A Fully Implicit General Purpose Finite-Difference Thermal Model For In Situ Combustion And Steam
Authors: Grabowski J.W. , Vinsome P.K. , Lin Ran C. , Behie G.A. , Rubin B. 
Published: December 2007

Abstract
This paper describes the development of a fully implicit general thermal model (ISCOM) for simulating in situ combustion or steam processes. The model includes four phases, a variable number of oil components, a variable number of chemical reactions, gravity and capillary pressure terms, and the possibility of modeling emulsions.
The finite-difference formulation of ISCOM operates in one, two or three dimensions and contains implicit and sequential implicit solution techniques as options. It is highly stable, averaging 30% saturation or molar fraction changes during each time step. The model includes the use of pseudo-phase equilibrium ratios which allows a single formulation, even though phases may disappear. The computer program was designed to emphasize clarity and to program was designed to emphasize clarity and to optimize storage. The matrix solution technique is a modified form of Gaussian elimination. The variables and fundamental equations have been aligned so that pivoting for numerical stability is not necessary. pivoting for numerical stability is not necessary. Other special features include Newtonian iteration with numerically calculated derivatives, embedding of the coke equation, two-point upstream and harmonic mobilities as options to reduce truncation error and the grid orientation effect, and an automatic time step selector. Results are presented showing the sensitivity to changes in number of grid blocks and time step size and showing the influence of harmonic weighting on the grid orientation effect.

Introduction
Thermal methods occupy a prominent position in the recovery of low API crudes. The processes taking place during thermal oil recovery are of a complex place during thermal oil recovery are of a complex nature. Experience has shown that in order to model such processes, any numerical simulator must be extremely stable to produce practical results. The trend, therefore, has been towards increasing degrees of implicitness in the construction of such simulators. This demands, however, the utilization of large computer storage and run times, especially for multi-dimensional problems.
This paper describes the development of a fully implicit, finite-difference, general purpose thermal simulator (ISCOM) for modeling in situ combustion and steam processes. The storage and computation time problems have been resolved by the development of a problems have been resolved by the development of a special matrix hand reducing option.
Another feature of thermal recovery simulations in heavy oils is the severity of the grid orientation effect. In ISCOM this effect is alleviated by an option which introduces harmonic mobility weighting.
The steam drive/soak options are subsets of the in situ combustion model, whereby unnecessary reactions and equations are removed. The steam versions are described here only briefly. Therefore this paper concentrates primarily on the in situ combustion option.
The formulation of the model, physical property package, and method of solution will be described, package, and method of solution will be described, together with the results of some test calculations.

FORMULATION OF THE MODEL

Basic Assumptions
The mathematical model is based on the following assumptions:The model can operate in one, two or three dimensions with variable grid spacing.The number of components is variable, and components are distributed among four phases: water (w), oil (o), gas (g), and solid (c).Water and oil components may be present in both oil and water phases, allowing for an approximate treatment of emulsions.The number and type of chemical reactions is variable.