Kinetic modelling of the methanol synthesis from CO 2 and H 2 over a CuO/CeO 2 /ZrO 2 catalyst

This work addresses the kinetics of the CO 2 hydrogenation to methanol over a Cu/CeO 2 /ZrO 2 catalyst studied using single-site, dual-sites and three adsorption sites kinetic models. Physicochemical constraints and statistical indicators are used as tool for model discrimination. The best performing model is used to elucidate the reaction mechanism and the relative roles of the Cu-sites and oxygen vacancies. The results show that the dissociative adsorption of H 2 occurs on the Cu 0 sites, while CO 2 is attracted to the oxygen vacancies created by the CeO 2 -ZrO 2 solid solution. Then, the adsorbed H interacts preferentially with the carbon atom, favouring the so-called “ formate ” route . The CO formed via the r-WGS reaction could either desorb to the gas phase or react via hydrogenation to methanol. Analysis of the relative contributions of the CO 2 and CO hydrogenation (i.e. direct and indirect pathways, respectively) to the methanol synthesis reveals that the latter is in fact preferential at high temperatures (i.e. about 100% of methanol is produced from CO at 260 ⁰ C and 30 bar), and it shows an optimum vs the H 2 :CO 2 ratio (c.a. 7 at 200 ⁰ C and 30 bar), which corresponds to the saturation of the Cu 0 sites with H 2 . Thus, this work provides an essential tool (i.e., kinetic model) for the design of reactors and processes based on novel catalysts, and importantly, it offers a deeper understanding of the reaction mechanism as basis for further catalyst development.


Introduction
The combustion of hydrocarbons to produce energy entails a critical global challenge that needs to be tackled with urgency.The usage of fossil fuels correlates directly to the release of greenhouse gassesespecially CO 2 -into the atmosphere, which is the main responsible of global warming [1,2].Hence, in the last century research has been focusing on the development of carbon capture and storage technologies (CCS) first and, more recently, on the alternatives for CO 2 utilization (CCU) [3][4][5][6].An interesting approach for CCU is the CO 2 reduction with renewable H 2 to produce valuable chemicals and/or energy carriers [7].In this context, the CO 2 conversion to methanol is particularly appealing due to the high methanol demand worldwide (i.e. about 200 kton of methanol are used every day as chemical feedstock and transportation fuel) [8].Indeed, methanol could be used directly as an alternative fuel or as intermediate for the production of dimethyl ether, olefins, gasoline and aromatics [9][10][11].The CO 2 hydrogenation to methanol is a catalytic gas phase process which follows three main reactions: the direct hydrogenation of CO 2 to methanol (reaction 1), the production of CO through the r-WGS reaction (reaction 2) and the hydrogenation of CO to methanol (reaction 3).
Among these reactions, the CO 2 hydrogenation to methanol is the most desired.Inevitably, the r-WGS takes place in parallel, accelerating the H 2 depletion and, at the same time, contributing to the production of water.As a matter of fact, water is the main reaction by-product, which limits the system thermodynamically and causes catalyst deactivation [12].Depending on the catalyst, the CO hydrogenation to methanol (reaction 3) could take place simultaneously, partially balancing the negative effect of the r-WGS.Nowadays, methanol is produced industrially from syngas feedstock (i.e., mixture of CO, H 2 and c.a. 3% of CO 2 ) at pressures of 50-80 bar and temperatures of 200-300 ⁰C, over CuO/ ZnO/Al 2 O 3 catalytic beds [13,14].Since the benchmark technology involves only traces of CO 2 in the feedstock [15], the corresponding catalyst is not necessarily optimal when using pure CO 2 , i.e., a thermodynamically very stable molecule, as the sole carbon source.Usually CO 2 adsorption is not strong enough [16] and efforts are required specifically on novel catalyst formulations [17].Over the years, researchers have proposed a variety of different catalysts for the CO 2 hydrogenation to methanol, with particular focus on Cu-based systems, in combination with different metal oxides as carrier and/or promoters [18][19][20][21].First, important research efforts aimed at replacing the hydrophilic Al 2 O 3 support, which could deactivate in presence of the large amounts of water produced in all the reactions [22].In most of the catalyst formulations, the ZnO oxide still acts as main promoter, since it guarantees both a higher Cu dispersion and the formation of Cu δ+ sites at the Cu-ZnO interface [23][24][25].On the other hand, various carriers/promoters have been proposed in literature such as ZrO 2 [17,[25][26][27][28][29], CeO 2 [22,[30][31][32][33][34], Fe 2 O 3 [34][35][36], SiO 2 [37][38][39], and TiO 2 [30,[40][41][42][43].Most recently, the synergistic effect of CeO 2 -ZrO 2 mixed oxides has received particular attention due to their high redox ability, improved thermal stability [44] and superior oxygen storage capacity (OCS) [45], properties that have proved highly beneficial for different reactive systems, such as the oxidation of aliphatic C2 [46], the conversion of NOx [47], the reduction of NO by propene [48] and, most recently, for the CO 2 hydrogenation to methanol [49][50][51].The introduction of smaller Zr 4+ ions into the CeO 2 tetrahedron creates a defective fluorite structure, which facilitates the adsorption of oxygen [52].Shi et al., [49] proposed for the first time a ternary CuO/CeO 2 /ZrO 2 catalyst for the CO 2 hydrogenation to methanol.They found that a Ce:Zr mass ratio of 1 optimizes the basicity of the system in favour of the CO 2 adsorption capacity.Their Cu 30 Ce 35 Zr 35 O catalyst showed excellent reducibility and Cu dispersion, as well as a balanced distribution of Cu 0 and strong basic sites to enhance the H 2 dissociative-adsorption and the formation of the H 2 CO intermediate, which preferentially hydrogenates to form methanol.Wang et al., [50] investigated the reaction pathway via in situ DRIFTS analysis.They showed that a calcination temperature of 450 ⁰C increases the CuO surface area and the formation of Cu-Ce-Zr sites, which favour the formation of H* and bi/m-HCOO*, responsible for the high selectivity to methanol.
In any catalytic process, kinetic modelling is an essential tool to support efforts on catalyst development, to elucidate reaction mechanisms as well as to aid reactor design and process optimization.Numerous kinetic models have been proposed over the years to describe the methanol synthesis, mostly on commercial catalysts [13,[53][54][55][56][57].However, the majority of the kinetic models trace back to the works of Graaf et al., [58] and Bussche and Froment [59].Both models propose a Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism with the

Symbol, Definition, Units S Cu
Copper surface area, (m Stoichiometric number of component i in reaction j, (− ) Total number of reaction, (− ) Pre-exponential factor of the kinetic constant of reaction j, (depending on model) where methanol is produced from CO 2 and CO simultaneously.On the contrary, Bussche and Froment considered a mechanism where Cu is the sole active site and CO 2 is the only carbon source for the methanol production.Even today, literature shows disagreements on the relative contribution of CO and CO 2 to the methanol synthesis.For example, Liu et al., [60] propose at least four parallel reactions: CO-CO 2 exchange, CO hydrogenation, CO 2 hydrogenation and WGS, while Bowker et al., [61] proposed that CO 2 is the only responsible of methanol synthesis, even when feeding CO/CO 2 /H 2 mixtures.Interestingly, Yang et al., [62] proved that the CO 2 and CO contributions to methanol synthesis varies with the operating conditions.More recently, Niels et al., [63] found that CO 2 is the immediate source for methanol (i.e., CO 2 pathway is one order of magnitude faster), whereas the presence of CO is inhibitory at low conversion due to competitive adsorption, and beneficial at higher conversion due to the removal of water via the WGS.Finally, L.C. Grabow and M. Mavrikakis [64] showed through DFT calculations that about 2/3 of the methanol comes from CO 2 in the conventional process (i.e., syngas feed).However, the situation could be completely different with CO 2 -rich streams and other catalyst formulations.
More recently, Park et al., [65] developed a model considering threesites adsorption, where CO 2 and CO adsorb on two distinct sites.In this study the authors carried out a rate determining step analysis (RDS) based on the mechanistic hypotheses earlier proposed by Graaf et al., to find the rate expressions that best fit the experimental data.Seidel et al., [56] reviewed the elementary steps involved in the three-sites adsorption mechanism, proposing an even more complex kinetic model.This was recently simplified by Slotboom et al., [66], who reduced the number of kinetic parameters considerably.
Despite the extensive literature database of kinetic models and rate expressions for the Cu:ZnO system supported on either Al 2 O 3 (i.e., benchmark formulation) or other metal oxides, kinetic modelling of the methanol synthesis remains an intriguing research topic, with at least two important open questions: 1) what are the type and number of the catalyst active sites involved in the methanol synthesis; and 2) which is the dominant C-source for methanol formation (i.e., CO/CO 2 ) and the corresponding prevailing reaction pathway.In addition, and to the best of our knowledge, the kinetics of this reaction on novel catalysts such as Cu-Ce-Zr mixed oxides (i.e., better performant catalysts for the conversion of CO 2 ) has not been investigated yet.
Herein, the kinetic model of methanol synthesis from CO 2 and H 2 over a Cu-Ce-Zr mixed oxide catalyst is investigated by means of an RDS analysis for the single-site, dual-site and three-sites adsorption kinetic model, based on the most relevant mechanistic hypotheses retrieved from literature.A total of 6 kinetic models are compared with a complete set of 96 experimental data in the range of temperature, pressure, H 2 :CO 2 molar ratio and GHSV of 200-260 ⁰C and 10-40 bar, 3-7 and 7500-24000 NL⋅kg − 1 cat ⋅h − 1 , respectively.The preparation of the ternary catalyst according to the works of Shi et al., [49] and Wang et al., [50] is followed by in depth catalyst characterization and extensive kinetic tests.Statistical analysis of the data combined with physicochemical constraints are used as tool for model discriminations.This work pays particular attention to the relative contribution of CO 2 and CO to the formation of methanol (i.e., methanol synthesis from direct and indirect route, respectively) under various reaction conditions, by means of a theoretical differential analysis.The identification of the kinetic model, together with a detailed analysis of the reaction rates and the interplay between CO 2 and CO hydrogenation will lead to a better understanding of this system.In this study, we will gain insights into the reaction mechanisms, identify the active sites and their role within the methanol formation, which is key for further improvement of this catalyst formulation, as well as an essential tool for reactor and process design.

Kinetic models for methanol synthesis: State of the art
To elucidate on the reaction pathway involved in the CO 2 hydrogenation to methanol over a copper-cerium-zirconium mixed oxides catalyst, the most relevant kinetic models reported in literature have been explored and re-parametrized.All the available kinetic models can be sorted in three groups, based on the number of active sites considered in the formulation of the mechanism.A detailed discussion is given below.

Single-site adsorption mechanism
The most relevant kinetic model considering a single-site adsorption mechanism is the one developed by Bussche and Froment in 1996 [59].The most important assumption is that CO 2 is the sole carbon source for methanol synthesis.As a result, only reaction (1) and ( 2) take place on the Cu surface of the catalyst, where both H 2 and CO 2 undergo dissociative adsorption.According to the authors, the rate determining steps are: 1) the CO 2 dissociation on the active sites, which releases surface oxygen for the rWGS reaction and 2) the hydrogenation of the formate species for the CO 2 hydrogenation to methanol.The rate equations are reported in Eq. 3-5.
The Bussche and Froment model considers three adsorption constants (i.e., b H2 O/H2/8/9 , b H2 and b H2O ) and two kinetic constants (i.e., k 1 and k 2 ), for a total of 10 parameters to be optimized.

Dual-site adsorption mechanism
The most important and widely employed kinetic model describing the methanol synthesis is the model developed by Graaf et al., [58] in 1988.In their first publication, the authors had already recognized the lack of agreement in the literature on whether the carbon source for the methanol production is CO or CO 2 .As a result, they developed a model including both pathways (reaction 1, 2 and 3).All the reactions are assumed to be based on a dual-site LHHW mechanism, where CO and CO 2 adsorb competitively on one site (s 1 ) and H 2 and H 2 O adsorb competitively on a second site (s 2 ), with dissociation of H 2 .The adsorption of methanol is once again neglected.The rate equations are reported in Eq. 6-8, with the two adsorption terms (i.e., Θ 1 and Θ 2 ) related to the site s 1 and site s 1 described in Eq. 9-10. ) ) − 1 (10) where A, B, and C represents the driving force of the CO hydrogenation, r-WGS and CO 2 hydrogenation to methanol, respectively.As a matter of fact, the authors provided also different expressions for the driving forces terms, which depends on the particular RDS for the specific  [54].His reparameterization was based on two sets of experimental results, obtained from two distinct set-ups: 1) a Berty reactor and 2) a micro-fixed bed reactor, from which he obtained two different set of kinetic parameters [55].The rate equations proposed for the CO 2 hydrogenation and the rWGS are reported in Eq. 11-12, which lead to a total of 10 kinetic parameters.

Three-sites adsorption mechanism
In 2014, Park et al., [65] proposed a reaction pathway, based on the mechanism developed by Graaf et al., with the introduction of a third adsorption site exclusively for CO 2 .The authors considered the methanol dehydration to dimethyl ether in their reaction scheme, which was discarded in our analysis since no traces of DME were detected during the experimentation.The rate equations are summarized in Eq. 13-15.The model from Park et al., involves 14 kinetic parameters to be optimized.
Few years later, in 2018, Seidel et al., [56] developed an even more detailed model based on three adsorption sites, reviewing also the elementary reactions involved and the rate determining step of each reaction.The active sites are distinguished as follows: ⊙ for oxidized surface centers, assumed as active center for CO hydrogenation ⋇ for reduced surface centers, assumed as active center for CO 2 hydrogenation ⊗ as the active surface center for the decomposition of H 2 The rate expressions are reported in Eq. 16-18 with the corresponding adsorption terms in Eq. 19-21. ) The parameter ϕ represents the total amount of reduced center, while (1 − ϕ) represents the number of oxidized centers.Slootbom et al., [66] have recently corrected the definition of ϕ, assuming a maximum coverage of the reduced center of 90% (Eq.22).
The authors used the relation of Ovesen et al., [67] for the calculation of ϕ w , as follows: where γ * γ 0 is the relative contact free energy of Cu and Zn, for the benchmark formulation, and of Cu and the CeZr solution for our system.The γ * γ 0 ratio is calculated according to Eq. 24-25, with the introduction of a new kinetic parameter (ΔG 3 ).
In this model, the adsorption constant dependency on temperature is neglected.This lead to a total of 12 parameters, if the group is parametrized as a single constant.
In 2020 Slotboom et al., [66] simplified the three-sites model, drastically reducing the amount of parameters (i.e., 6 in the simplified version).The authors revisited the elementary reaction steps of Bussche and Froment, thus, considering only CO 2 as the carbon source for methanol production, with the updates from recent literature.As Graaf et al., proposed in their study for the dual-sites adsorption mechanism, Slotboom et al., provided a tool for identifying the rate determining step for both the CO 2 hydrogenation and the rWGS (i.e., the CO hydrogenation is neglected).All the possible rate expressions are summarized in Table 2, with a total of 30 kinetic models, with 6 parameters each.The adsorption term, θ ⋇ , is defined by Eq. 26.

Table 1
Expressions of the driving force terms for reaction 1, 2 and 3 according to the rate determining steps (RDS) A, B and C provided by Graaf et al.,

RDS
Driving force

Catalyst synthesis and characterization
The Cu-Ce-Zr mixed oxides catalyst was prepared with a CuO loading of 50 wt%, to be comparable to the benchmark formulation, and a CeO 2 : ZrO 2 mass fraction of 1, as recently optimized by Shi et al., [49].The catalyst was synthesized via the gel-oxalate coprecipitation method [27].The required amount of metal nitrate precursors (i.e., Cu (NO 3 ) 2 ⋅2.5H 2 O, Ce(NO 3 ) 3 ⋅6H 2 O and ZrO(NO 3 ) 2 ⋅6H 2 O) were solubilized in ethanol and coprecipitated by adding an oxalic acid solution (20 wt% excess) dropwise, at room temperature and under continuous stirring.The precipitate was stirred for 3 h, aged overnight, centrifuged and washed with deionized water, dried at 95 ⁰C for 16 h and calcined at 450 ⁰C for 4 h.The catalyst was pelletized, crushed and sieved to produce 50-125 µm particle size, to be used for the characterization techniques and reaction tests.The chemical composition of the synthesized catalyst was measured via microwave plasma atomic emission spectroscopy, using an Agilent MP-AES 4200 elemental analyzer.Prior to the analysis, about 0.1 g of catalyst sample was digested in 70 v.% HNO 3 solution at 80 ⁰C overnight and then diluted with 5 v.% HNO 3 solution (i.e., blank solution), to reach ppm values of the metal content.The specific surface area (S.A.) and pore volume (P.V.) were determined via the BET and BJH elaboration of the N 2 adsorption-desorption isotherms at − 196 ⁰C, obtained using a Micromeritics ASAP 2020 gas adsorption device.Before the measurement, the sample was degassed at 250 ⁰C for 2 h.The catalyst reducibility was studied via temperature programmed reduction (TPR) analysis performed using a Micromeritics AutoChem 2920 equipment with a TCD detector.The analysis was carried out in the range 50-400 ⁰C with a heating rate of 10 ⁰C⋅min − 1 , feeding 50 mL⋅min − 1 of a 10% H 2 /Ar mixture.Prior to the TPR analysis, the sample was outgassed under inert conditions as for the N 2 physisorption.The copper surface area (S Cu ), dispersion (D Cu ) and average surface-volume diameter (d SV Cu ) were determined via N 2 O oxidation followed by H titration method developed by Van der Grift [68].The analysis was carried out in the same equipment used for the TPR and consists in performing a first TPR measurement, whose hydrogen consumption is indicated by X.Thereafter, the temperature was reduced to 90 ⁰C and the sample was outgassed under Ar flow for 2 h.The surface copper was oxidized feeding 50 mL⋅min − 1 of a 2% N 2 O/Ar mixture for 1 h.A second TPR analysis was carried out, whose hydrogen consumption (Y), is indicative of the number of Cu atoms dispersed on the surface of the catalyst.The copper surface area, dispersion and diameter were calculated with Eq. 26, Eq. 27 and Eq. 28, respectively, considering a Cu/N 2 O = 2 titration stoichiometry and a surface atomic density of 1.4⋅10 Cu at ⋅m − 2 .

S Cu =
2Y⋅N av X⋅M Cu ⋅1.410 19  (26) where N av , M Cu and ρ Cu are the Avogadro's number, the copper molecular weight and density, respectively.X-ray diffraction (XRD) analysis in the 2θ range 10-120 • was performed on the reduced catalyst with a MiniFlex600 machine (Rigaku) operating with a Ni β-filtered Cu-Kα radiant at 40 kV and 30 mA and a scan step of 0.05 • /min.The diffraction peaks were identified according to the JCPDS database of reference compounds.The average diameter of the Cu-crystals was estimated via the Scherrer's equation (Eq.29).
where d Cu is the dimension of the crystallites as if they were cubes, monodisperse in size, λ is the wavelength, FWMH is the width of the peak, 2θ is the scattering angle and b is a constant usually varying between 0.89 and 0.94.XPS measurements were performed both on the calcined and reduced catalyst, using a Kratos AXIS Ultra spectrometer, equipped with a monochromatic X-ray source, and a delay-line detector (DLD).Spectra were obtained using an aluminum anode (Al Kα = 1486.6eV) operating at 150 W. The binding energies were internally calibrated setting the C1s peak position at 285 eV.The catalyst real density (ρ cat ) was measured using an automatic gas pycnometer instrument (Ultrapyc 1200e).The apparent density of the catalyst (ρ b,cat ) was calculated via the catalyst porosity (ε cat ), determined from the N physisorption analysis.The catalytic tests were carried out in a stainlesssteel reactor (d int , 10 mm), loaded with 0.25 g of catalyst, diluted with 0.75 g of SiC, to ensure isothermal operation and prevent sintering phenomena.The catalyst and the SiC used for dilution were introduced in the reactor with the same particle size of 50-125 µm.Larger SiC particles were used as pre-heating bed, separated from the catalytic bed with c.a. 1 cm 3 of quartz-wool.The reactor was placed in an electric oven and heated more precisely via a heating mantle.
rWGS with ⋇ and ⊙ similar sites 10-40 bar, respectively, feeding H 2 /CO 2 /N 2 mixtures in different proportion, to have a H 2 :CO 2 molar ratio from 3 to 7, and a GHSV ranging from 7500 to 24000 NL⋅kg − 1 cat ⋅h − 1 .The carbon balance in the reaction was respected with a maximum error of 3%.The catalyst stability was observed within a long-term (100 h) test performed at 250 ⁰C, 30 bar, H 2 :CO 2 molar ratio of 3 and a GHSV of 9600 NL⋅kg − 1 cat ⋅h − 1 .The CO 2 conversion (X CO2 ), product yield (Y i ), product space time yield (STY i ) and product selectivity (S i ) were calculated according to Eq. 30-33, where i is either methanol or CO and w cat is the catalyst weight.Methanol and CO where detected as the sole carbon species in the product mixture.
A commercial Cu/ZnO/Al 2 O 3 catalyst from Johnson Matthey (i.e.Katalko-51) was tested in the exact same conditions, to compare the novel catalyst with the benchmark technology.

Fitting procedure and model discrimination
The fitting procedure was carried out entirely in MATLAB R2019a.The kinetic parameters were determined via the fminsearch optimization procedure, based on the Nelder-Mead simplex algorithm [69], which minimizes an error objective function (OF) that we defined as the sum of the root mean square errors (RMSE) between the experimental and calculated molar fraction of the carbon containing species (i.e., CO 2 , CO and methanol) as follows: Where N data is the number of experimental data used for the kinetic fitting and y exp i and y calc i are the molar fractions of the component i at the exit of the catalytic bed determined experimentally and via the model prediction, respectively.The experimental data were imported in terms of y exp i , together with the corresponding boundary conditions, such as inlet flow (ϕ o ), inlet composition (y 0 i ), temperature (T) and total pressure (P).On the other hand, the y calc i were determined, within the algorithm iterations, via the integral analysis method, thus solving the ODEs describing the mole balance equations in a fixed bed reactor (Eq.36).
where F i is the molar flow rate of the component i, w cat is the catalyst weight, N r is the total number of the reactions involved, ν ji is the stoichiometric number of the component i in the reaction j, and r j is the corresponding reaction rate expression, which is unknown.The mole balance equations were solved under the hypothesis of steady state regime, isothermal operation, negligible pressure drop along the catalytic bed and absence of internal diffusion and external mass transfer limitation.The first three hypothesis were confirmed experimentally: 1) the reaction performance was evaluated at steady state (i.e., when no changes in the outlet composition were recorder over time); 2) the temperature difference between the gas inlet and outlet positions was less than 1 ⁰C and 3) the pressure difference between the gas inlet and outlet positions was less than 0.2 bar.The absence of mass transfer limitations was explored with preliminary experiments (details in S.I.) and was later confirmed with the Mear's [70] and Weisz-Prater [71] testing criteria.The reaction rates (r j ) are function of the partial pressure of the components, and parameters such as kinetic (k j ), adsorption (b i ) and equilibrium constants (K eq j ).The equilibrium constants (Table 3) were retrieved from literature [72].
The kinetic constant of each reaction (k j ) and adsorption constants of the components (b i ) are the parameter to be optimized throughout the algorithm.The kinetic constants were described as a function of a preexponential factor and an activation energy, following the Arrhenius'

Table 3
Equilibrium constant of all the reactions as a function of temperature [72].law (Eq.37) [73].The adsorption constants, instead, were expressed as a function of the standard entropy (ΔS 0 ads,i ) and enthalpy of adsorption (ΔH 0 ads,i ), according to the van 't Hoff equation (Eq.38).However, in some of the kinetic models considered in this study, the dependency on temperature of the adsorption constants is neglected (i.e., ΔH 0 ads,i ≈ RT) [5666].Furthermore, to reduce the number of fitting parameters, some authors lumped the adsorption constants of some components together.

Equilibrium constant Expression Units
The selected algorithm (fminsearch) requires an initial guess for the fitting parameters.Kinetic constant found in literature for the Cu-Zn-Al catalyst were implemented as initial guess, assuming these are likely of similar order of magnitude that the corresponding for our Cu-Ce-Zr catalyst [5513].This minimizes the strong dependence that the algorithm has on the initial guess itself, and therefore increases the probability of obtaining meaningful results.To increase robustness of the model results, we setup a routine that evaluated the sensitivity of the model to the initial guess.This procedure consists of running the optimization algorithm in a loop, with newly obtained results as the initial guess.Thus, the convergence was reached when the difference between the algorithm output and the initial guess was less than 1%.Once the parameters of the best fit were obtained, the covariance matrix was computed with a second algorithm based on Levenberg-Marquardt method (lsqnonlin).From the covariance matrix, the standard deviation and the 95% confidence intervals, first indicators of the quality of the fit, were determined using the nlparci function in MATLAB.However, model discrimination techniques were necessary to find the set of rate expressions that best describe our system and, therefore, to gain insight into the reaction mechanism.A model was discarded at first when the physicochemical constraints (Table 4) were not respected.Thereafter, the significance of the model was assessed via the comparison of the variance of the lack of fit (s 2  1 ) and the experimental error (s 2 2 ), where s 2 1 > s 2 2 .The F-test (Eq.40) was carried out in combination with the analysis of the p-value (Eq.41) (i.e., probability that the data belong to the non-critical area of the Fisher distribution), assuming 95% level of confidence (i.e., α = 0.05).The F statistic was first calculated according to Eq. 39, where s 2  1 is the variance of the lack of fit and s 2 2 is the variance of the experimental error.The F critical was retrieved from the Fisher distribution tables, considering N var and (N data − N var ) as degree of freedom, where N var is the number of variables (parameters).The F statistic was then compared to the F critical (F-test, Eq.40).
As a result, the kinetic models fulfilling the physicochemical constraints were evaluated according to: 1) the value of the objective function, 2) the parity plots of the experimental and calculated flow rates of the carbon species, and 3) the outcome of the F-test and p-value.

Testing criteria for mass transfer limitation
The absence of mass transfer (MT) limitations was evaluated according to the criteria reported in Table 5, where the Carberry (Ca) and the second Damkohler number (Da II ) are defined per component.The order of reaction with respect to the component i (n i ) was estimated with Eq. 42, where r + i is its forward reaction rate [74].Such derivation is specifically defined for complex reaction rates equation such as a LHHW kinetic.The correlations used for the mass transfer coefficient (k gs ) and the effective diffusivity (D e ) are reported in SI.

Catalyst properties and reaction performance
Table 6 summarizes the main physical properties of the Cu/CeO 2 / ZrO 2 catalyst.The textural properties of the catalyst are in line with the literature [49,50].The N 2 physisorption analysis revealed an isotherm of type IV with hysteresis (Figure S1), which is typical of a mesoporous material (i.e., pores in the range of 2-50 nm).The TPR profile (Figure S4a) exhibits two peaks at 204 ⁰C and 231 ⁰C, after deconvolution.No further reduction of the support, due to H 2 spillover, was measured.As a result, a reduction temperature of 250 ⁰C is believed to be sufficient to reduce all the CuO, prior to the reaction tests.The XRD spectra on the calcined and reduced catalyst (Figure S2) show the typical diffraction peaks of CuO at 2θ of 35.5⁰ and 38.7⁰ and of Cu at 2θ of 43.3⁰ and 50.4⁰, respectively.The disappearance of the CuO peak in the XRD spectrum of the reduced sample (Figure S2b) does not necessarily indicate the presence of sole metallic Cu, as CuO crystals smaller than 3-5 nm cannot be detected, as well as the Cu that is in contact with the Ce-Zr phases via O-bridges.The more complex Ce-Zr oxide phase was analyzed via XPS (Figure S3).We confirmed the presence of the Ce 3+ valence, which is introduced by the zirconia phase, as reported elsewhere [49,50].The CuCeZr catalyst of this study is characterized by a Ce 4+ /Ce 3+ ratio of c.a. 3.53, which was calculated through the integration of the corresponding peaks of the XPS spectra.A detailed discussion on the XPS results is given in S.I.The catalyst composition according to the MP-AES method is 52 wt% of CuO, 22 wt% of CeO 2 and 26 wt% of ZrO 2 .This composition is very close to the theorical value, indication of the reliability of the synthesis method.In Fig. 2a the catalyst performance during CO 2 hydrogenation is compared to that of the benchmark formulation (i.e., the CuZnAl from JM).The CuCeZr catalyst shows a much higher methanol production compared to CO, with a crossover temperature (i.e., T cross temperature beyond which STY CO > STY MeOH ) of ca.240 ⁰C.On the contrary, the benchmark catalyst shows a STY CO larger than STY MeOH over the entire temperature range.Since our catalyst formulation and preparation methods is a reproduction of previous works [49,50], we also compare the performance of this catalyst with that of the original reports by Shi et al., [49] (Fig. 2b).The catalyst synthesized in this work shows higher methanol yield with respect to the different formulations proposed by Shi et al., However, the physicochemical properties of our CuCeZr are further   2b.The agreement of our results with literature underline the credibility of the method.Furthermore, they emphasize the promising performance of the CuCeZr catalyst with respect to the benchmark technology, in view of the CO 2 valorization to methanol.

Model discrimination and proposed reaction mechanism
Table 7 reports the information required for the model discrimination procedure, as discussed in Section 4.1.The rate determining step analysis (RDS) is carried out only when the author(s) reported the details behind the model derivations (i.e., Graaf and Slotboom).The discrimination between the different options proposed by Graaf and Slotboom is reported in S.I. and is based on the same criteria shown here.Both the models developed by Park and Seidel did not fulfil all the physicochemical constraints, thus, the statistics analysis was not carried out.It is worth noticing that all the models which do not consider the formation of methanol from CO (reaction 3), resulted in a low p-MeOH (i.e., p-value for methanol) which indicates the tendency of the model towards a scarce prediction of the methanol outlet molar fraction.This result anticipates the importance of considering the contribution of both CO and CO 2 to the methanol synthesis, especially when CO 2 is the sole carbon source.
The model with the lowest RMSE (which corresponds to the final value of the objective function) and the largest p-values for the carbon species is the one proposed by Graaf.As a result, we select this model (Graaf-A 3 B 1 C 3 , where A 3 B 1 C 3 refer to the specific combination of RDS) to be the most representative of our system.The kinetic parameters obtained from the fitting procedure are provided in Table 8.The accuracy of the parameter estimation is represented by the parity plots of CO 2 , CO, H 2 and methanol (Fig. 3).The orders of magnitude of all the parameters are in line with the literature, especially when compared to the values retrieved from Graaf et al.Nevertheless, given the differences in the reaction rate expressions (i.e., A 3 B 1 C 3 for our CuCeZr catalyst versus the A 3 B 2 C 3 for the CuZnAl reported by Graaf), the comparison between the two kinetic modelsand catalystis fair when observed in terms of reaction rates, rather than kinetic constants.Such analysis is addressed in Section 5.5.On the other hand, the adsorption term corresponding to the first and second active sites (i.e., Θ 1 and Θ 2 , respectively) do not differ from the original model.Therefore, in Table 9 we compare the values of our adsorption constants to the same constants

Table 7
Comparison of the kinetic models reparametrized for the CuCeZr catalyst.
Property BF calculated by Graaf at 200 and 260 ⁰C.From the reaction rate expressions (Eq.6-10), we see that the adsorption constants of CO 2 and CO contribute also to the driving force (i.e., numerator of the reaction rate).As a result, the prediction of their effect on the reaction rate is not straightforward.On the contrary, the combined adsorption of H 2 O and H 2 (i.e., b H2O / ̅̅̅̅̅̅̅ b H2 √ ) contributes only to the adsorption term in the denominator, hindering the reaction rate.Since our constant is order of magnitude higher than the one derived by Graaf, this leads to the conclusion that our catalyst is either more sensitive to water or to H 2 adsorption.
The model discrimination allows us not only to identify a model which better predicts the performance of our catalyst, but, most importantly, to gain some insights into the reaction mechanism itself.According to the assumptions behind the model developed by Graaf

Table 8
Kinetic parameters for the Graaf model (A 3 B 1 C 3 ).The adsorption constants b i need to be calculated according to Eq. 13, considering b i,0 = exp ) .
Kinetic parameter Value Units   et al., we can distinguish between two active centers in the structure of the CuCeZr catalyst, which is in agreement with what was hypothesized in literature [49]: 1) the metallic copper (i.e., Cu 0 ), where the dissociative adsorption of H 2 occurs and 2) the oxygen defects within the Ce/ Zr interface, where the CO 2 molecule adsorbs and activates.The H species spillover towards the carbon atom of the activated CO 2 to begin a series hydrogenation steps, knowns as "formate" route.The reaction pathway is sketched in Fig. 4. According to the formate path, methanol can be either synthesized directly from CO 2 (direct route) or indirectly from the CO produced via the rWGS reaction.The two routes overlaps when the H 2 CO intermediate forms, sharing the last two steps which then lead to the formation of methanol.However, at the point where the CO s1 (i.e., CO adsorbed) intermediates appears, an equilibrium between the adsorbed CO and the CO released to the gas phase explains a certain selectivity to CO.The relative contribution of CO and CO 2 to the methanol synthesis depends on different factors such as temperature, H 2 concentration and the distribution of the Cu 0 active sites with respect to the oxygen vacancies.Nevertheless, for a fixed catalyst composition, only reaction conditions can affect the fraction of methanol produced via the direct and indirect paths.A detailed discussion on this aspect is given in Section 5.5.In Fig. 4, the limiting steps of the three reactions are also marked.In particular, the slowest steps are the formation of the H 3 COO s1 , HCOO s1 and H 3 CO s1 intermediates for the reaction 1, 2 and 3, respectively.This result is in agreement with the in situ DRIFT studies carried out by Wang et al., [50], where the formation of the formate (i.e., HCOO s1 ) through the first hydrogenation of the carbon atom is defined as "the slowest and key step".
At this stage, being the reaction rate expressions determined, we could estimate the order of the reaction with respect to CO 2 (n CO2 ) and evaluate the Ca and Da II numbers.We observed that in our experimental conditions, n CO2 ranges between 0.094 and 0.62.Furthermore, both the external mass transfer and internal diffusion limitation resulted to be negligible, being the maximum value of Ca and Da II of 1.4⋅10 -3 and 7.1⋅10 -5 , respectively.This result confirms our earlier conclusion that the experiments were carried out under kinetic regime.

Analysis of the catalyst performance: Experiments vs model prediction
In this section, we discuss the catalyst performance as a function of the reaction conditions explored both experimentally and via model predictions.Experimental points and simulation results are combined in the same graphs, to show at the same time the quality of the fit.A detailed analysis of the thermodynamic equilibrium is reported in S.I.. Furthermore, to underline the compatibility of our results with the adopted equilibrium constant, the catalyst performance as a function of temperature and pressureboth experimental and modeling dataare reported together with the corresponding thermodynamic limit in Figure S10.
First, from Fig. 5 we observe that the kinetic model (solid lines) describes accurately the experimental reaction performance (points), in terms of X CO2 (Fig. 5a), Y MeOH (Fig. 5b) and Y CO (Fig. 5c) as a function of the space velocity (GHSV) at various temperatures.As expected from a kinetically controlled system, the conversion decreases with the space velocity, being the contact time of the gases with the catalytic bed shorter.Furthermore, Y MeOH and Y CO show the same trend as X CO2 , leading to the conclusion that the contact time does not affect the product distribution in the range we explored.As a result, when employing a GHSV in the range 7500-24000 NL⋅kg − 1 cat ⋅h − 1 , the CO contribution to the formation of methanol appears instantaneously, so that CO does not require additional contact time to react with the adsorbed hydrogen.Indeed, if that was the case, we would have observed an optimum in Y CO as a function of GHSV.Additionally, X CO2 , Y MeOH and Y CO all show a clear increase with temperature, resulting from the positive effect that temperature has on all the reaction rates.Finally, it is important to notice that at the lowest GHSV (Figure S10), the catalyst performance approach the thermodynamic equilibrium only at 260 ⁰C (i.e., highest reaction rate), where the thermodynamic value of X CO2 , Y MeOH and Y CO at 30 bar is 21.1 %, 8.04 % and 13.1 %, respectively.As a result, in the temperature region 200-260 ⁰C X CO2 , Y MeOH and Y CO still displays an exponential increase with temperature (i.e., kinetic regime).
Fig. 6 displays the effect of temperature and total pressure on the methanol (Y MeOH ) and CO yield (Y CO ).As anticipated from Fig. 5, temperature positively affects all the reactions, since the effect of kinetics (i.e., Arrhenius type) overcomes the thermodynamics.Besides, we observe that the effect of temperature on Y MeOH (Fig. 6a) is more significant as total pressure increases (i.e., the increase in Y MeOH from 200 to 260 ⁰C is of 91% and 193% at 10 and 40 bar, respectively).On the contrary, Y CO decreases with pressure and, at the same time, it keeps the same trend vs temperature, independently on the total pressure.As a result, the temperature of crossover shifts to higher values when pressure increases: at 10 bar the crossover occurs at c.a. 216 ⁰C, while at 40 bar Y MeOH > Y CO in the temperature region we explored (i.e., 200-260 ⁰C).
In Fig. 6b the effect of total pressure in the range of 10-40 bar is underlined: Y CO and Y MeOH exhibit two opposite trends, and the effect becomes more significant at higher temperatures (i.e., faster increase/ decrease vs pressure).As discussed in section 4.2, methanol is formed via two parallel routes: 1) the direct one, which involves only reaction 1 and 2) the indirect one, which involves reaction 2 and 3, in series.As a result, when feeding only CO 2 and H 2 or, more generally, with CO 2 -rich streams, the direct route is faster than the indirect, since the latter needs the formation of CO first (i.e., r 3 is negligible for low values of p CO ).As soon as CO is formed, r 3 increases, causing an increase in methanol formation and, at the same time, a consumption of CO, which acts both Fig. 4. Schematic representation of the reaction mechanism.On the left: dissociative adsorption of the H 2 molecule on metallic copper and oxygen adsorption of the CO 2 molecule onto the oxygen vacancies created by the CeZr oxide solution.The adsorbed H tends to interact with the carbon leading to the formate path.On the right: the formate path proceeds according to a series of hydrogenation steps, where methanol can be formed either via the direct route (i.e., directly from CO 2 ) or via the indirect one (i.e., via CO coming from the rWGS reaction).

S. Poto et al.
as a product and a reactant.Such an effect is more noticeable at greater temperatures, because of faster reactions (i.e., the effect of pressure anticipates).
Besides the effect of total pressure, a higher H 2 concentration in the feed (i.e., higher molar feed ratio H 2 :CO 2 ) causes an increase in both Y MeOH and Y CO (Fig. 7a), independently of temperature.However, Y MeOH  increases more than Y CO , shifting again the crossover point towards higher temperatures.As shown in Fig. 7a, the model describes quite precisely the crossover point (T cross ).Therefore, we used the model to predict the reaction performance in a wider range of H 2 :CO 2 (1-10).We found that T cross monotonically increases up to an asymptotic value of 258 ⁰C at around H 2 :CO 2 of c.a. 7 (Fig. 7b).As a matter of fact, a higher H 2 concentration facilitates its adsorption on the active sites, increasing the surface concentration of H s2 .As a result, as soon as CO forms, its hydrogenation is faster than its desorption to the gas phase, which enhances the indirect pathway once again (i.e., higher Y MeOH ).However, when all the active sites for H 2 adsorption (i.e., Cu 0 ) are saturated with H 2 , a further increase in its partial pressure does not affect the reaction rates anymore.

Predictive capability of the kinetic model
Once defined the reaction rates, we tested the predictive capability of the model by using the model to calculate both X CO2 and Y MeOH and comparing those values to an independent set of experiments (i.e., experimental data not used for the kinetic fitting).The kinetic model predicts quite accurately the experimental points obtained at lower GHSV (i.e., 2880 NL⋅kg − 1 cat ⋅h − 1 , last 4 points) and at lower pressure (i.e., 28 bar, first two points), with a maximum deviation of 2.1% and 2.2% for X CO2 and Y MeOH , respectively (Fig. 8).

Analysis of the reaction rates: Role of CO and CO 2 hydrogenation
In this section, we analyse in more details the reaction rates and the relative contribution of the CO 2 and CO hydrogenation (i.e., direct and indirect pathway, respectively) to the methanol formation.First, we calculate the reaction rates at different temperatures, via a theoretical differential analysis (i.e., assuming conversion values lower than 5%) at 30 bar and H 2 :CO 2 ratio of 3 (Fig. 9a).We observe that r 1 is the highest reaction rate at temperatures below c.a. 240 ⁰C.Therefore, at low temperatures, the CO 2 hydrogenation to methanol is the fastest reaction, being its activation energy the lowest (Table 8).However, r 1 is the only reaction rate showing an optimum in the temperature range we explored.It is clear indeed, that r 1 approaches the equilibrium as temperature increases, being its value very close to zero at 260 ⁰C.As a result, we observe here the two opposite effects of kinetics and thermodynamics of an exothermic reaction.On the contrary, r 2 and r 3 are  S1).
quite far from the equilibrium and both display the typical exponential behaviour of kinetically controlled reactions.In addition, reaction 2 and 3 proceed with similar velocities, with r 2 being slightly faster as temperature increases (i.e., r 2 /r 3 = 1.1 at 260 ⁰C).We clearly see that the two pathways for methanol formation behave differently with temperature.As a result, the relative contribution of CO 2 and CO to methanol synthesis changes as temperature increases (Fig. 9b).At 200 ⁰C, CO and CO 2 contributes almost equally (i.e., 51.5% and 47.4% at 200 ⁰C, respectively).As temperature increases, CO-to-MeOH and CO 2 -to-MeOH exhibit opposite trends, with CO-to-MeOH reaching a value of c.a. 100% at 260 ⁰C.This result reveals why methanol selectivity does not decay with temperature as fast as it does on the CuZnAl catalyst (Fig. 2a) and underlines the importance of designing a catalyst in such a way that CO adsorption is strong enough, to be able to proceed with the hydrogenation steps and form methanol, rather than desorb to the gas phase and contaminate the product stream.In Fig. 10a, instead, we report the reaction rates as a function of the H 2 :CO 2 ratio at 200 ⁰C and 30 bar.All the reaction rates remarkably increase with the H 2 concentration.In particular, when H 2 :CO 2 goes from 1 to 10, r 1 , r 2 and r 3 increase by ca. 30, 17 and 60%, respectively.As a matter of fact, all the direct reactions exhibit a positive order with respect to H 2 .However, expectedly, when the Cu 0 active sites are saturated with H 2 , a further increase in the H 2 concentration corresponds to a dilution of the carbon species, such as CO 2 and CO, which also influence positively the reaction rates.This explains the slight decrease of the reaction rate (more noticeable for r 2 and r 3 ) beyond H 2 : CO 2 of c.a. 7, which is in agreement with the result reported in Fig. 7b.For completion, in Fig. 10b we also report the relative contribution of CO 2 -to-MeOH and CO-to-MeOH crosses at H 2 :CO 2 of c.a. 1.5, with CO showing the predominant contribution beyond the crossing point.This is a clear consequence of the influence that the H 2 :CO 2 ratio has on the reaction rate.For H 2 :CO 2 larger than 1.5, r 3 > r 1 and the contribution of CO surpasses that of CO 2 , following a trend which corresponds to the reaction rates r 3 and r 1 , respectively.
To underline the potential of the CuCeZr catalyst, we propose here a comparison with the benchmark formulation (i.e., CuZnAl) in terms of reaction rates.First, the model derived by Graaf et al., was implemented and validated with the experimental results obtained for the CuZnAl catalyst (details on the validation are given in S.I.).Therefore, the kinetic model we adopted for such comparison is representative of the CuZnAl system and can be used for predictive studies.As depicted in Fig. 11a, the CO 2 consumption rate ( − r CO2 ) increases exponentially with temperature and it is quite similar for both catalysts, with the CuCeZr showing a slightly faster consumption.However, the CuCeZr catalyst converts CO 2 more selectively to methanolincluding both direct and indirect routethan the CuZnAl catalyst.As shown in Fig. 11b, methanol formation rate (r MeOH ) its higher for the CuCeZr and crosses with CO (r CO ) only at c.a. 256 ⁰C.On the contrary, the CuZnAl shows a much faster production of CO than methanol over the entire temperature range, which indicates that the CO hydrogenation does not contribute significantly to the synthesis of methanol, being CO the main reaction product.This demonstrates that the CuCeZr catalyst allows for a delay in the selectivity decay with increasing temperature when compared to the benchmark.It is clear that, in principle, lower temperatures favour the methanol production over CO.On the contrary, a higher temperature would correspond to much faster reactions, requiring less amount of catalyst to achieve equilibrium.In the end, when the desired productin this case methanolcomes from an exothermic reversible reaction, the choice of the optimal temperature lies on a trade-off between reaction performance and economics.However, it is clear that the CuCeZr would facilitate the conflict between the demand of high performance and catalyst/reactor costs, since it allows to achieve higher methanol selectivity and faster CO 2 /CO conversion at higher temperature, when compared to the benchmark formulation.

Conclusions
In this work, we investigate the kinetics of the CO 2 conversion to methanol over a Cu/CeO 2 /ZrO 2 catalyst, which remarkably outperforms the conventional Cu/ZnO/Al 2 O 3 in terms of methanol yield/selectivity.The cross-over temperature (i.e., T cross , defined as the temperature above which the yield to CO exceeds that of methanol) increases up to 240 ⁰C for the CuCeZr, while CuZnAl shows a higher selectivity to CO in the entire temperature range.
We analyse in detail the one-site, dual-site and three adsorption sites kinetic models, based on hypothesis retrieved from literature, and accordingly derived the kinetic parameters of all the models via an optimization algorithm based on the minimization of the RMSE (root mean square error).Physicochemical constraints and statistical indicators were used as tool for model discrimination.The best performing kinetic model (i.e., dual-site model of Graaf et al.,) suggests that the reaction mechanism proceeds via the adsorption of one of the oxygens of CO 2 on the oxygen vacancies of the CeO 2 -ZrO 2 phase (i.e., 1st active site), while H 2 adsorbs and dissociate on the metallic copper (i.e., 2 nd active site).The adsorbed hydrogen preferentially hydrogenates the carbon atom giving rise to the formate route.According to this mechanism, methanol can be formed either directly from CO 2 , or indirectly from the CO produced via the rWGS.The resulting kinetic model (i.e., rate expressions and fitted parameters) predicts the experimental data quite accurately, particularly the cross-over temperature (i.e., the model predicts that T cross stabilizes at 258 ⁰C at around H 2 :CO 2 of c.a. 7.) Further, analysis of the individual reaction rates and the relative contributions of CO 2 and CO to the methanol synthesis (i.e., COx-to-MeOH) reveal that CO 2 and CO contribute evenly at 30 bar, H 2 :CO 2 of 3 and 200 ⁰C (i.e., 51.5% and 47.4%, respectively), while the pathway CO-to-MeOH takes over at higher temperatures and/or higher H 2 concentration.For H 2 :CO 2 above 1.5, the CO contribution is predominant and exhibits an optimum at c.a. H 2 :CO 2 of 7 (at 30 bar and 200 ⁰C) , which likely corresponds to the saturation of the Cu 0 sites.This analysis underlines the importance of the indirect CO hydrogenation pathway in the reaction mechanism.
In conclusion, these findings lead to a deeper understanding of the reaction mechanism of CO 2 hydrogenation to methanol on novel CuCeZr systems, and serve as basis for future research into this catalyst formulation.For example, a more hydrophobic surface (i.e., weaker H 2 O adsorption and faster desorption from Cu 0 sites) could lead to faster reaction rates and lower H 2 requirement in the feed.Furthermore catalyst modification that lead to stronger CO binding would facilitate CO hydrogenation and, thus increase the selectivity to methanol even at higher temperatures.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Schematic representation of the experimental setup used for the catalytic tests.Gases (H 2 , CO 2 and N 2 ) are fed from bottles (Linde).FC indicates mass flow controllers, TI and TC represent thermocouples and controllers, respectively.Pressure is controlled via a back pressure control system.

Fig. 2 .
Fig. 2. Methanol (MeOH) and CO space time yield (STY) as a function of temperature for the CuCeZr and the benchmark CuZnAl catalyst (a) and comparison of the methanol space time yield (STY MeOH ) at 250 ⁰C with the performance of CuCe x Zr y O retrieved from literature [49] (b).Other experimental conditions: total pressure of 30 bar, H 2 :CO 2 molar ratio of 3.

− 1 bH 2 1 * 2 (Fig. 3 .
Fig. 3. Parity plot representing the accuracy of the parameter estimation for the outlet flow rate of CO 2 (a), CO (b), Methanol (c) and H 2 (d).The corresponding experimental data points are reported in S.I.

Fig. 6 .
Fig. 6.Methanol (black) and CO (red) as a function of a) temperature at 10 (solid lines, empty markers) and 40 bar (dashed lines and filled markers) and b) pressure at 200 (solid lines, empty markers) and 260 ⁰C (dashed lines and filled markers).Other experimental conditions: H 2 :CO 2 molar ratio of 3, GHSV of 9600 NL⋅kg − 1 cat ⋅h − 1 .Markers and lines represent experimental points and simulation results, respectively.

Fig. 7 .Fig. 8 .
Fig. 7. Methanol (solid lines with circles) and CO (dashed lines with stars) as a function of temperature at H 2 :CO 2 = 3 (fr3, light blue lines) and H 2 :CO 2 = 6 (fr6, red lines); markers and lines represent experimental points and simulation results, respectively (a).Temperature of crossover between methanol and CO yield (T cross ) as a function of the H 2 :CO 2 molar ratio, as predicted by the kinetic model (b).Other experimental/modeling conditions: total pressure of 30 bar, GHSV of 9600 NL⋅kg − 1 cat ⋅h − 1 .

Fig. 9 .Fig. 10 .
Fig. 9. Reaction rates of the CuCeZr system as a function of temperature (a) and relative contribution of CO and CO 2 to the formation of methanol as a function of temperature on the CuCeZr catalyst (b).The results were obtained via simulations, at a pressure of 30 bar, a H 2 :CO 2 ratio of 3 and a GHSV of 2.15⋅10 5 NL⋅kg − 1 cat ⋅h − 1 .

Table 2
[66]temperature was measured with two thermocouples, one at the beginning of the catalytic bed and one placed at the exit of the gases.Prior to the reaction tests, the catalyst was reduced in situ at 250 ⁰C, with 50 mL⋅min − 1 of a 50% H 2 /N 2 mixture for 4 h.The reaction mixture was analysed with a compact gas chromatograph (Global Analyzer Solution Rate determining step for the CO 2 hydrogenation and rWGS reaction and the corresponding rate expression adapted from Slotboom et al.,[66]. TM , G.A.S.) equipped with a TCD detector and two packed columns (HayeSep Q 60-80 mesh and 5A molecular sieve) for the analysis of permanent gases (i.e., H 2 , CO 2 , CO and N 2 ) and an FID detector with capillary columns (Rtx-1, MTX-1 and MTX-QBond) for the analysis of the hydrocarbons.The experimental setup is sketched in Fig.1.The reaction tests were performed in a range of temperature and pressure of 200-260 ⁰C and

Table 4
Physicochemical constraints of the kinetic parameters.

Table 5
[50]ing criteria for the exclusion of internal (intraparticle) and external (gas-solid) mass transfer limitation.with the calcination temperature (i.e., 450 ⁰C), according to the optimization reported by Wang et al.,[50].Unfortunately, insufficient details on the results reported by Wang et al., made a direct comparison with our results unreliable.However, assuming a catalyst density of 2.56 g⋅cm − 3 (i.e., value we measured), the STY MeOH they obtained at the same conditions is c.a. 6.6 mmol⋅h − 1 ⋅g − 1 cat , which compares with the value reported in Fig. improved

Table 6
Physical properties of the Cu/CeO 2 /ZrO 2 catalyst.

Table 9
Comparison of the values of the adsorption constants obtained in this work and by Graaf at 200 and 260 ⁰C.