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We consider the self heating process in a two dimensional spatially dependent model of a compost pile which incorporates terms that account for self heating due to both biological and oxidation mechanisms. As moisture is a crucial factor in both the degradation process and spontaneous ignition within a compost pile, this model consists of four mass-balance equations, namely, energy, oxygen, vapour and liquid water concentrations. Analyses are undertaken for different initial water contents within the compost pile. We show that when the water content is too low, the reaction is almost negligible; whereas when it is too high, the reaction commences only when the water content evaporates and the water ratio drops to within an appropriate range. However, for an intermediate water content range, the biological reaction is at its optimum and there is a possibility of spontaneous ignition within the compost pile.

We formulate and investigate a one-dimensional model for self-heating in compost piles. The selfheating occurs through a combination of biological and chemical mechanisms. Biological heat generation is known to be present in most industrial processes handling large volumes of bulk organic materials. The heat release rate due to biological activity is modelled by a function which at sufficiently low temperatures is a monotonic increasing function of temperature. At higher temperatures, it is a monotonic decreasing function of temperature. This functionality represents the fact that micro-organisms die or become dormant at high temperature. The heat release due to oxidation reaction is modelled by Arrhenius kinetics. The model consists of mass balance equations for oxygen and energy. Steady-state temperature diagrams are determined as a function of the size of the compost pile and the flow rate of air through the pile. We show that there is a range of flow rates for which elevated temperatures, including the possibility of spontaneous ignition, occur within the pile. We also investigate the effects of variations in the ambient temperature.