Spatial Statistics of Permeability Data from Carbonate Outcrops of West Texas and New Mexico

RI0258. Spatial Statistics of Permeability Data from Carbonate Outcrops of West Texas and New Mexico: Implications for Improved Reservoir Modeling, by J. W. Jennings, Jr. 50 p., 31 figs., 9 tables, 2 appendices, 2000. Print.


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ABSTRACT
This report presents a statistical analysis of outcrop-permeability data for quantifying spatial patterns of petrophysical heterogeneity in carbonates that are difficult or impossible to observe in the subsurface.

In the study, workers made permeability measurements using plug samples and mechanical field permeameters (MFP) from Permian and Cretaceous shallow-water platform carbonate outcrops in West Texas and New Mexico. The report includes a detailed discussion of factors affecting the accuracy of the measurements and the portability of resulting spatial statistics to subsurface studies.

The permeability data from these carbonate outcrops vary by two to five orders of magnitude, much of the variation occurring within distances of a few feet or less in single rock-fabric units. This short-range variability, present in every outcrop, composes most of the overall variance in each case. It has weak spatial correlation that can be modeled by using semivariograms having asymptotic power-law behavior at small lags.

A variety of longer range features were also observed, including (1) vertical trends within grainstone bodies, (2) vertical average permeability contrasts between grainstone bodies, (3) 140- to 180-ft lateral periodicities within high-frequency cycles, and (4) lateral trends at scales ranging from several hundred to several thousand feet in high-frequency cycles. The longer range features, composing a smaller fraction of the overall variability, may require careful analysis to detect. They can, however, have a significant effect on fluid displacement, and special attention should be given to modeling them in reservoir-performance predictions.

Keywords: carbonates, geostatistics, permeability

CONTENTS
Abstract

Introduction

            Organization of the Report

 Background

            Contributing Outcrop Studies

            Measurement Types and Methods

            Statistical Analysis Methods

                        Semivariograms

Permeability Measurement Methods

            Effects of Measurement Errors on Spatial Statistics

            Hassler-Sleeve Permeability Measurements

                        Hassler-Sleeve-Measurement Accuracy

                        Plug-Size Effects

            MFP Permeability Measurements

                        MFP-Measurement Accuracy

                        MFP Surface Preparation

                        MFP Data Averaging

            Hassler Sleeve and MFP Comparison in a Carbonate Outcrop

                        Basic Statistical and Digital Filtering Comparison

                        Semivariogram Comparison

            Hassler Sleeve and MFP Pros and Cons

Outcrop Exposure and Surface Weathering Effects

Lawyer Canyon Ramp-Crest Window

            General Observations

            Semivariogram Observations

                        Horizontal Semivariograms

                        Vertical Semivariograms

                        Horizontal to Vertical Semivariogram Range Anisotropy

            Semivariogram Models

Lawyer Canyon Outer-Ramp Window

Plowman Ridge and West Dog Canyon

Apache Canyon

Painted Canyon

Discussion

            Permeability Heterogeneity Patterns

                        Small-Scale spatial correlation

                        Longer Range Variability

            Implications for Fluid-Flow Modeling and Scaleup

Summary and Conclusions

            Permeability Heterogeneity Patterns

            Outcrop-Permeability Measurement

            Exposure Effects and Portability to the Subsurface

Acknowledgments

References

Appendix A: Digital Transect Filters

Appendix B: Monte Carlo Test for Semivariograrn Oscillations

Nomenclature

            Variables

            Subscripts

Figures

1. Locations of Permian outcrops having petrophysical data used in this study. Guadalupian paleogeography of West Texas and New Mexico and major Permian shallow-water platform carbonate reservoirs, including those for which outcrops are analogs

2. Location of Painted Canyon outcrop and Cretaceous paleogeography of Texas and northern Mexico

3. Illustration of stable semivariogram model for exponents in the range 0 ≤ p ≤ 2 on Cartesian and double logarithmic coordinates

4. Two-dimensional random fields simulated by using the stable semivariogram model with exponents in the range 0≤p  2 and a 5:1 anisotropy ratio illustrating the link between the power-law exponent and the strength of spatial correlation

5. Vertical semivariograms of permeability in the cycle-1 grainstone at the Lawyer Canyon ramp-crest window, illustrating the effect of data averaging in groups of as many as eight individual MFP measurements located within 1-inch² "pads"

6. Cross plot and histograms of Hassler-sleeve and MFP permeabilities from a vertical transect of plug samples in the Lawyer Canyon outer-ramp window

7. Hassler-sleeve and MFP permeabilities from a vertical transect of plug samples in the Lawyer Canyon outer-ramp window

8. Semivariograms of unfiltered Hassler-sleeve and MFP permeabilities from the upper 60 ft of a vertical transect of plug samples in the Lawyer Canyon outer-ramp window on Cartesian and logarithmic coordinates

9. Semivariograms of unfiltered Hassler-sleeve and MFP permeabilities from the lower 150 ft of a vertical transect of plug samples in the Lawyer Canyon outer-ramp window on Cartesian and logarithmic coordinates

10. Bedding diagrams and petrophysical measurement locations for the Lawyer Canyon ramp-crest window

11. Lawyer Canyon ramp-crest horizontal MFP transects, raw measurements, and transects smoothed by means of the digital filter described in appendix A

12. Lawyer Canyon rarnp-crest vertical MFP transects in cycles 7 through 9, data from grain- dominated rock fabrics, and transects smoothed by means of the digital filter described in appendix A

13. Lawyer Canyon ramp-crest vertical MFP transects in cycle 2, raw measurements, and transects smoothed by means of the digital filter described in appendix A

14. Lawyer Canyon ramp-crest cycle-2 permeability statistics by grainstone bed number

15. Lawyer Canyon ramp-crest permeability measurements in the cycle-1 grainstone vertical transects, geometric averages grouped by depth, and 95-percent confidence intervals on the geometric averages

16. Horizontal semivariograms of permeability in the Lawyer Canyon ramp-crest window, Cartesian coordinates, logarithmic coordinates, estimated semivariograms, and models

17. Horizontal semivariograms of permeability in the Lawyer Canyon ramp-crest window, emphasizing fine-scale structure

18. Vertical semivariograms of permeability in grain-dominated rock fabrics of the Lawyer Canyon ramp-crest window, Cartesian and logarithmic coordinates

19. Comparison of horizontal and vertical semivariograms from the 1-inch and 1-ft grids in the Lawyer Canyon ramp-crest cycle-1 grainstone

20. Comparison of horizontal and vertical semivariograms from transect H1 and 31 vertical transects in the Lawyer Canyon ramp-crest cycle-1 grainstone

21. Lawyer Canyon outer-ramp horizontal-plug transects, raw measurements, and transects smoothed by means of the digital filter described in appendix A

22. Lawyer Canyon outer-ramp horizontal-permeability semivariograms Cartesian and logarithmic coordinates

23. Plowman Ridge and West Dog Canyon horizontal-permeability transects, raw measurements, and filtered transects

24. Plowman Ridge and West Dog Canyon horizontal-permeability semivariograms, Cartesian coordinates

25. Plowman Ridge and West Dog Canyon horizontal-permeability semivariograms, logarithmic coordinates

26. Apache Canyon horizontal-permeability transect, raw measurements, and smoothed transects, making use of all the plugs, only the unfractured and nonvuggy plugs, and the digital filter described in appendix A

27. Apache Canyon horizontal-permeability semivariogram, Cartesian coordinates, logarithmic coordinates, estimated semivariogram, and smoothed semivariogram

28. Painted Canyon horizontal-permeability transect, raw measurements, and transects smoothed by means of the digital filter described in appendix A

29. Painted Canyon horizontal-permeability semivariograrn, Cartesian coordinates, and logarithmic coordinates

30. Unconditional, stochastic, vertical cross-section simulations of permeability in the cycle-1 grainstone at the Lawyer Canyon ramp-crest window, with the small-scale variability alone and with a vertical trend component in addition

31. Unconditional, stochastic, 2-D areal simulations of permeability in the cycle-1 grainstone at the Lawyer Canyon ramp-crest window with small-scale variability, an isotropic 140-ft periodicity, and both structures combined

Tables

 1. Carbonate outcrops in West Texas and New Mexico whose petrophysical data are summarized in this report

2. Petrophysical data compiled in this study from carbonate outcrops in West Texas and New Mexico

3. Plug lengths and data-set sizes for significance tests of plug-size effects on porosity and permeability means and variances

4. Plug-depth categories and data-set sizes for significance tests of plug-depth effects on porosity and permeability means and variances: plug-depth A is nearest the outcrop surface; plug-depth D is farthest behind the outcrop surface

5. Comparison of porosity and permeability statistics from the Lawyer Canyon outcrop and wells 1,000 ft behind the outcrop

6. Comparison of MFP statistics from the grainstone portion of selected Lawyer Canyon ramp-crest transects and grids

7. Porosity and permeability statistics from Lawyer Canyon outer-ramp plug transects

8. Comparison of porosity and permeability statistics from horizontal-plug transects at Plowman Ridge and West Dog Canyon

9. Comparison of porosity and permeability statistics from a horizontal plug transect at Apache Canyon



Citation
Jennings, J. W., Jr., 2000, Spatial Statistics of Permeability Data from Carbonate Outcrops of West Texas and New Mexico: Implications for Improved Reservoir Modeling: The University of Texas at Austin, Bureau of Economic Geology, Report of Investigations No. 258, 50 p.