Non-Adiabatic Effects on Combustion Front Propagation in Porous Media: Multiplicity of Steady States (original) (raw)

The sustained propagation of combustion fronts in porous media is a necessary condition for the success of an in situ combustion project for oil recovery, Compared to other recovery methods, in situ combustion involves the added complexity of exothermic reactions and t emperature-dependent chemical kinetics. In the presence of heat losses, the possibility of ignition and extinction (quenching) exists. In this report, we address the properties of combustion fronts propagating at a constant velocity in the presence of heat losses. We describe an analytical method for solving this problem by treating the reaction region as a discontinuity. Using a rigorous perturbation approach, similar to that used in the smoldering combustion [3] and the propagation of flames [6], we derive appropriate jump conditions that relate the change in dependent variables across the front. These conditions account for the kinetics of the reaction between oxygen and fuel, and the heat and mass transfer in the reaction zone, Then, the problem reduces to the modeling of the dynamics of a combustion front, on either side of which transport of heat and mass, but not chemical reactions, must be considered. Properties of the two regions are coupled using the jump conditions. Expressions for temperature and velocity of the combustion front, concentration of oxygen left unreacted, as well as spatial profiles for temperature and concentrations are obtained under both adiabatic and nonadiabatic conditions. The heat losses to the surrounding are incorporated to the energy balance using two different modes (1) a linear convective term in terms of an overall heat transfer coefficient, and (2) a conductive integral term, which allows for heat transfer by vertical conduction to the surrounding porous medium. The sensitivity of the variables to parameters, such as the injection rate and air content is analyzed. The combustion front in the presence of heat losses to the surrounding behaves markedly different than an adiabatic one. We observe the existence of multiple steady-state solutions with stable low and high temperature branches, and an unstable intermediate branch. Conditions for a self-sustaining front propagation are investigated as a function of injection and reservoir properties. A critical extinction threshold exists and is expressed in terms of the system properties. For fixed inlet conditions, the thickness of the reservoir, the heat capacity of solid, heat of reaction, the initially available fuel concentration, and the reaction activation energy are the most influential reservoir parameters. Using the expressions obtained with the two nonadiabatic models an explicit formulation is obtained for the overall heat transfer coefficient in terms of reservoir thickness and front velocity. The coefficient is observed to be not only dependent on the thermal properties of the porous medium but also to the front dynamics.