A Spatially Uniform Model of Self-Heating in Compost Piles
We formulate and investigate a uniformly distributed mathematical model for the thermal response of cellulosic materials in compost piles. The model incorporates the heat release due to biological activity within the pile as well as the heat release due to the oxidation of the cellulosic materials. Both types of heat generation are known to be present in most industrial processes handling large volumes of bulk organic materials, 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 (mainly as a consequence of the biological activity). Indeed such a temperature increase is one of the goals of the composting waste. Elevated temperatures of the order of 70 - 90 degrees Celsius have been documented within a few months (or even a few days) of forming the compost pile.
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. Whilst a compost pile must be sufficiently large to allow degradation of the organic material, there is a critical size beyond which spontaneous ignition of the pile is very likely. In this work 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.