Transport in Porous Media

, Volume 69, Issue 3, pp 383–409 | Cite as

Efficient integration of stiff kinetics with phase change detection for reactive reservoir processes

  • Morten R. KristensenEmail author
  • Margot G. Gerritsen
  • Per G. Thomsen
  • Michael L. Michelsen
  • Erling H. Stenby
Orginal Paper


We propose the use of implicit one-step Explicit Singly Diagonal Implicit Runge–Kutta (ESDIRK) methods for integration of the stiff kinetics in reactive, compositional and thermal processes that are solved using operator-splitting type approaches. To facilitate the algorithmic development we construct a virtual 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. As case study, two chemical kinetics models with 6 and 14 components, respectively, are implemented for in situ combustion, a thermal oil recovery process. Through benchmark studies using the 14 component reaction model the new ESDIRK solvers are shown to improve computational speed when compared to the widely used multi-step BDF methods DASSL and LSODE. Phase changes are known to cause convergence problems for the integration method. We propose an algorithm for detection and location of phase changes based on discrete event system theory. Experiments show that the algorithm improves the robustness of the integration process near phase boundaries by lowering the number convergence and error test failures by more than 50% compared to direct integration without the new algorithm.


Reactive transport processes Stiff ODE solvers ESDIRK methods Discrete event systems Phase change detection Differential-algebraic equations Multi-scale methods Operator splitting Enhanced oil recovery In situ combustion 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Morten R. Kristensen
    • 1
    Email author
  • Margot G. Gerritsen
    • 2
  • Per G. Thomsen
    • 3
  • Michael L. Michelsen
    • 1
  • Erling H. Stenby
    • 1
  1. 1.Department of Chemical EngineeringTechnical University of DenmarkLyngbyDenmark
  2. 2.Department of Energy Resources EngineeringStanford UniversityStanfordUSA
  3. 3.Informatics and Mathematical ModellingTechnical University of DenmarkLyngbyDenmark

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