A New 3D ROP Equation Considering the Rotary Speed of Bit

In order to fully consider the factors affecting the ROP and improve the accuracy of predicting the ROP and wellbore trajectory, the 3D ROP equation involving the interaction between bit and formation was studied. Considering the effect of rotary speed of the bit, the bit anisotropic index and the formation anisotropic index were redefined. Based on the definition of both anisotropic indexes and the coordinate transformation, a new 3D ROP equation considering the rotary speed of bit and the bit-formation interaction was established. Using the new 3D ROP equation, a practical case was taken to analyze the effect of rotary speed on ROP.It was found that all ROPs in Xd direction, Yd direction and normal Zd direction increased with the increase of rotary speed, but to different extents.ROP in normal Zd direction increased more than that in Xd and Yd directions.The results showed that the new model could be used to predict the change of ROP and wellbore trajectory with the change of rotary speed in drilling operations, and that the wellbore trajectory could be controlled by adjusting the rotary speed, bit anisotropic index, bit mechanical force and other parameters.