# A reaction-diffusion model of stored bagasse

## Author

C. Macaskill, M.J. Sexton and B.F. Gray

## Status

Research Report 98-33
Date: 14 Dec 1998, revised 3 Nov 2000
To appear in: Journal of the Australian Mathematical Society, Series B

## Abstract

The storage of bagasse, which is principally cellulose, presents many problems 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 used as a fuel by sugar mills, and for cogeneration of electricity. Self-heating 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 maximum, similar to the heat release curves found in cool-flame problems.

Bagasse 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 two 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 60-70C.

An existing mathematical model is used, but modified to take into account the newly observed peak in the moisture dependent reaction. Most of the previously reported complex bifurcation behaviour possible in this model is not realized when physically realistic parameter values are used. The bifurcation 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 an elevated temperature (around 60-70C) which persists for long periods of time. Approximate equations can then be defined which predict this intermediate state, and hence a different hysteresis curve is found. A simple explanation for the process by which water is lost from the pile is obtained from these equations and an analytical expression is given for the exponential decay of water levels in the pile.

## Key phrases

mathematical combustion. reaction-diffustion. wet bagasse.

## AMS Subject Classification (1991)

Primary:
Secondary: 80A25, 35K57

## Content

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