Advertisement

Mathematical Geology

, Volume 23, Issue 6, pp 833–840 | Cite as

Use of the geometric average for effective permeability estimation

  • Jerry L. Jensen
Articles

Abstract

The geometric average is often used to estimate the effective (large-scale) permeability from smaller-scale samples. In doing so, one assumes that the geometric average is a good estimator of the geometric mean. Problems with this estimator arise, however, when one or more of the samples has a very low value. The estimate obtained becomes very sensitive to the small values in the sample set, while the true effective permeability may be only weakly dependent on these small values. Several alternative methods of estimating the geometric mean are suggested. In particular, a more robust estimator of the geometric mean, the jth Winsorized mean, is proposed and several of its properties are compared with those of the geometric average.

Key words

permeability geometric average geometric mean jth Winsorized mean robust estimation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bakr, A. A., Gelhar, L. W., Gutjahr, A. L., and MacMillan, J. R., 1978, Stochastic Analysis of Spatial Variability in Subsurface Flows 1. Comparison of One- and Three-Dimensional Flows: Water Resour. Res., v. 14, p. 263–271.Google Scholar
  2. Barnett, V., and Lewis, T., 1984, Outliers in Statistical Data: J. Wiley & Sons, New York, 463 p.Google Scholar
  3. Begg, S. H., Carter, R. R., and Dranfield, P., 1989, Assigning Effective Values to Simulator Gridblock Parameters for Heterogeneous Reservoirs: Soc. Pet. Eng. Res. Eng., v. 4, p. 455–463.Google Scholar
  4. Dagan, G., 1979, Models of Groundwater Flow in Statistically Homogeneous Porous Formations: Water Resour. Res., v. 15, p. 47–63.Google Scholar
  5. Dagan, G., 1981, Analysis of Flow Through Heterogeneous Random Aquifers by the Method of Embedding Matrix 1. Steady Flow: Water Resour. Res., v. 17, p. 107–121.Google Scholar
  6. Davis, S. N., 1969. Porosity and Permeability of Natural Materials,in R. J. M. De Wiest (Ed.), Flow Through Porous Media: Academic Press, Orlando, Florida, p. 54–90.Google Scholar
  7. Desbarats, A. J., 1987, Numerical Estimation of Effective Permeability in Sand-Shale Formations: Water Resour. Res., v. 23, p. 273–286.Google Scholar
  8. Dixon, W. J., 1960, Simplified Estimation from Censored Normal Samples: Ann. Math. Stat., v. 31, p. 385–391.Google Scholar
  9. Goggin, D. J., Chandler, M. A., Kocurek, G., and Lake, L. W., 1988, Patterns of Permeability in Eolian Deposits: Page Sandstone (Jurassic), Northeastern Arizona: Soc. Pet. Eng. Form. Eval., v. 3, p. 297–306.Google Scholar
  10. Gomez-Hernandez, J. J., and Gorelick, S. M., 1989, Effective Groundwater Model Parameter Values: Influence of Spatial Variability of Hydraulic Conductivity, Leakance, and Recharge: Water Resour. Res., v. 25, p. 405–419.Google Scholar
  11. Gutjahr, A. L., Gelhar, L. W., Bakr, A. A., and MacMillan, J. R., 1978, Stochastic Analysis of Spatial Variability in Subsurface Flows 2. Evaluation and Application: Water Resour. Res., v. 14, 953–959.Google Scholar
  12. Jensen, J. L., Hinkley, D. V., and Lake, L. W., 1987, A Statistical Study of Reservoir Permeability: Distributions, Correlations, and Averages: Soc. Pet. Eng. Form. Eval., v. 2, p. 461–468.Google Scholar
  13. Johnson, C. R., and Greenkorn, R. A., 1962, Comparison of Core Analysis and Drawdown-Test Results from a Water-Bearing Upper Pennsylvanian Sandstone of Central Oklahoma: Bull. Int. Assoc. of Scientific Hydrology, v. 7, p. 46–52.Google Scholar
  14. Johnson, N. L., and Kotz, S., 1970, Continuous Univariate Distributions-1: John Wiley & Sons, New York, 300 p.Google Scholar
  15. King, P. R., 1988, Effective Values in Averaging,in S. Edwards and P. R. King (Eds.), Mathematics in Oil Production: Oxford University Press, Oxford, p. 217–234.Google Scholar
  16. King, P. R., 1989, The Use of Renormalization for Calculation Effective Permeability: Transport in Porous Media, v. 4, p. 37–58.Google Scholar
  17. Matheron, G., 1967, Elements Pour une Theorie des Milieux Poreux, Masson et Cie, Paris, 166 p.Google Scholar
  18. Richardson, J. G., 1990, Letter to the Editor: J. Pet. Tech., v. 42, p. 1524.Google Scholar
  19. Warren, J. E., and Price, H. S., 1961, Flow in Heterogeneous Porous Media: Soc. Pet. Eng. J., v. 1, p. 153–169.Google Scholar
  20. Warren, J. E., Skiba, F. F., and Price, H. S., 1961, An Evaluation of the Significance of Permeability Measurements: J. Pet. Tech., v. 13, p. 739–744.Google Scholar

Copyright information

© International Association for Mathematical Geology 1991

Authors and Affiliations

  • Jerry L. Jensen
    • 1
  1. 1.Department of Petroleum EngineeringHeriot-Watt UniversityEdinburghScotland

Personalised recommendations