The analysis of drill string dynamics for extra-deep wells based on successive over-relaxation node iteration method

The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells. It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string. Due to the super slenderness ratio of drill string, strong nonlinearity implied in dynamic analysis and the complex load environment, dynamic simulation of drill string faces great challenges. At present, many simulation methods have been developed to analyze drill string dynamics, and node iteration method is one of them. The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall, but its drawback is that the calculation consumes a considerable amount of time. This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method (SOR node iteration method). Through theoretical analysis and numerical examples, the correctness and validity of this method were verified, and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed. The results demonstrate that, in contrast to the conventional node iteration method, the SOR node iteration method can increase the computational efficiency by 48.2% while achieving comparable results. And the whirl trajectory of the extra-deep well drill string is extremely complicated, the maximum rotational speed downhole is approximately twice the rotational speed on the ground. The dynamic torque increases rapidly at the position of the bottom stabilizer, and the lateral vibration in the middle and lower parts of drill string is relatively intense.