a b s t r a c tThe problem about identification of resistance forces acting on a drill column moving in an inclined borehole is stated. It is supposed that the well trajectories can have geometrical imperfections in the shape of cylindrical spiral or plane cosinusoidal curves. The system of ordinary differential equations is derived on the basis of the theory of curvilinear flexible elastic rods. It permits one to describe static effects of the drill column bending accompanying the processes of its raising, lowering and rotating inside the borehole. Through the use of this system the direct and inverse problems of the drill column deforming are formulated for calculation of internal and external resistance forces acting on the drill column tube. The methods for numerical solution of the constructed equations are elaborated. With their use the phenomena of the drill columns motion and their frictional seizure inside the bore-holes are simulated for different geometrical imperfections and relations between the velocities and directions of their rotation and axial motion.
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...
ACTING UPON CURVILINEAR DRILL STRINGS V. I. Gulyaev, a V. V. Gaidaichuk, b I. L. Solov'ev, a UDC 539.3:622.24 and L. V. Glovach aOn the basis of the statement and solution of direct and inverse problems of statics of flexible curvilinear rods, we study the stress-strain state of drill strings for deep drilling in a curvilinear well with given geometric parameters. We deduce the resolving equations aimed at the evaluation of the internal forces and moments in a drill string, the forces of contact interaction, and the friction forces between the wall of the well and the drill string in the processes of its lifting, lowering, and rotation. A procedure for the solution of these equations is proposed. An example is presented for a drill string of curvilinear shape.Keywords: curvilinear drill strings, internal forces, friction forces, moment of friction forces, direct and inverse problems.Introduction. The development of the technology of drilling of oil and gas wells of complex space orientation is one of the most important engineering problems connected with the elevation of the efficiency of extraction of mineral fuels. Since the output of curvilinear wells is higher than the output of vertical wells by an order of magnitude, the problem of drilling of curvilinear wells of complex shape should become principal in the nearest future both for the Ukraine and for many other countries [1]. In practice, the implementation of the technology of drilling of wells with complex space orientation requires the application of both the procedures of mathematical simulation (to design their paths) and the contemporary equipment and technologies of drilling. In this case, the problems of determination of external and internal forces acting upon a drill string (DS) in a curvilinear well in the processes of its lowering, lifting, and operation are of significant interest. Since the contour of the axial line of the DS in the drilled well is given, the functions of the acting bending moments and shear forces can be regarded as known. Thus, to determine the internal longitudinal forces and torques in the curvilinear DS, one can pose the direct problem of statics of a curvilinear rod and compute the forces of contact interaction between the drill string and the wall of the well as a result of the solution of the inverse problem.In the practice of designing of curvilinear wells, it is customary to use the method of minimum curvature. Its basic idea is based on the representation of the path of the well in the form of a family of smoothly conjugated circular arcs and segments of straight lines [1,2]. The points of conjugation and the planes of orientation are specified according to the condition of attainment of the prescribed geological purposes. In [3], it is shown that the rectilinear segments of the axial line of the well are connected by catenary lines. The possibility of designing of oil and gas wells in the form of circles of catenary lines, brachistochrones, Cornu spirals, clothoids, etc. is discussed in [4,6]. In the cited works, ...
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