Considerations on Numerical Procedure for Stick-Slip Analysis of Drill String

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Stick-slip is one of the typical phenomenon which is observed in offshore drilling and considered as a critical problem for the drilling operation. The stick-slip makes a large fluctuation of drill bit rotation, even though the top of the drill pipe is rotating at a steady velocity and sometimes causes the damage of the drill bit. Additionally, it leads a crushing of the sediment layer which is a big problem especially for the scientific drilling [1][2][3]. The main purpose of the scientific drilling is to correct high quality core samples of sediment layers under the seabed. However, once the stick-slip occurs, it makes difficult to recover a high-quality sediment layer core sample. Therefore, it is necessary to detect the occurrence of stick-slip and its fundamental characteristics such as oscillation periods and amplitudes by simulation with the aid of surface drilling data, which can be monitored during the drilling operation to mitigate or prevent stick-slip. It would be advantageous to identify the characteristics of the stick-slip from the surface drilling data. The past study [4][5][6] investigated a numerical method to analyze the stick-slip by solving the NDDE (Neutral Delay Differential Equation) which is derived from torsional vibration equation. A small-scale model experiment was conducted in a water tank to observe the stick-slip phenomenon, and the result from the analytical model is evaluated with that obtained from the experiments. In this study, the numerical model is applied for the stick-slip analysis not only of the drill pipe model but also the actual drill pipe in operation. The solutions of the NDDE is depend on not the initial value but the initial history of the solution, because NDDE contains a delayed function term. Especially, the initial history settings have much effect on the numerical solution of NDDE in case of the actual drill pipe. Additionally, to solve the NDDE for stick-slip analysis, we must set some model parameters concerned with the frictional torque on drill bit. The present study investigated the effects of the initial history and the model parameters settings on numerical solutions in detail and presented an procedure to determine the appropriate settings of the initial history and the model parameters by reference to the measured top drive torque.