Dynamic Model for Stiff-String Torque and Drag
Authors: Tikhonov Vadim , Valiullin Khaydar , Nurgaleev Albert , Ring Lev , Gandikota Raju , Chaguine Pavel , Cheatham Curtis 
Published: September 2014

A dynamic stiff-string torque-and-drag (T&D) model is presented that assumes steady-state motion of the drillstring as its basis for calculations. Results are compared with previously published T&D models that are based on static equilibrium. The novelty of the new dynamic model is the ability to solve T&D operations of the entire drillstring from bit to topdrive in reasonable time by use of standard engineering computers.

The new approach is modeled after a 3D dynamic model of drillstring and bottomhole assembly in an elastic borehole. It considers bending stiffness, torsional stiffness, contact forces, and friction with localization of contact points. A numerical method is described that has proved to have excellent convergence. Complete governing equations are provided, and the method is described in detail to permit readers to replicate results.

The dynamic model is compared with two static stiff-string models. Comparisons are also provided for three conventional soft-string models, including the Lubinski-Paslay-Cernocky bending-stress-magnification factor. Four field case studies are presented for horizontal wells. One well is short radius with dogleg severity greater than 50°/100 ft, and three wells are unconventional shale wells with doglegs up to 15°/100 ft. Predictions for surface T&D up/down for the new dynamic stiff-string model are compared with the static stiff- and soft-string models. In many situations modeled, the top-level results for surface T&D up/down are close enough for all six models to be within the uncertainty range associated with the commonly used, lumped-parameter friction factor. However, some major differences in hookload for sliding and slackoff operations are observed, which are shown to be caused by differences in location and magnitude of contact force between the drillstring and wellbore. Further, significantly lower surface torque is predicted by the new dynamic stiff-string model compared with other models for one case history because of lower contact forces in the vertical section of the well. In fact, the key finding of this paper is that major differences are observed for contact forces for the new dynamic stiff-string model compared with all five other models, including the two static stiff-string models. These differences in contact forces are most significant when the drillstring has helically buckled or when doglegs in the wellbore are high. Contact forces have a large impact on local stress behavior, which is important for predictions of casing and drillpipe wear, drillstring fatigue, and failure points in the drillstring.

Although several previous papers have published stiff-string models, there is no industry-standard formulation. The main problem holding back the development of an industry-standard stiff-string model is perhaps the complexity of the numerical algorithm and substantial running time. To address this problem, some previous stiff-string models account for bending stiffness of the drillstring but not for radial clearance, whereas others appear to model only portions of the drillstring as stiff. The new stiff-string model accounts for bending stiffness and radial clearance for the entire drillstring while still giving reasonable computational times. For stiff-string models, the advantage of the use of a dynamic approach to solve the steady-state position of the drillstring is mainly related to superior convergence of the numerical algorithm compared with static stiff-string models because the calculation of contact points is faster.