CN101387198A - Monitoring method for drilled wellbore trajectories - Google Patents

Abstract

The invention relates to a drilling engineering technology in petroleum engineering, in particular to a method for monitoring the track of an actually drilled wellbore. The method comprises the following steps: acquisition of inclination survey data and naturalization treatment; determination of characteristic parameters of a wellbore track model; determination of a hole inclination equation and an azimuth equation; calculation of coordinate increment; calculation of surveying point coordinates; and so on. As for large-displacement wells containing catenary or parabola tracks and various directional wells and horizontal wells, the method can accurately monitor the coordinates of various surveying points, so as to make the monitoring result accord with the practice of the drilling engineering, thereby effectively improving the construction precision and the reliability of catenary drilling and parabola drilling.

Description

A kind of monitoring method of drilled wellbore trajectories

Technical field

The present invention relates to the drilling engineering technology of petroleum works, be specifically related to the monitoring method of drilled wellbore trajectories.

Background technology

The real inclinometer that bores track is the important step in the oil drilling, also is the important foundation data of well cementation completion, oil production technology, underground work and oil field development.No matter be measurement while drilling in the drilling process or the repetition measurement after the completion, can obtain a series of measuring point, each measuring point has provided corresponding to the hole angle of well depth and azimuth.The main task that deviational survey calculates is exactly to go out the coordinate position of these measuring points according to the deviational survey data computation, thereby obtains the shape of drilled wellbore trajectories.

Drilled wellbore trajectories is a continuous smooth space curve, but can only obtain the basic parameter at each discrete measuring point place during deviational survey, can't know the actual form of well track in each survey section, so the computational methods of drilled wellbore trajectories all are to be based upon on certain assumed condition and the Mathematical Modeling basis.Up to the present, the deviational survey computational methods of drilled wellbore trajectories have kind more than 20, and the typical calculation method that obtains through induction-arrangement also has 10 kinds.Traditional deviational survey computational methods are that the well track that will survey in the section is assumed to be comparatively simple curve form such as straight line, broken line, cylindrical spiral, space circular arc and natural curve.

Since the nineties in 20th century, extended reach well has worldwide obtained applying, and has particularly brought into play important function in the oil-gas field development in platform and sea, beach at sea, has obtained huge economic benefit.The frictional resistance and the moment of torsion that how to reduce drill string are key technologies that realizes the extended reach well drilling well.For frictional resistance and the moment of torsion, the force-bearing situation that improves drill string that reduce drill string, help improving rate of penetration and cementing quality, new technologies such as drilling well of stretched wire collimation method and parabolic method drilling well have appearred.Drilling well of stretched wire collimation method and parabolic method drilling well are that well track is designed to catenary and parabola.

But, also do not have corresponding with it deviational survey computational methods for catenary shape profile and parabolic path.In other words, even be drilled to the well track that meets catenary or parabolic fully, existing deviational survey computational methods also can not get precise calculation result.At present, all only be used for the borehole track design for the research of catenary track and parabolic orbit, and only limit to two-dimentional well bore section.But the well track that no matter designs is two dimension or three-dimensional, and the well track of Zuaning all is three-dimensional in fact.The monitoring method of present catenary shape profile and parabolic path can only be continued to use conventional method and carry out deviational survey calculating, usually use minimum-curvature method or cylinder helix method, i.e. method among the proposed standard SY/T5435-2003 " directional well orbit Design and track calculate SY/T5435-2003 " of State Economic and Trade Commission's issue on March 30th, 2003.

Summary of the invention

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

At the deficiency that does not have catenary, parabola well track monitoring method in the prior art, the purpose of this invention is to provide a kind of drilled wellbore trajectories monitoring method, make for comprising catenary or parabolical well track, can monitor out the real coordinate that bores each measuring point on the track exactly.Make the result more meet drilling engineering reality.

Use inclinometer can record real hole angle and azimuth of boring each measuring point on the track, and with well depth as sign.Therefore, the deviational survey data are measuring points of series of discrete, and its basic parameter is: well depth, hole angle, azimuth.The basic task that deviational survey calculates is: calculate the increment of coordinate of surveying in the section.Like this,, pursue the increment of coordinate that adds up with surveying section, just can obtain the coordinate figure of each measuring point from well head.

A bite well can comprise multiple multi-form well section, as straightway, arc section, cylindrical spiral section, stretched wire line segment, parabolic segment or the like.When deviational survey calculated, each was surveyed section and all should adopt and the actual well track model that conforms to of engineering.

The present invention comes down to specific well track, by specific step, determines the coordinate figure of each measuring point, thereby realizes the effective monitoring to real brill track.

In the present invention, specific well track is meant: catenary or parabola.

When the well track in surveying section is other general types, can obtain the coordinate figure of each measuring point, not belong to content of the present invention with known conventional method.

Technical scheme of the present invention is:

A kind of monitoring method of drilled wellbore trajectories for comprising catenary or parabolical well track, obtains the real trajectory coordinates of boring of this catenary well section or parabola well section.Comprise following basic step:

In the 1st step, obtain the deviational survey data, and do naturalization and handle:

Measure: go up measuring point well depth L ₁, go up measuring point hole angle α ₁, go up measuring point azimuth φ ₁, following measuring point well depth L ₂, following measuring point hole angle α ₂, following measuring point azimuth φ ₂

Provide: go up measuring point north coordinate N ₁, go up measuring point east coordinate E ₁, go up measuring point vertical depth coordinate H ₁

This metering system is a usual manner of the prior art, for example uses deviational survey instruments such as MWD, electronics multiple spot to measure hole angle α and azimuth φ corresponding to certain well depth L.The present invention does not relate to concrete measuring apparatus and measuring method, uses the measuring apparatus of various routines and method can obtain these data.

According to the oil and gas industry standard, according to selected northern coordinate basis, the consideration magnetic declination and the convergence of meridians are carried out the azimuth naturalization, are about to the azimuth reduction to selected northern coordinate basis.

Well section between two adjacent measuring points is referred to as to survey section.For a survey section, measuring point and following measuring point are used subscript " 1 " and subscript " 2 " sign respectively on it, do not represent the numbering of measuring point.Therefore, the deviational survey data of measuring point are respectively (L up and down ₁, α ₁, φ ₁) and (L ₂, α ₂, φ ₂).

With the starting point that well head calculates as deviational survey, its three-dimensional coordinate generally all is taken as 0.Each surveys the increment of coordinate of section by calculating, and adds up piecemeal, obtains the coordinate figure of each measuring point.This is the conventional method that deviational survey calculates.

The 2nd step, definite well track model and characteristic parameter of surveying section:

According to drilling engineering design and the actual mode of creeping into and drilling technology measure, the well track model of selecting for use deviational survey to calculate.The present invention only relates to catenary or parabolic path, for the well track of other types, carries out the oil and gas industry standard, does not belong to content of the present invention.

The characteristic parameter of catenary shape profile represents that with small letter English alphabet a it is a mathematic parameter describing the catenary curve, has determined the shape of catenary.Hole angle is represented with alpha.

For catenary shape profile, the calculating formula of catenary characteristic parameter a is:

$a=\frac{L_2-L_1}{\frac{1}{\tan {\mathrm{\α}}_1}-\frac{1}{\tan {\mathrm{\α}}_2}}---\left(1\right)$

L in the formula: well depth, unit: m,

α: hole angle, unit: degree;

A: catenary characteristic parameter, unit: m;

The characteristic parameter of parabolic path represents that with capitalization English letter P it is a mathematic parameter describing parabolic curve, has determined parabolical shape.

For parabolic path, the calculating formula of parabola characteristic parameter P is:

$P=\frac{2(L_2-L_1)}{f\left({\mathrm{\α}}_1\right)-f\left({\mathrm{\α}}_2\right)}---\left(2\right)$

P in the formula: parabola parameter, unit: m;

$f\left(x\right)=\frac{1}{\sin x\tan x}-\ln \left(\tan \frac{x}{2}\right)---\left(3\right)$

The characteristic parameter a of catenary shape profile and the characteristic parameter P of parabolic path have determined the two dimensional character of well track, have promptly determined the shape of well track on the vertical cross section, and they have reflected the Changing Pattern of hole angle along well depth.As the real deviational survey computation model that bores track, also need the parameter of a reflection well track three-dimensional feature.In the present invention, for catenary shape profile and parabolic path, this characteristic parameter all is taken as rate of azimuth change.

For catenary shape profile and parabolic path, the calculating formula of rate of azimuth change is:

${\mathrm{\κ}}_{\mathrm{\φ}}=\frac{{\mathrm{\φ}}_2-{\mathrm{\φ}}_1}{L_2-L_1}---\left(4\right)$

In the formula: φ: azimuth, unit: degree;

κ _φ: rate of azimuth change, unit: degree/m;

In the 3rd step, determine hole deviation equation and azimuth equation:

For catenary shape profile, the hole deviation equation is:

$\mathrm{\α}=\arctan \left(\frac{1}{\frac{1}{\tan {\mathrm{\α}}_1}-\frac{L-L_1}{a}}\right)---\left(5\right)$

For parabolic path, the hole deviation equation is:

$f\left(\mathrm{\α}\right)=f\left({\mathrm{\α}}_1\right)-\frac{2(L-L_1)}{P}---\left(6\right)$

For catenary and parabola borehole track, azimuth equation is identical, for:

φ＝φ ₁+κ _φ(L-L ₁)(7)

Parameter is the same in various.In (5), (6), (7) formula, the characteristic parameter κ of the characteristic parameter a of catenary, parabolical characteristic parameter P and reflection orientation Changing Pattern _φDetermine by (1), (2), (4) formula respectively.

In the 4th step, calculate the increment of coordinate of surveying in the section:

North increment of coordinate Δ N, eastern increment of coordinate Δ E, vertical depth increment of coordinate Δ H are respectively:

$\mathrm{\ΔN}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\cos \mathrm{\φdL}---\left(8\right)$

$\mathrm{\ΔE}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\sin \mathrm{\φdL}---\left(9\right)$

$\mathrm{\ΔH}={\∫}_{L_1}^{L_2}\cos \mathrm{\α}\mathrm{dL}---\left(10\right)$

According to the 3rd step fixed well track model, hole deviation equation (5) or (6) that the 3rd step was determined, and in the above-mentioned formula of azimuth equation (7) substitution,, calculate increment of coordinate respectively by numerical integration method.Promptly use (5) or (6) and (7) formula substitution (8), (9) formula, (5) or (6) formula substitutions (10) formula.

Because α and φ are the functions of L, so with behind hole deviation equation α and the above-mentioned equation of azimuth equation φ substitution, they have just become with L is the integration type of independent variable.Adopt conventional numerical integration method, for example Simpson's integration method, Long Gekuta integration method etc. can be carried out numerical integration.For a survey section, because integrating range [L ₁, L ₂] determine, so can obtain three above-mentioned integrated values, and then obtain the increment of coordinate in this survey section.Δ N, Δ E and Δ H both can be on the occasion of also can being negative value.

In the 5th step, calculate measuring point coordinate down:

Following measuring point north coordinate N ₂, following measuring point east coordinate E ₂, following measuring point vertical depth coordinate H ₂Be respectively:

N ₂＝N ₁+ΔN (11)

E ₂＝E ₁+ΔE (12)

H ₂＝H ₁+ΔH (13)

According to increment of coordinate Δ N, the Δ E, the Δ H that calculate in the 4th step, and the coordinate N that goes up measuring point ₁, E ₁, H ₁, just can calculate down the coordinate N of measuring point by (11), (12), (13) formula ₂, E ₂, H ₂

By above-mentioned steps, draw down the real trajectory coordinates of boring of measuring point.

Like this, from well head point, just can determine the coordinate of each measuring point successively.

Usually, the D coordinates value of three directions has been enough to determine the well track position, in the engineering real work, also often increases the notion of using a horizontal length S.Can further expand basic technical scheme of the present invention, increase monitoring horizontal length:

In the 1st step, increase provides: go up measuring point horizontal length S ₁

In the 4th step, increase calculated level length increment Δ S:

$\mathrm{\ΔS}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\mathrm{dL}---\left(14\right)$

Hole deviation equation (5) or (6) substitution (14) formula with the 3rd step was determined by numerical integration method, calculate the increment of horizontal length;

Because the excursion of hole angle α is 0 °～180 °, thus Δ S always on the occasion of.

In the 5th step, increase and calculate the horizontal length S of measuring point down ₂:

S ₂＝S ₁+ΔS (15)

Draw down the real track three-dimensional coordinate and the horizontal length of boring of measuring point.

Measuring point horizontal length on also promptly increasing by one in given data increases (a 14) formula in integral equation, use the numerical integration mode equally, can draw down the horizontal length of measuring point.

In in the technique scheme the 4th step, all increment of coordinate all will use numerical integrating to find the solution.By Mathematical treatment, vertical depth increment of coordinate Δ H and horizontal length increment Delta S can be reduced to analytic expression respectively, make it not use numerical integration just can obtain its exact solution, are more convenient for using.

For catenary shape profile, in the 4th step, northern increment of coordinate Δ N, eastern increment of coordinate Δ E, vertical depth increment of coordinate Δ H, horizontal length increment Delta S are respectively:

$\mathrm{\ΔN}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\cos \mathrm{\φdL}---\left(8\right)$

$\mathrm{\ΔE}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\sin \mathrm{\φdL}---\left(9\right)$

$\mathrm{\ΔH}=a(\frac{1}{\sin {\mathrm{\α}}_1}-\frac{1}{\sin {\mathrm{\α}}_2})---\left(16\right)$

$\mathrm{\ΔS}=a\ln \left(\frac{\tan \frac{{\mathrm{\α}}_2}{2}}{\tan \frac{{\mathrm{\α}}_1}{2}}\right)---\left(17\right)$

(8), (9) formula calculates with numerical integration method, (16), (17) formula analytic calculation calculate three-dimensional coordinate increment and horizontal length increment respectively.

Promptly (8), (9) formula are the same with basic technical scheme, and hole deviation equation (5) and azimuth equation (7) substitution with the 3rd step was determined still calculate northern increment of coordinate Δ N and eastern increment of coordinate Δ E by numerical integration.And vertical depth increment of coordinate Δ H and horizontal length increment Delta S can use (1) formula and known parameters, are come out by (16), the direct analytical Calculation of (17) formula.

For parabolic path,,, can obtain concrete parabolic path hole deviation equation and be (3) formula substitution (6) formula in the 3rd step:

$\frac{1}{\sin \mathrm{\α}\tan \mathrm{\α}}-\ln \left(\tan \frac{\mathrm{\α}}{2}\right)=\frac{1}{\sin {\mathrm{\α}}_1\tan {\mathrm{\α}}_1}-\ln \left(\tan \frac{{\mathrm{\α}}_1}{2}\right)-\frac{2(L-L_1)}{P}---\left(18\right)$

Azimuth equation still is (7) formula.

In the 4th step, northern increment of coordinate Δ N, eastern increment of coordinate Δ E, vertical depth increment of coordinate Δ H, horizontal length increment Delta S are respectively:

$\mathrm{\ΔN}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\cos \mathrm{\φdL}---\left(8\right)$

$\mathrm{\ΔE}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\sin \mathrm{\φdL}---\left(9\right)$

$\mathrm{\ΔH}=\frac{P}{2}(\frac{1}{{\tan }^2{\mathrm{\α}}_1}-\frac{1}{{\tan }^2{\mathrm{\α}}_2})---\left(19\right)$

$\mathrm{\ΔS}=P(\frac{1}{\tan {\mathrm{\α}}_1}-\frac{1}{\tan {\mathrm{\α}}_2})---\left(20\right)$

Hole deviation equation (17) and azimuth equation (7) formula substitution (8), (9) formula that the 3rd step was determined are calculated by numerical integration method, and (19), (20) formula analytic calculation calculate three-dimensional coordinate increment and horizontal length increment respectively.

Promptly (8), (9) formula and basic technical scheme are similar, and the azimuth equation of substitution (7) is constant, and substitution improvement back the 3rd step determined new hole deviation equation (18), still calculate northern increment of coordinate Δ N and eastern increment of coordinate Δ E by numerical integration.And vertical depth increment of coordinate Δ H and horizontal length increment Delta S can use (2) formula and known parameters, are come out by (19), the direct analytical Calculation of (20) formula.

The present invention discloses the monitoring method of a kind of specific well track (catenary or parabola) in fact, can obtain a specific following measuring point coordinate figure of surveying section.Reuse method of the present invention, can obtain the coordinate figure of each measuring point on this specific well track.

Monitoring method of the present invention is mainly used in specific well track.In practical engineering application, because the well track of a bite well is not only catenary or parabola, thus should not use method of the present invention for other well sections, and should determine computational methods according to relevant industry standard.

Use method of the present invention monitoring catenary or parabolic path, calculate the measuring point coordinate of other types track, just can obtain each measuring point coordinate figure on the whole well track in conjunction with other known method.

The invention has the beneficial effects as follows:

Reality of the present invention is bored the track monitoring method, meets the actual conditions of catenary shape profile or parabolic path, and degree of accuracy height has improved the well track monitoring accuracy in the drilling engineering.Can be applicable to develop extended reach well and various directional well and horizontal well marine and sea, beach oil gas field, can improve drilling well success rate, wellbore quality and oil field development effect, reduce drill string and sleeve pipe frictional resistance and down-hole accident, save drilling cost.

Description of drawings

Fig. 1 is the design track vertical cut-away schematic view of typical catenary shape profile and parabolic profile.

Fig. 2 is the real horizontal projection schematic diagram that bores track.

Each symbol implication is as follows among the figure:

H _t: the vertical depth coordinate of target spot, m;

S _t: the horizontal length of target spot, m;

A _t: the horizontal movement of target spot, m;

O point: well head;

T point: target spot;

Oa section: steady tilted section

The ab section: arc section, radius of curvature are R;

Bc section: catenary or parabola, i.e. the well section that the present invention is suitable for;

Ct section: steady tilted 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.

During practical application, after basic step of the present invention, can also increase the real track monitoring chart that bores of step drafting: according to the oil and gas industry standard, list real tables of data of boring track result of calculation, draw out the vertical projection diagram, horizontal projection and the three-dimensional track figure that bore track in fact.

Example 1

Deviational survey data on the catenary shape profile (well depth, hole angle and azimuth), as shown in table 1.Table 1 has provided result of calculation summary of the present invention, and table 2 is the result of calculation summary of prior art minimum-curvature method.For simplifying length, only list the data of a part of well depth point in the table.

Table 1 catenary shape profile result of calculation of the present invention

Well depth m	Hole angle (°)	The azimuth (°)	North coordinate m	East coordinate m	Vertical depth m	Horizontal length m
							426.00	42.00	66.36	17.23*	40.65*	415.02*	44.15*
678.85	43.98	56.25	99.96	191.60	600.00	216.51
							1259.88	49.12	56.25	333.95	541.79	999.99	637.68
3382.95	76.40	98.71	697.88	2313.09	1999.96	2487.65
							3482.98	78.00	98.71	683.11	2409.50	2022.12	2585.19

The catenary shape profile result of calculation of table 2 minimum-curvature method

From well depth 426.00m to 3482.98m, the northern increment of coordinate of catenary shape profile, eastern increment of coordinate, vertical depth increment of coordinate and horizontal length increment are respectively 665.88m, 2368.85m, 1607.10m and 2541.04m, and are respectively 608.51m, 2381.3m, 1605.09m and 2541.71m with the result of calculation of minimum-curvature method.As seen, use the deviational survey computational methods such as minimum-curvature method of present widespread usage to calculate the very big error of catenary shape profile existence.

Example 2

Deviational survey data on the parabolic path, as shown in table 3.Table 3 has provided result of calculation summary of the present invention, and table 4 is the result of calculation summary of prior art minimum-curvature method.For simplifying length, only list the data of a part of well depth point in the table.

Table 3 parabolic path result of calculation of the present invention

The parabolic path result of calculation of table 4 minimum-curvature method

More than each the table in, ^*Represent known initial value.

Parabolic path from well depth 426.00m to 3322.34m, if the northern increment of coordinate, eastern increment of coordinate, vertical depth increment and the horizontal length increment that calculate with minimum-curvature method, to compare with the present invention, its error is respectively-54.39m, 28.82m ,-31.91m and 16.69m.

Claims (4)

1. The monitoring method of 1 one kinds of drilled wellbore trajectories for comprising catenary or parabolical well track, obtains the real trajectory coordinates of boring of this catenary well section or parabola well section; It is characterized in that, comprise the steps:

   In the 1st step, obtain the deviational survey data, and do naturalization and handle:

   Measure: go up measuring point well depth L ₁, go up measuring point hole angle α ₁, go up measuring point azimuth φ ₁, following measuring point well depth L ₂, following measuring point hole angle α ₂, following measuring point azimuth φ ₂

   Provide: go up measuring point north coordinate N ₁, go up measuring point east coordinate E ₁, go up measuring point vertical depth coordinate H ₁

   The 2nd step, definite well track model and characteristic parameter of surveying section:

   For catenary shape profile, the calculating formula of catenary PARAMETER ALPHA is:

   $a=\frac{L_2-L_1}{\frac{1}{\tan {\mathrm{\α}}_1}-\frac{1}{\tan {\mathrm{\α}}_2}}---\left(1\right)$

   L in the formula: well depth, unit: m,

   α: hole angle, unit: degree;

   A: catenary characteristic parameter, unit: m;

   For parabolic path, the calculating formula of parabola characteristic parameter P is:

   $P=\frac{2(L_2-L_1)}{f\left({\mathrm{\α}}_1\right)-f\left({\mathrm{\α}}_2\right)}---\left(2\right)$

   P in the formula: parabola parameter, unit: m;

   $f\left(x\right)=\frac{1}{\sin x\tan x}-\ln \left(\tan \frac{x}{2}\right)---\left(3\right)$

   For catenary shape profile and parabolic path, the calculating formula of rate of azimuth change is:

   ${\mathrm{\κ}}_{\mathrm{\φ}}=\frac{{\mathrm{\φ}}_2-{\mathrm{\φ}}_1}{L_2-L_1}---\left(4\right)$

   In the formula: φ: azimuth, unit: degree;

   κ _φ: rate of azimuth change, unit: degree/m;

   In the 3rd step, determine hole deviation equation and azimuth equation:

   For catenary shape profile, the hole deviation equation is:

   $\mathrm{\α}=\arctan \left(\frac{1}{\frac{1}{\tan {\mathrm{\α}}_1}-\frac{L-L_1}{a}}\right)---\left(5\right)$

   For parabolic path, the hole deviation equation is:

   $f\left(\mathrm{\α}\right)=f\left({\mathrm{\α}}_1\right)-\frac{2(L-L_1)}{P}---\left(6\right)$

   For catenary shape profile and parabolic path, azimuth equation is identical, for:

   φ＝φ ₁+κ _φ(L-L ₁) (7)

   In the 4th step, calculate the increment of coordinate of surveying in the section:

   North increment of coordinate Δ N, eastern increment of coordinate Δ E, vertical depth increment of coordinate Δ H are respectively:

   $\mathrm{\ΔN}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\cos \mathrm{\φdL}---\left(8\right)$

   $\mathrm{\ΔE}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\sin \mathrm{\φdL}---\left(9\right)$

   $\mathrm{\ΔH}={\∫}_{L_1}^{L_2}\cos \mathrm{\αdL}---\left(10\right)$

   With definite hole deviation equation (5) or (6) of the 3rd step, and in the above-mentioned formula of azimuth equation (7) substitution,, calculate the three-dimensional coordinate increment respectively by numerical integration method.

   In the 5th step, calculate measuring point coordinate down:

   Following measuring point north coordinate N ₂, following measuring point east coordinate E ₂, following measuring point vertical depth coordinate H ₂Be respectively:

   N ₂＝N ₁+ΔN (11)

   E ₂＝E ₁+ΔE (12)

   H ₂＝H ₁+ΔH (13)

   By above-mentioned steps, draw down the real trajectory coordinates of boring of measuring point.
2. The monitoring method of 2 drilled wellbore trajectories according to claim 1 is characterized in that:

   Increase is to the monitoring of horizontal length:

   In the 1st step, increase provides: go up measuring point horizontal length S ₁

   In the 4th step, increase calculated level length increment Δ S:

   $\mathrm{\ΔS}={\∫}_{L_1}^{L_2}\sin \mathrm{\αdL}---\left(14\right)$

   Hole deviation equation (5) or (6) substitution (14) formula with the 3rd step was determined by numerical integration method, calculate the increment of horizontal length;

   In the 5th step, increase and calculate the horizontal length S of measuring point down ₂:

   S ₂＝S ₁+ΔS (15)

   Draw down the real track three-dimensional coordinate and the horizontal length of boring of measuring point.
3. The monitoring method of 3 drilled wellbore trajectories according to claim 1 and 2 is characterized in that:

   For catenary shape profile, in the 4th step, northern increment of coordinate Δ N, eastern increment of coordinate Δ E, vertical depth increment of coordinate Δ H, horizontal length increment Delta S are respectively:

   $\mathrm{\ΔN}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\cos \mathrm{\φdL}---\left(8\right)$

   $\mathrm{\ΔE}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\sin \mathrm{\φdL}---\left(9\right)$

   $\mathrm{\ΔH}=a(\frac{1}{\sin {\mathrm{\α}}_1}-\frac{1}{\sin {\mathrm{\α}}_2})---\left(16\right)$

   $\mathrm{\ΔS}=a\ln \left(\frac{\tan \frac{{\mathrm{\α}}_2}{2}}{\tan \frac{{\mathrm{\α}}_1}{2}}\right)---\left(17\right)$

   (8), (9) formula calculates with numerical integration method, (16), (17) formula analytic calculation calculate three-dimensional coordinate increment and horizontal length increment respectively.
4. 4 monitoring methods according to the described drilled wellbore trajectories of claim 1 to 3 is characterized in that:

   For parabolic path, in the 3rd step, the hole deviation equation is:

   $\frac{1}{\sin \mathrm{\α}\tan \mathrm{\α}}-\ln \left(\tan \frac{\mathrm{\α}}{2}\right)=\frac{1}{\sin {\mathrm{\α}}_1\tan {\mathrm{\α}}_1}-\ln \left(\tan \frac{{\mathrm{\α}}_1}{2}\right)-\frac{2(L-L_1)}{P}---\left(18\right)$

   In the 4th step, northern increment of coordinate Δ N, eastern increment of coordinate Δ E, vertical depth increment of coordinate Δ H, horizontal length increment Delta S are respectively:

   $\mathrm{\ΔN}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\cos \mathrm{\φdL}---\left(8\right)$

   $\mathrm{\ΔE}={\∫}_{L_1}^{L_2}\sin \mathrm{\α}\sin \mathrm{\φdL}---\left(9\right)$

   $\mathrm{\ΔH}=\frac{P}{2}(\frac{1}{{\tan }^2{\mathrm{\α}}_1}-\frac{1}{{\tan }^2{\mathrm{\α}}_2})---\left(19\right)$

   $\mathrm{\ΔS}=P(\frac{1}{\tan {\mathrm{\α}}_1}-\frac{1}{\tan {\mathrm{\α}}_2})---\left(20\right)$

   Hole deviation equation (17) and azimuth equation (7) formula substitution (8), (9) formula that the 3rd step was determined are calculated by numerical integration method, and (19), (20) formula analytic calculation calculate three-dimensional coordinate increment and horizontal length increment respectively.

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