Mathematical modelling of biodigestion in an Indian biodigester and its stability analysis via Lyapunov technique

Biodigesters are vessels in which a microbiological consortium converts an organic residue into biogas and biofertilizer. This bioprocess, anaerobic biodigestion, plays an important environmental role since the residue at the end of the reaction has a reduced organic load, in addition to lower toxicity, and can therefore be disposed of with less impact on the environment. Moreover, biodigestion produces biogas, which is of great interest in view of the current shortage of fossil fuels. In this sense, this work proposes a nonlinear mathematical model based on the mass flux balance of an Indian biodigester and it also analyses its properties, in particular the Lyapunov stability of its equilibrium solutions, and verifies the non-negativity of its solutions to be consistent with the biology of the issue. The proposed model represents an important tool to describe anaerobic biodigestion in an Indian biodigester, providing information for further planning, scenario prediction and control of the bioprocess. Simulations of the model in different scenarios showed that lower initial bacteria/substrate concentration ratios (≈0.14) can promote better biogas production performance.