# Characterizing Fracture Geometry from Borehole Images

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## Abstract

The use of borehole image logs in natural-fracture evaluation has traditionally focused on mapping the strikes and dips of the individual fractures that intersect the borehole, estimating their apertures, and from these computing fracture attributes such as fracture density. These fracture attributes are commonly used to build three-dimensional fracture-network models. However, these attributes do not directly constrain an important aspect of these models—fracture geometry—specifically, the size, shape, and rotation of three-dimensional fractures within the model. The published formulas of Ozkaya estimate the radius of circular fractures from the statistics of fracture intersections observed in a borehole image. These formulas are shown to be approximate, only applying to circular fractures with shallow relative dip, and are replaced with exact formulas for elliptical fractures that are valid over the entire range of relative dip. A new statistic is defined, the measured distribution of relative azimuths for fracture-trace midpoints, that is sufficient for estimating both the elongation ratio and the rotation angle of elliptically shaped fractures. As estimation accuracy for this fracture geometry is dependent on the number of observed fracture traces, practical methodologies are provided for computing the uncertainty of these estimates. Finally, since natural fracture size is typically not constant, but follows a distribution such as a power law, solutions are provided for using these same borehole image statistics to estimate the fracture-size distribution. Numerical examples with exponential and Pareto distributions demonstrate that a single parameter of a parametric size distribution can be estimated along with its uncertainty.

## Keywords

Natural fractures Fracture geometry Elliptical fracture Cylindrical exposure Length distribution Elongation ratio Fracture uncertainty Fracture-network model Ozkaya formula## Notes

### Acknowledgements

The authors would like to thank Laure Pizzella for her active contribution to the first part of this project. Thanks also go to their colleagues from Schlumberger in Cambridge (USA) and Clamart (France), who provided insight and expertise that greatly assisted the research. They are grateful to Fikri Kuchuk for his insightful comments on an earlier version of the manuscript.

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