Stress impact on elastic anisotropy of triclinic porous and fractured rocks

Abstract

Understanding the stress dependence of elastic properties of rocks is important for reservoir characterization and seismic-hazard monitoring. Several known approaches describing this dependence are the following: the nonlinear elasticity theory, effective-medium theories for fractured rocks with stress-dependent crack densities, and the piezosensitivity approach (also called the porosity deformation approach). Here I propose a generalization of the piezosensitivity approach to triclinic rocks. I assume the isotropy of the tensor describing sensitivity of elasticity to small strains of the pore space, and generalize known linear and exponential stress dependencies of compliances. This generalization is capable of describing the effect of loads on elastic properties of anisotropic rocks when the principal stresses are not necessarily aligned with the symmetrical axes of the unstressed anisotropic material. For example, the generalization describes how monoclinic anisotropy changes under isostatic stress or pore pressure, and how tilted transverse isotropy changes to monoclinic anisotropy due to a pseudo-triaxial (or a uniaxial) load. The results are expected to be valid up to several hundred megapascals. This theory is closely related to the two other approaches mentioned above. On the one hand, for unloaded rocks, the theory is consistent with the noninteracting scalar-crack approximation. On the other hand, the theory's predictions of mutual relations between isotropic third-order elastic moduli is in good agreement with literature data on corresponding laboratory measurements. Thus, using the piezosensitivity approach, the physical nonlinearity of rocks can quantitatively be rather well explained by the strain of compliant pores.