ACTIVATION ENERGY-ASYMPTOTIC MODELING OF REVERSE COMBUSTION INSTABILITIES IN POROUS MEDIA: APPLICATION TO IN SITU COAL GASIFICATION

A comprehensive theory describing the dynamics of a reverse combustion (RC) front propagating in a combustible porous medium, supported by a forced oxidant flow, has been developed based on the method of matched asymptotic expansions in the activation energy of the combustion reaction. This combustion process has important applications as a borehole linking technique prior to underground coal gasification and as a method for in-situ retorting of tar sands.; Models developed in this work consider combustion of gaseous fuel devolatilized from the porous medium, heterogeneous combustion of fixed carbon comprising the medium, and the effects of heat losses on RC dynamics. These models appear to be the first to treat correctly the asymptotic structure of high Lewis number combusion processes, and they resolve contradictions of earlier semi-empirical models of RC. Basic-state solutions describing the propagation of a steady planar RC front were developed. The linear stability of the steady wave solutions to perturbations in the upstream gas flow then was analyzed. A planar RC front was found to be unstable when the permeability of the medium is increased upon combustion. The planar RC front in this case will break down to burn channels of carbonized material through the medium. Model predictions for effects of process and physical parameters on RC dynamics are in excellent agreement with experimental and field test observations. Applications of this type of modeling to other combustion systems are identified.; A model coupling hydrodynamics to the combustion process to describe steady propagation of a curved two-dimensional RC surface has been developed using conformal mapping techniques. This model was found inadequate due to the inability of the integral theorems to treat discontinuous extinction phenomena on the burning surface. A model for a limiting case of flame extinction at zero gas flux predicts that the channel width depends only on the width of the combustible sample, and not on the upstream oxidant flux, while the burn velocity depends on the square root of the upstream flux. Direction for future research efforts to understand this process have been identified.