STONELEY AND FLEXURAL MODES IN PRESSURIZED BOREHOLES

The propagation of Stoneley and flexural waves in a fluid-filled boreh ole is adequately described by the linear equations of elasticity. How ever, when the borehole fluid is pressurized either due to the hydrost atic 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 i s described by the equations of motion for small dynamic fields superp osed on a bias. The resulting formulation allows us to study the influ ence of a change in the quid pressure on the Stoneley and flexural mod e dispersion curves. Since the biasing stresses in the surrounding for mation exhibit a radial decay away from the borehole, it is expedient to employ a perturbation technique to calculate changes in the borehol e Stoneley and flexural wave dispersion curves asa function of hydrost atic pressure change in the fluid. A key advantage of this perturbatio n technique is that it separates contributions of the acoustoelastic e ffect due to the borehole fluid ana 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 acoustoe lastic coefficient of the formation for the borehole Stoneley and flex ural wave velocities for a given change in the fluid pressure. The for mation acoustoelastic coefficient can be expressed as a fractional cha nge in the acoustic wave velocity caused by a unit change in the boreh ole pressure. Computational results show that acoustoelastic coefficie nts for the Stoneley and flexural waves are larger for formations with higher degree of nonlinearity which is typically associated with poor ly consolidated rocks.