The Effect of Surface and Downhole Boundary Conditions on the Vibration of Drillstrings

Abstract

Abstract Surface and downhole boundary conditions are identified for a typical drill string using a 17.5 inch Tri-cone bit. A case study is presented using surface vibration data acquired in production operations in southern France. The data presented include high bandwidth force, torque and acceleration measurements, made on the surface with an instrumented sub. The sub was inserted in the drill string just below the power swivel The results include direct impedance measurements of the rig in torsional and axial motion. Comparisons are made between simulated and measured impedance functions. The results also include estimates of the boundary condition at the bit in torsional and axial motion. Surface measurements are compared to simulated transfer function models of the entire drill string for torsional and axial vibration. A relative displacement source is introduced as a realistic model of the action of a tri-cone bit. Introduction The control of bit bounce, optimization of shock subs and effective use of jars depend on one's understanding of axial dynamic response of the drill string. Understanding torsional dynamic properties is important m the control of stick slip, and in the prevention of twistoffs. Furthermore, the successful detection and interpretation of down hole phenomena from surface measurements depend on one's phenomena from surface measurements depend on one's understanding of the nature of the torsional and axial transfer functions between the surface and down hole. References 1, 2, and 3 are examples of papers which have made useful contributions to advancing the understanding of drill string vibration behavior. However, in practice, many phenomena observed in the field are more complex than can be explained by these existing models. One weakness is in the modelling of the effective boundary conditions on the surface and at the bit. In this paper surface measurements of the topside torsional and paper surface measurements of the topside torsional and axial boundary conditions of a drilling rig equipped with a power swivel are shown to be adequately modelled by a power swivel are shown to be adequately modelled by a simple linear mechanical system. The boundary condition at the bit presents a more challenging problem. An example 17.5 inch tri-cone bit, drilling in hard limestone, is evaluated by comparing measured and predicted surface dynamic response in axial and torsional motion. The natural frequencies of the BHA in torsion are best modelled by a free stiffness boundary condition at the bit. However, in torsion substantial damping at the bit is necessary to obtain good correlation between measured and simulated dynamic properties. This end condition appears to be relatively insensitive to variations in WOB and RPM. These conclusions are illustrated by comparisons between predicted and measured surface response. An axial boundary condition model is proposed which simulates the stiffness and the damping properties of the rock by a simple equivalent linear spring and dashpot. The action of a tri-cone bit is simulated by a relative displacement source placed between the rock and the end of the drill string. This source is used to simulate the lifting action of both the teeth and the irregular in the rock, such as the well known tri-lobed pattern. P. 431