Drilling tool well track drawing method based on spherical coordinate system

Abstract

The invention relates to the technical field of directional drilling, in particular to a drilling tool well track drawing method based on a spherical coordinate system, according to the method, after a well track coordinate system is established, the spherical coordinate system is combined, multiple sets of well track coordinates are calculated through an iteration method, and finally well track drawing is completed. According to the method, the simplified processing that the drilling tool azimuth angle variable quantity is equivalent to the horizontal angle variable quantity is avoided, so that the well track drawing precision is effectively improved, and data support is provided for well track control and track trend prediction.

Description

Technical Field

[0001] The invention relates to the field of directional drilling, and in particular to a method for drawing a drilling tool wellbore trajectory based on a spherical coordinate system. Background Art

[0002] The wellbore trajectory drawing method can intuitively reflect the movement state of the drilling tool underground, and has important application value in the real-time control and trend prediction of the wellbore trajectory. However, the traditional method usually equates the azimuth change of the drilling tool with the horizontal angle change. This simplified processing ignores the difference between the two, resulting in insufficient accuracy in wellbore trajectory drawing. Under complex geological conditions, the impact of this lack of accuracy is particularly significant: it may cause the wellbore to deviate from the design target and increase drilling risks; it will also reduce the accuracy of trajectory control, affect drilling efficiency and increase operating costs; in addition, the lack of wellbore trajectory accuracy may cause the wellbore quality to decline, thereby affecting completion and oil production operations, and even leading to safety issues such as wellbore instability or collapse. Therefore, improving the accuracy of wellbore trajectory drawing is crucial to ensuring the success rate and safety of drilling operations. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the present invention proposes a method for drawing a borehole trajectory of a drilling tool based on a spherical coordinate system. After establishing the borehole trajectory coordinate system, the method combines the spherical coordinate system and uses an iterative method to calculate multiple sets of borehole trajectory coordinates, and finally completes the borehole trajectory drawing. Compared with the traditional method, this method avoids the simplified processing of equating the change in the azimuth angle of the drilling tool with the change in the horizontal angle, thereby effectively improving the accuracy of the borehole trajectory drawing. The algorithm flow of the borehole trajectory drawing based on the spherical coordinate system is as follows: Figure 1 shown.

[0004] The specific technical solution adopted by the present invention comprises the following steps:

[0005] Step 1: Construct the wellbore trajectory coordinate system and set the initial conditions. The specific implementation process is as follows:

[0006] Step 1.1, establish the wellbore trajectory coordinate system with the initial position of the drilling tool as the coordinate origin O, and the east direction, north direction and vertical downward direction as the positive directions of the X axis, Y axis and Z axis respectively.

[0007] Step 1.2: In this coordinate system, the drill bit drills from point O to point A after time t, as shown in the schematic diagram. Figure 2 As shown in the figure, the drilling speed of the drilling tool is set to be V, the magnitude of the guiding force is F, the direction of the guiding force, that is, the guiding angle is ω, and the wellbore trajectory coordinates (X O ,Y O ,Z O ), the vertical angle and horizontal angle of the drilling direction of the drill bit at point O are θ' O , Φ'O 。

[0008] Step 2: Based on the initial conditions, calculate the changes in well inclination angle and azimuth angle during the process of the drill string drilling from point O to point A. The specific implementation steps are as follows:

[0009] Step 2.1, According to the drill string guiding force F and guiding angle ω, calculate the build-up rate K, well inclination change rate K θ , and azimuth change rate K Φ :

[0010]

[0011] Experimental analysis shows that under the condition of unchanged external environment, the build-up rate of the drill string has a linear relationship with the guiding force, as Figure 3 shown. In formula (1), ɑ is the linear relationship parameter between the build-up rate of the drill string and the guiding force, and its value is affected by factors such as the elastic modulus of the drill string material and the formation anisotropy index. Under the condition of unchanged external environment, ɑ can be regarded as a constant.

[0012] Step 2.2, Under normal circumstances, the wellbore trajectory of the drill string is in a curved shape. After calculating the build-up rate, well inclination change rate, and azimuth change rate at point O based on formula (2), first calculate the straight-line distance D between points O and A, and then calculate the change in well inclination angle Δθ and the change in azimuth angle ΔΦ during this drilling process:

[0013]

[0014] According to the formula for the straight-line distance interval D, when K approaches 0, the interval D = V * t.

[0015] Step 3: Establish a spherical coordinate system and iteratively calculate multiple groups of wellbore trajectory coordinates. The specific implementation process is as follows:

[0016] Step 3.1, In the wellbore trajectory coordinate system, with point O as the origin of the spherical coordinate system and the interval D as the spherical radius, construct a spherical coordinate system. Mark the vertical angle θ’ O and horizontal angle Φ’ O of the trajectory point O, the straight-line distance interval D between points O and A, as well as the change in well inclination angle Δθ and the change in azimuth angle ΔΦ during this drilling process. The specific schematic diagram is as Figure 4 shown.

[0017] Step 3.2, After analysis, under the spherical coordinate system, the change in vertical angle Δθ’ of the OA section of the trajectory is equal to the change in well inclination angle Δθ, while the change in horizontal angle ΔΦ’ is not equal to the change in azimuth angle ΔΦ. Combining Figure 4 , derive the conversion formula between the two and calculate the vertical angle θ’ A and horizontal angle Φ’A As shown in Equation (3):

[0018]

[0019] In Step 3.3, combining the coordinates of point O, the linear distance between points O and A, and the vertical and horizontal angles of the drill string at point A, calculate the wellbore trajectory coordinates of point A as shown in Equation (4):

[0020]

[0021] After calculating the wellbore trajectory coordinates of point A, taking point A as the origin of the new spherical coordinate system, as the drill string drills to the next point within time t, repeat the above operations to iteratively obtain multiple sets of wellbore trajectory point coordinates.

[0022] Step 4: When the wellbore trajectory coordinate points calculated in Step 3 meet a certain number of conditions, draw the wellbore trajectory curve. Brief Description of the Drawings

[0023] Figure 1 is the flowchart of the method of the present invention;

[0024] Figure 2 is Figure 1 the schematic diagram of "the trajectory of section OA of the drill string in the wellbore trajectory coordinate system" in Step 1 of the method shown;

[0025] Figure 3 is Figure 1 the schematic diagram of "the relationship between the build rate of the drill string and the guiding force" in Step 2 of the method shown;

[0026] Figure 4 is Figure 1 the schematic diagram of "constructing a spherical coordinate system in the wellbore trajectory coordinate system" in Step 3 of the method shown;

[0027] Figure 5 is the wellbore trajectory effect diagram obtained by the present invention in the embodiment. Detailed Description of the Invention

[0028] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0029] Step 1, in the embodiment of the present invention, set the magnitude of the drill string guiding force to 60 MPa, the drill string guiding angle to 120°, the drill string penetration speed to 10 m / h, the linear relationship parameter between the build rate of the drill string and the guiding force in this environment to 0.04° / (m·MPa), the initial vertical angle of the drill string to 90°, and the initial horizontal angle to 0°. Taking the initial position of the drill string as the origin O, and taking the due east direction, due north direction, and vertically downward direction as the positive directions of the X-axis, Y-axis, and Z-axis respectively, construct a wellbore trajectory coordinate system. In this coordinate system, the drill string starts from point O and reaches point A after 1 s.

[0030] Step 2, according to the set guiding force and guiding angle of the drill string, calculate the build rate, well inclination change rate, and azimuth change rate of the drill string at point O. Then, based on the initial conditions set in Step 1, calculate the straight-line distance between points O and A of the drill string. Finally, use this straight-line distance to calculate the changes in well inclination angle and azimuth angle of the drill string in the wellbore trajectory section OA.

[0031] Step 3, in the wellbore trajectory coordinate system, taking point O as the origin of the spherical coordinate system and the straight-line distance between points O and A of the drill string as the spherical radius, construct a spherical coordinate system, and mark the vertical angle and horizontal angle of point O of the trajectory, the straight-line distance between points O and A, and the changes in well inclination angle and azimuth angle of the drill string in the trajectory section OA on the spherical coordinate system.

[0032] Step 4, combining the spherical coordinate system and the data marked on the spherical coordinate system in Step 3, calculate the vertical angle and horizontal angle of the drill string at point A.

[0033] Step 5, given the wellbore trajectory coordinates of the drill string at point O, calculate the wellbore trajectory coordinates of the drill string at point A. After 1 second, when the drill string drills from point A to point B, taking point A as the new origin of the spherical coordinate system, repeat the above calculation process to obtain the wellbore trajectory coordinates of point B. By analogy, calculate multiple sets of wellbore trajectory coordinates, and finally complete the drawing of the wellbore trajectory. In this example, a total of 360 sets of wellbore trajectory coordinates were calculated, and the obtained wellbore trajectory curve is as Figure 5 shown

[0034] From the above process, it can be seen that a wellbore trajectory drawing method based on the spherical coordinate system provided by the present invention can effectively distinguish the change amount of the azimuth angle and the change amount of the horizontal angle of the drill string, and can obtain more accurate wellbore trajectory results, providing data support for subsequent wellbore trajectory control and trajectory trend prediction.

Claims

1. A method for drawing drilling tool wellbore trajectory based on a spherical coordinate system, characterized in that: The wellbore trajectory coordinates are iteratively calculated based on the spherical coordinate system to complete the wellbore trajectory drawing, providing data support for wellbore trajectory control and trajectory trend prediction. The main steps of the method are as follows: after establishing the wellbore trajectory coordinate system, combined with the spherical coordinate system, an iterative method is used to calculate multiple groups of wellbore trajectory coordinates, and finally the wellbore trajectory drawing is completed.

2. The method for drawing drilling tool wellbore trajectory based on a spherical coordinate system according to claim 1, characterized in that: Combined with the spherical coordinate system, an iterative method is used to calculate multiple sets of wellbore trajectory coordinates, including the following steps: Step 1: In the borehole trajectory coordinate system, take point O as the origin of the spherical coordinate system and the interval D as the spherical radius to construct a spherical coordinate system. Mark the vertical angle θ' of the trajectory point O in the spherical coordinate system O Angle with horizontal Φ' O , the trajectory straight line distance interval D between the two points OA, and the change in the well inclination angle Δθ and the change in the azimuth angle ΔΦ during the drilling process; Step 2: After analysis, the vertical angle change Δθ' of the trajectory OA segment in the spherical coordinate system is equal to the well inclination change Δθ, while the horizontal angle change ΔΦ' is not equal to the azimuth change ΔΦ. Combined with Figure 4, the conversion formula between the two is derived, and the vertical angle θ' of point A is calculated A Angle with horizontal Φ' A As shown in formula (1): Step 3: Combine the coordinates of point O, the straight-line distance between points OA, and the vertical and horizontal angles of the drill bit at point A to calculate the coordinates of the wellbore trajectory at point A as shown in formula (2): After calculating the coordinates of the wellbore trajectory at point A, point A is taken as the origin of the new spherical coordinate system. As the drill bit drills to the next point within time t, the above operation is repeated to iteratively obtain multiple sets of wellbore trajectory point coordinates.

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