P2F-7 Formation Stress Effects on Wave Propagation in a Fluid-Filled Borehole

Formation stress magnitudes provide useful input to design decisions in wellbore planning, wellbore stability, and reservoir management in the oil and gas industry. It has been known for the past 50 years that elastic wave velocities in rocks change as a function of applied stress. Yet reliable inversion techniques are not available for estimating formation stresses from measured changes in sonic velocities. Borehole wave propagation in such formations can be described by equations of motion for small dynamic fields superposed on a bias. These equations are derived from the rotationally invariant equations of nonlinear elasticity by making a Taylor expansion of the quantities for the dynamic state about their values in the biasing (or intermediate) state. The effective elastic constants in these equations become position-dependent in the presence of inhomogeneous stresses. These equations can be solved either by a finite- difference or perturbation techniques. A finite-difference formulation of equations of motion in the presence of such stresses yields a complete wave solution produced by either a monopole or dipole band-limited source placed in a fluid- filled borehole. Processing of synthetic waveforms by a modified matrix pencil algorithm isolates various dispersive and non-dispersive arrivals. While a perturbation method is an expedient way of solving equations of motion with spatially varying coefficients, results from this method is limited to changes in modal dispersions caused by the presence of such near-wellbore stresses. Results provide changes in both the Stoneley and flexural dispersions caused by an increases in borehole overpressure, effective overburden, maximum and minimum horizontal stresses. The increase in formation shear velocity caused by a given increase in the overburden stress is the same as that caused by the horizontal stress of the same magnitude and parallel to the radial polarization. In contrast, changes in flexural velocities at high- frequencies caused by an increase in the overburden stress are similar to that caused by the horizontal stress of the same magnitude and perpendicular to the radial polarization.