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Controllability and observability in two-phase porous media flow

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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.

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Authors and Affiliations

  1. Delft Center for Systems and Control, Delft University of Technology, Postbus 5, 2600 AA, Delft, The Netherlands

    Jorn F. M. Van Doren & Okko H. Bosgra

  2. Department of Electrical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ, Eindhoven, The Netherlands

    Paul M. J. Van den Hof

  3. Department of Geoscience and Engineering, Delft University of Technology, Postbus 5048, 2600 GA, Delft, The Netherlands

    Jan Dirk Jansen

Authors
  1. Jorn F. M. Van Doren
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  2. Paul M. J. Van den Hof
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  3. Okko H. Bosgra
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  4. Jan Dirk Jansen
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Correspondence to Jan Dirk Jansen.

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Van Doren, J.F.M., Van den Hof, P.M.J., Bosgra, O.H. et al. Controllability and observability in two-phase porous media flow. Comput Geosci 17, 773–788 (2013). https://doi.org/10.1007/s10596-013-9355-1

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  • DOI: https://doi.org/10.1007/s10596-013-9355-1

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