In this work we formulate and investigate a uniformly distributed mathematical model (based upon Semenov's theory) for the thermal response of cellulosic materials in compost piles. The model describes the thermal behaviour of compost heaps when self-heating is entirely due to the presence of micro-organisms (biomass) undergoing oxidative exothermic reactions. This is a constructive first-step to understanding the thermal behaviour of compost heaps when self-heating is due to a combination of low-temperature heating effects, from the biomass, and higher-temperature effects, from the oxidation of cellulosic material; the behaviour of the model when self-heating is entirely due to cellulosic oxidation is well-known. We also analyse the effects of flow of air through the pile.

Examples of industrial compost processes include the use of large-scale composting operations for biorecycle purposes, the storage of industrial waste fuel, such as municipal solid waste (MSW), and landfills. Although MSW may not seem an obvious source of combustible materials, in one set of reported experiments approximately 85% of the industrial waste was deemed to be combustible. In each of these industrial processes there is an inherent increase in temperature as a consequence of the biological activity. Although the basic theory of spontaneous combustion relating to organic materials is well understood, there has been very little work undertaken with regard to the mechanism for fires involving biological self-heating. We utilize dynamical systems theory to investigate the generic properties of the model, as well as to determine the critical sizes of the compost piles under various conditions.