Mathematical modeling for anaerobic digestion under the influence of leachate recirculation
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, prod...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231547?viewType=HTML |
| _version_ | 1827674948587487232 |
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| author | Miled El Hajji |
| author_facet | Miled El Hajji |
| author_sort | Miled El Hajji |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T04:54:18Z |
| format | Article |
| id | doaj.art-6c57588ab9b64fbfb86124eba8500ff7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-10T04:54:18Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-6c57588ab9b64fbfb86124eba8500ff72023-11-23T02:22:22ZengAIMS PressAIMS Mathematics2473-69882023-11-01812302873031210.3934/math.20231547Mathematical modeling for anaerobic digestion under the influence of leachate recirculationMiled El Hajji 0Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi ArabiaIn 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.https://www.aimspress.com/article/doi/10.3934/math.20231547?viewType=HTMLchemostatanaerobic digestion processleachate recirculationstabilityuniform persistenceoptimal strategy |
| spellingShingle | Miled El Hajji Mathematical modeling for anaerobic digestion under the influence of leachate recirculation AIMS Mathematics chemostat anaerobic digestion process leachate recirculation stability uniform persistence optimal strategy |
| title | Mathematical modeling for anaerobic digestion under the influence of leachate recirculation |
| title_full | Mathematical modeling for anaerobic digestion under the influence of leachate recirculation |
| title_fullStr | Mathematical modeling for anaerobic digestion under the influence of leachate recirculation |
| title_full_unstemmed | Mathematical modeling for anaerobic digestion under the influence of leachate recirculation |
| title_short | Mathematical modeling for anaerobic digestion under the influence of leachate recirculation |
| title_sort | mathematical modeling for anaerobic digestion under the influence of leachate recirculation |
| topic | chemostat anaerobic digestion process leachate recirculation stability uniform persistence optimal strategy |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231547?viewType=HTML |
| work_keys_str_mv | AT miledelhajji mathematicalmodelingforanaerobicdigestionundertheinfluenceofleachaterecirculation |