Multi-Frequency Inversion of Modal Dispersions for Estimating Formation Anisotropy Constants

摘要

Systems and methods for the estimating a plurality of anisotropic elastic constants (Cij) using borehole dispersions and refracted compressional headwave velocity at a single logging depth in a vertical, deviated, or horizontal wellbore in a transversely-isotropic with a vertical axis of symmetry (“TIV”) formation. The estimated elastic constants can then be used to calculate near-wellbore stress distributions in the wellbore, which aids in an optimal completion design, such as for shale-gas production in the presence of shale heterogeneity.

主权项

1. A method for determining a plurality of anisotropic elastic constants, Cij, for a transversely isotropic formation, comprising:
generating a broadband acoustic wave at an acoustic source located within a borehole; receiving data corresponding to an acoustic dispersion of the broadband acoustic wave at an acoustic receiver located within the borehole; calculating a frequency-dependent sensitivity of the acoustic dispersion to an incremental change in each of the anisotropic elastic constants, CijΔVk/VkΔCij; and sequentially inverting a difference between the acoustic dispersion and a reference acoustic dispersion to obtain each of the anisotropic elastic constants, wherein each inversion is performed over a select bandwidth where the frequency-dependent sensitivity of the acoustic dispersion to an incremental change in each of the anisotropic elastic constants, CijΔVk/VkΔCij, is adequate, where Cij represents an anisotropic elastic constant, Vk represents a reference modal phase velocity, ΔCij represents a change in an anisotropic elastic constant, ΔVk represents a change in a modal phase velocity from the reference modal phase velocity Vk, and indices i and j can be integers 1-6 and index k is a chosen frequency.