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Using Euler-Bernoulli beam theory, a finite element model with six degrees of freedom per node is developed for a drill-string assembly. The drill-string is driven by a DC motor on the top and is subjected to distributed loads due to its own weight as well as bit/formation interaction. The model is axial-torsional, lateral-torsional coupled. Under deterministic excitations, the model captures stick-slip behavior in drilling operation. Analysis on its negative effect on drilling performance are made, and potential mitigation measures are also discussed. In random model, the excitations to the drill-bit are modeled as combination of deterministic and random components. Monte Carlo (MC) simulation is employed to obtain the statistics of the response. Two cases of random excitation with different intensities are investigated. The results from MC simulation are compared against that from deterministic case.

Using a finite element model, this paper investigates the torsional vibration of a drill string under combined deterministic excitation and random excitation. The random excitation is caused by the random friction coefficients between the drill bit and the bottom of the hole and assumed as white noise. Simulation shows that the responses under random excitation become random too, and the probabilistic distribution of the responses at each discretized time instant is obtained. The two points, entering and leaving the stick stage, are examined with special attention. The results indicate that the two points become random under random excitation, and the distributions are not normal even when the excitation is assumed as Gaussian white noise.

A dynamic bottom hole assembly (BHA) model is built with finite element method (FEM) in this paper. This model is used for evaluation the influence of externally added vibration to the BHA system. With this dynamic model along with a general bit-rock interaction formula, the BHA’s motion in axial and torsional directions are examined. Parametric study is carried out by varying the parameters of the applied vibration force, including the mean value, amplitude, angular frequency, and the location of this force excitation. The simulation results indicate that externally applied vibration force is indeed able to improve drilling performance. In particular, the mean value and amplitude of the applied force have a almost linear relation with ROP and WOB. The stresses distributions along BHA are investigated as well.