Mathematical and Numerical Modeling of the Valorization of Household Waste in Morocco Based on the Model of Brooks

Methanization consists of fermenting organic matter in a tank known as digester without oxygen. The material degrades gradually, producing a gas composed mainly of methane and a residue called digest. This natural process is assured by the action of various microorganisms. The main objective of this work is study the mathematical and numerical modeling of the degradation of household waste. We consider a bioreactor as a porous medium reagents, this problem is governed by the equations of conservation of mass, energy and the empirical equations of Brooks. These equations do not admit analytical solutions, therefore numerical method becomes mandatory. In our study, the equations are solved using the numerical method of finite volumes. This study allows the understanding of the phenomena of the Degradation of household waste and it can be adapted to other industrial applications. This mathematical model which shows the role of the Methanogenesis biomass in the production of gas and heat, contributes to a better understanding of the processes which take place during the time of stabilization for household waste.