A model of anaerobic digestion for biogas production using Abel equations

TL;DR

This paper develops a mathematical approach using Abel equations and Hamiltonian Algebrization to model and solve biogas production processes, aiding in control and optimization of renewable energy resources.

Contribution

It introduces a novel method combining algebraic techniques to obtain Liouvillian solutions of Abel equations in biogas production modeling.

Findings

Solutions of Abel equations are obtained and visualized.

The method enhances understanding of biogas production dynamics.

Mathematical tools facilitate control and optimization of biogas systems.

Abstract

Some time ago has been studied mathematical models for biogas production due to its importance in the use of control and optimization of re\-new\-able resources and clean energy. In this paper we combine two algebraic methods to obtain solutions of Abel equation of first kind that arise from a mathematical model to biogas production formulated in France on 2001. The aim of this paper is obtain Liouvillian solutions of Abel's equations through Hamiltonian Algebrization. As an illustration, we present graphics of solutions for Abel equations and solutions for algebrized Abel equations.