Fast-forward modeling of compressional arrival slowness logs in high-angle and horizontal wells

Abstract

Compressional (P) and shear (S) sonic propagation modes are routinely measured with modern borehole acoustic logging instruments. Slownesses (inverse of velocity) of P- and S-modes provide information on compressional and shear slownesses of rock formations surrounding the wellbore, respectively. When a high-angle well penetrates horizontal thin layers, the layers function as waveguides for the propagation of sonic waves. Layer-trapped and borehole-guided waves interfere with each other, giving rise to abnormal amplitude variations and phase discontinuity in the time waveforms acquired at receivers. Consequently, waveforms measured across the receiver array often exhibit low semblance, which renders conventional waveform semblance-based processing techniques inadequate for reliable estimation of formation slowness. Instead of calculating waveform semblance, we invoke compressional first-arrival times to describe the propagation properties of the P-mode in high-angle and horizontal (HA/HZ) wells, and we derive P-arrival slownesses from the first-arrival times of the measured waveforms. Because the first-arrival time at a particular receiver is associated with the fastest P-wave, the P-arrival slowness log is much less affected by mode interference than the conventional log obtained using semblance-based processing techniques. Furthermore, numerical tests with high-angle wells indicate that compressional first arrivals are mainly associated with converted P-waves through deviated layers. Accordingly, we introduce a 1D layered simulation method to model P-mode first-arrival times in HA/HZ wells across thinly bedded formations. Synthetic examples confirm that P-arrival slowness logs obtained with our simulation method in HA/HZ wells agree to within 5% with logs obtained using 3D finite-difference simulations. In addition, because the new method simplifies the geometric complexity of the models from 3D to 1D, it saves 99% of CPU time compared with rigorous numerical simulations.