Physical bounds on C₁₃ and δ for organic mudrocks

Abstract

We have used a reliable, updated database of ultrasonic measurements on organic mudrocks that contains components {C ij } of the transversely isotropic elastic tensor, and hence the Thomsen's anisotropy parameters ε and δ, to establish a more useful upper bound of feasible values for C 13 , and hence δ in unconventional mudrock reservoirs than that introduced earlier. The new upper bound δ max ¼ ε is consistent with elliptical anisotropy and represents a much better constraint for these mudrocks. We derive the upper bound C 13 max (and hence δ max) from Postma's inequality applicable to a thin-layered effective medium composed of kerogen and inorganic phases. The anisotropic moduli of such a composite as given by the Postma-Backus model are well-matched by the experimental data at least in the bedding-normal direction. As for the lower bound δ min , which was suggested by others, we confirm its reliability and usefulness for organic mudrocks.

Rock Physics Model of Shale: Predictive Aspect

“…(2016) gave the physical constrains for a specified type of TI medium which is stiffer along the bedding/layering than the symmetry axis, based on the relationships among Poisson's ratios. Chichinina and Vernik (2018) further tighten the upper bound of C 13 from Postma's inequality applicable to a thin‐layered effective medium composed of kerogen and inorganic phase. The impact of measurement frequency should also be noted.…”

“…For ultrasonic velocities measurements, the accuracy of the calculated anisotropy parameter δ depends on the accuracy of the measurements of the P ‐wave velocity propagating at an oblique angle to the bedding‐normal symmetry axis (e.g., Chichinina & Vernik, 2018; Dellinger & Vernik, 1994; Yan et al., 2018). The confusion between the group and phase velocities arises when relatively large transducers are used.…”