Article Contents
Article Contents

# Analysis of an anaerobic digestion model in landfill with mortality term

• *Corresponding author

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

• 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.

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

 Citation:

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

Figure 2.  Graphs of Monod and Haldane functions

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

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

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

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

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

 $K_h$ $Y$ $f_1$ $f_2$ $\alpha$ 0.176 0.05 0.7 0.76 0.9
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