@ARTICLE\{IMM2008-05663,
    author       = "M. R. Kristensen and M. Gerritsen and P. G. Thomsen and M. L. Michelsen and E. H. Stenby",
    title        = "Efficient Reaction Integration for  In Situ Combustion",
    year         = "2008",
    keywords     = "Enhance Oil Recovery, In situ Combustion, Sensitivity, Compositional model.",
    journal      = "Transport in Porous Media",
    volume       = "",
    editor       = "",
    number       = "",
    publisher    = "Springer",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5663-full.html",
    abstract     = "In numerical simulations of the in-situ combustion enhanced oil
recovery process, a major task is the integration of the stiff systems of
differential-algebraic equations describing chemical reactions and phase equilibrium.
It is therefore of great importance to identify suitable integration
methods and to design efficient and robust solvers that are tailored to the
specific application. Using a time-stepping methodology based on operator
splitting we propose the use of implicit one-step methods of the {ESDIRK} 
class for integration of reactions. To facilitate the algorithmic development
we construct a kinetic cell model. The model serves both as a tool for the development
and testing of tailored solvers as well as a testbed for studying the
interactions between chemical kinetics and phase behavior. Through bench-
mark studies the new {ESDIRK} solvers are shown to improve computational
speed when compared to off-the-shelf stiff {ODE} solvers.
Fluid phase changes are known to cause convergence problems for the integration
method. We propose an algorithm for detecting and locating phase
changes based on discrete event system theory. Experiments show that the
algorithm improves the robustness of the integration process when near phase
boundaries by significantly reducing the number convergence and error test
failures."
}