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.

中文翻译：

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印度生物消化池生物消化的数学模型及其通过李亚普诺夫技术进行的稳定性分析

生物消化器是微生物群落将有机残留物转化为沼气和生物肥料的容器。这种生物过程，即厌氧生物消化，在环境方面发挥着重要作用，因为反应结束时的残留物除了毒性较低之外，还具有减少的有机负荷，因此可以在对环境影响较小的情况下进行处理。此外，生物消化产生沼气，鉴于目前化石燃料的短缺，沼气引起了人们的极大兴趣。从这个意义上说，本文提出了一种基于印度生物沼气池质量通量平衡的非线性数学模型，并分析了其性质，特别是其平衡解的李亚普诺夫稳定性，并验证了其解的非负性是一致的与问题的生物学有关。所提出的模型是描述印度生物消化器中厌氧生物消化的重要工具，为生物过程的进一步规划、情景预测和控制提供信息。模型在不同场景下的模拟表明，较低的初始细菌/底物浓度比（0.14）可以促进更好的沼气生产性能。