Development of a rock-bit interaction analytical model by considering the in-situ stresses for a bottom-hole element

Abstract PDC drill bits are an important part of drilling engineering, but improper selection or design can lead to decreased performance and increased costs. Then, accurate modeling of rock-bit interaction for Oil/gas well drilling is critical. Although several mathematical models are presented for this purpose, they have not been able to present a comprehensive model for the rock-bit interaction. In-situ stresses in real drilling conditions affect the force required for rock failure. However, the models proposed so far either have not considered the effects of in-situ stresses or have assumed that the rock failure angle in the downhole conditions is equal to the one calculated in the atmospheric conditions. In this work, after reviewing the background of studies conducted on the rock and bit interaction, with an analytical method, stresses applied to the bottom hole element are examined, including stresses resulting from bit and in-situ stresses. Based on the principle of superposition, the total stress imposed on the bottom hole element is calculated to determine the angle and force of rock cutting. Finally, a novel mathematical model of rock-bit interaction in vertical and deviated oil/gas wells drilling by Considering In-Situ Stresses is presented. Also, the study compares the current model to the Nishimatsu and Xin Ling models using data from a southwest field in Iran. The results show that the simplifying assumption made by previous models leads to a significant underestimation of the failure angle and the amount of force required to the rock failure, with reductions of up to 21% and 48%, respectively, in the case of a vertical well. In an inclined well, the current model predicts cutting force at about 0.14 of that predicted by the previous model.