Determining Stress Regime And Q Factor From Sonic Data

Extracting quantitative information on formation rock stresses from borehole log measurements is fundamental to the analysis and prediction of geomechanical problems encountered in the petroleum industry. Today there is no direct measurement to fully characterize the formation rock in-situ stresses tensor (three principal stress magnitudes, σ1, σ2, σ3 and three angles to describe the directions, with σ1>σ2>σ3). Generally, it can be reasonably assumed that the vertical stress is one principal stress, so we will have four parameters to describe the in-situ stresses: vertical (σv), minimum horizontal (σh), maximum horizontal (σH) stress magnitudes and the azimuth of minimum horizontal stress. The vertical stress may be estimated from an integral of the density log, while the minimum horizontal stress can be estimated using fracturing or leak-off test data, and its direction from borehole caliper or images analysis. However, the maximum horizontal stress is more difficult to estimate, the conventional approach is to use some correlations such as the poro-elastic strain correlation, or the approximations such as equating the maximum horizontal stress to some multiple of the minimum horizontal stress. Since model-based or empirical correlations for maximum horizontal stress are always associated with a big uncertainty, a correlation or model of the maximum horizontal stress to that of the vertical and minimum horizontal stresses, interpreted directly from logging, is to be preferred. Recent developments in sonic logging have made it possible to measure accurately the formation rock anisotropic wave velocities induced by in-situ stress anisotropy. This technology of sonic logging provides us the data and information to interpret the deviatoric stress ellipsoid shape factor, R (0 < R =(σ2-σ3)/(σ1-σ3) < 1) and the stress regime or its equivalent the stress regime factor Q (Q=R for normal, Q=2-R for strikeslip and Q=R+2 for thrust), and then estimate the maximum horizontal stress. This paper presents a model for estimating the stress regime Q factor from anisotropic sonic measurements in sand or shale formations penetrated by a vertical wellbore. The model is based on a perturbation theory of stress-dependent elastic properties. For an intrinsic isotropic medium such as a sand formation, borehole measured wave anisotropy can be identified to be stress-induced, and an equation to compute stress regime factor Q from anisotropic shear moduli is deduced. For laminated formations, such as shale, by considering a relatively homogeneous interval of interest, an equation to estimate Q from sonic anisotropy is also provided.