Evaluation of Kinetic Models for the Catalytic Hydrogenation of Levulinic Acid to γ-Valerolactone over Nickel Catalyst Supported by Titania
Abstract
1. Introduction
2. Experimental Tests
2.1. Catalyst Synthesis
2.2. Catalytic Reaction—Experimental
3. Kinetic Model
levulinic acid + hydrogen → 4-hydroxypentanoic acid → γ-valerolactone + water
3.1. Considerations About the Mechanism of Reaction
3.2. Proposed Mechanism for the Reactions
- -
- adsorption–desorption:
- -
- reactions on the surface:
- ▪
- Adsorption of levulinic acid as the determining step.
- ▪
- Adsorption of hydrogen as the determining step.
- ▪
- Desorption of 4-hydroxypentanoic acid as the determining step.
- ▪
- Reaction on the surface as the determining step.
4. Numerical Approach
4.1. Mathematical Model
4.2. Fitting of the Kinetic Model Parameters
4.3. Numerical Methods
5. Kinetic Model Evaluation
5.1. Evaluating the Kinetic Models
5.2. Comparing with Other Studies
6. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
List of Symbols
concentration of species in the liquid phase (mol/m3) | |
adsorption equilibrium constant for species | |
catalyst mass (g) | |
pressure (MPa) | |
rate of reaction | |
sum of square errors | |
selectivity for product | |
time | |
temperature (K) | |
molar fraction of hydrogen in the liquid phase | |
conversion | |
product yield | |
Subscripts | |
GVL | γ-valerolactone |
LA | levulinic acid |
HPA | 4-hydroxypentanoic acid |
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Experiment | H2 Pressure (MPa) | LA Initial Concentration (mol·m−3) | Temperature (°C) |
---|---|---|---|
1 | 2.07 | 169 | 175 |
2 | 1.03 | 290 | 175 |
3 | 2.07 | 290 | 175 |
4 | 2.07 | 290 | 175 |
5 | 2.07 | 290 | 175 |
6 | 2.07 | 410 | 175 |
7 | 3.10 | 290 | 175 |
8 | 3.10 | 410 | 200 |
9 | 1.03 | 410 | 200 |
10 | 1.03 | 169 | 200 |
11 | 2.07 | 290 | 200 |
12 | 3.10 | 169 | 200 |
13 | 1.03 | 169 | 150 |
14 | 3.10 | 410 | 150 |
15 | 3.10 | 169 | 150 |
16 | 1.03 | 410 | 150 |
17 | 2.07 | 290 | 150 |
Model | Rate Equation | Determining Step | Kind of Adsorption | Hydrogen Adsorption |
---|---|---|---|---|
1 | 04 | C | M | |
2 | 04 | C | D | |
3 | 04 | NC | B | |
4 | 07 | NC | B | |
5 | 07 | C | M | |
6 | 08 | C | D | |
7 | 06 | NC | B | |
8 | 06 | C | D | |
9 | 06 | C | M | |
10 | 12 | NC | M | |
11 | 12 | C | M | |
12 | 13 | NC | D | |
13 | 13 | C | D | |
14 | 14 | NC | D | |
15 | 14 | C | D |
Iteration | Model Eliminated | Model Eliminated | ||
---|---|---|---|---|
01 | 679.0 | 23.7 | 1 | 188.1 |
02 | 597.3 | 22.4 | 2 | 186.9 |
03 | 474.5 | 21.0 | 3 | 183.5 |
04 | 257.2 | 19.7 | 7 | 47.6 |
05 | 230.2 | 18.3 | 4 | 43.5 |
06 | 197.5 | 16.9 | 14 | 33.1 |
07 | 176.5 | 15.5 | 10 | 25.3 |
08 | 164.3 | 14.1 | 8 | 24.6 |
09 | 148.3 | 12.6 | 9 | 23.5 |
10 | 126.3 | 11.1 | 12 | 22.1 |
11 | 90.6 | 9.5 | 13 | 12.8 |
12 | 75.6 | 7.8 | 6 | 10.2 |
13 | 59.8 | 6.0 | 5 | 10.0 |
14 | 0.2 | 3.8 | – | – |
Iteration | Model Eliminated | Model Eliminated | ||
---|---|---|---|---|
01 | 604.9 | 23.7 | 4 | 252.5 |
02 | 566.2 | 22.4 | 2 | 241.7 |
03 | 521.4 | 21.0 | 1 | 236.5 |
04 | 460.8 | 19.7 | 3 | 235.4 |
05 | 365.9 | 18.3 | 6 | 214.7 |
06 | 221.1 | 16.9 | 5 | 167.1 |
07 | 6.8 | 15.5 | – | – |
Iteration | Model Eliminated | Model Eliminated | ||
---|---|---|---|---|
01 | 1633.4 | 23.7 | 5 | 7397.3 |
02 | 1354.9 | 22.4 | 4 | 5004.2 |
03 | 986.4 | 21.0 | 6 | 2647.3 |
04 | 597.3 | 19.7 | 2 | 609.4 |
05 | 508.2 | 18.3 | 1 | 603.4 |
06 | 350.6 | 16.9 | 3 | 535.0 |
07 | 8.9 | 15.5 | – | – |
Parameter | Value | Bounds (95% Interval) | Units | |
---|---|---|---|---|
Lower | Upper | |||
12.6 | 11.3 | 14.4 | dm3/mol | |
20.0 | 17.3 | 23.4 | dm3/mol | |
32.5 | 26.7 | 40.5 | dm6/mol·gcat·h | |
47.0 | 45.7 | 48.2 | kJ/mol | |
2.1 | 1.5 | 2.8 | dm3/mol |
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Sepulveda Lanziano, C.A.; Rodella, C.B.; Guirardello, R. Evaluation of Kinetic Models for the Catalytic Hydrogenation of Levulinic Acid to γ-Valerolactone over Nickel Catalyst Supported by Titania. Molecules 2025, 30, 1400. https://doi.org/10.3390/molecules30071400
Sepulveda Lanziano CA, Rodella CB, Guirardello R. Evaluation of Kinetic Models for the Catalytic Hydrogenation of Levulinic Acid to γ-Valerolactone over Nickel Catalyst Supported by Titania. Molecules. 2025; 30(7):1400. https://doi.org/10.3390/molecules30071400
Chicago/Turabian StyleSepulveda Lanziano, Carlos Alberto, Cristiane Barbieri Rodella, and Reginaldo Guirardello. 2025. "Evaluation of Kinetic Models for the Catalytic Hydrogenation of Levulinic Acid to γ-Valerolactone over Nickel Catalyst Supported by Titania" Molecules 30, no. 7: 1400. https://doi.org/10.3390/molecules30071400
APA StyleSepulveda Lanziano, C. A., Rodella, C. B., & Guirardello, R. (2025). Evaluation of Kinetic Models for the Catalytic Hydrogenation of Levulinic Acid to γ-Valerolactone over Nickel Catalyst Supported by Titania. Molecules, 30(7), 1400. https://doi.org/10.3390/molecules30071400