Recent advances in the modeling of a drillstring inside a curved borehole
Accurate calculation of the position of the contacts between the drillstring and the borehole as well as the determination of the extent of these contacts is the true challenge of a torque-and-drag analysis. Such calculations are required to estimate the loss of torque from the rig to the bit under some assumed friction models, but also to assess the axial force on the bit (the “weight on bit”) given the known axial force at the rig (the “hook load”). Indeed, the weight on bit directly influences the rate of penetration, but also the drilling tendency of bottomhole-assemblies equipped with rotary steerable systems [3, 6]. The accurate and efficient structural analysis of such a slender body, which is constrained to deform inside a borehole, is thus of paramount importance for the modeling of drilling operations. In the late 1990’s, the state-of-the-art in torque-and-drag modeling has shifted from the “soft string model,” based on the assumption that the drillstring coincides with the borehole axis [4], to advanced numerical methods with built-in management of the contacts. Standard finite element techniques have been applied to the torque-and-drag problem, but they require a fine mesh to properly capture the response of the system in the vicinity of contacts [5]. Furthermore, the slenderness of the drillpipe, combined with the limited clearance between the drillstring and the borehole wall are two of the reasons that make the application of such standard techniques rather inefficient [2]. As an alternative, we have developed an approach that segments the drillstring between contacts and treats the series of unconstrained (or classical) elastica problems between successive contacts as a sequence of simpler auxiliary
Steady-state solutions of a propagating borehole: Helical trajectory
Deep boreholes with complex geometries are now drilled with the help of rotary steerable systems (RSS), which are downhole robots capable of steering the bit by either applying a force on the borehole walls (push-the-bit systems) or by tilting the bit (point-the-bit systems). This paper explores the existence of stationary borehole geometries in the form of vertical helical trajectories. These non-trivial solutions, which represent the equilibrium points of the dynamical equations governing the evolution of the borehole, correspond to situations where the deformed configuration of the bottomhole assembly (BHA) remains invariant during the propagation of the borehole, i.e., the BHA moves inside the created borehole as a rigid body. Formulation of the model yields a system of linear equations in terms of the radius and pitch of the helical boreholes. A parametric analysis of the solution for the idealized case of rigid BHA with one stabilizer shows the region of existence of helical trajectories and the dependence of the pitch and radius of the helix on the control parameters.
Torsional deformation of an endoscope probe
A recent US patent due to Shan describes a method for identifying the location of the colonoscope in the body during endoscopy. The method depends upon the integration of measurements recorded by a flexible probe inserted in the biopsy channel at the end of a flexible rod. In this paper, classical results for the elastic rod are used to determine the equations required for this integration process. Particular attention is paid to the effect of initial curvature or non-axisymmetry of the rod. It is shown that these effects cause predictive errors that increase quadratically with the angle subtended by the space curve of the channel, and quite stringent limits must be placed on straightness and symmetry if these errors are not to be significant.