The Simulation of the In-Situ Combustion Process In One Dimension Using a Highly Implicit Finite-Difference Scheme
Authors: El-Khatib Noaman 
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 junction and uses a highly implicit Newton iteration to find the appropriate roots ojthese junctions. 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.
This paper has generated an interesting discussion. It is the policy of the Editorial Board to encourage a high level of participation from its readership, hence the publication of:Dr. N. El-Khatib's discussion of the paper. This discussion was reviewed by the JCPT Editorial Board.Response to the discussion by the authors, B. Rubin and P.K. W. Vinsome.
In their paper. Rubin and Vinsome (1) presented a simulator that is meant to rigorously model the complex forms of mass and energy transfer that occur during the in-situ combustion process. The basic equations of the model are essentially those of Crookston et at.(2). The energy equation used in these two models is also similar to that presented by Youngren(3) and Coats(4).
(Equation in full paper)
The summation is over the total number of chemical reactions that take place, Nr. The term Σ Hi ri appears in the form of an energy source term. This is not a source term and is implicitly included in the terms representing the change of energy of the different components (products and reactants). Therefore, it should not appear explicitly in the energy equation in the form given by the authors. To demonstrate this, one needs only to consider an isolated closed system with no heat or mass leaving or entering the boundaries of the system.
(Equation in full paper)
It is becoming clear from this discussion that the heat of reaction term Σ Hi ri should not appear in the energy equation as presented by the authors.
The inclusion of this term in the energy equation will result in higher values of temperature in the reaction zone. Furthermore, the continuity and energy equations are strongly coupled, as most of fluid and rock properties, in addition to phase equilibrium constants and reaction rate, are temperature dependent. This will affect the values of all variables obtained by the numerical solution of the mathematical model and may invalidate the findings of the authors.