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The equations of balance of external and internal forces acting on a drillstring in a curved well are set up based on the formulations of direct and inverse problems in the mechanics of flexible curvilinear rods. The lowering, lifting, and rotation of a drillstring are studied. A method is proposed to calculate the internal longitudinal force, the forces of interaction between the drillstring and the well wall, and the forces of friction. An example is considered. It is shown that even small geometrical imperfections of the well path have a significant effect on the balance of external and internal forces Keywords: curvilinear drillstring, force of friction, direct problem, inverse problem Introduction. Today, approximately 95% of all the energy consumed by mankind is accounted for by fossil hydrocarbon fuels of which oil and gas are the major ones. Under normal conditions, only 35% of these fuels filling underground cracks and pores can be extracted with traditional production technology [12]. One of the ways to increase fuel production is to drill curved wells that would penetrate oil-and gas-bearing strata along their stratified structure, thus covering large areas of fuel extraction [3,5]. Since such a technology allows reducing the total number of wells, and the production rate of curved wells appears an order of magnitude higher than that of vertical wells, in the near future most countries will prioritize drilling of complex-shaped wells.However, such a technology can be introduced into practice only after mathematical design of optimal well paths and only with modern drilling equipment. Of particular interest is to determine the external and internal forces and the torques acting on the drillstring in a curved well during lowering, lifting, and rotation. Modeling the forces of resistance and dynamic phenomena accompanying the drilling process would allow resolving fundamental issues such as obtaining a well of necessary shape, suppression of longitudinal and transverse vibrations of the drillstring, and reduction of contact forces and frictional interaction between the drillstring and the well wall. All of this would reduce the wear of drillstrings and their joints and prevent unplanned curving of the well's axial line, which, in turn, prevents severe accidents during drilling.One of the widely known methods to design curved wells is the minimum-curvature method. It represents a well path as a series of smoothly joined circular arcs and straight-line segments. Their junction points and orientation planes are defined so as to achieve a set geological objective [15]. In [8,16], rectilinear segments of a well's axial line are connected with catenaries. Oil and gas wells in the form of a catenary, a Cornu spiral, a clothoid, etc. are discussed in [1,6]. The conclusions on the advantages of one well shape or another are drawn after calculation of forces of friction and internal forces using the theory of a perfectly flexible filament that models a drillstring [10]. Indeed, by its geometry the drillstring in we...

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539.3: 622.24 and O. V. GlushakovaWe address a problem of self-excitation of elastic torsional vibrations of a rotating drill string due to frictional interaction between the drill bit and rock at the deep well bottom. Using the d'Alembert solution to a wave equation, a mathematical model is constructed for a wave torsional pendulum in the form of a nonlinear ordinary differential equation with delayed argument. Special features of generation of self-excited vibrations of drill strings have been determined through computer simulation.Introduction. Rotary drilling is the most widely accepted method for producing oil and gas wells; it involves rock destruction at the well bottom by means of a drill bit attached to the lower end of the drill string (DS) to which rotation is imparted through the torque applied to the DS top end. In the course of drilling, a drill string experiences a number of mechanical actions the most significant of which are the longitudinally nonuniform DS tension force, torque, centrifugal and compound centrifugal forces induced by the drilling fluid flow inside DS, forces of frictional interaction between the DS and the formation, etc. The factors listed above initiate longitudinal, torsional, and bending vibrations in the string and contribute to its flexural buckling. This may cause a stuck DS, wellbore wall falling in, and overall instability of the system [1-5]. One of the dynamic phenomena that may eventually lead to an emergency occurrence in drilling is the self-excitation of torsional vibration of a rotating DS. Since a DS is a torsional pendulum, where an outflow of energy from the drive to environment occurs at the DS bottom part due to energy-dissipative interaction between the drill bit and the formation, the string may pass from the steady equilibrium rotation to torsional self-excited vibration when the conditions of this energy outflow are upset. To study this phenomena we will use here a wave model of a torsional pendulum, which allows for the effects of the finite-velocity propagation of torsional strains along the DS.Special Features of Processes of Self-Excitation of Torsional Vibration in Long Drill Strings. The effects of self-excitation vibration fundamentally differ from other types of vibration processes in dissipative systems in that no periodic external action is needed for their excitation [6,7]. If a mechanical system's transition from some initial state to self-excited vibration conditions occurs without any addition "push," this is a soft self-excitation. If a vibration starts increasing spontaneously only from some limiting amplitude, this is called the hard self-excitation. To periodic self-excited vibration there corresponds a closed loop path in the phase space, which all neighbor paths tend to; this path has been named the stable limit cycle or the attractor [8].With regard to the phenomena that accompany the DS rotation, a study of generation of the DS self-excited torsional vibration enables one to answer three important questions: (i) at what values of the...

539.3:622.24 and E. I. BorshchThe paper is focused on a problem of flexural vibrations of a rotating drillstring bottom hole assembly under the action of the friction (cutting) moment. The mechanism of self-excitation of the vibrations has been analyzed. The induced moment is shown to be nonconservative and represents the main source of dynamic instability of the system. The flexural mode shapes of the drillstring bottom hole assembly motion have been plotted for various values of the characteristic parameters.