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Computational Geosciences

, Volume 17, Issue 5, pp 773–788 | Cite as

Controllability and observability in two-phase porous media flow

  • Jorn F. M. Van Doren
  • Paul M. J. Van den Hof
  • Okko H. Bosgra
  • Jan Dirk Jansen
Article

Abstract

Reservoir simulation models are frequently used to make decisions on well locations, recovery optimization strategies, etc. The success of these applications is, among other aspects, determined by the controllability and observability properties of the reservoir model. In this paper, it is shown how the controllability and observability of two-phase flow reservoir models can be analyzed and quantified with aid of generalized empirical Gramians. The empirical controllability Gramian can be interpreted as a spatial covariance of the states (pressures or saturations) in the reservoir resulting from input perturbations in the wells. The empirical observability Gramian can be interpreted as a spatial covariance of the measured bottom-hole pressures or well bore flow rates resulting from state perturbations. Based on examples in the form of simple homogeneous and heterogeneous reservoir models, we conclude that the position of the wells and of the front between reservoir fluids, and to a lesser extent the position and shape of permeability heterogeneities that impact the front, are the most important factors that determine the local controllability and observability properties of the reservoir.

Keywords

Reservoir engineering Reservoir simulation Controllability Observability Two-phase flow Porous media Empirical Gramians Covariance matrix Proper orthogonal decomposition POD 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Jorn F. M. Van Doren
    • 1
  • Paul M. J. Van den Hof
    • 2
  • Okko H. Bosgra
    • 1
  • Jan Dirk Jansen
    • 3
  1. 1.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands
  2. 2.Department of Electrical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.Department of Geoscience and EngineeringDelft University of TechnologyDelftThe Netherlands

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