Estimation of Rock Stiffness Coefficients in VTI Formations Using LWD Acoustic Measurements
- Elsa Maalouf (The University of Texas at Austin) | Carlos Torres-Verdin (The University of Texas at Austin)
- Document ID
- Society of Petrophysicists and Well-Log Analysts
- SPWLA 58th Annual Logging Symposium, 17-21 June, Oklahoma City, Oklahoma, USA
- Publication Date
- Document Type
- Conference Paper
- 2017. copyright held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors
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Vertical transverse isotropy (VTI) is commonly observed in shales due to azimuthal variations of stress around the borehole or intrinsic variations in rock composition within a layer. In VTI formations, the stiffness coefficient matrix consists of five independent coefficients: 𝑐11, 𝑐33, 𝑐44, 𝑐13, and 𝑐66. Estimation of these five coefficients is fundamental to successfully locating and designing hydraulic fractures. However, compressional and shear slowness logs acquired in vertical wells yield information on 𝑐33 and 𝑐44 only. Calculating 𝑐44 from the quadrupole mode using logging-while-drilling (LWD) instruments remains challenging because low-frequency quadrupole slowness is smaller than formation shear slowness. Furthermore, presence of thin layers increases the complexity of estimating true layer elastic properties because of averaging effects on sonic logs.
This paper introduces a new workflow to calculate the five stiffness coefficients in layered VTI formations by inverting LWD sonic logs as follows: First, we calculate axial-sensitivity functions of Stoneley, compressional, and quadrupole slownesses to five properties, namely, vertical compressional slowness (𝑠𝑝𝑣), horizontal compressional slowness (𝑠𝑝ℎ), vertical shear slowness (𝑠𝑠𝑣), horizontal shear slowness (𝑠𝑠ℎ), and 1/√𝑐13. Next, we use the calculated sensitivities to forward model Stoneley, compressional, and quadrupole slownesses, and finally we estimate stiffness coefficients using multi-step inversion because borehole modes are predominantly sensitive to one of the coefficients at a given frequency.
We show that sensitivities vary when the formation is fast, intermediate, or slow; therefore, we apply the interpretation workflow to fast and slow formations with 17% anisotropy. The corrected 𝑐44 is calculated with a relative error below 6%, 𝑐13 and 𝑐11 are estimated by inverting the quadrupole logs from 4 kHz to 7 kHz, and 𝑐33 and 𝑐66 are calculated by inverting the compressional and Stoneley logs, respectively.
Using the new interpretation workflow, we successfully calculate the five stiffness coefficients corrected for averaging effects of VTI layers, which can be used for reliable and accurate design of hydraulic fracturing operations in organic mudrocks.
|File Size||850 KB||Number of Pages||6|