A casing running capacity evaluation method based on multi-arm correction reduction and feasible domain intersection

Abstract

The application discloses a casing and tubing string passing capacity evaluation method based on multi-arm correction reduction and feasible domain intersection, and belongs to the technical field of oil and gas well engineering logging interpretation and downhole string passing capacity evaluation. The method first pre-processes multi-arm caliper data, and reconstructs the casing inner contour by using the opposite measuring arm difference and closed circle center correction method; then, the corrected multi-arm caliper data and the inclination data are fused according to the depth to build the wellbore center line and the three-dimensional casing inner wall point. In the length range of the string to be evaluated, the string main shaft is fitted and the common reference plane is established, and the constraint region of each depth section is mapped to the reference plane. Through the internal shrinkage processing, intersection determination and dichotomy search of the feasible domain, the maximum passable outer diameter, the bottleneck depth, the bottleneck passable diameter and the passing capacity evaluation result of the string are obtained. The application can improve the accuracy and reliability of the casing and tubing string passing capacity evaluation of the casing and tubing string.

Description

Technical Field

[0001] This invention relates to the field of well logging interpretation in oil and gas well engineering, and specifically to a method for evaluating the throughput capacity of casing variable well strings based on the intersection of multi-arm correction and restoration and feasible region. Background Technology

[0002] During oil and gas well development and downhole operations, casing is susceptible to deformation due to factors such as hydraulic fracturing, formation slippage, non-uniform geostress, wellbore dogleg, and long-term production. This deformation can lead to issues like reduced diameter, ellipticization, breakage, localized depressions, or bulges. Casing deformation affects the insertion and passage of tubing, bridge plugs, perforating guns, and workover tools, potentially causing obstruction, jamming, or even operation failure. Therefore, accurately assessing the tubing's passage capacity in deformed sections is crucial for tubing and downhole tool selection and risk control during well operations.

[0003] Existing methods for evaluating the passage capacity typically employ mechanical or geometric analysis. Mechanical analysis methods often consider factors such as friction, axial load, tubing bending, and elastic deformation; geometric analysis methods rely on parameters such as the wellbore centerline trajectory, inclination angle, azimuth angle, wellbore curvature, minimum diameter, or maximum inscribed circle to determine whether the tubing string under evaluation can pass through. While these methods have some applicability in regular casing sections, they are still insufficient to accurately reflect the actual passage condition of the tubing string under evaluation in casing sections with significant local diameter reduction, non-circular deformation, and cross-sectional misalignment.

[0004] Multi-arm caliper logging can obtain radial data of the casing inner wall at different depths, which is an important basis for reconstructing the casing inner profile. However, multi-arm caliper data is susceptible to interference from instrument eccentricity, probe abnormalities, and local depressions. If directly used for 3D casing inner wall modeling and caliper calculation, it may lead to inaccurate reconstruction of the cross-section center and inner profile. At the same time, the tubing string to be evaluated with a certain length needs to meet the spatial constraints of multiple cross-sections simultaneously. Existing methods that evaluate based only on a single cross-section caliper or simplified geometric parameters suffer from insufficient evaluation accuracy. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a method for evaluating the throughput capacity of casing variable well strings based on the intersection of multi-arm correction restoration and feasible region. This method solves the problems in existing technologies where multi-arm well diameter data is affected by instrument eccentricity and local deformation, leading to inaccurate recovery of the casing inner contour, and insufficient accuracy in evaluating the throughput capacity of the string to be evaluated.

[0006] To achieve the aforementioned objectives, the present invention employs the following technical solution: a method for evaluating the throughput capacity of a casing-type well string based on the intersection of multi-arm correction and feasible region, comprising the following steps: S1. Preprocess the multi-arm well diameter data, correct the two-dimensional center offset of the cross section based on the differential closed circle center of the opposing arm, and restore the inner contour of each sounding section. S2. Merge the corrected and restored multi-arm well diameter data and well inclination data by depth, calculate the three-dimensional coordinates of the wellbore centerline and generate three-dimensional casing inner wall points; S3. Fit the principal axis of the tubing within the length window of the tubing to be evaluated, establish a common reference plane, and inversely map the constraint regions of each section to the common reference plane. S4. Find the intersection of the feasible regions of each section, and calculate the maximum passable outer diameter through a binary search. Output the bottleneck depth, bottleneck diameter, and passability evaluation results.

[0007] Furthermore, the multi-arm caliper data in S1 includes: depth, instrument rotation angle, and measurements from multiple probe arms; where the measurement from the i-th probe arm is denoted as... i = 1 to m, where m is an even number. In this embodiment, m is 24. The measured value of the measuring arm is used to characterize the radial distance of the inner wall of the casing at different positions on the corresponding depth measuring section.

[0008] Furthermore, S1 includes the following sub-steps: S11. Read the multi-arm caliper data, extract the depth, instrument rotation angle and the measurement values ​​of each arm, fill or correct missing or invalid values, and convert the measurement values ​​of each arm into radius data in a unified unit. S12. Determine the actual orientation of each measuring arm on the corresponding depth measurement section based on the number of measuring arms and the instrument rotation angle. S13. Pair the even number of measuring arms according to their opposing relationship, and calculate the center offset component in the corresponding direction based on the radius difference of the opposing measuring arms. S14. Determine the weights based on the degree of deviation of the closed diameter of each opposing measuring arm, and reduce the weights of abnormal measuring arm directions. S15. Based on the center offset components in each direction and their corresponding weights, solve for the two-dimensional center offset of each sounding section. S16. Correct and restore the radius data of each measuring arm according to the two-dimensional center offset to obtain the restored inner contour of each depth measuring section.

[0009] Furthermore, S2 includes the following sub-steps: S21. Using the corrected and restored multi-arm caliper data depth measurement as the main depth grid, determine the unified depth sequence for data merging; S22. Based on the unified depth sequence, interpolate the well inclination data to the corresponding depth measurement position to obtain the well inclination angle and azimuth angle corresponding to each depth measurement section; S23. Merge the corrected and restored multi-arm well diameter data with the interpolated well inclination data according to depth to form three-dimensional casing inner wall modeling data including the restored inner contour, instrument rotation angle, well inclination angle and azimuth angle. S24. Calculate the coordinate increments of the wellbore centerline in the north, east, and vertical directions based on the adjacent depth measurement intervals, well inclination angle, and azimuth angle; S25. Accumulate the coordinate increments point by point to obtain the three-dimensional coordinates of the wellbore centerline at each depth measurement location; S26. Generate three-dimensional casing inner wall points based on the three-dimensional coordinates of the wellbore centerline, the direction of the wellbore axis, and the inner contours of each sounding section after restoration.

[0010] Furthermore, the well inclination data in S22 includes: depth (DEPTH), well inclination angle (DEV), and azimuth angle (DAZ).

[0011] Furthermore, S3 includes the following sub-steps: S31. Based on the evaluation depth corresponding to the head position of the tubing to be evaluated. The length window of the tubing string to be evaluated is determined by the length L of the tubing string to be evaluated, and the three-dimensional coordinates of the three-dimensional casing inner wall points and the wellbore centerline within the length window of the tubing string to be evaluated are extracted. S32. Using the local sounding coordinates relative to the evaluation depth as independent variables, perform linear regression on the three-dimensional coordinates of the wellbore centerline within the length window of the tubing string to be evaluated to obtain the main axis direction and main axis reference point of the tubing string to be evaluated. S33. Based on the main axis direction and main axis reference point of the pipe column to be evaluated, establish a common reference plane perpendicular to the main axis of the pipe column to be evaluated, and establish a two-dimensional orthogonal coordinate system in the common reference plane; S34. Based on the three-dimensional casing inner wall points of each sounding section, form the cross-sectional constraint region of the corresponding sounding section; S35. Based on the geometric relationship between each sounding section and the common reference plane, the constraint region of each section is inversely mapped to the common reference plane.

[0012] Furthermore, the parameters for calculating the passability in S4 include: the candidate passability radius, the initial upper limit of the binary search, the initial lower limit of the binary search, and the calculation convergence accuracy.

[0013] Furthermore, S4 includes the following sub-steps: S41. Based on the candidate pass radius, the constraint regions of each section that are inversely mapped to the common reference plane are shrunk to obtain the feasible region of each section. The feasible region is the area in which the center of the pipe to be evaluated is allowed to be arranged in the corresponding section. S42. Find the intersection of the feasible regions of each section, and determine whether the candidate passable radius satisfies the passable condition based on whether the intersection is empty; S43. Based on the passing condition judgment result of the candidate passable radius, update the candidate passable radius by binary search; S44. Repeat the intersection and binary search update process of the feasible region until the preset calculation convergence accuracy is met, obtain the maximum passable radius at the current evaluation depth, and convert it to the maximum passable outer diameter; S45. Generate the throughput evaluation result based on the maximum passable outer diameter, and determine the bottleneck depth and bottleneck diameter within the evaluation well section; when inputting the outer diameter of the tubing string to be evaluated, further calculate the throughput margin.

[0014] The beneficial effects of this invention are: In the multi-arm caliper data processing stage, this invention first preprocesses the multi-arm caliper data and corrects the two-dimensional center offset of the calculation section based on the differential closed center of the opposing arm. This overcomes the limitations of existing technologies that directly use the original multi-arm caliper data for casing inner wall modeling and diameter calculation, reducing the impact of instrument eccentricity, arm anomalies, and local deformation on the restoration of the inner contour of the section. The corrected and restored multi-arm caliper data and well inclination data are merged by depth to generate three-dimensional casing inner wall points. The principal axis of the casing to be evaluated is fitted within the length window of the casing string to be evaluated, and a common reference plane is established. After inverse mapping of the constraint regions of each section to the common reference plane, the feasible region intersection calculation is performed. This comprehensively considers the spatial constraints of multiple sections within the length of the casing string to be evaluated, improving the accuracy of the evaluation results of the maximum passable outer diameter, bottleneck depth, and throughput capacity of the casing variable section casing string, effectively solving the problem of insufficient accuracy in the evaluation of the throughput capacity of casing variable section casing strings in existing technologies. Attached Figure Description

[0015] Figure 1 A flowchart of a method for evaluating the throughput capacity of a casing variable well string based on the intersection of multi-arm correction and restoration and feasible region; Figure 2 This is a schematic diagram illustrating the specific implementation process of the variable well string throughput capacity evaluation method of the present invention. Figure 3 This is a schematic diagram of the inner contour of the multi-arm wellbore diameter section before the differential closed circle center correction of the opposing measuring arm; Figure 4 This is a schematic diagram of the inner contour of the multi-arm wellbore diameter section after the differential closed circle center correction of the opposing measuring arms; Figure 5 A schematic diagram of constructing a feasible region for the inward contraction of the inner wall boundary of the multi-arm correction and restoration sleeve; Figure 6 A schematic diagram for determining the common feasible region by the intersection of multiple cross-section feasible regions. Detailed Implementation

[0016] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments.

[0017] For those skilled in the art, all variations and improvements made without departing from the spirit and essence of this invention should fall within the protection scope of this invention.

[0018] like Figure 1 As shown, a method for evaluating the throughput capacity of casing-type wellbore based on the intersection of multi-arm correction and feasible region includes the following steps: S1. Preprocess the multi-arm well diameter data, correct the two-dimensional center offset of the cross section based on the differential closed circle center of the opposing arm, and restore the inner contour of each sounding section. S2. Merge the corrected and restored multi-arm well diameter data and well inclination data by depth, calculate the three-dimensional coordinates of the wellbore centerline and generate three-dimensional casing inner wall points; S3. Fit the principal axis of the tubing within the length window of the tubing to be evaluated, establish a common reference plane, and inversely map the constraint regions of each section to the common reference plane. S4. Find the intersection of the feasible regions of each section, and calculate the maximum passable outer diameter through a binary search. Output the bottleneck depth, bottleneck diameter, and passability evaluation results.

[0019] like Figure 2 The diagram shown is a schematic of the specific implementation process of the casing variable well string throughput capacity evaluation method of the present invention. It is used to illustrate the processing flow of multi-arm well diameter data preprocessing and center offset correction, three-dimensional casing inner wall point generation, constraint section construction and mapping, feasible region intersection solution and binary search evaluation.

[0020] In this embodiment, the multi-arm caliper data in S1 includes: depth, instrument rotation angle, and multiple arm measurements; wherein, the measurement value of the i-th arm is denoted as... i = 1 to m, where m is an even number. In this embodiment, m is 24. The measured value of the measuring arm is used to characterize the radial distance of the inner wall of the casing at different positions on the corresponding depth measuring section.

[0021] In this embodiment, S1 includes the following sub-steps: S11. Read the multi-arm caliper data, extract the depth, instrument rotation angle and the measurement values ​​of each arm, fill or correct missing or invalid values, and convert the measurement values ​​of each arm into radius data in a unified unit. S12. Determine the actual orientation of each measuring arm on the corresponding depth measurement section based on the number of measuring arms and the instrument rotation angle. S13. Pair the even number of measuring arms according to their opposing relationship, and calculate the center offset component in the corresponding direction based on the radius difference of the opposing measuring arms. S14. Determine the weights based on the degree of deviation of the closed diameter of each opposing measuring arm, and reduce the weights of abnormal measuring arm directions. S15. Based on the center offset components in each direction and their corresponding weights, solve for the two-dimensional center offset of each sounding section. S16. Correct and restore the radius data of each measuring arm according to the two-dimensional center offset to obtain the restored inner contour of each depth measuring section.

[0022] In this embodiment, S11 specifically refers to: when the measuring arm measures the value When there are missing, non-numerical, or invalid values ​​less than or equal to zero, linear filling can be performed using data from adjacent valid sounding points; when the instrument rotation angle MITROT is missing or varies across cycles, it can be corrected using angle interpolation based on sine and cosine components; if the original measuring arm measurement value is in millimeters, it is divided by 1000 to convert it into radius data in meters.

[0023] S12 specifically refers to: Let the instrument rotation angle at the k-th sounding section be... Then the actual azimuth angle of the i-th measuring arm is: , Where i = 1 to m, Let be the actual azimuth angle of the i-th measuring arm on the k-th sounding section. Let MITROT be the instrument rotation angle at the k-th sounding section, and m be the number of measuring arms.

[0024] Based on the radius data of the i-th measuring arm and actual azimuth The two-dimensional coordinates of the end point of the measuring arm in the cross-sectional plane are obtained: , , in, and Let be the two-dimensional coordinates of the endpoint of the i-th measuring arm on the k-th sounding section within the section plane. The radius data of the i-th measuring arm on the k-th sounding section is the corresponding depth measurement. .

[0025] S13 specifically states: Assuming the number of measuring arms m is even, then the number j of the opposite measuring arm of the i-th measuring arm is: , Where i = 1 to m / 2.

[0026] The center offset component of the i-th pair of opposing measuring arms on the k-th sounding section is: , in, Let be the center offset component of the k-th sounding section in the direction of the i-th pair of opposing sounding arms. The radius data is for the i-th measuring arm on the k-th sounding section. The radius data of its opposing measuring arm.

[0027] The closed diameter corresponding to the i-th pair of opposing measuring arms on the k-th sounding section is: , in, The closed diameter is the diameter of the i-th pair of opposing measuring arms on the k-th sounding section. The closed diameter is used to characterize the total span measured by the measuring arms on both sides in the opposing direction, and is used to determine whether there are local depressions, bulges or abnormal measuring arms in this direction.

[0028] S14 specifically involves: first calculating the median of the closed diameter of each group of opposing measuring arms within the k-th sounding section. Then calculate the absolute deviation of the median of each closed diameter: , in, is the median absolute deviation of the closed diameter of the k-th sounding section, used to characterize the dispersion of the closed diameter in each direction of the section.

[0029] Let the deviation of the closed diameter of the i-th pair of opposing measuring arms be: , in, It represents the deviation of the closed diameter of the i-th pair of opposing measuring arms on the k-th sounding section.

[0030] The weights of the opposing measuring arms in the i-th group are determined based on the deviation of the closure diameter: when hour, , when hour, , in, The weight of the i-th pair of opposing measuring arms on the k-th sounding section; when the deviation of the closing diameter... Not greater than When the closed diameter in a given direction differs little from that in most other directions, the data for that direction is considered reliable, and a weight of 1 is assigned; when the closed diameter deviates by a certain amount... Greater than At that time, it was considered that the direction might be affected by local depressions, bulges, or abnormalities in the measuring arm, and according to The weight of this direction is reduced; thus, the greater the deviation of the closed diameter, the smaller the corresponding weight, thereby reducing the impact of abnormal directions on the subsequent solution of the two-dimensional circle center offset.

[0031] S15 specifically means: Let the unit vector of the i-th group facing the measuring arm be: , in, Let be the unit vector in the direction of the i-th pair of opposing measuring arms on the k-th sounding section. The actual azimuth angle corresponding to the direction of the opposing measuring arms in this group is T, where T is the matrix transpose. Let the offset of the two-dimensional center of the k-th sounding section be: , in, Let be the offset of the two-dimensional circle center to be determined. and These are the components of the center offset in the two directions of the cross-section in the two-dimensional coordinate system, and T is the matrix transpose.

[0032] Establish the weighted least squares objective function: , in, Let be the center offset component of the k-th sounding section in the direction of the i-th pair of opposing sounding arms. The weights corresponding to the i-th pair of opposing measuring arms are summed within the range of i = 1 to m / 2; this objective function is used to find a two-dimensional circular center offset. This ensures that its components in each opposing measuring arm direction are as close as possible to the corresponding center offset components. Furthermore, the impact of abnormal directions on the solution results is reduced by using weights.

[0033] The corresponding matrix form is: , , , in, Let be the constraint matrix for the k-th sounding section. Let T be the weighted composite vector of the k-th sounding section; by solving the above matrix equation, the center offset components of multiple opposing arm directions are fused into the two-dimensional center offset of the current sounding section, and T is the matrix transpose.

[0034] S16 specifically refers to: Let the original two-dimensional coordinates of the i-th end point of the measuring arm on the k-th sounding section be: , in, Let be the original two-dimensional coordinates of the i-th end point of the measuring arm on the k-th sounding section. and These are the coordinate components of the endpoint of the measuring arm in the two-dimensional coordinate system of the cross section, and T is the matrix transpose.

[0035] Based on the two-dimensional circle center offset The coordinates of the probe end point are corrected, and the corrected coordinates of the probe end point are as follows: .

[0036] Calculate the corrected radius based on the corrected coordinates of the probe end point: , in, Let be the corrected radius of the i-th measuring arm on the k-th sounding section. and These are the corrected two-dimensional coordinate components; the endpoints of each corrected measuring arm within the same sounding section are connected in azimuth order to obtain the restored inner contour of the sounding section.

[0037] like Figure 3 and Figure 4 As shown, Figure 3 The inner profile of the multi-arm wellbore diameter section before differential closed circle center correction of the opposing measuring arms. Figure 4 This is the inner contour of the cross-section of the multi-arm wellbore after center offset correction, used to represent the change in the inner contour of the cross-section before and after the center offset correction of the multi-arm wellbore data.

[0038] In this embodiment, S2 includes the following sub-steps: S21. Using the corrected and restored multi-arm caliper data depth measurement as the main depth grid, determine the unified depth sequence for data merging; S22. Based on the unified depth sequence, interpolate the well inclination data to the corresponding depth measurement position to obtain the well inclination angle and azimuth angle corresponding to each depth measurement section; S23. Merge the corrected and restored multi-arm well diameter data with the interpolated well inclination data according to depth to form three-dimensional casing inner wall modeling data including the restored inner contour, instrument rotation angle, well inclination angle and azimuth angle. S24. Calculate the coordinate increments of the wellbore centerline in the north, east, and vertical directions based on the adjacent depth measurement intervals, well inclination angle, and azimuth angle; S25. Accumulate the coordinate increments point by point to obtain the three-dimensional coordinates of the wellbore centerline at each depth measurement location; S26. Generate three-dimensional casing inner wall points based on the three-dimensional coordinates of the wellbore centerline, the direction of the wellbore axis, and the inner contours of each sounding section after restoration.

[0039] In this embodiment, S21 specifically involves: using the multi-arm caliper data depth measurement sequence as a unified depth sequence. , in, A unified depth sequence for merging multi-arm wellbore caliper and well inclination data. Let k be the kth uniform depth point.

[0040] S22 specifically involves: interpolating the well inclination data to the corresponding depth measurement positions based on the unified depth sequence to obtain the well inclination angle and azimuth angle corresponding to each depth measurement section; assuming the depth measurement sequence of the well inclination data is: , in, This is a depth measurement sequence of well inclination data. This is the nth wellbore depth sounding point.

[0041] For any depth point in a uniform depth sequence Find two adjacent wellbore depth measurement points in the wellbore depth measurement sequence. and To satisfy: , Let the depth scaling factor be: , in, Representing a uniform depth point At adjacent wellbore depth sounding points and The positional ratio between them.

[0042] For the wellbore inclination angle DEV, linear interpolation is used for calculation: , in, To unify depth points The corresponding well inclination angle, and These represent the well inclination angles at adjacent well inclination sounding points.

[0043] For the azimuth angle (DAZ), circular interpolation is used to avoid erroneous jumps when the azimuth angle crosses a circle near 0° or 360°; specifically: , , , in, and Each azimuth angle is at a uniform depth point The cosine and sine components at the point, To unify depth points The corresponding azimuth angle; if the calculated... If the value is negative, it can be converted to the range of 0° to 360°; It is a two-parameter arctangent function that can determine the quadrant of the azimuth angle based on the signs of the sine component S and the cosine component C, thereby obtaining the correct azimuth angle.

[0044] S23 specifically refers to: for any depth point in a unified depth sequence... The corrected and restored multi-arm wellbore diameter data at this depth is merged with the well inclination data obtained by S22 interpolation to obtain the three-dimensional casing inner wall modeling data at this sounding location: , in, For the 3D casing inner wall modeling data corresponding to the k-th uniform depth point, To standardize depth points, The instrument rotation angle at this sounding section. This is the two-dimensional center offset of the sounding section. This is the set of points representing the inner contour of the sounding section after reconstruction. This represents the well inclination angle at that depth. Let be the azimuth angle at that depth; wherein, the restored inner contour point set can be represented as: ;in, Let be the corrected and restored two-dimensional endpoint coordinates of the i-th measuring arm on the k-th sounding section, and m be the number of measuring arms.

[0045] Arrange the 3D casing inner wall modeling data corresponding to all uniform depth points in the order of depth measurement to form a 3D casing inner wall modeling data sequence: Where G is the data sequence used for subsequent calculation of the three-dimensional coordinates of the wellbore centerline and generation of three-dimensional casing inner wall points, and k is the number of uniform depth points.

[0046] S24 specifically states: Let the depth measurement interval between the (k-1)th unified depth point and the kth unified depth point be... The well inclination angle corresponding to the kth uniform depth point is... ; azimuth angle is The vertical coordinate increment of the wellbore centerline is: , The coordinate increment of the wellbore centerline in the northward direction is: , The coordinate increment of the wellbore centerline in the eastward direction is: , in, This represents the vertical coordinate increment between the (k-1)th and kth unified depth points. This represents the northward coordinate increment. This represents the eastward coordinate increment.

[0047] S25 specifically refers to: Assuming the three-dimensional coordinates of the wellbore centerline at the initial sounding point are: , in, The three-dimensional coordinates of the wellbore centerline at the initial sounding point. , and Here, represents the north, east, and vertical coordinates of the initial sounding point, respectively, and T is the matrix transpose; typically, we can take: .

[0048] For the k-th uniform depth point, the three-dimensional coordinates of the wellbore centerline are recursively calculated based on the coordinate increments obtained from S24: , Right now: , , , in, Let the three-dimensional coordinates of the well centerline at the k-th uniform depth point be denoted as . Let be the three-dimensional coordinates of the well centerline at the (k-1)th uniform depth point; , and Let T be the north, east, and vertical coordinates of the k-th unified depth point, respectively, and T be the matrix transpose. By accumulating the coordinate increments corresponding to each depth measurement interval point by point, the three-dimensional trajectory of the continuous wellbore centerline along the depth measurement direction can be obtained.

[0049] S26 specifically involves: First, based on the inclination angle and azimuth angle at the k-th uniform depth point, calculating the unit direction vector of the wellbore axis at that depth measurement location: , in, Let be the unit direction vector of the wellbore axis at the k-th uniform depth point. Let the inclination angle be the wellbore at the k-th uniform depth point. Let be the azimuth angle at the k-th uniform depth point, and T be the matrix transpose.

[0050] In the unit direction vector perpendicular to the wellbore axis Establish a two-dimensional orthogonal basis in the cross-sectional plane; let the global vertical reference vector be: Then the first basis vector in the cross-sectional plane is: , The second basis vector in the cross-sectional plane is: , in, and Let g be a two-dimensional orthogonal basis in the plane of the k-th sounding section; if g and Nearly parallel, resulting in If the mold length is too small, then a length that is equal to the mold length can be selected. Construction of other non-parallel reference vectors .

[0051] Let the three-dimensional coordinates of the well centerline at the k-th uniform depth point be: , Let the corrected and restored two-dimensional endpoint coordinates of the i-th measuring arm on the k-th sounding section be: , Then the i-th point on the inner wall of the three-dimensional casing on the k-th sounding section is: , in, Let T be the three-dimensional casing inner wall point corresponding to the i-th measuring arm on the k-th sounding section, and T be the matrix transpose. By calculating each sounding section and each measuring arm endpoint in the above manner, a set of three-dimensional casing inner wall points for subsequent string passage capacity evaluation can be obtained.

[0052] In this embodiment, S3 includes the following sub-steps: S31. Based on the evaluation depth corresponding to the head position of the tubing to be evaluated. The length window of the tubing string to be evaluated is determined by the length L of the tubing string to be evaluated, and the three-dimensional coordinates of the three-dimensional casing inner wall points and the wellbore centerline within the length window of the tubing string to be evaluated are extracted. S32. Using the local sounding coordinates relative to the evaluation depth as independent variables, perform linear regression on the three-dimensional coordinates of the wellbore centerline within the length window of the tubing string to be evaluated to obtain the main axis direction and main axis reference point of the tubing string to be evaluated. S33. Based on the main axis direction and main axis reference point of the pipe column to be evaluated, establish a common reference plane perpendicular to the main axis of the pipe column to be evaluated, and establish a two-dimensional orthogonal coordinate system in the common reference plane; S34. Based on the three-dimensional casing inner wall points of each sounding section, form the cross-sectional constraint region of the corresponding sounding section; S35. Based on the geometric relationship between each sounding section and the common reference plane, the constraint region of each section is inversely mapped to the common reference plane.

[0053] In this embodiment, S31 specifically involves: evaluating depth. As the head position of the tubing string to be evaluated is defined, the depth measurement increases along the well depth direction. Therefore, the starting and ending depth measurements for the length window of the tubing string to be evaluated are as follows: ; ;in, This refers to the depth sounding location corresponding to the tail end of the tubing to be evaluated. L represents the depth measurement position corresponding to the head of the string to be evaluated, and L represents the length of the string to be evaluated.

[0054] Based on the initial and final depth measurements, determine the set of depth measurement sections within the string length window to be evaluated: , in, To evaluate the head depth of the tubing The set of depth measurement section numbers within the window of the string length to be evaluated, determined by the string length L to be evaluated. Let k be the kth uniform depth point.

[0055] For any sounding section belonging to the string length window to be evaluated Extract the three-dimensional coordinates of the wellbore centerline of the sounding section: , And the three-dimensional casing inner wall point set of the sounding section: , in, Let be the three-dimensional coordinates of the wellbore centerline at the k-th sounding section. Let k be the set of points on the inner wall of the casing in three dimensions. Let m be the three-dimensional casing inner wall point corresponding to the i-th measuring arm on the k-th sounding section, and m be the number of measuring arms.

[0056] Through the above processing, a three-dimensional coordinate sequence of the wellbore centerline and a three-dimensional casing inner wall point sequence within the length range of the tubing to be evaluated can be obtained, which can be used for subsequent fitting of the main axis of the tubing to be evaluated and construction of the cross-sectional constraint region.

[0057] S32 specifically refers to: the window for the length of the tubing to be evaluated. The k-th sounding section within the depth is defined relative to the evaluation depth. The local sounding coordinates are: , in, Here are the local sounding coordinates of the k-th sounding section. For the depth measurement of the k-th sounding section, This represents the evaluation depth corresponding to the head of the tubing to be evaluated; since the length window of the tubing to be evaluated is... ,therefore The range of values ​​is .

[0058] The three-dimensional coordinates of the wellbore centerline within the window of the tubing length to be evaluated are: , The main axis of the column to be evaluated was fitted using linear regression: , Where o is the reference point of the principal axis of the tubing to be evaluated, and v is the principal axis direction vector obtained by fitting.

[0059] After obtaining o and v through least squares fitting, the direction vectors are normalized to obtain the main axis direction of the pipe column to be evaluated: , Where 'a' represents the principal axis direction of the pipe column to be evaluated; the purpose of this step is to approximate the axial direction of the pipe column to be evaluated within the length window with a spatial straight line, providing a geometric reference for the subsequent establishment of a common reference plane and inverse mapping of the cross-sectional constraint region.

[0060] Specifically, S33 is as follows: Let the principal axis direction of the pipe string to be evaluated obtained in S32 be a, and the principal axis reference point be o. Then the common reference plane can be represented as: , in, Let X be any point in space, a be the direction of the principal axis of the pipe to be evaluated, and o be the principal axis reference point. This formula indicates that the common reference plane passes through the principal axis reference point and is perpendicular to the principal axis of the pipe to be evaluated.

[0061] Two mutually perpendicular unit direction vectors, u and v, are selected within the common reference plane as the two-dimensional coordinate axes of the plane; any point within the common reference plane can be represented as: , in, and Here are the two-dimensional coordinates of the point in the common reference plane. Through the above processing, the problem of calculating the passability in three-dimensional space can be transformed into the same two-dimensional reference plane, providing a unified coordinate basis for the subsequent inverse mapping of the constraint regions of each section and the intersection of the feasible regions.

[0062] S34 specifically involves connecting the inner wall points of each three-dimensional casing within the same sounding section according to the orientation of the measuring arm, forming the section boundary of the sounding section, and using this section boundary to enclose the section constraint area. , in, This represents the cross-sectional constraint region of the k-th sounding section; This function represents the construction of a polygonal region by connecting the boundary points in a given order and closing the loop. This region represents the occupiable space defined by the inner wall of the casing at the sounding section. In subsequent capacity calculations, the circular section corresponding to the outer diameter of the pipe to be evaluated should be located within the constraint area of ​​this section.

[0063] S35 specifically involves establishing a correspondence between this point and the kth sounding section along the main axis direction a of the pipe string to be evaluated. , in, Points in a common reference plane Corresponding to the spatial point on the k-th sounding section, The distance parameter is along the main axis of the pipe string to be evaluated; based on the cross-sectional plane conditions of the k-th sounding section, it can be obtained. This allows us to determine the correspondence between points in the common reference plane and points in the sounding section.

[0064] The cross-sectional constraint region of the k-th sounding section Transform the above relationships into the common reference plane to obtain the corresponding planar constraint region: , in, This represents the constrained region after the k-th sounding section is inversely mapped to the common reference plane. The coordinates are two-dimensional coordinates within the common reference plane. This formula means that a position within the common reference plane is considered to satisfy the passage constraint of the section only if it is still within the constraint area of ​​the k-th sounding section after corresponding to the main axis of the pipe to be evaluated along the direction of the main axis of the pipe to be evaluated.

[0065] In this embodiment, S4 includes the following sub-steps: S41. Based on the candidate pass radius, the constraint regions of each section that are inversely mapped to the common reference plane are shrunk to obtain the feasible region of each section. The feasible region is the area in which the center of the pipe to be evaluated is allowed to be arranged in the corresponding section. S42. Find the intersection of the feasible regions of each section, and determine whether the candidate passable radius satisfies the passable condition based on whether the intersection is empty; S43. Based on the passing condition judgment result of the candidate passable radius, update the candidate passable radius by binary search; S44. Repeat the intersection and binary search update process of the feasible region until the preset calculation convergence accuracy is met, obtain the maximum passable radius at the current evaluation depth, and convert it to the maximum passable outer diameter; S45. Generate the throughput evaluation result based on the maximum passable outer diameter, and determine the bottleneck depth and bottleneck diameter within the evaluation well section; when inputting the outer diameter of the tubing string to be evaluated, further calculate the throughput margin.

[0066] In this embodiment, S41 specifically involves: assuming the candidate can pass through a constraint region with radius r, after the k-th sounding section is inversely mapped to the common reference plane. To ensure that the cross-section of the pipe column to be evaluated, with radius r, lies entirely within the constrained area, it is necessary to... By contracting the boundary inward by a distance r, we obtain the corresponding feasible region: , in, Let r be the feasible region of the k-th sounding section under the candidate passable radius r. Let r be a circular region. This represents geometric indentation operations.

[0067] like Figure 5 The diagram shows a feasible region formed by shrinking within the cross-sectional constraint area.

[0068] S42 specifically refers to the feasible region of each sounding section within the window of the length of the string to be evaluated. Then, perform an intersection operation on the feasible regions of all cross-sections: , in, The candidate can be considered as a common feasible region within the entire length window of the pipe to be evaluated, defined by radius r. The position of the head of the tubing to be evaluated The length window of the tubing to be evaluated is determined by the length L of the tubing to be evaluated.

[0069] If the common feasible region is not empty, it means that there is at least one center position of the pipe to be evaluated in the common reference plane, such that the cross section of the pipe to be evaluated with radius r can simultaneously satisfy the spatial constraints of all sounding sections within the length window of the pipe to be evaluated. The candidate is determined to be able to pass the radius to meet the passing condition.

[0070] If the common feasible region is empty, it means that there is no unified center position of the pipe to be evaluated that can simultaneously satisfy the constraints of all sections, and the candidate is determined to be passable because the radius does not meet the pass condition.

[0071] like Figure 6 The diagram shows a common feasible region obtained by intersecting multiple feasible regions.

[0072] S43 specifically involves: First, setting the initial lower bound and initial upper bound of the binary search, denoted as [insert values ​​here]. and ;in, Take 0, The radius can be determined based on the maximum allowable inscribed radius of each cross-sectional constraint region within the length window of the pipe to be evaluated; calculate the radius of the current candidate pipe that can pass through: , in, The radius is the passable radius for the candidate obtained from the current binary search.

[0073] Will Substitute S41 and S42 to calculate the feasible region of each section and determine if the common feasible region is empty; if the common feasible region is not empty, it means the radius is... If the tubing to be evaluated meets the pass criteria, then we can continue to try larger radii, and update the lower limit as follows: If the common feasible region is empty, it means the radius is... If the tubing to be evaluated does not meet the pass criteria, then the candidate pass radius needs to be reduced, and the upper limit updated is: .

[0074] S44 specifically refers to: Assuming a preset convergence accuracy of [value missing], In each binary search process, the intersection of feasible regions corresponding to the candidate passable radii is calculated according to S41 to S43, and the results are updated based on the passable condition judgment. and When the search interval satisfies: When the binary search has converged, the iteration stops, and the current lower bound is taken as the maximum passable radius. ;in, The head of the tubing to be evaluated is located in The maximum passable radius when the length of the tubing to be evaluated is L; calculate the maximum passable outer diameter based on the maximum passable radius: .

[0075] S45 specifically refers to selecting the location within the evaluation well section where the maximum passable outer diameter is minimized as the bottleneck depth. , in, This indicates that the objective function The independent variable that reaches its minimum value .

[0076] The corresponding minimum and maximum allowable diameters can be used as the bottleneck diameters: , When inputting the outer diameter of the tubing to be evaluated When calculating the margin: .

[0077] Table 1 Evaluation results of multi-section tubing string throughput capacity ; Table 1 shows the results of tubing throughput capacity evaluation using the method of this invention for different well sections. To avoid revealing the actual well numbers, the table uses the serial numbers of Well 1 to Well 5 instead of the actual well numbers. In this embodiment, the length of the tubing to be evaluated is 1m, and the outer diameter of the tubing to be evaluated is 80mm. The evaluation well section in the table represents the depth range of each well participating in the throughput capacity calculation. The bottleneck depth represents the position of the minimum maximum throughput outer diameter within the corresponding evaluation well section. The bottleneck diameter represents the maximum throughput outer diameter calculated at the bottleneck depth. The minimum throughput margin is the difference between the bottleneck diameter and the outer diameter of the tubing to be evaluated.

[0078] As shown in Table 1, the minimum throughput margins for wells 1, 3, and 5 are 5.220 mm, 3.724 mm, and 17.008 mm, respectively, all greater than 0, therefore the evaluation result is "pass". The minimum throughput margins for wells 2 and 4 are -42.429 mm and -25.456 mm, respectively, both less than 0, therefore the evaluation result is "fail". This result shows that the present invention can output bottleneck depth, bottleneck diameter, throughput margin, and throughput capacity evaluation results based on the three-dimensional casing inner wall constraint conditions of different well sections.

Claims

1. A method for evaluating the throughput capacity of casing-type well tubing based on the intersection of multi-arm correction and feasible region, characterized in that, Includes the following steps: S1. Preprocess the multi-arm well diameter data, correct the two-dimensional center offset of the cross section based on the differential closed circle center of the opposing arm, and restore the inner contour of each sounding section. S2. Merge the corrected and restored multi-arm well diameter data and well inclination data by depth, calculate the three-dimensional coordinates of the wellbore centerline and generate three-dimensional casing inner wall points; S3. Fit the principal axis of the tubing within the length window of the tubing to be evaluated, establish a common reference plane, and inversely map the constraint regions of each section to the common reference plane. S4. Find the intersection of the feasible regions of each section, and calculate the maximum passable outer diameter through a binary search. Output the bottleneck depth, bottleneck diameter and passability evaluation results. The multi-arm caliber data in S1 includes: depth of sounding, instrument rotation angle, and m arm measurement values; where m is an even number, and the i-th arm measurement value corresponds to the radial distance of the casing inner wall in the i-th orientation, i=1~m; S1 includes the following steps: S11. Read the multi-arm caliper data, extract the depth, instrument rotation angle and the measurement values ​​of each arm, fill or correct missing or invalid values, and convert the measurement values ​​of each arm into radius data in a unified unit. S12. Determine the actual orientation of each measuring arm on the corresponding depth measurement section based on the number of measuring arms and the instrument rotation angle. S13. Pair the even number of measuring arms according to their opposing relationship, and calculate the center offset component in the corresponding direction based on the radius difference of the opposing measuring arms. S14. Determine the weights based on the degree of deviation of the closed diameter of each opposing measuring arm, and reduce the weights of abnormal measuring arm directions. S15. Based on the center offset components in each direction and their corresponding weights, solve for the two-dimensional center offset of each sounding section. S16. Correct and restore the radius data of each measuring arm according to the two-dimensional center offset to obtain the restored inner contour of each depth measuring section. In S13, the pairing relationship of the opposing measuring arms is as follows: the i-th measuring arm and the i+m / 2-th measuring arm form a pair of opposing measuring arms, and the center offset component is calculated based on the radius difference of the pair of opposing measuring arms, and the closed diameter is calculated based on the radius of the pair of opposing measuring arms. In step S14, the median and median absolute deviation of the closed diameters of each pair of opposing measuring arms within the same sounding section are first calculated. Then, the corresponding weights are determined based on the deviation of each closed diameter relative to the median. When the deviation of the closed diameter is not greater than the median absolute deviation, the weight is 1. When the deviation of the closed diameter is greater than the median absolute deviation, the weight of that direction is reduced based on the deviation of the closed diameter.

2. The method for evaluating the throughput capacity of casing variable well tubing based on the intersection of multi-arm correction restoration and feasible region as described in claim 1, characterized in that, In step S15, the weighted least squares method is used to fuse the center offset components of multiple opposing measuring arms into a two-dimensional center offset of the current sounding section.

3. The method for evaluating the throughput capacity of casing variable well tubing based on the intersection of multi-arm correction restoration and feasible region as described in claim 1, characterized in that, S2 includes the following steps: S21. Using the corrected and restored multi-arm caliper data depth measurement as the main depth grid, determine the unified depth sequence for data merging; S22. Based on the unified depth sequence, interpolate the well inclination data to the corresponding depth measurement position to obtain the well inclination angle and azimuth angle corresponding to each depth measurement section; S23. Merge the corrected and restored multi-arm well diameter data with the interpolated well inclination data according to depth to form three-dimensional casing inner wall modeling data; S24. Calculate the coordinate increments of the wellbore centerline in the north, east, and vertical directions based on the adjacent depth measurement intervals, well inclination angle, and azimuth angle; S25. Accumulate the coordinate increments point by point to obtain the three-dimensional coordinates of the wellbore centerline at each depth measurement location; S26. Generate three-dimensional casing inner wall points based on the three-dimensional coordinates of the wellbore centerline, the direction of the wellbore axis, and the inner contours of each sounding section after restoration.

4. The method for evaluating the throughput capacity of casing variable well tubing based on the intersection of multi-arm correction restoration and feasible region as described in claim 3, characterized in that, The wellbore inclination data includes: depth of sounding (DEPTH), wellbore inclination angle (DEV), and azimuth angle (DAZ); in step S22, linear interpolation is performed on the wellbore inclination angle, and circular interpolation based on sine and cosine components is performed on the azimuth angle.

5. The method for evaluating the throughput capacity of casing variable well tubing based on the intersection of multi-arm correction restoration and feasible region as described in claim 1, characterized in that, S3 includes the following steps: S31. Based on the evaluation depth corresponding to the head position of the tubing to be evaluated. The length window of the tubing string to be evaluated is determined by the length L of the tubing string to be evaluated, and the three-dimensional coordinates of the three-dimensional casing inner wall points and the wellbore centerline within the length window of the tubing string to be evaluated are extracted. S32. Using the local sounding coordinates relative to the evaluation depth as independent variables, perform linear regression on the three-dimensional coordinates of the wellbore centerline within the length window of the tubing string to be evaluated to obtain the main axis direction and main axis reference point of the tubing string to be evaluated. S33. Based on the main axis direction and main axis reference point of the pipe column to be evaluated, establish a common reference plane perpendicular to the main axis of the pipe column to be evaluated, and establish a two-dimensional orthogonal coordinate system in the common reference plane; S34. Based on the three-dimensional casing inner wall points of each sounding section, form the cross-sectional constraint region of the corresponding sounding section; S35. Based on the geometric relationship between each sounding section and the common reference plane, the constraint region of each section is inversely mapped to the common reference plane.

6. The method for evaluating the throughput capacity of casing variable well tubing based on the intersection of multi-arm correction restoration and feasible region as described in claim 1, characterized in that, S4 includes the following steps: S41. Based on the candidate pass radius, the constraint regions of each section that are inversely mapped to the common reference plane are shrunk to obtain the feasible region of each section. The feasible region is the area in which the center of the pipe to be evaluated is allowed to be arranged in the corresponding section. S42. Find the intersection of the feasible regions of each section, and determine whether the candidate passable radius satisfies the passable condition based on whether the intersection is empty; S43. Based on the passing condition judgment result of the candidate passable radius, update the candidate passable radius by binary search; S44. Repeat the intersection and binary search update process of the feasible region until the preset calculation convergence accuracy is met, obtain the maximum passable radius at the current evaluation depth, and convert it to the maximum passable outer diameter; S45. Generate the throughput evaluation result based on the maximum passable outer diameter, and determine the bottleneck depth and bottleneck diameter within the evaluation well section; when inputting the outer diameter of the tubing string to be evaluated, further calculate the throughput margin.

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