RU2135730C1 - Process of borehole drilling - Google Patents

Abstract

FIELD: gas and oil production, drilling of vertical and inclined boreholes. SUBSTANCE: in accordance with invention rock breaking tool is rotated relative to face of borehole with speed ω, axial force on rock-breaking tool is fixed, speed ω is varied till its nonresonance value determined from solution of linear differential equation of fourth order with regard to sagging of arrangement of bottom part of drill pipe string with which lateral force acting on drill bit does not exceed deviation of drill bit on face is established. After this deviation of drilling of borehole from previous value is corrected by increase or decrease of axial force with preservation of drilling azimuth. Usage of invention ensures reduction of amplitude of lateral vibrations of bottom part of drill pipe string and 12% increase on the average of speed of drilling of borehole. EFFECT: reduced amplitude of lateral vibrations of bottom part of drill pipe string and increased speed of drilling. 2 dwg, 1 tbl

Description

 The invention relates to the field of well drilling and can be used for sinking vertical and deviated wells.

A well-known method of drilling a well (Mitchell RF, Allen MB "Study of transverse vibrations of the heavy bottom of the drill string", World Oil, 1985, N 4, p. 101), including the solution of a system of linear equations in a selected frequency range, given to mind
([K] + [M] ω ² ) {u} = {f},
where K is the stiffness matrix;
M is the mass matrix;
ω is the frequency of changes in forces and solutions;
u is the magnitude of the displacement vector;
f is the magnitude of the force
determination of the critical resonant rotational speed of the drill string and the rotation of the rock cutting tool relative to the bottom of the well in the region of non-resonant frequencies.

где n - частота вращения ротора, при которой подавляются резонансные явления в бурильной колонне и достигается максимум механической скорости проходки, 1/с;
ω - собственная частота вращения вала забойного двигателя, 1/с;
k - количество шарошек в долоте;
b = 2k^m - гармонический коэффициент, где m - номер гармоники.Coincide with the essential features of the proposed method, the rotation of the rock cutting tool relative to the bottom of the well in the field of non-resonant frequencies. A known method of drilling a well (a.s. N 1441047, E 21 B 7/00), selected as a prototype, comprising rotating a rock cutting tool relative to the bottom of the well in the region of non-resonant frequencies, the rotational speed in the bit-downhole motor-drill string system being determined from the relation

where n is the rotor speed at which the resonance phenomena in the drill string are suppressed and the maximum mechanical penetration speed is reached, 1 / s;
ω is the natural frequency of rotation of the shaft of the downhole motor, 1 / s;
k is the number of cones in the bit;
b = 2k ^m is the harmonic coefficient, where m is the number of harmonics.

 Using the known method does not effectively reduce the amplitude of transverse vibrations, because the experimentally obtained dependence of the antiresonance frequency in the prototype has a large error due to the insignificant number of drilling process parameters taken into account, which affect the accuracy of determining the desired rotor speed. For example, they did not take into account: the axial force on the rock cutting tool, the weight of the drill string, the zenith angle of the well, and the density of the drilling fluid.

 The task is to improve the method of drilling a well, in which by optimizing the parameters of the drilling process, including the axial force on the rock cutting tool and the rotational speed of the rock cutting tool, it is possible to increase the efficiency of reducing the amplitude of transverse vibrations of the bottom of the drill string and thereby increase the rate of well penetration.

где E - модуль Юнга, Н/м²;
I(x) - осевой момент инерции сечения бурильных труб, м⁴;
x - координата, отсчитываемая от нижней точки на компоновке низа бурильной колонны, м;
w - прогиб буровой колонны в сечении с коррдинатой x, м;
P - осевая сила на долоте, Н;
q(x) - вес единицы длины бурильной колонны в буровом растворе, Н/м;
α - зенитный угол скважины, град;
ω - частота поперечных колебаний буровой колонны, равная произведению скорости вращения бурового инструмента на число возмущений, поперечных оси компоновки, за один оборот с коэффициентом 2π, 1/с;
γ - плотность материала бурильных труб, кг/м³;
ρ - плотность бурового раствора, кг/м³;
S(x) - площадь поперечного сечения колонны, м²,
с граничными условиями

где w₀ - амплитуда прогиба колонны на забое скважины, м;

в первой от забоя скважины точке касания колонны к стенке скважины при
Δ(x) = 0,5(d_c-d_к),
где d_с - диаметр скважины, м;
d_к - диаметр колонны в точке касания, м;

в местах расстановки x_i центраторов при
δ_i= 0,5(d_c-d_ц),
где i = 1, 2,..., N;
N - количество центраторов;
d_ц - диаметр центратора, м;

где j = 1, 2,...k;
x_j - расстояние от забоя скважины до места соединения бурильных труб различного диаметра, м;
k - число соединений бурильных труб различного диаметра,
путем варьирования величины ω до значения, при котором поперечная сила на долоте

и угол его наклона

меньше их заданных значений и амплитуда w_max на интервале [x_i, x_i+1] не превышает отклонения долота w(0) на забое, после чего выполняют коррекцию отклонения направления проходки скважины от предшествующего значения увеличением или уменьшением осевой силы при сохранении азимута проходки.This problem is solved in that in a method of drilling a well, comprising rotating the rock cutting tool relative to the bottom of the well in the region of non-resonant frequencies, according to the invention, the axial force on the rock cutting tool is fixed, for example, by installing weighted drill pipes, the rotational speed of the rock cutting tool relative to the bottom of the well is determined from the linear solution fourth order differential equation

where E is Young's modulus, N / m ² ;
I (x) - axial moment of inertia of the section of the drill pipe, m ⁴ ;
x is the coordinate counted from the bottom point on the layout of the bottom of the drill string, m;
w is the deflection of the drill string in cross section with coordinate x, m;
P - axial force on the bit, N;
q (x) is the weight per unit length of the drill string in the drilling fluid, N / m;
α is the zenith angle of the well, deg;
ω is the frequency of transverse vibrations of the drill string, equal to the product of the rotational speed of the drilling tool by the number of perturbations transverse to the layout axis, per revolution with a coefficient of 2π, 1 / s;
γ is the density of the material of the drill pipe, kg / m ³ ;
ρ is the density of the drilling fluid, kg / m ³ ;
S (x) is the cross-sectional area of the column, m ² ,
with boundary conditions

where w ₀ - the amplitude of the deflection of the column at the bottom of the well, m;

at the first point from the bottom of the well touching the column to the wall of the well at
Δ (x) = 0.5 (d _c -d _k ),
where d _with - the diameter of the well, m;
d _to - the diameter of the column at the point of contact, m;

in places of arrangement x _{i of} centralizers at
δ _i = 0.5 (d _c -d _c ),
where i = 1, 2, ..., N;
N is the number of centralizers;
d _c - centralizer diameter, m;

where j = 1, 2, ... k;
x _j is the distance from the bottom of the well to the junction of drill pipes of various diameters, m;
k is the number of connections of drill pipes of various diameters,
by varying the value of ω to a value at which the transverse force on the bit

and its angle

less than their specified values and the amplitude w _max in the interval [x _i , x _{i + 1} ] does not exceed the deviation of the bit w (0) at the bottom, and then the deviation of the direction of the penetration from the previous value is corrected by increasing or decreasing the axial force while maintaining the azimuth of penetration .

 The combination of the above essential features of the proposed method provides a solution to the problem, increasing the efficiency of reducing the amplitude of the transverse vibrations of the bottom of the drill string and thereby increasing the speed of penetration of the well.

 In FIG. 1 is a schematic layout of the bottom of a drill string.

 In FIG. 2 shows graphs of the amplitude of the deflections of the drill string.

 The implementation of the proposed method is illustrated using the layout of the bottom of the drill string, which includes a rock cutting tool in the form of a cone bit 1, drill pipes 2 and N centralizers 3 installed along its axis.

 The work of the layout of the bottom of the drill string is as follows.

The arrangement is lowered into the well, the drilling fluid is supplied and rotated. The number of perturbations transverse to the layout axis, for one revolution in the face of a three-cone bit, is n = 3. Solve the equation, substituting the necessary data, example 2 of the table, obtain the frequency of transverse vibrations of the drill string ω and the frequency of rotation of the bit f. The obtained calculated ratio of the amplitude of the deflections of the layout of the bottom of the drill string w (x) to the amplitude of the oscillations of the bit w ₀ in Example 2, illustrating the proposed method, is shown, as can be seen from FIG. 2, that the bottom of the drill string rotates without touching the borehole wall at a distance of up to 40 m from the bottom, curve 1, and in example 1, where the f value is 2 times less, the drilling process is complicated by overcoming the friction forces in this section, curve 2. When the first extremes of the deviations w (x) / w ₀ from the bottom are in example 1 equal to 1; 0.8; 2.5; 2.4, and in example 2 - 1; 0.8; 0.35; 0.3; 0.04. The deviation of the direction of the well sinking from the previous direction is corrected in the conditions of variation specified for solving the equation, controlling w (x) / w ₀ ≤ 1 according to the schedule constructed in accordance with the changed axial load. In example 2, such a correction was carried out within not more than 04 kN of additional axial force.

Examples 3 and 4 are shown for an deviated well, the first extrema from the bottom of the extrema of the deviation relations w (x) / w ₀ in Example 3, curve 3, are 1; 1; 2.9; 7.3, in example 4, curve 4 illustrating the proposed method, -1; 0.39; 0.23; 0.21. The correction of the deviation of the direction of the penetration of the well in example 4 was carried out within not more than 0.35 kN of additional axial force.

 Using the proposed method improves the energy supply to the bit, the destruction of rocks, and also stabilizes the deflecting force on the bit and its angle of inclination both during turbine and rotary drilling of wells.

 The penetration rate is increased by an average of 12%.

Claims (1)

A method of drilling a well, comprising rotating the rock cutting tool relative to the bottom of the well in the non-resonant frequency region, characterized in that the axial force on the rock cutting tool is fixed, the rotation of the rock cutting tool relative to the bottom of the well is produced with a frequency that is determined from the solution of the fourth-order linear differential equation

where E is Young's modulus, N / m ² ;
I (x) - axial moment of inertia of the section of the drill pipe, m ⁴ ;
x is the coordinate measured from the bottom point on the layout of the bottom of the drill string, m;
w is the deflection of the drill string in cross section with the coordinate x, m;
P - axial force on the bit, N;
q (x) is the weight per unit length of the drill string in the drilling fluid, N / m;
α is the zenith angle of the well, deg;
ω is the frequency of transverse vibrations of the drill string, equal to the product of the rotational speed of the drilling tool by the number of perturbations transverse to the layout axis, one revolution with a coefficient of 2π, 1 / s;
γ is the density of the material of the drill pipe, kg / m ³ ;
ρ is the density of the drilling fluid, kg / m ³ ;
S (x) is the cross-sectional area of the column, m ² , with boundary conditions
1)

at x = 0,
where w ₀ - the amplitude of the deflection of the column at the bottom of the well;
2)

at the first point from the bottom of the well touching the column to the wall of the well at
Δ (x) = 0.5 (d _c -d _k ),
where d _c is the diameter of the well, m;
d _to - the diameter of the column at the point of contact, m;
3)

in places of arrangement x _{i of} centralizers at
δ _i = 0.5 (d _c -d _c ),
where i = 1, 2, ..., N;
N is the number of centralizers;
d _c - centralizer diameter, m;
4)

where J = 1, 2, ... k;
X _J is the distance from the bottom of the well to the junction of drill pipes of various diameters, m;
k is the number of connections of drill pipes of various diameters,
by varying x _i until the conditions under which
W _max ⁽ⁱ⁾ ≤ W (o) and W _max ^{(i + 1)} ≤ W _max ⁽ⁱ⁾ ,
where W _max ^{(i + 1)} is the maximum value of the amplitude in the interval [x _i , x _{i + 1} ] for the lateral forces specified at x = 0

and inclination

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