Fracture density is similar to brittleness and is an important variable for efficient gas and oil production, particularly from tight reservoirs. G.C. Sih has 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 (Fd)(Ua) = Uv where Fd is the fracture density; Ua is the energy needed to create fracture area A; and Uv is the strain energy density.

Using simplifying assumptions, an equation can be derived that relates fracture density to KIc, the critical fracture toughness for mode I fractures; Young's Modulus; Poisson's Ratio; and the strain state. The simplifying assumptions include linear elasticity, Mode I fracturing, and uniform far field strain.

Measurements of fracture density and material properties under conditions of uniform far-field strain as well as numerical simulations are underway to test the fracture density and material properties relationship.

Results will improve estimates of the brittleness of tight reservoirs, and how effective hydraulic fracturing will be. Currently, brittleness, or fracture density, is estimated primarily from the elastic properties determined from acoustic logs. The theory suggests that fracture toughness is also an important variable to consider. Preliminary data suggests that fracture density can be predicted using an equation derived from the relationship between fracture density and strain energy.


The relationship between strain energy and fracturing has a long theoretical history, but little has been done in the geosciences to investigate the relationship between strain energy and fracture density.

Fracture density, and its related concept fracture spacing, has been studied extensively for decades (Narr and Lerche, 1984; Watts, 1983; Willemse et al., 1997; Julander et al., 1999; Tapp et al., 1999; Mauldon, Dunne and Rohrbaught, 2001; Di Naccio et al., 2005; Ortega, Marrett and Laubach, 2006; Lorenz Cooper and Olsson, 2006; McLennan et al., 2009; Zahm and Hennings, 2009; Barthelemy, Guiton and Daniel, 2009; and many others).

More recently, seismic methods have been used to characterize subsurface fractures from P-wave velocity reduction (Karaman et al., 1997), shear-wave splitting (Lou and Rial, 1997), frequency dependent anisotropy (Maultzsch et. al., 2003), and Azimuthal AVO analysis (Xu and Tsvankin, 2007), as well as to monitor the artificial fracturing process in real time (Maxwell and Urbancic, 2005).

Finally using damage rheology, computer models of propagating fractures have been developed that can relate fluid pressure, far field stress and material properties to a propagating fracture and its geometry (Busetti, S., K. Mish, and Z. Reches, 2012; and Busetti, S. K. Mish, P. Hennings, and X. Reches, 2012).

URTeC 1619745

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