Quantitative Analysis of Porosity Heterogeneity: Application of Geostatistics to Borehole Images
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Quantitative Analysis of Porosity Heterogeneity: Application of Geostatistics to Borehole Images1 Peter G. Tilke,2 David Allen,3 and Asbjorn Gyllensten4 High levels of heterogeneity in many carbonate reservoirs have raised concerns about the validity and relevance of small-scale measurements from core plugs and high-resolution logs. While the measurements themselves may be accurate, they may not be representative of the average formation properties. A related question is one of reconciling the measurements made in small volume of investigation data (e.g., core plugs), with the measurements from relatively large volume of investigation data (e.g., wireline logs). This paper presents a technique to quantitatively describe the porosity heterogeneity in a borehole at the scale of several tenths of an inch. The method involves treating high-resolution borehole imagery as a 2D sample from a 3D data volume, and applying geostatistical analysis to these data. We compute the experimental semi-variogram and upscale its range and sill to larger (several inches) scales of measurement to predict the impact of heterogeneity on conventional core plug and logging tool porosity measurements. The resulting dispersion variance between the different measurement scales support the interpretation, application and comparison of these porosity measurements. This technique was applied to an Early Cretaceous carbonate reservoir in Abu Dhabi. We found that the scale of the heterogeneity is typically less than 1– 2in., so that while significant heterogeneity is observed at the core plug and smaller scales of measurement, the larger-volume logging tool measurements smooth out the heterogeneity and show considerably less variability. The differences between porosity measured in core plugs can be completely accounted for by this upscaling effect. KEY WORDS: borehole; carbonate; electrical imagery; geostatistics; heterogeneity; image analysis; porosity.
INTRODUCTION A common challenge in petrophysics and geology is to determine the relevance and reliability of measurements of rock properties such as porosity made at the borehole scale with the same property at the reservoir scale. This challenge is particularly apparent in heterogeneous carbonates. 1 Received
15 March 2004; accepted 10 May 2005; Published online: 16 May 2006.
2 Schlumberger-Doll Research, 320 Bent St, Cambridge, Massachusetts, 02141; e-mail: [email protected]. 3 Schlumberger-Doll 4 Abu
Research, 36 Old Quarry Rd, Ridgefield, Connecticut, 06877, USA. Dhabi Company for Onshore Oil Operations (ADCO), P.O. Box 270, Abu Dhabi, UAE. 155 C 2006 International Association for Mathematical Geology 0882-8121/06/0200-0155/1
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Published studies have emphasized the widespread impact of heterogeneity on the rock properties of certain carbonate reservoirs. The results presented in this paper are based on a well in an Aptian field in Abu Dhabi (Russell and others, 2002). In this field, numerous small-scale accurate measurements were made in the laboratory on c
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