Example of Instability in Drive Mechanisms
Stability of rotation of a drillstring in curved oil wellbores is studied. The drillstring is considered as a Cosserat rod and the equations for a spatially curved drillstring and hole are derived and studied in detail for circular cross sections. The cas
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Abstract Stability of rotation of a drillstring in curved oil wellbores is studied. The drillstring is considered as a Cosserat rod and the equations for a spatially curved drillstring and hole are derived and studied in detail for circular cross sections. The cases which allow for the solution in closed form are analysed. The rotation with a constant angular velocity is shown to be feasible only for a straight drillstring. In all other cases the rotation is unstable and for some relations between the parameters it is accompanied by a quasi-static transition to a new configuration. The instability is caused by the energy exchange between the torsional and bending modes. The increasing torque on the end of the drillstring improves the rotational stability at expenses of the increasing stresses in the string.
1 Introduction Drillstring failures caused by unstable rotation of the drilling assembly are continually ranked as one of the most frequent and costly problems in the oil industry. Although many other methods of oilwell drilling have been tried historically, rotary drilling technique dominates the industry. The drillstring components, i.e. drillpipes, are typically 5” in outside diameter and 4.275” in inside diameter. Depthwise the assemblies can extend up to 8 km or more downhole, i.e. drillstring is an extremely flexible slender rod. Directional drilling toward the desired target, which is very popular nowadays, complicates the problem as oil wells are drilled with substantial curvatures and three-dimensional characteristics. In order to provide pressure for
A.K. Belyaev () Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O. Bolshoy pr.61, 199178 St.Petersburg, Russia e-mail: [email protected] H. Irschik et al. (eds.), Advanced Dynamics and Model-Based Control of Structures and Machines, DOI 10.1007/978-3-7091-0797-3 5, © Springer-Verlag/Wien 2012
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forcing the drillbit into formation, especially in the case of horizontal drilling, the drillstring is axially compressed, i.e. it is buckled in its static configuration and rotates in a curved well. The objective of the paper is to analyse the stability of the drillstring rotation. The paper is organised as follows. The first part is concerned with the modelling of the string by means of the rod theory. The second part deals with the most important case, in which no friction is assumed, and in addition to this, the string and the wellbore have circular cross sections. The cases of the helical and circular initial forms of the string and the wellbore are studied in detail. It is shown that the rotation is unstable and for some relations between the parameters it is accompanied by jump transition to a new configuration. The influence of the torque at the hole bottom on the rotational stability and the string strength is studied in the last part.
2 Drillstring as a Cosserat line. Geometry and governing equations The drillstring under consideration is considered as a rod, i.e. a 1D line. All the equations of
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