Modeling of hydrogen production in a continuous process of dark fermentation of a pretreated feedstock: effect of the feeding rate

To kinetically model hydrogen production from the recycling of food waste, the volume of which increases annually, an experimental setup for dark fermentation of organic waste was developed. This study aimed to assess the effect of the feeding rate of pretreated substrate in a vortex layer apparatus (VLA) on the kinetic and dynamic parameters of biohydrogen production during dark fermentation. According to the data obtained, the feeding rate of pretreated substrate in a VLA to the dark fermentation reactor significantly influences both the kinetics and dynamics of biohydrogen formation from organic matter. When considering various models (modified Gompertz, first-order, Cauchy, logistic, and Feller) to determine the kinetic parameters, the most accurate model was found to be the Cauchy model, with a determination coefficient more than 0.997 across the entire range of feeding rates. Increasing the feeding rate (reducing the time interval between feedstock loading) resulted in a more than twofold increase in kinetic parameters: theoretically maximum biohydrogen yield increased by 2.03 times, and the hydrolysis constant by 2.35 times with a threefold increase in the feeding rate (from single to three times per day), while the lag phase remained virtually unchanged (the difference was less than 5 %). Increasing the feeding rate to 3 also resulted in a 2.71-fold decrease in the amplitude of the biohydrogen production rate. Furthermore, it was found that the biohydrogen production rate during the time interval between feedstock loading varies according to a model that can also be described by a trigonometric function – the cosine. The abscissa depends on the feeding rate, namely, on the duration of the time interval between feedstock loading, and this relationship is inverse. The coefficient of determination of the proposed model was 0.891 for a twentyfourhour period between feedstock loadings, decreasing to 0.6135 for an eight-hour period, which requires further research, including the use of artificial intelligence, for a more accurate prediction of the kinetic and dynamic parameters of biohydrogen production in the dark fermentation process.

1. . Abu Hatab A., Cavinato M. E. R., Lindemer A., Lagerkvist C. -J. Urban Sprawl, Food Security and Agricultural Systems in Developing Countries: A Systematic Review of the Literature // Cities. – 2019; 94:129-142. https://doi.org/https://doi.org/10.1016/j.cities.2019.06.001.

2. . Kovalev A. A., Kovalev D. A., Panchenko V. A., Vivekanand V., Pareek N., Masakapalli Sh. K., Zhuravleva E. A., Laikova A. A., Shekhurdina S. V., Ivanenko A. A., Litti Yu. V. The effect of different feeding rates of substrate pretreated in a vortex layer apparatus on dark fermentative biohydrogen production // Alternative Energy and Ecology (ISJAEE). – 2025; (3):83-102. (In Russ.) https://doi.org/10.15518/isjaee.2025.03.083-102

3. . Kovalev, А. A.; Kovalev, D. A.; Panchenko, V. A.; Vivekanand, V.; Pareek, N.; Masakapalli, S. K.; Zhuravleva, E. A.; Laikova, A. A.; Shekhurdina, S. V; Ivanenko, A. A.; Litti, Y. V. The Effect of Different Feeding Intervals of Substrate Pretreated in a Vortex Layer Apparatus on Dark Fermentative Biohydrogen Production // International Journal of Hydrogen Energy. – 2025; 146:149975. https://doi.org/https://doi.org/10.1016/j.ijhydene.2025.06.165.

4. . Sinha S., Tripathi P. Trends and Challenges in Valorization of Food Waste in Developing Economies: A Case Study of India // Case Studies in Chemical and Environmental Engineering. – 2021; 4:100162. https://doi.org/ https://doi.org/10.1016/j.cscee.2021.100162.

5. . Filimonau V., Ermolaev V. A. A Sleeping Giant? Food Waste in the Foodservice Sector of Russia // Journal of Cleaner Production. – 2021, 2.

6. . Scherhaufer S., Moates G., Hartikainen H., Waldron K., Obersteiner G. Environmental Impacts of Food Waste in Europe // Waste Management. – 2018; 77:98-113. https://doi.org/https://doi.org/10.1016/j.wasman.2018.04.038.

7. . Ivanenko A.A., Laikova A.A., Zhuravleva E.A., Shekhurdina S. V., Vishnyakova A. V., Kovalev A. A., Kovalev D. A., Trchounian K. A., Litti Yu. V. Biological production of hydrogen: from basic principles to the latest advances in process improvement // Alternative Energy and Ecology (ISJAEE). – 2023; (10):103-141. (In Russ.) https://doi.org/10.15518/isjaee.2023.10.103-141

8. . Ivanenko, A. A.; Laikova, A. A.; Zhuravleva, E. A.; Shekhurdina, S. V; Vishnyakova, A. V; Kovalev, A. A.; Kovalev, D. A.; Trchounian, K. A.; Litti, Y. V. Biological Production of Hydrogen: From Basic Principles to the Latest Advances in Process Improvement // International Journal of Hydrogen Energy. – 2024; 55:740-755. https://doi.org/https://doi.org/10.1016/j.ijhydene.2023.11.179.

9. . Ivanenko A. A., Laikova A. A., Zhuravleva E. A., Shekhurdina S. V., Parshina S. N., Potokina V. V., Kovalev A. A., Kovalev D. A., Rybkin I. A., Orlov M. V., Alahmari M., Litti Yu. V. Unlocking biodegradation of major components of produced fluids // Alternative Energy and Ecology (ISJAEE). – 2025; (4):91-125. (In Russ.) https://doi.org/10.15518/isjaee.2025.04.091-125

10. . Ivanenko, A. A.; Laikova, A. A.; Zhuravleva, E. A.; Shekhurdina, S. V; Parshina, S. N.; Potokina, V. V; Kovalev, A. A.; Kovalev, D. A.; Rybkin, I. A.; Orlov, M. V; Alahmari, M.; Litti, Y. V. Dark Fermentation as a Potential Method for Biodegradation of Polysaccharide Gels Used in Hydraulic Fracturing // International Journal of Hydrogen Energy. – 2025; 147:149976. https://doi.org/https://doi.org/10.1016/j.ijhydene.2025.06.166.

11. . Kovalev A. A., Kovalev D. A., Panchenko V. A., Zhuravleva E. A., Laikova A. A., Shekhurdina S. V., Vivekanand V., Litti Y. V. Approbation of an Innovative Method of Pretreatment of Dark Fermentation Feedstocks // International Journal of Hydrogen Energy. – 2022; 47 (78):33272-33281. https://doi.org/https://doi.org/10.1016/j.ijhydene.2022.08.051.

12. . Kovalev A. A. Energy analysis of a two-stage anaerobic processing system for liquid organic waste to produce hydrogen- and methane-containing biogases // Alternative Energy and Ecology (ISJAEE). – 2020; (25-27):95-106. https://doi.org/10.15518/isjaee.2020.09.009

13. . Kovalev, A. A.; Kovalev, D. A.; Zhuravleva, E. A.; Laikova, A. A.; Shekhurdina, S. V; Vivekanand, V.; Litti, Y. V. Biochemical Hydrogen Potential Assay for Predicting the Patterns of the Kinetics of Semi-Continuous Dark Fermentation // Bioresource Technology. – 2023; 376:128919. https://doi.org/https://doi.org/10.1016/j.biortech.2023.128919.

14. . Murphy, L.; He, Q.; Wang, J. A Modified Gompertz Model and Its MATLAB Implementation for Microbial Growth Performance Assessment // MethodsX. – 2025; 15:103642. https://doi.org/https://doi.org/10.1016/j.mex.2025.103642.

15. . Gogoi, U. N.; Saikia, P.; Devi, L.; Khataniar, L.; Mahanta, D. J. Rapid Parameter Estimation of Modified Gompertz and Logistic Model for Analyzing the Growth of Escherichia Coli K2 // International Journal of Thermofluids. – 2024; 24:100851. https://doi.org/https://doi.org/10.1016/j.ijft.2024.100851.

16. . Salakkam, A.; Phukoetphim, N.; Laopaiboon, P.; Laopaiboon, L. Mathematical Modeling of Bioethanol Production from Sweet Sorghum Juice under High Gravity Fermentation: Applicability of Monod-Based, Logistic, Modified Gompertz and Weibull Models. Electronic Journal of Biotechnology 2023, 64, 18–26. https://doi.org/https://doi.org/10.1016/j.ejbt.2023.03.004.

17. . Pilco, E. J.; Cano, N. F.; Ayala-Arenas, J. S.; Suárez-Navarro, J. A.; Benavente, J. F. Numerical Studies to Validate Mathematical Models Based on First-Order and General-Order Kinetic Approaches for Fitting TL Glow Curves // Physics Letters A. – 2025; 553:130674. https://doi.org/https://doi.org/10.1016/j.physleta.2025.130674.

18. . Zhou, S.; Xiang, D.; Wang, G.; Zhang, L.; Lv, Z.; Qi, S.; Li, W. Reevaluating Multi-Pool First-Order Kinetic Models for Fitting Soil Incubation Data // Geoderma. – 2025; 455:117218. https://doi.org/https://doi.org/10.1016/j.geoderma.2025.117218.

19. . Mulargia, L. I.; Lemmens, E.; Reyniers, S.; Gebruers, K.; Wouters, A. G. B.; Warren, F. J.; Goderis, B.; Delcour, J. A. Investigation of the Link between First-Order Kinetic Models of the in Vitro Digestion of Native Starches and the Accompanying Changes in Their Crystallinity and Structure // Carbohydrate Polymers. – 2024; 343:122440. https://doi.org/https://doi.org/10.1016/j.carbpol.2024.122440.

20. . Santos, A. D.; Silva, J. R.; Castro, L. M.; Quinta-Ferreira, R. M. Kinetic Prediction of Biochemical Methane Potential of Pig Slurry // Energy Reports. – 2022; 8:159-165. https://doi.org/https://doi.org/10.1016/j.egyr.2022.01.128.

21. . Pitt, R. E.; Cross, T. L.; Pell, A. N.; Schofield, P.; Doane, P. H. Use of in Vitro Gas Production Models in Ruminal Kinetics // Mathematical Biosciences. – 1999; 159 (2):145-163. https://doi.org/https://doi.org/10.1016/S0025-5564(99)00020-6.

22. . Pererva, Y.; Miller, C. D.; Sims, R. C. Existing Empirical Kinetic Models in Biochemical Methane Potential (BMP) Testing, Their Selection and Numerical Solution // Water. – 2020. https://doi.org/10.3390/w12061831.

23. . Meraz, M.; Castilla, P.; Vernon-Carter, E. J.; Alvarez-Ramirez, J. Biogas Production Modeling: Developing a Logistic Equation Satisfying the Zero Initial Condition // Renewable Energy. – 2024; 237:121816. https://doi.org/https://doi.org/10.1016/j.renene.2024.121816.

24. . Nguyen, D. D.; Jeon, B. -H.; Jeung, J. H.; Rene, E. R.; Banu, J. R.; Ravindran, B.; Vu, C. M.; Ngo, H. H.; Guo, W.; Chang, S. W. Thermophilic Anaerobic Digestion of Model Organic Wastes: Evaluation of Biomethane Production and Multiple Kinetic Models Analysis // Bioresource Technology. – 2019; 280:269-276. https://doi.org/https://doi.org/10.1016/j.biortech.2019.02.033.

25. . Hosseinzadeh, A.; Zhou, J. L.; Altaee, A.; Li, D. Machine Learning Modeling and Analysis of Biohydrogen Production from Wastewater by Dark Fermentation Process // Bioresource Technology. – 2022; 343:126111. https://doi.org/https://doi.org/10.1016/j.biortech.2021.126111.

26. . Nascimento, T. R.; Cavalcante, W. A.; de Oliveira, G. H. D.; Zaiat, M.; Ribeiro, R. Modeling Dark Fermentation of Cheese Whey for H2 and N-Butyrate Production Considering the Chain Elongation Perspective // Bioresource Technology Reports. – 2022; 17:100940. https://doi.org/https://doi.org/10.1016/j.biteb.2021.100940.

27. . Wang, W.; Liu, S.; Li, Y. Chapter 1 – Modeling of Biohydrogen Production by Dark Fermentation; Zhang, Q., He, C., Ren, J., Goodsite, M. E. B. T. -W. to R. B., Eds. // Academic Press. – 2023; pp. 1-14. https://doi.org/https://doi.org/10.1016/B978-0-12-821675-0.00009-8.

28. . Kim, B.; Jeong, J.; Kim, J.; Hee Yoon, H.; Khanh Thinh Nguyen, P.; Kim, J. Mathematical Modeling of Dark Fermentation of Macroalgae for Hydrogen and Volatile Fatty Acids Production // Bioresource Technology. – 2022; 354:127193. https://doi.org/https://doi.org/10.1016/j.biortech.2022.127193.

29. . Montoya-Rosales, J. de J.; Chango-Cañola, A.; Delgado-Espitia, P. J.; Razo-Flores, E.; Carrillo-Reyes, J. Potential and Trade-Offs of Native versus Sludge-Derived Microbiota in Dark Fermentation of Agro-Industrial Effluents // International Journal of Hydrogen Energy. – 2026; 215:153820. https://doi.org/https://doi.org/10.1016/j.ijhydene.2026.153820.

30. . Ripoll, V.; Núñez, R.; Sillero, L.; Solera, R.; Pérez, M. Biohydrogen Production via Dark Fermentation of Brewery Wastewater and Sewage Sludge: Influence of Substrate Mixture on Process Kinetics and Microbial Community // Process Biochemistry. – 2026; 166:73-84. https://doi.org/https://doi.org/10.1016/j.procbio.2026.04.004.