Skip to main content
SpringerLink
Log in

High-dimensional geostatistical history matching

Vectorial multi-objective geostatistical history matching of oil reservoirs and uncertainty assessment

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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. 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)

  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)

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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)

  7. Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, vol. 1960. Chapman & Hall/CRC, New York (2001)

    Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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. 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. 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

    Article  Google Scholar 

  13. Evensen, G.: Data Assimilation: The Ensemble. Kalman Filter, 2nd edn (2009). https://doi.org/10.1007/978-3-642-03711-5

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  16. Hajizadeh, Y., Christie, M., Demyanov, V.: Engineering, P.: SPE 121193 Ant Colony Optimization for History Matching and Uncertainty Quantification of Reservoir Models (2009)

  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. Hajizadeh, Y., Christie, M., Demyanov, V.: History matching with differential evolution approach—a look at new search strategies. Eage 14–17 (2010)

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  21. Hutahaean, J., Demyanov, V., Christie, M.: Many-objective optimization algorithm applied to history matching, pp. 0–7 (2016)

  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

    Article  Google Scholar 

  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. Le Ravalec-Dupin, M.: Inverse Stochastic Modeling of Flow in Porous Media. Editions Technip, Paris (2005)

    Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  28. Min, B., Wheeler, M.F., Sun, A.Y.: Parallel Multiobjective Optimization for the Coupled Compositional/Geomechanical Modeling of Pulse Testing. Montgomery (2017)

  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

    Article  Google Scholar 

  30. Oliver, D.S., Reynolds, A.C., Liu, N.: Inverse Theory for Petroleum Reservoir Characterization and History Matching. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  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

    Article  Google Scholar 

  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. 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

    Article  Google Scholar 

  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. Schulze-Riegert, R., Ghedan, S.: Modern techniques for history matching. In: 9th International Form on Reservoir Simulation. Abu Dhabi, United Arab Emirates (2007)

  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. Soares, A.: Direct sequential simulation and cosimulation. Math. Geol. 33(8), 911–926 (2001). https://doi.org/10.1023/A:1012246006212

    Article  Google Scholar 

  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. 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

    Article  Google Scholar 

Download references

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®;.

Author information

Authors and Affiliations

  1. CERENA - University of Lisbon, Av. Rovisco Pais, Lisboa, Portugal

    João Carneiro, Leonardo Azevedo & Maria Pereira

Authors
  1. João Carneiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leonardo Azevedo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maria Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to João Carneiro.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carneiro, J., Azevedo, L. & Pereira, M. High-dimensional geostatistical history matching. Comput Geosci 22, 607–622 (2018). https://doi.org/10.1007/s10596-017-9712-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-017-9712-6

Keywords

Mathematics Subject Classification (2010)

Search

Navigation