Developing correlations for velocity models in vertical transverse isotropic media: Bakken case study

Abstract

The vertical and horizontal mechanical properties of a Vertically Transverse Isotropic (VTI) medium can be obtained from five stiffness coefficients (C33, C44, C66, C13 and C12) using velocities at different angles and density measurements. Particularly, when using well log data for vertical wells, only three out of the five elastic constants can be calculated. The sonic tool cannot measure C13 and C12, leading to introduction and application of empirical models to estimate them. However, most of the existing empirical models employ C66, a key stiffness coefficient, whose value depends on Stoneley wave velocity measured by the sonic tool. Due to the environment present in the wellbore as well as other reasons, C66 estimated in this way contains uncertainty. This in turn impacts the other stiffness coefficients thus increasing the uncertainty in VTI characterization of shale as well as increased error margin in in-situ horizontal stress estimation. This article presents a methodology to improve our understanding of the VTI anisotropy in shale.In this paper, extensive datasets from different shale formations all around the world, have been analyzed to establish linear correlations for the stiffness coefficients C13, C11, C66, and C12, without using the Stoneley wave velocity that has lots of uncertainties. The linear correlations used the stiffness coefficients C33 or C44 as the dependent variable, and were determined for individual shale formations and all compiled shale formations.In general, correlations for C11, C66, and C12, seem to work well, providing better results when using as input C33 than C44. Specifically, correlations for C11 and C66 seem to work really well, giving R-squared values greater than 0.7. Additionally, C12 as a function of C33 showed better predictions than the C12 M-ANNIE assumption, and lastly, for C13 it is concluded that there is no correlation.Finally, the correlations have been applied to well log data from a vertical well in the Bakken Formation, and compared to the stiffness coefficients obtained using the M-ANNIE assumptions. Moreover, minimum horizontal stress is calculated and compared using ANNIE, M-ANNIE, and the proposed correlations, these last ones determined from Bakken Formation velocity measured data. Generally, the new correlations provide results for the minimum horizontal stress a little bit lower than the M-ANNIE model, but greater than the ANNIE model. It is also shown that C13 M-ANNIE assumption works really well for shales, however, C12 M-ANNIE assumption does not work for shales. Furthermore, C66 calculated and used for the ANNIE and M-ANNIE models, is based on the Stoneley wave velocity which has been indicated not to be a reliable measurement. For these setbacks, the proposed correlations provide an alternative and practical solution for the in-situ stress estimation.