Optimizing Biomethane Production from Industrial Pig Slurry and Wine Vinasse: A Mathematical Approach
Abstract
1. Introduction
2. Materials and Methods
2.1. Organic Substrates and Inoculum
2.2. Analytical Methods
2.3. Biochemical Methane Potential Test (BMP)
2.4. Design of Experiments (DoE) Using Box–Behnken Design
2.5. Kinetic Analysis in BMP Assays
- H = biomethane generation (cumulative) in time (t) (mL/gVS);
- P = potential for maximum biomethane generation (mL/gVS);
- Rm = biomethane generation rate (mL of biogas/gVS/d);
- Λ = the lag phase during biomethane generation (d);
- T = time required for the cumulative production of biomethane.
3. Results
3.1. Biomethane Production Using a Box–Behnken Design for AcoD of Pig Slurry and Wine Vinasse
3.2. tVFA Using a Box–Behnken Design for AcoD of Pig Slurry and Wine Vinasse
3.3. Biomethane Yield Using a Box–Behnken Design for AcoD from Pig Slurry and Wine Vinasse
3.4. Mathematical Optimization of Biomethane Yield Form AcoD of Pig Slurry and Wine Vinasse Through a Box–Behnken Design
3.5. Kinetic Analysis of Biomethane Production of Pig Slurry and Wine Vinasse via a Box–Behnken Design
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
PS | Pig slurry |
WV | Wine vinasse |
AcoD | Anaerobic co-digestion |
DoE | Design of Experiments |
VS | Volatile Solids |
BMP | Biochemical Methane Potential |
BBD | Box–Behnken design |
AD | Anaerobic digestion |
RSM | Response Surface Methodology |
CCD | Central Composite Design |
DM | Doehlert Matrix Design |
tVFA | Volatile Fatty Acids |
WWTP | Wastewater treatment plant |
TS | Total Solids |
tCOD | Total Chemical Oxygen Demand |
sCOD | Soluble Chemical Oxygen Demand |
FID | Flame ionization detector |
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Substrate | pH | tCOD (g/L) | sCOD(g/L) | TS (g/L) | VS (g/L) | TVFA (mgAcH/L) | C/N |
---|---|---|---|---|---|---|---|
PS | 7.86 ± 0.36 | 18.67 ± 0.03 | 6.97 ± 0.05 | 13.32 ± 0.02 | 8.57 ± 0.02 | 192.41 ± 12.27 | 6.63 ± 0.02 |
WV | 3 ± 0.36 | 36.10 ± 0.06 | 32.36 ± 0.05 | 19.19 ± 0.08 | 16.23 ± 0.07 | 973.88 ± 8.40 | 75.29 ± 0.03 |
I 35 °C | 7.17 ± 0.36 | 20.24 ± 0.07 | 0.80 ± 0.03 | 18.85 ± 0.04 | 11.47 ± 0.03 | 326.13 ± 11.75 | 15.65 ± 0.03 |
I 52.5 °C | 8.37 ± 0.36 | 6.803 ± 0.04 | 0 | 11.38 ± 0.02 | 7.22 ± 0.01 | 557.92 ± 9.18 | 7.62 ± 0.02 |
I 70 °C | 78.51 ± 0.36 | 16.17 ± 0.03 | 0 | 16.39 ± 0.04 | 9.62 ± 0.03 | 676.30 ± 14.03 | 4.96 ± 0.03 |
Test | pH | T°C | Ratio | tCOD (g/L) | sCOD (g/L) | TS(g/L) | VS (g/L) | TVFA (mgAcH/L) | C/N Ratio |
---|---|---|---|---|---|---|---|---|---|
1 | 7 ± 0.36 | 35 | 50 | 33.3 ± 0.04 | 11.78 ± 0.04 | 15.57 ± 0.03 | 10.32 ± 0.02 | 604.97 ± 10.08 | 5.99 ± 0.03 |
2 | 8 ± 0.36 | 35 | 50 | 29.20 ± 0.05 | 11.62 ± 0.05 | 14.96 ± 0.05 | 9.83 ± 0.03 | 523.20 ± 12.35 | 5.70 ± 0.06 |
3 | 7 ± 0.36 | 70 | 50 | 34.02 ± 0.07 | 17.59 ± 0.02 | 14.43 ± 0.07 | 9.27 ± 0.07 | 1231.05 ± 16.04 | 5.38 ± 0.04 |
4 | 8 ± 0.36 | 70 | 50 | 36.01 ± 0.07 | 19.75 ± 0.09 | 15.17 ± 0.02 | 9.16 ± 0.06 | 1017.75 ± 9.47 | 5.31 ± 0.07 |
5 | 7 ± 0.36 | 52.5 | 25 | 26.38 ± 0.04 | 16.34 ± 0.02 | 13.31 ± 0.12 | 8.82 ± 0.17 | 276.34 ± 9.33 | 5.12 ± 0.15 |
6 | 8 ± 0.36 | 52.5 | 25 | 35.68 ± 0.07 | 21.90 ± 0.02 | 13.70 ± 0.05 | 9.09 ± 0.02 | 209.40 ± 11.60 | 5.27 ± 0.01 |
7 | 7 ± 0.36 | 52.5 | 75 | 23.65 ± 0.04 | 11.78 ± 0.08 | 12.69 ± 0.05 | 7.76 ± 0.03 | 761.00 ± 8.76 | 4.50 ± 0.02 |
8 | 8 ± 0.36 | 52.7 | 75 | 30.37 ± 0.04 | 16.43 ± 0.04 | 13.26 ± 0.08 | 7.60 ± 0.02 | 754.46 ± 14.78 | 4.41 ± 0.02 |
9 | 7.5 ± 0.36 | 35 | 25 | 38.50 ± 0.04 | 24.81 ± 0.01 | 16.36 ± 0.02 | 10.00 ± 0.05 | 129.64 ± 13.03 | 5.80 ± 0.08 |
10 | 7.5 ± 0.36 | 70 | 25 | 33.64 ± 0.01 | 26.55 ± 0.02 | 17.10 ± 0.03 | 10.68 ± 0.01 | 443.67 ± 6.22 | 6.20 ± 0.02 |
11 | 7.5 ± 0.36 | 35 | 75 | 23.31 ± 0.04 | 9.87 ± 0.05 | 13.07 ± 0.04 | 7.85 ± 0.02 | 588.16 ± 12.59 | 4.56 ± 0.03 |
12 | 7.5 ± 0.36 | 70 | 75 | 23.14 ± 0.03 | 14.27 ± 0.04 | 16.78 ± 0.05 | 9.28 ± 0.02 | 419.54 ± 16.06 | 5.38 ± 0.02 |
13 | 7.5 ± 0.36 | 52.5 | 50 | 25.47 ± 0.05 | 14.68 ± 0.05 | 12.74 ± 0.04 | 7.24 ± 0.05 | 858.75 ± 11.87 | 4.20 ± 0.04 |
14 | 7.5 ± 0.36 | 52.5 | 50 | 26.05 ± 0.03 | 14.66 ± 0.06 | 13.01 ± 0.03 | 5.69 ± 0.02 | 809.18 ± 11.65 | 3.30 ± 0.02 |
15 | 7.5 ± 0.36 | 52.5 | 50 | 24.80 ± 0.04 | 12.86 ± 0.03 | 13.03 ± 0.26 | 7.73 ± 0.03 | 803.39 ± 14.79 | 4.48 ± 0.11 |
I 35° | - | 35 | - | 6.97 ± 0.01 | 0.66 ± 0.05 | 6.51 ± 0,20 | 3.60 ± 0.07 | 8.90 ± 13.03 | 2.09 ± 0.12 |
I 52.5° | - | 52.5 | - | 4.81 ± 0.07 | 0 | 6.14 ± 0.05 | 3.38 ± 0.03 | 32.87 ± 16.60 | 1.96 ± 0.03 |
I 70° | - | 70 | - | 11.28 ± 0.06 | 0.33 ± 0.02 | 8.56 ± 0.05 | 4.12 ± 0.02 | 653.90 ± 8.25 | 0 |
Test | pH | T °C | Ratio | % VS | % sCOD | VCH4 (mL) | Y CH4/gVS |
---|---|---|---|---|---|---|---|
1 | 7 | 35 | 50 | 36.66 | 53.98 | 870.18 | 199.32 |
2 | 8 | 35 | 50 | 31.45 | 36.05 | 293.90 | 89.68 |
3 | 7 | 70 | 50 | 31.98 | 5.88 | 3.26 | 0.71 |
4 | 8 | 70 | 50 | 21.62 | 5.88 | 26.15 | 5.39 |
5 | 7 | 52.5 | 25 | 47.63 | 87.00 | 1093.88 | 339.73 |
6 | 8 | 52.5 | 25 | 46.21 | 47.14 | 746.73 | 277.23 |
7 | 7 | 52.5 | 75 | 36.96 | 89.95 | 1685.08 | 279.81 |
8 | 8 | 52.5 | 75 | 24.73 | 74.70 | 900.55 | 208.79 |
9 | 7.5 | 35 | 25 | 42.17 | 90.53 | 254.64 | 92.89 |
10 | 7.5 | 70 | 25 | 4.81 | 28.95 | 9.37 | 3.09 |
11 | 7.5 | 35 | 75 | 11.08 | 56.28 | 1101.76 | 189.45 |
12 | 7.5 | 70 | 75 | 18.39 | 2.06 | 3.59 | 0.56 |
13 | 7.5 | 52.5 | 50 | 50.50 | 65.38 | 1354.93 | 542.88 |
14 | 7.5 | 52.5 | 50 | 45.89 | 76.99 | 1270.60 | 326.52 |
15 | 7.5 | 52.5 | 50 | 46.80 | 80.06 | 1055.69 | 291.16 |
Models | Parameters | Test 2 | Test 9 | Test 5 | Test 15 | Test 3 | Test 10 |
---|---|---|---|---|---|---|---|
First-Order | P (mL) | 8.704 | 4.163 | 113.416 | 78.022 | 60.009 | 3.265 |
Kh (1/h) | 0.033 | 0.035 | 0.002 | 0.002 | 0.006 | 0.009 | |
R2 | 0.870 | 0.889 | 0.920 | 0.958 | 0.954 | 0.959 | |
Modified Gompertz | P (mL) | 8.617 | 4.125 | 60.234 | 51.533 | 55.064 | 3.107 |
Rm (mL/h) | 20.753 | 20.273 | 168.434 | 102.138 | 35.119 | 28.436 | |
λ (h) | 0.816 | 0.402 | 0.769 | 0.262 | 0.294 | 0.032 | |
R2 | 1 | 0.999 | 0.995 | 0.990 | 0.984 | 0.988 |
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Cañadas, B.; Fernández-Rodríguez, J.; Solera, R.; Pérez, M. Optimizing Biomethane Production from Industrial Pig Slurry and Wine Vinasse: A Mathematical Approach. ChemEngineering 2025, 9, 61. https://doi.org/10.3390/chemengineering9030061
Cañadas B, Fernández-Rodríguez J, Solera R, Pérez M. Optimizing Biomethane Production from Industrial Pig Slurry and Wine Vinasse: A Mathematical Approach. ChemEngineering. 2025; 9(3):61. https://doi.org/10.3390/chemengineering9030061
Chicago/Turabian StyleCañadas, Belén, Juana Fernández-Rodríguez, Rosario Solera, and Montserrat Pérez. 2025. "Optimizing Biomethane Production from Industrial Pig Slurry and Wine Vinasse: A Mathematical Approach" ChemEngineering 9, no. 3: 61. https://doi.org/10.3390/chemengineering9030061
APA StyleCañadas, B., Fernández-Rodríguez, J., Solera, R., & Pérez, M. (2025). Optimizing Biomethane Production from Industrial Pig Slurry and Wine Vinasse: A Mathematical Approach. ChemEngineering, 9(3), 61. https://doi.org/10.3390/chemengineering9030061