The Simulation of the In-situ Combustion Process In One Dimension Using a Highly Implicit Finite-difference Scheme
Authors: Rubin B. , Vinsome P.K.W. 
Published: March 2010

Abstract
This paper describes a model for numerically simulating in-situ combustion, and the technique used for solving the resulting system of nonlinear finite-difference equations. The numerical model developed accounts for the flow of oil, water and gas phases, as well as the formation of a solid coke phase. The oil phase contains two volatile components. The gas phase is comprised of two hydrocarbon gases, steam, oxygen and a non-condensable gas.
The reaction model employed considers low-temperature oxidation, thermal cracking and high-temperature burning reactions. The solution technique employed by the simulator treats each conservation equation as a function and uses a highly implicit Newton iteration to find the appropriate roots of these functions. Furthermore, the basic conservation equations have been modified to obtain a more convenient set of primary variables and to allow a single problem formulation in one-, two- and three-phase regions.
The simulator generates results which are consistent with experimental findings. The results of this simulator and combustion tube experiments have been compared in detail. Further comparisons have been made with an existing simulator. This paper does not attempt to investigate the in-situ combustion process itself or describe sensitivity studies.

Introduction
The main objective of this work is to develop a simple, highly implicit one-dimensional finite-difference simulator that can rigorously model the complex forms of mass and energy transfer that occur during the in-situ combustion process. Other objectives were to make the model flexible enough to test various numerical approaches so that the best methods would be known before extension to two and three dimensions was attempted.
In view of these objectives, the programming philosophy was ranked in the following order of importance:simplicity and clarity;robustness; andefficiency.
Of greater importance are simplicity and clarity. The reasons here are to allow the maximum flexibility possible, and to avoid programming errors which occur when the code is complicated.
Of secondary importance is robustness. We believe that a robust simulator is an advantage in the modelling of a process as complex as in-situ combustion. This consideration narrows the search for solution techniques to those capable of higher stabilities.
Finally, of least importance is efficiency. We believe that once a simple robust scheme is operational, it is easily made more efficient at a later stage.

Description of the Model

Physical System
The conservation equations used in this simulator are for a system of six species distributed among four phases (Table 1).
The six species are: oxygen, inert gas, light oil, heavy oil water and coke. The inert gas is considered to be composed of nitrogen, carbon dioxide and any non-condensable hydrocarbons. To allow the simulation of distillation effects, the oil phase is assumed to be volatile and to contain two components, a light fraction, say (C3-C8), and a heavy fraction, say (C +9). The water phase is supposed to be immiscible with the oil phase and is also volatile. The quantities of both oil and water which exist in the gas phase are governed by phase equilibria.