# 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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