Development of an Improved Kinetic Model for CO₂ Hydrogenation to Methanol

Round 1

Reviewer 1 Report

In this work, an improved kinetic model for the hydrogenation of CO2 and CO mixture to methanol was developed, which gives a better prediction on the CO2 conversion, methanol formation and CO formation than old models, but with less parameters. In addition, the application of the improved model and calculation results were discussed, which correlate well with the reaction behavior and known reaction mechanism in the CO/CO2 hydrogenation to methanol and the reverse water-gas shift reactions.

As the methanol synthesis from CO/CO2 are now considered as effective measures in the storage of instant energy (power-to-methanol) as well as the exploitation of renewable carbon resources and sustainable production of fuels and chemicals, such results are rather interesting and meaningful. Meanwhile, although current manuscript is somewhat too lengthy, the narration of results and discussion was relatively clear. As a result, this reviewer suggests that it may be accepted for publication in the journal of Catalysts after proper revision.

(1) The superiority of using CO2/CO mixture to synthesize methanol was well demonstrated thermodynamically in two recent papers:

(a) J. Fuel Chem. Technol., 2023, 51(4): 482–491; https://doi.org/10.1016/S1872-5813(23)60346-9; http://rlhxxb.sxicc.ac.cn/cn/article/doi/10.1016/S1872-5813(23)60346-9.

(b) Ind. Eng. Chem. Res., 2022, 61(46): 17027–17038; https://doi.org/10.1021/acs.iecr.2c02898.

which consider the WGS/RWGS reaction as a communicating vessel connecting CO and CO2 and clearly depict the variation of equilibrium conversion of CO/CO2 and methanol yield with the reaction temperature and pressure and the feed composition. This reviewer strongly recommends that the authors may cite and refer to these two papers when expounding the results and discussion on the effect of feed composition and reaction conditions on the CO2 conversion, methanol formation and CO formation.

(2) The stoichiometric number (SN) may be better defined as SN = y-H2/(2y-CO+3yCO2). In this case, SN =1 means a stoichiometric amount of H2 to hydrogenate CO/CO2 to methanol.

(3) Figs. 2, 3, 4 and 6, the parity plots for the feed without CO at inlet may be omitted, just like Fig. 5, as the left three graphs for the parity plots for feed without CO at inlet have already been included in the right three graphs for the parity plots for the feed with CO at inlet.

(4) Table 10 and related other Tables, the unit of parameters may be only specified in the first column, whereas remain columns just give the digital values of the parameters.

(5) The authors may try to make the manuscript more concise. In addition, a carful proofreading is necessary and the writing of symbol and formulae should accord with related criterion. For example, lines 396–399, “Y” for productivity should be italic and the unit “mol/g/t” and equation (7) are confusing. Many other symbols in the texts and formulae should also be italic.

The narration of results and discussion was relatively clear, although current manuscript is somewhat too lengthy. The authors may try to make the manuscript more concise and have a carful proofreading.

Author Response

Comments from the Reviewer: #1

This study aims to evaluate the intrinsic kinetics of methanol synthesis based on CO2 hydrogenation and reverse water-gas shift in the overall reactions. Utilizing the industrial catalyst, Cu/ZnO/Al2O3/MgO, the research assessed the capabilities of an optimal kinetic model to predict experimental data, ranging from differential to integral conditions—a deviation from the conventional method of fitting only integral conditions. This analysis was conducted across varied temperatures, pressures, stoichiometric numbers, H₂/CO₂ ratios, and carbon oxide ratios. A comparison of multiple literature-based kinetic models was undertaken. Although the original Seidel model effectively fit the kinetic data, it comprised twelve parameters. The paper introduces a modified (MOD) model derived from the Seidel model but simplified to nine parameters, focusing on morphological changes of active sites and CO adsorption while excluding CO hydrogenation. The MOD model stood out for its exceptional fit to all data sets.

Comments to editor:

Accept after major change.

Comment 1) It is unclear to me about why the author can neglect CO hydrogenation step in the mechanism. Does the model perform better because the reaction condition in paper only has very low CO content. The reaction mechanism could be different if CO is more enriched in the inlet gas phase. Neglecting CO hydrogenation step in the reaction mechanism could hinder the applicability of the model at different feed condition.

1A) Author’s response

We thank the reviewer for this valuable comment. We would like to highlight that for re-fitted Seidel et al. (denoted as OR-SD) model in this paper, we compared the reaction rate kinetic constant resulting from the experimental fitting and for all fittings, the determined reaction kinetic constant for the CO hydrogenation reaction is not significant and this was discussed, for example in line 593, 635 and it is conjunction with most literature findings about the negligible role of CO hydrogenation to methanol.

The authors in the most recent published literature kinetic papers cited as reference Slotboom et al (2020), Nestler et al. (2021, 2020), and de Oliveira et al. (2021b) in our paper considered here discussed this negligible role of CO hydrogenation to methanol at length and this was briefly discussed in the literature review of our submission. The authors in reference paper Nestler et al. (2021) i.e. “ F. Nestler, V.P. Müller, M. Ouda, M.J. Hadrich, A. Schaadt, S. Bajohr, T. Kolb, A novel approach for kinetic measurements in exothermic fixed bed reactors: Advancements in non-isothermal bed conditions demonstrated for methanol synthesis, React. Chem. Eng. 6(6) (2021) 1092–1107, https://doi.org/10.1039/D1RE00071C.”  also discussed it was observed that the CO hydrogenation to methanol can be neglected due to its low reaction rate (|r_co|<6.0 ×10^–8 mol s^–1 kg_cat^–1) compared to the CO₂ hydrogenation to methanol (|r_co2|>3.2 × 10^–3 mol s^–1 kg_cat^–1) and RWGS (|r_rwgs|>1.5 ×10^–3 mol s^–1 kg_cat^–1) reactions. This agrees with other literature findings (Nielsen et al., 2021; de Oliveira Campos et al., 2021b). This was discussed in lines 219 to 222 of our submission.   These insights are in line with most recent literature findings even though we agree that final conclusive agreements have not been reached about the role CO hydrogenation and the better models to postulate this could be advanced microkinetic modelling. Even the authors in reference de Oliveira Campos et al. (2021b) i.e. “B.L. de Oliveira Campos, K. Herrera Delgado, S. Pitter, J. Sauer, Development of consistent kinetic models derived from a microkinetic model of the methanol synthesis, Ind. Eng. Chem. Res. 60 (42) (2021) 15074–15086, https://doi/full/10.1021/acs.iecr.1c02952.” who considered the insights from microkinetic models did agree to say in their abstract that and we quote “At last, a third model, which has six fitted parameters and neglects the CO hydrogenation adequately simulates the CO₂ containing feed.”  Furthermore in section 2.3 of the previous highlighted published paper by the authors in reference de Oliveira Campos et al. (2021b) clearly state that and we quote “From simulations of the microkinetic model, it was concluded that the contribution of CO direct hydrogenation to the methanol synthesis is only significant at low CO₂ content in feed, because formate (an intermediate species derived from CO₂) binds strongly on the copper surface, almost completely inhibiting CO hydrogenation.” To help the reader we have clearly added in line 248 the clarifying statement: “Recently, de Oliveira Campos et al. (2021b) deduced from microkinetic modelling that the role of CO hydrogenation to methanol is negligible at high CO₂/CO and as a result without CO hydrogenation, their six parameter model predicted CO₂ containing feed adequately. Such insights, as they will be first proven by refitting the Seidel et al. (2020, 2018) model in this paper and if true, then adopted in our model formulation, have already been considered in most recent models such Nestler et al. (2021, 2020).” We already highlighted the performance of the Nestler et al. (2021, 2020)] model in the section from line 206 to 231 and since its mechanism is not far off from that of Graaf et al. (1988), we did not consider refitting Nestler et al. (2020) further in our work. The distinction of our model though is that, although it takes these insights and following the proof from fitting discussed in line 593 about neglecting CO hydrogenation, it uses Seidel et al. (2020, 2018) mechanism with consideration of active sites morphological changes in contrast to the previous most recent model such as Nestler et al. (2021, 2020).  The authors believe that the literature evidence in conjunction with our findings on just simplified comparisons of kinetic factor substantiate the neglect of the CO hydrogenation reaction, at most under the conditions of high CO₂ in the feed as considered in our submission.  The paper is mainly focused on developing a model for CO₂ hydrogenation to methanol as a premise and this is important to emphasize. Although some mechanistic questions are still under discussion, the results highlight good agreement between the experiments and the model in the considered range of operating conditions. Future work can consider testing the capability of the model in detailed design of the methanol reactor and this was beyond the scope of our current submission.

Comment 2) How did some of the fitted parameters connected with DFT calculations such as rate constant of adsorption steps?

2A) Author’s response

We thank the reviewer for this valuable comment. Upon our literature search, Most DFT studies report heat of adsorption and in our case the data fitting in a small range of temperature does not allow precise determination of heat of adsorption. However, the value of adsorption constant we found for CO and CO₂ adsorption are similar order than the ones found in reference 41 i.e. "T. Henkel, Modellierung von Reaktion und Stofftransport in geformten Katalysatoren am Beispiel der Methanolsynthese, PhD thesis Technical University of Munich, 2011". We have compared our parameters to other literature findings and  added the statement “ The values of adsorption constant we found for CO and CO₂ adsorption are in the similar order to the ones found by Henkel [41].” in line 688.

Comment 3) It would be better if we learn how surface coverage of two active sites in MOD model change at different reaction conditions, which could be a good support for the analysis from line 933 – 939.

3A) Author’s response

We thank the reviewer for this comment. Although there was lack of clarity as to which line the reviewer was referring to, since the quoted line number refers to a reference on the reference list, we have plotted the GAMA factor which represent the fraction of reduced active sites against the mass of the catalytic bed for further clarification to the reviewer.  This is plotted for two experimental conditions. Two experiments have 2.0% CO at the inlet but at different pressures (40 and 65 bar). While other experiment has no CO in the feed. From the curves, the fraction of reduced sites increases with addition of CO and hence changes in experimental conditions.

Comment 4) Uncertainty quantification on fitted parameters could be valuable to add in the regression step, which provides the importance of each parameter in determining the reaction rate. There could be several methods to be used, such as Metropolis-Hasting sampling, or just evaluate the inverse of covariance matrix.

4A) Author’s response

It is the view of the authors that realistically, there is so many parameters to quantify the uncertainty for which could encompass the flow rate, temperature, pressure, instruments, GC analysis, etc. This will be quite a challenge and cumbersome to carry on.

Comment 5) Microkinetic modelling “Mechanism of Methanol Synthesis on Cu through CO2 and CO Hydrogenation” should also be cited and discussed.

5A) Author’s response

We thank the reviewer for this valuable comment and suggestion to cite and discuss the work of Grabow and Mavrikakis. For example, in line 242-246 we have added a statement and citation of the said paper as follows:

“The contribution of CO hydrogenation to methanol formation was found to vary with the CO feed composition, and conditions such as temperature and pressure. This finding is similar to that of Grabow and Mavrikakis [34] who, from their microkinetic modelling, also deduced that the contribution of CO₂ and CO hydrogenation is dependent on the prevailing conditions.”

Comment 6) The notion of the coverage of different active site in the model description is unclear, such as Θ∗Θ⨀, ΘBF, etc. The author should make a note that those symbols represent different active sites.

6A) Author’s response

A statement was added on line 580 i.e. “These symbols represent the different active sites”

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments for author File: Comments.pdf

Author Response

Comments from the Reviewer: 2

In this work, an improved kinetic model for the hydrogenation of CO₂ and CO mixture to methanol was developed, which gives a better prediction on the CO₂ conversion, methanol formation and CO formation than old models, but with less parameters. In addition, the application of the improved model and calculation results were discussed, which correlate well with the reaction behaviour and known reaction mechanism in the CO/CO₂ hydrogenation to methanol and the reverse water-gas shift reactions.
As the methanol synthesis from CO/CO₂ are now considered as effective measures in the storage of instant energy (power-to-methanol) as well as the exploitation of renewable carbon resources and sustainable production of fuels and chemicals, such results are rather interesting and meaningful. Meanwhile, although current manuscript is somewhat too lengthy, the narration of results and discussion was relatively clear.

As a result, this reviewer suggests that it may be accepted for publication in the journal of Catalysts after proper revision.

Comment 1) The superiority of using CO₂/CO mixture to synthesize methanol was well demonstrated thermodynamically in two recent papers:

(a) J. Fuel Chem. Technol., 2023, 51(4): 482–491; https://doi.org/10.1016/S1872-5813(23)60346-9; http://rlhxxb.sxicc.ac.cn/cn/article/doi/10.1016/S1872-5813(23)60346-9.

(b) Ind. Eng. Chem. Res., 2022, 61(46): 17027–17038; https://doi.org/10.1021/acs.iecr.2c02898.

which consider the WGS/RWGS reaction as a communicating vessel connecting CO and CO₂ and clearly depict the variation of equilibrium conversion of CO/CO₂ and methanol yield with the reaction temperature and pressure and the feed composition. This reviewer strongly recommends that the authors may cite and refer to these two papers when expounding the results and discussion on the effect of feed composition and reaction conditions on the CO₂ conversion, methanol formation and CO formation.

1) Author’s response

We thank the reviewer for this valuable comment. After careful study, the citations have been incorporated to the manuscript in line 242 of the updated manuscript and as reference 35,36.

Comment 2) The stoichiometric number (SN) may be better defined as SN = y-H2/(2y-CO+3yCO2). 2) Author’s response

We thank the reviewer for this valuable comment. We have thus made improvements as suggested. In line 810, we have changed the formula of the SN as suggested by the reviewer. “SN = ”     

Comment 3)   Figs. 2, 3, 4 and 6, the parity plots for the feed without CO at inlet may be omitted, just like Fig. 5, as the left three graphs for the parity plots for feed without CO at inlet have already been included in the right three graphs for the parity plots for the feed with CO at inlet.

3) Author’s response

We thank the reviewer for this valuable comment. We have looked closely at the comment and in the said graphs or figures, the points are not the same on the parity plots. We made the optimisation of the kinetic parameter for experiments with and without CO. So, the points are very close but not the same. Thus, we cannot remove the left three graphs in each of the figures.

Comment 4) Table 10 and related other Tables, the unit of parameters may be only specified in the first column, whereas remain columns just give the digital values of the parameters.

  4) Author’s response

We thank the reviewer for this valuable comment. We have looked closely at the comment and made changes as requested in the said tables. The changes are highlighted in red in the tables, for example Table 8 (previously table 10 in the reviewed manuscript).       

Comment 5) The authors may try to make the manuscript more concise. In addition, a carful proofreading is necessary and the writing of symbol and formulae should accord with related criterion. For example, lines 396–399, “Y” for productivity should be italic and the unit “mol/g/t” and equation (7) are confusing. Many other symbols in the texts and formulae should also be italic.          

  5) Author’s response

We have made changes as requested to the formulae and did careful proofreading of the manuscript. For example, see line 802, 803, 810.

 Comment 6) Comments on the Quality of English Language: The narration of results and discussion was relatively clear, although current manuscript is somewhat too lengthy. The authors may try to make the manuscript more concise and have a carful proofreading. Please also move ‘Results and discussion’ before ‘Experimental part’ according to our journal template.                  

  5) Author’s response

We have made carefully proofread the manuscript and tried to shorten the sentences where possible and we also moved the ‘results and discussion’ before the experimental part.   

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

It seems that most of the issues raised by the reviewers to the old version manuscript have been properly responded in the revised manuscript.

As a result, this reviewer suggests that the revised manuscript may now be acceptable for publication in the journal of Catalysts, although a carful proofreading is still proposed by this reviewer to correct some minor mistakes.

[Note: Comments in .pdf and .doc files are also provided.]

(1) The stoichiometric number (SN) has been defined as:

Where ,  and are the  molar fraction of H₂, CO and CO₂, respectively, in the initial feed. SN = 1 means a stoichiometric amount of H₂ to hydrogenate CO/CO₂ to methanol.

By using this new definition, the values of SN discussed in the text should be re-calculated. However, it seems that the revised manuscript still used old values. For example, in the abstract, “for different stoichiometric numbers (1.9–3.8)” may be “for different stoichiometric numbers (0.95–1.9)”, when the new definition is adopted.

(2) Equation (1) – (3);  may be .

(3) The unit of productivity Y cannot be “mol/g/t”. “(Y in mol/g/t)” may be “(Y, in mol/g/h)” or “(Y, in mol g⁻¹ h⁻¹)”, by using equation (30)–(31).

(4) There are some mistakes for the newly cited references. Page 6, “in the work of Kyrimis et al. [2], Gou et al. [35], [36]” should be “in the work of Kyrimis et al. [2] and Guo et al. [35,36]”. In addition, two references may be modified to:

[35] Guo, S.; Wang, H.; Qin, Z.; Li, Z.; Wang, G.; Dong, M.; Fan, W.; Wang, J. Conversion of the CO and CO₂ mixture to alcohols and hydrocarbons by hydrogenation under the influence of the water-gas shift reaction, a thermodynamic consideration. J. Fuel Chem. Technol. 2023, 51, 482–491. (https://doi.org/10.1016/S1872-5813(23)60346-9)

[36] Guo, S.; Wang, H.; Qin, Z.; Li, Z.; Wang, G.; Dong, M.; Fan, W.; Wang, J. Feasibility, limit, and suitable reaction conditions for the production of alcohols and hydrocarbons from CO and CO₂ through hydrogenation, a thermodynamic consideration. Ind. Eng. Chem. Res. 2022, 61, 17027–17038. (https://doi.org/10.1021/acs.iecr.2c02898)

(5) Table 6 and others, the symbols in the texts and formulae, like E, k, and b, should also be in italic, e.g.,  may be

(6) Some Figures, e.g., Figures 1 and 2, are improperly displayed in the revised manuscript, please have a check.

Comments for author File: Comments.pdf

It seems that the quality of English Language is acceptable.

Author Response

Answers to Reviewer 1

We are grateful to the Reviewer 1 for helping us to further improve the quality of our manuscript.

All the comments have taken into account in the final revised version. In addition, a careful reading has been performed to try to reduce the maximum: typos, mistakes etc…

All the changes have been marked in red.