TY - GEN
T1 - Eulerian formulation of a drillstring constrained inside a curved borehole
AU - Denoël, Vincent
AU - Detournay, Emmanuel
PY - 2011
Y1 - 2011
N2 - We address the problem of computing the deformed configuration of a drillstring, constrained to deform inside a curved borehole. This problem is encountered in applications such as torque-and-drag and directional drilling. In contrast to the traditional Lagrangian approach, the deformed drillstring is described by means of the distance from the borehole axis, in terms of the curvilinear coordinate defined along the borehole. This model is further implemented within a segmentation algorithm where the borehole and the drillstring are divided into segments limited by contacts, which interestingly transforms the problem into a sequence of analogous auxiliary problems. This Eulerian view of the drillstring flow into the borehole 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) 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 drillstring and/or decreasing clearance between the drillstring and the borehole. Theoretical developments related to this Eulerian formulation of the drillstring are presented, along with an example illustrating the advantages of this approach.
AB - We address the problem of computing the deformed configuration of a drillstring, constrained to deform inside a curved borehole. This problem is encountered in applications such as torque-and-drag and directional drilling. In contrast to the traditional Lagrangian approach, the deformed drillstring is described by means of the distance from the borehole axis, in terms of the curvilinear coordinate defined along the borehole. This model is further implemented within a segmentation algorithm where the borehole and the drillstring are divided into segments limited by contacts, which interestingly transforms the problem into a sequence of analogous auxiliary problems. This Eulerian view of the drillstring flow into the borehole 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) 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 drillstring and/or decreasing clearance between the drillstring and the borehole. Theoretical developments related to this Eulerian formulation of the drillstring are presented, along with an example illustrating the advantages of this approach.
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U2 - 10.1109/CCA.2011.6044413
DO - 10.1109/CCA.2011.6044413
M3 - Conference contribution
AN - SCOPUS:80155199665
SN - 9781457710629
T3 - Proceedings of the IEEE International Conference on Control Applications
SP - 899
EP - 904
BT - 2011 IEEE International Conference on Control Applications, CCA 2011
T2 - 2011 20th IEEE International Conference on Control Applications, CCA 2011
Y2 - 28 September 2011 through 30 September 2011
ER -