was ruled out based on experiments performed in the absence of the catalyst). The effect of CO2 was evaluated while keeping the partial pressures of CH4 and O2 and total pressure constant, by using helium as balance gas [102]. Thus, the CO2 effect was not related to total pressure or methane partial pressure effects. In line with results from previous studies [92,93], the increase in the CO2 partial pressure resulted in lower methane conversions, as shown in Figure 13b, and lower formation rates of C2 and COx products (not shown). Therefore, it has been concluded that CO2 might be adsorbed on catalyst active sites, resulting in an inhibiting effect on C2 formation [18]. For instance, the competition between CO2 and O2 for the same surface active sites was proposed to explain the rate of ethane formation (Table 4, reaction 2) and the inhibiting effect of CO2 was also taken into account in oxidation reactions (Table 4, reactions 1, 3, 4, 5 and 6) [92]. This hypothesis is Therefore, it has been concluded that CO 2 might be adsorbed on catalyst active sites, resulting in an inhibiting effect on C2 formation [18]. For instance, the competition between CO 2 and O 2 for the same surface active sites was proposed to explain the rate of ethane formation (Table 4, reaction 2) and the inhibiting effect of CO 2 was also taken into account in oxidation reactions (Table 4, reactions 1, 3, 4, 5 and 6) [92]. This hypothesis is in line with previous suggestions [102], as it has been verified that the C2 selectivity can remain constant with the increase in the CO 2 feed partial pressure (even though reaction rates were reduced), indicating a possible common CH 4 activation site for both C2 and COx species, which would be poisoned by CO 2 .
Following the kinetic model proposed by Stansch et al. [92], an extended model in which the presence of gas-phase reactions was also considered has also been proposed [93]. This approach initially considered 10 catalytic reaction steps, being further expanded to 14 [104] and finally to 26 [105] catalytic reaction steps, which were coupled to the system of 39 gas-phase reaction steps described in Section 3.1. Table 5 illustrates the 26 catalytic reaction steps as proposed by these authors. In this table, a catalytic surface site is represented by '*', while active oxygen species are represented by 'O*'. According to this reaction network, the formation of methyl radicals is believed to occur in accordance with the Eley-Rideal mechanism, where gas-phase methane reacts with oxygen active species at the catalyst surface, reaction 2, Table 5 [93,[106][107][108][109].
This approach would also imply a unique identity for oxygen active species, which would be produced from the dissociative adsorption of O 2 . Indeed, the dissociative adsorption of O 2 over MgO, Li-MgO and Sn-Li-MgO catalysts has been demonstrated by experiments involving isotopes of O 2 . According to these experiments, the switch from a gas feed containing 16 O 2 to a gas feed containing 18 O 2 over a catalytic bed at steady-state conditions at 750 • C allowed for the observation of 16 O 18 O species by mass spectrometry, supporting the dissociative adsorption hypothesis [106].
However, the participation of oxygen active species from catalyst surfaces has also been demonstrated. In this case, CH 4 pulse experiments performed in the absence of O 2 have proven the production of CH 3 • radicals and CO over Sm 2 O 3 and CH 3 • radicals, CO and CO 2 over MgO catalysts at 450 and 550 • C, respectively [107]. Table 5. Catalytic surface reaction steps as proposed by Kechagiopoulos et al. [105].

No Catalytic Reaction No Catalytic Reaction
Broadly, the above general reaction network has been supported by experimental studies conducted at atmospheric pressures. For instance, the degradation of C2 compounds involving catalytic surface steps is in agreement with the positive effect that short spatial times have on C2 selectivities [110,111]. However, the type of reactor where the above reaction network occurs can also play a very important role to explain the process outputs. For this reason, modelling approaches used to describe OCM reactors are discussed in the following sections.
Indeed, the present analysis focused on the modelling and simulation of OCM reactors and found that the great majority (48% of a sample of 30 scientific publications) of available studies was dedicated to PBR, while FBR and MR were investigated in 26 and 9% of the analysed studies, respectively, with the remaining 17% being related to other reactor types, including gas-solid vortex reactors (GSVR) and spouted bed reactors ( Figure 14a). The developed models were based mainly on the homogeneous (or pseudo-homogeneous) kinetic approach, considering that this approach is simpler and more suitable to describe OCM reactions than more complex heterogeneous models ( Figure 14b). It was also possible to verify that the large majority of these works used the kinetic mechanism developed by Stansch et al. [92] (Table 4) as a reference, due to its simplicity and applicability (Figure 14c), whereas distinct types of catalysts have been considered (Figure 14d). Regarding the energy balances, most studies assumed that reactions were performed in adiabatic or isothermal mode, which can constitute a major drawback for the interpretation of large-scale industrial reactors and somewhat hide the important heat transfer effects that take place in the catalyst bed. In the next sections, some of these models and their characteristic features are discussed.

Modelling Approaches for Packed-Bed Reactors
As introduced in Section 3.3, PBR has been one of the most investigated OCM reactor types and its modelling approaches can be classified according to the phenomena in the reactor and catalyst scale. For instance, one-or two-dimensional models are usually applied when significant radial gradients of concentration and/or temperature are considered absent or present, respectively, whereas pseudo-homogeneous or heterogeneous models are often employed to describe one or more phases in the system, usually associated with the absence or presence of concentration and/or temperature gradients inside catalyst particles [123,125].
( Figure 14a). The developed models were based mainly on the homogeneous (or pseudo-homogeneous) kinetic approach, considering that this approach is simpler and more suitable to describe OCM reactions than more complex heterogeneous models ( Figure  14b). It was also possible to verify that the large majority of these works used the kinetic mechanism developed by Stansch et al. [92] (Table 4) as a reference, due to its simplicity and applicability (Figure 14c), whereas distinct types of catalysts have been considered (Figure 14d). Regarding the energy balances, most studies assumed that reactions were performed in adiabatic or isothermal mode, which can constitute a major drawback for the interpretation of large-scale industrial reactors and somewhat hide the important heat transfer effects that take place in the catalyst bed. In the next sections, some of these models and their characteristic features are discussed.

Modelling Approaches for Packed-Bed Reactors
As introduced in Section 3.3, PBR has been one of the most investigated OCM reactor types and its modelling approaches can be classified according to the phenomena in the reactor and catalyst scale. For instance, one-or two-dimensional models are usually applied when significant radial gradients of concentration and/or temperature are considered absent or present, respectively, whereas pseudo-homogeneous or heterogeneous Pioneering studies on the modelling of OCM PBRs considered an isothermal, heterogeneous model at steady-state conditions, where mass balances described the external gas phase and the gas phase contained within the catalyst pores [118]. These authors showed the importance of considering mass transport limitations for the proper reactor description of reaction events even when no significant concentration gradients were present for stable compounds, such as main reactants and products. Due to the high reactivity of radical intermediates, significant concentration gradients of radical species could be expected to develop, so that the neglection of gradients might result in erroneous predictions of C2 selectivity [18,118]. However, temperature gradients and pressure drops were considered unimportant.
The model proposed by Couwenberg et al. [93,118], briefly illustrated by Equations (5) and (6), where ε b , F v , A s , D i , D e,i and ε c represent bed porosity, volumetric flow rate, reactor cross-sectional area, molecular diffusion coefficient, effective internal diffusion coefficient and catalyst porosity, respectively, represented a great advance when compared to previous and simpler models, such as the one proposed by Stansch et al. [92]. For the first time, concentration gradients of molecular and radical species between the inner catalyst particle and the bulk reactor gas phase were explicitly considered in a model which simultaneously coupled the distinct reaction networks occurring at the gas phase, R i,g , and catalytic surface, R i,c . In this model, the gas-phase reaction network was considered to follow the mechanism involving the 39 reaction steps as described in Section 3.1, while the reaction network on the catalyst surface was described using 10 reaction steps for which kinetic parameters were either estimated with available experimental data or calculated from physico-chemical relationships [93].
− D e,i However, while this approach allowed for a good description of experimental observations within the range of conditions used in the regression analysis (which involved pressures between 1.1 and 1.5 atm), the predicted catalytic performance was unable to describe conversion levels at higher pressure conditions, as illustrated in Figure 15. As mentioned previously, the description of the reaction network on the catalyst surface was later extended from 10 to 14 [104], and later to 26 elementary steps [105], as described in Table 5. Further model improvements included the explicit consideration of the effects of temperature, pressure and gas composition on the previously mentioned molecular and effective internal diffusion coefficients, Di and De,i, as illustrated by Equations (7) and (8) [105], where Di,j is the molecular diffusion coefficient of component i in j; Mi and Mj are the molecular weights of compounds i and j; Σvi represents the sum of atomic diffusion volumes for the atoms of the molecule i; xi is the molar fraction of the component i; Nmol and Nrad are the total number of molecules and radicals, respectively, and τc is the catalyst pellet tortuosity.
It is interesting to note that this modelling approach, initially built from experimental observations using Li/MgO and Sn-doped Li/MgO catalysts [118], was also applied to, and able to explain experimental data from Sr/La2O3 [126], La-Sr/CaO and Na-Mn-W/SiO2 catalysts [16,17]. However, the investigated pressure conditions were limited to values below 1.9 atm.
Additional modelling approaches have also been reported. For instance, Valadkhani et al. [91] considered a transient, one-dimensional pseudo-homogeneous model with axial mixing to describe mass and energy balances for reacting species, where the reaction network involved up to 10 steps, similar to the ones proposed by Stansch et al. [92], and reaction rate equations were described by power law relationships. However, while a good agreement between model simulations and experimental catalytic performances obtained over a Na-Mn-W/SiO2 catalyst was reported, pressure conditions were also limited to values below 2 atm. In another study [14], a steady-state, two-dimensional pseudo-homogeneous model with axial mixing was used to describe mass and energy balances. Using reaction networks such as the one suggested by Stansch et al. [92], the authors were also able to validate their model with experimental observations, although this validation was limited to atmospheric pressure conditions.
Further OCM PBR developments have explored experimentally the feasibility of operation under autothermal conditions, by using the feed as coolant [127]. However, to Further model improvements included the explicit consideration of the effects of temperature, pressure and gas composition on the previously mentioned molecular and effective internal diffusion coefficients, D i and D e,i , as illustrated by Equations (7) and (8) [105], where D i,j is the molecular diffusion coefficient of component i in j; M i and M j are the molecular weights of compounds i and j; Σv i represents the sum of atomic diffusion volumes for the atoms of the molecule i; x i is the molar fraction of the component i; N mol and N rad are the total number of molecules and radicals, respectively, and τ c is the catalyst pellet tortuosity.
It is interesting to note that this modelling approach, initially built from experimental observations using Li/MgO and Sn-doped Li/MgO catalysts [118], was also applied to, and able to explain experimental data from Sr/La 2 O 3 [126], La-Sr/CaO and Na-Mn-W/SiO 2 catalysts [16,17]. However, the investigated pressure conditions were limited to values below 1.9 atm.
Additional modelling approaches have also been reported. For instance, Valadkhani et al. [91] considered a transient, one-dimensional pseudo-homogeneous model with axial mixing to describe mass and energy balances for reacting species, where the reaction network involved up to 10 steps, similar to the ones proposed by Stansch et al. [92], and reaction rate equations were described by power law relationships. However, while a good agreement between model simulations and experimental catalytic performances obtained over a Na-Mn-W/SiO 2 catalyst was reported, pressure conditions were also limited to values below 2 atm. In another study [14], a steady-state, two-dimensional pseudo-homogeneous model with axial mixing was used to describe mass and energy balances. Using reaction networks such as the one suggested by Stansch et al. [92], the authors were also able to validate their model with experimental observations, although this validation was limited to atmospheric pressure conditions.
Further OCM PBR developments have explored experimentally the feasibility of operation under autothermal conditions, by using the feed as coolant [127]. However, to understand reactor performance behaviour under this operational mode, an analysis of the multiple steady states of the OCM reaction network is necessary. Unfortunately, due to the complexity of the reactor fluid dynamic and kinetics, there is no unequivocal theoretical study available in the literature showing these complex nonlinear behaviours for real OCM reactors, even though efforts have been dedicated to explain involved phenomena using ideal reactor models, such as plug flow reactors (PFR), continuously stirred tank reactors (CSTR) and lumped thermal reactors (LTR) [20,21,123,127,128].
For instance, as an attempt to demonstrate the existence of multiple steady states, bifurcation analyses considering CSTR, LTR and PFR reactor configurations have been reported by Vandewalle et al. [128]. The authors showed that only CSTR and LTR reactors present regions with multiple steady states and hysteresis, although the LTR reactor presented the best performance (higher CH 4 conversion with lower feed temperature). Although this study indicated the potential feasibility of autothermal operation, it must be noted that the considered reactor models present significant simplifications, as they neglect the occurrence of mass and energy radial gradients, and that validation of simulated autothermal conditions and resulting catalytic performance has yet to be confirmed experimentally. Therefore, further studies on this area are greatly needed, as previously pointed out by Sarsani et al. [127].

Modelling Approaches for Fluidized Bed Reactors
Fluidized bed reactors (FBRs) have been proposed as an alternative OCM reactor concept in order to facilitate the management of produced heat and avoid thermal runaway [112,113,129]. Additionally, according to Pannek and Mleczko [112], comparable or higher CH 4 conversions and C 2 selectivities could be achieved in a FBR when compared with the more usual PBR configuration, although these results could be strongly influenced by operational conditions.
To describe this reactor, as illustrated in Figure 16, one must observe that the gaseous stream flows through the bed in the emulsion in the form of bubbles. Pannek and Mleczko [112] considered a model which was based on the two-phase theory of fluidization and in accordance with the bubble assemblage model (BAM) [130], assuming a constant emulsion porosity. understand reactor performance behaviour under this operational mode, an analysis of the multiple steady states of the OCM reaction network is necessary. Unfortunately, due to the complexity of the reactor fluid dynamic and kinetics, there is no unequivocal theoretical study available in the literature showing these complex nonlinear behaviours for real OCM reactors, even though efforts have been dedicated to explain involved phenomena using ideal reactor models, such as plug flow reactors (PFR), continuously stirred tank reactors (CSTR) and lumped thermal reactors (LTR) [20,21,123,127,128]. For instance, as an attempt to demonstrate the existence of multiple steady states, bifurcation analyses considering CSTR, LTR and PFR reactor configurations have been reported by Vandewalle et al. [128]. The authors showed that only CSTR and LTR reactors present regions with multiple steady states and hysteresis, although the LTR reactor presented the best performance (higher CH4 conversion with lower feed temperature). Although this study indicated the potential feasibility of autothermal operation, it must be noted that the considered reactor models present significant simplifications, as they neglect the occurrence of mass and energy radial gradients, and that validation of simulated autothermal conditions and resulting catalytic performance has yet to be confirmed experimentally. Therefore, further studies on this area are greatly needed, as previously pointed out by Sarsani et al. [127].

Modelling Approaches for Fluidized Bed Reactors
Fluidized bed reactors (FBRs) have been proposed as an alternative OCM reactor concept in order to facilitate the management of produced heat and avoid thermal runaway [112,113,129]. Additionally, according to Pannek and Mleczko [112], comparable or higher CH4 conversions and C2 selectivities could be achieved in a FBR when compared with the more usual PBR configuration, although these results could be strongly influenced by operational conditions.
To describe this reactor, as illustrated in Figure 16, one must observe that the gaseous stream flows through the bed in the emulsion in the form of bubbles. Pannek and Mleczko [112] considered a model which was based on the two-phase theory of fluidization and in accordance with the bubble assemblage model (BAM) [130], assuming a constant emulsion porosity.  The minimum fluidization velocity (u mf ), the bed height at minimum fluidized velocity (H mf ), the bubble diameter (d b ), bubble growth and bubble velocity were calculated with empirical correlations. The fluidized bed was discretised into several domains along the distance above the gas distributor, represented by h in Figure 16. In each of these domains the bubble and emulsion phases were modelled as perfectly mixed reactors. For the reaction network, both gas-phase [98] and catalytic surface reaction steps [131] were considered. Main model equations are briefly illustrated by Equations (9) and (10) [130], where F and f are the volumetric fraction of gas in the bubble and emulsion phases, respectively; C i is the reactant concentration in phase i; D i is the axial dispersion coefficient in phase i; u is the superficial gas velocity; F 0 is the gas interchange coefficient per unit of volume of gas bubble; F s is the volumetric fraction of solid in the bubble phase; γ is the throughflow factor, which represents the flows through the emulsion phase; u e is the superficial gas velocity in the emulsion phase; and the subscripts "b" and "e" represent the bubble and emulsion phases, respectively.
Pannek and Mleczko [112] showed through simulations that C2 selectivities were affected by mass transfer limitations between the phases and that, as expected, C2 selectivities and yields can be a function of temperature and gas velocity.
In another study, computational fluid dynamics (CFD) simulation tools were used to study the reactor performance and reactions pathways [114]. In this case, the authors coupled the CFD description of fluid-solid flow with the ten steps of the catalytic reaction network, as proposed by Stansch et al. [92]. Their simulations were carried out using the Euler-Euler (EE) model approach based on the kinetic theory of granular flow. In the EE approach, both gas and solid phases are interpenetrating fluids [132]. For each gas and solid phase, the model comprises momentum conservation equations, which are linked by interphase momentum transfer, energy conservation equations, including a radiative heat transfer between the reactor wall and the feed, and mass conservation equations for each compound. The authors showed that their results of C 2 selectivity and methane conversion agreed well with available experimental data, and that mass transfer limitations between phases can significantly affect the reaction pathways.

Modelling Approaches for Membrane Reactors
Membrane reactor configurations, which can allow for the separation of CH 4 and O 2 feed streams, have attracted significant attention, as the limited contact between O 2 and CH 4 and achievable low oxygen concentrations can limit methane conversion, increasing selectivity to ethane and ethylene [113,[115][116][117]124,133]. In this case, the reactor design comprises two concentric tubes that are separated by a membrane, as presented in Figure 17. The most common type of membranes used in OCM processes include porous and dense membranes. These two groups are subject to different gas permeation mechanisms, following the Knudsen diffusion and the mixed electron/ion conduction in porous and dense membranes, respectively [124]. In some cases, a catalyst is coated on the membrane wall and reaction occurs at the membrane surface, as illustrated in Figure 18.
Holst et al. [115] proposed a two-dimensional, pseudo-homogeneous model to describe the OCM packed-bed membrane reactor (PBMR), which used a generic ceramic membrane and a catalyst bed of La 2 O 3 /CaO. The model comprised steady-state mass, energy, and momentum balances, as illustrated by Equations (11)- (13), where boundary conditions accounted for the flux through the membrane for the reactor tube and shell (not shown) and the ten elementary steps of the reaction network developed by Stansch et al. [92] were used to represent the net reaction rates. In Equations (11)-(13), C i is the concentration of reactant i; u z is the superficial velocity in the z axis ( Figure 18); D r is Processes 2021, 9, 2196 20 of 48 the effective diffusion coefficient in the r axis; R i,j is the reaction rate for component i in reaction j; T is the temperature; c p is the heat capacity; λ r is the heat transfer coefficient in the radial direction; ∆H Rj is the reaction enthalpy of reaction j; P is the pressure; ρ g and ε k are the gas density and bed porosity, respectively; Re is the Reynolds number; and d k is the catalyst pellet size.  Holst et al. [115] proposed a two-dimensional, pseudo-homogeneous model to describe the OCM packed-bed membrane reactor (PBMR), which used a generic ceramic membrane and a catalyst bed of La2O3/CaO. The model comprised steady-state mass, energy, and momentum balances, as illustrated by Equations (11)-(13), where boundary conditions accounted for the flux through the membrane for the reactor tube and shell (not shown) and the ten elementary steps of the reaction network developed by Stansch et al. [92] were used to represent the net reaction rates. In Equations (11)- (13), Ci is the concentration of reactant i; uz is the superficial velocity in the z axis ( Figure 18); Dr is the effective diffusion coefficient in the r axis; Ri,j is the reaction rate for component i in reaction j; T is the temperature; cp is the heat capacity; λr is the heat transfer coefficient in the radial direction; ΔHRj is the reaction enthalpy of reaction j; P is the pressure; ρg and εk are the gas density and bed porosity, respectively; Re is the Reynolds number; and dk is the catalyst pellet size.
Good agreement between the experimental data and simulations was observed (for CH4/O2 feed molar ratio of 2, at 1.1 bar and inlet temperature of 750 °C) and the authors concluded that fast OCM reactions can cause concentration gradients due to oxygen de-  Holst et al. [115] proposed a two-dimensional, pseudo-homogeneous model to describe the OCM packed-bed membrane reactor (PBMR), which used a generic ceramic membrane and a catalyst bed of La2O3/CaO. The model comprised steady-state mass, energy, and momentum balances, as illustrated by Equations (11)-(13), where boundary conditions accounted for the flux through the membrane for the reactor tube and shell (not shown) and the ten elementary steps of the reaction network developed by Stansch et al. [92] were used to represent the net reaction rates. In Equations (11)- (13), Ci is the concentration of reactant i; uz is the superficial velocity in the z axis ( Figure 18); Dr is the effective diffusion coefficient in the r axis; Ri,j is the reaction rate for component i in reaction j; T is the temperature; cp is the heat capacity; λr is the heat transfer coefficient in the radial direction; ΔHRj is the reaction enthalpy of reaction j; P is the pressure; ρg and εk are the gas density and bed porosity, respectively; Re is the Reynolds number; and dk is the catalyst pellet size.
(1 ) 150(1 ) 1.75 Re Good agreement between the experimental data and simulations was observed (for CH4/O2 feed molar ratio of 2, at 1.1 bar and inlet temperature of 750 °C) and the authors concluded that fast OCM reactions can cause concentration gradients due to oxygen de- Figure 18. Catalytic membrane reactor configuration [115].
∂T ∂z ∂P ∂z Good agreement between the experimental data and simulations was observed (for CH 4 /O 2 feed molar ratio of 2, at 1.1 bar and inlet temperature of 750 • C) and the authors concluded that fast OCM reactions can cause concentration gradients due to oxygen depletion in the vicinity of the membrane [115].
Onoja et al. [117] proposed a different approach, where the optimisation of the axial thickness of the membrane was carried out to maximise the C 2 selectivity. A twodimensional, steady-state model coupled with the kinetic mechanism proposed originally by Stansch et al. [92] was employed to describe mass and energy balances in the tube phase, in accordance with Equations (14) and (15).
Additionally, no reactions were assumed to take place in the membrane itself, which was based on its inherent contribution to mass and energy balances through the permeation flux, J i , Equations (16) and (17), where C i is the concentration of reactant i; u z-tube and u z-shell are the superficial velocity in the tube and shell, respectively; D er is the effective bulk diffusivity of gas mixture; R i,j is the reaction rate for component i in reaction j; T is the temperature; c p is the heat capacity; λ er is the effective radial thermal conductivity; ∆H Rj is the reaction enthalpy of reaction j; d t is the tube diameter; and U a is the overall heat transfer coefficient through the membrane.
In a first analysis, the authors compared the performance of a conventional packedbed reactor (PBR) with the performance of a membrane reactor (MR) without varying the membrane thickness. Simulations performed at 1 bar and 800 • C indicated that larger catalytic bed lengths could be required in an MR to achieve similar methane conversion when compared with a PBR. However, a yield of 11.63% and C 2 selectivity of 47.86% were achieved in the MR in opposition to 8.28% and 29.86%, respectively, obtained with the PBR. By using the variable thickness membrane reactor (VTMR) configuration, C 2 selectivities and yields of nearly 60% and 14% could be achieved, respectively. Interestingly, these authors have also shown how the VTMR could allow for the minimisation of hot spot formation, as the increase in membrane thickness along the axial direction could contribute to managing O 2 permeation flux and its consumption rate, resulting in a smoother axial temperature profile when compared to MR and PBR configurations, as illustrated in Figure 19 [117]. However, although these results seem very promising, simulations have yet to be validated by experimental observations. Processes 2021, 9, x FOR PEER REVIEW 23 of 51 Figure 19. Simulated temperature profiles for PBR, MR and VTMR in adiabatic operation (adapted from [117]).
Furthermore, although membrane reactors seem quite attractive for OCM due to their higher C2 selectivity and the reduction in inlet air separation costs, some drawbacks should be noted, such as the costs associated with the use of membranes, difficulties in reaction heat management, the appropriate sealing of membrane packs and the membrane long-term stability. In addition, membrane catalytic activity can itself become a limiting factor for OCM yields [124]. Figure 19. Simulated temperature profiles for PBR, MR and VTMR in adiabatic operation (adapted from [117]). Furthermore, although membrane reactors seem quite attractive for OCM due to their higher C 2 selectivity and the reduction in inlet air separation costs, some drawbacks should be noted, such as the costs associated with the use of membranes, difficulties in reaction heat management, the appropriate sealing of membrane packs and the membrane long-term stability. In addition, membrane catalytic activity can itself become a limiting factor for OCM yields [124].

Thermal Effects
As discussed in the previous sections, OCM reaction networks and associated kinetic constants estimated for packed-bed reactors have been mostly obtained assuming the occurrence of negligible temperature gradients in the catalytic bed. However, it has been shown experimentally that this assumption is hardly achieved due to the formation of hot spots [134][135][136]. Typically, a fast increase in temperature is observed as CH 4 and O 2 enter the reactor, due to fast rates of exothermic oxidation reactions, as illustrated in Figure 20. As O 2 is consumed along the reactor length, temperature tends to stabilise [91,135]. The difference between the nominal reactor temperature and the maximum axial catalytic bed temperature in PBRs has also been shown to depend on both the inlet gas flow composition and gas flow velocity [134,135], as shown in Figure 20. Figure 19. Simulated temperature profiles for PBR, MR and VTMR in adiabatic operation (adapted from [117]). Furthermore, although membrane reactors seem quite attractive for OCM due to their higher C2 selectivity and the reduction in inlet air separation costs, some drawbacks should be noted, such as the costs associated with the use of membranes, difficulties in reaction heat management, the appropriate sealing of membrane packs and the membrane long-term stability. In addition, membrane catalytic activity can itself become a limiting factor for OCM yields [124].

Thermal Effects
As discussed in the previous sections, OCM reaction networks and associated kinetic constants estimated for packed-bed reactors have been mostly obtained assuming the occurrence of negligible temperature gradients in the catalytic bed. However, it has been shown experimentally that this assumption is hardly achieved due to the formation of hot spots [134][135][136]. Typically, a fast increase in temperature is observed as CH4 and O2 enter the reactor, due to fast rates of exothermic oxidation reactions, as illustrated in Figure 20. As O2 is consumed along the reactor length, temperature tends to stabilise [91,135]. The difference between the nominal reactor temperature and the maximum axial catalytic bed temperature in PBRs has also been shown to depend on both the inlet gas flow composition and gas flow velocity [134,135], as shown in Figure 20. To minimise the effects associated with hot spots in packed-bed reactors, efforts have been dedicated to evaluate strategies for heat management, including the dilution of the feed stream with inert gases [136] and water steam [137], and the dilution of the catalytic bed with inert solids [16]. However, the effectiveness of these strategies and their economic implications at actual high-pressure industrial operation conditions must still be evaluated.

Thermodynamic Considerations
This section presents a detailed analysis about the behaviour of OCM mixtures at equilibrium conditions. Although previous reports have discussed thermodynamic aspects of the OCM reaction system [138], there has been no extensive evaluation of equilibrium compositions in a wide range of reaction conditions, taking into account the impact of pressure, CH 4 /O 2 feed molar ratio, temperature, the presence of inert gases, and the co-feeding of ethane, CO 2 and H 2 O on the resultant thermodynamic ethene yield. For instance, Geerts et al., (1990) [138] reported the equilibrium thermodynamics of methane pyrolysis and its oxidation, presenting equilibrium compositions for the OCM reaction as cumulative molar fractions for different temperatures at a single fixed condition of CH 4 /O 2 feed molar ratio and pressure.
More recently, Gibbs energies for four global oxidative reactions at 800 • C and 1 atm have been reported [139], highlighting their negative magnitudes and therefore their thermodynamic feasibility. Equilibrium carbon-based selectivity distributions for different CH 4 /O 2 feed ratios at 800 • C and 1 atm in the presence [57] and the absence [139] of solid graphite formation have also been considered, indicating the formation of coke as predominant at high CH 4 /O 2 feed ratios (above 4), while CO was the most favoured carboncontaining gaseous product. Similarly, equilibrium molar-based selectivity distributions for a large range of temperatures, at 1 bar and CH 4 /O 2 feed molar ratio equal to 9 [140] and 4 [21], have also been discussed, illustrating the high thermodynamic compositions of H 2 and CO obtained at typical OCM temperatures between 700 and 1000 • C.
Thermodynamic constraints also impose the maximum conversion that can be achieved at a certain condition of temperature, pressure and initial reactants composition [141]. Thus, it is possible to estimate the maximum yield of a desired product that can be obtained at the ideal selectivity reached under the kinetic regime. In this aspect, efforts have been dedicated to estimate an upper bound for the C2 yield [18,142], given the importance of this information for analysing the economic feasibility of the industrial OCM process implementation.
Surprisingly, and to the best of our knowledge, no upper bound based exclusively on thermodynamic constraints has been discussed in a wide range of reaction conditions. Thus, this section aims to expand the current understanding on the equilibrium behaviour of the OCM system by assessing the impact of pressure, CH 4 /O 2 feed molar ratio, temperature, the presence of inert content, and the co-feeding of ethane and CO 2 on the resulting thermodynamic ethene yield. As thermodynamic effects may also affect kinetic regimes to some extent, through, for instance, equilibrium constants within reaction rate equations, we hope to shed more light into the understanding of this complex reaction system.
Thermodynamic calculations were performed with help of the Gibbs energy minimisation method, using the 'GPREC-Gas-phase reaction equilibrium calculator' [143] and the 'ThermoSolver' software version 1.0 [144]. Unless otherwise stated, yields and selectivities have been defined in carbon bases (see Section S1 in the Supplementary Materials) and equilibrium compositions have been investigated assuming the presence of eight compounds, which included CH 4 , O 2 , CO, CO 2 , H 2 , H 2 O, C 2 H 6 , and C 2 H 4 . As will be shown later, the formation of additional compounds, such as propene, propane and acetylene, can be neglected at the equilibrium due to their low thermodynamic yields. In addition, this study also neglected the formation of coke to calculate the maximum achievable thermodynamic yield. Table S1 in the Supplementary Materials summarises standard Gibbs energies in increasing order at 900 • C and standard reaction enthalpies for possible global OCM reactions, which will be further discussed in the following sections.

The Effect of Temperature and CH 4 /O 2 Feed Ratio on Equilibrium Compositions
The effect of temperature and CH 4 /O 2 feed molar ratio at 1 bar is illustrated in Figure 21a-f, where the ethene yield (a), CH 4 conversion (b), and carbon-based selectivity for C 2 H 4 (c), CO (d) and CO 2 (e) are plotted as functions of temperature between 700 and 950 • C for CH 4 /O 2 feed molar ratios ranging between 1.5 and 9. In the present study, the CH 4 /O 2 feed molar ratio was varied while keeping the total number of mols of reactants constant.
As one can see in Figure 21a, the thermodynamic temperature window for ethene production lies above 700 • C, with ethene yields increasing with the continuous increase in temperature and CH 4 /O 2 feed molar ratio. Similar behaviour is verified for the combined ethene and ethane yields, presented in Figure S1 of the Supplementary Materials. In contrast, CH 4 conversion presents only a slight increase with the increase in temperature for the same CH 4 /O 2 feed molar ratio, Figure 21b, while a more pronounced reduction in conversion is observed with the continuous increase in the CH 4 /O 2 feed molar ratio. Thus, higher ethene yields observed with the continuous increase in temperature for a fixed CH 4 /O 2 feed molar ratio should result from a change in the product's selectivity distribution, as illustrated in Figure 21c-e. Indeed, as temperature is increased, exothermic oxidation reactions that lead to CO and CO 2 formation are unfavoured, while the endothermic dehydrogenation of ethane can be promoted (Table S1). It is also interesting to note the complex behaviour of CO selectivity, which presents a point of maximum as a function of temperature that also depends on the CH 4 /O 2 feed molar ratio, Figure 21d. For higher feed oxygen contents (CH 4 /O 2 feed molar ratios smaller than 3), CO selectivity increases with temperature, whereas at lower oxygen contents, the selectivity is reduced. In this case, the less exothermic character of oxidation reactions that lead to CO, when compared to the ones that lead to CO 2 , plays a role: as CO 2 formation is more largely unfavoured with the temperature increase, the CO selectivity can increase. acetylene, can be neglected at the equilibrium due to their low thermodynamic yields. In addition, this study also neglected the formation of coke to calculate the maximum achievable thermodynamic yield. Table S1 in the Supplementary Materials summarises standard Gibbs energies in increasing order at 900 °C and standard reaction enthalpies for possible global OCM reactions, which will be further discussed in the following sections.

The Effect of Temperature and CH4/O2 Feed Ratio on Equilibrium Compositions
The effect of temperature and CH4/O2 feed molar ratio at 1 bar is illustrated in Figure 21a-f, where the ethene yield (a), CH4 conversion (b), and carbon-based selectivity for C2H4 (c), CO (d) and CO2 (e) are plotted as functions of temperature between 700 and 950 °C for CH4/O2 feed molar ratios ranging between 1.5 and 9. In the present study, the CH4/O2 feed molar ratio was varied while keeping the total number of mols of reactants constant. Figure 21f also illustrates the molar-based selectivity distribution at the CH 4 /O 2 feed molar ratio equal to 9 at 1 bar as a function of temperature. As previously pointed out [21,140], thermodynamic equilibrium does not favour ethene production in the OCM reaction network, as CO and H 2 are the most favoured gaseous products, stressing the need for the process to operate under a kinetic regime.

The Effect of Inert Dilution and Pressure
The effect of feed composition dilution and pressure at 900 • C is illustrated in Figure 22a-c, where CH 4 conversion (a), ethene yield (b) and carbon-based selectivity distribution (c) are presented as functions of the inert composition. In the present study, the CH 4 /O 2 feed molar ratio was kept constant and equal to 9, while also keeping constant the total number of mols in the feed. Thus, the increase in the inert content could also be translated as the reduction in the partial pressures of CH 4 and O 2 . In line with the above discussion, the change in the distribution of carbon-based products selectivity with the inert content can be related to the favouring of ethane dehydrogenation at more diluted conditions. A similar behaviour of the products selectivity distribution can be verified at 5 bar (not shown) when the inert content is changed, exhibiting, however, a less pronounced change in CO and ethene selectivity, which changed from 96.8 and 2.3% in the absence of N2 to 79 and 21% in the presence of 95% of the inert in the feed, respectively.
It is interesting to note that the effect of an inert composition agrees with kinetic observations in respect to ethene selectivities (Figure 11), as lower CH4 and O2 partial pressures promote ethene selectivity. However, the thermodynamic effect of total pressure on CH4 conversion is contrary to the effect observed under a catalytic kinetic regime. In this case, higher total pressures lead to increased methane conversions (respecting Higher inert contents promote CH 4 conversion, Figure 22a, resulting in larger ethene yields, Figure 22b, while also increasing ethene carbon-based selectivity, Figure 22c. The increase in conversion with more diluted feed compositions can be more easily understood when the stoichiometry of OCM reactions is considered, as illustrated in Table S1. In this case, the higher number of mols among most reactions products favours the forward reaction at higher inert contents, as the probability of molecular collisions among the smaller number of reactant mols is higher when compared to the number of collisions required for the backward reaction [141]. This very same molecular explanation can be used to explain the reduction in CH 4 conversion at higher total pressure conditions (Figure 22a) as the backward reaction direction is promoted in this case.
In line with the above discussion, the change in the distribution of carbon-based products selectivity with the inert content can be related to the favouring of ethane dehydrogenation at more diluted conditions. A similar behaviour of the products selectivity distribution can be verified at 5 bar (not shown) when the inert content is changed, exhibiting, however, a less pronounced change in CO and ethene selectivity, which changed from 96.8 and 2.3% in the absence of N 2 to 79 and 21% in the presence of 95% of the inert in the feed, respectively.
It is interesting to note that the effect of an inert composition agrees with kinetic observations in respect to ethene selectivities (Figure 11), as lower CH 4 and O 2 partial pressures promote ethene selectivity. However, the thermodynamic effect of total pressure on CH 4 conversion is contrary to the effect observed under a catalytic kinetic regime. In this case, higher total pressures lead to increased methane conversions (respecting thermodynamic limits), likely due to increased rates of gas-phase reaction rates.

The Combined Effect of Temperature, CH 4 /O 2 Feed Ratio and Inert Composition
The effect of operation variables including temperature, CH 4 /O 2 feed molar ratio and inert composition on equilibrium compositions was combined in Figure 23 For the same temperature and inert composition, higher thermodynamic ethene yields are achieved as the O2 content is decreased, despite the resulting lower methane conversions. As the O2 is reduced, oxidation reactions involving O2 can be suppressed, leading to an increase in the ethene selectivity, as previously illustrated in Figure 21c. Figure 23 illustrates that the maximum achievable thermodynamic ethene yield at each condition of temperature and inert composition is closely related to the point at which methane conversion can be performed solely by pyrolysis, assuming no coke formation, as previously reported [138], as in this case the undesirable formation of CO and CO2 can be avoided.
While Figure 23 illustrates how the thermodynamic ethene yield is limited by CH4 conversion as the O2 content is reduced, one should also note that even in an ideal scenario where OCM reactions can be performed and simultaneously suppress coke, CO and CO2 formation, the thermodynamic ethene yield would still be limited by CH4 con- For the same temperature and inert composition, higher thermodynamic ethene yields are achieved as the O 2 content is decreased, despite the resulting lower methane conversions. As the O 2 is reduced, oxidation reactions involving O 2 can be suppressed, leading to an increase in the ethene selectivity, as previously illustrated in Figure 21c. Figure 23 illustrates that the maximum achievable thermodynamic ethene yield at each condition of temperature and inert composition is closely related to the point at which methane conversion can be performed solely by pyrolysis, assuming no coke formation, as previously reported [138], as in this case the undesirable formation of CO and CO 2 can be avoided.
While Figure 23 illustrates how the thermodynamic ethene yield is limited by CH 4 conversion as the O 2 content is reduced, one should also note that even in an ideal scenario where OCM reactions can be performed and simultaneously suppress coke, CO and CO 2 formation, the thermodynamic ethene yield would still be limited by CH 4 conversion, as illustrated in Figure 24.
leading to an increase in the ethene selectivity, as previously illustrated in Figure 21c. Figure 23 illustrates that the maximum achievable thermodynamic ethene yield at each condition of temperature and inert composition is closely related to the point at which methane conversion can be performed solely by pyrolysis, assuming no coke formation, as previously reported [138], as in this case the undesirable formation of CO and CO2 can be avoided.
While Figure 23 illustrates how the thermodynamic ethene yield is limited by CH4 conversion as the O2 content is reduced, one should also note that even in an ideal scenario where OCM reactions can be performed and simultaneously suppress coke, CO and CO2 formation, the thermodynamic ethene yield would still be limited by CH4 conversion, as illustrated in Figure 24.  Figure 24 illustrates methane conversions and ethene yields as functions of temperature at 1 and 10 bar, calculated by assuming a reactant feed composition comprising only CH 4 and O 2 at the CH 4 /O 2 feed molar ratio equal to 9, and assuming the presence of six compounds, which included CH 4 , O 2 , H 2 , H 2 O, C 2 H 6 and C 2 H 4 . As the formation of CO and CO 2 was assumed to be null, the difference between CH 4 conversion and ethene yield represents the yield towards ethane (not shown). As one can see, even in this case methane conversions are far from 100%.

Effect of Co-Feeding Ethane and CO 2
Several works have investigated the kinetic aspects of separately co-feeding ethane and CO 2 along with CH 4 and O 2 mixtures in the OCM reactor, either in the presence or absence of heterogeneous catalysts [99,145]. This section evaluates the thermodynamic benefits and drawbacks associated with these approaches.

Co-Feeding of Ethane
It has been shown that the addition of C 2 H 6 into the CH 4 and O 2 feed mixtures can lead to an increase in ethene yields both in the presence and absence of catalyst, with the increase being more pronounced when ethane dehydrogenation is performed without any catalyst [99,145]. However, while ethene yield is increased, CH 4 conversion is reduced and can even cease in the presence of catalyst, while it can slightly increase in its absence, depending on the ethane composition [99,145]. Thus, the present study also evaluated the thermodynamics effect of co-feeding ethane into the OCM reactor in a wide range of operational conditions. As illustrated in Figure 25a,b, which presents ethene yield as a function of temperature at a CH 4 /O 2 feed molar ratio equal to 9 and pressure of 1 (a) and 10 (b) bar for different ethane feed compositions ranging between 0 and 30 mol%, the co-feeding of ethane increases thermodynamic ethene yields in significant amounts.

Co-Feeding of CO2
Research has long aimed to evaluate the potential feasibility of recycling OCM produced CO2 into the catalytic OCM reactor. As discussed in the previous section, the co-feeding of CO2 with CH4 and O2 mixtures over catalytic OCM reactors has been demonstrated to result in significantly lower methane conversions and ethene yields, a fact usually associated with the competitive adsorption of CO2 and O2 on catalyst active sites [92,102,147,148]. However, it has also been suggested that the co-feeding of CO2 can play a role in improving catalyst stability [147] and even present a positive impact on ethene yield, either through its interaction with the catalyst surface [28] or by enabling changes in CH4 and O2 diffusivities when used as a diluent, which could create local environments of higher CH4/O2 molar ratios within the catalyst bed [149]. Indeed, in an excellent review covering the advances in catalyst development for the CO2-OCM process [150], the authors summarise how different reducibility features from catalytic systems, such as CeO2/ZnO and SrMnO2.5 oxides, could result in improved performances in C2 formation. In this mechanism, CO2 would decompose at the catalyst surface, forming While CH 4 and C 2 H 6 as reactants can compete for O 2 , leading to a reduction in the CH 4 conversion, as illustrated in Figure 25c, both ethane oxidation and pyrolysis can produce CH 4 [146], resulting in the net increase in the CH 4 composition with the ethane feed composition, as illustrated in Figure 25d (right axis), and, thus, in artificially negative methane conversion values, purposely omitted in Figure 25c. Figure 25d also illustrates the equilibrium molar distribution among remaining compounds as a function of ethane feed composition at 900 • C, 1 bar and CH 4 /O 2 molar feed ratio equal to 9, where both CO and H 2 compositions are reduced at higher ethane feed composition conditions. While the reduction in CO composition can be associated with the preferential ethane oxidation, which can reduce O 2 availability for oxidising CH 4 , the reduction in H 2 composition can be either associated with its consumption in reactions involving the formation of CH 4 or its lower production through ethane dehydrogenation.

Co-Feeding of CO 2
Research has long aimed to evaluate the potential feasibility of recycling OCM produced CO 2 into the catalytic OCM reactor. As discussed in the previous section, the co-feeding of CO 2 with CH 4 and O 2 mixtures over catalytic OCM reactors has been demonstrated to result in significantly lower methane conversions and ethene yields, a fact usually associated with the competitive adsorption of CO 2 and O 2 on catalyst active sites [92,102,147,148]. However, it has also been suggested that the co-feeding of CO 2 can play a role in improving catalyst stability [147] and even present a positive impact on ethene yield, either through its interaction with the catalyst surface [28] or by enabling changes in CH 4 and O 2 diffusivities when used as a diluent, which could create local environments of higher CH 4 /O 2 molar ratios within the catalyst bed [149]. Indeed, in an excellent review covering the advances in catalyst development for the CO 2 -OCM process [150], the authors summarise how different reducibility features from catalytic systems, such as CeO 2 /ZnO and SrMnO 2.5 oxides, could result in improved performances in C2 formation. In this mechanism, CO 2 would decompose at the catalyst surface, forming CO and an oxygen active site, and this step would involve CO 2 oxidising a reduced metal, such as Zn +1 or Mn 2+ .
Despite previous works on the thermodynamic aspects of methane dry reforming [151], involving reactant mixtures of CH 4 and CO 2 , which indicated the preferential thermodynamic production of CO and H 2 over ethene and ethane, to the best of our knowledge, the effect of CO 2 co-feeding with CH 4 and O 2 mixtures on thermodynamic ethene yields in a wide range of OCM operational conditions has not been reported. Thus, one objective of the present study was the investigation of the thermodynamic effects of CO 2 co-feeding. Figure 26a shows thermodynamic ethene yields as a function of temperature at 1 bar for different feed mixtures of CO 2 , CH 4 and O 2 , where the CO 2 composition was varied between 0 and 30 mol% while the CH 4 /O 2 molar ratio was kept constant and equal to 9. As one can see, the use of CO 2 as a diluent results in lower thermodynamic ethene yields, driven by a shift in the products selectivity distribution, as illustrated in the molar composition distribution at 900 • C in Figure 26c, towards the increased formation of CO and H 2 , which also can boost thermodynamic CH 4 conversions, as illustrated in Figure 26b. Thus, while CO 2 recycling can be favourable for the production of synthesis gas (as previously stated [151]), any observed positive effects of CO 2 co-feeding on ethene yields should not result from thermodynamic effects.

The Importance of Considering Additional Products on Equilibrium Compositions
The effect of the operation variables temperature, pressure, inert composition, CH 4 /O 2 feed ratio and co-feeding on equilibrium compositions has so far been analysed assuming the existence of eight compounds: CH 4 , O 2 , CO, CO 2 , H 2 , H 2 O, C 2 H 6 , and C 2 H 4 . In this section, this group is expanded in order to assess the impact of the formation of additional compounds, including propene, propane and acetylene, on equilibrium compositions, as these compounds have been reported as constituents in stream flows, exemplifying the outlet of OCM reactors designed to produce up to 1000 kt per year of polymer-grade ethylene [152].
As illustrated in Figure 27, no significant changes in CH 4 conversions and C 2 H 4 selectivities could be verified after the inclusion of propane, propene, and acetylene in the thermodynamic calculations, as these compounds are not favoured at equilibrium. Therefore, previously observed operational variable effects can be considered the same when these compounds are present in the reacting system as co-products. driven by a shift in the products selectivity distribution, as illustrated in the molar composition distribution at 900 °C in Figure 26c, towards the increased formation of CO and H2, which also can boost thermodynamic CH4 conversions, as illustrated in Figure 26b. Thus, while CO2 recycling can be favourable for the production of synthesis gas (as previously stated [151]), any observed positive effects of CO2 co-feeding on ethene yields should not result from thermodynamic effects. Figure 26. Effect of co-feeding CO2 on carbon-based ethene yield (a) and CH4 conversion (b) as a function of temperature at the CH4/O2 molar feed ratio equal to 9 and pressure of 1 bar; and (c) equilibrium molar distribution as a function of CO2 feed composition at 900 °C, 1 bar and CH4/O2 molar feed ratio equal to 9. CO2 composition in the feed was varied while keeping the total number of mols and the CH4/O2 feed molar ratio constant. Ethene yield was calculated considering both methane and CO2 in the feed.

The Importance of Considering Additional Products on Equilibrium Compositions
The effect of the operation variables temperature, pressure, inert composition, CH4/O2 feed ratio and co-feeding on equilibrium compositions has so far been analysed assuming the existence of eight compounds: CH4, O2, CO, CO2, H2, H2O, C2H6, and C2H4. In this section, this group is expanded in order to assess the impact of the formation of additional compounds, including propene, propane and acetylene, on equilibrium compositions, as these compounds have been reported as constituents in stream flows, Figure 26. Effect of co-feeding CO 2 on carbon-based ethene yield (a) and CH 4 conversion (b) as a function of temperature at the CH 4 /O 2 molar feed ratio equal to 9 and pressure of 1 bar; and (c) equilibrium molar distribution as a function of CO 2 feed composition at 900 • C, 1 bar and CH 4 /O 2 molar feed ratio equal to 9. CO 2 composition in the feed was varied while keeping the total number of mols and the CH 4 /O 2 feed molar ratio constant. Ethene yield was calculated considering both methane and CO 2 in the feed. exemplifying the outlet of OCM reactors designed to produce up to 1000 kt per year of polymer-grade ethylene [152]. As illustrated in Figure 27, no significant changes in CH4 conversions and C2H4 selectivities could be verified after the inclusion of propane, propene, and acetylene in the thermodynamic calculations, as these compounds are not favoured at equilibrium. Therefore, previously observed operational variable effects can be considered the same when these compounds are present in the reacting system as co-products. Figure 27. CH4 conversion and C2H4 selectivity (in C%) as a function of temperature at 9 bar and CH4/O2 feed molar ratio of 9. Reactant composition comprised CH4 and O2 only. Equilibrium compositions were calculated assuming the initial group of eight compounds (including CH4, O2, CO, CO2, H2, H2O, C2H6, and C2H4) and an expanded group containing eleven compounds in which propane, propene and acetylene were added.

Active OCM Catalysts
According to the generally accepted kinetic mechanism, the main role of a catalyst in ethene formation is to assist the generation of methyl radicals, CH3 • , by either homolytic or heterolytic C-H bond cleavage in the CH4 molecule [109], as illustrated in Figure 28.

Active OCM Catalysts
According to the generally accepted kinetic mechanism, the main role of a catalyst in ethene formation is to assist the generation of methyl radicals, CH 3 • , by either homolytic or heterolytic C-H bond cleavage in the CH 4 molecule [109], as illustrated in Figure 28. Figure 27. CH4 conversion and C2H4 selectivity (in C%) as a function of temperature at 9 bar and CH4/O2 feed molar ratio of 9. Reactant composition comprised CH4 and O2 only. Equilibrium compositions were calculated assuming the initial group of eight compounds (including CH4, O2, CO, CO2, H2, H2O, C2H6, and C2H4) and an expanded group containing eleven compounds in which propane, propene and acetylene were added.

Active OCM Catalysts
According to the generally accepted kinetic mechanism, the main role of a catalyst in ethene formation is to assist the generation of methyl radicals, CH3 • , by either homolytic or heterolytic C-H bond cleavage in the CH4 molecule [109], as illustrated in Figure 28. The activation of methane via homolytic scission is believed to involve O − active species, which act as Lewis acid [29,109]. These active species can be created by either the doping of metal oxides with dopants capable of promoting the creation of lattice oxygen vacancies, which may enable the formation of O − species in the vicinities of O 2− lattice oxygen, and/or by the adsorption of molecular oxygen on Lewis base centres on the catalyst surface, which can lead to the formation of electrophilic O − species depending on the amount of charge exchanged [107,109]. Unfortunately, the adsorption of molecular O2 can also lead to the formation of weakly bounded nucleophilic O2 − species, believed to be The activation of methane via homolytic scission is believed to involve O − active species, which act as Lewis acid [29,109]. These active species can be created by either the doping of metal oxides with dopants capable of promoting the creation of lattice oxygen vacancies, which may enable the formation of O − species in the vicinities of O 2− lattice oxygen, and/or by the adsorption of molecular oxygen on Lewis base centres on the catalyst surface, which can lead to the formation of electrophilic O − species depending on the amount of charge exchanged [107,109]. Unfortunately, the adsorption of molecular O 2 can also lead to the formation of weakly bounded nucleophilic O 2 − species, believed to be involved in the conversion of CH 4 , C 2 H 6 and C 2 H 4 to oxygenated compounds [109,153]. On the other hand, CH 4 activation via a heterolytic route would involve a Lewis acidbase pair centre on the catalyst surface, such as M 2+ −O 2− , resulting in the formation of a hydroxyl group and a methyl anion, which would then desorb as a methyl radical after losing an electron. Moreover, the catalyst surface would also be involved in radicals quenching by promoting termination reactions which reduce the concentration of radicals, leading to unselective pathways [93].
While the mechanism and nature of active sites is still in debate, as illustrated by the fact that several catalyst properties, such as surface oxide reducibility [154], acid-base properties [28,155], metal oxide-support interactions and morphology, may play an important role in C2 formation, as recently reviewed [156]. This section aims to quantitatively review and compare the catalytic performances of OCM heterogeneous catalysts. By focusing on quantitative aspects of catalytic performance, we hope to provide an overview that can contribute to future analyses of OCM economic viability at an industrial scale. Catalysts in this section have been organised in terms of the number of metals that constitute the oxide. Thus, it will be shown in the next sections that there are many different metal combinations which are OCM active.  4 and O 2 has been correlated with their surface acid-base and/or redox properties [67,110].

Monometallic Oxides
In order to better understand the relationship between single oxides basicity and their OCM activity, La 2 O 3 , Nd 2 O 3 , ZrO 2 , and Nb 2 O 5 were evaluated individually by Kús et al. [110]. These authors found La 2 O 3 and Nd 2 O 3 oxides to be more active and C2 selective when compared to ZrO 2 and Nb 2 O 5 . The results were well correlated with the total basicity of the evaluated catalysts, which was measured by CO 2 temperatureprogrammed desorption (CO 2 -TPD) experiments and by reactions of 2-butanol conversion. Interestingly, La 2 O 3 presented the highest total basicity, CH 4 conversion and C2 selectivity. More recently, a comparison among single lanthanoid oxides further confirmed the findings of Kús et al. [110,157].
C2 selectivity over monometallic oxides can be observed to fluctuate around 32.3 ± 1.5%, as illustrated in Figure 29a, while C2 yield and CH 4 conversion vary and reach up to approximately 14 and 40%, respectively. In this figure, 54 experimental data points for C2 yields as a function of CH 4 [110,111,[158][159][160][161][162][163], indicate that despite differences in catalyst chemical composition, an average selectivity could be calculated. Obviously, while a linear increase in yield with conversion was expected, a similar average slope among catalysts with different catalytic properties could indicate that effects other than kinetics could be limiting catalytic performance.
Moreover, Figure 29b summarises C2 yields obtained after reaction times longer than 16 h, suggesting that the assessment of thermal stability among different monometallic oxides deserves further attention. For instance, Arndt et al. [111] demonstrated how different catalyst preparation methodologies could significantly impact the thermal stability of obtained oxides, which despite presenting similar selectivities to C2, could be more active for longer.

Bimetallic Oxides
Alkali-metal-doped basic oxides have shown promising catalytic performance for C2 selectivities in the OCM process. However, the evaporation of alkali metals at high temperature is reported as a cause of catalyst deactivation [164]. For instance, Li-doped MgO (Li/MgO) oxide has been a classic catalyst used in OCM reaction studies [102,103,165], this system receiving great attention due to its high initial selectivity and activity towards C2 compounds [52]. However, its stability has been proved to be limited due to Li volatility [106,111].
In an attempt to improve the thermal stability of Li-doped MgO catalysts, different catalyst preparation procedures have been investigated, using different lithium loadings [111]. However, regardless of the synthesis preparation method, catalyst activity has been observed to significantly reduce with reaction times, resulting in recommendations against the use of Li/MgO systems for industrial applications.
The doping of CaO with alkali metals has also been reported to improve the catalytic performance towards C2 compounds when compared with the single oxides (including Figure 29. C2 yields as a function of CH 4 conversion over monometallic oxides (a) and C2 yields for different catalysts after reaction times (time on stream (TOS)) longer than 16 h (b). Data sourced from [110,111,[158][159][160][161][162][163]. Dashed circle indicates data from La 2 O 3 nanowires [163]. Moreover, Figure 29b summarises C2 yields obtained after reaction times longer than 16 h, suggesting that the assessment of thermal stability among different monometallic oxides deserves further attention. For instance, Arndt et al. [111] demonstrated how different catalyst preparation methodologies could significantly impact the thermal stability of obtained oxides, which despite presenting similar selectivities to C2, could be more active for longer.

Bimetallic Oxides
Alkali-metal-doped basic oxides have shown promising catalytic performance for C2 selectivities in the OCM process. However, the evaporation of alkali metals at high temperature is reported as a cause of catalyst deactivation [164]. For instance, Li-doped MgO (Li/MgO) oxide has been a classic catalyst used in OCM reaction studies [102,103,165], this system receiving great attention due to its high initial selectivity and activity towards C2 compounds [52]. However, its stability has been proved to be limited due to Li volatility [106,111].
In an attempt to improve the thermal stability of Li-doped MgO catalysts, different catalyst preparation procedures have been investigated, using different lithium loadings [111]. However, regardless of the synthesis preparation method, catalyst activity has been observed to significantly reduce with reaction times, resulting in recommendations against the use of Li/MgO systems for industrial applications.
The doping of CaO with alkali metals has also been reported to improve the catalytic performance towards C2 compounds when compared with the single oxides (including Li-CaO, Na-CaO, K-CaO, Rb-CaO, Cs-CaO) [164]. These authors further investigated the effect of the doping metal composition on the catalytic performance, by testing two alkali metal to Ca ratios, as illustrated in Figure 30a. However, unlike the findings from Kús et al. [110], no clear relationship between catalyst surface basicity and catalytic performance could be quantified, as illustrated in Figure 30b, where the linear correlation coefficient between surface basicity, in mol·m 2 , and CH 4 conversion, C2 selectivity and C2 yield are plotted as a function of reaction conditions. As can be seen, the obtained correlations are all below 0.4, suggesting a weak or non-existent relationship. A similar lack of clear relationship between catalyst properties, such as surface ba sicity and specific area and catalytic performance, was reported for La-doped CaO cata lysts prepared from different sources of starting materials [159], leading the authors to conclude that surface acidity could also be important in the OCM mechanism, even though surface acidity was not characterised.
In contrast, a clear relationship between CH4 conversion, C2 selectivity and surface basicity was reported for catalysts based on Sr-Al mixed oxides [160]. In this study, the authors demonstrated how tailoring the Sr/Al atomic ratio could allow for improving C2 selectivities and yields, as illustrated in Figure 31, as Sr atoms substituted on the amor phous fraction of the Al2O3 oxide could contribute to the formation of both oxygen va cancies and oxygen electrophilic species through O2 adsorption on Lewis base centres supporting therefore that CH4 activation could occur via a homolytic route ( Figure 28) However, an increase in the ratio between Al IV /Al VI species with Sr composition was also observed, and thus a contribution from acid-base pairs through a heterolytic route could not be ruled out. The Sr/Al-1.25 catalyst would, in addition, be able to keep its catalyti performance without significant signs of deactivation for 48 h at 810 °C [160]. A similar lack of clear relationship between catalyst properties, such as surface basicity and specific area and catalytic performance, was reported for La-doped CaO catalysts prepared from different sources of starting materials [159], leading the authors to conclude that surface acidity could also be important in the OCM mechanism, even though surface acidity was not characterised.
In contrast, a clear relationship between CH 4 conversion, C2 selectivity and surface basicity was reported for catalysts based on Sr-Al mixed oxides [160]. In this study, the authors demonstrated how tailoring the Sr/Al atomic ratio could allow for improving C2 selectivities and yields, as illustrated in Figure 31, as Sr atoms substituted on the amorphous fraction of the Al 2 O 3 oxide could contribute to the formation of both oxygen vacancies and oxygen electrophilic species through O 2 adsorption on Lewis base centres, supporting therefore that CH 4 activation could occur via a homolytic route ( Figure 28). However, an increase in the ratio between Al IV /Al VI species with Sr composition was also observed, and thus a contribution from acid-base pairs through a heterolytic route could not be ruled out. The Sr/Al-1.25 catalyst would, in addition, be able to keep its catalytic performance without significant signs of deactivation for 48 h at 810 • C [160].
The concentration of basic sites was also demonstrated to correlate with C2 yields over Sm 2 O 3 /MgO, TbO x /MgO, CeO 2 /MgO and PrO y /MgO systems [52], according to measurements of CO 2 -TPD. In this case, the volume of CO 2 desorbed at around 360 • C followed the order of Sm 2 O 3 /MgO > TbO x /MgO > PrO y /MgO > MgO > CeO 2 /MgO, which was similar to the order of obtained C2 yields between 500 and 800 • C. cancies and oxygen electrophilic species through O2 adsorption on Lewis base cen supporting therefore that CH4 activation could occur via a homolytic route ( Figure  However, an increase in the ratio between Al IV /Al VI species with Sr composition was observed, and thus a contribution from acid-base pairs through a heterolytic route co not be ruled out. The Sr/Al-1.25 catalyst would, in addition, be able to keep its cata performance without significant signs of deactivation for 48 h at 810 °C [160]. The concentration of basic sites was also demonstrated to correlate with C2 yi over Sm2O3/MgO, TbOx/MgO, CeO2/MgO and PrOy/MgO systems [52], accordin measurements of CO2-TPD. In this case, the volume of CO2 desorbed at around 360 Catalytic systems based on Sr-doped La 2 O 3 [126,163,166] have also been reported as promising, with more recent findings supporting their high concentration of basic sites [63,157]. However, catalytic stability seems to be limited to reaction times up to 30 h, with longer stability up to 60 h being demonstrated upon the doping of Sr/La 2 O 3 with zirconium [63].
Besides the distinct chemical properties obtained from different combinations of metal oxides, morphological properties have also been demonstrated to exert an important role in the OCM process, as demonstrated by the advent of nanocatalysts showing catalytic advantages when compared to their bulk powder counterparts [163,167]. For instance, nanocatalysts have been demonstrated to be active at lower reaction temperatures [167,168], a fact which has been associated with their larger surface area and well-defined surface structure [167]. Improved thermal stability has also been suggested as a potential advantage due to higher levels of surface organisational stoichiometry, which could minimise the likelihood of deactivation due to particles sintering and metal agglomeration [169,170]. In this context, the development of nanocatalysts with particular morphologies, such as nanofibers and nanowires, has been receiving great attention, in particular due to the large surface-to-volume ratios achievable with these systems, enabling higher fractions of atoms to be located at the surface, and thus increasing the availability of active sites. However, as pointed by Yunarti et al. [161], typical high OCM temperatures may negatively impact the above-mentioned morphological features, minimising their catalytic advantages.
It can be observed that CH 4 conversions are typically lower than 30% and that the maximum experimental C2 yields fluctuate around 15-20%. When overall C2 yields are evaluated as a function of the methane conversion, a similar mean C2 selectivity approximately equal to 53% can be calculated, indicating that bimetallic oxides could present an overall similar catalytic performance, with C2 yield being a function of CH 4 conversion. In addition, with only a few exceptions, we have verified experimental CH 4 conversions to be far from equilibrium, as illustrated in Figure S2a-c in the Supplementary Materials, suggesting that similar C2 selectivities could not be explained by global thermodynamic equilibrium. As discussed in Section 4 and illustrated in Figure 24, the maximum achievab thermodynamic yield corresponds to conditions in which CO and CO2 formation can suppressed, in which case the thermodynamic C2 yield approaches CH4 conversio Therefore, if observed experimental CH4 conversions would be assumed as approachi the maximum C2 thermodynamic yield, it would be possible to verify that experimen yields could be further increased in most cases if the formation of CO and CO2 could avoided, as illustrated in Figure 33. Additionally, the above could also suggest th ethane and ethene formation could indeed be affected by a thermodynamic factor, sin experimental C2 yields are not so far from this hypothetical maximum achievable in t absence of CO and CO2. Thus, ethane and ethene formation reactions could be at the cinity of a 'pseudo-equilibrium' state, in which the formation of CO and CO2 would rep sent the lowest limiting surface steps. As discussed in Section 4 and illustrated in Figure 24, the maximum achievable thermodynamic yield corresponds to conditions in which CO and CO 2 formation can be suppressed, in which case the thermodynamic C2 yield approaches CH 4 conversion. Therefore, if observed experimental CH 4 conversions would be assumed as approaching the maximum C2 thermodynamic yield, it would be possible to verify that experimental yields could be further increased in most cases if the formation of CO and CO 2 could be avoided, as illustrated in Figure 33. Additionally, the above could also suggest that ethane and ethene formation could indeed be affected by a thermodynamic factor, since experimental C2 yields are not so far from this hypothetical maximum achievable in the absence of CO and CO 2 . Thus, ethane and ethene formation reactions could be at the vicinity of a 'pseudo-equilibrium' state, in which the formation of CO and CO 2 would represent the lowest limiting surface steps.

Trimetallic Oxides
A wide variety of trimetallic oxide catalysts have also been investigated for ethene production from OCM, including Ba-substituted LaInO3 perovskites [172], alkali or alkaline metal (Li, Na, Ca or Mg)-doped lanthanoid oxides (Sm2O3, TbOx, CeO2, and PrOy) supported on MgO [52], substituted titanates SrTiO3 and Sr2TiO4, promoted with Mg, Ca, Ba, Pb and Al [173], structured rings and monoliths based on bismuth-yttrium-samarium oxide [175] and Mg-Na-doped La2O3 nanowires [163]. Figure 34 summarises the ranges of CH4 conversion and C2 yields reported over these catalytic systems, in which it can be noted that most of the conversions and yields are concentrated in the range below 30 and 20%, respectively, and that an average C2 selectivity of 54 ± 1.2% can describe reasonably well overall catalytic performances, in agreement with the average C2 selectivity calculated for bimetallic systems, Section 5.2.

Trimetallic Oxides
A wide variety of trimetallic oxide catalysts have also been investigated for ethene production from OCM, including Ba-substituted LaInO 3 perovskites [172], alkali or alkaline metal (Li, Na, Ca or Mg)-doped lanthanoid oxides (Sm 2 O 3 , TbO x , CeO 2 , and PrO y ) supported on MgO [52], substituted titanates SrTiO 3 and Sr 2 TiO 4 , promoted with Mg, Ca, Ba, Pb and Al [173], structured rings and monoliths based on bismuth-yttrium-samarium oxide [175] and Mg-Na-doped La 2 O 3 nanowires [163]. Figure 34 summarises the ranges of CH 4 conversion and C2 yields reported over these catalytic systems, in which it can be noted that most of the conversions and yields are concentrated in the range below 30 and 20%, respectively, and that an average C2 selectivity of 54 ± 1.2% can describe reasonably well overall catalytic performances, in agreement with the average C2 selectivity calculated for bimetallic systems, Section 5.2. CH 4 conversions higher than 30% at C2 yield levels of 20-25% have been reported over structured rings and monoliths based on bismuth-yttrium-samarium oxide [175]. According to these authors, the superior activity of the monolith-like structured catalytic reactor would relate to its organised flow pattern, which can contribute to more efficient interaction between reactants and the catalyst surface, as also concluded by others [56]. More recently, La 2 Ce 1.5 Ca 0.5 O 7 oxides have also been reported to reach similar catalytic performances, with demonstrated thermal stability for up to 100 h [38]. Processes 2021, 9,   CH4 conversions higher than 30% at C2 yield levels of 20-25% have been reported over structured rings and monoliths based on bismuth-yttrium-samarium oxide [175]. According to these authors, the superior activity of the monolith-like structured catalytic reactor would relate to its organised flow pattern, which can contribute to more efficient interaction between reactants and the catalyst surface, as also concluded by others [56]. More recently, La2Ce1.5Ca0.5O7 oxides have also been reported to reach similar catalytic performances, with demonstrated thermal stability for up to 100 h [38].
Ba-substituted LaInO3 catalytic activity has been rationalized to result from the production of active oxygen species upon Ba addition [172]. For alkali or alkaline metal (Li, Na, Ca or Mg)-doped lanthanoid oxides (Sm2O3, TbOx, CeO2, and PrOy) supported on nanoparticles MgO catalysts [52], Li-TbOx/MgO and Na-TbOx/MgO systems have demonstrated the most promising performances, albeit presenting poor thermal stability in a 30 h-long reaction test at 700 °C, with a CH4/O2 feed molar ratio equal to 4 and reactant stream diluted in nitrogen. Interestingly, the catalytic activity observed at 700 °C for the Li, Na, Ca or Mg-doped TbOx/n-MgO systems could be well explained by its correlation with the distribution of basic sites per unit of surface area, as illustrated in Figure S3 in the Supplementary Materials. For substituted titanates SrTiO3 and Sr2TiO4, promoted with Mg, Ca, Ba, Pb and Al [173], a positive effect of these metal additions on the initial SrTiO3 and Sr2TiO4 materials has also been observed. In particular, Mg addition demonstrated the best improvement in C2 yield, which could also be associated with the resultant increase in the concentration of basic sites, as suggested by CO2 adsorption experiments followed by infrared spectroscopic analysis.
Finally, it is also interesting to compare the catalytic activity reported over Mg-Na-doped La2O3 nanowire oxides [163], prepared using a biological template, reported as the key factor for the final oxide morphology, and a slow multi-step calcination procedure. In this case, Mg and Na addition resulted in only minor improvement in C2 selectivity at the cost of slightly lower CH4 conversions, affording similar C2 yields between the Mg-Na-doped (11-15%) and monometallic La2O3 (13-15%) nanowire oxides.

Multimetallic Oxides
In the search for more efficient catalysts, multi-component systems have also been explored. By using computer-aided design with an artificial neural network, Huang et al. (2001Huang et al. ( , 2003 [176,177] reported an optimal chemical composition for a catalytic system constituted by Na, Mn, Zr, S, W and P supported on SiO2. According to these authors' results, the optimised catalysts would be able to achieve selectivities towards C2 compounds as high as 70% even at CH4 conversion levels of 35%, at nearly 800 °C and using a Ba-substituted LaInO 3 catalytic activity has been rationalized to result from the production of active oxygen species upon Ba addition [172]. For alkali or alkaline metal (Li, Na, Ca or Mg)-doped lanthanoid oxides (Sm 2 O 3 , TbO x , CeO 2 , and PrO y ) supported on nanoparticles MgO catalysts [52], Li-TbO x /MgO and Na-TbO x /MgO systems have demonstrated the most promising performances, albeit presenting poor thermal stability in a 30 h-long reaction test at 700 • C, with a CH 4 /O 2 feed molar ratio equal to 4 and reactant stream diluted in nitrogen. Interestingly, the catalytic activity observed at 700 • C for the Li, Na, Ca or Mg-doped TbO x /n-MgO systems could be well explained by its correlation with the distribution of basic sites per unit of surface area, as illustrated in Figure S3 in the Supplementary Materials. For substituted titanates SrTiO 3 and Sr 2 TiO 4 , promoted with Mg, Ca, Ba, Pb and Al [173], a positive effect of these metal additions on the initial SrTiO 3 and Sr 2 TiO 4 materials has also been observed. In particular, Mg addition demonstrated the best improvement in C2 yield, which could also be associated with the resultant increase in the concentration of basic sites, as suggested by CO 2 adsorption experiments followed by infrared spectroscopic analysis.
Finally, it is also interesting to compare the catalytic activity reported over Mg-Nadoped La 2 O 3 nanowire oxides [163], prepared using a biological template, reported as the key factor for the final oxide morphology, and a slow multi-step calcination procedure. In this case, Mg and Na addition resulted in only minor improvement in C2 selectivity at the cost of slightly lower CH 4 conversions, affording similar C2 yields between the Mg-Na-doped (11-15%) and monometallic La 2 O 3 (13-15%) nanowire oxides.

Multimetallic Oxides
In the search for more efficient catalysts, multi-component systems have also been explored. By using computer-aided design with an artificial neural network, Huang et al. (2001Huang et al. ( , 2003 [176,177] reported an optimal chemical composition for a catalytic system constituted by Na, Mn, Zr, S, W and P supported on SiO 2 . According to these authors' results, the optimised catalysts would be able to achieve selectivities towards C2 compounds as high as 70% even at CH 4 conversion levels of 35%, at nearly 800 • C and using a reactant stream of CH 4 and O 2 with no diluent. However, their thermal stability for long reaction times was not reported. Another example involves Na-Co-doped LiMnMgB and undoped LiMnMgB oxide systems [178], for which high selectivities (64-68%) at relatively high CH 4 conversion levels (24-29%) have also been reported. In this case, the main advantage in doping the LiMnMgB system seems to have been the resultant higher activity at lower temperatures, affording a C2 yield increase from 1 to 12% between the undoped and doped system at 750 • C [178].
However, to the best of our knowledge, multimetallic catalyst systems comprising Me-W-Mn-O/SiO 2 , in which Me stands for Na or Ce, and TiO 2 -doped Na-W-Mn-O/SiO 2 , represent some of the few catalytic systems for which thermal stability has been shown to endure for up to 500 and 1000 h [50,134,179,180]. Not surprisingly, these catalysts have been extensively investigated in an attempt to understand the reasons for their outstanding stability and identify active sites [44,181]. However, as noted previously 181 , the identity of active sites associated with these systems remains under debate [182,183], with more recent findings suggesting sodium oxide species as active sites which would remain stable due to 'synergistic' effects between Na 2 WO 4 and Mn 7 SiO 12 phases [182].
In addition, several studies have explored the impact of different preparation procedures [48,54,174,184,185], alternative supports to SiO 2 [178,[186][187][188], dopants [183] and the substitution of Na [46,49,51,179,186,189] or Mn [186] by different elements in the abovementioned system. Incipient wetness impregnation was suggested to produce a more active catalyst when compared to sol-gel synthesis for athe same chemical composition in a study involving Na-W-Mn-O/SiO 2 [184]. In contrast, sol-gel synthesis was indicated as the most suitable method for obtaining higher ethylene yields when compared to impregnation or physical mixing in a study involving Li-W-Mn-O/SiO 2 [179]. According to these authors [179], the high degree of homogenisation enabled by the sol-gel method would be responsible for the formation of a highly crystalline structure, which would be important to obtain higher C2 yields, even though similar catalytic performances were observed for catalysts prepared by physical mixing, which presented poor crystallinity. More recently, the preparation of core-shell structures has been claimed to result in more C2-selective Na-W-Mn-O/SiO 2 catalysts due to a greater dispersion of active components, even though reported selectivities could not be regarded as statistically different from bulk Na-W-Mn-O/SiO 2 catalysts [190].
The evaluation of alternative supports to SiO 2 has in general confirmed SiO 2 as the most promising support for this catalytic system [178,[186][187][188], as further illustrated in Figure 35, which was compiled from data reported by [53,178,[185][186][187][188][189]191], where reports in a molar base [183,187,192] were excluded. In addition, it was demonstrated that the use of ordered mesoporous silica, as opposed to commercial silica gel, could improve catalytic performance by enabling better dispersion of active sites on the catalyst surface, as suggested by energy-dispersive X-ray spectroscopy (EDX) mapping measurements, even after the collapse of the mesoporous structure upon thermal treatment around 750 • C [53,192].  [53,178,[185][186][187][188][189]191]. The continuous black line denotes the slope where selectivity is 55%.
The doping of the Na-W-Mn-O/SiO2 catalyst with Pt, Ir and Rh has also been reported to improve catalyst reducibility, as suggested by H2 temperature-programmed reduction experiments (H2-TPR), resulting in a shift in the product selectivity distribution in which smaller amounts of CO and CO2 compounds were observed at 750 °C [183]. More recently, high-throughput screening has also been applied to assess the effect of substituting Na or Mn by different elements in the above-mentioned system in a wide range of reaction operational conditions [186], further supporting previous indications that the best catalytic performance is associated with the Na-W-Mn-O/SiO2 system [189].  [53,178,[185][186][187][188][189]191]. The continuous black line denotes the slope where selectivity is 55%.
The doping of the Na-W-Mn-O/SiO 2 catalyst with Pt, Ir and Rh has also been reported to improve catalyst reducibility, as suggested by H 2 temperature-programmed reduction experiments (H 2 -TPR), resulting in a shift in the product selectivity distribution in which smaller amounts of CO and CO 2 compounds were observed at 750 • C [183]. More recently, high-throughput screening has also been applied to assess the effect of substituting Na or Mn by different elements in the above-mentioned system in a wide range of reaction operational conditions [186], further supporting previous indications that the best catalytic performance is associated with the Na-W-Mn-O/SiO 2 system [189].
Finally, it is interesting to note that most promising catalytic performances, as illustrated in Figure 35, could still be described by an average C2 selectivity approximately equal to 55 ± 20%, with slightly higher selectivities being observed at lower CH 4 conversions.

Environmental Concerns: Can OCM Be Sustainable?
OCM has been described as one of the most promising routes to convert methane into more valuable hydrocarbons [35,193,194]. However, economic feasibility analyses have shown that greater C2 yields are needed to enable profit [123]. For this reason, many efforts focused on optimising C2 yields have been made, as also shown in previous sections. In contrast, little attention has been focused on addressing the huge amounts of CO and CO 2 produced. As a matter of fact, OCM implementation should only be encouraged if produced CO and CO 2 can be realistically recycled in the process or managed by alternative solutions.
Prospects for CO 2 utilisation can be broadly divided into two main process categories. The first involves the direct consumption of CO 2 , for example, its use in the production of food, beverages, and chemicals. The second class of processes involves its conversion into other compounds. However, although such applications exist, their viable scales are still small and, therefore, they have a small impact on current global CO 2 emissions [195][196][197]. Additional pathways and their associated challenges are discussed in [198].
Therefore, integrating OCM with an ethane cracker could represent an alternative for reutilising the CO and CO 2 produced, although not necessarily representing a complete solution. In this case, OCM-generated CO and CO 2 could be coupled with H 2 from ethane cracking in a methanation reactor for producing methane. In addition, this approach can present the advantage of energy savings, as the heat produced in the methanation reactor could be used as supply in endothermic ethane dehydrogenation [199]. However, questions arise on the impact of the impurities present in OCM output streams on the stability and performance of methanation catalysts. Clearly, more studies must be carried out in this area to prove the technical and economic feasibility of these integrations.

Conclusions and Outlook
The present review on the oxidative coupling of methane for ethylene production has highlighted important challenges to be addressed if OCM technology is to be implemented at an industrial scale. Firstly, the proposed bibliometric analysis of OCM scientific publications and patents indicated that the focuses of academic and industrial research have been distinct, with the former concentrating efforts towards catalyst development and the latter being concerned with broader aspects of process flow diagrams. Therefore, further scientific studies to support the industrial focus on optimising OCM flow diagrams seem to be needed.
Secondly, the proposed analysis of OCM reactions and kinetics, involving chemical reactor modelling approaches, suggests that further studies are greatly needed to enable the prediction (and thus optimisation) of catalytic performances at reaction conditions of industrial interest (involving high pressures), despite the significant advances in the understanding of kinetic mechanisms and the modelling of catalytic activity. Additionally, how experimental studies have indicated the existence of different active sites on OCM catalyst surfaces was discussed, including, for instance, different oxygen active species. Despite this, the kinetic models developed so far have considered a unique entity to represent existing active catalyst sites. Moreover, the fact that both simpler (involving 10 catalytic reaction steps) and more complex (involving 26 catalytic reaction steps) kinetic models can well represent catalytic performances at atmospheric conditions suggests that kinetic descriptions can be improved and that further studies are urgently needed for discriminating among OCM kinetic models and, thus, determining the most suitable one for reactor and process design.
The analysis of chemical reactor modelling approaches also suggests the lack of consensus on the importance of describing mass and energy balances in the reactor and catalyst scale, as the vast majority of scientific papers concerning modelling studies (58% of a sample of 30 papers) reports a preference for the use of homogeneous or pseudo-homogeneous models, despite undeniable previous research on the importance of considering concentration gradients of radical intermediate species inside catalyst particles. Thus, further studies are needed for developing heterogenous and two-dimensional models that can embrace mass and energy transport among the distinct reactor phases simultaneously. These models could then be applied for assessing the feasibility of autothermal operation, which could represent a great technological breakthrough for OCM operation.
Furthermore, the proposed review on some thermodynamic aspects of the OCM reactions stressed how maximum ethylene yields are limited by CH 4 thermodynamic conversions, although favoured by high inert feed compositions and high temperatures (above 850 • C). As thermodynamics favour H 2 and CO formation at typical OCM conditions, it appears that economic feasibility should be pursued while integrating OCM with alternative processes.
Finally, the analysis of OCM active catalysts and their performances suggests that a common average selectivity of approximately 55% can be observed among promising catalytic materials, despite operating far from global thermodynamic equilibrium, indicating that OCM catalytic performance may be affected (and limited) by thermodynamic factors, further supporting the need for additional studies on OCM kinetic models, as already mentioned. However, the review also stresses the need for further assessments on catalyst stability at reaction conditions of industrial interest, as thermal stability has been largely overlooked, despite its fundamental importance for OCM industrial feasibility.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/pr9122196/s1, Section S1: Yields and Selectivities definitions, Table S1: Standard Gibbs energies in increasing order at 900 • C and standard reaction enthalpies for global OCM reactions, Figure S1: Effect of the CH 4 /O 2 feed ratio and temperature at 1 bar on the combined ethene and ethane (C2) yield, Figure S2: Comparison between experimental and equilibrium CH 4 conversions for bimetallic oxides, Figure S3: Relationship between C2 yield and basicity distribution per unit of surface area.