*3.1. CO2 Methanation*

Carbon dioxide hydrogenation was considered for the first time by Paul Sabatier and Jean B. Senderens in 1902. In the paper "Nouvelles syntheses du methane" [57] they proved that one mole of methane may be obtained in the reaction of one mole of carbon dioxide with four moles of hydrogen, acc. to reaction:

$$\text{CO}\_2 + 4\text{H}\_2 \rightleftharpoons \text{CH}\_4 + 2\text{H}\_2\text{O}$$

This reaction is exothermic and spontaneous. At room temperature (~25 ◦C) its enthalpy ( ΔH) is −165 kJ/mol and the Gibbs free energy ( ΔG) is −113.5 kJ/mol [10]. Δ G describes the maximum free energy (energy that can be turned into work) that can be released or adsorbed when it goes from the initial state to the final state. In the CO2 methanation, a negative ΔG indicates that the substrates (initial state) have more free energy than the products (final state). Therefore, the move towards products involves the release of energy. Energy does not have to be provided for the reaction to occur—it occurs spontaneously. In turn, ΔH refers to the difference between the bond energy of products and substrates. A negative ΔH means a heat release during the reaction towards the products. In the temperature range from 25 to 500 ◦C, ΔG and ΔH is presented in Figure 5. If the reaction is exo-energetic in one direction, it is also endo-energetic in the opposite direction. Therefore, if the Gibbs free energy in methanation increases rapidly with the rise of temperature (provision of thermal energy), so that above 500 ◦C it becomes positive, then in the high temperature range, the reverse reaction—methane reforming (CH4 + H2O CO + 3H2)—prevails and disturbs the obtaining of methane [58]. However, the course of CO2 methanation is more complicated and may comprise many intermediate or side reactions. Jiajian Gao specifies them in Table 2 and gives their equilibrium constant K from 200 to 800 ◦C in Figure 6 [59].

**Figure 5.** Enthalpy and Gibbs free energy for CO2 methanation in the temperature range from 25 to 500 ◦C. Data extracted from [10].


**Table 2.** Main possible reactions during carbon dioxide methanation. Data extracted from [59].

**Figure 6.** The equilibrium constants (K) for the reactions presented in Table 2, in the temperature range from 200 to 800 ◦C. © Adopted from [59].

Analysis of the above data can conclude that the temperature is the main parameter affecting the equilibrium. Therefore, from the thermodynamic point of view, the methanation reaction of carbon dioxide should be carried out at low temperatures. However, under such conditions the reaction rate goes down. Hence the CO2 hydrogenation requires the application of a catalyst [23,60]. It allows the achievement of an acceptable reaction rate and a reduction in the cost of the process itself [61,62].

## *3.2. Catalyst in Methanation*

Metals from group VIII to XI stand out among methanation catalysts [63]. Nickel is probably the most frequently studied metal [64–67]. It features the most favorable ratio of metal price to its activity. Additionally, ruthenium and rhodium show interesting properties [67–71]. In the case of Ru and Rh catalysts, apart from a high activity, their ability to prevent sintering and accumulation of carbon particles is their important advantage, which makes them additionally resistant to deactivation. In addition, Ru stands out in the low-temperature methanation, e.g., in the Ru/TiO2 system [72] or Ru/Ni\_nanowires [73]. A low temperature is an important parameter optimizing the thermodynamic and energy efficiency. Numerous studies are related to the possibility of lowering the temperature. Using the example of selective carbon monoxide (CO) methanation [74], Table 3 presents a summary of studies in this field.



1 WHSV—weight hourly space velocity (flow of reagents per unit of catalyst mass in the unit of time). 2 GHSV—gas hourly space velocity (volumetric flow of reagents per unit of catalyst volume in the unit of time). 3 Tmin and Tmax—minimum and maximum temperature, setting the range in which CO concentration in the reformate is less than 10, or 20 ppm in a few cases. Smin and Smax—reaction selectivity at Tmin and Tmax, respectively.

Another issue is the catalyst activity dependence on the support, on which the selected metal has been placed. For the catalyzed reaction it is favorable to maximize the metal surface area for a specific metal weight [75]. Therefore, small metal particles are synthesized (usually smaller than 1–10 nm), with a narrow size distribution, but with a uniform location on a large specific surface of a thermally stable substrate [23,63,76]. Hence, support in the form of oxides (e.g., SiO2, Al2O3, TiO2), zeolites, carbon, or metaloorganic compounds is distinguished. Support affects also the adsorption and catalytic properties. Figure 7 may be an example, presenting the difference between the selected oxide support of nickel catalyst and the yield of CO2 methanation.

**Figure 7.** Impact of catalyst supports on the yield of CO2 to CH4 conversion. Reaction conditions: 1 mol% CO2, 50 mol% H2, 49 mol% He, F/W = 1000 mL/min/gcat. © Adopted from [77].

Studies on the support of methanation catalyst were enhanced with studies on catalytic promoters, that is, substances added to improve or change the catalyst operation. MgO is an example of a catalyst promoter which, introduced to Ni/Al2O3 catalyst, increases the thermal stability [78] and resistance to carbon parts precipitation [79]. La2O3 increases the Ni/Al2O3 catalyst activity via the increase in the nickel dispersion and hydrogen capture [80]. The enhancement of nickel catalyst with V2O3 improves its activity, thermal stability, and resistance to sintering [81]. The addition of CeO2 allows the achievement of a higher susceptibility to reduction and long-term stability [82]. In turn, potassium increases the selectivity towards conversion to higher hydrocarbons [83]. In the context of obtaining methane this is obviously not a desired effect.

The type of support is significant for the CO2 methanation mechanism [71,84–87]. Hydrogenation of carbon dioxide may proceed via various paths through different structures, which include CO, -OCH3, and HCOO- groups. Their origination, further reaction, as well as adsorption and desorption frequently depend on the morphology of the support surface. For example, mezostructural silica, which due to the presence of internal and interparticle pores increases the number of free oxygen sites in the catalyst, is decisive in a particular mechanism of the reaction [88–90]. It is schematically presented in Figure 8. According to this theory, CO2 and H2 are adsorbed on the metallic catalyst. As a result of the dissociation of molecular forms, CO, O, and H originate then, which can migrate to the carrier surface. In the next stage CO reacts with oxygen from the carrier surface, forming formate or carbonyl groups in a bridge or bidentate system. In addition, the formation of bidentate formate requires an additional reaction with hydrogen. An oxygen atom is subject to surface stabilization through interaction with electron gaps of the oxide carrier, close to the metal. Oxygen stabilized in this way reacts with hydrogen forming a hydroxyl group, which in a further reaction with hydrogen will form a molecule of water. Oxygen-rich forms of carbon formed on the surface, that is, carbonyl and formate, are hydrogenated to methane.

**Figure 8.** Likely mechanism of CO2 methanation using the catalyst that is based on mesostructured nanosilica support. © Adopted from [88].

The subsequent essence of matters is the diffusion effect [91,92]. It is a process on the catalyst site that, in a simplified description, may include the following steps: (1) transport of the reactants from the gas phase to the catalyst surface (external diffusion), (2) diffusion of substrates to the surface inside the catalyst pores (internal diffusion), (3) surface operations (chemisorption and catalytic reaction), (4) diffusion of reaction products from inside the catalyst pores to the outside surface (internal diffusion), and (5) migration of reaction products from the catalyst surface to the gas phase (external diffusion). Depending on the morphology of the catalytic surface, the effect of external and internal diffusion is considered. The external diffusion effect depends on the size of the catalyst grains, the flow rate, and the diffusion properties of the reactants. In turn, the internal diffusion effect depends on the porosity of the material, the pore size and distribution, pore connectivity, and the size of the catalytic material grains. The diffusion effect is even more significant when considering the concentration and temperature gradients inside and over the catalyst surface. This topic is discussed in detail in the review [93]. Nevertheless, it is worth noting that this effect is often wrongly ignored, which causes a misinterpretation of the results. Diffusion plays a role in such essential factors as the rate and bottleneck of the reaction or the conversion and product distribution.

The combination of metal and specified support is also frequently studied in the photocatalytic methanation [94]. It was observed that the application of heat and light together can minimize the energy consumption and ensure unique features which cannot be achieved in conventional thermocatalytic reactions [95–97]. Light absorbed by metallic nanoparticles of the catalyst and by reagents existing on their surface is a source of intraband or interband transformations, which generate electrons with a high kinetic energy, so-called hot electrons [97–99]. Hot electrons are effective activators of reagents or intermediate compounds. As a result, a reduced activation energy is observed [100]. For example, in the reaction of carbon dioxide methanation, at 150 ◦C, hot electrons formed as a result of light absorption by a CO2 molecule (adsorbed on the metallic surface of Ru/SiO2 catalyst) increase the conversion of carbon dioxide to methane from 1.6% to 32.6% [101]. Figures 9 and 10 compare Ru/SiO2 and Rh/SiO2 catalysts in the CO2 methanation with the involvement of light and without.

**Figure 9.** CO2 conversion on Ru/SiO2 catalyst with and without light. Data extracted from [101]. Conditions: 0.5% vol. CO2/N2 (50 sccm) and H2 (1.5 sccm). Lamp parameters: Xe 35 mW cm<sup>−</sup><sup>2</sup> with water cooling to exclude the heat effect from the light.

**Figure 10.** CO2 conversion on Rh/SiO2 catalyst with and without light. Data extracted from [101]. Conditions: 0.5% vol. CO2/N2 (50 sccm) and H2 (1.5 sccm). Lamp parameters: Xe 35 mW cm<sup>−</sup><sup>2</sup> with water cooling to exclude the heat effect from the light.

The activity of these catalysts is additionally conditioned by the size of metal nanoparticles (Figure 11). Larger nanoparticles, e.g., ≥5 nm, reduce the activation barrier for CO2 molecule dissociation on the metal surface. In the case of a photosensitive system this results in a larger number of hot electrons, which improve the reaction kinetics.

**Figure 11.** CO2 conversion on Ru/SiO2 for different sizes of Ru nanoparticles. Data extracted from [101].

The last issue is the method of catalyst preparation. The selection of preparative method may determine such factors as the size and shape of metal nanoparticles, their uniform distribution on the support, limitation of nanoparticle aggregation, as well as minimization of the used metal [75,102]. Many various methods have been presented in the review entitled "Methods for Preparation of Catalytic Materials" [102]. However, in the context of the aforementioned silica becoming increasingly popular in nanomethods, a proprietary method of our team may draw attention. The method comprises two main stages. The first of them consists in the synthesis of amorphous silica, which plays the role of an intermediate carrier and matrix for metallic nanoparticle generation. The second is the matrix digesting and transferring nanoparticles of the selected metal onto the target support. It is graphically presented in Figure 12. Silica is synthesized by the Stöber method [103]. The aim consists in obtaining spherical, monodisperse, and uniform sizes of silica nanoparticles from the water solution of alcohol and silicon alcoxides at the presence of ammonia as the catalyst. Two basic reactions are distinguished:

> Hydrolysis: Si-(OR)4 + H2O Si-(OH)4 + 4R-OH

Condensation: 2Si-(OH)4 2(Si-O-Si) + 4H2O

Hydrolysis leads to the formation of silanol groups, while siloxane bridges result from the condensation polymerization. The reaction product depends on the type of silicon alcoxide and alcohol. The authors of the methods emphasize that particles prepared in solutions are the smallest, and the particle size increases with the growing length of the alcohol carbon chain. Rao et al. [104] in turn pay attention to the size and deviation of silica grain size through modification of the concentration of silicon alcoxide and alcohol, ammonia concentration, water content, and the change of reaction temperature. This allows the fine-tuning of the physical properties of silica, which is extremely important for later generation of specified sizes of metal nanoparticles. The second stage comprises nanometal growing on the matrix, reducing the intermediate conjugate (metal-silica) with hydrogen, digesting the silica with lye (when other support is needed), transferring metallic nanoparticles onto the surface of the target support, or separating metal nanoparticles. This method allows for nanomanipulation of nanoparticles' size and shape, reduction of their tendency to aggregate and form lumps, and for reduction of the amount of used material. So far this method has worked well in preparing high-performance catalysts for ammonia cracking [105], CO2 methanation [73,106,107], glycerol oxidation [108], and Sonogashira coupling [109].

**Figure 12.** Preparation method of Ru/Ni catalyst for CO2 methanation. © Adopted from [106].

#### **4. Modeling of the Methanation Catalysis—The Determination of Research Clues**

Modelling and simulations in silico are more and more often used in designing and optimizing methanation processes [68,110,111]. In such studies the kinetics of CO2 methanation is usually modelled by a combination of CO methanation and reversed water-gas shift reaction (RWGSR) [112–114]. The resultant process depends on the rates of both these reactions. The quality of the forecasted model depends on the knowledge of reaction mechanisms and elementary stages, which determine expressions for reaction rates. However, the learning of an exact mechanism and kinetic description is not always unambiguous. This may be explained by varying reaction conditions (e.g., different values of temperatures or partial pressures), the concept of reactor and the applied catalyst, or by assumptions or the

computational method (Langmuir-Hinshelwood, Power Law, elementary reactions, stages of reaction rate) [111]. However, theoretical models are necessary to design catalysts [115]. It was observed that activation energies for elementary surface reactions on catalyst are strongly correlated with adsorption energies, which facilitates identification of significant descriptors [68]. This is illustrated in Figure 13, using the example of CO methanation.

The effect of high dissociation energy is typical of a densely packed surface, while certain surface features (edges, angles, steps, and kinks) enable us to lower the energy barrier [116,117]. Therefore, an active place on the catalyst surface is identified by a convenient nucleation place. The comparison of various metallic surfaces of catalysts (Figure 13a) allows us to state that the activation barrier for CO, CH4, and H2O is related to the surface stability of carbon (C) and oxygen (O) forms [68]. The more stable these atoms are, the lower the CO and CH4 dissociation barrier, and the higher the H2O formation barrier. It was found that the activation energies also essentially depend linearly on the reaction energy acc. to the so-called Brønsted-Evans-Polanyi relationship (BEP) (Figure 13b) [118]. This enables us to make the rate of reaction on metal surfaces of various catalysts directly dependent on the CO dissociation energy (Figure 13c) [119]. In the case of poor adsorption (right part of graph in Figure 13c), the barrier for product dissociation is high, which limits the reaction rate. For a strong adsorption the rate of removing the adsorbed C and O from the surface is small, hence the barrier for product formation is high. The optimum is situated between these two limits. This effect is a well-known Sabatier rule [120]. In addition, for combinations of different materials, the scaling relationships for the adsorption and energy of transition state of the reaction are unlimited and it becomes possible to optimally adjust the catalysts' activity or selectivity even in the next catalytic sequences [121,122]. Furthermore, this search for catalytic materials is currently supported by machine learning [123]. For example, a sample of a heterogeneous catalyst in a set of different catalysts—catalyst space (defined by composition, carrier type, and particle size) can be described by its features in a certain feature space that is defined by physical properties, atomic properties, and electronic structure. Then machine learning algorithms can generate models or find descriptors that map the features that describe catalysts to their figures of merit (defined by selectivity, activity, and stability). The latest research shows that, thanks to machine learning methods, it is already possible to predict catalytic activity values, reaction descriptors, and potential energy surfaces, and to screen optimal catalysts [123–125].

The designing of catalytic materials with target properties must be described by both the basic (descriptors of anticipated properties) and empirical (measured properties) data. In addition, it is important to gather the data in a structured way, and to consider the possibility of their reorganization and export to any format, so that their processing would be easy and widely available. As a team we have drawn attention to this in the paper "Functional and Material Properties in Nanocatalyst Design: A Data Handling and Sharing Problem" [126], and by creating the "Catalytic Material Database" (CMD), available at cmd.us.edu.pl. The experimental data for heterogeneous catalysts, used mainly in carbon oxides methanation, are gathered in this database. More information on this is available on the database website.

**Figure 13.** Identification of a descriptor for the CO methanation. © Adopted from [115,119]. (**a**) Calculated energy diagrams for CO methanation over Ni, Ru, and Re. (**b**) Brønsted–Evans–Polanyi relation for CO dissociation over transition metal surfaces. The transition state potential energy, Ea, is linearly related to the CO dissociation energy. (**c**) The corresponding measured volcano-relation for the methanation rate.

**Author Contributions:** Conceptualization, D.L.; methodology, D.L. and J.P.; validation, D.L., J.P. and M.K.; formal analysis, D.L. and M.K.; investigation, D.L., J.P. and M.K.; resources, J.P.; data curation, D.L., J.P. and M.K.; writing—original draft preparation, D.L. and J.P.; writing—review and editing, D.L., J.P. and M.K.; visualization, D.L. and M.K.; supervision, J.P. and D.L.; project administration, D.L.; funding acquisition, J.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Science Center OPUS 2018/29/B/ST8/02303.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Jaroslaw Polanski would like to acknowledge Zielony Horyzont: New Energy project ZFIN 40001022 for support.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
