A reaction-diffusion model of stored bagasse

The storage of bagasse, which is principally cellulose, presents many probl ems for the sugar industry, one of which is bagasse loss due to spontaneous combustion. This is an expensive problem for the industry as bagasse is us ed as a fuel by sugar mills, and for cogeneration of electricity. Self-heat ing occurs in the pile through an oxidation mechanism as well as a moisture dependent reaction. The latter reaction is now known to exhibit a local ma ximum, similar to the heat release curves found in cool-flame problems. Bag asse typically contains 45-55% by weight of water when milling is completed and the question of how to reduce the moisture content is important for tw o reasons. Firstly, wet bagasse does not burn nearly as efficiently as dry bagasse, and secondly, self-heating is greatly enhanced in the presence of water, for temperatures less than 60-70 degreesC. An existing mathematical model is used, but modified to take into account t he newly observed peak in the moisture dependent reaction. Most of the prev iously reported complex bifurcation behaviour possible in this model is not realized when physically realistic parameter values are used. The bifurcat ion diagram describing the long-time steady-state solution is the familiar S-shaped hysteresis curve. In the presence of the new form of the moisture dependent reaction, an intermediate state can be found which is not a true steady-state of the system as, in reality, the characteristics of the pile slowly change as water is lost. This state corresponds to observations of a n elevated temperature (around 60-70 degreesC) which persists for long peri ods of time. Approximate equations can then be defined which predict this i ntermediate state, and hence a different hysteresis curve is found. A simpl e explanation for the process by which water is lost from the pile is obtai ned from these equations and an analytical expression is given for the expo nential decay of water levels in the pile.