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Computational Geosciences

, Volume 22, Issue 2, pp 607–622 | Cite as

High-dimensional geostatistical history matching

Vectorial multi-objective geostatistical history matching of oil reservoirs and uncertainty assessment
  • João Carneiro
  • Leonardo Azevedo
  • Maria Pereira
Original Paper

Abstract

Hydrocarbon reservoir modelling and characterisation is a challenging subject within the oil and gas industry due to the lack of well data and the natural heterogeneities of the Earth’s subsurface. Integrating historical production data into the geo-modelling workflow, commonly designated by history matching, allows better reservoir characterisation and the possibility of predicting the reservoir behaviour. We present herein a geostatistical-based multi-objective history matching methodology. It starts with the generation of an initial ensemble of the subsurface petrophysical property of interest through stochastic sequential simulation. Each model is then ranked according the match between its dynamic response, after fluid flow simulation, and the observed available historical production data. This enables building regionalised Pareto fronts and the definition of a large ensemble of optimal subsurface Earth models that fit all the observed production data without compromising the exploration of the uncertainty space. The proposed geostatistical multi-objective history matching technique is successfully implemented in a benchmark synthetic reservoir dataset, the PUNQ-S3, where 12 objectives are targeted.

Keywords

Multi-objective optimisation History matching Geostatistics Uncertainty assessment 

Mathematics Subject Classification (2010)

86A32 

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Notes

Acknowledgements

The authors wish to thank the Petroleum Group of CERENA at Instituto Superior Técnico (University of Lisbon) for supporting this work, TNO (Netherlands Organisation for Scientific Research) for making this dataset available and Schlumberger for the donation of the academic licenses of Eclipse®;.

References

  1. 1.
    Abbass, H.A.: The self-adaptive Pareto differential evolution algorithm. In: Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002, vol. 1, pp. 831–836 (2002).  https://doi.org/10.1109/CEC.2002.1007033
  2. 2.
    Caeiro, M.H., Demyanov, V., Christie, M., Soares, A.: Uncertainty quantification for history- matching of non-stationary models using geostatistical algorithms. In: Proceedings Geostats 2012, pp. 1–15. Oslo (2012)Google Scholar
  3. 3.
    Caeiro, M.H., Demyanov, V., Soares, A.: Mo P37 multi-objective history matching of a deltaic reservoir with non-stationary geostatistical modelling. Ecmor Xiv 8–11 (2014)Google Scholar
  4. 4.
    Caeiro, M.H., Demyanov, V., Soares, A.: Optimized history matching with direct sequential image transforming for non-stationary reservoirs. Math. Geosci. 47(8), 975–994 (2015).  https://doi.org/10.1007/s11004-015-9591-0 CrossRefGoogle Scholar
  5. 5.
    Caers, J.: Efficient gradual deformation using a streamline-based proxy method. J. Pet. Sci. Eng. 39(1–2), 57–83 (2003).  https://doi.org/10.1016/S0920-4105(03)00040-8 CrossRefGoogle Scholar
  6. 6.
    Christie, M., Mohamed, L., Demyanov, V.: History matching and uncertainty quantification-multiobjective particle swarm optimisation approach (SPE 143067). In: 73rd EAGE Conference & Exhibition, Vienna, Austria. SPE EUROPEC/EAGE Annual Conference and Exhibition, Vienna (2011)Google Scholar
  7. 7.
    Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, vol. 1960. Chapman & Hall/CRC, New York (2001)Google Scholar
  8. 8.
    De Freitas, A.R., Fleming, P.J., Guimarães, F.G.: Aggregation Trees for visualization and dimension reduction in many-objective optimization. Inf. Sci. 298, 288–314 (2015).  https://doi.org/10.1016/j.ins.2014.11.044 CrossRefGoogle Scholar
  9. 9.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).  https://doi.org/10.1109/4235.996017 CrossRefGoogle Scholar
  10. 10.
    Hajizadeh, Y, Christie, MA, Demyanov, V: Towards multiobjective history matching faster convergence and uncertainty quantification. In: SPE Reservoir Simulation Symposium (2011).  https://doi.org/10.2118/141111-MS
  11. 11.
    Dubuisson, M.P., Jain, A.: A modified Hausdorff distance for object matching. In: Proceedings of 12th international conference on pattern recognition, vol. 1(1), pp. 566–568 (1994).  https://doi.org/10.1109/ICPR.1994.576361
  12. 12.
    Emerick, A.A., Reynolds, A.C.: Ensemble smoother with multiple data assimilation. Comput. Geosci. 55, 3–15 (2013).  https://doi.org/10.1016/j.cageo.2012.03.011 CrossRefGoogle Scholar
  13. 13.
    Evensen, G.: Data Assimilation: The Ensemble. Kalman Filter, 2nd edn (2009).  https://doi.org/10.1007/978-3-642-03711-5
  14. 14.
    Floris, F.J.T., Bush, M.D., Cuypers, M., Roggero, F., Syversveen, A.R.: Methods for quantifying the uncertainty of production forecasts: a comparative study. Pet. Geosci. 7(S), S87–S96 (2001).  https://doi.org/10.1144/petgeo.7.S.S87 CrossRefGoogle Scholar
  15. 15.
    Gao, G., Zafari, M., Reynolds, A.: Quantifying uncertainty for the PUNQ-S3 problem in a Bayesian setting with RML and EnKF. SPE J. 11(4), 506–515 (2006).  https://doi.org/10.2118/93324-PA CrossRefGoogle Scholar
  16. 16.
    Hajizadeh, Y., Christie, M., Demyanov, V.: Engineering, P.: SPE 121193 Ant Colony Optimization for History Matching and Uncertainty Quantification of Reservoir Models (2009)Google Scholar
  17. 17.
    Hajizadeh, Y., Christie, M., Demyanov, V.: Comparative study of novel population-based optimization algorithms for history matching and uncertainty quantification: PUNQ-S3 Revisited (SPE 136861). Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE (2010).  https://doi.org/10.2118/136861-MS
  18. 18.
    Hajizadeh, Y., Christie, M., Demyanov, V.: History matching with differential evolution approach—a look at new search strategies. Eage 14–17 (2010)Google Scholar
  19. 19.
    Heidari, L., Gervais, V., Ravalec, M.L., Wackernagel, H.: History matching of petroleum reservoir models by the Ensemble Kalman Filter and parameterization methods. Comput. Geosci. 55, 84–95 (2013).  https://doi.org/10.1016/j.cageo.2012.06.006 CrossRefGoogle Scholar
  20. 20.
    Horta, A., Soares, A.: Direct sequential Co-simulation with joint probability distributions. Math. Geosci. 42(3), 269–292 (2010).  https://doi.org/10.1007/s11004-010-9265-x CrossRefGoogle Scholar
  21. 21.
    Hutahaean, J., Demyanov, V., Christie, M.: Many-objective optimization algorithm applied to history matching, pp. 0–7 (2016)Google Scholar
  22. 22.
    Kam, D., Datta-Gupta, A.: Streamline-based history matching of bottomhole pressure and three-phase production data using a multiscale approach. J. Pet. Sci. Eng. 154, 217–233 (2017).  https://doi.org/10.1016/j.petrol.2017.04.022 CrossRefGoogle Scholar
  23. 23.
    Le Gallo, Y., Le Ravalec-Dupin, M.: History matching geostatistical reservoir models with gradual deformation method. In: SPE Annual Technical Conference and Exhibition, pp. 20–22. Society of Petroleum Engineers, Dallas (2000).  https://doi.org/10.2118/62922-MS
  24. 24.
    Le Ravalec-Dupin, M.: Inverse Stochastic Modeling of Flow in Porous Media. Editions Technip, Paris (2005)Google Scholar
  25. 25.
    Mata-Lima, H.: Reservoir characterization with iterative direct sequential co-simulation: integrating fluid dynamic data into stochastic model. J. Pet. Sci. Eng. 62(3–4), 59–72 (2008).  https://doi.org/10.1016/j.petrol.2008.07.003 CrossRefGoogle Scholar
  26. 26.
    Min, B., Kang, J.M., Chung, S., Park, C., Jang, I.: Pareto-based multi-objective history matching with respect to individual production performance in a heterogeneous reservoir. J. Pet. Sci. Eng. 122, 551–566 (2014).  https://doi.org/10.1016/j.petrol.2014.08.023 CrossRefGoogle Scholar
  27. 27.
    Min, B., Park, C., Jang, I., Kang, J.M., Chung, S.: Development of Pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction. Appl. Soft Comput. J. 35, 75–112 (2015).  https://doi.org/10.1016/j.asoc.2015.06.007 CrossRefGoogle Scholar
  28. 28.
    Min, B., Wheeler, M.F., Sun, A.Y.: Parallel Multiobjective Optimization for the Coupled Compositional/Geomechanical Modeling of Pulse Testing. Montgomery (2017)Google Scholar
  29. 29.
    Oliver, D.S., Chen, Y.: Recent progress on reservoir history matching: a review. Comput. Geosci. 15(1), 185–221 (2011).  https://doi.org/10.1007/s10596-010-9194-2 CrossRefGoogle Scholar
  30. 30.
    Oliver, D.S., Reynolds, A.C., Liu, N.: Inverse Theory for Petroleum Reservoir Characterization and History Matching. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  31. 31.
    Park, H.Y., Datta-Gupta, A., King, M.J.: Handling conflicting multiple objectives using Pareto-based evolutionary algorithm during history matching of reservoir performance. J. Pet. Sci. Eng. 125, 48–66 (2015).  https://doi.org/10.1016/j.petrol.2014.11.006 CrossRefGoogle Scholar
  32. 32.
    Sarma, P., Durlofsky, L.J., Aziz, K., Chen, W.H.: A new approach to automatic history matching using kernel PCA. In: SPE Reservoir Simulation Symposium (1974) (2007).  https://doi.org/10.2118/106176-MS
  33. 33.
    Scheidt, C., Caers, J.: Representing spatial uncertainty using distances and kernels. Math. Geosci. 41(4), 397–419 (2009).  https://doi.org/10.1007/s11004-008-9186-0 CrossRefGoogle Scholar
  34. 34.
    Schölkopf, B., Smola, A., Müller, K.R.: Kernel principal component analysis. In: Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference, vol. 1, pp. 583–588 (1997).  https://doi.org/10.1007/BFb0020217. http://link.springer.com/10.1007/BFb0020217
  35. 35.
    Schulze-Riegert, R., Ghedan, S.: Modern techniques for history matching. In: 9th International Form on Reservoir Simulation. Abu Dhabi, United Arab Emirates (2007)Google Scholar
  36. 36.
    Schulze-Riegert, R., Krosche, M., Pajonk, O.: Hybrid optimization coupling EnKF and evolutionary algorithms for history matching: a case example. In: Proceedings of EUROPEC/EAGE Conference and Exhibition (Evensen 1994) (2009).  https://doi.org/10.2118/121965-MS
  37. 37.
    Soares, A.: Direct sequential simulation and cosimulation. Math. Geol. 33(8), 911–926 (2001).  https://doi.org/10.1023/A:1012246006212 CrossRefGoogle Scholar
  38. 38.
    Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics (2005).  https://doi.org/10.1137/1.9780898717921
  39. 39.
    Zhou, H., Gómez-Hernández, J., Hendricks Franssen, H.J., Li, L.: An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering. Adv. Water Resour. 34(7), 844–864 (2011).  https://doi.org/10.1016/j.advwatres.2011.04.014 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • João Carneiro
    • 1
  • Leonardo Azevedo
    • 1
  • Maria Pereira
    • 1
  1. 1.CERENA - University of LisbonLisboaPortugal

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