An Upgraded FOS/TAC Titration Model Integrating Phosphate Effects for Accurate Assessments of Volatile Fatty Acids and Alkalinity in Anaerobic Media
Abstract
1. Introduction
2. Materials and Methods
2.1. FOS/TAC Titration
2.2. Numerical Simulation of FOS/TAC Titration by Scilab
3. Results
3.1. Comparison of Model Accuracy
3.2. Model Parameter Variation with Calibration Ranges
3.3. Effect of Total Phosphate Level on the Modeling Parameters
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Acid/Base Couple | Dissociation Reaction | pKa (−) |
---|---|---|
Volatile fatty acid | ||
Acetic acid | 4.76 | |
Propionic acid | 4.87 | |
Butyric acid | 4.82 | |
Valeric acid | 4.82 | |
Alkalinity | ||
H2CO3/HCO3− | 6.35 | |
HCO3−/CO32− | 10.35 | |
H3PO4/H2PO4− | 2.15 | |
H2PO4−/HPO42− | 7.20 | |
HPO42−/PO43− | 12.4 | |
NH4+/NH3 | 9.24 |
[HAc]max | 100 | 300 | 500 | 1000 | 3000 | 5000 | 7000 | 10,000 | 13,000 | 15,000 | 17,000 | 20,000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[NaHCO3]max | |||||||||||||
100 | |||||||||||||
300 | |||||||||||||
500 | |||||||||||||
1000 | |||||||||||||
3000 | |||||||||||||
5000 | 1822 * | ||||||||||||
7000 | |||||||||||||
10,000 | |||||||||||||
13,000 | |||||||||||||
15,000 | |||||||||||||
17,000 | |||||||||||||
20,000 |
[HAc]max | 100 | 300 | 500 | 1000 | 3000 | 5000 | 7000 | 10,000 | 13,000 | 15,000 | 17,000 | 20,000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[NaHCO3]max | |||||||||||||
100 | −1996 | −2002 | −2003 | −2027 | −2013 | ||||||||
300 | |||||||||||||
500 | |||||||||||||
1000 | |||||||||||||
3000 | |||||||||||||
5000 | −2011 * | ||||||||||||
7000 | |||||||||||||
10,000 | −2050 | −2016 | |||||||||||
13,000 | −1948 | −2000 | |||||||||||
15,000 | −2096 | −2033 | |||||||||||
17,000 | −2031 | −2014 | |||||||||||
20,000 | −2033 | −2031 |
[HAc]max | 100 | 300 | 500 | 1000 | 3000 | 5000 | 7000 | 10,000 | 13,000 | 15,000 | 17,000 | 20,000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[NaHCO3]max | |||||||||||||
100 | |||||||||||||
300 | |||||||||||||
500 | |||||||||||||
1000 | |||||||||||||
3000 | |||||||||||||
5000 | −219 * | ||||||||||||
7000 | |||||||||||||
10,000 | |||||||||||||
13,000 | |||||||||||||
15,000 | |||||||||||||
17,000 | |||||||||||||
20,000 |
[HAc]max | 100 | 300 | 500 | 1000 | 3000 | 5000 | 7000 | 10,000 | 13,000 | 15,000 | 17,000 | 20,000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[NaHCO3]max | |||||||||||||
100 | −131 | −120 | −114 | −118 | −123 | −153 | −133 | ||||||
300 | −134 | −131 | −133 | −125 | |||||||||
500 | −134 | −135 | |||||||||||
1000 | |||||||||||||
3000 | |||||||||||||
5000 | −126 * | ||||||||||||
7000 | |||||||||||||
10,000 | |||||||||||||
13,000 | |||||||||||||
15,000 | |||||||||||||
17,000 | |||||||||||||
20,000 |
[HAc]max | 100 | 300 | 500 | 1000 | 3000 | 5000 | 7000 | 10,000 | 13,000 | 15,000 | 17,000 | 20,000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[NaHCO3]max | |||||||||||||
100 | 3794 | 3770 | |||||||||||
300 | 3770 | 3761 | |||||||||||
500 | 3771 | 3774 | |||||||||||
1000 | |||||||||||||
3000 | |||||||||||||
5000 | 3763 * | ||||||||||||
7000 | |||||||||||||
10,000 | 3805 | ||||||||||||
13,000 | 3696 | ||||||||||||
15,000 | 3873 | 3792 | 3780 | 3774 | |||||||||
17,000 | |||||||||||||
20,000 | 3775 | 3789 | 3773 | 3776 |
[HAc]max | 100 | 300 | 500 | 1000 | 3000 | 5000 | 7000 | 10,000 | 13,000 | 15,000 | 17,000 | 20,000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[NaHCO3]max | |||||||||||||
100 | |||||||||||||
300 | |||||||||||||
500 | |||||||||||||
1000 | |||||||||||||
3000 | |||||||||||||
5000 | −11.1 * | ||||||||||||
7000 | |||||||||||||
10,000 | |||||||||||||
13,000 | |||||||||||||
15,000 | |||||||||||||
17,000 | |||||||||||||
20,000 |
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[PO43−] (mg·L−1) | (mg·L−1) | (mg·L−1) | MAPE for [NaHCO3] (%) | MAPE for [HAc] (%) | ||||
---|---|---|---|---|---|---|---|---|
Nordmann’s | Formula 2021 | Formula 2025 | Nordmann’s | Formula 2021 | Formula 2025 | |||
0 | 8.06 | −21.9 | 525 | 0.139 | 0.151 | 60.9 | 0.117 | 0.118 |
250 | −105 | −16.3 | 539 | 16.4 | 0.151 | 61.0 | 0.880 | 0.135 |
500 | −218 | −11.3 | 555 | 33.0 | 0.145 | 61.1 | 1.68 | 0.153 |
750 | −333 | −4.99 | 570 | 49.6 | 0.176 | 61.2 | 2.50 | 0.141 |
1000 | −445 | −0.290 | 585 | 66.1 | 0.123 | 61.3 | 3.30 | 0.156 |
1500 | −673 | 11.3 | 616 | 99.1 | 0.180 | 61.4 | 4.99 | 0.129 |
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Liu, X.; Pauss, A.; André, L.; Ribeiro, T. An Upgraded FOS/TAC Titration Model Integrating Phosphate Effects for Accurate Assessments of Volatile Fatty Acids and Alkalinity in Anaerobic Media. ChemEngineering 2025, 9, 53. https://doi.org/10.3390/chemengineering9030053
Liu X, Pauss A, André L, Ribeiro T. An Upgraded FOS/TAC Titration Model Integrating Phosphate Effects for Accurate Assessments of Volatile Fatty Acids and Alkalinity in Anaerobic Media. ChemEngineering. 2025; 9(3):53. https://doi.org/10.3390/chemengineering9030053
Chicago/Turabian StyleLiu, Xiaojun, André Pauss, Laura André, and Thierry Ribeiro. 2025. "An Upgraded FOS/TAC Titration Model Integrating Phosphate Effects for Accurate Assessments of Volatile Fatty Acids and Alkalinity in Anaerobic Media" ChemEngineering 9, no. 3: 53. https://doi.org/10.3390/chemengineering9030053
APA StyleLiu, X., Pauss, A., André, L., & Ribeiro, T. (2025). An Upgraded FOS/TAC Titration Model Integrating Phosphate Effects for Accurate Assessments of Volatile Fatty Acids and Alkalinity in Anaerobic Media. ChemEngineering, 9(3), 53. https://doi.org/10.3390/chemengineering9030053