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
Eulerian formulation of constrained elastica
The formulation of the constrained elastica problem proposed in this paper is predicated on two key concepts: first, the deformed elastica is described by means of the distance from the conduit axis; second, the problem is formulated in terms of the Eulerian curvilinear coordinate of the conduit rather than the natural curvilinear coordinate of the elastica. This approach is further implemented within a segmentation algorithm, which transforms the global constrained elastica problem into a sequence of analogous auxiliary problems that result from dividing the conduit and the elastica into segments limited by contacts. Each auxiliary segment entails solving a segment of elastica subject to isoperimetric constraints corresponding to the assumed positions of the segment ends along the conduit. This new formulation resolves in one stroke a series of issues that afflict the classical Lagrangian approach: (i) the contact detection is reduced to checking whether a threshold on the distance function is violated, (ii) the isoperimetric conditions are transformed into regular boundary conditions, instead of being treated as external integral constraints, (iii) the method yields a well-conditioned set of equations that does not degenerate with decreasing flexural rigidity of the elastica and/or decreasing clearance between the conduit and the elastica.
Archaeological Survey of Dangoyama Kofun by 3DGPR
We presented a three-dimensional ground penetrating radar (3DGPR) system for the archeological investigation in a harsh site, where we have to deal with many trees and/or great topographic variations. This system consists of a commercial GPR system with a laser positioning system. With this system, we can move the GPR antenna freely, on which a positioning detector can record accurate position for each GPR data trace. We applied our 3DGPR system at Dangoyama Kofun, a burial mound, in Fukushima prefecture, Japan. A lot of trees and bushes covered the survey area and cannot be cut. We acquired six datasets in two days in this area. We successfully imaged the boundary between the original surface of the burial mound and the covering soil clearly at about 0.3 m depth around the mound. Furthermore, we found some strong reflections appeared at 0.8 m depth in the top area of the mound, which can be from the artificial parts of the burial mound. The results would greatly aid the following archaeological excavation. In addition, we compared the non-interpolated depth slice with interpolated depth slice at same position and demonstrated that the interpolation process on threedimensional GPR data may introduce some artifacts which might mislead our interpretation.