Abstract

Fracture Density is defined as Fracture surface area/volume. At a particular stress or strain state, one rock with greater Fracture Density than another is considered to be more brittle and easier to frack. Over the past 2 years, we have been testing a geomechanical equation that predicts fracture density and our definition of brittleness. G.C. Sih (1985) pointed out that “the surface and volume energy density of each material element are related by the rate of change of volume with surface”. This suggests that (F_d)(U_a) = U_v where F_d is the fracture density; U_a is the energy needed to create fracture area ’a’; and U_v is the strain energy density, or strain state. The dimensionless form of our equation, assuming linear elasticity, is:

Where Fd is Fracture Density (or brittleness); K_Ic is the Critical Fracture Toughness for mode I fractures; m is the Shear Modulus; n is Poisson’s Ratio; and A and B are strain invariants representing the strain state. Note that the dimensionless equation should plot as a straight line with the slope and intercept representing the strain state, A and B.

We have been testing this equation by measuring fracture density of joints in outcrops of a variety of rocks primarily in West Texas. Specimens of those rocks are then brought to the Geomechanics lab where mass density and both compressional and shear sonic velocities are measured. From that information the dynamic elastic properties are calculated. The variable that is most difficult to measure is Fracture Toughness, K_Ic. Instead of measuring it directly, we use regression equations in the literature that relate material properties and sonic velocities to Fracture Toughness for various rock types.

While we are still testing the equation, the results so far suggest it works. The next step is to apply the equation to well logs. Any well with dipole sonic logs and density logs can also produce a “Brittleness” log, by equating fracture density at a particular strain state with brittleness.