CN104594881B - Method for determining relative special positions of adjacent well parallel sections - Google Patents

Abstract

The invention provides a method for determining relative special positions of adjacent well parallel sections. The method comprises the steps of obtaining well condition information of a drilled well and a drilling well; processing the well condition information, and obtaining a wellhead coordinate of the drilled well in a drilling well wellhead coordinate system; obtaining data collected by a downhole exploring tube in a downhole electromagnetic detecting instrument; inclinometry calculation is performed on the drilling well and the drilled well, drawing an adjacent well distance sscannogram, determining a range of relative direction of horizontal sections of two horizontal wells; obtaining a relative position of the downhole exploring tube and a magnetic sub according to the data collected by the downhole exploring tube and the range of the relative direction of the horizontal sections of the two horizontal wells; determining relative spatial positions of the drilling well and the drilled well in the drilling well wellhead coordinate system according to the wellhead coordinate of the drilled well in the drilling well wellhead coordinate system and the relative position of the downhole exploring tube and the magnetic sub. In this way, the relative spatial positions of the adjacent well parallel sections can be determined, and the problems that in the prior art, the distance between the drilling well and the drilled well can not determined when axial magnetic induction intensity signals collected by the downhole exploring tube reach saturation are solved.

Description

Method for determining relative spatial position of parallel section of adjacent well

Technical Field

The invention relates to the technical field of underground resource drilling and production engineering, in particular to a method for determining the relative spatial position of parallel sections of adjacent wells.

Background

The reserves of the residual oil and natural gas in China mostly belong to low-grade or difficultly-used resources, the development difficulty is more and more high, and the development problem of coal bed gas also puts forward higher and higher urgent demands on the technology of wells with complex structures. In order to improve the recovery efficiency, wells with complex structures such as double horizontal wells, communication wells, U-shaped wells, multifunctional combination wells, cluster wells and the like are widely popularized in China. The modern complex structure well drilling and production technologies require accurate detection of the distance between two adjacent wells so that two adjacent wells are communicated or are drilled according to a designed interval, and an ideal well track control effect is difficult to achieve only by means of a traditional well track error analysis theory and a measurement while drilling tool.

The prior art discloses an adjacent well distance electromagnetic detection system while drilling and an underground electromagnetic detector. The hardware of the adjacent well distance while-drilling electromagnetic detection system mainly comprises a magnetic short section and an underground electromagnetic detector, and can detect the adjacent well distance while drilling and accurately realize the guiding well drilling control target of the well with the complex structure. The magnetic short section is composed of a plurality of permanent magnets which are arranged in a transverse mode and installed in a non-magnetic drill collar with API standard openings at two ends, and an alternating magnetic field generated by rotation of the magnetic short section and a drilling tool is a signal source of an adjacent well distance while-drilling electromagnetic detection system after the magnetic short section is closely connected with a drilling bit. The underground electromagnetic detector mainly comprises an underground probe and a ground system, and is mainly used for detecting magnetic signals of magnetic short sections connected with a drill bit in series and transmitting the detected magnetic signal data to the ground system through a cable.

The prior art also discloses a calculation method for Steam Assisted Gravity Drainage (SAGD) dual horizontal well electromagnetic distance measurement while drilling guidance, but when the distance between a well being drilled and a drilled well is close, an axial magnetic signal detected by a downhole electromagnetic detector of an electromagnetic detection system while drilling is saturated by using an adjacent well, and the method cannot be applied to determine the distance between the well being drilled and the drilled well.

In view of this, when an axial magnetic induction signal acquired by an underground probe in the detection of an underground electromagnetic detector reaches saturation, how to determine the relative spatial position of the parallel section of the adjacent well, and further determine the distance from the drilling well to the drilled well becomes a technical problem to be solved at present.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a method for determining the relative spatial position of the parallel section of the adjacent well.

In a first aspect, the present invention provides a method for determining the relative spatial positions of parallel sections of adjacent wells, comprising:

acquiring well condition information of a drilled well and a drilling well;

processing the well condition information to obtain well mouth coordinates of the drilled well in a well mouth coordinate system of the well mouth of the well, which is established by taking the well mouth position of the drilled well as a reference;

acquiring data collected by an underground probe in an underground electromagnetic detector;

carrying out inclination measurement calculation on the normal drilling well and the drilled well, drawing a distance scanning graph of adjacent wells of the normal drilling well and the drilled well, and determining the range of the relative position of the horizontal section of the double horizontal wells;

acquiring the relative position of the underground probe and the magnetic short section according to the data acquired by the underground probe and the range of the relative position of the horizontal section of the double-horizontal well;

and determining the relative spatial positions of the drilling well and the drilled well in the well head coordinate system of the drilling well according to the well head coordinate of the drilled well in the well head coordinate system of the drilling well and the relative positions of the underground probe and the magnetic short section.

Optionally, the well condition information comprises: measuring information of well track of the drilled well and the drilled well, wellhead coordinates of the drilled well and the drilled well, the plane height and the ground altitude of a drilling rig of the drilled well and the drilled well structure; and

the data collected by the downhole probe comprises: triaxial magnetic induction B generated by magnetic short section in well drilling_x、B_yAnd B_ZHigh Hs and unit vector of drilled wellIncluded angle A between_hx。

Optionally, the processing the well condition information to obtain wellhead coordinates of the drilled well in a wellhead coordinate system of the drilling well established with the position of the wellhead of the drilling well as a reference comprises:

establishing a well mouth coordinate system of the well by taking the well mouth position of the well as a reference according to the well condition information;

according to the drilling rig plane height and the ground altitude of the drilling and the drilling, obtaining the height of the drilling rig plane of the drilling which is higher or lower than the height of the drilling rig plane of the drilling;

determining whether the wellbore trajectory measurement information is relative to a rig floor height or a surface elevation;

acquiring the offset of the drilled well mouth relative to the drilled well mouth according to the coordinates of the drilled well mouth and the drilled well mouth;

adding or subtracting the offset to or from actual vertical depth, north and east coordinate data of a downhole sonde in a downhole electromagnetic sonde in the open well wellhead coordinate system.

Optionally, the acquiring data collected by a downhole probe in a downhole electromagnetic probe comprises:

according to the estimated distance D from the drilling well to the drilled well, a drilling rod or a crawler is used for descending a downhole probe in a downhole electromagnetic detector to a proper position of the drilled well, and the axial distance from the downhole probe to a drill bit in the drilling well is D;

and the drill bit continues to drill for a distance of 2D, and data collected at the distance from the underground probe is acquired.

Optionally, the acquiring the relative position of the downhole probe and the magnetic sub according to the data collected by the downhole probe and the range of the relative position of the horizontal section of the dual-horizontal well includes:

according to the data collected by the underground probe, calculating the radial distance r from the magnetic short section to the underground probe, the height Hs of the drilled well and the unit vectorIncluded angle A between_hr；

Determining an included angle A according to the range of the relative position of the horizontal section of the double horizontal well_hrThe value range of (a);

according to the radial distance r between the magnetic short section and the underground probe and the included angle A_hrAnd an included angle A_hrAnd obtaining the relative position of the underground probe and the magnetic short section.

Optionally, the radial distance r from the magnetic sub to the downhole probe is:

wherein,is at t₂The well depth where the magnetic short section is located at the moment,is represented at t₁The well depth of the magnetic short section is in the moment.

Optionally, the high side Hs of the drilled wellbore is associated with a unit vectorIncluded angle A between_hrComprises the following steps:

or,

wherein, | B_x|、|B_yI is the magnetic induction intensity B generated by the magnetic short section detected by the alternating magnetic field sensor x and y axes in the underground exploring tube_x、B_yAmplitude of the waveform, unit vector, in a uphole coordinate system established with reference to the uphole positionThe directions of the three-axis alternating magnetic field sensor are respectively the directions of the x axis and the y axis of the three-axis alternating magnetic field sensor in the underground probe tube, and are also the directions of the x axis and the y axis of other three-axis sensors, and the unit vectorIs drilling into the radial direction of the drilled well.

Optionally, after determining the relative spatial positions of the drilling well and the drilled well in the drilling wellhead coordinate system, further comprising:

adjusting the drill bit to continuously drill the next position according to the calculation result of the relative spatial positions of the forward drilling well and the drilled well in the forward drilling well head coordinate system;

and returning to the step of acquiring the data acquired by the underground probe in the underground electromagnetic detector until the drilling is finished.

According to the technical scheme, the method for determining the relative spatial position of the parallel section of the adjacent well comprises the steps of acquiring and processing well condition information of a drilled well and a drilled well, acquiring well mouth coordinates of the drilled well in a well mouth coordinate system of the drilled well, and acquiring data acquired by an underground probe in an underground electromagnetic detector; the method comprises the steps of carrying out inclination measurement calculation on a normal drilling well and a drilled well, drawing a distance scanning graph of an adjacent well, determining the range of the relative position of the horizontal section of a double-horizontal well, obtaining the relative position of the underground probe and a magnetic short section according to data acquired by the underground probe and the range of the relative position of the horizontal section of the double-horizontal well, and determining the relative spatial position of the normal drilling well and the drilled well in a normal drilling well mouth coordinate system according to the well mouth coordinate of the drilled well in the normal drilling well mouth coordinate system and the relative position of the underground probe and the magnetic short section.

Drawings

FIG. 1 is a schematic diagram illustrating the working principle of an adjacent well distance electromagnetic detection while drilling system used in the present invention in a cluster well;

FIG. 2 is a schematic flow chart illustrating a method for determining relative spatial positions of parallel sections of adjacent wells according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of the relative positions of a drilling well and a drilled well according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of a relative orientation calculation model of a drilling well and a drilled well according to an embodiment of the present invention;

FIG. 5 is a schematic illustration of a three-axis magnetic induction curve received over a period of time by a downhole probe in a downhole electromagnetic survey provided in accordance with an embodiment of the present invention;

FIG. 6 is a schematic diagram of a radial magnetic induction density variation curve with time according to an embodiment of the present invention;

FIG. 7 is a schematic diagram of the upper envelope of a radial magnetic induction curve according to an embodiment of the present invention;

reference numerals:

1. drilling a well; 2. drilling a well; 3. a magnetic nipple; 4. a downhole probe in the downhole electromagnetic survey instrument; 5. a drill bit; 6. a drill stem; 7. a cable; 8. a drilling tower; 9. a cable car; 31. magnetic lines of force.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.

Fig. 2 is a schematic flow chart of a method for determining the relative spatial position of a parallel section of an adjacent well according to an embodiment of the present invention, as shown in fig. 2, the method utilizes the adjacent well distance electromagnetic detection while drilling system shown in fig. 1, fig. 1 is a schematic diagram of the working principle of the adjacent well distance electromagnetic detection while drilling system used in the present invention in a cluster well, the method according to the present invention is a core method of the system applied to active collision prevention of the cluster well, and the method for determining the relative spatial position of a parallel section of an adjacent well according to the present embodiment is described as follows.

201. Well condition information of the drilled well and the well being drilled is obtained.

Wherein the well condition information comprises: borehole trajectory measurement information for drilled and drilled wells, wellhead coordinates for drilled and drilled wells, drill floor plan height KB and ground elevation GL for drilled and drilled wells, and well bore configuration for drilled wells

202. And processing the well condition information to obtain well mouth coordinates of the drilled well in a well mouth coordinate system of the drilled well, which is established by taking the well mouth position of the drilled well as a reference.

In a particular application, the present step 202 may include steps 202a-202e not shown in the figures:

202a, establishing a well mouth coordinate system of the well mouth of the well by taking the well mouth position of the well mouth of the well as a reference according to the well condition information.

202b, obtaining the height of the drilling platform plane of the drilling well higher or lower than the height of the drilling platform plane of the drilling well according to the height of the drilling platform plane of the drilling well and the ground altitude.

202c, determining whether the borehole trajectory measurement information is relative to a rig floor level or a surface elevation.

202d, obtaining the offset of the drilled well mouth relative to the drilled well mouth according to the coordinates of the drilled well mouth and the drilled well mouth.

202E adding or subtracting said offset to or from True Vertical Depth (TVD) data, north N and east E data of a downhole sonde in a downhole electromagnetic sonde in said uphole coordinate system.

203. And acquiring data acquired by an underground probe in the underground electromagnetic detector.

Wherein, the data that the exploration tube in the pit in the electromagnetic detection instrument was gathered includes: triaxial magnetic induction B generated by magnetic short section in well drilling_x、B_yAnd B_ZHigh Hs and unit vector of drilled wellIncluded angle A between_hx。

It should be noted that B_x、B_yAnd B_ZCan be measured by a triaxial alternating magnetic field sensor in an underground probe tube in an underground electromagnetic detecting instrument, and the included angle A_hxCan be measured by a triaxial acceleration sensor in a downhole probe in a downhole electromagnetic survey instrument.

In a specific application, the step 203 may include steps 203a and 203b not shown in the figure:

and 203a, according to the estimated distance D from the drilling well to the drilled well, a drill pipe or a crawler is used for descending a downhole probe in a downhole electromagnetic detector to the proper position of the drilled well, wherein the axial distance D from the downhole probe to a drill bit in the drilling well is provided.

203b, the drill bit continues to drill for a distance of 2D, and data collected at this distance from the downhole probe is acquired.

204. And carrying out inclination measurement calculation on the normal drilling well and the drilled well, drawing a distance scanning graph of adjacent wells of the normal drilling well and the drilled well, and determining the range of the relative azimuth of the horizontal section of the double horizontal wells.

It is to be understood that the inclination measurement calculation method in this step is an inclination measurement calculation method in the prior art, and the present invention is not limited thereto, and for example, a balanced tangent method, an average angle method, a minimum curvature method, a cylindrical spiral method, a corrected average angle method, a sinusoidal method, a natural parameter method, a constant device angle curve method, and the like may be used.

205. And acquiring the relative position of the underground probe and the magnetic short section according to the data acquired by the underground probe and the range of the relative position of the horizontal section of the double-horizontal well.

In a particular application, the present step 205 may include steps 205a-205c not shown in the figures:

205a, calculating the radial distance r from the magnetic short section to the underground probe, the height Hs of the drilled well and the unit vector according to the data collected by the underground probeIncluded angle A between_hr。

205b, determining an included angle A according to the range of the relative position of the horizontal section of the double horizontal well_hrThe value range of (a).

205c, according to the radial distance r between the magnetic short joint and the underground probe and the included angle A_hrAnd an included angle A_hrAnd obtaining the relative position of the underground probe and the magnetic short section.

Wherein, the radial distance r from the magnetic short section to the underground probe is as follows:

wherein,is at t₂The well depth where the magnetic short section is located at the moment,is represented at t₁The well depth where the magnetic short section is located at any time;

the high side Hs and unit vector of the drilled wellIncluded angle A between_hrComprises the following steps:

or

Wherein, | B_x|、|B_yI is the magnetic induction intensity B generated by the magnetic short section detected by the alternating magnetic field sensor x and y axes in the underground exploring tube_x、B_yAmplitude of the waveform, unit vector, in a uphole coordinate system established with reference to the uphole positionThe directions of the three-axis alternating magnetic field sensor are respectively the directions of the x axis and the y axis of the three-axis alternating magnetic field sensor in the underground probe tube and are also the directions of the x axis and the y axis of the three-axis alternating magnetic field sensorIts three-axis sensor has x, y directions and unit vectorIs drilling into the radial direction of the drilled well.

206. And determining the relative spatial positions of the drilling well and the drilled well in the well head coordinate system of the drilling well according to the well head coordinate of the drilled well in the well head coordinate system of the drilling well and the relative positions of the underground probe and the magnetic short section.

It can be understood that according to the relative spatial positions of the drilling well and the drilled well in the well head coordinate system of the drilling well, the drilling well-to-drilled distance can be determined.

In this embodiment, the included angle a is determined according to the range of the relative orientation of the horizontal section of the bi-horizontal well_hrSo as to finally determine the included angle A_hrBy r and an angle A_hrThe relative position of the underground probe and the magnetic short section can be determined, so that the relative spatial position of the drilling well and the drilled well in a well head coordinate system of the drilling well is determined, and scientific basis is provided for a directional drilling engineer to adjust the next well track.

According to the method for determining the relative spatial position of the parallel section of the adjacent well, the information of the well conditions of the drilled well and the drilled well is obtained and processed, the coordinates of the drilled well mouth in a well mouth coordinate system of the drilled well are obtained, and data collected by an underground exploring tube in an underground electromagnetic detector are obtained; the method comprises the steps of carrying out inclination measurement calculation on a drilling well and a drilled well, drawing a distance scanning graph of an adjacent well, determining the range of the relative position of the horizontal section of a double-horizontal well, obtaining the relative position of the drilling probe and a magnetic short section according to data acquired by the drilling probe and the range of the relative position of the horizontal section of the double-horizontal well, determining the relative spatial position of the drilling well and the drilled well in a drilling well head coordinate system according to the well head coordinate of the drilling well in the drilling well head coordinate system and the relative position of the drilling probe and the magnetic short section, determining the relative spatial position of the parallel section of the adjacent well, and solving the problem that the distance from the drilling well to the drilled well cannot be determined when axial magnetic induction intensity signals acquired by the drilling probe in the prior art are saturated.

In a specific application, after the step 206, the method may further include steps 207 and 208 not shown in the figure:

207. and adjusting the drill bit to continue to drill the next position according to the calculation result of the determined relative spatial positions of the drilling well and the drilled well in the well head coordinate system of the drilling well.

208. And returning to the step 203 until the drilling is completed.

In a specific application, in the step 205a, the radial distance r from the magnetic nipple to the downhole probe, the height Hs of the drilled well hole and the unit vector are calculated according to the data collected by the downhole probeIncluded angle A between_hr"in the process, reference may be made to fig. 3 and 4, fig. 3 shows a schematic diagram of relative positions of a drilling well and a drilled well provided in this embodiment, as shown in fig. 3, where an qrw orthogonal coordinate system takes a center of a magnetic sub as an origin, an extending direction of the drilling well as a w axis, a radial direction from the drilling well to the drilled well as an r axis, and a q axis is orthogonal to the w axis and the r axis at the same time; FIG. 4 is a schematic diagram of a relative orientation calculation model of a drilling well and a drilled well provided by the embodiment, as shown in FIG. 4, wherein a unit vector is in a drilling wellhead coordinate system established by taking a drilling wellhead position as a referenceAndrespectively represent the directions of the x, y and z axes of the three-axis alternating magnetic field sensor, and also represent the directions of the x, y and z axes of other three-axis sensors, and unit vectorsThe direction of (A) represents the direction of the equivalent magnetic moment of the magnetic short piece at a certain moment, Hs represents the high edge of a drilled well at the position of the underground probe, and A_mrRepresenting unit vectorsSum unit vectorAngle therebetween, A_hrRepresenting the high Hs and unit vector of the drilled wellboreAngle therebetween, A_hxRepresenting the high Hs and unit vector of the drilled wellboreAngle therebetween, A_xrRepresenting unit vectorsAndthe included angle between them;

when the distance between the drilling well and the drilled parallel well section is relatively short, the axial sensor in the underground probe tube in the underground electromagnetic detector is saturated, and in a coordinate system shown in figure 2, the distribution rule of a far-field magnetic field around the rotary magnetic short section can be obtained as follows:

the radial magnetic induction B can be obtained from the formulas (3) and (4)_R：

Due to B_ZCan be measured by a z-axis alternating magnetic field sensor in a downhole sonde in a downhole electromagnetic survey instrument, and

therefore, it is not only easy to use

When the magnetic short section passes through an underground exploring tube in the underground electromagnetic detecting instrument, the triaxial magnetic induction intensity B measured by a triaxial alternating magnetic field sensor in the underground exploring tube in the underground electromagnetic detecting instrument_x、B_yAnd B_ZThe time-dependent curve is shown in FIG. 5, and B can be obtained_RThe time-dependent profile is shown in FIG. 6;

as can be seen from FIG. 6, B is the magnetic nipple per rotation_RAll have a maximum value B_RupFrom the formula (5) to obtain B_RCan be expressed as:

B_Rupthe time profile is shown in fig. 7. From the formula (8):

when the formula (9) is equal to zero, it is understood that when z is 0, B is_RupReaches a maximum value, and

when z is equal to r/2,

the following equations (10) and (11) can be given:

as can be seen from FIG. 6, B_RupAt t₁And t₂Reach all the timeThus, the radial spacing r between the drilling and drilled parallel sections can be determined by:

r＝MD_t2-MD_t1(13)

wherein,is at t₂The well depth where the magnetic short section is located at the moment,is represented at t₁The well depth where the magnetic short section is located at any time;

at t₁Time of day or t₂At that time, the following expressions (1) to (3) can be used:

as shown in fig. 4, the magnetic field induction strength components detected by the x-axis and y-axis alternating magnetic field sensors in the downhole probe in the downhole electromagnetic detector are as follows:

B_x＝B_rcos(A_xr)-B_qsin(A_xr) (17)

B_y＝B_rsin(A_xr)+B_qcos(A_xr) (18)

substituting expressions (14) to (16) into expressions (17) and (18) can yield:

wherein,

the following equations (19) and (20) can be given:

wherein, | B_x|、|B_yI is the magnetic induction intensity B generated by the magnetic short section detected by the alternating magnetic field sensor x and y axes in the underground exploring tube_x、B_yThe amplitude of the waveform;

from the equation (25), the high side Hs and unit vector of the well-drilled well are knownIncluded angle A between_hrCan be obtained by the following formula:

or

The method for determining the relative spatial position of the parallel section of the adjacent well can determine the relative spatial position of the parallel section of the adjacent well, and solves the problem that the distance from a drilling well to the drilled well cannot be determined when axial magnetic induction intensity signals acquired by the underground probe in the prior art are saturated.

Those of ordinary skill in the art will understand that: all or a portion of the steps of implementing the above-described method embodiments may be performed by hardware associated with program instructions. The program may be stored in a computer-readable storage medium. When executed, the program performs steps comprising the method embodiments described above; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (1)

1. A method of determining the relative spatial positions of parallel sections of adjacent wells, comprising:

acquiring well condition information of a drilled well and a drilling well;

processing the well condition information to obtain well mouth coordinates of the drilled well in a well mouth coordinate system of the well mouth of the well, which is established by taking the well mouth position of the drilled well as a reference;

acquiring data collected by an underground probe in an underground electromagnetic detector;

carrying out inclination measurement calculation on the normal drilling well and the drilled well, drawing a distance scanning graph of adjacent wells of the normal drilling well and the drilled well, and determining the range of the relative position of the horizontal section of the double horizontal wells;

acquiring the relative position of the underground probe and the magnetic short section according to the data acquired by the underground probe and the range of the relative position of the horizontal section of the double-horizontal well;

determining the relative spatial positions of the drilling well and the drilled well in the well head coordinate system of the drilling well according to the well head coordinate of the drilled well in the well head coordinate system of the drilling well and the relative positions of the underground probe and the magnetic short section;

wherein, according to the data that the exploring tube in the pit gathered and the scope in the horizontal segment relative position of two horizontal wells, acquire the exploring tube in the pit and the relative position of magnetic nipple joint, include:

according to the data collected by the underground probe, calculating the radial distance r from the magnetic short section to the underground probe, the height Hs of the drilled well and the unit vectorIncluded angle A between_hr；

Determining an included angle A according to the range of the relative position of the horizontal section of the double horizontal well_hrThe value range of (a);

according to the radial distance r between the magnetic short section and the underground probe and the included angle A_hrAnd an included angle A_hrObtaining the relative position of the underground probe and the magnetic short section;

wherein, the radial distance r from the magnetic short section to the underground probe is as follows:

$r={\mathrm{MD}}_{t_2}-{\mathrm{MD}}_{t_1},$

wherein, B_RupAt t₁And t₂Reaches the moment B_Rupmax/1.9965，Is at t₂The well depth where the magnetic short section is located at the moment,is represented at t₁The well depth where the magnetic short section is located at any time; b is_RupRepresents that the magnetic short section rotates for one circle B_RThe maximum value of (a) is,B_Rupmaxrepresents B_RupMaximum value of (d); b is_x、B_yRepresenting the magnetic induction intensity generated by the magnetic short section detected by the X and Y axes of the alternating magnetic field sensor in the underground probe;

the high side Hs and unit vector of the drilled wellThe included angle Ahr between them is:

$A_{hr}=A_{hx}+\frac{1}{2}\arccos \left(\frac{37\left(\right|B_x{|}^2-\left|B_y{|}^2\right)}{12\left(\right|B_x{|}^2+\left|B_y{|}^2\right)}\right),$

or,

$A_{hr}=\mathrm{\π}+A_{hx}-\frac{1}{2}\arccos \left(\frac{37\left(\right|B_x{|}^2-\left|B_y{|}^2\right)}{12\left(\right|B_x{|}^2+\left|B_y{|}^2\right)}\right),$

wherein, | B_x|、|B_yI is the magnetic induction intensity B generated by the magnetic short section detected by the alternating magnetic field sensor x and y axes in the underground exploring tube_x、B_yAmplitude of the waveform, unit vector, in a uphole coordinate system established with reference to the uphole positionThe directions of the three-axis alternating magnetic field sensor are respectively the directions of the x axis and the y axis of the three-axis alternating magnetic field sensor in the underground probe tube, and are also the directions of the x axis and the y axis of other three-axis sensors, and the unit vectorIs drilling into the radial direction of the drilled well.