Computational Geosciences

, Volume 13, Issue 2, pp 235–244 | Cite as

An iterative ensemble Kalman filter for reservoir engineering applications

  • M. V. Krymskaya
  • R. G. Hanea
  • M. Verlaan
Open Access
Original paper


The study has been focused on examining the usage and the applicability of ensemble Kalman filtering techniques to the history matching procedures. The ensemble Kalman filter (EnKF) is often applied nowadays to solving such a problem. Meanwhile, traditional EnKF requires assumption of the distribution’s normality. Besides, it is based on the linear update of the analysis equations. These facts may cause problems when filter is used in reservoir applications and result in sampling error. The situation becomes more problematic if the a priori information on the reservoir structure is poor and initial guess about the, e.g., permeability field is far from the actual one. The above circumstance explains a reason to perform some further research concerned with analyzing specific modification of the EnKF-based approach, namely, the iterative EnKF (IEnKF) scheme, which allows restarting the procedure with a new initial guess that is closer to the actual solution and, hence, requires less improvement by the algorithm while providing better estimation of the parameters. The paper presents some examples for which the IEnKF algorithm works better than traditional EnKF. The algorithms are compared while estimating the permeability field in relation to the two-phase, two-dimensional fluid flow model.


Reservoir engineering History matching Permeability Ensemble Kalman fitler Iterative ensemble Kalman filter 


  1. 1.
    Burgers, G., Leeuwen, P., Evensen, G.: Analysis scheme in the ensemble Kalman filter. Mon. Weather Rev. 126, 1719–1724 (1998)CrossRefGoogle Scholar
  2. 2.
    Ertekin, T., Abou-Kassen, J.H., King, G.R.: Basic Applied Reservoir Simulation. Society of Petroleum Engineers, Richardson (2001)Google Scholar
  3. 3.
    Evensen, G.: The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367 (2003)CrossRefGoogle Scholar
  4. 4.
    Gu, Y., Oliver, D.S.: History matching of the PUNQ-S3 reservoir model using the ensemble Kalman filter. In: SPE 89942, SPE Annual Technical Conference and Exhibition, Houston, 26–29 September 2004Google Scholar
  5. 5.
    Gu, Y., Oliver, D.S.: The ensemble Kalman filter for continuous updating of reservoir simulation models. J. Energy Resour. Technol. 128, 79–87 (2006)CrossRefGoogle Scholar
  6. 6.
    Jazwinski, A.H.: Stochastic Processes and Filtering Theory. Academic, New York (1970)MATHGoogle Scholar
  7. 7.
    Lorentzen, R.J., Nævdal, G., Vallès, B., Berg, A.M.: Analysis of the ensemble Kalman filter for estimation of permeability and porosity in reservoir models. In: SPE 96375, SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October 2005Google Scholar
  8. 8.
    Ruijian, L., Reynolds, A.C., Oliver, D.S.: History matching of three-phase flow production data. SPE J. 8(4), 328–340 (2003)Google Scholar
  9. 9.
    Simon, D.: Kalman filtering. Embedded Syst. Program. 14, 72–79 (2001)Google Scholar
  10. 10.
    Wen, X.-H., Chen, W.C.: Real-time reservoir model updating using ensemble Kalman filter. SPE 92991, SPE Reservoir Simulation Symposium, Houston, 31 January–2 February 2005Google Scholar
  11. 11.
    Zafari, M., Reynolds, A.C.: Assessing the uncertainty in reservoir description and performance predicitions with the ensemble Kalman filter. SPE 95750, SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October 2005Google Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering, Mathematics and Computer ScienceDelft University of TechnologyCD DelftThe Netherlands
  2. 2.TNO Built Environment and Geosciences, Business Unit Geo Energy and Geo InformationTNOCB UtrechtThe Netherlands
  3. 3.Faculty of Civil Engineering and GeosciencesDelft University of TechnologyCN DelftThe Netherlands

Personalised recommendations