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.