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The problem about identification of elastic bending deformation of a drill string in a curve wells based on the theory of flexible curved rods and the direct inverse problems of drill string bending in the channels of curvilinear bore-holes is stated. The problem is solved which determines the resistance forces and moments during performing ascending-descending operations in curvilinear bore-holes with trajectories of the second order curve shapes. The sensitivity of the resistance forces relative to geometric parameters of the bore-hole axial line trajectories is analyzed.

Currently the time of easy oil and natural gas is completed [

However, the practical implementation of the technology of drilling such wells is associated with the necessity of theoretical modelling of mechanical phenomena that occur in the construction of drilling equipment in order to prevent the critical and emergency operation modes. Meanwhile the greatest interest is focused on determination of contact and friction forces, as well as the full resistance force acting on the drill string (DS) in a curved borehole during its descent, ascent and operation.

However, in the structural mechanics of curved rods, the methods of theoretical modelling of these phenomena are not developed yet. This state of matter is associated with significant complexity of these processes caused by the great length of the drill string (DS) and conditions of contact interaction with the walls of curved holes.

Given that the current depth of the wells is 9 to 10 km, the range of their routing is over 12 km, more than USD 50 million worth, and every third hole is in emergency condition, so it can be noted that the problem of theoretical modelling of the tube boring columns bending mechanics in channels of deep curved holes in view of their contact interaction is very important. In this paper, for theoretical modelling of elastic bending deformation of the DS in a curved borehole the classical theory of flexible curved rods is used [

Many researches and papers deal with this issue, A. Abdul-Ameer, 2012, the unsupported deflection of drill strings which are subjected to increasing gravitational loading and distortion is discussed here, taking into account borehole depth and twisting. Also eccentric loading configurations which include the lateral reaction to mud flow pressure, compression, bending forces and twisting moments are taking into account too. Also in this study the bending-buckling deflections and twist angle dynamics following drill string drive motor voltage changes are discussed. At specified cutting velocities the principal stress level is identified [

V. I. Gulyayev, et al. (2013) discussed the computer simulation behaviour of drill strings in hyper deep vertical, inclined and horizontal wells. Stability and post-critical non-linear deforming of the drill strings are considered. It is found that all of these parameters are singularly perturbed from the mathematical point of view and because of this; such parameters are poorly amenable to theoretical analysis. The software used in this study of these phenomena is elaborated. Such elaborated software permits one to construct its trajectory securing the smallest values of resistance forces and to choose the least energy-consuming and safe regimes of drilling [

Nabil W. Musa, et al. (2015) discussed the problem of simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. It was showed that the problem on rolling of a rigid ellipsoidal drill bit on a bore-hole bottom plane, the bit is supposed to be attached to the lower end of an elastic rotating drill string. In this study two mechanical models of the bit motions based on assumption of the possibilities of its pure rolling whirling and rolling with sliding are discussed. The paper discussed the analogy between the phenomena of nonholonomic motions of the Celtic stones and the ellipsoidal bits. Also techniques of solution of the equations of the bit whirling were proposed [

The critical buckling of drill strings in cylindrical cavities of inclined bore- holes was been discussed by Nabil W. Musa, et al. (2016) [

The general formulations of direct and inverse problems of deformation of the curved rods were presented in [

In practice, the DS descent and ascent are usually performed by simultaneous provision of two types of movement to the column, axial and rotational. Using such technology of the descent-ascent operations one can achieve a favourable redistribution of axial and circular friction contact forces between the DS surface and well wall, upon which the whole selected operation will be less energy- intensive and, and the axial force at the top of the DS performing this procedure will be reduced significantly. The problem of quasi-static modelling of the drill strings during the descent-ascent operations with concomitant rotation depends on the contour of its axial line.

If the axial line of the well is preset by the equalities

where

The curvature and torsion options of this curve can be presented as:

(2)

Here

Let’s assume that in the initial state the axial line of the well is straight and

where

In deriving Equations (3) it was taken into account that for the tubular drill string

The components of these forces are obtained by projecting the left and right sides of Equation (4) on axes

where the gravitational forces are calculated as follows

(6)

Here γ is the string mass per unit length; g = 9.82 m/s^{2}, while

After introduction of designations

of relevant transformations we bring system (3) to the following form

(7)

(8)

where

Using the developed approach the influence of the type of well axial line outlines on the value of static parameters of the deformed DS status upon descent-ascent operations. The case when the coordinates of the start and end points of the well coincide, and its axial line is located in the vertical plane passing through these points was considered. The simplest laws of their geometry (

The start and end points of all these curves coincide, however, between these points the mentioned curves have a shape with different curvature. A characteristic feature of the ellipse arc (curve 1) is that the tangents to it at points

and

Above it was assumed that the parameter affecting the critical state of DS in the performance of descent-ascent operations is a function of the curvature of the axial line of the channel well within small values

R is calculated by using the equation:

It shows that upon transfer from an elliptic curve to a hyperbolic one the

Based on the theory of flexible curved rods, the direct and inverse problems of bending deformation of the drill strings in the channels of curve wells are formulated. The problems of determination of the resistance forces and their momentums during the descent-ascent operations in the curved wells with trajectories

Curve type | |||
---|---|---|---|

1 | Ellipse | 500 | 32,000 |

2 | Parabola | 250 | 131,012 |

3 | Hyperbola (e = 0.01) | 170 | 289,586 |

4 | Hyperbola (e = 0.015) | 129 | 504,969 |

in the form of curves of the second order are solved. The investigation of sensitivity of the resistance forces acting on the drill string during the descent-ascent operations with respect to geometric parameters of the trajectory of the well axial line was carried out.

The Author would like to express his sincere gratitude to the University of Philadelphia represented by the faculty of Engineering and the Deanship of scientific research and higher education for their support.

Musa, N.W. (2017) Elastic Bending Deformation of the Drill Strings in Channels of Curve Wells. Modern Mechanical Engineering, 7, 1-7. https://doi.org/10.4236/mme.2017.71001