LWD Quadrupole Dispersion Characteristics of a Prestressed Formation - Numerical Simulation and Field Data Example

Determination of horizontal formation stress is critical for evaluating wellbore stability and predicting formation pressure in the logging while drilling (LWD) environment. This study provide the acoustoelastical equations in the LWD theory model. We analyzed the dispersion characteristics of LWD quadrupole wave in prestressed formation and compared it with that of wireline logging. The results of numerical simulation and field measured data processing both show that in a prestressed formation the phase velocity of LWD quadrupole wave is close to the original formation shear wave velocity at the cut-off frequency, and, at high frequencies, is controlled by the near-borehole formation shear wave velocity that is sensitive to stress concentration. Velocity variation of formation shear waves outside the well caused by imbalance formation stress can be indicated by the difference between the measured LWD quadrupole dispersion data and the theoretical dispersion curve calculated using the homogeneous formation model.