Analysis of an anaerobic digestion model in landfill with mortality term

S. Ouchtout; Z. Mghazli; J. Harmand; A. Rapaport; Z. Belhachmi

doi:10.3934/cpaa.2020101

Article Contents

2020, Volume 19, Issue 4: 2333-2346. Doi: 10.3934/cpaa.2020101

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Analysis of an anaerobic digestion model in landfill with mortality term

1.
Interdisciplinary Laboratory for Natural Resources and Environment, Ibn Tofaïl University, Kénitra, Morocco
2.
IRIMAS, University of Haute-Alsace, Mulhouse, France, University of Strasbourg, France
3.
LBE, University of Montpellier, INRA, Narbonne, France
4.
MISTEA, University of Montpellier, INRA, Montpellier SupAgro, Montpellier, France
5.
University of Haute-Alsace, IRIMAS UR 7499, F-68100 Mulhouse, France, University of Strasbourg, France

^*Corresponding author
^*Corresponding author

Dedicated to Professor Tomás Caraballo on the occasion of his 60-th birthday

Received: July 31, 2019

Revised: September 30, 2019

Published: January 2020

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Abstract

We study a mathematical model of anaerobic digestion with biomass recirculation, dedicated to landfill problems, and analyze its asymptotic behavior. We show that the global attractor is composed of an infinity of non-hyperbolic equilibria. For non-monotonic growth functions, this set is non connected, which impacts the performances of the bioprocess.

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Mathematics Subject Classification: Primary: 37N25, 93D20; Secondary: 34C11, 34D35.

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Figure 1. Overall scheme of the anaerobic degradation of organic matter

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Figure 2. Graphs of Monod and Haldane functions

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Figure 3. Graph of the Haldane function considered in the example

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Figure 4. Graph of $ S(\cdot) $ for initial conditions $ X_0 = 340 $ to $ X_0 = 360 $ with a step of 5

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Figure 5. Threshold on $ X_0 $ as a function of $ K_d $ for model parameters indicated in Table 1

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Figure 6. Biogas production as a function of $ X_0 $ for $ K_d = 0.02 $

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Figure 7. $ \lambda^- $, $ \lambda^+ $ (on top) $ {\rm Biogas}^- $ and $ {\rm Biogas}^+ $ (on bottom) as functions of $ K_d $

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$ K_h$ $Y $ $f_1 $ $ f_2$ $ \alpha$

0.176 0.05 0.7 0.76 0.9

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