Borehole imaging is the best means of direct fracture characterization and identification in the reservoir. Along with defining single fracture properties such as orientation, more advanced fracture analysis can be computed in conjunction with standard petrophysically-derived calculations. These include fracture aperture, fracture trace length, and population parameters like density (intensity) and connectivity. The various types of fractures that can be present in a reservoir can hinder or amplify the production rates depending on whether they are open, sealed or partially healed, whether they show some offset across them, and their abundance in certain lithologies or structural positions.

It is essential in fracture interpretation to consistently evaluate the differences between fracture types and differentiate what is really a natural fracture from other similar features such as incipient breakout, bit marks and induced fractures of a variety of geometries.

By properly interpreting borehole breakout and drilling-induced fracturing from borehole image logs, the directions of relative in-situ stresses can be evaluated to understand their impact on reservoir properties and performance and borehole stability.

## Fracture Classification

## Fracture Density (intensity)

In its simplest terms, fracture density can be expressed in a linear sense as the number of fractures encountered per unit of length, similar to counting the fractures on an outcrop transect. This kind of count density is inappropriate as it does not account for the geometric bias between the intersection line (the borehole) and the fractures (which may be oriented steeply relative to the borehole). The first attempt to account for this is a simple geometric correction commonly called the Terzaghi correction:

Dens = Counted Fractures * 1 / sin(intersection angle)

This kind of linear correction is generally too large and inappropriate for borehole data as the borehole is a three-dimensional volume (not a linear sample). Fractures should be counted in terms of trace length in the borehole per unit of surface area, or up-scaled to account for geometric bias to a volume density where each fracture’s surface area is counted relative to an imaginary volume of reservoir rock around the borehole (Jamison et. al, 2004).

**Fracture density block diagrams -** Density can be linear, such as a line count on an outcrop (left); two-dimensional, such as a length summation within a defined surface area (right); or, ideally, represents a summation of all fractures in an idealized and well-estimated volume (middle).

We find that this approach falters because of three issues: (1) the image log is sampling a cylindrical volume of rock rather than line, (2) most natural fractures do not cut entirely across the wellbore, and (3) fractures that cross only a minor portion of the wellbore and/or intersect the wellbore at very low angles are difficult to detect on the image logs.

HEF, in conjunction with William Jamison from The Upper Crust, have developed an alternative density correction procedure based on stochastic models of various fracture populations intersected by the wellbore, and which considers only those fractures intersecting at least 50% of the wellbore. Having compared these results with other methods, we have the highest confidence in this particular method.

**Fracture density plot** - Our fracture density plot shows the image and fracture tadpoles, and then separates the open fractures (and large fractures and open shear features) from the healed fractures (and sealed shear features). We show the stochastically corrected density (the shaded magenta and yellow curves) as well as the uncurrected raw intersection data.** **Click image to enlarge

## Fracture Aperture

The trace of a fracture as it appears on a resistivity-based image log results from the contrast in conductivity between the material in the fracture and the surrounding rock. A dark fracture trace generally results from the invasion of high-conductivity drilling mud into the fracture aperture. On the images, we see this fracture trace as a dark band, generally much wider than the actual fracture aperture. The image log tool is actually measuring the variations of conductivity along and around the wellbore. This conductivity information can, theoretically, be used to calculate the physical fracture aperture provided a number of variables are known.

The determination of the fracture aperture begins by fitting a sinusoidal curve to the borehole fracture trace and forming a “gather window” around this sinusoid. The excess conductance (K) associated directly with the fracture is derived as shown in the diagrams at right.

There are several implicit assumptions embedded in this procedure, such as:

- The fracture is planar and extends entirely through the wellbore.
- The fracture dip is less than ~45° to the wellbore.
- The fracture is situated in a homogeneous medium with a known mud-invaded zone resistivity (Rxo).
- The fracture aperture is invaded by drilling mud of known resistivity (Rm), and all excess conductance in the gather window is due to the mud-invaded fracture.

If these assumptions hold (and they rarely do), fracture aperture can be calculated from the Luthi and Souhaite (1990) equation:

W = c * K * Rmb * Rxo(1-b)

Where:

W is the physical aperture of the fracture

K is the excess conductance associated with the fracture trace

Rm is the drilling mud resistivity

Rxo is the invaded zone formation resistivity

c and b are constants that depend on tool type and aperture units (c=0.004801 and b=0.863)

Even assuming that the equation shown is accurate, there are several aspects of this fracture aperture analysis that can result in large errors in the aperture determination. These error sources fall into two general categories: uncertainty of the appropriate values for the drilling mud resistivity Rm and the mud-invaded zone resistivity Rxo, and discord between the model fracture geometry and the natural fracture geometry in the wellbore. For this reason, fracture aperture calculation results are very mixed.

Assuming fracture aperture can be calculated correctly (or, alternatively, if it is assumed based on core measurements or other reservoir studies), fracture porosity can be calculated as the sum of discrete fracture aperture times discrete fracture area. Since most fractures are relatively hairline (in the order of tens to hundreds of microns), even in very high fracture densities of, say, 20 m/m2, with large (0.1mm fractures), calculated fracture porosities are very small:

F_{f} = Af * Df

F_{f} = 20 m/m^{2} * 10^{-4} m

F_{f} = 0.002 m2/m3, or 0.2%, or 0.2 p.u.

**Fracture aperture plot -** In addition to the image and fracture tadpoles as well as the fracture density, we typically display fracture aperture data in two forms: the first is an average aperture for each individual fracture (this is a discrete number, one per fracture), and the second is a mean and mean hydraulic aperture, which sums all fracture aperture contributions over a 1 metre sliding window.** **Click image to enlarge

## Breakout and Drilling-Induced Fracture Interpretation

Image logs produce a clear image of both borehole breakout and drilling-induced fractures. Analyzing these features (their shape, width and orientation) gives valuable insight into in situ stresses. Stress-induced features are used to model principal stress, which cannot be accurately measured, calculated or estimated using any other approach.

**Stress-induced features - **Drilling-induced (tensile) fractures usually appear as a pair of vertical, inclined or curved en échelon conductive cracks as seen in the image on the left. In the image on the right, breakouts appear as a pair of borehole-parallel conductive blobs of varying width depending on drilling conditions and rock mechanical properties. Tensile fractures can also be seen at the top of the right-hand image, oriented roughly 90° to the wellbore breakouts.

**Borehole breakout stereonet.** Borehole breakouts give us the best means to estimate the maximum horizontal stress direction in a wellbore. With every image interpretation, we pick breakouts and drilling-induced fractures and display the data in a plot such as this one which includes an average breakout orientation as well as a reading of the principle horizontal stress direction. Click image to enlarge

Client Testimonial:

In order to understand the complex geology of our fractured carbonate reservoirs in Iraqi Kurdistan, we needed to be able to identify and describe natural fractures and wellbore damage with the highest confidence. We were able to communicate our specific needs to the staff at HEF, and with their extensive expertise, generate a data set that we could really work with.

Robert Leckenby, PhD. Geol, Senior Geologist, Oryx Petroleum