Drilling-vibration response characteristics of rocks based on Hilbert–Huang transform

Abstract

AbstractCurrently, there are no in-situ methods to quantify drilling-vibration response characteristics of different lithologies. Here, we quantified the vibration responses of four lithologies (limestone, sandstone, coal, and mudstone) using a combination of theoretical deduction and numerical simulation. First, a drilling-vibration model of a particular rock was established, and the differential equations of motion and vibration responses to rock/drill bit interactions with the formation were derived. Next, finite-element simulation was adopted to simulate the rock/drill-bit interactions of the four lithologies. Finally, the Hilbert–Huang transform (HHT) was applied to extract characteristic waveforms, frequency bands, peak frequencies, and marginal spectra of vibration signals. Simulations revealed that the highest and lowest vibration responses were observed in limestone and mudstone, respectively. Vibration acceleration was proportional to the Young's modulus of rocks, whereas vibration displacement and velocity were inversely proportional to Young's modulus, compressive strength, and density. Based on the HHT results, among the four lithologies, vibration responses had the largest characteristic frequency segments and peak frequencies in limestone (28.1–34.6 kHz and 33.4 kHz, respectively), whereas those of mudstone were the smallest (15.6–21.3 kHz and 19.6 kHz, respectively). The results of this study provide a theoretical basis for establishing an identification method and expert knowledge database of lithology based on drilling-vibration responses.