Facies Modeling of Heterogeneous Carbonates Reservoirs by Multiple Point Geostatistics

Document Type : Research Paper


1 Petrophysicist

2 Associate Professor of University of Tehran

3 Petroleum Engineer


Facies modeling is an essential part of reservoir characterization. The connectivity of facies model is very critical for the dynamic modeling of reservoirs. Carbonate reservoirs are so heterogeneous that variogram-based methods like sequential indicator simulation are not very useful for facies modeling. In this paper, multiple point geostatistics (MPS) is used for facies modeling in one of the oil fields in the southwest of Iran. MPS uses spatial correlation of multiple points at the same time to characterize the relationships between the facies. A small part of the oil field, in the vicinity of the simulation grid, is used as a training image, in which there is 25 well data for creating suitable training image by the principal component analysis (PCA) method. In this study, MPS is successfully applied to facies modeling and the spatial continuity of facies is reasonably reproduced. The facies model verifies the reproduction of facies proportion in training image and wells. Also, five wells are used for the cross correlation of the facies model. The results indicate that the facies model shows a strong correlation with the facies of these five wells. Additional hard data, which is extracted from high confidence seismic data, is so useful for the improvement of the facies model.


      [1]     Duke J. H. and Hanna P. J., “Geological Interpretation for Resource Modeling and Estimation,” in Edwards, A. C. ed., Mineral Resource and Reserve Estimation, the Australasian Institute of Mining andMetallurgy, Melbourne, Australia, 2001, 147-156.
      [2]     Sinclair A. J. and Blackwell G. H., “Applied Mineral Inventory Estimation,” Cambridge University Press, 2002, Cambridge, 381.
      [3]     Pranter M. J., Vargas M. F., and Davis T. L., “Characterization and 3D Reservoir Modeling of Fluvial Sandstones of the Williams Fork Formation, Rulison Field, Piceance basin, Colorado, USA,” Journal of Geophysics & Engineering, 2008, 5, 158-172.
      [4]     Deutsch C. V., Geostatistical Reservoir Modeling, Oxford University Press, Oxford, 2002.
      [5]     Armstrong M., Galli A. G., Le Loc’h G., Geffroy F., et al., Plurigaussian Simulations in Geosciences, Berlin, Springer, 2003, 149.
      [6]     Guardiano F., and Srivastava M., “Multivariate Geostatistics: beyond Bivariate Moments, in A Soares, Editor, Geostatistics-Troia, Kluwer Academic Publications,” Quantitative Geology and Geostatistics, 1993, 5, 133–144.
      [7]     Journel A., “Beyond Covariance: The Advent of Multiple-point Geostatistics, in Leuangthong, O. and Deutsch, C. Eds.,” 7th International Geostatistics Congress. Banff, Canada, Springer, 2004, 1, 225-235.
      [8]     Strebelle S. and Journel A., “Reservoir Modeling Using Multiple Point Statistics,” SPE 71324, 2001.
      [9]     Liu, Y., “Downscaling Seismic Data into A Geologically Sound Numerical Model,” Ph.D. Thesis, Stanford University, Stanford, 2003.
    [10]    Jolliffe I. T., Principal Component Analysis, 2nd ed., UK: Springer Series in Statistics, Springer, 2002, 487.
    [11]    Scheevel J. R. and Payrazyan K., “Principal Component Analysis Applied to 3D Seismic Data for Reservoir Property Estimation,” SPE Presented In The SPE Annual Technical Conference Held in Houston, Texas, USA, 1999.
    [12]    Caers J., and Zhang T., “Multiple-point Geostatistics: A Quantitative Vehicle for Integrating Geologic Analogs into Multiple Reservoir Models,” Stanford University, Stanford Center for Reservoir Forecasting, Stanford, 2002, CA 94305-2220.
    [13]    Strebelle S., “Sequential Simulation Drawing Structures from Training Images,” Ph.D. Thesis, Stanford University, Stanford, USA, 2000.
    [14]    Arpat G. B. and Caers J., “A Multiple-scale, Pattern-based Approach to Sequential Simulation,” Department of Petroleum Engineering Stanford University, Stanford, USA, 2005, 255-264.
    [15]    Zhang T., Filter-based Training Pattern Classification for Spatial Pattern Simulation, Ph.D. Thesis, Stanford University, USA, 2006.
    [16]    Honarkhah M., “Stochastic Simulation of Patterns Using Distance-based Pattern Modeling,” Ph.D. Thesis, Stanford University, USA, 2011.
    [17]    Tahmasebi P., Hezarkhani A., and Sahimi M., “Multiple Point Geostatistical Modeling Based on the Cross Correlation Functions,” Computational Geosciences, 2012, 16,779-797.
    [18]    Srivastava M., “An Overview of Stochastic Methods for Reservoir Characterization, in Yarus, J., and Chambers, R., Eds., Stochastic Modeling and Geostatistics: Principles, Methods, and Case Studies,” Computer Applications in Geology, AAPG, 1995, 3, 3-16.
    [19]    Isaaks, E., “The Application of Monte Carlo Methods to the Analysis of Spatially Correlated Data,” Ph.D. Thesis, Stanford University, Stanford, USA, 1990.
    [20]    Gomez J. and Srivastava R., “ISIM3D: An ANSI-C Three Dimensional Multiple Indicator Conditional Simulation,” Computer & Geosciences, 1990, 16, 395–410.
    [21]    Haldorsen H. and Damsleth E., “Stochastic Modeling,” Journal of Petroleum Technology, 1990, 404- 412.
    [22]    Deutsch C. and Wang L., “Hierarchical Object-Based Stochastic Modeling of Fluvial Reservoirs, Mathematical Geology,” 1996, 28, 857- 880.
    [23]    Holden L., Hauge R., Skare O., and Skorstad A., “Modeling of Fluvial Reservoirs with Object Models,” Mathematical Geology, 1988, 24, 473-496.
    [24]    Viseur S., “Stochastic Boolean Simulation of Fluvial Deposits: A New Approach Combining Accuracy and Efficiency,” Presented at the Annual Technical Conference and Exhibition, Houston, SPE 56688, 1999.
    [25]    Wen R., Martinius A., Nass A., and Ringrose P., “Three Dimensional Simulation of Small Scale Heterogeneity in Tidal Deposits A Process-based Stochastic Simulation Method,” International Association for Mathematical Geology, 1998, 399-400.