Skip to main content

Advertisement

SpringerLink
Log in

Combining meta-modeling and categorical indicators for global sensitivity analysis of long-running flow simulators with spatially dependent inputs

  • ORIGINAL PAPER
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

Variance-based global sensitivity analysis (GSA) is a powerful procedure for importance ranking of the uncertain input parameters of a given flow model. The application of GSA is made possible for long-running flow simulators (computation (CPU) time more than several hours) by relying on meta-modeling techniques. However, such flow models can involve one or several spatial inputs, for instance, the permeability field of a reservoir and of a caprock formation in the context of CO2 geological storage. Studying the sensitivity to each of these spatial inputs motivated the present work. In this view, we propose a strategy which combines (1) a categorical indicator (i.e., a pointer variable taking discrete values) assigned to the set of stochastic realizations associated with each spatial input (spatial maps) and (2) meta-modeling techniques, which jointly handle continuous and categorical inputs. In a first application case, a costless-to-evaluate numerical multiphase flow model was used to estimate the sensitivity indices. Comparisons with results obtained using the meta-model showed good agreement using a two-to-three ratio of the number of learning samples to the number of spatial maps. On this basis, the strategy can be recommended for cases where the number of maps remains tractable (i.e., a few hundred), for example, for moderately complex geological settings, or where a set of such maps can be selected in a preliminary stage using ranking procedures. Finally, the strategy was applied to a more complex multiphase flow model (CPU time of a few hours) to analyze the sensitivity of CO2 saturation and injection-induced pressure build-up to seven homogeneous rock properties and two spatial inputs.

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. André, L., Audigane, P., Azaroual, M., Menjoz, A.: Numerical modeling of fluid–rock chemical interactions at the supercritical CO2–liquid interface during CO2 injection into a carbonate reservoir, the Dogger aquifer (Paris Basin, France). Energy Convers Manag 48, 1782–1797 (2007)

    Article  Google Scholar 

  2. Busby, D., Romary, T., Touzani, S., Feraille, M., Noetinger, B., Hu, L.Y.: Reservoir forecasting under uncertainty: an integrated approach. In: Proceedings of the International Meeting on Complexity in Oil Industry, Natal, Brazil (2007)

  3. Craven, P., Wahba, G.: Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 31, 377–403 (1979)

    Article  Google Scholar 

  4. Crosetto, M., Tarantola, S.: Uncertainty and sensitivity analysis: tools for GIS-based model implementation. Int. J. Geogr. Inf. Sci. 15, 415–437 (2001)

    Article  Google Scholar 

  5. de Rocquigny, E., Devictor, N., Tarantola, S. (eds.).: Uncertainty in Industrial Practice. Wiley, Chichester (2008)

    Google Scholar 

  6. Eigestad, G.T., Dahle, H.K., Hellevang, B., Riis, F., Johansen, W.T., Øian, E.: Geological modeling and simulation of CO2 injection in the Johansen formation. Comput. Geosci. 13, 435–450 (2009)

    Article  Google Scholar 

  7. Formaggia, L., Guadagnini, A., Imperiali, I., Lever, V., Porta, G., Riva, M., Scotti, A., Tamellini, L.: Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model. Comput. Geosci. 17, 25–42 (2013). doi:10.1007/s10596-012-9311-5

    Article  Google Scholar 

  8. Glimm, J., Hou, S., Kim, H., Lee, Y.-H., Sharp, D.H., Ye, K., Zou, Q.: Risk management for petroleum reservoir production: a simulation-based study of prediction. Comput. Geosci. 5, 173–197 (2001)

    Article  Google Scholar 

  9. Gu, C.: Smoothing Spline ANOVA Models. Springer, New York (2002)

    Book  Google Scholar 

  10. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn.Springer, New York (2009)

    Book  Google Scholar 

  11. Iooss, B., Ribatet, M.: Global sensitivity analysis of computer models with functional input. Reliab. Eng. Syst. Saf. 94, 1194–1204 (2009)

    Article  Google Scholar 

  12. Jacques, J., Lavergne, C., Devictor, N.: Sensitivity analysis in presence of model uncertainty and correlated inputs. Reliab. Eng. Syst. Saf. 91, 1126–1134 (2006)

    Article  Google Scholar 

  13. Kohavi, R.: A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montreal, Canada, 2, 1137–1143 (1995)

  14. Le Guénan, T., Rohmer, J.: Corrective measures based on pressure control strategies for CO2 geological storage in deep aquifers. Int. J. Greenh. Gas Control 5, 571–578 (2011). doi:10.1016/j.ijggc.2010.05.009

    Article  Google Scholar 

  15. Lin, Y., Zhang, H.: Component selection and smoothing in smoothing spline analysis of variance models. Ann. Stat. 34, 2272–2297 (2006)

    Article  Google Scholar 

  16. Lilburne, L., Tarantola, S.: Sensitivity analysis of spatial models. Int. J. Geogr. Inf. Sci. 23, 151–168 (2009). doi:10.1080/13658810802094995

    Article  Google Scholar 

  17. Marrel, A., Iooss, B., Jullien, M., Laurent, B., Volkova, E.: Global sensitivity analysis for models with spatially dependent outputs. Environmetrics 22, 383–397 (2011)

    Article  Google Scholar 

  18. McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239–245 (1979)

    Google Scholar 

  19. Pebesma, E., Wesseling, C.G.: Gstat: a program for geostatistical modelling, prediction and simulation. Comput. Geosci. 24, 17–31 (1998)

    Article  Google Scholar 

  20. Pruess, K.: ECO2N: A TOUGH2 Fluid Property Module for Mixtures of Water, NaCl, and CO2. Report LBNL-57952. Lawrence Berkeley National Laboratory, Berkeley (2005)

    Book  Google Scholar 

  21. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, (2012). ISBN 3-900051-07-0, http://www.R-project.org/

  22. Refsgaard, J.C., Christensen, S., Sonnenborg, T.O., Seifert, D., Højberg, A.L., Troldborg, L.: Review of strategies for handling geological uncertainty in groundwater flow and transport modeling. Adv. Water Res. 36, 36–50 (2012). doi:10.1016/j.advwatres.2011.04.006

    Article  Google Scholar 

  23. Rohmer, J.: Dynamic Sensitivity Analysis of Long Running Landslide Models Through Basis Set Expansion and Meta-Modelling. Natural Hazards, available online at: http://rd.springer.com/article/10.1007/s11069-012-0536-3 (2013)

  24. Saltelli, A.: Making best use of model evaluations to compute sensitivity indices. Comput. Phys. Commun. 145, 280–297 (2002)

    Article  Google Scholar 

  25. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis—the Primer. Wiley, New-York (2008)

    Google Scholar 

  26. Scheidt, C., Caers, J.: Representing spatial uncertainty using distances and kernels. Math. Geosci. 41, 397–419 (2008). doi:10.1007/s11004-008-9186-0

    Article  Google Scholar 

  27. Silin, D., Patzek, T.W., Benson, S.M.: A one-dimensional model of vertical gas plume migration through a heterogeneous porous medium. Int. J. Greenh. Gas Control 3, 300–310 (2009). doi:10.1016/j.ijggc.2008.09.003

    Article  Google Scholar 

  28. Sobol’, I.M.: Sensitivity estimates for non linear mathematical models. Math. Model. Comput. Exp. 1, 407–414 (1993)

    Google Scholar 

  29. Storlie, C.B., Swiler, L.P., Helton, J.C., Sallaberry, C.J.: Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models. Reliab. Eng. Syst. Saf. 94, 1735–1763 (2009)

    Article  Google Scholar 

  30. Storlie, C.B., Bondell, H.D., Reich, B.J., Zhang, H.H.: Surface estimation, variable selection, and the nonparametric oracle property. Stat. Sin. 21, 679–705 (2010)

    Article  Google Scholar 

  31. Storlie, C.B., Reich, B.J., Helton, J.C., Swiler, L.P., Sallaberry, C.J.: Analysis of computationally demanding models with continuous and categorical inputs. Reliab. Eng. Syst. Saf. 113, 30–41 (2013)

    Article  Google Scholar 

  32. Tahmasebi, P., Hezarkhani, A., Sahimi, M.: Multiple-point geostatistical modeling based on the cross-correlation functions. Comput. Geosci. 16, 779–797 (2012)

    Article  Google Scholar 

  33. Volkova, E., Iooss, B., Van Dorpe, F.: Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site. Stoch. Env. Res. Risk. A. 22, 17–23 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. BRGM, 3 av. C. Guillemin, B.P. 36009, 45060, Orléans Cédex 2, France

    Jeremy Rohmer

Authors
  1. Jeremy Rohmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeremy Rohmer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rohmer, J. Combining meta-modeling and categorical indicators for global sensitivity analysis of long-running flow simulators with spatially dependent inputs. Comput Geosci 18, 171–183 (2014). https://doi.org/10.1007/s10596-013-9391-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-013-9391-x

Keywords

Search

Navigation