Multi-frequency inversion of modal dispersions for anisotropy estimation
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Solution Overview
Problem
Current methods for estimating anisotropic elastic constants in wellbores require data from multiple boreholes and assume homogeneous formations, leading to unreliable stress estimates in heterogeneous shale-gas plays, particularly affecting hydraulic fracture propagation and shale-gas production.
Innovation Solution
A method that generates broadband acoustic waves and uses acoustic dispersion data from a single logging depth in a transversely-isotropic formation to calculate frequency-dependent sensitivity, allowing sequential inversion to determine all five independent anisotropic elastic constants, enabling accurate near-wellbore stress distribution and optimal completion design.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If data from multiple boreholes are used to estimate anisotropic elastic constants, then the assumption of homogeneous formations simplifies the estimation process, but the reliability of stress estimates deteriorates in heterogeneous shale-gas plays
Solution Approach 1:
The patent changes the fundamental parameters of the estimation approach by using acoustic dispersion data from a single borehole across multiple frequencies instead of combining data from multiple boreholes. This allows the method to capture formation heterogeneity along the wellbore while still estimating all five independent anisotropic elastic constants, thereby improving stress estimate reliability without sacrificing excessive complexity
Solution Approach 2:
The patent transitions from a spatial approach (multiple boreholes at single depth) to a frequency-based approach (single borehole at multiple frequencies). By exploiting frequency-dependent acoustic dispersion, the method extracts additional dimensional information about formation properties along the wellbore, enabling reliable stress estimation in heterogeneous formations
2Productivity
If only three anisotropic elastic constants are obtained from cross-dipole and Stoneley data, then the measurement process remains standard, but the completeness of anisotropic characterization deteriorates
Solution Approach 1:
The patent utilizes the frequency-dependent nature of acoustic dispersion to extract additional independent elastic constants. By analyzing how acoustic wave velocity varies with frequency in cross-dipole and Stoneley modes, the method recovers all five independent anisotropic elastic constants from the same single borehole data, completing the anisotropic characterization without requiring additional measurements
Solution Approach 2:
The patent makes the acoustic dispersion measurement serve multiple functions: it simultaneously provides information for determining all five independent anisotropic elastic constants (C11, C33, C44, C66, C13) from a single borehole, whereas traditionally the same data could only yield three constants. This multi-functionality eliminates information loss while maintaining measurement efficiency
3Device complexity
If low-frequency asymptote of flexural dispersion is used to obtain shear velocities in slow formations, then the measurement setup remains simple, but the accuracy of shear velocity estimation deteriorates
Solution Approach 1:
The patent moves beyond relying solely on the low-frequency asymptote by utilizing the complete frequency-dependent dispersion curve. By performing multi-frequency inversion of the full dispersion data, the method extracts more accurate shear velocity information and all five anisotropic elastic constants while maintaining the simplicity of the borehole acoustic measurement setup
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables reliable estimation of all five independent anisotropic elastic constants from a single wellbore, providing more accurate near-wellbore stress distributions and improving hydraulic fracture effectiveness in shale-gas production by accounting for formation heterogeneity.
Implementation Method 1
A standard sonic measurement system consists of placing a piezoelectric source and an array of hydrophone receivers inside a fluid-filled borehole
Implementation Method 2
An incident compressional wave in the borehole fluid produces critically refracted compressional waves in the formation. Those refracted along the borehole surface are known as compressional headwaves. The critical incidence angle θi=sin−1(Vf/Vc)
Implementation Method 3
A standard sonic measurement system consists of placing a piezoelectric source and an array of hydrophone receivers inside a fluid-filled borehole
Implementation Method 4
Both the lowest-order axi-symmetric Stoneley and flexural modes are dispersive, i.e., velocity changes as a function of frequency
Data Source
AI summary
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.