# Modeling the Effect of Borehole Orientation on Stereonets

## Abstract

It has long been known that borehole direction affects the number of fractures encountered in a well. In other words, if a well is drilled perpendicular to the dominant fracture direction, more fractures will be encountered than in a well parallel to the same fractures. However, when analyzing stereonets this is seldom taken into account, either qualitatively or quantitatively. Methods exist to model fracture distributions on stereonets. What has been missing is the ability to display the effect that borehole orientation has on them. Equations derived for calculating fracture density can be modified to estimate attenuation. Attenuation is modeled by first generating a unimodal or bimodal distribution of fractures and then culling those fractures based on the expected attenuation. The culling is done by randomly eliminating dips based on an attenuation value. For example, for an attenuation of 90%, only 10% of the fractures will be kept. Modeling can demonstrate that two wells drilled through the same basic fracture set can have a very different appearance because of differing borehole deviations. The modeling has been especially useful in the study of joints, which are defined here as fractures that are roughly perpendicular to bedding dip and that end at bedding interfaces. (Joints are arguably the most common type of fracture in sedimentary rock.) A bimodal distribution is used to simulate a pattern of joints, because they tend to have a pattern in which the fractures form a girdle surrounding the great circle of the plane of dip. The angular scatter above and below the plane of dip was calculated using a normal distribution about the plane, while the broader angular scatter along the plane was centered on an arbitrary axis within the plane. The wells showing the greatest attenuation were where the borehole was roughly perpendicular to dip. This is actually quite common, because a vertical well in horizontal beds fits this description. In this type of well, attenuation can reduce the number of fractures by 80% or more. Horizontal wells are very different. This is immediately apparent when the fractures are widely distributed over a stereonet. At first glance, it will appear that there are two broad sets of fractures, but actually there is a band, perpendicular to the borehole direction, where the fractures have been sharply reduced.