A Semenov model of self-heating in compost piles

In this paper we model the thermal behaviour of cellulosic materials in the presence of micro-organisms undergoing exothermic reactions. For simplicity we consider a spatially uniform model which is based upon Semenov's theory for thermal explosions. The singularity theory has been used to investigate the generic properties of the model. We consider first the case in which chemical reactions are absent, which represents heat generation in low-oxygen-containing environments. Here we show that there are two generic steady-state diagrams including one in which the temperature-response curve is the standard S-shaped curve familiar from combustion problems. Thus biological self-heating can cause jumps in the steady temperature. We then investigate the full model, which is shown to have three generic steady-state diagrams. If the energy released from the chemical reaction is sufficiently small, then the steady-state diagram may contain an elevated temperature branch, which is the feature of practical interest in facilities such as industrial compost heaps and municipal tips. If the chemical reaction is too strong the energy released by biological action increases the local temperature sufficiently high that spontaneous ignition of the cellulosic material occurs. For a given degree of chemical activity it is possible to predict the biological activity at which combustion is initiated.