Estimation of horizontal stress magnitudes and stress coefficients of velocities using borehole sonic data

Abstract

We described a nondestructive method to estimate the maximum and minimum horizontal stresses and formation nonlinear elastic constants using sonic data from a vertical wellbore. This method for the estimation of horizontal stress magnitudes consists of using radial profiles of the three shear moduli obtained from the Stoneley and cross-dipole sonic data in a vertical wellbore. These shear moduli change as a function of formation stresses, which in turn change as a function of the radial position away from the wellbore. Two difference equations were constructed from the three far-field shear moduli and the other two were constructed from differences in the shear moduli at radial positions with different stresses in the presence of near-wellbore stress concentrations. Outputs from this inversion algorithm included the maximum and minimum horizontal stress magnitudes, and two rock nonlinear constants referred to a local hydrostatically loaded reference state. The underlying acoustoelastic theory behind this inversion algorithm assumes that differences in the three shear moduli are caused by differences in the formation principal stresses. Additionally, the orientation of the maximum horizontal stress direction was identified from the fast-shear azimuth in the presence of a dipole dispersion crossover. Hence, the principal horizontal stress state was fully determined. Good agreement was obtained between the predicted minimum horizontal stress magnitude and that measured from an extended leak-off test in a vertical offshore wellbore in Malaysia. One of the nonlinear constants was obtained from differences between compressional velocity at two depths caused by differences in the overburden stress and the maximum and minimum horizontal stresses. Estimates were obtained for the stress coefficients of the compressional, fast-shear, and slow-shear velocities referred to a local reference state. These stress coefficients of velocities helped in the interpretation of observed time-lapse changes in seismic traveltimes caused by fluid saturation and reservoir stress changes.