We formulate and investigate a spatially distributed mathematical model for the thermal response of cellulosic materials in compost piles. The model incorporates not only the heat release due to biological activity within the pile and the heat release due to the oxidation of the cellulosic materials, but also the production of heat due to moisture content (both liquid and vapour) in the compost 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.

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 the present work we investigate the effect of moisture content within the pile. We show that there is a critical range of moisture content which enhances the self-heating process. Beyond this critical range, the compost heap is either too dry, or too wet to enhance the biological activity within the compost pile. We investigate the system in both one- and two-dimensions in order to determine these critical values of moisture content within the compost piles.