CN104895553A - Actual drilling track obtaining method based on non-equal changeable cylinder spiral tilt checking algorithm - Google Patents

Abstract

The invention relates to an actual drilling track obtaining method based on a non-equal changeable cylinder spiral tilt checking algorithm. The actual drilling track obtaining method comprises the steps of obtaining tilt checking data of two adjacent measuring points; according to the tilt checking data of the two adjacent measuring points, utilizing a cylinder spiral model of a non-equal changeable spiral angle to calculate tilt checking data of a random point P between the two adjacent measuring points; obtaining space coordinate information of the point according to the obtained tilt checking data of the point P; and calculating an actual drilling track according to the obtained space coordinate information. The actual drilling track obtaining method is suitable for a well track drilled by a drill disc and can reduce errors.

Description

A kind of based on the non-drilling trajectory acquisition methods waiting change cylindrical spiral inclinometry algorithm

Technical field

The present invention relates to drilling prospection technical field, particularly relate to a kind of based on the non-drilling trajectory acquisition methods waiting change cylindrical spiral inclinometry algorithm.

Background technology

Geological prospecting refers to the needs according to national economy, national defense construction and scientific technological advance, carries out the different enquiry based work of emphasis to geological conditions such as the rock in a given area, stratum, structure, mineral products, underground water, landforms.In geological prospecting process, drilling prospection and probing are two kinds of methods often adopted.In drilling prospection field, the clinometers calculation method of drilled wellbore trajectories is the focus of research always.

In clinometers calculation, nineteen sixty-eight G J Wilson proposes the design formulas of hole curvature first, nineteen eighty-three E.E.Fitchard and S.A.Fitchard proposes the borehole torsion design formulas of cylindrical spiral well track, and during this period, clinometers calculation method has had kind more than 20.Facts have proved, for directional well or the horizontal well of upper km, the result maximum deviation utilizing clinometers calculation method to try to achieve can reach 10 meters, and in order to improve computational accuracy, foreign scholar is devoted to the research of clinometers calculation theory always, makes its development and perfect.Due to the theoretical application in clinometers calculation of numerical radius, clinometers calculation theory is made to achieve remarkable development.Clinometers calculation method is when theoretical side reaches its maturity, and the analysis of clinometers calculation method error more and more comes into one's own, and becomes the focus that researcher pays close attention to.

Typical clinometers calculation method has four kinds, and the Mathematical Modeling of these four kinds of inclinometry algorithms is straight line, broken line, space circular arc and cylindrical spiral.

(1) straight line well track model, supposes that surveying section shape is straight line;

(2) broken line well track model, suppose to be divided into two straightways in a survey section, the length of two straightways equals the half surveying segment length, and its direction is consistent with the well direction of upper and lower two measuring points respectively;

(3) space circular arc well track model, suppose survey intersegmental be a space circular arc track, two measuring point places up and down of this circular arc and well direction tangent;

(4) cylindrical spiral well track model, supposes that surveying intersegmental is a cylindrical spiral, and the Mathematical Modeling of traditional cylindrical spiral inclinometry algorithm is one and waits the cylindrical spiral becoming helical angle, and its end points place is tangent with the well direction of upper and lower two measuring points respectively.

Utilize the inclinometry algorithm of cylindrical spiral model mainly contain radius-of-curvature method and correct average angle method, although the well track model of two kinds of methods is identical, clinometers calculation process is not identical.

(1) radius-of-curvature method

Becoming the character of cylindrical spiral according to waiting, surveying and waiting change cylindrical spiral track to be all circular arc on vertical cross section and horizontal projection in section.Utilize this character to release, the clinometers calculation formula of radius-of-curvature method is as follows:

$\mathrm{\Δ}{H}_i=\left\{\begin{array}{c}\mathrm{\Δ}{L}_i\cos {\mathrm{\α}}_i,{\mathrm{\α}}_i-{\mathrm{\α}}_{i-1}=0\\ R_i(\sin {\mathrm{\α}}_i-\sin {\mathrm{\α}}_{i-1}),{\mathrm{\α}}_i-{\mathrm{\α}}_{i-1}\≠0\end{array}\right.---\left(1\right)$

$\mathrm{\Δ}{E}_i=\left\{\begin{array}{c}\mathrm{\Δ}{S}_i\sin {\mathrm{\φ}}_i,{\mathrm{\φ}}_i-{\mathrm{\φ}}_{i-1}=0\\ r_i(\cos {\mathrm{\φ}}_{i-1}-\cos {\mathrm{\φ}}_i),{\mathrm{\φ}}_i-{\mathrm{\φ}}_{i-1}\≠0\end{array}\right.---\left(2\right)$

$\mathrm{\Δ}{N}_i=\left\{\begin{array}{c}\mathrm{\Δ}{S}_i\cos {\mathrm{\φ}}_i,{\mathrm{\φ}}_i-{\mathrm{\φ}}_{i-1}=0\\ r_i(\sin {\mathrm{\φ}}_i-\sin {\mathrm{\φ}}_{i-1}),{\mathrm{\φ}}_i-{\mathrm{\φ}}_{i-1}\≠0\end{array}\right.---\left(3\right)$

Wherein, $\mathrm{\Δ}{S}_i=\left\{\begin{array}{c}\mathrm{\Δ}{L}_i\sin {\mathrm{\α}}_i,{\mathrm{\α}}_i-{\mathrm{\α}}_{i-1}=0\\ R_i(\cos {\mathrm{\α}}_i-\cos {\mathrm{\α}}_{i-1}),{\mathrm{\α}}_i-{\mathrm{\α}}_{i-1}\≠0\end{array}\right.,R_i=\frac{\mathrm{\Δ}{L}_i}{{\mathrm{\Δ\α}}_i},r_i=\frac{\mathrm{\Δ}{S}_i}{{\mathrm{\Δ\φ}}_i}.$

(2) average angle method is corrected

Correcting average angle method is the approximation method of radius-of-curvature method, and approximate condition is that the difference at the difference of hole angle between two adjacent measuring points and azimuth is all very little.

Its clinometers calculation formula is as follows:

ΔH _i＝f _v,iΔL _icosα _V(4)

ΔE _i＝f _h,iΔL _isinα _Vsinφ _V(5)

ΔN _i＝f _h,iΔL _isinα _Vcosα _V(6)

Wherein, $f_{v,i}=1-\frac{{{\mathrm{\φ\α}}_i}^2}{24},f_{h,i}=1-\frac{{{\mathrm{\Δ\α}}_i}^2+{{\mathrm{\Δ\φ}}_i}^2}{24}.$

At present, studies in China scholar prove, average angle method is model owing to selecting to be straight line, therefore error can be relatively bigger than normal, minimum-curvature method selects space circular arc to be Mathematical Modeling, therefore error can be less than average angle method, becomes to wait the inclinometry algorithm that cylindrical spiral is model, error can be less than minimum-curvature method, but still there is error.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of based on the non-drilling trajectory acquisition methods waiting change cylindrical spiral inclinometry algorithm, is applicable to the well track that brill dish gets out, can reduces error.

The technical solution adopted for the present invention to solve the technical problems is: provide a kind of and wait based on non-the drilling trajectory acquisition methods becoming cylindrical spiral inclinometry algorithm, comprise the following steps:

(1) the deviational survey data of two adjacent measuring points are obtained;

(2) the deviational survey data of any point P between two adjacent measuring points are calculated according to the deviational survey data separate of two the adjacent measuring points cylindrical spiral model becoming helical angle such as non-;

(3) spatial coordinated information of this point is obtained according to the deviational survey data of the some P obtained;

(4) drilling trajectory is calculated according to the spatial coordinated information obtained.

Described step (2) comprises following sub-step:

(21) tool face azimuth of well section initial point in two adjacent measuring points is calculated;

(22) hole angle and the azimuth of a P is calculated according to the tool face azimuth of well section initial point obtained and well depth.

The described cylindrical spiral model becoming helical angle such as non-is set up based on local coordinate system; Described local coordinate system is with well section initial point in two adjacent measuring points for the origin of coordinates, and ξ axle points to the principal normal direction of well track, and η axle points to the binormal direction of well track, and ζ axle points to the tangential direction of well track.

Beneficial effect

Owing to have employed above-mentioned technical scheme, the present invention compared with prior art, there is following advantage and good effect: the present invention with etc. to become cylindrical spiral well track algorithm absolute error less, larger with space circular arc well track algorithm absolute error, larger with space line well track algorithm absolute error, this meets expected results, because the inclinometry algorithm precision of cylindrical spiral model is greater than space circular arc well track inclinometry algorithm, space circular arc well track inclinometry algorithm is greater than space line well track inclinometry algorithm.Secondly, the present invention becomes the absolute error of three kinds of inclinometry algorithms such as cylindrical spiral well track inclinometry algorithm, space circular arc well track inclinometry algorithm, space line well track inclinometry algorithm within error range with grade respectively, describes the non-correctness waiting change cylindrical spiral inclinometry algorithm.Finally, for the well track using ground turntable rotation boring method to get out, there is generality, utilize the non-of hypothesis to wait the cylindrical spiral well track becoming helical angle, have more rationally and applicability.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention;

Fig. 2 is that in the present invention, non-grade becomes helical angle cylindrical spiral and coordinate system figure.

Detailed description of the invention

Below in conjunction with specific embodiment, set forth the present invention further.Should be understood that these embodiments are only not used in for illustration of the present invention to limit the scope of the invention.In addition should be understood that those skilled in the art can make various changes or modifications the present invention, and these equivalent form of values fall within the application's appended claims limited range equally after the content of having read the present invention's instruction.

Embodiments of the present invention relate to a kind of based on the non-drilling trajectory acquisition methods waiting change cylindrical spiral inclinometry algorithm, as shown in Figure 1, comprise the following steps: the deviational survey data obtaining two adjacent measuring points; The deviational survey data of any point P between two adjacent measuring points are calculated according to the deviational survey data separate of two the adjacent measuring points cylindrical spiral model becoming helical angle such as non-; The spatial coordinated information of this point is obtained according to the deviational survey data of the some P obtained; Drilling trajectory is calculated according to the spatial coordinated information obtained.

Non-etc. become helical angle with etc. become the cylindrical spiral model of helical angle difference be the change of helical angle.Cylindrical spiral Deng becoming helical angle: be defined as the cylindrical spiral of helical angle with spiral corner linear change.The cylindrical spiral becoming helical angle such as non-: be defined as the cylindrical spiral of helical angle with spiral corner nonlinear change.Fig. 2 is the non-graph of a relation waited between the cylindrical spiral well track of change helical angle and mouth coordinate.

Because the cylindrical screw model becoming helical angle such as non-is set up based under local coordinate system.As shown in Figure 2, local coordinate A-ξ η ζ is with measuring point A for the origin of coordinates, and ξ axle points to the principal normal direction of well track, and η axle points to the binormal direction of well track, and ζ axle points to the tangential direction of well track.The local coordinate system of AB well section is converted to mouth coordinate system to portray description, is conducive to characterizing cylindrical spiral well section track and placing attitude thereof.Therefore, mouth coordinate and local coordinate transformational relation as follows:

$\left\{\begin{array}{c}\mathrm{\ΔN}=T_{11}*\mathrm{\ξ}+T_{21}*\mathrm{\η}+T_{31}*\mathrm{\ζ}\\ \mathrm{\ΔE}=T_{12}*\mathrm{\ξ}+T_{22}*\mathrm{\η}+T_{32}*\mathrm{\ζ}\\ \mathrm{\ΔH}=T_{13}*\mathrm{\ξ}+T_{23}*\mathrm{\η}+T_{33}*\mathrm{\ζ}\end{array}\right.---\left(7\right)$

Wherein, ω _afor the tool face azimuth of measuring point A, φ _afor the azimuth of measuring point A, α _afor the hole angle of measuring point A.

$\left\{\begin{array}{c}{T}_{11}=\cos {\mathrm{\α}}_A\cos {\mathrm{\φ}}_A\cos {\mathrm{\ω}}_A-\sin {\mathrm{\φ}}_A\sin {\mathrm{\ω}}_A\\ T_{12}=\cos {\mathrm{\α}}_A\sin {\mathrm{\φ}}_A\cos {\mathrm{\ω}}_A+\cos {\mathrm{\φ}}_A\sin {\mathrm{\ω}}_A\\ T_{13}=-\sin {\mathrm{\α}}_A\cos {\mathrm{\ω}}_A\\ T_{21}=-\cos {\mathrm{\α}}_A\cos {\mathrm{\φ}}_A\sin {\mathrm{\ω}}_A-\sin {\mathrm{\φ}}_A\cos {\mathrm{\ω}}_A\\ T_{22}=-\cos {\mathrm{\α}}_A\sin {\mathrm{\φ}}_A\sin {\mathrm{\ω}}_A+\cos {\mathrm{\φ}}_A\cos {\mathrm{\ω}}_A\\ T_{23}=\sin {\mathrm{\φ}}_A\sin {\mathrm{\ω}}_A\\ T_{31}=\sin {\mathrm{\φ}}_A\cos {\mathrm{\φ}}_A\\ T_{32}=\sin {\mathrm{\φ}}_A{\sin \mathrm{\φ}}_A\\ T_{31}={\cos \mathrm{\α}}_A\end{array}\right.---\left(8\right)$

The general equation of well track is as follows:

$\left\{\begin{array}{c}\mathrm{\ξ}=\frac{1}{2}\mathrm{\κ\Δ}{L}^2\\ \mathrm{\η}=\frac{1}{6}\mathrm{\κ\τ\Δ}{L}^2\\ \mathrm{\ζ}=\mathrm{\ΔL}\end{array}\right.---\left(9\right)$

Wherein, κ is hole curvature, τ is borehole torsion.Δ L is certain some well depth length difference to well section initial point in well section.In drilled wellbore trajectories, suppose that the intersegmental well track of well non-ly waits the cylindrical spiral becoming helical angle, then what the hole curvature of well section and borehole torsion were got is average hole curvature and average borehole torsion.According to average hole curvature, average borehole torsion definition, obtain design formulas:

$\left\{\begin{array}{c}\mathrm{\κ}=\frac{\mathrm{\ϵ}}{\mathrm{\ΔL}}\\ \mathrm{\τ}=\mathrm{sgn}\left(\mathrm{\Δ\φ}\right)\frac{\mathrm{\θ}}{\mathrm{\ΔL}}\end{array}\right.---\left(10\right)$

Wherein, ε surveys the angle of bend between section initial point and terminal, be always on the occasion of.θ is the angle of torsion surveying section, and Δ φ is the difference at the azimuth of lower measuring point B and upper measuring point A.Because cylindrical spiral is divided into left-handed and dextrorotation, and be determined by the azimuth surveying section two-end-point.Therefore, $\mathrm{sgn}\left(\mathrm{\Δ\φ}\right)=\left\{\begin{array}{c}+1,\mathrm{\Δ\φ}>0\\ 0,\mathrm{\Δ\φ}>0\\ -1,\mathrm{\Δ\φ}>0\end{array}\right..$

ε and θ formula is as follows

$\left\{\begin{array}{c}\cos \mathrm{\ϵ}=\cos {\mathrm{\α}}_A\cos {\mathrm{\α}}_B+\sin {\mathrm{\α}}_A\sin {\mathrm{\α}}_B\cos \mathrm{\Δ\φ}\\ \cos \mathrm{\θ}=\frac{1}{k_A{k}_B}[k_V^2\cos \mathrm{\Δ\φ}-k_V{k}_H({\sin }^2{\mathrm{\α}}_B\cos {\mathrm{\α}}_B-{\sin }^2{\mathrm{\α}}_A\cos {\mathrm{\α}}_A)\sin \left(\mathrm{\Δ\φ}\right)+{\mathrm{ck}}_H^2{\sin }^2{\mathrm{\α}}_A{\sin }^2{\mathrm{\α}}_B]\end{array}\right.---\left(11\right)$

Wherein, α _a, α _bfor the hole angle of A, B, k _v, k _hfor the hole curvature of cylindrical spiral in horizontal projection and vertical projection diagram, k _a, k _bfor the hole curvature of well section AB two end points, d is intermediate parameters and is obtained by following formula:

d＝sinα _Asinα _B+cosα _Acosα _BcosΔφ。

Found out by formula (7) and formula (8), for obtaining the space coordinates of any point P on well section AB, need the tool face azimuth of measuring measuring point A, but the data generally recorded due to inclinometer are the well depth of measuring point A, hole deviation and azimuth, therefore on existing measuring point data basis, suppose that well section AB is a non-cylindrical spiral well track waiting change helical angle, give the tool face azimuth method for solving of measuring point A, for the hole angle and azimuth measuring well section AB any point P is removed the obstacles.

Usually, no matter be designed path or actual well drilled track, be all using the trajectory parameters of well section initial point as given data, from the tool face azimuth of well section initial point and the hole angle relation of lower measuring point, can convert with the hole angle of terminal B in the tool face azimuth of the initial point A of well section AB.When the tool face azimuth of known initial point A, hole angle and the azimuth of terminal B can be obtained.As the hole angle α of known terminal B _b, then the tool face azimuth of initial point A is obtained by following formula:

${\mathrm{\ω}}_A=\arccos \frac{m}{\sqrt{n^2+k^2}}+\arccos \frac{n}{\sqrt{n^2+k^2}}---\left(12\right)$

Wherein, $\left\{\begin{array}{c}m=\cos {\mathrm{\α}}_B-\frac{{\mathrm{\ζ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}\cos {\mathrm{\α}}_A\\ n=-\frac{{\mathrm{\ξ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}\sin {\mathrm{\α}}_A\\ k=-\frac{{\mathrm{\η}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}\sin {\mathrm{\α}}_A\end{array}\right.---\left(13\right)$

By the definition of tool face azimuth, ω _aspan be 0 ° ~ 90 °.

Because the actual well drilled track between two measuring point A and B cannot be determined at present, suppose that well section AB is a non-cylindrical spiral well track waiting change helical angle, set up cylindrical spiral well track equation, object is in order to when measuring point A and measuring point B deviational survey data are known, measure the deviational survey data such as the hole angle of well section AB any point P, azimuth, thus draw the space coordinates of P point under general cylindrical spiral well track.

Hole angle and azimuth are all characterize with the tangent line of well track.Due to the unit tangent vector t of any point P on well section AB _punder mouth coordinate system and local coordinate system, can be expressed as:

$\left\{\begin{array}{c}{t}_P=t_{N}i+t_{E}j+t_{H}k\\ t_P=\frac{{\mathrm{\ξ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{e}_{\mathrm{\ξ}}+\\ \frac{{\mathrm{\η}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{e}_{\mathrm{\η}}+\frac{{\mathrm{\ζ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{e}_{\mathrm{\ζ}}\end{array}\right.---\left(14\right)$

And by the relation of Coordinate Conversion, know:

$\left\{\begin{array}{c}{e}_{\mathrm{\ω}}=T_{11}i+T_{12}j+T_{13}k\\ e_{\mathrm{\η}}=T_{21}i+T_{22}j+T_{23}k\\ e_{\mathrm{\ζ}}=T_{31}i+T_{32}j+T_{33}k\end{array}\right.---\left(15\right)$

So

$\left\{\begin{array}{c}{t}_N=\frac{{\mathrm{\ξ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{11}+\frac{{\mathrm{\η}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{21}+\frac{{\mathrm{\ζ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{31}\\ t_E=\frac{{\mathrm{\ξ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{12}+\frac{{\mathrm{\η}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{22}+\frac{{\mathrm{\ζ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{32}\\ t_H=\frac{{\mathrm{\ξ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{13}+\frac{{\mathrm{\η}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{23}+\frac{{\mathrm{\ζ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{33}\end{array}\right.---\left(16\right)$

In above formula, i, j, k are respectively N, the unit vector in E and H coordinate axes; e _ξ, e _η, e _ζbe respectively ξ, the unit vector in η, ζ coordinate axes, ξ ', η ', ζ ' is the derivative of the local coordinate of some P; t _n, t _e, t _hrepresent t _pcoordinate position under mouth coordinate system.According to hole angle and azimuthal definition, have

$\left\{\begin{array}{c}\cos \mathrm{\α}=t_H=\frac{{\mathrm{\ξ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{13}+\\ \frac{{\mathrm{\η}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{23}+\\ \frac{{\mathrm{\ζ}}^{\′}}{\sqrt{{\mathrm{\ξ}}^{\′2}+{\mathrm{\η}}^{\′2}+{\mathrm{\ζ}}^{\′2}}}{T}_{33}\\ \tan \mathrm{\φ}=\frac{t_E}{t_N}=\frac{{\mathrm{\ξ}}^{\′}{T}_{12}+{\mathrm{\η}}^{\′}{T}_{22}+{\mathrm{\ζ}}^{\′}{T}_{32}}{{\mathrm{\ξ}}^{\′}{T}_{11}+{\mathrm{\η}}^{\′}{T}_{21}+{\mathrm{\ζ}}^{\′}{T}_{31}}\end{array}\right.---\left(17\right)$

Non-grade becomes cylindrical spiral rail well track well depth L and initial tool face angle ω _acharacterize the non-shape and the placement state that wait change cylindrical spiral track, based on well section measuring point A, the trajectory parameters at B place can calculate the hole angle at any well depth place on well section AB, azimuth and space coordinates.In attention formula (17), the value value interval of hole angle is-90 ° ~ 90 °, and azimuthal span is 0 ° ~ 360 °.

On actual well drilled track, gather the well depth of measuring point, hole angle, azimuth and angle, computational tool face by inclinometer, suppose that well section AB is a non-cylindrical spiral locus model waiting change, is all the spatial shape in order to portray drilled wellbore trajectories.Space coordinates (the x of arbitrfary point P in well section _p, y _p, z _p) determination, need A point hole angle α in well section AB _a, azimuth φ _a, well depth L _a, tool face azimuth ω _a, space coordinates (x _a, y _a, z _a) and B point hole angle α _b, azimuth φ _b, well depth L _band non-etc. become cylindrical spiral equation of locus, obtained by formula (7) and (8).

$\left\{\begin{array}{c}{x}_P=\frac{1}{6}\mathrm{\κ\τ}{T}_{21}{(L_P-L_A)}^3+\frac{1}{2}\mathrm{\κ}{T}_{11}{(L_P-L_A)}^2+T_{31}(L_P-L_A)+x_A\\ y_P=\frac{1}{6}\mathrm{\κ\τ}{T}_{22}{(L_P-L_A)}^3+\frac{1}{2}\mathrm{\κ}{T}_{12}{(L_P-L_A)}^2+T_{32}(L_P-L_A)+x_A\\ z_P=\frac{1}{6}\mathrm{\κ\τ}{T}_{23}{(L_P-L_A)}^3+\frac{1}{2}\mathrm{\κ}{T}_{13}{(L_P-L_A)}^2+T_{33}(L_P-L_A)+x_A\end{array}\right.---\left(18\right)$

So far, measuring point A and measuring point B deviational survey data and hypothesis two measuring points between be one non-wait change cylindrical spiral well track condition under, the computational methods giving the deviational survey data of any point P on the well track between two measuring points also finally determine the locus of P point, the well track compared between hypothesis two measuring point is wait the cylindrical spiral well track becoming helical angle, have more generality, result also has more generality.

Comparison before and after improving: from clinometers calculation in drilling process, deviational survey data are discrete point data, goes simulation for the drilling trajectory between adjacent two measuring points by assumed curve.Therefore, assumed curve is different, and the measuring point locus coordinate (vertical depth, eastern coordinate, northern coordinate) calculated by clinometers calculation method is also different.In view of in clinometers calculation methods all at present, drilling trajectory is all carry out calculating on the curve model basis of hypothesis, therefore be not definitely accurate computational methods, it is variant with actual drilling trajectory that this must result through the drilling trajectory that clinometers calculation method calculates.Therefore, by based on non-etc. become drilling trajectory that cylindrical spiral clinometers calculation method calculates and tradition etc. become cylindrical spiral inclinometry algorithm, based on the space circular arc curve inclinometry algorithm that is hypothesized model, be that the inclinometry algorithm of hypothesized model carries out error analysis and is necessary based on space line.

Now have chosen the measuring point data in 20 directional wells, each directional well measuring point data amount average out to 2000 carries out relative error analysis, analyzes data result as shown in table 1:

Table 1 four kinds of inclinometry algorithm Comparative result

Computational methods	North coordinate (m)	East coordinate (m)	Vertical depth (m)	Absolute error (m)
					Non-grade becomes cylindrical spiral	-39.4011	27.4846	1330.17	0
Deng change cylindrical spiral	-39.388	27.479	1330.16	0.0197
					Minimum-curvature method	-39.3925	27.4602	1330.16	0.0301
Average angle method	-39.378	27.46	1330.16	0.03519

In above table, northern coordinate, eastern coordinate, vertical depth are all average, and absolute error is square root sum square of difference of average of sample data Middle East coordinate, northern coordinate, vertical depth, and absolute error is all become cylindrical spiral relative to non-grade.In above-mentioned four kinds of arithmetic result, because on actual well drilled well track, the actual parameter of any point cannot be learnt, error analysis becomes cylindrical spiral into benchmark with non-grade, and error Producing reason is the Mathematical Modeling difference of selection and produces.At present, studies in China scholar prove, and average angle method is model owing to selecting to be straight line, therefore error can be relatively bigger than normal, minimum-curvature method selects space circular arc to be Mathematical Modeling, therefore error can be less than average angle method, become to wait the inclinometry algorithm that cylindrical spiral is model, error can be less than minimum-curvature method.

Can draw through data analysis, first, it is less that non-data result such as deviational survey such as cylindrical spiral such as change such as grade and grade become cylindrical spiral well track algorithm absolute error, larger with space circular arc well track algorithm absolute error, larger with space line well track algorithm absolute error, this meets expected results, because the inclinometry algorithm precision of cylindrical spiral model is greater than space circular arc well track inclinometry algorithm, space circular arc well track inclinometry algorithm is greater than space line well track inclinometry algorithm.Secondly, non-wait become cylindrical spiral inclinometry algorithm respectively with wait the absolute error becoming three kinds of inclinometry algorithms such as cylindrical spiral well track inclinometry algorithm, space circular arc well track inclinometry algorithm, space line well track inclinometry algorithm within error range, describe the non-correctness waiting change cylindrical spiral inclinometry algorithm.Finally, for the well track using ground turntable rotation boring method to get out, there is generality, utilize the non-of hypothesis to wait the cylindrical spiral well track becoming helical angle, have more rationally and applicability.

Claims (3)

1. wait based on non-the drilling trajectory acquisition methods becoming cylindrical spiral inclinometry algorithm, it is characterized in that, comprise the following steps:

(1) the deviational survey data of two adjacent measuring points are obtained;

(2) the deviational survey data of any point P between two adjacent measuring points are calculated according to the deviational survey data separate of two the adjacent measuring points cylindrical spiral model becoming helical angle such as non-;

(3) spatial coordinated information of this point is obtained according to the deviational survey data of the some P obtained;

(4) drilling trajectory is calculated according to the spatial coordinated information obtained.

2. according to claim 1 based on the non-drilling trajectory acquisition methods waiting change cylindrical spiral inclinometry algorithm, it is characterized in that, described step (2) comprises following sub-step:

(21) tool face azimuth of well section initial point in two adjacent measuring points is calculated;

(22) hole angle and the azimuth of a P is calculated according to the tool face azimuth of well section initial point obtained and well depth.

3. according to claim 2ly wait based on non-the drilling trajectory acquisition methods becoming cylindrical spiral inclinometry algorithm, it is characterized in that, the described non-cylindrical spiral model of change helical angle that waits is set up based on local coordinate system; Described local coordinate system is with well section initial point in two adjacent measuring points for the origin of coordinates, and ξ axle points to the principal normal direction of well track, and η axle points to the binormal direction of well track, and ζ axle points to the tangential direction of well track.