Multiphase, Multidimensional Simulation Of In Situ Combustion
Authors: Ali S.M. Farouq 
Published: December 2007

Abstract
A two-dimensional, three-phase, multicomponent simulator is developed for in situ combustion modeling. The in-place oil is assumed to be consumed by oxidation, represented by an Arrhenius-type reaction equation. The combustion process is taken to be complete, so that only carbon dioxide is formed, which, together with nitrogen, is considered to be a single component (in view of computer memory limitations). The other two gas phase components are oxygen and water vapor. Condensation and vaporization of water is accounted for; oil is taken to be undistillable.
The solution scheme employs iterative solution of the time change in pressure, and explicit solution for time changes in other variables. In effect, it is similar to a previously reported solution method, except for the implicit treatment of the source terms.
The model was tested for a number of situations: dry combustion, wet combustion, and combustion following steam injection. Sample results are presented for hypothetical reservoirs. In one case, the model indicates initiation of combustion in the vicinity of the producing well, where channeling of air occurs in an underlying water layer.
While the model simulated the above cases satisfactorily the execution times were excessive, being 20 to 30 milliseconds/block/time step. The total fluid volume injected or produced over a time step was 0.20 to 1.0 pore volume of the injection block.

Introduction
Many investigators have reported various types of models for in situ combustion simulation. The earliest treatments of this type relied on single-phase conduction and/or convection in an infinite one or two-dimensional system, containing a moving heat source. Examples are the models of Ramey, Bailey and Larkin, Baker, Thomas, and Selig and Couch all of which utilized an analytical solution approach. Chu first employed a numerical approach, which permitted the simulation of a finite thickness, and other features. In a later work, he investigated the varporization-condenstation phenomena. phenomena. The above works considered single phase fluid flow. Wilson, Wygal, Reed, Gergins, and Henderson developed the bank theory to predict oil, gas and water saturation distributions ahead of the combustion zone. Gottfried first developed a one-dimensional, multiphase combustion simulator, incorporating most of the features of in situ combustion, except the heat losses. Couch and Rodriguez used essentially the same model for a study on the effect of permeability and porosity on fuel content. Other one-and two-phase models of in situ combustion include the works of Thurnau and Kuo. El-Khatib and Fulton developed a multiphase, one-dimensional in situ combustion model, incorporating the fuel deposition feature, as well as other modifications of earlier works. Adler has also described a somewhat unconventional approach to one-dimensional modelling. Smith and Perkins describe a one-dimensional wet combustion simulator; mathematical details were not given. Smith an d Farouq Ali and Eggeschwiler and Farouq Ali have reported single phase, two-dimensional in situ combustion simulators, based upon a constant gas permeability ratio ahead and behind a moving front. Grabowski and Aziz have proposed a rather comprehensive one-dimensional in situ combustion model.
The present two-dimensional model of multiphase in situ combustion was reported in.

MODEL DEVELOPMENT

Assumptions
The present model is based upon three-phase, oil, water, and vapor flow. The oil component is undistillable, and is consumed by oxidation. (Reaction kinetics are discussed below). Water is assumed to be vaporizable and condensable, under equilibrium conditions.