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Updating joint uncertainty in trend and depositional scenario for reservoir exploration and early appraisal

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Abstract

Computationally efficient updating of reservoir models with new production data has received considerable attention recently. In this paper however, we focus on the challenges of updating reservoir models prior to production, in particular when new exploration wells are drilled. At this stage, uncertainty in the depositional model is highly impactful in terms of risk and decision making. Mathematically, such uncertainty is often decomposed into uncertainty of lithological trends in facies proportions which is typically informed by seismic data, and sub-seismic variability often modeled geostatistically by means of training images. While uncertainty in the training image has received considerable attention, uncertainty in the trend/facies proportion receives little to no consideration. In many practical applications, with either poor geophysical data or little well information, the trend is often as uncertain as the training image, yet is often fixed, leading to unrealistic uncertainty models. The problem is addressed through a hierarchical model of probability. Total model uncertainty is divided into first uncertainty in the training image, then uncertainty in the trend given the uncertain training image. Our methodology relies on an efficient Bayesian updating of these model parameters (trend and training image) by modeling forward-simulated well facies profiles in low-dimensional metric space. We apply this methodology to a real field case study involving wells drilled sequentially in the subsurface, where as more data becomes available, uncertainty in both training image and trend require updating to improve characterization of the facies.

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References

  1. Aanonsen, S.I., Nævdal, G., Oliver, D.S., Reynolds, A.C., Vallès, B.: Ensemble Kalman filter in reservoir engineering—a review. SPE J. 14(3), 393–412 (2009)

    Article  Google Scholar 

  2. Boisvert, J.B., Pyrcz, M.J., Deutsh, K.V.: Multiple-point statistics for training image selection. Nat. Resour. Res. 16(4), 313–321 (2007)

    Article  Google Scholar 

  3. Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications. Springer, New York (1997)

    Book  Google Scholar 

  4. Caumon, G., Strebelle, S., Caers, J., Journel, A.: Assessment of Global Uncertainty for Early Appraisal of Hydrocarbon Fields. In: SPE Annual Technical Conference and Exhibition, SPE Paper 89943, Houston, TX (2004)

  5. Chugunova, T., Hu, L. Y.: Multiple-point simulations constrained by continuous auxiliary data. Math. Geosci. 40(2), 133–146 (2008)

    Article  Google Scholar 

  6. Cwik, J., Mielniczuk, J.: Data-dependent bandwidth choice for a grade density kernel estimate. Stat. Probabil. Lett. 16(5), 397–405 (1993)

    Article  Google Scholar 

  7. Deutsch, C., Gringarten, E.: Accounting for multiple-point continuity in geostatistical modeling. In: 6th International Geostatistics Congress of Southern Africa, pp 156–165. Geostatistics Association, Cape Town (2000)

  8. Deutsch, C.V., Wang, L.: Hierarchical object-based stochastic modeling of fluvial reservoirs. Math. Geol. 28(7), 857–880 (1996)

    Article  Google Scholar 

  9. Evensen, G.: The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53(4), 343–367 (2003)

    Article  Google Scholar 

  10. Khodabakhshi, M., Jafarpour, B.: A Bayesian mixture-modeling approach for flow-conditioned multiple-point statistical facies simulation from uncertain training images. Water Resour. Res. 49(1), 328–342 (2013)

    Article  Google Scholar 

  11. Lange, K., Frydendall, J, Cordua, K S, Hansen, T M, Melnikova, Y., Mosegaard, K.: A frequency matching method: solving inverse problems by use of geologically realistic prior information. Math. Geosci. 44, 783–803 (2012)

    Article  Google Scholar 

  12. Lantuéjoul, C.: Geostatistical Simulation; Models and Algorithms. Springer, Berlin (2002)

    Book  Google Scholar 

  13. Maharaja, A, Journel, A G, Caumon, G, Strebelle, S.: Assessment of net-to-gross uncertainty at reservoir appraisal stage: application to a turbidite reservoir offshore West Africa. In: Ortiz, J., Emery, X. (eds.) Proc Eighth Geostatistics Congress, vol. 2, pp 707–716. Gecamin, Santiago (2008)

  14. Mariethoz, G., Caers, J.: Multiple-point Geostatistics: Stochastic Modeling with Training Images. Wiley (2014)

  15. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)

    Article  Google Scholar 

  16. Park, H., Scheidt, C., Fenwick, D H, Boucher, A., Caers, J.: History matching and uncertainty quantification of facies models with multiple geological interpretations. Comput. Geosci. 17(4), 609–621 (2013)

    Article  Google Scholar 

  17. Rousseeuw, P J: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)

    Article  Google Scholar 

  18. Scheidt, C, Caers, J.: Representing spatial uncertainty using distances and kernels. Math. Geosci. 41(4), 397–419 (2009a)

    Article  Google Scholar 

  19. Scheidt, C., Caers, J.: Uncertainty quantification in reservoir performance using distances and kernel methods—application to a West-Africa deepwater turbidite reservoir. SPE J. 14(4), 680–692 (2009b)

    Article  Google Scholar 

  20. Scheidt, C., Jeong, C., Caers, J., Mukerji, T.: Updating uncertainty in geological scenario based on geophysical data. In: 2014 AGU Fall Meeting (2014)

  21. Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London (1986)

    Book  Google Scholar 

  22. Strebelle, S., Payrazyan, K., Caers, J.: Modeling of a deepwater turbidite reservoir conditional to seismic data using principal component analysis and multiple-point geostatistics. SPE J. 8(3), 227–235 (2003)

    Article  Google Scholar 

  23. Strebelle, S., Levy, M.: Using multiple-point statistics to build geologically realistic reservoir models: the MPS/FDM workflow. In: Robinson, A., Griffithd, P., Price, S., Hegre, J., Muggeridge, A. (eds.) The Future of Geological Modelling in Hydrocarbon Development. Geological Society London Special Publication, 309(1), 67–74 (2008)

  24. Tahmasebi, P., Sahimi, M., Caers, J.: MS-CCSIM: Accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space. Comput. Geosci. 67, 75–88 (2014)

    Article  Google Scholar 

  25. Tahmasebi, P., Hezarkhani, A., Sahimi, M.: Multiple-point geostatistical modeling based on the cross-correlation functions. Comput. Geosci. 16(3), 779–797 (2012)

    Article  Google Scholar 

  26. Tan, X., Tahmasebi, P., Caers, J.: Comparing training-image based algorithms using an analysis of distance. Math. Geosci. 46, 149–169 (2014)

    Article  Google Scholar 

  27. Tjelmeland, H., More, H.: Semi-Markov random fields. In: Soares, A. (ed.) Geostatistics Troia 1992, vol. 2, pp 493–504. Kluwer, Dordrecht (1993)

  28. Tyler, K., Henriquez, A., Svanes, T.: Modeling heterogeneities in fluvial domains: a review on the influence on production profile. In: Yarus, J.M., Chambers, R.L. (eds.) Stochastic Modeling and Geostatistics: Principles, Methods, and Case Studies AAPG Computer Applications in Geology, vol. 3, pp 77–89 (1995)

  29. Wand, M.P., Jones, M.C.: Kernel Smoothing. Chapman and Hall, London (1995)

    Book  Google Scholar 

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Correspondence to Céline Scheidt.

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Scheidt, C., Tahmasebi, P., Pontiggia, M. et al. Updating joint uncertainty in trend and depositional scenario for reservoir exploration and early appraisal. Comput Geosci 19, 805–820 (2015). https://doi.org/10.1007/s10596-015-9491-x

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  • DOI: https://doi.org/10.1007/s10596-015-9491-x

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