Calculating Fracture Intensity - Crain’s Method
The various log derived fracture indicators can be merged through a computer program which allows a wide variety of inputs. The input curves are assigned a threshold value, a median value, and a maximum probability as a fracture detector. In addition, each input is weighted according to its correlation to natural fracturing in the specific area. This form of program lends itself to a small rule based expert system.

In most areas, the major weighting is assigned to the shear attenuation from the sonic waveforms and to dipmeter differential conductivity. Lesser weighting is assigned to compressional attenuation, caliper rugosity, density correction, deep to shallow resistivity ratio, and uranium content. Where oblique fracturing are expected, the shear input may be weighted lower and the compressional input weighted higher. The output of the program is a fracture probability curve.

A simple form of the equation would look something like this
      1. CFI = ((RESS<RESD) + (PHID>PHIN+0.05) + (DELT>200) + (GR>150) + (PE>5.5) + (CAL>250)
                + (DCOR>250) + DELTA_CAL>50)) / NTEST

WHERE:
  CFI = calculated fracture index (fractional)
  RESS = shallow resistivity
  RESD = deep resistivity
  PHID = density porosity
  PHIN = neutron porosity
  DELT= sonic travel time
  GR = gamma ray
  PE = photo electric effect
  CAL = caliper
  DCOR = density correction
  DELTA_CAL = differential caliper
  NTEST = number of thresholds tested

This equation is written for a specific case; curves can be added or deleted and thresholds adjusted to suit the circumstances. Note that the thresholds are in Metric units for the example shown above, all curves have equal weight, and the amount of excursion of a curve beyond its threshold is not considered. The result is normalized between 0.0 and 1.0 by the value of NTEST. More elaborate fracture intensity indicators are common.

Open hole fracture indicator (CFI) compared to FMI results

The CFI curve and micro-scanner fracture intensity (frequency or fractures per meter, labeled FREQ) track each other reasonable well. There is a strong correlation between the FMI data, which represents ‘ground truth’, and the CFI curve. This does not always happen and the CFI must be calibrated to each specific case.

Note the Fracture Aperture (APER) and Fracture Porosity (PHIf) curve values are very small, but typical of most fractured reservoirs. Matrix porosity (PHIe) is significant and overwhelms the fracture pore volume.

It is sometimes possible to relate the sum of CFI over an interval to drill stem test flow capacity (KH) or to well productivity (IPR or AOF). CFI can also be compared and calibrated to fracture intensity (fractures per meter) from formation micro-scanner processing. This is useful when only a few wells have FMS or FMI data while others do not.