Preprint C88/2009
Grigori Chapiro
Keywords: Porous media | combustion wave | traveling wave | Singular perturbation | finite difference scheme
There is a renewed interest in using combustion for medium viscosity oil recovery. In-situ combustion involves the injection of air, pure oxygen or air enriched with oxygen or nitrogen to enable the combustion of oil and other consecutive reactions within the reservoir formation leading to the release of heat. Heat is conducted ahead of the combustion front, reduces the oil viscosity and leads to in situ distillation (upgrading). Carbon dioxide created during combustion can also assist the recovery by increasing pressure and by mixing with the oil, thus reducing its viscosity and enhancing flow. To perform computations with the model we need data on the combustion process, which is described in terms of chemical and transport aspects. Data on the combustion process must be converted to a form that can be used in the modeling. We describe in detail how this can be done. In this work one dimensional gas-solid combustion is studied with the combustion rate described by the first order mass action law combined with the Arrhenius' law. We consider a thermally insulated cylindrical porous rock containing solid fuel. Standard simplifications are made in order to formulate the physical model, for example, the gas thermal capacity is considered small. The reactive flow of air in porous rock containing solid fuel is governed by a system of balance laws for gas mass, oxygen mass and enthalpy. We are interested in examining the Riemann solutions for the parabolic partial differential equations governing the system, which support a combustion traveling wave. The Riemann problem for adiabatic forward combustion between gas and solid fuel is solved and the combustion wave profile is obtained. In order to solve the Riemann problem we use an asymptotic expansion to construct a first order approximation of the traveling wave for a given combustion wave speed. Thus we obtain the internal structure of the combustion traveling wave. The results are validated with numerical simulations using a time-step adaptive, hybrid finite difference scheme.