Abstract
The p-normal transformation plays an important role in reservoir characterization for data sets that are neither normally nor log-normally distributed. The key step in the transformation is to estimate the value of pfor a given data set. Even though there are several ways to determine p,these are more inconvenient than the quicker and easier type curve approach to estimate pwe present in this paper. In addition, the method provides the p-normal transformation with a visual interpretation. We demonstrate the technique by analyzing reservoir permeability and porosity data from the East Velma West Block Sims Sand Unit, Oklahoma.
Similar content being viewed by others
Abbreviations
- [=]:
-
means “has units of”
- a :
-
Bottom truncation [=] percent
- b :
-
Top truncation [=] percent
- c :
-
A point betweena andb [=] percent
- k :
-
Permeability [=]L 2
- p :
-
Exponent of a power transformation
- x :
-
Random variable
- y :
-
Standard random variable
- φ :
-
Porosity [=] percent
- 1:
-
Scaled from the original random variable
- 2:
-
Scaled from the truncations
- a :
-
Bottom truncation
- b :
-
Top truncation
- c :
-
A point betweena andb
- k :
-
Permeability
- min:
-
Minimum of a random variable
- max:
-
Maximum of a random variable
- φ :
-
Porosity
- (p):
-
Power transformation
- ^:
-
Estimate
References
Bennion, D. W., 1965, A stochastic model for predicting variations in reservoir rock properties: unpubl. doctoral dissertation, Penn. State Univ., University Park, 126 p.
Bennion, D. W., and Griffiths, J. C., 1966, A stochastic model for predicting variations in reservoir rock properties: Soc. Petrol. Eng. Jour., Trans. ATME, v. 237, p. 9–16.
Box, G. E. P., and Cox, D. R., 1964, An analysis of transformations; Jour. Roy. Stat. Soc., Ser. B, v. 26, no. 2, p. 211–252.
Cressie, N. A. C., 1991, Statistics for spatial data: Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 900 p.
Dagan, G., 1989, Flow and transport in porous formations: Springer-Verlag, Berlin, 465 p.
Deutsch, C. V., and Journel, 1992, A. G., GSLIB Geostatistical Software Library and User's Guide; Oxford Univ. Press, Oxford, 340 p.
Elneser, M., 1994, Simulation modeling of flow through the Ferron complex: unpubl. masters thesis, Univ. Texas, Austin, 143 p.
Emerson, J. D., and Stoto, M. A., 1982, Exploratory methods for choosing power transformations: Jour. Am. Stat. Assoc., v. 77, no. 377, p. 103–108.
Freeze, R. A., 1975, A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media: Water Resources Res., v. 11, no. 5, p. 725–741.
Hinkley, D. V., 1975, On power transformations to symmetry: Biometrika, v. 62, no. 1, p. 101–111.
Isaaks, E. H., and Srivastava, R. M., 1989, An introduction to applied geostatistics: Oxford Univ. Press, New York and Oxford, 561 p.
Jensen, J. L., 1986, Reservoir characterization: unpubl. doctoral dissertation, Univ. Texas, Austin, 234 p.
Jensen, J. L., Hinkley, D. V., and Lake, L. W., 1985, Optimization of regression-based porosity-permeability predictions: Trans. Can. Well Logging Soc. (CWLS) 10th Symposium, Calgary, Alberta, Canada, p. R1–R22.
Jensen, J. L., Hinkley, D. V., and Lake, L. W., 1987, A statistical study of reservoir permeability: distributions, correlations, and averages: SPE Formation Evaluation, v. 2, no. 4, p. 461–468.
Journel, A. G., and Huijbregts, C. J., 1978, Mining geostatistics: Academic Press, New York, 600 p.
Lambert, M. E., 1981, A statistical study of reservoir heterogeneity: unpubl. masters thesis, Univ. Texas, Austin, 180 p.
Law, J., 1944, Statistical approach to the interstitial heterogeneity of sand reservoirs: Trans. AIME, v. 155, p. 103–108.
Li, D., 1995, Scaling fluid flow through permeable media: unpubl. doctoral dissertation, The Univ. Texas, Austin, 546 p.
Marechal, A., 1975. The practice of transfer functions; numerical methods and their applications,in Guarascio, M., ed., Proc. NATO Advanced Study Institute: D. Reidel Publ. Co., Dordrecht, p. 253–276.
Marechal, A., 1983, Recovery estimation: a review of models and methods,in Verly, G., and others, eds., Geostatistics for natural resources characterization: D. Reidel Publ. Co., Dordrecht, p. 385–420.
Tukey, J. W., 1977, Exploratory data analysis: Addison-Wesley, Reading, Massachusetts, 688 p.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, D., Lake, L.W. A type curve approach to estimatingp for ap-normal transformation. Math Geol 27, 359–371 (1995). https://doi.org/10.1007/BF02084607
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02084607