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# A Mathematical Model of Spontaneous Combustion in Wet Lignite

Abstract (Summary)
Restricted Item. Print thesis available in the University of Auckland Library or available through Inter-Library Loan. A comprehensive mathematical model on spontaneous combustion of wet lignite is developed in this thesis. The variables in this model are temperature, oxygen concentration, water vapour concentration in the pore spaces, and water content in the coal. This model considers specifically the effects of water in the coal, called liquid water, on the oxidation reaction, and the effect of equilibrium water content value of the coal on water phase changes. A quadratic function of water content is introduced for the wet reaction based on the experimental data from data published in the open literature. This function shows that the oxidation reaction is enhanced by the presence of water in the coal. Water phase changes are determined by the difference between the water content in the coal and the equilibrium value of water in the coal. The equilibrium value is a function of local relative humidity. The behaviour of the model equations is investigated by analysing simplified well-stirred, and 2-D models. The steady-state solutions, the stabilities of the solutions, and the structures of the solutions are discussed. Hopf-bifurcation can occur in the well-stirred models. The analytical discussion of stability becomes difficult when the equation of liquid water is involved. Multiple steady states occur in the 2-D model, and the "dead core" structure of one of the multiple steady states is studied. This model is applied on a coal stockpile storage. A numerical method is used to solve the model equations for realistic physical conditions. Solutions are obtained with different ambient humidities, different initial water content in the coal and different physical parameters of the stockpile. The results show that humid ambient conditions and the coal with a high water content make the stockpile less safe than a dry atmosphere and dry coal. The various physical parameters of the coal pile have different effects on temperature and the concentrations of gases in the stockpile. The complexity of this model restricts knowledge of the contributions of all of the parameters on the stability of steady-state solutions of this model, and the application of the full features of the model on a storage example. However, sufficient analysis is carried out to study the behaviour of this model. The results of the numerical solutions show that the principal novel feature of this model, the effects of water on self-heating process, is a useful and significant advance in the modelling of self-heating systems.
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