Theoretical identification of forces resisting longitudinal movement of drillstrings in curved wells

Abstract

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...

Application of nonsmooth transformations to analyze a vibroimpact duffing system

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Stability of drillstrings in ultradeep wells: an integrated design model

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An asymptotic linear thin-walled rod model coupling twist and bending

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