Static, Dynamic, and Stress Dependent Anisotropy of Shale

Shales and mudstones comprise about 75% of all the sedimentary rocks. In, particular, organic rich shales are considered as a petroleum source rock and more recently with the advent of hydraulic fracturing technology to be a reservoir in their own right. In this sense, the aforesaid motivates our work with laboratory measurements of elastic properties of these geologic materials, which are known to be anisotropic. As such, assuming Vertical Transverse Isotropy (VTI) symmetry, the dynamic and static moduli of a series of cores from various geological formations in Alberta, Canada are simultaneously investigated as a function of confining pressure using the ultrasonic pulse transmission method and strain gages. Dynamic moduli were obtained from ultrasonic P- and S-wave velocities measured on a prism cut with faces perpendicular, parallel and oblique to the assumed vertical axis of symmetry. Static moduli were calculated from strain-stress curves obtained along the directions perpendicular and parallel to the assumed axis of symmetry as well. Velocity measurements show that samples are highly anisotropic, but that the pressure-dependent behaviour of the wave speeds differs. VP(90°) and VSH(90°) both with layer parallel propagation and polarizations change little with pressure while VP(0°) and VS(0°) (both with layer perpendicular propagation) display significant nonlinear responses particularly at pressures < 25 MPa. These characters transfer to the derived full set of elastic constants. In order to effect a proper comparison of the dynamic and static moduli, we convert the dynamic elastic constanst to linear compressibilities pependicular (Kdyn1) and parallel (Kdyn3) which are directly comparable to the static tangent compressibiities obtained by differentiation of the observed strains. Both sets highlight the anisotorpic nature of the material but most interestingly Kdyn1 _ Ksta1 but Kdyn3 > Ksta3 by nearly 40% for one of the samples. The other samples measured respond similarly suggesting that conceptually the structure of such materials could be considered to be constructed of alternating stiff or compliant layers. This finding has implications in the response of the formation to stress particularly during hydraulic fracturing and the interpreation of acoustic logs in providing appropriate measures of elastic properties for engineering purposes.