Correction: Surface reaction kinetics of the methanol synthesis and the water gas shift reaction on Cu/ZnO/Al₂O₃

Abstract

Correction for ‘Surface reaction kinetics of the methanol synthesis and the water gas shift reaction on Cu/ZnO/Al₂O₃’ by Bruno Lacerda de Oliveira Campos et al., React. Chem. Eng., 2021, 6, 868–887; DOI: 10.1039/D1RE00040C

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A mistake was found in the Matlab program used for the simulations. That is, a parameter of the Gibbs free energy change of zinc reduction (ΔG⁰_{Zn red.}) was wrongly typed, which participates in eqn (31) and (37) of the original paper. ΔG⁰_{Zn red.} is calculated from the thermodynamic data of Goos et al.,¹ and the equation with the correct data is as follows.

ΔG⁰_{Zn red.} = R·[8411.4 − 8.3237·T + 1.9335 × 10⁻⁴·T² − 2.2728 × 10⁻⁷·T³−4.3047 × 10⁻¹⁰·T⁴ + 1.6777 × 10⁻¹³·T⁵ + 0.9824·T·ln(T)] (1)

With the corrected parameter, the zinc solubility in copper (X_Zn) and, consequently, the zinc coverage (ϕ_Zn) have lower values than the originally published ones, as shown in the revised Fig. 4.

Fig. 4 Solubility of zinc in the Cu-bulk (A and C) and zinc coverage (B and D) as functions of the gas reducing power.

With the corrected parameter, new simulations of the experiments were performed, with the normalized residues and statistical indicators shown in the revised Fig. 6 and Table 4, respectively. The deviations after the parameter correction (χ² = 120.67) are in fact higher than that originally published (χ² = 74.74).

Fig. 6 Two-case model simulation: normalized residues of the simulation of the experiments from this work (1–359), from Seidel et al.² (360–498), from Park et al.³ (499–596), and from Slotboom et al.⁴ (597–690). A) Carbon monoxide. B) Carbon dioxide. C) Methanol.

Table 4 Statistical indicators of the model performance in predicting the carbon-containing compounds

Feed:		H2/CO/CO2			H2/CO		H2/CO2		All
Data:		This work	Seidel et al.	Park et al.	This work	Seidel et al.	Seidel et al.	Slotboom et al.
N° of points		324	46	98	35	61	32	94	690
χ ^2		38.63	1.45	17.62	2.44	9.29	1.26	49.98	120.67
CO	ME	0.0275	0.0698	0.1481	0.0105	0.0269	0.1010	0.3752	0.0973
	MSE	0.0017	0.0097	0.0526	0.0002	0.0013	0.0164	0.2324	0.0415
CO2	ME	0.0215	0.0292	0.0537			0.0315	0.0441	0.0315
	MSE	0.0008	0.0013	0.0056			0.0016	0.0036	0.0021
CH3OH	ME	0.2732	0.1283	0.2831	0.2300	0.3220	0.1198	0.4672	0.2864
	MSE	0.1167	0.0204	0.1216	0.0698	0.1510	0.0190	0.2957	0.1315

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By using a constant zinc coverage approach, the model accuracy is improved and the complexity of the model decreases. As it is known that the zinc coverage on the catalyst is reduced by an increase in the CO₂/CO_X ratio ,^5,6 we divide the operating region into three sectors, the 1st with very low CO₂ content , the 2nd with very high CO₂ content , and the 3rd being an intermediate region . For each sector, a separate constant zinc coverage was determined, as shown in Table 5.

Table 5 Zinc coverage value depending on the CO₂ to CO_X ratio in the feed

Condition	Zn value
CO2/COX ratio < 0.001	0.90 (for Campos' data)
	0.95 (for Seidel's data)
0.001 ≤ CO2/COX ratio ≤ 0.90	0.50
CO2/COX ratio > 0.90	0.10

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With this approach, corresponding simulations were repeated, and results are shown regarding the normalized residues (Fig. 16), methanol output concentration for selected experiments (Fig. 17), and statistical indicators (Table 6). The overall model performance is thereby improved (χ² = 75.97 against 120.67 with Kuld's method⁷), in particular for the intermediate region .

Fig. 16 Two-case model simulation: normalized residues of the simulation of the experiments from this work (1–359), from Seidel et al.² (360–498), from Park et al.³ (499–596), and from Slotboom et al.⁴ (597–690). A) Carbon monoxide. B) Carbon dioxide. C) Methanol.

Fig. 17 Experimental and simulated values of the methanol output concentration under different conditions. Databases: A) this work, B) Seidel et al.²

Table 6 Statistical indicators of the model performance in predicting the carbon-containing compounds

Feed:		H2/CO/CO2			H2/CO		H2/CO2		All
Data:		This work	Seidel et al.	Park et al.	This work	Seidel et al.	Seidel et al.	Slotboom et al.
N° of points		324	46	98	35	61	32	94	690
χ ^2		13.05	0.55	15.31	2.44	9.29	3.02	32.31	75.97
CO	ME	0.0192	0.0431	0.1371	0.0105	0.0269	0.1751	0.2978	0.0830
	MSE	0.0008	0.0035	0.0444	0.0002	0.0013	0.0342	0.1530	0.0295
CO2	ME	0.0227	0.0430	0.0601			0.0301	0.0309	0.0321
	MSE	0.0010	0.0027	0.0067			0.0011	0.0017	0.0022
CH3OH	ME	0.1499	0.0643	0.2559	0.2299	0.3220	0.2275	0.3749	0.2128
	MSE	0.0385	0.0057	0.1051	0.0695	0.1510	0.0535	0.1890	0.0785

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The reaction flow analysis and the sensitivity analysis have no significant changes compared to the originally published ones, with the exception being the zinc coverage profile, which has now constant values. The revised Fig. 11 is given below:

Fig. 11 Zinc coverage along the methanol synthesis reactor with a length of 100 cm. Operating conditions: 220 °C, 60 bar, GHSV = 4.8 L_S h⁻¹ g_cat⁻¹, feed concentration: H₂/CO_x = 80/20% v/v.

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

References

1. E. B. Goos, A. Burcat and B. Ruscic, New NASA thermodynamic polynomials databasehttp://garfield.chem.elte.hu/Burcat/THERM.DAT Accessed Aug 2020.
2. C. Seidel, A. Jörke, B. Vollbrecht, A. Seidel-Morgenstern and A. Kienle, Kinetic modeling of methanol synthesis from renewable resources, Chem. Eng. Sci., 2018, 175, 130–138,  DOI:10.1016/j.ces.2017.09.043.
3. N. Park, M.-J. Park, Y.-J. Lee, K.-S. Ha and K.-W. Jun, Kinetic modeling of methanol synthesis over commercial catalysts based on three-site adsorption, Fuel Process. Technol., 2014, 125, 139–147,  DOI:10.1016/j.fuproc.2014.03.041.
4. Y. Slotboom, M. J. Bos, J. Pieper, V. Vrieswijk, B. Likozar, S. R. A. Kersten and D. W. F. Brilman, Critical assessment of steady-state kinetic models for the synthesis of methanol over an industrial Cu/ZnO/Al2O3 catalyst, Chem. Eng. J., 2020, 389, 124181,  DOI:10.1016/j.cej.2020.124181.
5. C. V. Ovesen, B. S. Clausen, J. Schiøtz, P. Stoltze, H. Topsøe and J. K. Nørskov, Kinetic Implications of Dynamical Changes in Catalyst Morphology during Methanol Synthesis over Cu/ZnO Catalysts, J. Catal., 1997, 168, 133–142,  DOI:10.1006/jcat.1997.1629.
6. J. D. Grunwaldt, A. M. Molenbroek, N. Y. Topsøe, H. Topsøe and B. S. Clausen, In Situ Investigations of Structural Changes in Cu/ZnO Catalysts, J. Catal., 2000, 194, 452–460,  DOI:10.1006/jcat.2000.2930.
7. S. Kuld, M. Thorhauge, H. Falsig, C. F. Elkjær, S. Helveg, I. Chorkendorff and J. Sehested, Quantifying the promotion of Cu catalysts by ZnO for methanol synthesis, Science, 2016, 352, 969–974,  DOI:10.1126/science.aaf0718.

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