The problem of a postbuckling dynamic behavior of weighted rod, which is inserted into an arbitrary profile hole with some clearance, under the axial compression load is considered. In practice, this analysis is important for calculation of the friction drag of the drillstring in inclined and horizontal wellbores. The mathematical model and numerical method of the rod-in-hole contact interaction are developed. The contact model is based on a nonlinear dependence of the normal-directed contact force on the depth of interpenetration of rod in hole. The tangential interaction of bodies with the contact surfaces is described using a model of “elastic-plastic” friction. The developed system of substantially nonlinear differential equations with partial derivatives of 3-D rod dynamics is approximated by the finite differences and integrated by the Runge-Kutta method. A simplified model for axial motion of rod is suggested to make the process of numerical integration faster. The results of numerical simulation of stress-deformed state of rod in horizontal, inclined and curved holes are presented. The results of numerical simulation are compared with the results of experiment. The effect of the friction factor on the rod buckling has been studied. The effect of local outside bulges of the drillstring on a postbuckling behavior of the drillstring is considered.

One of the most serious concerns of extended-reach drilling is the dynamic behavior of the drillstring and the cleaning of well. Good cleaning requires an increased angular velocity. This paper presents a 3D nonlinear dynamic model of drillstring in a wellbore of 3D profile. The model suggests possible contact/lift-off of drill pipes with/from the wellbore wall. The interaction of lateral, torsional, and axial vibrations is taken into account. The relation between the normal component of contact force and the deformation of the wellbore wall is taken as quadratic-elastic. The friction force is described based on a hysteretic dynamic model. The friction force model also takes into account, the transition from a sliding to whirling. The equations of drillstring dynamics are solved numerically using the method of lines. The DYNTUB software is developed to analyze the drillstring time-varying processes under different loads. The program is used to study the effects of angular velocity, compression load, torque, friction factor, well profile, and availability of connectors on the drillstring dynamic behavior. From the study follows the key conclusions: (1) The friction factor has a considerable effect on the drillstring rotational behavior in the wellbore; (2) no whirling of drillstring at real value of rolling friction factor in a horizontal well in the discussed examples could be seen at all; (3) when whirling takes place, the contact force shows a dramatic times increase; and (4) snaking can be seen in any wells at moderate compressive load and angular velocity.

A numerical solution is suggested for the problem of drillstring buckling under the action of compressive load, torque and drillstring rotation in a hole of an arbitrary axial line. This problem is of great practical importance when assessing the pass ability and wear of drillstring. The developed 3D dynamic model of drillstring-in-hole and numerical solution of the problem provide a means to analyze stress-deformed state of the drillstring in contact with the wellbore. The model of normal contact force is based on nonlinear dependence of the contact force on the depth of interpenetration of bodies. The tangential contact is described using a model of modified Coulomb friction. The model of transition of sliding friction to rolling friction is suggested to take account of the effect of drillstring planetary motion. The set of partial differential equations is solved numerically based on the method of lines. A number of examples are presented to analyze the drillstring motion under the action of compressive load, torque and angular velocity, and other parameters.

Significant part of axial compression load transferred to the bit while drilling of wells with high zenith angles is resisted by service drill pipes. By the action of static critical load, buckling of drillstring occurs initially in the shape of a sinusoid and subsequently, as the load increases, in the shape of a helix. Drillstring rotation promotes the occurrence of critical modes. As a result the drillstring can start snaking motion at the low side of the hole. When the rotary speed grows, whirling of the drillstring can occur with axial load much lower than the buckling load. In this paper, a nonlinear mathematical model of lateral vibrations of a rotating drillstring in straitened space of a straight inclined hole is proposed. A numerical method to solve drillstring motion equations has been developed that allowed to reduce time of computation. This made it possible to conduct a detailed study of how the main drilling parameters (compression load, drillstring rotary speed, hole angle, friction factor, etc.) effect drillstring motion in the well. Results of the study may be used to choose drillstring operation modes for rotary drilling of inclined and horizontal wells.

One of the most topical problems of drilling mechanics is development of a software program for 3D string dynamic simulation in a 3D well on various operation regimes with maximum account of all external factors. The paper describes the results of long-term development of general-purpose DYNTUB software designed for string dynamic simulation. The software calculates: String torque and drag;Drillstring lateral and torsional vibrations;Drillstring buckling and whirling;Well path while drilling in sliding regime and in rotary regime with Rotary Steerable Systems (RSS) or systems controlled by downhole motor angular velocity modulation;Standoffs between the casing and the wellbore wall with various centralizers. The software is based on the stiff string dynamic model. It accounts for deformation of the wellbore walls contacted by the string, initial drill pipe bending, PDC bit interaction with the bottomhole under downhole and pore pressure, rock anisotropy, refined multicomponent string friction model, etc. The software proved applicability of the "soft" drill string model to calculate torque and drag, enabled study of multicomponent friction effects on string buckling, well path calculation while RSS drilling, and solving other complex problems of drilling mechanics. Software efficiency is demonstrated based on case studies; the paper also includes results of comparative analysis using data from other references. The software is designed for expert analysis of drilling, casing, coil tubing and similar object parameters while well drilling and completion.