Research of Mathematical Model of Biogas Production from Plant Raw Materials

Abstract

This paper is devoted to the description and analysis of the mathematical model of the technological process of biogas production from plant raw materials.The mathematical model is based on a nonlinear system of differential equations that describes three fundamental processes: hydrolysis (primary decomposition) of the initial substrate (reaction, in the first approximation, proceeding without external catalysts or enzymes); methanogenesis - the formation of biogas from products of organic raw materials primary decomposition under the action of specific anaerobic microorganisms (thus, the stages of acito- and acetogenesis are implicitly included in the description of the generalized process of methanogenesis); dynamics of growth and decomposition of microbial biomass necessary for the course of anaerobic fermentation processes. A well-known stoichiometric model for the production of biomethane by V. A. Vavilin is taken as a basis; its modification was made for the case of a flow bioreactor.The paper is aimed at studying the stability of stationary solutions of a non-linear system of differential equations. The problem is solved by linearizing the equations on stationary solutions. A qualitative study of phase curves behavior with the help of the eigenvalues of the matrix for the linearized system is conducted.The carried out research will be helpful to perform the numerical optimization of the model principal parameters that determine the corresponding technological process.DOI 10.14258/izvasu(2018)1-23