Multi-Frequency Inversion of Modal Dispersions for Estimating Formation Anisotropy Constants
AssigneeSchlumberger Technology Corporation
InventorBikash K. Sinha
Life of this patent
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Abstract
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.
Claims20
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.
A system for determining a plurality of anisotropic elastic constants, Cij, for a transversely isotropic formation, comprising:
- an acoustic tool including an acoustic source configured to generate a broadband acoustic wave and an acoustic receiver configured to receive data corresponding to an acoustic dispersion of the broadband acoustic wave;
- and
- a control unit comprising at least one processor and a memory, wherein the control unit is configured to:
- calculate a frequency-dependent sensitivity of the acoustic dispersion to an incremental change in each of the anisotropic elastic constants, CijΔVk/VkΔCij;
- and
- sequentially invert 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.
Dependencies are inferred from the claim text.