Theoretical Considerations of Reverse Combustion in Tar Sands

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Abstract
Published in Petroleum Transactions, AIME, Volume 219, 1960, pages 109–123. Abstract The behavior of the reverse-combustion process in a linear adiabatic system is theoretically investigated by means of an idealized physical model. This model is described by a pair of non-linear equations involving heat and mass transfer which are coupled by a concentration-dependent reaction-rate function of the Arrhenius type. The differential equations governing the quasi steady-state temperature and concentration distributions are approximately solved by using either physical or mathematical simplifications. It is shown that the reverse-combustion process can be mechanistically described by simple physical models whose behavior equations can be solved formally. It is further demonstrated that the derived reverse-combustion equations can be solved numerically within the error limits for the experimental data. The theoretically predicted peak temperature-flux-velocity relationship exhibits reasonable agreement with experimental data obtained from Athabasca tar sand. The principal contribution of this work lies in its usefulness as a starting point for developing a more comprehensive theory. A description of the vaporization-coking process must be obtained; then, the theory must be extended to three dimensions to include geometrical effects and heat losses. Introduction In another paper, the physical processes visualized as occurring during reverse combustion have been described. In this paper, the extent to which an elementary theory can account for experimental observations is determined. Theoretical results that can be used to estimate some of the behavior characteristics of importance to this process are also presented. Since it is not possible to include all the features of the combustion mechanism of which we are currently aware, the mathematical formulation refers to the highly idealized system developed herein. This simplified physical model is based on the simultaneous transfer of mass and heat accompanied by a chemical reaction; it is described mathematically by a pair of coupled, nonlinear differential equations. Similar sets of equations have been studied extensively in the field of flame propagation; an excellent review of these investigations has been published by Evans.

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