Acoustic waves in pressurized boreholes: A finite difference formulation

Abstract

A velocity‐stress, finite difference formulation of acoustic waves in a fluid‐filled, pressurized borehole yields synthetic waveforms for monopole or dipole sources before and after borehole pressurization. Processing of these waveforms using a variation of Prony's procedure isolates dominant arrivals in the full wave field. Differences between the slownesses of individual arrivals before and after pressurization provide stress‐induced changes in propagation characteristics that are of importance in estimating mechanical properties of the formation. The borehole pressurization in an isotropic formation produces insignificant changes in the compressional head wave slownesses; and small changes in the shear head wave slownesses. The most significant changes occur in the Stoneley and flexural slownesses at relatively higher frequencies in the range of 5–10 kHz for a borehole of diameter 20.32 cm (8 inches). These differences in the Stoneley and flexural slowness dispersions for a known increase in the borehole pressure can be used to calculate the acoustoelastic coefficients of the formation. These coefficients are measures of nonlinear elastic parameters of the formation that are generally larger for poorly consolidated slow formations than those of tightly consolidated fast formations.