Cu/Zn/Zr/Ga Catalyst for Utilisation of Carbon Dioxide to Methanol—Kinetic Equations

: This paper presents the kinetics of methanol synthesis from carbon dioxide and hydrogen over a Cu/Zn/Zr/Ga catalyst. Kinetic studies were carried out in a continuous-ﬂow ﬁxed-bed reactor in a temperature range from 433 to 513 K, pressures from 3 to 8 MPa, and GHSV from 1660 to 10,000 1/h for initial molar fractions of hydrogen from about 0.48 to 0.70, carbon dioxide from 0.05 to about 0.22, and carbon monoxide from 0 to about 0.07. Signiﬁcant effects of temperature and the composition of the reaction mixture on the conversion degrees α 1 and α 2 were found. The Cu/Zn/Zr/Ga catalyst showed good stability over 960 h. XRD and CO 2 TPD characterisa-tion were performed. Theﬁnally obtained results of kinetic tests were developed in the form of Langmuir–Hinshelwood kinetic equations. The numerical Levenberg–Marquardt method was used to estimate the kinetic equations. The average relative error of ﬁtting the kinetic equations to the experimental data was 18%. in productivity. The formation of ZnCO 3 is attributed to the prolonged residence of the catalyst at elevated pressure (8 MPa) [50]. In a study by Asha-Kurlander et al. [51] on methanol synthesis from H 2 and CO 2 , ZnCO 3 was found to be formed in an acidic environment, which is responsible for the partial dissolution of ZnO in a mixture of H 2 O and CO 2 .


Introduction
Global warming caused, among other things, by the increase in the carbon dioxide (CO 2 ) concentration in the atmosphere (from 381 ppm in 2006 to 427 ppm in 2021) and the depletion of fossil fuels, i.e., natural gas, oil, and coal, is becoming a huge challenge for modern society [1]. The continuous growth of CO 2 emissions (reaching 37 billion t in 2019) is caused by the rapid development of the global economy. There are numerous sources thereof, among which are the energy, heating, and chemical industries. In order to reduce the CO 2 content in the atmosphere, two methods [2] for its utilisation have been developed and implemented: carbon capture and storage (sequestration) (CCS) andcarbon capture and utilisation (CCU), as well as CO 2 methanation [3][4][5]. The catalytic conversion of CO 2 to methanol is a promising and environmentally friendly route that can help solve the problem of managing and disposing of excess anthropogenic CO 2 and reducing the exploitation of fossil fuels [6].
Available data in the literature concerning kinetic studies of methanol synthesis from carbon dioxide and hydrogen refer mainly to experiments carried out in the presence of a Cu/Zn/Al catalyst, under various conditionsand for various compositions of the reaction mixture. Table 1 summarises selected kinetic equations and parameters ofthe methanol synthesis process described in the literature. Graaf et al. [36] presented kinetic equations for methanol synthesis based on the Langmuir-Hinshelwood mechanism, considering the reactions of hydrogenation of carbon dioxide (1) and carbon monoxide (CO + 2H 2 ↔ CH 3 OH) to methanol as well as the accompanying RWGS reaction (2). The experiments were carried out in a spinning basket reactor. Graaf's equations are the most commonly used kinetic models in industrial practice [41,42].
Malinovskaya et al. [37] conducted kinetic studies of methanol synthesis considering only reactions (1) and (2). These experiments were conducted in the flow reactor, using a Cu/Zn/Al industrial catalyst (SNM-3) at T = 473-553 K and p = 5-10 MPa including the effect of CO 2 and CO concentrations ( Table 1). The fit of the kinetic equations to the experimental data was about 10%.
Skrzypek et al. [38] carried out a full kinetic study of methanol synthesis in a continuousflow fixed-bed reactor with an industrial Cu/Zn/Al catalyst (Błasiak catalyst). This study extensively considered the effects of temperature and pressure and the different initial composition of the reaction mixture on the reaction rates (1) and (2) ( Table 1). The kinetic equations developed were based on 70 measurement points and took into account the possibility of the occurrence of maxima in the relationship between the reaction rates (1) and (2) and the inlet concentrations of CO 2 and H 2 (in the absence of CO at the reactor inlet). The proposed kinetic equations correspond to Langmuir-Hinshelwood sequences with the surface reaction between hydrogen and carbon dioxide as the rate-limiting step. In preliminary studies that preceded the kinetic studies, it was found that methanol in the presence of the copper catalyst used was formed from CO 2 and not from CO.
Vanden Bussche and Froment [39] carried out a full kinetic investigation of methanol synthesis in a continuous-flow fixed-bed reactor with the Cu/Zn/Al industrial ICI catalyst. These studies included determining the effects of temperature, pressure, and composition of the initial reaction mixture on the reaction rate ( Table 1). The mass balance equations with the proposed kinetic equations based on reactions (1) and (2) were integrated using the numerical method of Runge and Kutta IV and V, and the calculated values of the transformation rates were compared with the experimental values. Nine parameters were estimated simultaneously using the Levenberg and Marquard nonlinear regression method. A good agreement of the model fit to the experimental data was obtained over the range of parameters studied. A very good model fit to their experimental data (30 points), which did not exceed 10%, was obtained by Kubota et al. [40]. This team developed kinetic equations for methanol synthesis based on data obtained from a continuous-flow fixed-bed reactor with a Cu/Zn/Zr/Al/Si catalyst. These equations were developed under the assumptions that methanol is formed from the transformation of intermediates (including HCOO*), the rate-limiting step in the overall process being the surface reaction between intermediates adsorbed on the catalyst surface and hydrogen atoms. Furthermore, it was assumed that the RWGS reaction (2) occurs by direct decomposition of CO 2 to CO on the Cu surface. In the denominator of both equations, the partial pressure of hydrogen was omitted because of the small change, and the quotient of the partial pressure of water to hydrogen was omitted because it is less than zero.
Ladera et al. [35] carried out an activity investigation of the Cu/Zn/Zr/Ga catalyst and an incomplete kinetic study of methanol synthesis in a continuous-flow fixed-bed reactor, determining the effects of temperature and pressure on the reaction rate. It was found that above about 520 K the rate of the RWGS reaction increases, while high CO 2 partial pressures (>1.25 MPa) favour the reaction (1). Ladera et al. [35] suggest that the hydrogenation of CO 2 to methanol can occur according to the Eley-Rideal mechanism. Furthermore, based on the obtained kinetic results for reactions (1) and (2), this group determined the kinetic equations in power monomial form, and estimated its parameters without considering the sorption terms (Table 1).
Kinetic investigations presented in the literature mainly concern methanol synthesis on a Cu/Zn/Al catalyst. This catalyst, as mentioned previously, is not resistant to high CO 2 content and the presence of water in the reaction mixture. The aim of this work is to estimate the kinetics of methanol synthesis from carbon dioxide and hydrogen on a copper-zinc-zirconium catalyst modified with gallium oxide. The scope of the research includes the investigation of the influence of temperature, pressure, reactant flow rate, and initial composition of substrates on the course of methanol synthesis on a Cu/Zn/Zr/Ga catalyst. The final activity of the kinetic investigations of methanol synthesis was to estimate the kinetic equations and its parameters (pre-exponential constants, activation energies, sorption constants).

Characteristics of the Catalyst
The structures of the fresh and spent Cu/Zn/Zr/Ga catalyst were compared using XRD ( Figure 1). Kinetic investigations presented in the literature mainly concern methanol synthesis on a Cu/Zn/Al catalyst. This catalyst, as mentioned previously, is not resistant to high CO2content and the presence of water in the reaction mixture. The aim of this work is to estimate the kinetics of methanol synthesis from carbon dioxide and hydrogen on a copper-zinc-zirconium catalyst modified with gallium oxide. The scope of the research includes the investigation of the influence of temperature, pressure, reactant flow rate, and initial composition of substrates on the course of methanol synthesis on a Cu/Zn/Zr/Ga catalyst. The final activity of the kinetic investigations of methanol synthesis was to estimate the kinetic equations and its parameters (pre-exponential constants, activation energies, sorption constants).

Characteristics of the Catalyst
The structures of the fresh and spent Cu/Zn/Zr/Ga catalyst were compared using XRD ( Figure 1). Analysis of the XRD diffractograms ( Figure 1) of the fresh Cu/Zn/Zr/Ga catalyst indicates the presence of CuO, which corresponds to an intense peak (at 2θ= 35 and 38º) and weakly intense peaks of zirconium (at 2θ= 31, 55 and 67º) and Ga2O3 (2θ= 34º), among others. It is worth mentioning that the spectrum of the fresh Cu/Zn/Zr/Ga catalystshows the presence of an amorphous phase and a weakly developed crystalline phase [32]. The spectrum of the spent Cu/Zn/Zr/Ga catalyst shows an intense band characteristic of metallic Cu (i.e.,around 2θ= 43 and 50°) and a weak intensity of spinel ZnGa2O4 (2θ= 54, 56 and 62°) and ZnCO3 (2θ= 25, 33 and 39°). The spent catalyst shows increased phase crystallinity.
Crystallite sizes calculated using the Scherrer method and basic parameters of the porous structure of the Cu/Zn/Zr/Ga catalyst are presented in Table 2. Analysis of the XRD diffractograms ( Figure 1) of the fresh Cu/Zn/Zr/Ga catalyst indicates the presence of CuO, which corresponds to an intense peak (at 2θ = 35 and 38 • ) and weakly intense peaks of zirconium (at 2θ = 31, 55 and 67 • ) and Ga 2 O 3 (2θ = 34 • ), among others. It is worth mentioning that the spectrum of the fresh Cu/Zn/Zr/Ga catalystshows the presence of an amorphous phase and a weakly developed crystalline phase [32]. The spectrum of the spent Cu/Zn/Zr/Ga catalyst shows an intense band characteristic of metallic Cu (i.e., around 2θ = 43 and 50 • ) and a weak intensity of spinel ZnGa 2 O 4 (2θ = 54, 56 and 62 • ) and ZnCO 3 (2θ = 25, 33 and 39 • ). The spent catalyst shows increased phase crystallinity.
Crystallite sizes calculated using the Scherrer method and basic parameters of the porous structure of the Cu/Zn/Zr/Ga catalyst are presented in Table 2. The BET and S Cu surface area for the investigated catalyst are markedly lower than those presented by the Ladera [35] and Natesakhawat [43] groups, which may be due to the different method of catalyst preparation.
The CO 2 TPD experiment was performed in order to evaluate the surface basicity of the synthesized catalyst. The recorded TPD profile ( Figure 2) was analysed in the temperature range corresponding with the temperature at which the methanol synthesis had been carried out. The BET and SCu surface area for the investigated catalyst are markedly lower than those presented by the Ladera [35] and Natesakhawat [43] groups, which may be due to the different method of catalyst preparation.
The CO2TPD experiment was performed in order to evaluate the surface basicity of the synthesized catalyst. The recorded TPD profile ( Figure 2) was analysed in the temperature range corresponding with the temperature at which the methanol synthesis had been carried out. In the recorded CO2TPD profile ( Figure 2) for the Cu/Zr/Zn/Ga catalyst, the desorption signal in the low temperature range is visible. The position of deconvoluted peaks 1 and 2, which is between 323 K and 423 K, shows that solely weak basic sites are present on the surface of the Cu/Zr/Zn/Ga [44].The total basicity is low and equal to 15.5 µmol/gcat (Table 3).  In the recorded CO 2 TPD profile ( Figure 2) for the Cu/Zr/Zn/Ga catalyst, the desorption signal in the low temperature range is visible. The position of deconvoluted peaks 1 and 2, which is between 323 K and 423 K, shows that solely weak basic sites are present on the surface of the Cu/Zr/Zn/Ga [44]. The total basicity is low and equal to 15.5 µmol/g cat. (Table 3). The observed increase in the CO 2 line above ca. 470 K is related to the desorption of CO 2 that originates from the atmosphere [45,46]. This CO 2 was not removed upon sample activation prior to TPD because the temperature was not high enough. The contribution of atmospheric CO 2 in the TPD profile was marked with a blue line ( Figure 2) and was not taken into consideration for the total basicity calculation. Additionally, the ratio of CO 2 desorbing in the temperature range 323-343 K (Tot des ) to adsorbed CO 2 via pulses (Tot ads .) is close to one (Table 3). This also shows that CO 2 desorbing at higher temperatures is atmospheric.
Thermogravimetric analysis of the spent Cu/Zn/Zr/Ga catalyst performed using a nitrogen and air atmosphere is presented in Figure 3a,b. not taken into consideration for the total basicity calculation. Additionally, the ratio of CO2 desorbing in the temperature range 323-343 K (Totdes) to adsorbed CO2 via pulses (Totads.) is close to one (Table 3). This also shows that CO2 desorbing at higher temperatures is atmospheric.
Thermogravimetric analysis of the spent Cu/Zn/Zr/Ga catalyst performed using a nitrogen and air atmosphere is presented in Figure 3a,b. Heating the Cu/Zn/Zr/Ga catalyst after kinetic studies to 773 K in an N2 atmosphere resulted in a mass loss of about 5% in the 520-615 K range, associated with the decomposition of ZnCO3 to ZnO and CO2 at 573 K [47] (Figure 3a).
The DTG curve of the catalyst heated in the atmosphere of air ( Figure 3b) shows a mass increase of about 8% in the range of 400-728 K. This growth is presumably related to the oxidation of the reduced active form of the catalyst, i.e., Cu 0 + 0.5O2→CuO. The overlapping small mass loss at 586 K is associated with the decomposition of ZnCO3 to ZnO and CO2 [47,48]. The amount of O2 calculated from DTG, assuming that there are no carbon deposits in the spent catalyst, indicates that 85 wt.% of copper was in the reduced form Cu 0 . Since the presence of a carbon deposit in the spent catalyst cannot be excluded, part of the oxygen was certainly used for its oxidation. Therefore, the amount of the reduced form Cu 0 was smaller than 85 wt.%, but it cannot be precisely determined.

KineticsTests
The carried out kinetic tests yielded dozens of measurement points, which were used to plot kinetic curves,on the basis of which a preliminary analysis of the data was carried out in terms of the influence of process parameters on the reaction rate. The results of kinetic tests are presented in Figures4-9 as curves of the dependence of the conversion degrees α1 exp and α2 exp on temperature, pressure, GHSV, and initial composition of the reaction mixture for reactions (1) and (2). Heating the Cu/Zn/Zr/Ga catalyst after kinetic studies to 773 K in an N 2 atmosphere resulted in a mass loss of about 5% in the 520-615 K range, associated with the decomposition of ZnCO 3 to ZnO and CO 2 at 573 K [47] (Figure 3a).
The DTG curve of the catalyst heated in the atmosphere of air ( Figure 3b) shows a mass increase of about 8% in the range of 400-728 K. This growth is presumably related to the oxidation of the reduced active form of the catalyst, i.e., Cu 0 + 0.5O 2 → CuO. The overlapping small mass loss at 586 K is associated with the decomposition of ZnCO 3 to ZnO and CO 2 [47,48]. The amount of O 2 calculated from DTG, assuming that there are no carbon deposits in the spent catalyst, indicates that 85 wt.% of copper was in the reduced form Cu 0 . Since the presence of a carbon deposit in the spent catalyst cannot be excluded, part of the oxygen was certainly used for its oxidation. Therefore, the amount of the reduced form Cu 0 was smaller than 85 wt.%, but it cannot be precisely determined.

KineticsTests
The carried out kinetic tests yielded dozens of measurement points, which were used to plot kinetic curves, on the basis of which a preliminary analysis of the data was carried out in terms of the influence of process parameters on the reaction rate. The results of kinetic tests are presented in Figures 4-9 as curves of the dependence of the conversion degrees α 1 exp and α 2 exp on temperature, pressure, GHSV, and initial composition of the reaction mixture for reactions (1) and (2).                  (1), this influence declines with alower pressure of more than 50%. For reaction (2), this effect can be observed above a temperature of about 490 K (more than 30% change). It is important to mention that the methanol synthesis is an exothermic process, so further increase in temperature over 513 K is unfavourable, as reaction (2) is endothermic and becomes dominant, causing a decrease in the conversion degree of α1 exp from 2 to 25% (Figure 3a).   (1), this influence declines with alower pressure of more than 50%. For reaction (2), this effect can be observed above a temperature of about 490 K (more than 30% change). It is important to mention that the methanol synthesis is an exothermic process, so further increase in temperature over 513 K is unfavourable, as reaction (2) is endothermic and becomes dominant, causing a decrease in the conversion degree of α 1 exp from 2 to 25% (Figure 3a). Figure 5a,b shows the pressure relationships of the conversion degrees α 1 exp and α 2 exp for different temperatures. The pressure dependences of α 1 exp and α 2 exp are smaller than the effect of temperature (Figure 4a,b and Figure 5a,b). The conversion degree α 1 exp increases with the pressure by more than 50%, while α 2 exp is almost constant for all tested temperatures. The differences occur only within temperatures of 453-513 K and reach up to 50% (Figure 5b). Figure 6a,b shows the GHSV relationships of the conversion degrees α 1 exp and α 2 exp for different pressures. For both, reactions α 1 exp and α 2 exp decrease with rising GHSV. This relationship appears to be stronger with higher pressure. Especially for the GHSV range 1660-3310 1/h, a decrease from about 5% to about 30% (α 2 exp for 8 MPa) occurs. Figure 7a,b shows the dependence of the conversion degrees α 1 exp and α 2 exp on the initial hydrogen concentration for temperatures of 433, 453, and 473 K. The influence of the initial hydrogen concentration was studied at the constant of X 0 CO 2 equal to 0.20. An increase in α 1 exp and α 2 exp isobserved for both reactions with increasing concentrations. This effect is more evident for higher temperatures. Figure 8a,b shows the dependence of the conversion degrees α 1 exp and α 2 exp on the initial carbon dioxide concentration for temperatures of 433, 453, and 473 K. The effect of initial carbon dioxide concentration was determined at a constant initial hydrogen concentration equal to 0.69.
For both reactions, increasing CO 2 content caused a decrease even more than fourfoldof α 1 exp and α 2 exp , as shown in Figure 8a,b. This effect is reversed and slightly weaker than for the hydrogen content (compare Figure 7a,b and Figure 8a,b). The largest reduction in α 1 exp , 70%, occurred for atemperature of 473 K (Figure 7a). Analysis of the effect of molar fractions ofhydrogen and carbon dioxide on α 1 exp and α 2 exp indicated that the size of the S Cu of the studied catalyst favours hydrogen adsorption, but negatively affects CO 2 adsorption, which in excess reduces its activity [49]. The excess of spherically large CO 2 molecules adsorbed on the catalyst surface, specifically on Zn and/or Zr oxides, blocks the access of much smaller H 2 molecules onto theCu surface; thus, α 1 exp and α 2 exp can be reduced. Figure 9a,b shows the dependence of the conversion degrees α 1 exp and α 2 exp on the initial carbon monoxide concentration for temperatures of 433, 453, and 473 K. The effect of the initial molar fraction of carbon monoxide was studied at constant initial concentrations of H 2 X 0 H 2 = 0.68 and X 0 CO 2 = 0.22. The presence of CO shifts the equilibrium state of the RWGS reaction towards the formation of CO 2 and the removal of the water, which is formed in reaction (1). This is beneficial for the process to be conducted because water can cause partial deactivation of the copper catalyst. The effect of the initial molar fraction of CO on reaction (1) is similar in nature to that of CO 2 . For reaction (2), the decrease in α 2 exp is more evident than for reaction (1), in particular at 473 K.

Stability
The catalyst should exhibit stable behaviour during operation. Its activity should not change; thus, it should be resistant to various factors (coking, sintering). In order to examine the stability, the dependence of α 1 exp and α 2 exp and the productivity as a function of time on stream were determined. The stability was checked for 1056 h by carrying out weekly measurements for identical process parameters: at atemperature of 453 K andpressure of 8 MPa, at a constant flow rate of 100 mL/min (GHSV = 3300 1/h) for a reaction mixture of 0.69 H 2 and 0.21 CO 2 ( Figure 10). Up to 700 h of the measurements, small (within the measurement error) deviations of α 1 exp and α 2 exp values (marked as points in Figure 10) from their average values (lines in Figure 10) were observed for both reactions. After about 700 hof stable work, the beginning of a downward trend in productivity appears so that, for 1000 h, the decrease in productivity reaches about 20%. The part of CO 2 can be bonded to ZnO, leading to the formation forming ZnCO 3 (Figures 1 and 3a,b). The CO 2 adsorption active centres were blocked, resulting in a decrease in productivity. The formation of ZnCO 3 is attributed to the prolonged residence of the catalyst at elevated pressure (8 MPa) [50]. In a study by Asha-Kurlander et al. [51] on methanol synthesis from H 2 and CO 2 , ZnCO 3 was found to be formed in an acidic environment, which is responsible for the partial dissolution of ZnO in a mixture of H 2 O and CO 2 .
talysts 2022, 12, x FOR PEER REVIEW 11 The part ofCO2can be bonded to ZnO,leading to the formation forming ZnCO3 (Figu  and 3a,b). The CO2 adsorption active centres were blocked, resulting in a decreas productivity. The formation of ZnCO3 is attributed to the prolonged residence of the alyst at elevated pressure (8 MPa) [50]. In a study by Asha-Kurlander et al. [51] on m anol synthesis from H2 and CO2, ZnCO3 was found to be formed in an acidic envi ment, which is responsible for the partial dissolution of ZnO in a mixture of H2O CO2.

Kinetic Equations
The next step of our work was to determine the kinetic equations for methanol thesis from CO2 and H2. The obtained results were developed in the form of kin equations of the Langmuir-Hinshewood type with the surface reaction between

Kinetic Equations
The next step of our work was to determine the kinetic equations for methanol synthesis from CO 2 and H 2 . The obtained results were developed in the form of kinetic equations of the Langmuir-Hinshewood type with the surface reaction between CO 2 and H 2 as the limiting step: where r 1 and r 2 (mol/(kg cat. ·h)) are, respectively, the rate of reactions (1) and (2) andk n (mol/(kg cat. ·h)) is the rate constant of the n-th reaction expressed by the Arrhenius equation: The partial pressures, p i (MPa), of the i-th reactant (i = H 2 , CO 2 , CH 3 OH, CO, H 2 O) are defined as: The sorption equilibrium constant, K i (MPa), of the i-th reactant changes with temperature according to the equation: The thermodynamic equilibrium constants of the n-th reaction (K eq n ) were calculated from theformulas in the publication [52] and have the following form: In the foregoing equations, a standard form of kinetic equations of the Langmuir-Hinshelwood type was assumed, including a kinetic group, a driving module of the process, and a sorption group. The kinetic group of these equations contains only the reaction rate constants k 1 and k 2 , while the sorption constants present in the equation of Skrzypek et al. [38] are not included. The sorption component takes into account all reagents involved in the present process. The values of exponents in Equations (3) and (4) were checked for the values proposed by Skrzypek et al. [38] (a = 3; b = 2), considering that these values were determined for slightly different systems of kinetic equations. Figure 11a,b shows α cal as a function of α exp for 59 experimental data.
Skrzypek et al. [38] are not included. The sorption component takes into account all reagents involved in the present process. The values of exponents in Equations (3) and (4) were checked for the values proposed by Skrzypek et al. [38] (a= 3; b= 2), considering that these values were determined for slightly different systems of kinetic equations. Figure 11a,b shows α cal as a function of α exp for 59 experimental data. The considered kinetic equations give the smallest difference between the experimental and calculated conversion degrees under the investigated process conditions on the Cu/Zn/Zr/Ga catalyst. For both high conversion degrees α1 exp and α2 exp a slight deviation of the points from the diagonal reaching only 10% is observed. It should be noted that the kinetic equations approximate the conversion degrees α1 exp and α2 exp with satisfactory accuracy for reaction mixtures containing small amounts of CO.
The fits of the experimental data and those calculated using the estimated kinetic equations, Equations (3) and (4)  The considered kinetic equations give the smallest difference between the experimental and calculated conversion degrees under the investigated process conditions on the Cu/Zn/Zr/Ga catalyst. For both high conversion degrees α 1 exp and α 2 exp a slight deviation of the points from the diagonal reaching only 10% is observed. It should be noted that the kinetic equations approximate the conversion degrees α 1 exp and α 2 exp with satisfactory accuracy for reaction mixtures containing small amounts of CO.
The fits of the experimental data and those calculated using the estimated kinetic equations, Equations (3) and (4), are shown in Figures 12a-α 1 and 12b-α 2 . tion of the points from the diagonal reaching only 10% is observed. It should be noted that the kinetic equations approximate the conversion degrees α1 exp and α2 exp with satisfactory accuracy for reaction mixtures containing small amounts of CO.
The fits of the experimental data and those calculated using the estimated kinetic equations, Equations (3) and (4)  The proposed kinetic equations, Equations (3) and (4), fit the experimental data well, reflecting the decrease in conversion degrees α1 and α2 with increases in GHSV.
The values of the determined kinetic parameters are summarised in Table 4. Table 4. The values of estimated kinetic parameters. The proposed kinetic equations, Equations (3) and (4), fit the experimental data well, reflecting the decrease in conversion degrees α 1 and α 2 with increases in GHSV.
The values of the determined kinetic parameters are summarised in Table 4. The estimated activation energies E 1 and E 2 ( Table 4) compared to those determined by Skrzypek et al. [38] (Table 1) are lower, for reaction (1) by about 40% and for reaction (2) by just over 20%. These differences may be due to the difference in the specificity of the catalyst used in the present study (Cu/Zn/Zr/Ga) compared to the Błasiak catalyst ( Table 1). The Cu/Zn/Zr/Ga catalyst shows greater resistance to higher concentrations of CO 2 in the synthesis gas and to water formed in the process than the Błasiak catalyst [53]. According to ICI's UK patent [54], methanol synthesis using a low-pressure method on a copper-zinc catalyst modified with, inter alia, chromium can be carried out in the presence of H 2 and CO with no more than 2% CO 2 addition due to the risk of catalyst deactivation. Furthermore, according to studies by Toyira et al. [55,56], the addition of gallium oxide improves the copper dispersion and its stabilisation by achieving a Cu 0 /Cu + ratio that is optimal for the productivity and lifetime of the catalyst. Ladera et al. [35], while investigating the methanol synthesis from CO 2 and H 2 on a Cu/Zn/Zr/Ga catalyst for other process conditions, obtained for reaction (1) a doubly lower activation energy, and for reaction (2) an activation energy almost one and a half times higher. Moreover, they obtained much higher differences between the activation energies of both reactions, reaching as far as 80,000 J/mol (Table 1). It is worth noting that the kinetic equations obtained by Ladera et al. [35] were in the form of a power monomial with fractional exponents, without taking into account the sorption group. Additionally, the presence of fractional exponents of powers at partial pressures for hydrogen and carbon dioxide in their work indicates a non-elementary course of both reactions. Analysing the data in Table 4, it can also be seen that the adsorption heats of carbon dioxide and hydrogen are similar and almost half the sorption heat of CO.
The average relative error of the model's fit to experimental results data was 18% for 59 measurement points.
The carbon dioxide, hydrogen, carbon monoxide, and nitrogen that were used in the preparation of gas mixtures for kinetic studies were from SIAD; all the gases were of technical purity.

Catalyst Preparation
The Cu/Zn/Zr/Ga catalyst was prepared by a citric acid homogenisation method called the "citrate method" [57]. The reason we used this method was to obtain perfectly mixed components thanks to the branched structure of citrates and consequently excellent homogeneity and fully repeatable properties of the prepared catalyst [58]. The conventional method of co-precipitation did not provide such results, although it is usually used, as it is described in the literature.
Stoichiometric amounts of Cu, Zn, Zr, and Ga nitrates were carefully added to a citric acid solution (2 mol/dm 3 + 2% excess). The composition of the obtained Cu/Zn/Zr/Ga catalyst was 65.3/26.3/4.5/3.9 (wt.%). The mixture was then evaporated in a rotary vacuum evaporator at 380 K for about 24 h. The resulting metal citrate precipitate was carefully oxidised to ensure that local overheating and explosive oxidation reactions were prevented (temperature programme: 360 K, 0.1 K/min; 403 K). The resulting oxide mixture was roasted in a muffle furnace with air access (temperature program: 373 K, 473 K, 523 K, 573 K, and 623 K for 1 h). Thefinal stages of preparation were tableting of the obtained powder and crushing and sieving to obtain the desired grain size (0.8-1 mm grain) [58].

Catalysts Characterization
Phase analysis based on X-ray powder diffraction (XRD) measurements was performed on a Bruker D8 Advance diffractometer with a Lynx Eye detectorand Johansson monochromator, working in Bragg-Brentano geometry. The XRD measurements (at 40 kV and 30 mA) were performed in the 2θ range from 5 • to 90 • with the interpolated step size 0.02 • . The crystallite sizes were calculated using the Scherrer method. XRD phase analysis was performed using reference standards from the International Centre for Diffraction Data (ICDD) PDF-4 database.
The BET surface area was measured with nitrogen adsorption at 77 K using Quantachrome Autosorb-1. Prior to the measurements, samples were preheated and degassed under vacuum at 373 K for 18 h. The pore size distribution profiles were obtained by using the Barrett-Joyner-Halenda (BJH) method from the desorption branch. The micropore area was obtained byusing the V-t plot method.
The active surface of copper (S Cu ) in the reduced catalyst was determined with the use ofreactive adsorption of N 2 O at 363 K (VG/Fisons Quartz 200D) according to the method described in [59]. It has been assumed in calculations that the reoxidation of surface copper follows the chemical equation 2Cu(s) + N 2 O(g) → Cu 2 O(s) + N 2 (g) and that 1 m 2 ofelemental copper corresponds to 6.1 µmol of O 2 .
The CO 2 TPD (CO 2 temperature-programmed desorption) measurements were carried out in a quartz fixed-bed flow reactor connected online to a mass spectrometer (QMG 220 PRISMA PLUS). Prior to the TPD run, the sample (50 mg) was reduced in 5% H 2 /Ar flow at 723 K for 1 h. Next, the reactor was cooled down to room temperature (RT) and pulses (250 µL) of 5% CO 2 /Ar were introduced until saturation. Then, the sample was flashed with He flow (40 mL/min) for 0.5 h until a stable CO 2 line (m/z = 44) was obtained. TPD was performed from RT to 973 K with ∆T = 10 K/min under He flow.
TG measurements were carried out on a STAR 850 Mettler Toledo apparatus in nitrogen and air, in the temperature range of 298-773 K with a linear temperature rise (10 K/min) and agas flow rate of 60 cm 3 /min.

Kinetic Tests
Kinetic tests were performed in the continuous-flow fixed-bed stainless steel reactor of 18 cm length and 1.3 cm inner diameter. The 2 g of the catalyst was placed between two layers of ceramic grains. After leaving the reactor, the reaction mixture was analysed with the Varian Star 3800 gas chromatograph. The methanol content was determined by the flame ionisation detector (FID) with CP-Wax column. Gases were analysed by the thermalconductivity detector (TCD) with the Carbo Plot column; additionally, carbon compounds were determined quantitatively in the methanizer. To activate the catalyst, reduction of the oxidised form of the catalyst was performed in a stream of dilute hydrogen (gas flow 50 mL/min, 7% H 2 in N 2 ) at 473 K under atmospheric pressure for 2 h. Schematic of the apparatus is shown in Figure 13.  Before starting the kinetic studies, it was necessary to stabilise the catalyst. This stabilisation was carried out in a reaction mixture consisting of 70 mol% H2 and 20 mol% CO2 and nitrogen, for a GHSV of 3300 1/h at 4 MPa, according to a temperature program: 443K, 1.5 deg/min; 553 K for 4 h. Kinetic studies were carried out under the conditions shown in Table 5. On the basis of the experimental data obtained, the following were calculated: (a) conversion degrees (α1 exp , α2 exp ) from the formulae: for reaction (1) Figure 13. Scheme of experimental system: 1-deoxidizer (BTS), 2-dryer, 3-reactor, GC-gas chromatograph, T-thermocouple, F-flowmeter, P-manometers.
Before starting the kinetic studies, it was necessary to stabilise the catalyst. This stabilisation was carried out in a reaction mixture consisting of 70 mol% H 2 and 20 mol% CO 2 and nitrogen, for a GHSV of 3300 1/h at 4 MPa, according to a temperature program: 443 K, 1.5 deg/min; 553 K for 4 h. Kinetic studies were carried out under the conditions shown in Table 5. On the basis of the experimental data obtained, the following were calculated: (a) conversion degrees (α 1 exp , α 2 exp ) from the formulae: for reaction (1) (b) productivity (P MeOH ): The integrative method was used to check the potential kinetic model. The kinetic data obtained were compared with the data obtained from the solution of differential equations, which are in fact the mass balance for the tubular reactor: The analysed forms of kinetic equations were inserted in place of r 1 and r 2 in Equations (13) and (14). The obtained differential Equations (13) and (14) were integrated using the numerical method of Runge and Kutta IV, and the calculated values of the α 1 cal and α 2 cal were compared with the corresponding experimental values α 1 exp and α 2 exp . The model for experimental data fitting was evaluated by the mean relative error determined by the following formula: k on , E n , K 0i , ∆H 0i = arg min The Levenberg-Marquardt nonlinear regression method was used to simultaneously determine the above parameter values. The algorithm was modified to adjustit to any objective function. The program code was written in BASIC.

Summary
This paper presents kinetic investigations on the methanol synthesis from carbon dioxide and hydrogen in a continuous-flow fixed-bed reactor in the presence of a Cu/Zn/Zr/Ga catalyst. The study showed strong effects of temperature and initial molar fractions of hydrogen and carbon dioxide and weak effects of pressure, GHSV, and initial molar fraction of CO ontheconversion degrees α 1 exp and α 2 exp . The Cu/Zn/Zr/Ga catalyst showed good stability over 960 h.
The kinetics of the investigated process can be described by determined in this work kinetic equations of the Langmuir-Hinshewood type, with the surface reaction between carbon dioxide and hydrogen as the limiting step. The average relative error of fitting the kinetic equations to the experimental data was 18%.
Due to the wide range of process parameters studied, the proposed kinetic equations can be used in design and optimization of industrial-scale chemical reactors manufacturing methanol.

Conflicts of Interest:
The authors declare no conflict of interest.