SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 772-791, January 2020.
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.

中文翻译：

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连接到微藻培养物的吸收柱的建模与分析

SIAM应用数学杂志，第80卷，第2期，第772-791页，2020年1月。
我们建立并分析了沼气升级系统的数学模型：连接微藻培养物的吸收塔。该模型的构建基于化学工程方法和微藻培养的经典模型。在我们的分析中，我们证明了描述吸收塔的边值问题解的存在性和唯一性。还证明了该解决方案的一些特性。然后，我们使用这些结果来研究描述耦合系统的数学模型的长期行为。我们为存在以微藻类为特征的全球性吸引的稳态存在提供了充分的条件。最后，我们从数字上找到系统的稳态，以测试系统净化沼气的效率。