The Characteristics of Numerical Solution of NDDE to Solve the Drill Pipe Stick-Slip

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Abstract The Stick-Slip is one of troublesome problems which happens in scientific drilling. In order to clarify the mechanism of Stick-Slip phenomenon, it is necessary to develop a reliable numerical model [1]-[4] to estimate drill bit motion for various drilling conditions. We have investigated on an NDDE (Neutral Delay Differential Equation) [5] to solve Stick-Slip of drill pipe [6]-[8]. In order to solve this NDDE, it is necessary to determine the frictional torque acting on the drill bit. In the previous study, we have employed the Balanov’s [4] frictional torque model which is the function of drill bit rotation with four unknown model parameters. This numerical model calculates the Stick-Slip phenomena of the drill pipe model in the laboratory experiments correctly under the appropriate four model parameter settings. On the other hand, it is quite difficult to calculate the actual drill pipe Stick-Slip [9], because the calculated results change drastically depending on the four unknown parameter settings. In the present study, the frictional torque acting on the drill bit is defined as a periodic function and solved the NDDE to calculate the stick-slip of the actual drill pipe. The average, variation and period of the frictional torque on the drill bit were set under the consideration of measured top drive torques. The calculated numerical solutions of the drill bit motion and the top drive torque agreed qualitatively with the measured ones.