CN1936263A - Design-while-drilling method for controlling borehole track while drilling well - Google Patents

Abstract

The invention relates to well bore rail control and design that includes the process of determining well bore section shape, building equation set, expanding equation set, giving known parameters, and solving the equation set. It could meet the request of target intake direction and coordinate location, and could select 4 random feature parameters as the indeterminate parameters. The invention could improve drilling speed and wellbore quality, lower drilling cost.

Description

A kind of control well-drilling borehole track with being drilled with the meter method

Technical field

The present invention relates to borehole track control and design in the oil drilling, be specifically related to well-drilling borehole track with being drilled with meter.

Background technology

Along with the development of directed-drilling technique, more and more higher to the requirement of borehole track control.In the wellbore construction process, it is impossible that well track that bores in fact and the borehole track that designs are in advance fitted like a glove, and always has certain deviation between the two.The target of borehole track control is exactly will be this Deviation Control in allowed limits, thereby ground auger reaches geologic objective smoothly.

The deviation of boring between track and the design track as fruit has exceeded allowed band, just need revise design, makes it get back on the design track or direct boring to impact point (or target area).In geologic steering drilling,, and when causing adjusting impact point midway, also need similarly to adjust design if do not conform to the actual conditions in the reservoir of estimating structure and position.

Borehole track control comprises the content of aspects such as control scheme, drilling assembly design and control technology.On the control scheme, just research was to well direction and the independent control that hits in the past, and these methods have played important function for the directional well construction of routine.Yet along with the continuous progress of drilling technology, such track control concept and method can not satisfy the needs of new technology.Mainly show: the first, for horizontal well, angle buildup interval is the key of track control.It not only requires to have rational landing point position, and the well direction when going into target has very high requirement.The second, in the design and construction of multi target well, reasonably can rarget direction be successfully hit the key in follow-up target spot (district), even be related to the success or failure of construction.The 3rd, because extended reach well has long extended reach well section, thus often not to serve as the control target with final target spot, but will be that benchmark carries out track control with the design track.

In a word, under many circumstances, if simultaneously the well direction is not limited with hitting, bring adverse effect will for the borehole track control in the wellbore construction, even can't realize drilling well target and the plan be scheduled to, thus bring serious consequence, cause great economic loss.Therefore, require to satisfy rarget direction simultaneously and the soft landing method for controlling scrolling that hits significant, also be a kind of practical technique of wellbore construction of combining closely.

During as aircraft landing, the point that reasonably lands is the basic assurance of successfully landing, and the allowed band of the point that lands depends on the effective width of runway; Reasonably the landing inclination angle can guarantee the stable landing of aircraft, and can not cause jolting of fuselage; The navigation control of azimuth the direct of travel of aircraft, and irrational navigation orientation will cause the aircraft drift off the runway during landing.

It is quite similar that horizontal well is gone into the situation of target and aircraft landing.Different is, the runway on the airport is a horizontal plane, and the target area of horizontal well is a cuboid, and the hole angle when going into target also not necessarily must be 90 °.Obviously, can horizontal well goes into target coordinate and rarget direction and will be directly connected to and successfully hit, successfully creep into net horizontal section and develop target zone effectively.For multi target well, owing to require to hit a plurality of target spots or target area successively, so the rarget direction of each target is very important equally.In addition, when carrying out various correction orbit Design, not the final objective point if revise the terminal point of design, but certain intermediate point on the former design track, also must assurance can hit limits rational rarget direction again, so that create favorable conditions for follow-up construction.

Present borehole track control scheme, or only control well direction (or claiming to turn round the orientation), or only require and hit.Research and The field all show: well direction of borehole track (hole angle, azimuth) and space coordinates are to influence each other, be mutually related, and have only simultaneously control is effectively implemented in these two aspects, just can reach the track control purpose and the effect of expection.Thisly can satisfy the control method that space coordinates and well direction require simultaneously, be called the soft landing control method of borehole track.

Summary of the invention

Because the control of soft landing track should be satisfied the requirement of space coordinates, satisfies the requirement of well direction again, so no matter adopt which type of well bore section and model trajectory, all must satisfy following equation:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{X}_i=X_T-X_B$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{Y}_i=Y_T-Y_B$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{Z}_l=Z_T-Z_B$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{\mathrm{\α}}_i={\mathrm{\α}}_T-{\mathrm{\α}}_B$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{\mathrm{\φ}}_i={\mathrm{\φ}}_T-{\mathrm{\φ}}_B$

In the formula, α, φ, X, Y, Z represent hole angle, azimuth, northern coordinate, eastern coordinate and vertical depth respectively; Subscript B and T represent to implement the starting point and the terminating point of track control respectively.

Above-mentioned equation shows: the increment of coordinate sum of forming each well section of well bore section equals the poor of the terminal point of master control well section and initial point coordinate, and hole angle and azimuthal increment sum also equal the poor of the terminal point of master control well section and initial point respectively.

Yet 5 above-mentioned constraint equations are not separate, and under the condition that satisfies all the other 4 constraint equations, the governing equation of hole angle can be met by nature.If attempt above-mentioned 5 constraint equations of simultaneous solution, design soft landing track control scheme, can not succeed.

Realize soft landing control, need 2 curve well sections at least borehole track.Soft landing control scheme proposed by the invention is applicable to by 2 or 2 any well bore sections of being formed with upper curve well section.In addition, for the borehole track model without limits, be applicable to various borehole track models such as space circular arc, cylindrical spiral, natural curve, permanent tool-face.

On design and computational methods, the present invention requires to satisfy 3 space coordinates constraint equations and 1 azimutal confinement equation, totally 4 equations.Corresponding to 4 constraint equations, need 4 undetermined parameters, they can be any 4 characteristic parameters on the well bore section.

The technical problem to be solved in the present invention is:

At the deficiencies in the prior art, provide a kind of control well-drilling borehole track with being drilled with the meter method, the requirement of well rarget direction and coordinate position two aspects can be satisfied simultaneously, and the undetermined parameter of any 4 characteristic parameters of well bore section can be chosen as the borehole track design.

Technical scheme of the present invention is:

A kind of control well-drilling borehole track with being drilled with the meter method, in drilling process, revise and when adjusting borehole track, be the double requirements that guarantees rarget direction and coordinate, adopt following step design borehole track:

The 1st step: determine the well bore profile type

Borehole track from position at the bottom of the current real drilling well to target constitutes one with drilling well body section, determine to form each well section form of this well bore section, promptly determine the quantity of well section and the straight line or the curve form of each well section, this well bore section comprises 2 curve well sections at least

The 2nd step: determine initial parameter

Given starting point coordinate and direction, target coordinate and rarget direction with drilling well body section promptly provide the northern coordinate X of borehole track starting point _B, eastern coordinate Y _B, vertical depth Z _B, the northern coordinate X of target spot _TEast coordinate Y _TVertical depth Z _T, and the hole angle α of starting point _B, azimuth φ _B, go into the hole angle α of target spot _T, azimuth φ _T

The 3rd step: set up equation

The space coordinates constraint equation:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{Y}_i=Y_T-Y_B---\left(1\right)$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{X}_i=X_T-X_B---\left(2\right)$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{Z}_i=Z_T-Z_B---\left(3\right)$

The azimutal confinement equation:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{\mathrm{\φ}}_i={\mathrm{\φ}}_T-{\mathrm{\φ}}_B---\left(4\right)$

In the formula:

N: well hop count amount

Δ X _i: the northern increment of coordinate of i well section, unit: rice

Δ Y _i: the eastern increment of coordinate of i well section, unit: rice

Δ Z _i: the vertical depth increment of i well section, unit: rice

Δ φ _i: the azimuth increment of i well section, unit: degree

The 4th step: EXPANSION EQUATION FOR STEEL formula

Equation (1) (2) (3) (4) launches in the following manner:

1. when i section well section is straight line well section:

Δφ _i＝φ _i-φ _i-1＝0

$\left\{\begin{array}{c}\mathrm{\Δ}{X}_i=\mathrm{\Δ}{L}_i\sin {\mathrm{\α}}_i\cos {\mathrm{\φ}}_i\\ \mathrm{\Δ}{Y}_i=\mathrm{\Δ}{L}_i\sin {\mathrm{\α}}_i\sin {\mathrm{\φ}}_i\\ \mathrm{\Δ}{Z}_i=\mathrm{\Δ}{L}_i\cos {\mathrm{\α}}_i\end{array}\right.$

In the formula:

Δ L _i: the length of i section well section, unit: rice

α _i: the hole angle of i section well section, unit: degree

φ _i: the azimuth of i section well section, unit: degree

2. when i section well section is space circular arc well section:

The hole curvature κ of this well section _iRemain constant, corresponding radius of curvature is R ₁If provide initial installation angle ω again _i, then have:

$\mathrm{tg}{\mathrm{\φ}}_i=\frac{\sin {\mathrm{\α}}_{i-1}\sin {\mathrm{\φ}}_{i-1}+(\cos {\mathrm{\α}}_{i-1}\sin {\mathrm{\φ}}_{i-1}\cos {\mathrm{\ω}}_i+\cos {\mathrm{\φ}}_{i-1}\sin {\mathrm{\ω}}_i)\mathrm{tg}{\mathrm{\ϵ}}_i}{\sin {\mathrm{\α}}_{i-1}\cos {\mathrm{\φ}}_{i-1}+(\cos {\mathrm{\α}}_{i-1}\cos {\mathrm{\φ}}_{i-1}\cos {\mathrm{\ω}}_i-\sin {\mathrm{\φ}}_{i-1}\sin {\mathrm{\ω}}_i)\mathrm{tg}{\mathrm{\ϵ}}_i}$

${\mathrm{\ϵ}}_i=\frac{180}{\mathrm{\π}}\·\frac{\mathrm{\Δ}{L}_i}{R_i}$

$\left\{\begin{array}{c}{\mathrm{\ξ}}_i=R_i(1-\cos {\mathrm{\ϵ}}_i)\\ {\mathrm{\η}}_i=0\\ {\mathrm{\ζ}}_i=R_i\sin {\mathrm{\ϵ}}_i\end{array}\right.$

$\left\{\begin{array}{c}\mathrm{\Δ}{X}_i\\ \mathrm{\Δ}{Y}_i\\ \mathrm{\Δ}{Z}_i\end{array}\right\}=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{i-1}\cos {\mathrm{\φ}}_{i-1}& -\sin {\mathrm{\φ}}_{i-1}& \sin {\mathrm{\α}}_{i-1}\cos {\mathrm{\φ}}_{i-1}\\ \cos {\mathrm{\α}}_{i-1}\sin {\mathrm{\φ}}_{i-1}& \cos {\mathrm{\φ}}_{i-1}& \sin {\mathrm{\α}}_{i-1}\sin {\mathrm{\φ}}_{i-1}\\ -\sin {\mathrm{\α}}_{i-1}& 0& \cos {\mathrm{\α}}_{i-1}\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\ω}}_i& -\sin {\mathrm{\ω}}_i& 0\\ \sin {\mathrm{\ω}}_i& \cos {\mathrm{\ω}}_i& 0\\ 0& 0& 1\end{array}\right]\left\{\begin{array}{c}{\mathrm{\ξ}}_i\\ {\mathrm{\η}}_i\\ {\mathrm{\ζ}}_i\end{array}\right\}$

In the formula:

Δ L _i: the length of i section well section, unit: rice

α _I-1: the initial hole angle of i section well section, unit: degree

φ _I-1: the initial azimuth of i section well section, unit: degree

α _i: the terminal hole angle of i section well section, unit: degree

φ _i: the terminal azimuth of i section well section, unit: degree

3. when i section well section is natural curve well section

The rate of deviation κ of this well section _{α, i}With rate of azimuth change κ _{φ, i}Remain constant respectively.Its described borehole track is made up of straight line and circular arc on vertical cross section, and has only steady lower curved section just to be rendered as circular arc in horizontal projection.

Δφ _i＝φ _i-φ _i-1＝κ _φ，iΔL _i

Wherein:

$\left\{\begin{array}{c}{F}_S(\mathrm{\β},x)=\frac{180}{\mathrm{\πx}}[\sin (\mathrm{\β}+\mathrm{x\Δ}{L}_i)-\sin \mathrm{\β}]\\ F_C(\mathrm{\β},x)=\frac{180}{\mathrm{\πx}}[\cos (\mathrm{\β}+\mathrm{x\Δ}{L}_i)-\cos \mathrm{\β}]\end{array}\right.$

$\left\{\begin{array}{c}{A}_P={\mathrm{\α}}_{i-1}+{\mathrm{\φ}}_{i-1}\\ A_Q={\mathrm{\α}}_{i-1}-{\mathrm{\φ}}_{i-1}\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\κ}}_P={\mathrm{\κ}}_{\mathrm{\α},i}+{\mathrm{\κ}}_{\mathrm{\φ},i}\\ {\mathrm{\κ}}_Q={\mathrm{\κ}}_{\mathrm{\α},i}-{\mathrm{\κ}}_{\mathrm{\φ},i}\end{array}\right.$

In the formula:

Δ L _i: the length of i section well section, unit: rice

α _I-1: the initial hole angle of i section well section, unit: degree

φ _I-1: the initial azimuth of i section well section, unit: degree

α _i: the terminal hole angle of i section well section, unit: degree

φ _i: the terminal azimuth of i section well section, unit: degree

4. when i section well section is cylindrical spiral well section:

This well section is respectively circular arc in vertical cross section and horizontal projection.If the radius of curvature of these two circular arcs is respectively R _i, r _i, then orbit parameter is:

$\mathrm{\Δ}{\mathrm{\φ}}_i={\mathrm{\φ}}_i-{\mathrm{\φ}}_{i-1}=\frac{R_i}{r_i}(\cos {\mathrm{\α}}_{i-1}-\cos {\mathrm{\α}}_i)$

$\left\{\begin{array}{c}\mathrm{\Δ}{X}_i=r_i(\sin {\mathrm{\φ}}_i-\sin {\mathrm{\φ}}_{i-1})\\ \mathrm{\Δ}{Y}_i=r_i(\cos {\mathrm{\φ}}_{i-1}-\cos {\mathrm{\φ}}_i)\\ \mathrm{\Δ}{Z}_i=R_i(\sin {\mathrm{\α}}_i-\sin {\mathrm{\α}}_{i-1})\end{array}\right.$

In the formula:

α _I-1: the initial hole angle of i section well section, unit: degree

φ _I-1: the initial azimuth of i section well section, unit: degree

α _i: the terminal hole angle of i section well section, unit: degree

φ _i: the terminal azimuth of i section well section, unit: degree

The 5th step: given known parameters

According to the needs of borehole track design with control, as unknown quantity, all the other parameters are given as known parameters according to design condition with any 4 characteristic parameters.

The 6th step: solving equation group

Above-mentioned equation group is carried out mathematics find the solution, solve 4 known variables, calculate each borehole track parameter, finish the While-drilling borehole orbit Design.

Above-mentioned equation group contains 4 known variables, has multiple known method to find the solution on mathematics; At above-mentioned specific set of equations, also can develop not known specific solution specially.Which kind of known or not known mathematics solution no matter, do not influence the present invention about in the drilling process with the technical spirit of boring rail design method.

The 6th step solving equation group for above-mentioned can adopt iterative method, uses conventional mathematical iterations method, till satisfying given required precision.

The 6th step solving equation group for above-mentioned also can adopt numerical method, utilizes any known numerical computation method, carries out numerical solution by computer program.

The invention has the beneficial effects as follows:

Compare with traditional control method, the present invention can satisfy more harsh borehole track controlled condition, the borehole track control target of realizing ideal, can control the rarget direction of well, can control again into the target coordinate simultaneously, can improve bit speed and wellbore quality, reduction drilling cost, help safety, high-quality, finish drillng operation apace.

Description of drawings

Fig. 1 is the soft landing track schematic diagram of five-part form space circular arc section.

The specific embodiment

Further describe the present invention below in conjunction with embodiment.Scope of the present invention is not subjected to the restriction of these embodiment, and scope of the present invention proposes in claims.

In following each embodiment, also can be with curvature as characteristic parameter.

On the mathematics, radius of curvature and curvature are reciprocal each other, and this moment, the unit of curvature was rad/m.And in drilling engineering, the conventional unit of hole curvature be (°)/m, (°)/30m, (°)/100m etc.At this moment, the pass between hole curvature and the radius of curvature is:

$R=\frac{{180C}_{\mathrm{\κ}}}{\mathrm{\π\κ}}$

In the formula:

κ---hole curvature;

R---radius of curvature, m;

C _κ---the unit conversion coefficient, its numerical value equals the numeral in the curvature unit.For example, when the unit of hole curvature κ be (°)/during 30m, C _κ=30.

(1) the soft landing track of five-part form space circular arc section control scheme

The landing point hole angle of horizontal well design is that 88 °, azimuth are 50 °.Be 76 ° when being drilled into hole angle, when the azimuth is 54 °, be that 14.6m, horizontal movement are that 93.5m, translation orientation are 48.4 ° apart from the vertical depth of the point that lands.Select the five-part form well bore section of " straight line-arc-straight line-arc-straight line " for use, and the curvature that requires the segment length of first and last section to be respectively 10m and 6m, two arc sections is selected 8 °/30m and 10 °/30m for use.

Initial tool face angle ω with the 2nd well section (i.e. the 1st arc section) ₂, the 3rd well section (i.e. the 2nd straightway) length Δ L ₃, the 3rd well section hole angle α ₃, the 3rd well section azimuth φ ₃Totally 4 characteristic parameters are unknown quantity.

Method for designing then according to the present invention gets: the initial tool face angle of the 2nd well section is 299.37 °, and the length of the 3rd well section is that 8.95m, hole angle are that 81.93 °, azimuth are 43.71 °.Design result sees Table 1.

The soft landing track control scheme of table 1 five-part form space circular arc section

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(2) the soft landing track of five-part form natural curve section control scheme

The landing point hole angle of horizontal well design is 90 °, go into the target azimuth is 265 °.Be 72 ° when being drilled into hole angle, when the azimuth is 260 °, be that 14m, horizontal movement are that 88m, translation orientation are 264 ° apart from the vertical depth of the point that lands.Select the five-part form well bore section of " straight line-arc-straight line-arc-straight line " for use, and the segment length who requires the first and last section selects 8 °/30m and 10 °/30m and the 1st well section and two arc sections for use for the rate of deviation of 6m and 10m, two arc sections and has the bearing swing rate of 2 °/30m, 5 °/30m and-4 °/30m respectively.

Length Δ L with the 3rd well section (i.e. the 2nd straightway) ₃, the 3rd well section hole angle α ₃, the 3rd well section rate of azimuth change be κ _{φ, 3}, the 5th well section (i.e. the 3rd straightway) rate of azimuth change κ _{φ, 5}, totally 4 characteristic parameters are unknown quantity.

Method for designing then according to the present invention gets: the length of the 3rd well section is that 13.35m, hole angle are that 80.34 °, rate of azimuth change are 2.54 °/30m, and the rate of azimuth change of the 5th well section is 6.36 °/30m.Design result sees Table 2.

The soft landing track control scheme of table 2 five-part form natural curve section

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Claims (3)

1 one kinds control well-drilling borehole track with being drilled with the meter method, it is characterized in that: when in drilling process, adjusting borehole track, adopt following step design borehole track:

The 1st step: determine the well bore profile type

Borehole track from position at the bottom of the current real drilling well to target constitutes one with drilling well body section, determine to form each well section form of this well bore section, promptly determine the quantity of well section and the straight line or the curve form of each well section, this well bore section comprises 2 curve well sections at least;

The 2nd step: determine initial parameter

Given starting point coordinate and direction, target coordinate and rarget direction with drilling well body section promptly provide the northern coordinate X of borehole track starting point _B, eastern coordinate Y _B, vertical depth Z _B, the northern coordinate X of target spot _T, eastern coordinate Y _T, vertical depth Z _T, and the hole angle α of starting point _B, azimuth φ _B, go into the hole angle α of target spot _T, azimuth φ _T

The 3rd step: set up equation

The space coordinates constraint equation:

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;\&Lambda;}{X}_i=X_T-X_B---\left(1\right)$

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{Y}_i=Y_T=Y_B---\left(2\right)$

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{Z}_i=Z_T-Z_B---\left(3\right)$

The azimutal confinement equation:

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{\mathrm{\&phi;}}_i={\mathrm{\&phi;}}_T-{\mathrm{\&phi;}}_B---\left(4\right)$

In the formula:

N: well hop count amount

Δ X _i: the northern increment of coordinate of i well section, unit: rice

Δ Y _i: the eastern increment of coordinate of i well section, unit: rice

Δ Z _i: the vertical depth increment of i well section, unit: rice

Δ φ _i: the azimuth increment of i well section, unit: degree

The 4th step: EXPANSION EQUATION FOR STEEL formula

Equation (1) (2) (3) (4) launches in the following manner:

1. when i section well section is straight line well section:

Δφ _i＝φ _i-φ _i-1＝0

$\left\{\begin{array}{c}\mathrm{\&Delta;}{X}_i=\mathrm{\&Delta;}{L}_i\sin {\mathrm{\&alpha;}}_i\cos {\mathrm{\&phi;}}_i\\ \mathrm{\&Delta;}{Y}_i=\mathrm{\&Delta;}{L}_i\sin {\mathrm{\&alpha;}}_i\sin {\mathrm{\&phi;}}_i\\ \mathrm{\&Delta;}{Z}_i=\mathrm{\&Delta;}{L}_i\cos {\mathrm{\&alpha;}}_i\end{array}\right.$

In the formula:

Δ L _i: the length of i section well section, unit: rice

α _i: the hole angle of i section well section, unit: degree

φ _i: the azimuth of i section well section, unit: degree

2. when i section well section is space circular arc well section:

The hole curvature K of this well section _iRemain constant, corresponding radius of curvature is R _iIf provide initial installation angle ω again _i, then have:

$\mathrm{tg}{\mathrm{\&phi;}}_i$ $=\frac{\sin {\mathrm{\&alpha;}}_{i-1}\sin +{\mathrm{\&phi;}}_{i-1}(\cos {\mathrm{\&alpha;}}_{i-1}\sin {\mathrm{\&phi;}}_{i-1}\cos {\mathrm{\&omega;}}_i+\cos {\mathrm{\&phi;}}_{i-1}\sin {\mathrm{\&omega;}}_i)\mathrm{tg}{\mathrm{\&epsiv;}}_i}{\sin {\mathrm{\&alpha;}}_{i-1}\cos {\mathrm{\&phi;}}_{i-1}+(\cos {\mathrm{\&alpha;}}_{i-1}\cos {\mathrm{\&phi;}}_{i-1}\cos {\mathrm{\&omega;}}_i-\sin {\mathrm{\&phi;}}_{i-1}\sin {\mathrm{\&omega;}}_i)\mathrm{tg}{\mathrm{\&epsiv;}}_i}$

${\mathrm{\&epsiv;}}_i=\frac{180}{\mathrm{\&pi;}}\&bull;\frac{\mathrm{\&Delta;}{L}_i}{R_i}$

$\left\{\begin{array}{c}{\mathrm{\&xi;}}_i=R_i(1-\cos {\mathrm{\&epsiv;}}_i)\\ {\mathrm{\&eta;}}_i=0\\ {\mathrm{\&zeta;}}_i=R_i\sin {\mathrm{\&epsiv;}}_i\end{array}\right.$

$\left\{\begin{array}{c}\mathrm{\&Delta;}{X}_i\\ \mathrm{\&Delta;}{Y}_i\\ \mathrm{\&Delta;}{Z}_i\end{array}\right\}=\left[\begin{array}{ccc}\cos {\mathrm{\&alpha;}}_{i-1}\cos {\mathrm{\&phi;}}_{i-1}& -\sin {\mathrm{\&phi;}}_{i-1}& \sin {\mathrm{\&alpha;}}_{i-1}\cos {\mathrm{\&phi;}}_{i-1}\\ \cos {\mathrm{\&alpha;}}_{i-1}\sin {\mathrm{\&phi;}}_{i-1}& \cos {\mathrm{\&phi;}}_{i-1}& \sin {\mathrm{\&alpha;}}_{i-1}\sin {\mathrm{\&phi;}}_{i-1}\\ -\sin {\mathrm{\&alpha;}}_{i-1}& 0& \cos {\mathrm{\&alpha;}}_{i-1}\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\&omega;}}_i& -\sin {\mathrm{\&omega;}}_i& 0\\ \sin {\mathrm{\&omega;}}_i& \cos {\mathrm{\&omega;}}_i& 0\\ 0& 0& 1\end{array}\right]\left\{\begin{array}{c}{\mathrm{\&xi;}}_i\\ {\mathrm{\&eta;}}_i\\ {\mathrm{\&zeta;}}_i\end{array}\right\}$

In the formula:

Δ L _i: the length of i section well section, unit: rice

α _I-1: the initial hole angle of i section well section, unit: degree

φ _I-1: the initial azimuth of i section well section, unit: degree

α _i: the terminal hole angle of i section well section, unit: degree

φ _i: the terminal azimuth of i section well section, unit: degree

3. when i section well section is natural curve well section:

The rate of deviation κ of this well section _{α, i}With rate of azimuth change κ _{φ, i}Remain constant respectively.Its described borehole track is made up of straight line and circular arc on vertical cross section, and has only steady lower curved section just to be rendered as circular arc in horizontal projection.

Δφ _i＝φ _i-φ _i-1＝κ _φ，iΔL _i

Wherein:

$\left\{\begin{array}{c}{F}_s(\mathrm{\&beta;},\mathrm{\&chi;})=\frac{180}{\mathrm{\&pi;\&chi;}}[\sin (\mathrm{\&beta;}+\mathrm{\&chi;\&Delta;}{L}_i)-\sin \mathrm{\&beta;}\&rsqb;\\ F_c(\mathrm{\&beta;},x)=\frac{180}{\mathrm{\&pi;\&chi;}}\&lsqb;\cos (\mathrm{\&beta;}+\mathrm{\&chi;\&Delta;}{L}_i)-\cos \mathrm{\&beta;}\&rsqb;\end{array}\right.$

$\left\{\begin{array}{c}{A}_P={\mathrm{\&alpha;}}_{i-1}+{\mathrm{\&phi;}}_{i-1}\\ A_Q={\mathrm{\&alpha;}}_{i-1}-{\mathrm{\&phi;}}_{i-1}\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\&kappa;}}_P={\mathrm{\&kappa;}}_{\mathrm{\&alpha;},i}+{\mathrm{\&kappa;}}_{\mathrm{\&phi;},i}\\ {\mathrm{\&kappa;}}_Q={\mathrm{\&kappa;}}_{\mathrm{\&alpha;},i}-{\mathrm{\&kappa;}}_{\mathrm{\&phi;},i}\end{array}\right.$

In the formula:

Δ L _i: the length of i section well section, unit: rice

α _I-1: the initial hole angle of i section well section, unit: degree

φ _I-1: the initial azimuth of i section well section, unit: degree

α _i: the terminal hole angle of i section well section, unit: degree

φ _i: the terminal azimuth of i section well section, unit: degree

4. when i section well section is cylindrical spiral well section:

This well section is respectively circular arc in vertical cross section and horizontal projection.If the radius of curvature of these two circular arcs is respectively R _i, r _i, then orbit parameter is:

$\mathrm{\&Delta;}{\mathrm{\&phi;}}_i={\mathrm{\&phi;}}_i-{\mathrm{\&phi;}}_{i-1}=\frac{R_i}{r_i}(\cos {\mathrm{\&alpha;}}_{i-1}-\cos {\mathrm{\&alpha;}}_i)$

$\left\{\begin{array}{c}\mathrm{\&Delta;}{X}_i=r_i(\sin {\mathrm{\&phi;}}_i-\sin {\mathrm{\&phi;}}_{i-1})\\ \mathrm{\&Delta;}{Y}_i=r_i(\cos {\mathrm{\&phi;}}_{i-1}-\cos {\mathrm{\&phi;}}_i)\\ \mathrm{\&Delta;}{Z}_i=R_i(\sin {\mathrm{\&alpha;}}_i-\sin {\mathrm{\&alpha;}}_{i-1})\end{array}\right.$

In the formula:

α _I-1: the initial hole angle of i section well section, unit: degree

φ _I-1: the initial azimuth of i section well section, unit: degree

α _i: the terminal hole angle of i section well section, unit: degree

φ _i: the terminal azimuth of i section well section, unit: degree

The 5th step: given known parameters

According to the needs of borehole track design with control, as unknown quantity, all the other parameters are given as known parameters according to design condition with any 4 characteristic parameters.

The 6th step: solving equation group

Above-mentioned equation group is carried out mathematics find the solution, solve 4 known variables, calculate each borehole track parameter, finish the While-drilling borehole orbit Design.

2 control well-drilling borehole tracks according to claim 1 with being drilled with the meter method, it is characterized in that:

Described the 6th step solving equation group is to adopt iterative method, uses conventional mathematical iterations method, till satisfying given required precision.

3 control well-drilling borehole tracks according to claim 1 with being drilled with the meter method, it is characterized in that:

Described the 6th step solving equation group is to adopt numerical method, utilizes any known numerical computation method, carries out numerical solution by computer program.