Computer simulation of resistance forces acting upon curvilinear drill strings

Abstract

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, ...

Elastic Bending Deformation of the Drill Strings in Channels of Curve Wells

“…The general formulations of direct and inverse problems of deformation of the curved rods were presented in [9] [10] [11]. The applied aspects of this problem were considered in [12] [13].…”

Computer Simulation of the Least Energy Consuming and Emergency-Free Regimes of Drilling of Hyper Deep Curvilinear Bore-Holes

“…Its pitch k / 2π λ = is determined by the wave number k and is considered to be constant (Fig.2) (23) With the aid of these correlations, one can determine geometrical factors (2)−(4), (21) used in constitutive Eqs. (15) together with equalities (11)− (14). In the general case, the simulated imperfections can be localized at several places c S s = of the bore-hole axis and have different parameters c h and α .…”

“…Often, their drivage is accompanied by emergency situations and failures. Amidst them, there are -loss of the bending stability of the drill string under action of gravity forces, torque, inertia forces of rotary motion, etc [1,6,9,10,13,15,17,20]; -self-excitation of torsion autovibration of the drill bit accompanied by alternation of its fast and slow motions [2,4,7,8,11,19,22]; -generation of whirling vibration of the bit connected with instability of the whole system and transition of the bit motion from the regime of pure spinning to its rolling on the bore-hole bottom [5,18,21]; -locking up and sticking of the drill strings in the zones of the bore-holes with enlarged contact and friction forces [3,12,14,16,23]. But the drivage of curvilinear bore-holes is fraught with great technological difficulties caused by permanent balance change of the forces of gravity, resistance (friction), inertia, and elasticity acting on the drill string and its bit.…”

Sensitivity of drill string drag forces to geometrical imperfections of curvilinear well bore trajectory

“…One of the important aspects of these efforts is to simulate the deep drill string (DS) behavior in curvilinear well bores at the running and pulling stages. Considering that the cost of well bore laying-out, in view of increasing well depth and distance, has already exceeded US$ 50 million [3] and, according to statistics, one in three wells experiences an accident [4], it becomes clear how important the problem of theoretical prediction of DS critical states is and how much a mistake in such predictions would cost.In our earlier publications, we addressed the stability of a deep-well vertical drill string [5], the problem of self-excitation of torsional oscillations [6], defined and solved the problem of initiation of critical states in directional wells [7,8]. In the present work, we have set and solved the problem of elastic bending of a drill string in a curvilinear well bore with geometrical imperfections.…”

“…In our earlier publications, we addressed the stability of a deep-well vertical drill string [5], the problem of self-excitation of torsional oscillations [6], defined and solved the problem of initiation of critical states in directional wells [7,8]. In the present work, we have set and solved the problem of elastic bending of a drill string in a curvilinear well bore with geometrical imperfections.…”