Mathematical modeling for anaerobic digestion under the influence of leachate recirculation

Miled El Hajji; Miled El Hajji

doi:10.3934/math.20231547

AIMS Mathematics

2023, Volume 8, Issue 12: 30287-30312. doi: 10.3934/math.20231547

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Research article

Mathematical modeling for anaerobic digestion under the influence of leachate recirculation

Miled El Hajji ^,

Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia

Received: 26 August 2023 Revised: 24 October 2023 Accepted: 03 November 2023 Published: 08 November 2023
MSC : 34D23, 34K13, 34K20, 37B25, 49K40, 92D30

In this paper, we proposed and studied a simple five-dimensional mathematical model that describes the second and third stages of the anaerobic degradation process under the influence of leachate recirculation. The state variables are the concentration of insoluble substrate, soluble substrate, produced hydrogen, acetogenic bacteria and hydrogenotrophic-methanogenic bacteria. The growth rates of used bacteria will be of general nonlinear form. The stability of the steady states will be studied by reducing the model to a 3D system. According to the operating parameters of the bioreactor described by the added insoluble substrate, soluble substrate and hydrogen input concentrations and the dilution rate, we proved that the model can admit multiple equilibrium points and we gave the necessary and sufficient assumptions for their existence, their uniqueness and their stability. In particular, the uniform persistence of the system was satisfied under some natural assumptions on the growth rates. Then, a question was answered related to the management of renewable resources where the goal of was to propose an optimal strategy of leachate recirculation to reduce the organic matter (either soluble or insoluble) and keep a limitation of the costs of the recirculation operation during the process. The findings of this work were validated by an intensive numerical investigation.
- chemostat,
- anaerobic digestion process,
- leachate recirculation,
- stability,
- uniform persistence,
- optimal strategy
Citation: Miled El Hajji. Mathematical modeling for anaerobic digestion under the influence of leachate recirculation[J]. AIMS Mathematics, 2023, 8(12): 30287-30312. doi: 10.3934/math.20231547

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Abstract

In this paper, we proposed and studied a simple five-dimensional mathematical model that describes the second and third stages of the anaerobic degradation process under the influence of leachate recirculation. The state variables are the concentration of insoluble substrate, soluble substrate, produced hydrogen, acetogenic bacteria and hydrogenotrophic-methanogenic bacteria. The growth rates of used bacteria will be of general nonlinear form. The stability of the steady states will be studied by reducing the model to a 3D system. According to the operating parameters of the bioreactor described by the added insoluble substrate, soluble substrate and hydrogen input concentrations and the dilution rate, we proved that the model can admit multiple equilibrium points and we gave the necessary and sufficient assumptions for their existence, their uniqueness and their stability. In particular, the uniform persistence of the system was satisfied under some natural assumptions on the growth rates. Then, a question was answered related to the management of renewable resources where the goal of was to propose an optimal strategy of leachate recirculation to reduce the organic matter (either soluble or insoluble) and keep a limitation of the costs of the recirculation operation during the process. The findings of this work were validated by an intensive numerical investigation.

References

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