Natural Resources Research

, Volume 26, Issue 3, pp 285–302

Geostatistical Modeling with Histogram Uncertainty: Confirmation of a Correct Approach

Original Paper
  • 318 Downloads

Abstract

There is always uncertainty in the representative histogram required as an input for geostatistical modeling. This uncertainty should be quantified correctly and incorporated into final modeling because it affects resource/reserve estimation, investment and development decisions. This paper confirms a correct approach of quantifying histogram uncertainty by comparing to reference uncertainty found by an automated scan-based approach. The true variance of the mean is considered as the reference uncertainty. This variance is calculated by finding similar patterns of a data configuration within a large image: The mean of the specified domain is computed for each pattern to attain the true variance of the mean. The correct quantification of histogram uncertainty is defined. The spatial bootstrap provides prior uncertainty that does not consider the domain limits and is not conditioned to the data. This uncertainty is updated in geostatistical modeling to consider the limits and data. The resulting uncertainty closely matches the scan-based approach. A realistic case study is presented.

Keywords

Geostatistics Reference uncertainty Image scanning Spatial resampling Posterior uncertainty 

References

  1. Babak, O., & Deutsch, C. V. (2009). Accounting for parameter uncertainty in reservoir uncertainty assessment: The conditional finite-domain approach. Natural Resources Research, 18(1), 7–17.CrossRefGoogle Scholar
  2. Chu, J., Xu, W., & Journel, A. G. (1994). 3-D implementation of geostatistical analyses—The Amoco case study. AAPG Special Volumes, 16, 201–216.Google Scholar
  3. Davis, M. W. (1987). Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Mathematical Geology, 19(2), 91–98.Google Scholar
  4. Deutsch, C. V. (1992). Annealing techniques applied to reservoir modeling and the integration of geological and engineering (well test) data. Technical report, Ph.D. Thesis. Stanford University.Google Scholar
  5. Deutsch, C. V. (2004). A statistical resampling program for correlated data: Spatial_Bootstrap. Technical report, CCG Annual Report 6-401, Centre for Computational Geostatistics, University of Alberta. Retrieved from http://www.ccgalberta.com/resources/reports/.
  6. Deutsch, C. V., & Journel, A. G. (1998). GSLIB: Geostatistical Software Library and User’s Guide (2nd ed.). Oxford: Oxford University Press.Google Scholar
  7. Deutsch, J. L., & Deutsch, C. V. (2010). Some geostatistical software implementation details. Technical report, CCG Annual Report 12-412, Centre for Computational Geostatistics, University of Alberta. Retrieved from http://www.ccgalberta.com/resources/reports/.
  8. Efron, B. (1979). Bootstrap methods: Another look at the Jackknife. The Annals of Statistics, 7(1), 1–26.CrossRefGoogle Scholar
  9. Journel, A. G., & Bitanov, A. (2004). Uncertainty in N/G ratio in early reservoir development. Journal of Petroleum Science and Engineering, 44(1), 115–130.CrossRefGoogle Scholar
  10. Kaleta, M. P., Bennett, R., Brint, J., Van Den Hoek, P., Van Doren, J., Van Essen, G., & Woodhead, T. J. (2012). Coupled static/dynamic modeling for improved uncertainty handling. In 74th EAGE Conference and Exhibition.Google Scholar
  11. Khan, K. D., & Deutsch, C. V. (2016). Practical incorporation of multivariate parameter uncertainty in geostatistical resource modeling. Natural Resources Research, 25(1), 51–70.CrossRefGoogle Scholar
  12. Manchuk, J. G., & Deutsch, C. V. (2012). A flexible sequential Gaussian simulation program: USGSIM. Computers & Geosciences, 41, 208–216.CrossRefGoogle Scholar
  13. McVay, D. A., & Dossary, M. N. (2014). The value of assessing uncertainty. SPE (Society of Petroleum Engineers) Economics & Management, 6(02), 100–110.Google Scholar
  14. Merrow, E. W. (2011). Oil industry megaprojects: Our recent track record. In SPE (Society of Petroleum Engineers) Offshore Technology Conference. Society of Petroleum Engineers.Google Scholar
  15. Pyrcz, M. J., & Deutsch, C. V. (2014). Geostatistical reservoir modeling (2nd ed.). Oxford: Oxford University Press.Google Scholar
  16. Rose, P. R. (2004). Delivering on our E&P promises. The Leading Edge, 23(2), 165–168.CrossRefGoogle Scholar
  17. Singh, V., Yemez, I., & Sotomayor, J. (2013). Key factors affecting 3D reservoir interpretation and modelling outcomes: Industry perspectives. British Journal of Applied Science & Technology, 3(3), 376–405.CrossRefGoogle Scholar
  18. Solow, A. R. (1985). Bootstrapping correlated data. Mathematical Geology, 17(7), 769–775.CrossRefGoogle Scholar
  19. Wang, F., & Wall, M. M. (2003). Incorporating parameter uncertainty into prediction intervals for spatial data modeled via a parametric variogram. Journal of Agricultural, Biological, and Environmental Statistics, 8(3), 296–309.CrossRefGoogle Scholar
  20. Wolff, M. (2010). Probabilistic subsurface forecasting—What do we really know? Journal of Petroleum Technology, 62(05), 86–92.CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2017

Authors and Affiliations

  1. 1.Centre for Computational Geostatistics, 6-247 Donadeo Innovation Centre For EngineeringUniversity of AlbertaEdmontonCanada

Personalised recommendations