Modeling and analysis of an Absorption Column Connected to a Microalgae Culture

Carlos Martinez (1, 2) , Francis Mairet (3) , Leslie Meier (4) , David Jeison (5) , Andrés Avila (4)

1 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
2 BIOCORE - Biological control of artificial ecosystems
3 IFREMER - Institut Français de Recherche pour l'Exploitation de la Mer
4 UFRO - Universidad de la frontera [Tecumo, Chile] = University of La Frontera [Tecumo, Chile] = Université de La Frontera [Tecumo, Chili]
5 Escuela de Ingeniería Bioquímica [Valparaíso]

We build and analyze a mathematical model of a system for biogas upgrading: an absorption column connected to a microalgae culture. The construction of the model is based on a chemical engineering approach and classical models of microalgae cultures. In our analysis, we prove the existence and uniqueness of solutions of a boundary value problem describing the absorption column. Some properties of this solution are also proved. Then, we use these results to study the long-term behavior of the mathematical model describing the coupled system. We state sufficient conditions for the existence of a globally attracting steady state characterized by the presence of microalgae. Finally, we find numerically the steady states of the system to test the efficiency of the system for purifying biogas.

Mots clés: Global asymptotic behavior; Boundary value problem; Shooting method; Absorption column; Biogas upgrading; Microalgae

Domaines: Automatique

Carlos Martinez, Francis Mairet, Leslie Meier, David Jeison, Andrés Avila. Modeling and analysis of an Absorption Column Connected to a Microalgae Culture. SIAM Journal on Applied Mathematics, 2020, 80 (2), ⟨10.1137/18M1225641⟩. ⟨hal-02432325⟩