Numerical simulation of borehole compressional wave and shear wave in 3D vug formation

The staggered grid finite difference method (SGFDM) of a monopole source is used to simulate a three-dimensional vug reservoir model and study the effect of acoustic logging responses of different vug models on radial probing depth. The results show that the first arrival of the head wave peak of the compressional wave (P-wave) and the shear wave (S-wave) is unrelated to the radius of the vug, and the amplitude of the head wave peak of the P-wave and S-wave decreases as the vug volume increases. Compared with the volume change of the vug, the radial distance from the vug wall has little influence, while the vertical source distance has large influence on the P-wave and S-wave. When there are multiple vugs in the model, the amplitudes of the P-wave and S-wave head wave peaks change sinusoidally with the angle between the vugs. The ellipsoidal vug model with the same volume has a greater influence on the P-wave and S-wave than the spherical vug model. In the ellipsoidal vug model, the axial vug size has a greater impact on the first arrival of the head wave peak, while the radial vug size significantly influences the amplitude of the head wave peak. Finally, we validate the numerical simulation conclusions by comparing them with actual logging data responses in complex formations, demonstrating the practical value of the elastic wave response simulations for vugs.