Stoneley and flexural modes in pressurized boreholes

Abstract

The propagation of Stoneley and flexural waves in a fluid‐filled borehole is adequately described by the linear equations of elasticity. However, when the borehole fluid is pressurized either due to the hydrostatic head at a given depth or with the aid of packers at the wellhead, both the fluid and the surrounding formation are subjected to biasing stresses. Under this situation, wave propagation along the borehole is described by the equations of motion for small dynamic fields superposed on a bias. The resulting formulation allows us to study the influence of a change in the fluid pressure on the Stoneley and flexural mode dispersion curves. Since the biasing stresses in the surrounding formation exhibit a radial decay away from the borehole, it is expedient to employ a perturbation technique to calculate changes in the borehole Stoneley and flexural wave dispersion curves as a function of hydrostatic pressure change in the fluid. A key advantage of this perturbation technique is that it separates contributions of the acoustoelastic effect due to the borehole fluid and that due to the formation. Insofar as the fluid nonlinear properties at a given pressure and temperature are known, the model provides a procedure for estimating the acoustoelastic coefficient of the formation for the borehole Stoneley and flexural wave velocities for a given change in the fluid pressure. The formation acoustoelastic coefficient can be expressed as a fractional change in the acoustic wave velocity caused by a unit change in the borehole pressure. Computational results show that acoustoelastic coefficients for the Stoneley and flexural waves are larger for formations with higher degree of nonlinearity which is typically associated with poorly consolidated rocks.