Inclusion of Biological and Chemical Self-Heating Processes in Compost Piles Model: A Semenov Formulation

In this study, a uniformly distributed mathematical model for the self-heating process within compost piles is formulated and investigated. It consists of mass balance equations for oxygen and energy as well as the heat-generation processes due to both biological and chemical activities. This model is an extension of the study of Luangwilai et al. [2013] which consists of only biological activity. The singularity and degenerate Hopf bifurcation theories are used to determine the loci of different singularities: the isola, cusp, double-limit points and boundary limit set as well as the double-Hopf, generalized Hopf (Bautin) and Bogdanov–Takens bifurcations. In this investigation it is found that these loci separate the secondary parameter plane into twenty-two regions of different steady-state solution behaviors, whereas the model in the earlier study reported only eight regions. With more topological detail in the parameter space, a clearer understanding of the thermal behavior of a compost pile can be obtained, thus assisting compost operators in controlling the temperature within the pile more effectively: for example, achieving desirable elevated temperature range for ideal composting conditions via periodic solutions and S-shaped solution branch, or alternatively, understanding conditions, if not monitored carefully, that can also increase the likelihood of spontaneous ignition within the pile.