A Study to Determine the Effect of Damping on Finite-Element-Based, Forced-Frequency-Response Models for Bottomhole Assembly Vibration Analysis

A computer based model for avoiding and characterizing dynamically induced drill string failures is presented. This model is applicable in both a planning and a real time mode of operation. The finite element model used in this study is designed to account for the forced frequency response of a Bottom Hole Assembly (BHA) drilling in an arbitrary curved three-dimensional wellbore. As a consequence of the greater simplicity of the resulting dynamic finite element model, it is standard operating procedure in drilling mechanics to exclude the effects of damping when carrying out a forced frequency response (FFR) vibrational failure analysis of a drilling BHA. Since damping, due to the presence of fluid, formation, friction and other effects, is the real world situation, the authors undertook the work described in this paper in order to determine the nature and the magnitude of the influence which damping exerts on drilling BHA's and their associated critical failure modes. The FFR analysis model presented herein enables a user to determine the forced frequency response (critical speeds) of a BHA due to imposed load and/or displacement excitations anywhere in the drill string. The FFR solution is computed about the displaced static configuration, which means that the Jacobian (i.e. stiffness) matrix contains the effects of contact, stress stiffening and friction. The mathematical formulation of the FFR solution algorithm has been developed in such a way as to admit damping in the steady-state response behavior. An important implication of damping is that while the response of the BHA will be at the same frequency as the excitation, it need not be in phase with it. A major benefit of this model is that it provides a mechanism to evaluate the effect of including (or neglecting) damping in conventional BHA FFR finite element analysis. With regard to the above described study, this paper first reviews the theoretical basis for the FFR model utilized and follows with a presentation of field data case studies. These studies validate the utility of employing the model to predict (and therefore avoid) critical rotating speeds and also demonstrate the significant role which damping plays in obtaining useful real world results from FFR finite element analysis. In this regard, the effects of both uniform and frequency dependent damping upon critical operating speed ranges and response magnitudes are examined.