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Analysis of Anaerobic Digestion Model With Two Serial Interconnected Chemostats
Thamer Hmidhi1, Radhouane Fekih-Salem2, Jérôme Harmand3
1University of Tunis El Manar, National Engineering School of Tunis, lamsin, 1002, Tunis, Tunisia.
Bulletin of Mathematical Biology
|June 10, 2025
Summary
This study analyzes a two-step anaerobic digestion model in series chemostats. Mathematical analysis reveals complex behaviors like bistability and tri-stability, impacting microbial species coexistence.
Area of Science:
- Biochemical Engineering
- Mathematical Modeling
- Environmental Biotechnology
Background:
- Anaerobic digestion is a key process for waste treatment and biogas production.
- Two-step models are essential for understanding complex microbial interactions and reaction kinetics.
- Chemostat systems are widely used to study microbial population dynamics under controlled conditions.
Purpose of the Study:
- To conduct a comprehensive mathematical analysis of a two-step anaerobic digestion model in a two-chemostat series configuration.
- To investigate the asymptotic behavior and stability of the system under varying operating parameters.
- To identify conditions leading to complex dynamic behaviors such as bistability and tri-stability.
Main Methods:
- Reduction of an eight-dimensional ordinary differential equation model to a four-dimensional system based on cascade structure.
- In-depth mathematical analysis of the system's asymptotic behavior using general growth rates.
- Determination of all equilibria and establishment of existence and local stability conditions.
- Theoretical analysis of operating diagrams to map process behavior against control parameters.
Main Results:
- Identification of up to fifteen equilibria for the model, particularly with non-monotonic growth rates.
- Establishment of necessary and sufficient conditions for the existence and local stability of all equilibria.
- Demonstration of rich dynamic behaviors including bistability and tri-stability.
- Characterization of the coexistence of two microbial species within the bioreactors.
Conclusions:
- The two-step anaerobic digestion model in series chemostats exhibits complex and rich dynamic behaviors.
- Operating parameters significantly influence the system's stability and asymptotic behavior, including multistability.
- The findings provide crucial insights for optimizing anaerobic digestion processes and understanding microbial ecology in bioreactors.
