Linear stability of planar reverse combustion in porous media

Abstract The method of activation energy asymptotics has been applied to analyze the dynamics of a planar combustion wave traveling in a porous medium in a direction opposed to the forced oxidant flux. Such a process finds practical application in “reverse combustion” of coal seams, used to create a permeable link between gas injection and production wells prior to in situ gasification, and for in situ retorting of tar sands. The model assumes an infinite effective Lewis number and one-step, first-order Arrhenius kinetics for this two-phase, oxygen-limited combustion process. The steady adiabatic front temperature is the eigenvalue for the basic-state problem and is related to the steady front velocity by the integral energy balance. The fuel is modeled as a single component gas-phase species devolatilized from the medium ahead of the combustion zone. The calculated steady front velocity and front temperature agree well with results obtained numerically. Combustion of the medium increases its permeability to gas flow. Thus, the combustion front can be visualized as an unstable displacement front. The linear stability of the basic state was investigated, considering nonoscillatory normal modes. It was found that for a zero permeability change across the front all modes are stable, and for positive changes a most highly ampified mode exists, which depends on the degree of permeability increase and the characteristics of the basic-state solution. Qualitative predictions of the theory agree very well with experimental and field test observations of reverse combustion dynamics.