Horizontal well trajectory curve smooth filling method

Abstract

The invention relates to a horizontal well trajectory curve smooth filling method, and belongs to the technical field of drilling curve drawing. Comprising the following steps: step 1, determining coordinates of a reference point; e, a and b are known to be three sequential track points, a point c and a point d are specified reference points, the point c is a point on an extension line of an ea line segment, and ac = ab / 4; the point d is the midpoint of the ab line segment; the coordinates of c and d points are solved according to the coordinates of a, b and e (xa, ya), (xb, yb) and (xe, ye); 2, a third-order Bezier curve between ab is drawn according to the reference points; according to the method, two reference points are determined, and a third-order Bezier curve between two adjacent track points is drawn. And repeating the method to draw a smooth curve among all track points. An actual drilling track is simulated, a reverse curve is avoided, and the calculated well deviation angle is more real and accurate.

Description

Technical Field

[0001] The invention relates to a horizontal well trajectory curve smooth filling method, belonging to the technical field of drilling curve drawing. Background Art

[0002] In horizontal well guidance work, there are two main methods to calculate the well inclination angle based on the horizontal well trajectory points: the first is to connect adjacent trajectory points with a straight line, such as Figure 1 As shown in , this method is simple to calculate, but the error is large; the second method is to use a smooth curve filling algorithm to connect all trajectory points. Figure 2 The cubic spline interpolation algorithm shown in Figure 1 is more complex to calculate but has higher accuracy. However, in areas with large turning angles of the well trajectory, such as Figure 3 As shown, an erroneous reverse curve will appear. Summary of the invention

[0003] In order to solve the above problems existing in the prior art, the present invention discloses a method for smoothly filling a horizontal well trajectory curve. By determining two reference points, a third-order Bezier curve between two adjacent trajectory points is drawn to simulate the actual drilling trajectory, avoid the occurrence of reverse curves, and calculate the well inclination angle to be more realistic and accurate.

[0004] The technical solution adopted by the present invention is: a method for smoothly filling a horizontal well trajectory curve, comprising the following steps:

[0005] Step 1: Determine the coordinates of the reference point;

[0006] It is known that e, a, and b are three sequential trajectory points, and points c and d are designated reference points: point c is a point on the extension line of line segment ea, and ac=ab / 4; point d is the midpoint of line segment ab;

[0007] According to the a, b, e coordinates (x a ,y a )、(x b ,y b )、(x e ,y e ) Find the coordinates of points c and d:

[0008] Step 2: Draw a third-order Bezier curve between a and b according to the reference point;

[0009] (1) Take an integer i∈[0,N], where N is the curve filling accuracy, usually N=100;

[0010] (2) Take a point p1 on line segment ac, a point p2 on line segment cd, and a point p3 on line segment db, so that From this we can get the coordinates of points p1, p2, and p3:

[0011] (3) Take a point q1 on the line segment p1p2 and a point q2 on the line segment p2p3, so that From this we can get the coordinates of points q1 and q2:

[0012] (4) Take a point n on the line segment q1q2 such that From this we can get the coordinates of point n:

[0013] Calculate all n points (x i ,y i ) is the desired smooth curve.

[0014] Furthermore, it is known in step 1 that point c is a point on the extension line of line segment ea

[0015] It can be seen that:

[0016] Given: ac = ab / 4

[0017] It can be seen that:

[0018] Solving the system of equations yields:

[0019]

[0020]

[0021]

[0022] Since d is the midpoint of ab, we know that:

[0023]

[0024]

[0025] The invention discloses a horizontal well trajectory curve smooth filling method, which has the beneficial effect that the method used in the invention determines two reference points and draws a third-order Bezier curve between two adjacent trajectory points. Repeating this method draws smooth curves between all trajectory points. The actual drilling trajectory is simulated to avoid the occurrence of reverse curves, and the calculated well inclination angle is more real and accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0027] Figure 1: Draw a schematic diagram using the straight line connection method;

[0028] Figure 2 :Schematic diagram of cubic spline interpolation algorithm;

[0029] Figure 3 : Schematic diagram of reverse drawing of cubic spline interpolation algorithm;

[0030] Figure 4 : A schematic diagram of the smooth filling method of the present invention.

[0031] Specific implementation methods

[0032] In order to make the purpose, 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 in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0033] In order to further understand the content of the present invention, the present invention is further described below in conjunction with specific implementation methods.

[0034] With the algorithm used in the present invention as the core algorithm, a software program is written to realize drilling trajectory simulation and drilling inclination angle calculation.

[0035] Embodiment 1:

[0036] like Figure 4 As shown, a horizontal well trajectory curve smooth filling method comprises the following steps:

[0037] Step 1: Determine the coordinates of the reference point;

[0038] It is known that e, a, and b are three sequential trajectory points, and points c and d are designated reference points: point c is a point on the extension line of line segment ea, and ac=ab / 4; point d is the midpoint of line segment ab;

[0039] According to the a, b, e coordinates (x a ,y a )、(x b ,y b )、(x e ,y e ) Find the coordinates of points c and d:

[0040] Known: Point c is a point on the extension line of line segment ea

[0041] It can be seen that:

[0042] Given: ac = ab / 4

[0043] It can be seen that:

[0044] Solving the system of equations yields:

[0045]

[0046]

[0047]

[0048] Since d is the midpoint of ab, we know that:

[0049]

[0050]

[0051] Step 2: Draw a third-order Bezier curve between a and b according to the reference point;

[0052] (1) Take an integer i∈[0,N], where N is the curve filling accuracy, N=100;

[0053] (2) Take a point p1 on line segment ac, a point p2 on line segment cd, and a point p3 on line segment db, so that From this we can get the coordinates of points p1, p2, and p3:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] (3) Take a point q1 on the line segment p1p2 and a point q2 on the line segment p2p3, so that From this we can get the coordinates of points q1 and q2:

[0061]

[0062]

[0063]

[0064]

[0065] (4) Take a point n on the line segment q1q2 such that From this we can get the coordinates of point n:

[0066]

[0067]

[0068] Calculate all n points (x i ,y i ) is the desired smooth curve.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A horizontal well trajectory curve smooth filling method, characterized in that: The following steps are involved: Step 1: Determine the coordinates of the reference point; It is known that e, a, and b are three sequential trajectory points, and points c and d are designated reference points: point c is a point on the extension line of line segment ea, and ac=ab / 4; point d is the midpoint of line segment ab; According to the a, b, e coordinates (x a ,y a )、(x b ,y b )、(x e ,y e ) Find the coordinates of points c and d: Step 2: Draw a third-order Bezier curve between a and b according to the reference point; (1) Take an integer i∈[0,N], where N is the curve filling accuracy, N=100; (2) Take a point p1 on line segment ac, a point p2 on line segment cd, and a point p3 on line segment db, so that From this we can get the coordinates of points p1, p2, and p3: (3) Take a point q1 on the line segment p1p2 and a point q2 on the line segment p2p3, so that From this we can get the coordinates of points q1 and q2: (4) Take a point n on the line segment q1q2 such that From this we can get the coordinates of point n: Calculate all n points (x i ,y i ) is the desired smooth curve.

2. A horizontal well trajectory curve smooth filling method according to claim 1, characterized in that: In step 1, we know that point c is the point on the extension line of line segment ea. It can be seen that: Given: ac = ab / 4 It can be seen that: Solving the system of equations gives the coordinates of point c: Since d is the midpoint of ab, we can know the coordinates of point d:

3. A horizontal well trajectory curve smooth filling method according to claim 1, characterized in that: The coordinates of points p1, p2, and p3 in step 2:

4. A horizontal well trajectory curve smooth filling method according to claim 1, characterized in that: The coordinates of points q1 and q2 in step 2 are:

5. A horizontal well trajectory curve smooth filling method according to claim 1, characterized in that: The coordinates of the n points in step 2:

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