RU2006560C1 - Method of control of well shaft trajectory (its variants ) - Google Patents

Abstract

FIELD: drilling pinpoint wells. SUBSTANCE: method of control of well shaft trajectory involves superposition of longitudinal oscillations whose frequency is equal to rotation speed. With employment of axial-symmetrical tool one of rock-destruction members is dulled or substituted by bearing member. Curvature of well shaft is controlled in accordance with dependence given in invention formula. When two-step rock-destruction tool is used curvature is in addition to it is controlled by means of changing axial distance between tool steps or by means of changing of angle between rock-destruction and dull members of tool. To enhance intensity of zenith curvature amplitude-modulated longitudinal oscillations are imparted to tool, their carrier frequency is selected to be equal to frequency of its rapid transverse automatic oscillations, and bending frequency is to be equal to speed of the tool rotation. In this case the process of zenith curving is controlled by means of changing bending frequency phase and curving intensity is controlled by means of changing of phase of carrier oscillations. EFFECT: enhanced accuracy. 4 cl, 17 dwg

Description

 The invention relates to the field of drilling directional wells.

 A known method of controlling the trajectory of a wellbore, comprising superimposing longitudinal vibrations on a tool with a frequency equal to the rotational speed, and controlling the curvature and direction of the wellbore.

 Since an asymmetric tool is used in the known technical solution, the cutting properties of the blades of this tool are approximately the same, and the geometric axial symmetry is broken: there is a non-zero axial distance between the tops of the cutting edges, the main angles in plan are different, i.e., the angles of inclination of the cutting edges relative to the axis tool.

 The intensity of curvature of the wellbore trajectory with such an instrument is very weak. Such tools are successfully used for straight drilling of wells.

 In connection with the foregoing, a known method for controlling the wellbore trajectory does not allow for a sufficiently high intensity of anti-aircraft curvature of the wellbore.

 The aim of the invention is to eliminate this drawback and to enable a sharp increase in the intensity of curvature.

] , где Δ S - амплитуда продольных колебаний инструмента;
Y_с - величина зенитного смещения;
S - средняя величина подачи на оборот инструмента;
l - общая длина проходки участка искривления, причем
K=

где φ - угол наклона режущей кромки и оси инструмента;
D - диаметр инструмента;
L - расстояние от режущей части до полюса поворота.This goal is achieved by the fact that for a tool on which longitudinal vibrations are superimposed with a frequency equal to its rotation frequency, at least one of the rock cutting elements is blunted or replaced with a supporting element, and the curvature of the wellbore is controlled in accordance with the dependence
Y _c = Δ ^S. k [

], where Δ S is the amplitude of the longitudinal vibrations of the tool;
Y _with - the value of the zenith shift;
S is the average value of the feed per revolution of the tool;
l is the total length of the penetration of the curvature, and
K =

where φ is the angle of inclination of the cutting edge and the axis of the tool;
D is the diameter of the tool;
L is the distance from the cutting part to the rotation pole.

 For example, use a drill cutter, one of the blades of which is blunt (Fig. 1.1), or a cone bit, in which one or two cones are replaced with smooth rollers (Fig. 2, 3). Longitudinal vibrations with a frequency equal to the rotation frequency are created due to the skew of the rotation drive bearing (Fig. 4).

We assume that the skew of the rotation drive bearing leads to the following law of the periodic change in the feed per revolution of the tool
S = S _o + ΔS sin (Ψ - Ψ _o ), where Ψ _o is an arbitrary angle of phase shift.

 To clarify the essence of the proposed method, we consider some mathematical models of drilling processes with tools of various types. Let us first assume that the dissymmetry of the rock-destroying properties of the elements of the drilling tool is so significant that the drilling process is dynamically stable, i.e., it does not arise fast transverse self-oscillations, and the inertial forces can be neglected.

First, consider two-element tools, for example, a drill cutter (Fig. 5). If, as a first approximation, we neglect the tangentially transverse forces and displacements giving the second-order small error components with dynamic stability of the process, then the equation of the static equilibrium of the drill bit is expressed as follows:
P _{1 pop} ^. L ₁ - P _{1 prod} ρ ₁ (ϑ) =
= P _{2 pop} ^. L ₂ - Р _2prod ρ ₂ (ϑ), (1) where Р _1поп and Р _2поп - radial components of the force on the blades 1 and 2 of the drill bit; and R _1prod and R _2prod are the longitudinal components of the forces on these blades;
ρ ₁ (ϑ) and ρ ₂ (ϑ) are the current radius vectors of the vertices of blades 1 and 2;
ϑ - current angle of rotation of the drill bit; ϑ = ω _bp t;
L ₁ ≈ L ₂ = L is the distance from the tops of the blades to the rotation pole.

For sufficiently large L >> D and for φ <90, ^the moments from the longitudinal forces can be neglected. Then the equation of static equilibrium (1) is expressed as
Р _1поп = Р _2поп , (2) in this case, it is supplemented by the geometric relation
ρ ₁ (ϑ) + ρ ₂ (ϑ) = D (3) The forces included in the equation of static equilibrium are approximately proportional to the areas Δ ₁ and Δ _{2 of the} rock being destroyed and the rock-breaking ability of the elements of the drilling tool K _r1 and K _r2
P _{1 pop} = K _r1 ^. Δ ₁ = K _r1 ^. h ₁ δ ₁ ; (4)
P _2pop = K _r2 ^. Δ ₂ = K _r2 ^. h ₂ δ ₂ , (5) where h ₁ is the height; δ ₁ - the width of the destructible rock layer.

From FIG. 6 it is easy to see that
Δ ₁ = ρ ₁ (ϑ) · (S / 2 + (ρ ₁ (ϑ) -ρ ₂ (ϑ-Π)) / tg φ) (6)
Δ ₂ = ρ ₂ (ϑ) · (S / 2 + (ρ ₂ (ϑ) -ρ ₁ (ϑ-Π)) / tg φ) (7)
Substituting equalities (6), (7), (4), (5), (3) into (2) and excluding ρ ₂ (ϑ), we obtain a nonlinear difference equation with respect to ρ ₁ (ϑ): K _r1 ρ ₁ (ϑ ) (S / 2 + (ρ ₁ (ϑ) -ρ ₂ (ϑ-Π) -D) / tg φ) = K _r2 (D-ρ ₁ (ϑ)) (S / 2 + (D-ρ ₁ (ϑ) -ρ ₁ ) / tg φ (8)
Numerical solutions of the nonlinear difference equation (8) show that for K _r1 ≠ K _r2 ; and with
S = S _o + ΔS ^. sin (ϑ - ϑ _o ), (9) where ϑ _o is an arbitrary phase shift angle, i.e., in the presence of longitudinal vibrations of the drilling tool with an amplitude Δ S and with a frequency equal to the rotation frequency (ϑ = ω _bp t), there is a transverse displacement of the drilling tool, i.e., anti-aircraft curvature of the well, the direction of which depends on the phase shift ϑ _about longitudinal vibrations (Fig. 7, 8, 9).

It can be noted that the curvature is observed in the angular direction in which the element of the drilling tool with the greatest destructive ability appears at the moments when the penetration speed S is maximum. Numerical calculations show that the greater the curvature, the greater the ratio K _r1 / K _r2 or K _r2 / K _r1 .

cos(ϑ-ϑ₀-u)·{ (1+(-1)^[u/Π])/2} du=
= (ΔS/2)tgφ [Ψ/Π] = (ΔS/2)tgφ [2l/S] , (11) где ϑ - угол в радианах, на который повернется вокруг своей оси инструмент за все время проходки, когда осуществляется искривление скважины;
l - длина проходки, на которой осуществляется искривление скважины, являющейся оценкой сверху максимальной интенсивности искривления трассы скважины.In particular, when K _r2 >> K _r1 (or K _r1 >> K _r2 ), equation (8) degenerates into a linear difference equation
ρ ₁ (θ) = D-ρ ₁ (θ-Π) + (S _0/2) tg φ + (ΔS / 2) tg φ · sin (θ- θ ₀₎ (10) for equation (10) Easy to obtain analytical solution that contains an unlimited growing term
(ΔS / 2) tg

cos (ϑ-ϑ ₀ -u) · {(1 + (- 1) ^{[u / Π]} ) / 2} du =
= (ΔS / 2) tgφ [Ψ / Π] = (ΔS / 2) tgφ [2l / S], (11) where ϑ is the angle in radians that the tool will rotate around its axis for the entire time of penetration when the curvature is performed wells;
l is the length of the penetration at which the well is curved, which is an estimate from above of the maximum intensity of the curvature of the well path.

 To clarify the physical meaning of the above, let us consider (Fig. 10) the position of the drill bit at some point in processing. The cutter (1) (shown schematically) is sharpened so that the cutting blade 2 cuts the rock, and the blunt edge 3 rests on the cutting surface.

Let at this moment, in addition to the feed S, the drill bit receive a feed increment ΔS, i.e., longitudinal vibrations with an amplitude Δ S are informed to it. The cutting edge (2) cuts the rock layer with a depth of t ₁ and the edge (3) rests on the cutting surface 4. Due to the supply of S + Δ S, the edge 3 begins to move along the cutting surface 4 to the left. The extreme point 5 of the cutting edge (2) will move from the axis of the hole to point 6.

When the cutter (1) rotates through 180 ^, it is informed ^{about the} feed S- Δ S. The cutting edge (2) continues to cut the rock, and the edge 3 rests on the cutting surface. The cutter has a feed S- ΔS, therefore, cuts the rock layer t ₂ less than the layer t ₁ . Edge 3 moves along the cutting surface 4 to the right, but since the feed at this moment is less than the maximum by 2 Δ S, the cutter will move to the right by Δ ₂ less than Δ ₁ . That is, the total displacement of the axis of the well in one revolution will be
Δ = Δ ₁ - Δ ₂ . This is the maximum axis offset per revolution of the drill tool.

Note that these estimates of the maximum curvature of the intensity can not be used when φ≈ ^90. In the case of the boring tool with φ = ⁹⁰ ° is necessary in static equilibrium equation tool (1) put P = P _{1pop 2pop} = 0.

, (12) которое математически аналогично уравнению (10), в котором (tg φ) заменен выражением (-2L/D).Having done the same calculations as above, for this case with K _2prod >> K _1prod (or K _1prod >> K _2prod ) from equation (1) we can obtain the equation
ρ ₁ (ϑ) = D- ρ ₁ (ϑ-π) -S

, (12) which is mathematically similar to equation (10), in which (tan φ) is replaced by the expression (-2L / D).

 The solution of equation (12) is similar to the solution of equation (10), however, the curvature goes in the opposite direction, i.e., in the direction diametrically opposite to the angular position, in which there is an element of a boring tool with great rock-breaking ability at times when the penetration speed is maximum.

при φ = 90^о.Similar mathematical models can also be constructed for a multi-element drilling tool, for example, carbide and diamond drill bits, cone bits, etc. For example, for a three-cone bit, in which one cone has the maximum breaking capacity and the other two are replaced with smooth rollers (Fig. . 3), the rock-breaking ability of which can be neglected, we obtain the equation ρ ₁ (ϑ) - (D / 2) = - {(sinϑ ₁ ) / (sin (ϑ ₂ -ϑ ₁ )} [ρ ₁ (ϑ -ϑ ₂ ) - (D / 2) + {(S · ϑ ₂ ) / 2Π} · K] + {(sinϑ ₂ ) / (sin (ϑ ₂ -ϑ ₁ )} [ρ ₁ (ϑ -ϑ ₁ ) - - (D / 2) + {(S · ϑ ₁ ) / 2Π} · K] where k = tan φ, for φ ≠ 90 ^о and L >> D,
or k = -

at φ = 90 ^about .

It can be noted that for ϑ ₂ = π the form and solution of equation (13) coincides with the form and solution of equations (10) and (12). The numerical solutions of equation (13) in the general case also show the occurrence of curvature of the well path in the presence of longitudinal vibrations of the drilling tool with a frequency equal to the rotation frequency (Fig. 11). This goal is also achieved by the fact that longitudinal vibrations, the frequency of which is equal to the rotational speed, inform the drilling tool with the same average rock-breaking abilities of the elements, which nevertheless the rock-breaking abilities of various elements at different times are not equal due to spontaneous rapid transverse vibrations drilling tools. Such kinematic asymmetry of the rock-cutting properties of the elements of the drilling tool arises due to the fact that the kinematic angles of cutting, for example, of a drill cutter are different due to the appearance of the portable speed of the center of the drill cutter. However, in this case, the amplitude of the slow longitudinal vibrations, whose frequencies are equal to the rotational speed, is additionally quickly changed with a frequency equal to the frequency of the transverse self-oscillations of the drilling tool.

 Thus, amplitude-modulated longitudinal vibrations, the so-called beats, are reported to the drilling tool, the carrier frequency of which is equal to the frequency of the fast transverse self-oscillations of the tool, and the envelope of these beats has a period equal to the period of rotation of the tool.

To draw up the corresponding mathematical model (Fig. 12), we use the fact that for fast transverse self-oscillations of the drill bit, the instantaneous values are K _τ1 >> K _τ2 or at other times K _τ1 << K _τ2 .

Далее квазикинематическую модель (14) можно решать алгоритмически.Then, for π · 2k / m <ϑ≅ (2k + 1) · π / m, the second blade is motionless, and for π · (2k + 1) <ϑ <π · (2k + 2) the first blade is motionless. The Cartesian coordinates of the radius vector of the first blade at the rolling points are numbered with odd numbers, and the Cartesian coordinates of the radius vector of the second blade at these points are numbered with even points. Without loss of generality, we can set tan φ = 1, then we have

Further, the quasinematic model (14) can be solved algorithmically.

Numerical solutions (Fig. 13) show that when superimposed modulated longitudinal vibrations of the form (Fig. 14)
S = S _o + ΔS cos m ϑ ^. sin (ϑ - ϑ _o ) there is a curvature of the well path in the direction depending on the phase shift ϑ _o .

 Note that the physical nature of the curvature when drilling with a geometrically symmetric tool with modulated longitudinal vibrations is similar to the physical nature of the curvature when drilling a geometrically symmetric tool with slow longitudinal vibrations.

 Indeed, we consider a two-blade symmetrical tool only at those moments when blade 1 does not cut, but rests on the surface of the bottom of the well. That is, the drilling process will be observed as if in a stroboscope with a flash rate equal to the frequency of fast transverse self-oscillations. With such a "stroboscopic" examination, this process is similar to a drilling process when one of the blades is completely dull. If, at the same time, longitudinal beats are applied to the tool, the carrier frequency of which is equal to the frequency of transverse self-oscillations, and the envelope period is equal to the rotation period, then we will see approximately the following picture in the strobe: at the moments when the “non-cutting” blade 1 is in the left half of the well, the penetration speed maximum, and at times when the "non-cutting" blade 1 is in the right half of the well, penetration speeds are minimal. Obviously, the same distortion effect will be observed as in FIG. 10. The picture observed in the stroboscope will not practically change if the phase of flashes is changed to half the period. We will only observe that when the “non-cutting” blade 2 is in the right half, the penetration speeds are minimal, and when the “non-cutting” blade 2 is in the left half, the penetration speeds are maximum.

 Obviously, observing the process at any time gives the same physical result - displacement and further curvature of the trajectory in the same direction.

 Although, the implementation of the proposed method in this part requires a vibrator of a more complex type, there is no need for artificial violation of the symmetry of the drilling tool.

Finally, the goal is also achieved by the fact that as a rock cutting tool, a two-stage tool is used, which is informed of longitudinal vibrations with a frequency equal to the rotational speed. A two-stage tool is performed, for example, in the form of two longitudinally spaced drill crowns of different diameters, with blunt or supporting elements of one stage (or crowns) placed opposite to the said elements of another stage (Fig. 15), and the angles in the plan of both stages are assigned the same . If one drill bit has an angle in the plan of φ <90 ^about , and the other - φ≥ 90 ^about , then they are oriented in the same way (Fig. 16). Indeed, with this orientation of the drill bits of a two-stage drilling tool, each of the asymmetric drill bits, when applying longitudinal vibrations with a frequency equal to the rotational speed, tends to shift in the direction opposite to the offset of the other drill bit. This sharply intensifies the set of curvature (Fig. 17).

 With this modification of the method, the curvature of the well can be further controlled by changing the axial distance between the drill bits. And if necessary, direction control is possible due to changes in the relative angular position of the drill bits.

 A comparative analysis of the proposed technical solution with the known evidence of the achievement of a new positive effect, which consists in providing the possibility of a sharp increase in the intensity of its curvature. A new positive effect is provided thanks to new technical actions, which allows us to conclude that the claimed solution meets the criterion of "Significant differences". Achieving a positive effect is justified theoretically and confirmed by laboratory experiments.

 In FIG. 1 shows a geometrically asymmetric drill bit, one of the blades of which is artificially blunt; in FIG. 2 and 3 - the same side view and bottom view of a geometrically asymmetric three-cone bit, in which two cones are replaced with smooth rollers, the rock-breaking ability of which can be neglected; in FIG. 4 is a diagram of creating longitudinal vibrations of a drilling tool, the frequency of which is equal to the rotational speed, due to the creation of a skew of the rotation drive bearing; in FIG. 5 is a design diagram for compiling a static equilibrium equation for a drill bit; in FIG. 6 is a design diagram for determining the thickness of a layer of destructible rock; in FIG. 7 - the trajectory of the tip of the cutting edge of the drill bit, one of the blades of which is blunt, in projection onto a plane perpendicular to the axis of rotation at zero phase shift of longitudinal vibrations; in FIG. 8 - curvature of the trajectory of this cutter with a phase shift equal to π / 2; in FIG. 9 - curvature of the trajectory of this cutter with a phase shift equal to π / 4; in FIG. 10 is a diagram of the formation of a curvature of a well path for one revolution of a drilling tool; in FIG. 11 - curvature of the path of the cone tool, in which two cones are replaced by a support element; in FIG. 12 is a motion diagram of a dynamically unstable symmetric drill bit; in FIG. 13 - its trajectory in projection onto a plane perpendicular to the axis of rotation; in FIG. 14 is a graph of amplitude-modulated longitudinal vibrations with a carrier frequency equal to the frequency of fast transverse self-oscillations, and with an envelope period equal to the period of rotation of the tool; in FIG. 15, 16, 17 - diagrams of the formation of the curvature of the well’s path during the drilling of wells with a two-stage drilling tool, for example picobur.

 The examples of the method were implemented in the course of laboratory experiments. The curvature and direction of the path of the wells were controlled by drilling plexiglass blanks with reduced models of drill cutters (Fig. 1) made of P18 steel with a diameter of 5-15 mm, the rotation frequency was 10 Hz, the average penetration speed was 0.2 mm per one revolution of the tool.

PRI me R 1. It was required to bend the well in a given direction by 10 ^about a length of 30 mm Used a model of the drilling tool with a diameter of 6 mm, forming a conical hole bottom with cone vertex angle 120 ^of one of the sharp edges which was blunted needle files to form a radius of curvature of 0.05-0.1 mm. During drilling, longitudinal vibrations of the drill bit were created with a frequency equal to its rotation frequency (10 Hz) and with an amplitude equal to 0.04 mm. At the same time, it was possible to do without the use of a special vibrator due to the placement of two wedge-shaped gaskets in the bearing assembly of the rotation drive (Fig. 4), one of which was fixed in the rotation drive housing, and the other on the rotating spindle, the thickness differences of the wedge gaskets were 0.04 mm . Moreover, the edge with a large thickness of the gasket mounted on the rotating spindle coincided in direction with the blunt edge of the drill bit, and the edge with the large thickness of the gasket installed in the housing of the rotation drive was turned in the direction in which the well was required to be bent.

PRI me R 2. It was required to bend the well in the opposite direction by the same amount. All parameters mentioned in the first embodiment have been retained, with the gasket secured in rotation actuator housing deployed ^about 180 and fastened again.

 PRI me R 3. It was required to bend the well in the opposite direction. All the parameters given in the first example were saved, however a drill cutter was used, giving a flat bottom of the well.

PRI me R 4. It was required to bend the well in a given direction by 30 ^about a length of 30 mm All parameters given in the first example were saved except for the bluntness of one of the cutting edges and the amplitude of the longitudinal vibrations. One of the cutting edges of the drill bit was blunted by the profile to completely exclude cutting by it, and the amplitude of the longitudinal vibrations was brought to 0.1 mm by changing the gaskets. The well bent in the same direction as in the first example, but three times more intensively.

PRI me R 5. It was required to bend the well in a given direction at 90 ^about 100 mm A two-stage drilling tool was used, the diameter of the first stage was 10 mm, and the diameter of the second was 15 mm. The hinged fastening of the tool on a rotating rod was also used. The amplitude of longitudinal vibrations was 0.1 mm. The longitudinal distance between the drill bits of the first and second stages was 50 mm. One of the blades of each drill bit was blunted until cutting with this blade was completely eliminated.

The experiment was carried out in two versions:
- in the first, the drill cutters had the same positive inclination of the blades φ = 30 ^° , but the sharp edges of the cutters of the first and second steps were located opposite;
- in the second embodiment, the sharp edges of the incisors of the first and second stages were directed in the same way, but the inclination of the blades of the incisor of the first stage was φ = 30 ^о , so that the bottom of the well was conical and concave, and the inclination of the blades of the incisor of the second stage was φ = -30 ^о so that the bottom of the well was convex-conical.

 In both cases, the experiment gave identical results.

 PRI me R 6. It was required to bend the well during penetration by a geometrically symmetric drill cutter, giving a flat bottom, with a diameter of 8 mm, and after 50 mm of penetration to change the direction of curvature to the opposite.

An electromechanical vibrator with a special electronic attachment was used for amplitude modulation of the input signal. First, the drill cutter was moved and rotated at a frequency of 10 Hz and longitudinal vibrations of the same frequency and amplitude of 0.1 mm were reported to it, while the frequency of transverse vibrations of the drill cutter was measured using a sensor capacitance and strain gauge station, which turned out to be 250 Hz. At this lead-in section L ₁ = 10 mm, the well was still straight. Then the amplitude of the longitudinal vibrations began to change with a frequency of 250 Hz due to periodic interruption of the input signal. In this section of the well began to curve to the left and a length of 30 mm deviated by ¹⁰ °. Then the phase of slow longitudinal vibrations was changed by 180 ^° , without stopping the change in their amplitude with a frequency of 250 Hz. In this station 50 mm long hole twisted in the opposite direction and deviated by ¹⁵ °. Obviously, in this embodiment of the method for the effective use of it is necessary to use feedback.

 The technical advantages of these options of the proposed method compared to the existing ones are that it becomes possible to bend wells with previously unattainable intensity, which expands the technological capabilities of drilling as a whole. (56) Copyright certificate of the USSR N 765494, cl. E 21 B 7/04, 1978.

Claims (4)

1. A method of controlling the path of a wellbore, including applying longitudinal vibrations to the tool with a frequency equal to the rotational speed, controlling the curvature and direction of the wellbore, characterized in that, in order to increase the intensity of the anti-aircraft curvature of the wellbore, one of the rock-cutting elements of an axisymmetric tool is dull or replaced on the support element, and the curvature of the wellbore is controlled in accordance with the dependence
Y ₀ = ΔS · K

,
where Δ S is the amplitude of the longitudinal vibrations of the tool;
Y is the magnitude of the zenith shift;
S is the average value of the feed per revolution of the tool;
I - the total length of the penetration of the curvature section,
where K =

where φ is the angle of inclination of the cutting edge to the axis of the tool;
D is the diameter of the tool;
L is the distance from the cutting part to the rotation pole.  2. The method according to p. 1, characterized in that as a rock cutting tool use a two-stage tool having a common axis of symmetry and rotation of the steps, different diameters and the same cutting angles in plan, moreover, blunt or supporting elements of one stage of the rock cutting tool are located opposite to the above elements of its other stage, and the curvature of the wellbore is additionally controlled by changing the axial distance between the steps of the rock cutting tool or by changing the angle between destructive and blunt or supporting elements of a rock cutting tool. 3. The method according to p. 1, characterized in that as a rock cutting tool use a two-stage tool having a common axis of symmetry and rotation of the steps, different diameters and different main angles in plan, which are less than 90 ^o on one stage and more on the other 90 ^o, blunt or supporting elements of each of the stages are located on one side of their common axis, wherein the curvature of the borehole is further controlled by changing the axial distance between the steps cutter tool or varying the angle between r zrushayuschimi and blunted or cutter tool support elements.  4. A method for controlling the path of a wellbore, including applying longitudinal vibrations to the tool with a frequency equal to the rotational speed, controlling the curvature and direction of the wellbore, characterized in that, in order to increase the intensity of the anti-aircraft curvature of the wellbore, the tool is informed by amplitude-modulated longitudinal vibrations, the carrier frequency of which is chosen equal to the frequency of its fast transverse self-oscillations, and the frequency of the envelope is equal to the frequency of its rotation, and the direction of the zenith curvature control by changing the phase of the envelope, and the intensity of the curvature is controlled by changing the phase of the carrier vibrations.

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