A tee erosion curved surface reconstruction and contact seal reliability evaluation method and system

Abstract

The application discloses a kind of ball seat erosion curved surface reconstruction and contact seal reliability evaluation method and system, it is related to the technical field of erosion damage evaluation, method includes: obtaining the three-dimensional surface erosion data of ball seat wall surface to be evaluated, establish axial-circumferential ball seat wall surface parameter domain;Constitute area weighted quantile erosion envelope;With dangerous peak value retention and periodic continuity constraint, carry out smoothing processing;Current wall surface normal vector and normal degradation depth are calculated, along normal update ball seat wall surface;Carry out material removal amount and geometric volume change consistency check;Establish contact model, screen effective contact patch, construct three-dimensional sealing risk field, output sealing reliability index and risk grade.The application is driven by area weighted quantile envelope to establish axial-circumferential parameter domain and three-dimensional peak-preserving smoothing and normal reconstruction, then combines contact model and three-dimensional sealing risk field evaluation, improves ball seat erosion degradation curved surface reconstruction precision and contact seal reliability evaluation accuracy.

Description

Technical Field

[0001] This application relates to the field of erosion damage evaluation technology, and in particular to a method and system for reconstructing the erosion surface of a ball seat and evaluating the reliability of contact seals. Background Technology

[0002] The ball seat is a critical pressure-bearing and sealing component in ball-type fracturing tools. As the proppant-carrying fracturing fluid passes through the constricted area of ​​the ball seat, solid particles continuously impact the inner wall of the ball seat, causing erosion damage that varies with spatial position and service time. The resulting localized pits, circumferential erosion, and high-erosion zones alter the actual contact position between the fracturing ball and the ball seat, the continuity of contact patches, and the contact pressure distribution, thus affecting the pressure-bearing and sealing performance of the ball seat.

[0003] While existing ball seat erosion analysis can obtain erosion data of three-dimensional surface elements on the inner wall of the ball seat through discrete phase models, the degradation morphology reconstruction process typically involves compressing the three-dimensional surface element data into a one-dimensional erosion distribution along the axial direction, and then generating an axisymmetric degradation entity by rotating the axial generatrix. This processing eliminates the circumferential non-uniformity of the erosion data and cannot reflect the circumferential erosion differences caused by flow deviation, local particle enrichment, or non-uniform impact.

[0004] Meanwhile, directly using the maximum surface erosion rate is easily affected by small-area abnormal surface elements; using ordinary averaging or unconstrained smoothing can weaken local dangerous erosion peaks; updating the ball seat geometry using a fixed radial deduction method cannot guarantee that the material removal direction is consistent with the normal of the real wall surface such as the conical surface and transition surface. These errors will further propagate to the fracturing ball-seat contact position, contact patch integrity, and sealing reliability evaluation results. In addition, although the high-resolution erosion envelope can retain the dangerous erosion area, its overall integral may not be consistent with the material removal amount corresponding to the original discrete erosion data. If the two are not verified, the overall material removal scale of the degraded geometry may not match the original erosion input.

[0005] In summary, the accuracy of reconstructing the erosion degradation surface of the ball seat and the accuracy of evaluating the reliability of the contact seal in existing ball seat erosion damage assessment technologies need to be improved. Summary of the Invention

[0006] This application provides a method and system for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal, in order to solve the problem that the accuracy of the reconstruction of the eroded and degraded surface of the ball seat and the accuracy of the evaluation of the reliability of the contact seal need to be improved in the prior art.

[0007] On the one hand, this application provides a method for reconstructing the erosion surface of a ball seat and evaluating the reliability of the contact seal, including the following steps: Step 1: Obtain three-dimensional surface erosion data of the wall to be evaluated on the spherical seat, and establish a set of wall surface data including spatial coordinates, surface area, and erosion rate.

[0008] Step 2: Establish an axial-periodic circumferential spherical seat wall parameter domain for the wall surface data set, and obtain the parameter partition surface set using an overlapping joint statistical window.

[0009] Step 3: Construct an area-weighted quantile erosion envelope for the parameter partitioned surface set using the actual area of ​​the surface as the weight.

[0010] Step four: The area-weighted quantile erosion envelope is smoothed with dangerous peak preservation and periodic continuity constraints to obtain a three-dimensional peak-preserving constrained smooth surface.

[0011] Step 5: Calculate the current wall normal vector and normal degradation depth based on the three-dimensional peak-preserving constraint smooth surface, update the spherical seat wall along the normal, and obtain the three-dimensional degradation surface.

[0012] Step six: Verify the consistency of material removal amount and geometric volume change of the three-dimensional degraded surface, correct the quality normalization coefficient, and obtain the three-dimensional degraded surface that passes the verification.

[0013] Step 7: Establish a contact model between the fracturing ball and the verified three-dimensional degenerate surface, screen effective contact patches, calculate the pressure-weighted contact center trajectory, area-weighted average contact pressure, contact stress, local effective contact width and circumferential coverage, and obtain the contact center offset from the pressure-weighted contact center trajectory.

[0014] Step 8: Construct a three-dimensional sealing risk field based on the normal degradation depth, the area-weighted average contact pressure, the contact stress, the contact center offset, and the circumferential coverage, and output the sealing reliability index and risk level.

[0015] In one possible implementation, in step one, three-dimensional surface erosion data of the wall surface to be evaluated on the spherical seat is obtained, and a one-to-one correspondence record of spatial coordinates, surface area, and erosion rate is established for each surface element; the erosion rate represents the amount of material mass loss per unit wall area per unit time; when the input data uses mass loss, volume loss, or normal degradation depth as the erosion characterization quantity, the erosion characterization quantity is converted into the erosion rate according to the corresponding surface area, action time, and spherical seat material density; a set of wall surface data containing spatial coordinates, surface area, and erosion rate is established, and non-physical records with an area not greater than zero, invalid coordinates, and negative erosion rates are deleted.

[0016] In one possible implementation, in step two, the wall surface data is registered to the spherical reference coordinate system to establish a wall parameter domain consisting of axial parameters and periodic circumferential parameters; the axial and circumferential parameters of each surface element are calculated, and axial and circumferential output nodes are set within the wall parameter domain. An axial and circumferential overlapping joint statistical window is established with each output node as the center; the circumferential direction uses periodic angular distance to measure the head-to-tail connection relationship, so that surface elements located near 0° and 360° enter the same statistical neighborhood, forming a parameter partitioned surface element set.

[0017] In one possible implementation, step three, which involves constructing an area-weighted quantile erosion envelope using the actual area of ​​the face cells as the weight, includes: For each joint statistical window, the erosion rate and area of ​​effective surface elements are extracted, and they are arranged in ascending order of erosion rate. The proportion of the cumulative area of ​​surface elements not exceeding any erosion rate threshold to the total area of ​​all effective surface elements within the window is calculated. The area-weighted quantile erosion rate and area-weighted average erosion rate are determined using the area-weighted cumulative distribution, and the E90, E95, and E99 quantile erosion rate surfaces are constructed, which are the area-weighted quantile erosion envelopes. Confidence weights are set according to the number of effective surface elements and the effective coverage area of ​​the window for subsequent smoothing and fitting.

[0018] In one possible implementation, step four, the smoothing process with dangerous peak preservation and periodic continuity constraints, includes: The axial and circumferential parameters are normalized, and the confidence weight is used as the data fitting weight. The area-weighted quantile erosion envelope is used as the fitting object. A smoothing objective function is established, which includes data fitting terms, axial second-order variation penalty terms, circumferential second-order variation penalty terms, and axial-circumferential coupling variation penalty terms. During the smoothing process, dangerous peak preservation constraints, area integral preservation constraints, different quantile surface order preservation constraints, and circumferential function value and periodic derivative continuity constraints are set to obtain a three-dimensional peak-preserving constrained smooth surface.

[0019] In one possible implementation, in step five, the three-dimensional peak-preserving constrained smooth surface is used as the erosion rate surface. The unit normal vector pointing to the interior of the spherical seat entity is calculated based on the tangent vectors of the current three-dimensional wall surface to the axial and circumferential parameters, i.e., the current wall surface normal vector. The mass normalization coefficient is calculated with the condition that the area integral of the erosion rate surface in the parameter domain is consistent with the erosion integral of the original surface element. The erosion rate surface is converted into a normal degradation depth. The wall nodes are updated along the current wall surface normal to obtain a temporary degradation surface. Then, the three-dimensional degradation surface is obtained by re-interpolating the surface to maintain the continuity of the circumferential period. The surface folding is prevented by a local area Jacobian threshold.

[0020] In one possible implementation, in step six, the first material removal mass is obtained by integrating the original wall element erosion data, and the second material removal mass is obtained by the volume difference of the spherical seat before and after degradation. The relative consistency error between the first and second material removal masses is calculated. When the relative consistency error exceeds a preset consistency threshold, the quality normalization coefficient is updated according to the correction formula, the normal degradation depth is recalculated, and the surface update in step five is performed. When the relative consistency error does not exceed the preset consistency threshold and the geometric validity meets the requirements, a verified three-dimensional degradation surface is obtained.

[0021] In one possible implementation, in step seven, the verified three-dimensional degenerate surface is directly constructed as the ball seat contact surface, a contact model between the fracturing ball and the ball seat contact surface is established, positive contact pressure records are extracted in the neighborhood of the theoretical sealing zone, and candidate contact records are screened based on the area-weighted quantile reference pressure and the lowest effective contact pressure; connected component identification is performed on the candidate contact records, and effective contact patches are retained according to area contribution or load contribution; the effective contact area is divided into circumferential partitions, and the pressure-weighted contact center trajectory, area-weighted average contact pressure, contact stress, local effective contact width, and circumferential coverage are calculated, and the contact center offset is calculated from the pressure-weighted contact center trajectory.

[0022] In one possible implementation, in step eight, for each parameter unit, the ratio of normal degradation depth to allowable normal degradation depth, insufficient contact pressure, excessive contact stress, and pressure-weighted contact center offset are normalized respectively. The insufficient contact pressure is determined by the area-weighted average contact pressure, the excessive contact stress is determined by the contact stress, and the pressure-weighted contact center offset is determined by the contact center offset. The normalized values ​​are combined with the risk weights for normal degradation depth, insufficient pressure, excessive stress, and contact center offset to obtain a local sealing risk value. All local sealing risk values ​​are arranged according to the parameter domain to form a three-dimensional sealing risk field. A three-dimensional comprehensive sealing risk index is synthesized by weighting the area-weighted average risk, area-weighted high quantile risk, and insufficient circumferential contact coverage. The insufficient circumferential contact coverage is determined by the circumferential coverage rate. The three-dimensional comprehensive sealing risk index determines the sealing reliability index and risk level.

[0023] On the other hand, this application provides a ball seat erosion surface reconstruction and contact seal reliability evaluation system, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of the above-described ball seat erosion surface reconstruction and contact seal reliability evaluation method.

[0024] The method and system for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal in this application have the following advantages: By establishing an axial-periodic circumferential parameter domain and driving three-dimensional peak-preserving smoothing and normal reconstruction with area-weighted quantile envelope, and then combining the contact model with three-dimensional sealing risk field evaluation, the accuracy of ball seat erosion degradation surface reconstruction and contact seal reliability evaluation is improved.

[0025] By uniformly converting 3D surface element erosion data into erosion rate and deleting records with non-physical area, coordinates, or rate, the consistency and effectiveness of wall surface element data are improved, avoiding unit inconsistencies and outliers from interfering with subsequent degenerate surface reconstruction.

[0026] By registering the wall surface elements to the spherical reference coordinate system and establishing an overlapping joint statistical window using the periodic angular distance, the continuity of axial and circumferential neighborhood partitioning is improved, avoiding artificial statistical discontinuities caused by circumferential start and end seams and curvature changes.

[0027] By constructing an area-weighted quantile erosion envelope with the actual area of ​​the surface element as the weight, the retention capacity of dangerous erosion areas is improved, and the excessive influence of small-area high-value surface elements on the statistical envelope is avoided, making the erosion degradation characterization more consistent with the actual material removal distribution.

[0028] By establishing a smooth objective function with axial, circumferential and coupling penalty terms in the normalized parameter domain and setting constraints for maintaining dangerous peaks and periodic continuity, the smoothness and fidelity of the erosion surface are improved, non-physical oscillations are suppressed while maintaining dangerous peaks and periodic continuity.

[0029] By using a three-dimensional peak-preserving constrained smooth surface as the erosion rate surface and calculating the normal degradation depth along the real wall normal, and then using reinterpolation and area Jacobian thresholding to prevent folding, the spatial position accuracy and geometric effectiveness of the degradation surface are improved.

[0030] By calculating the material removal mass from the original surface erosion data and the difference in solid volume before and after degradation, and performing consistency verification and iterative correction, the consistency of material removal between the reconstructed degradation geometry and the original erosion data is improved, ensuring the credibility of subsequent evaluations.

[0031] By directly constructing the three-dimensional degenerate surface as the contact surface and using robust pressure thresholds, theoretical sealing zone neighborhoods, and topological connectivity to screen effective contact patches, the accuracy of effective contact area identification is improved, while isolated numerical points and non-sealing contacts far from the sealing zone are excluded.

[0032] By normalizing and weighting the normal degradation depth, contact pressure, contact stress, and contact center offset to construct a three-dimensional sealing risk field, and combining the insufficient circumferential coverage to form a reliability index, the comprehensiveness and reliability of the risk assessment of erosion-degraded ball seat seals are improved. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart illustrating a method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal, as provided in an embodiment of this application. Detailed Implementation

[0035] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0036] like Figure 1 As shown in the figure, this application provides a method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal, including the following steps: Step 1: Obtain three-dimensional surface erosion data of the wall to be evaluated on the spherical seat, and establish a set of wall surface data including spatial coordinates, surface area, and erosion rate.

[0037] Step 2: Establish an axial-periodic circumferential spherical seat wall parameter domain for the wall surface data set, and obtain the parameter partition surface set using an overlapping joint statistical window.

[0038] Step 3: Construct an area-weighted quantile erosion envelope for the parameter partitioned surface set using the actual area of ​​the surface as the weight.

[0039] Step four: The area-weighted quantile erosion envelope is smoothed with dangerous peak preservation and periodic continuity constraints to obtain a three-dimensional peak-preserving constrained smooth surface.

[0040] Step 5: Calculate the current wall normal vector and normal degradation depth based on the three-dimensional peak-preserving constraint smooth surface, update the spherical seat wall along the normal, and obtain the three-dimensional degradation surface.

[0041] Step six: Verify the consistency of material removal amount and geometric volume change of the three-dimensional degraded surface, correct the quality normalization coefficient, and obtain the three-dimensional degraded surface that passes the verification.

[0042] Step 7: Establish a contact model between the fracturing ball and the verified three-dimensional degenerate surface, screen effective contact patches, calculate the pressure-weighted contact center trajectory, area-weighted average contact pressure, contact stress, local effective contact width and circumferential coverage, and obtain the contact center offset from the pressure-weighted contact center trajectory.

[0043] Step 8: Construct a three-dimensional sealing risk field based on the normal degradation depth, the area-weighted average contact pressure, the contact stress, the contact center offset, and the circumferential coverage, and output the sealing reliability index and risk level.

[0044] For example, in step one, three-dimensional surface erosion data of the wall surface to be evaluated on the spherical seat is obtained, and a one-to-one correspondence record of spatial coordinates, surface area, and erosion rate is established for each surface element; the erosion rate represents the amount of material mass loss per unit wall area per unit time; when the input data uses mass loss, volume loss, or normal degradation depth as the erosion characterization quantity, the erosion characterization quantity is converted into the erosion rate according to the corresponding surface area, action time, and spherical seat material density; a set of wall surface data containing spatial coordinates, surface area, and erosion rate is established, and non-physical records with an area not greater than zero, invalid coordinates, and negative erosion rates are deleted.

[0045] Specifically, the ball seat's reduced diameter sealing zone is the area where the flow velocity of the proppant-carrying fracturing fluid and the particle impact state change significantly. In order to preserve the actual spatial location of erosion damage during the subsequent degraded surface reconstruction process, this embodiment first obtains the three-dimensional surface erosion data of the ball seat's wall to be evaluated, and establishes a fixed correspondence between each erosion value and the three-dimensional position and actual area of ​​the corresponding surface element.

[0046] In this embodiment, the large end diameter of the ball seat is 100mm, the small end diameter is 46mm, the outer diameter is 122mm, the diameter of the fracturing ball is 70mm, and the half-angle of the ball seat cone surface is 30°. The erosion rate, area, center coordinates, and normal vector of each surface element on the wall to be evaluated are obtained. The erosion rate is uniformly expressed as the mass loss per unit area per unit time, with units of kg / (m²). 2 •s). When the input data uses mass loss rate, volume loss rate, or other erosion characterization quantities, it is first converted into a unified erosion rate according to the corresponding surface area, action time, and material density. The unified surface erosion data is used as the input for step two.

[0047] During the calculation, the ball seat diameter reduction sealing area and its adjacent areas are set as the wall surface to be evaluated. For each wall surface element to be evaluated, the three-dimensional spatial coordinates of the representative point of the element, the actual area of ​​the element, and the erosion rate are output. The above data are stored according to the element index to establish a wall surface data set: (1) In the formula, D w This represents the metadata set of the inner wall surface of the ball seat; d i Indicates the first i Data records corresponding to each wall element; x i Indicates the first i The three-dimensional coordinates of the center of each element; A i Indicates the first i The true surface area of ​​each element; E i Indicates the first i The erosion rate of each surface element; N f This represents the total number of face elements in the wall of the ball seat to be evaluated; N i Indicates the impact number i The number of particles in each face element; Indicates the first p The first particle or particle bundle pair i Mass flow rate contribution of each element; d p,i Indicates particle diameter; C( d p,i ) represents the particle size influence function; α p,i Indicates the angle of incidence of the particle; f ( α p,i ) represents the influence function of the incident angle; v p,i Indicates the particle impact velocity; bv This indicates the speed index.

[0048] When the liquid-solid two-phase flow solver directly outputs the erosion rate E i When the output value is read directly, there is no need to repeat the calculation formula for erosion rate in equation (1). To avoid inconsistencies in the output units of different software, the erosion rate is uniformly converted into the mass loss per unit area and per unit time when reading the data.

[0049] It should be noted that this embodiment does not require the liquid-solid two-phase flow solver to directly output the wall surface element normal vector. The wall normal vector will be recalculated in step five based on the current three-dimensional wall parameterized surface, so that it can be updated as the sphere degenerates.

[0050] After data reading is complete, check whether the three-dimensional coordinates, surface area, and erosion rate in each data record correspond one-to-one. Delete records with surface area not greater than zero or invalid coordinates, and mark non-physical values ​​with erosion rates less than zero as abnormal records. The resulting set of wall surface data is then examined.D w Proceed to step two, which is used to establish the correspondence between the three-dimensional spatial position and the coordinates of the ball seat wall parameters.

[0051] For example, in step two, the wall surface data is registered to the spherical reference coordinate system to establish a wall parameter domain consisting of axial parameters and periodic circumferential parameters; the axial and circumferential parameters of each surface element are calculated, and axial and circumferential output nodes are set in the wall parameter domain. An axial and circumferential overlapping joint statistical window is established with each output node as the center; the circumferential direction uses the periodic angular distance to measure the head-to-tail connection relationship, so that surface elements located near 0° and 360° enter the same statistical neighborhood, forming a parameter partition surface element set.

[0052] Specifically, the surface data of the wall is discretely distributed in three-dimensional spatial coordinates. If neighborhood statistics are performed directly in the Cartesian coordinate system, the curvature changes between the spherical conical surface, cylindrical surface, and transition surface will affect neighborhood identification, and the circumferential beginning and end positions may be incorrectly divided into two far apart regions. Therefore, this embodiment establishes a spherical wall parameter domain composed of axial parameters and periodic circumferential parameters to uniformly organize the three-dimensional surface data.

[0053] In this embodiment, output positions are set within the axial-periodic circumferential parameter domain, with an axial output interval of 1 mm and a circumferential output interval of 5°, thus forming 72 circumferential output positions within the complete circumferential range. A joint partition width is established centered on each output position, with an axial partition width of 5 mm and a circumferential partition width of 20°. Surface cells located near 0° and 360° in the circumferential direction are included in the same statistical window according to the periodic boundary relationship; windows near the axial boundary are truncated according to the actual wall area, and the area weights of the effective surface cells are renormalized. The set of surface cells, area weights, and erosion rates corresponding to each parameter domain position are output for step three to calculate the area-weighted quantile envelope.

[0054] When different erosion time periods or different calculation files use different coordinate axis directions or coordinate origins, the spherical seat axis and the spherical seat reference end face are first selected as registration references. Then, the surface data of each stage is registered to the same spherical seat reference coordinate system through rigid body coordinate transformation. In the unified spherical seat reference coordinate system, the spherical seat axis reference point o and the spherical seat axis unit vector e are determined. z and with e z orthogonal radial basis vectors e x and e y For an initial axisymmetric spherical seat, the wall to be evaluated is represented as: (2) In the formula, P Represents the parameter domain of the ball seat wall; z min and z maxThese represent the axial boundaries of the wall surfaces to be evaluated; i Represents the periodic circumferential parameter; X0(z, i ) represents the initial position vector of the inner wall of the sphere in three-dimensional space; o represents the origin of the sphere coordinate system; e x e y and e z Represents mutually orthogonal coordinate basis vectors; r 0( z () indicates the initial axial position of the inner wall of the ball seat. z The radius at that point.

[0055] Equation (2) is only used to establish the correspondence between the initial ball seat wall and the parameter domain. After the non-uniform erosion degradation is completed, the position of the three-dimensional degradation surface changes simultaneously with... z and i change.

[0056] For each effective wall element in step one, calculate its axial parameters and periodic circumferential parameters: (3) In the formula, z i Indicates the first i Axial parameter coordinates of each surface element; i i Indicates the first i The circumferential parameter coordinates of each element; "·" represents the vector dot product; atan2 represents the arctangent function with quadrant recognition capability; mod (·,2) π ) is used to unify the circumferential angle to [0, 2]. π ).

[0057] After completing the element mapping, set the axial output node in the parameter domain. z j and circumferential output node i k To enable adjacent output nodes to share a certain number of wall elements and reduce the impact of parameter element boundaries on statistical results, an overlapping joint statistical window is established centered on each output node: (4) In the formula, B jk Indicates the first j The first axial partition and the first k A set of face element indexes within a circumferential partition; z j and i k These represent the center coordinates of the corresponding partitions; Δ z and Δ iThese represent the axial partition width and the circumferential partition width, respectively. This indicates that 0 and 2 are considered. π The periodic angular distance between the two ends in a connected relationship; Represents the circumferential parameter of the i-th face element. i i The unit is radians; This represents the circumferential parameter of the k-th circumferential output node. i k The unit is radians; This represents an integer periodic translation index, where 2mπ represents an angular translation amount that is an integer multiple of the complete circumferential period. Z Represents a set of integers, obtained by iterating through m∈Z and taking... The minimum value is used to obtain the shortest period angular distance between two circumferential angles.

[0058] Based on the periodic angular distance, located at circumferential angles close to 0 and 2... π Wall elements at a given location can enter the same statistical neighborhood, avoiding artificial discontinuities at parameter domain seams. The set of wall elements corresponding to each joint statistical window. B jk (Parameter partition face set) Proceed to step three.

[0059] For example, in step three, constructing the area-weighted quantile erosion envelope using the actual area of ​​the face cells as the weight includes: For each joint statistical window, the erosion rate and area of ​​effective surface elements are extracted, and they are arranged in ascending order of erosion rate. The proportion of the cumulative area of ​​surface elements not exceeding any erosion rate threshold to the total area of ​​all effective surface elements within the window is calculated. The area-weighted quantile erosion rate and area-weighted average erosion rate are determined using the area-weighted cumulative distribution, and the E90, E95, and E99 quantile erosion rate surfaces are constructed, which are the area-weighted quantile erosion envelopes. Confidence weights are set according to the number of effective surface elements and the effective coverage area of ​​the window for subsequent smoothing and fitting.

[0060] Specifically, the wall mesh used in liquid-solid two-phase flow calculations is usually not a uniform-area mesh. If ordinary quantiles are calculated directly based on the number of surface cells, a surface cell with a very small area but a high erosion value will have the same statistical weight as a surface cell with a large coverage area, which may lead to local discrete outliers excessively controlling the erosion envelope. Therefore, this embodiment uses the actual area of ​​the surface cells as the statistical weight.

[0061] Specifically, regarding the ( ) j , k ) joint statistical windows, from the set B jk Extract the erosion rate and area of ​​all valid surface elements, and sort them in ascending order of erosion rate. For any erosion rate threshold...e Calculate the proportion of the cumulative area of ​​face cells not exceeding this threshold to the total area of ​​all valid face cells within the window: (5) In the formula, F jk ( e ) indicates the ( j , k The erosion rate in each parameter partition is no greater than ) e The area-weighted cumulative ratio; e The threshold value for the erosion rate to be statistically analyzed is represented by I(·); I(·) represents the indicator function, which takes the value 1 when the condition is met and 0 otherwise. E i and A i They represent the first i The erosion rate and actual area of ​​each surface element.

[0062] Compared to accumulating based on the number of facets, Equation (5) makes the contribution of each facet to the cumulative proportion correspond to its actual coverage area. Abnormally high-value facets with very small areas can only affect the cumulative distribution according to their actual area, while continuous large-area erosion areas will receive a statistical contribution that matches their true area.

[0063] After obtaining the area-weighted cumulative distribution, determine the area-weighted quantile erosion rate and the area-weighted average erosion rate: (6) In the formula, E q,A ( z j ,i k ) indicates the ( j , k Area weighting of ) parameter partitions q Fractional erosion rate; q denoted by quantile; inf represents the minimum erosion rate that satisfies the cumulative proportion condition; This represents the area-weighted average erosion rate for the corresponding parameter partition. E q,A Used to construct a three-dimensional erosion envelope with the ability to retain dangerous erosion; Used to characterize the average material removal level.

[0064] In this embodiment, three area-weighted 90% quantile surfaces, E90, E95, and E99, are constructed. E95 is used as the principal degradation reconstruction surface for subsequent 3D geometric updates and contact seal reliability evaluation. E90 and E99 are used as the lower and higher degradation boundaries, respectively, to evaluate the uncertainty introduced by quantile selection. For parameter domain locations with insufficient effective surface elements within the statistical window, periodic continuous interpolation is performed using the quantile results of adjacent effective output locations, and the interpolation locations are marked. Step three outputs three sets of original quantile envelopes: E90, E95, and E99, and proceeds to step four.

[0065] Since the grid density may vary at different locations on the sphere, relying solely on quantile results is insufficient to distinguish between data-sufficient windows and data-sparse windows. Therefore, confidence weights are set based on the number of effective cells and the effective coverage area within the window: (7) In the formula, w jk Indicates the ( j , k The credibility weights of the joint statistical windows; n jk This indicates the number of valid face cells in the partition; n med This represents the median number of all valid window elements. A jk This represents the total area of ​​the cells in the partition (i.e., the effective coverage area). A med This represents the median of the total area of ​​all valid parameter partition cells.

[0066] When a statistical window lacks valid cells, the erosion rate of that window is not directly set to zero. Instead, the axial or circumferential support range of the window is increased, or periodic neighborhood interpolation is performed based on adjacent valid windows. The resulting area-weighted quantile erosion envelope is then calculated. E q,A ( z j ,i k ) and credibility weight w jk Let's proceed to step four together.

[0067] For example, in step four, the smoothing process with dangerous peak retention and periodic continuity constraints includes: The axial and circumferential parameters are normalized, and the confidence weight is used as the data fitting weight. The area-weighted quantile erosion envelope is used as the fitting object. A smoothing objective function is established, which includes data fitting terms, axial second-order variation penalty terms, circumferential second-order variation penalty terms, and axial-circumferential coupling variation penalty terms. During the smoothing process, dangerous peak preservation constraints, area integral preservation constraints, different quantile surface order preservation constraints, and circumferential function value and periodic derivative continuity constraints are set to obtain a three-dimensional peak-preserving constrained smooth surface.

[0068] Specifically, the area-weighted quantile erosion envelope obtained in step three is still composed of discrete parameter nodes. Directly updating the geometry based on discrete nodes easily leads to the formation of jagged degenerate surfaces between adjacent nodes; while ordinary unconstrained smoothing can reduce local oscillations, it may simultaneously weaken dangerous erosion peaks and potentially affect the circumferential parameters 0 and 2. π The seam locations create discontinuities. Therefore, this embodiment establishes a three-dimensional surface smoothing model with dangerous peak preservation and periodic continuity constraints.

[0069] because( z , i Since the parameters in the two directions have different scales, to avoid the difference in dimensions between the axial length and the circumferential angle affecting the smoothing intensity, they are first normalized: (8) In the formula, Indicates the normalized axial parameter; This represents the normalized circumferential parameter; both parameters have a value range of [0,1].

[0070] Using the area-weighted quantile erosion envelope of equation (6) as the fitting object and the confidence weight as the data fitting weight, a smoothing objective function is established: (9) In the formula, ( , ) represents quantiles q The corresponding continuous erosion rate surface; J ( s q ) represents the smoothing objective function; N z and N θ These represent the number of axial partitions and the number of circumferential partitions, respectively. P n =[0,1]×[0,1] represents the normalization parameter domain; l z Indicates the axial curvature penalty coefficient; l θ This represents the circumferential curvature penalty coefficient; l zθ This represents the penalty coefficient for axial-circumferential coupling variation.

[0071] The data fitting term in Equation (9) is used to keep the smooth surface close to the area-weighted quantile erosion envelope; the axial and circumferential second-order variation penalty terms are used to suppress non-physical oscillations along the corresponding directions; and the axial-periodic circumferential coupling variation penalty term is used to suppress local sawtooth patterns that propagate obliquely in the parameter domain.

[0072] To prevent dangerous peaks from being weakened during the smoothing process and to limit the overall erosion integral change of the smoothed surface, the following constraints are imposed on equation (9): (10) in, P q This represents the set of dangerous erosion peak zones determined by the local high points in equation (6); or - p This indicates the lower limit coefficient for maintaining the peak value; or + p Indicates the upper limit coefficient of the peak value; or - A and or + A These represent the lower and upper bounds for preserving the area integral, respectively; q 1 and q 2 represents two distinct quantiles, and satisfies q 1< q 2.

[0073] In this embodiment, Peak Preservation Constraint Surface Smoothing (PPCSS) is performed on each quantile envelope, with an axial penalty coefficient of 1.5, a circumferential penalty coefficient of 1.0, and an axial-circumferential coupling penalty coefficient of 0.20. The smoothing result should meet the following requirements: the peak value in the danger zone should not be lower than 0.85 and not higher than 1.10 of the corresponding peak value before smoothing; the area integral of the smoothed surface should not be lower than 0.95 and not higher than 1.05 of the integral before smoothing; and the function value and periodic derivative should remain continuous at 0° and 360° in the circumferential direction. If any constraint is not met, the corresponding penalty coefficient is readjusted and smoothing is performed until the constraint is met. If the constraint is still not met after a preset maximum number of iterations (e.g., 10), a constraint not met flag is output, and the current optimal result along with the flag is passed to step five. The consistency check in step six determines whether to backtrack. The E90, E95, and E99 smoothed envelopes that meet the constraints are used as inputs to step five.

[0074] For example, in step five, the three-dimensional peak-preserving constrained smooth surface is used as the erosion rate surface. The unit normal vector pointing to the interior of the spherical seat entity is calculated based on the tangent vectors of the current three-dimensional wall surface to the axial and circumferential parameters, which is the current wall surface normal vector. The mass normalization coefficient is calculated with the condition that the area integral of the erosion rate surface in the parameter domain is consistent with the erosion integral of the original surface element. The erosion rate surface is converted into the normal degradation depth. The wall nodes are updated along the current wall surface normal to obtain a temporary degradation surface. Then, the three-dimensional degradation surface is obtained by re-interpolating the surface to maintain the continuity of the circumferential period. The surface folding is prevented by a local area Jacobian threshold.

[0075] Specifically, the ball-end diameter reduction region includes a conical surface and a transition surface. In these regions, the fixed radial direction typically does not coincide with the true wall normal. Directly subtracting the wall coordinates radially would cause the same material removal depth to correspond to an incorrect spatial location and could potentially alter the position of subsequent contact areas. Therefore, this embodiment calculates the material removal direction in real time based on two tangent vectors of the current three-dimensional wall.

[0076] For the n The surface X corresponding to each erosion time increment n ( z , i The unit normal vector pointing into the interior of the spherical base is: (11) In the formula, v n ( z , i ) represents the unit normal vector on the current wall surface pointing from the fluid side into the interior of the spherical seat entity; "×" represents the cross product of vectors; ||·|| represents the vector magnitude; k n This is the normal orientation factor, which takes the value of +1 or -1, and is used to ensure that all normal vectors point to the degradation direction after material removal.

[0077] To convert the erosion rate surfaces obtained from equations (9) and (10) into geometric degradation, a mass normalization coefficient is introduced: (12) In the formula, Indicates the first n The mass normalization coefficient corresponding to each erosion time increment; h n ( z , i ) indicates the first n Normal degradation depth within a single erosion time increment; r s Indicates the density of the ball seat material; J nThis represents the area Jacobian of the current parametric surface, with the erosion rate measured per unit actual wall area. This represents the actual wall area element corresponding to the area element of the parameter domain; Δ t n This indicates the current increment in erosion time.

[0078] Equation (12) is applicable when the input data is the mass loss per unit area and per unit time. The mass loss per unit area is obtained by multiplying the erosion rate by the erosion time interval, and then divided by the material density to obtain the corresponding normal degradation depth. This conversion no longer uses empirical conversion factors with uncertain meanings.

[0079] Update the current 3D wall based on the normal degradation depth: (13) In the formula, X represents the temporary degenerate surface obtained by direct normal offset; n+1 This represents a degenerate surface after reinterpolation or reparameterization in the parametric domain. I p Represents a surface reinterpolation operator that preserves circumferential periodic continuity; J n+1 Jacobian represents the local area of ​​a degenerate surface; J min This represents the minimum threshold required to prevent a surface from folding or locally degenerating to zero area.

[0080] When the ball seat is made of steel, the material density in this embodiment is... r s Take 7.85×10 3 kg / m 3 When using other materials, r s Take the measured density of the material or the density recorded in the material standard or material handbook. Based on the erosion rate, element area, action time, and material density, obtain the material removal depth along the wall normal, and update the element node positions along the current wall normal, thereby obtaining the E90, E95, and E99 three-dimensional degenerate surfaces respectively. Material density is only used for the conversion between mass removal and volume removal, and is not a limitation on the applicable materials for this method. The obtained three-dimensional degenerate surfaces proceed to step six.

[0081] For example, in step six, the first material removal mass is obtained by integrating the original wall element erosion data, and the second material removal mass is obtained by the difference in the solid volume of the spherical seat before and after degradation. The relative consistency error between the first material removal mass and the second material removal mass is calculated. When the relative consistency error exceeds a preset consistency threshold, the quality normalization coefficient is updated according to the correction formula, the normal degradation depth is recalculated, and the surface update in step five is performed. When the relative consistency error does not exceed the preset consistency threshold and the geometric validity meets the requirements, a verified three-dimensional degradation surface is obtained.

[0082] Specifically, the high-resolution erosion envelope is mainly used to preserve dangerous erosion areas, and its area integral may be higher or lower than the integral corresponding to the original wall element erosion data. Although Equation (12) has been initially adjusted by the mass normalization coefficient, finite offset, curvature change, and surface reparameterization may still cause the actual three-dimensional solid volume change to differ from the target material removal mass. Therefore, in this embodiment, the material removal mass is calculated from both the original erosion data and the degraded geometry.

[0083] Calculate the first material removal mass and the second material removal mass based on the original wall surface erosion data: (14) In the formula, M DPM This represents the material removal mass obtained by integrating the original DPM wall erosion data (i.e., the first material removal mass). M rec This represents the mass of material removed (i.e., the second material removal mass) calculated from the difference in the volume of the solid before and after degradation. r s Indicates the density of the ball seat material; V (Ω) n )and V (Ω n+1 ) represent the volumes of the spherical seat entity before and after the degradation update, respectively.

[0084] In practice, the spherical surface before and after degradation is enclosed as a triangular mesh with consistent facet orientation, and the solid volume is calculated based on the enclosed triangular mesh. Geometric validity checks include: the area Jacobian at each parameter location of the degraded surface is not less than the minimum threshold required to prevent surface folding. J min The degenerate surface must not self-intersect; the closed triangular mesh topology must be consistent before and after degradation, and the facet orientations must be consistent. If any of these checks are not met, the geometric validity is deemed unsatisfactory. The relative error between the removal quality of the two materials is then calculated. (15) In the formula, Indicates the first rConsistency error of material removal amount in each reconstruction iteration (i.e., relative consistency error); e 0 represents a tiny positive number to prevent the denominator from being zero; and These represent the quality normalization coefficients used in two consecutive iterations; α M This represents the relaxation factor, which takes a value greater than 0 and not greater than 1.

[0085] When relative consistency error When the value exceeds the preset consistency threshold (5% in this embodiment), the quality normalization coefficient is corrected according to equation (15), the normal degradation depth is recalculated, and the surface update in step five is performed. The modified degradation surface is used as the input for the next iteration. This correction changes the overall scale of the normal degradation depth, but does not change the axial-periodic circumferential relative distribution and the location of the dangerous peak determined in steps three and four.

[0086] In this embodiment, the amount of material removed based on the erosion mass and material density, and the amount of material removed based on the geometric difference between the initial wall and the degraded wall, are calculated, and the relative consistency error between the two is calculated. When the relative consistency error does not exceed 5% and the geometric validity meets the requirements, the corresponding degraded surface is determined to have passed the consistency check, and the three-dimensional degraded surface is transferred to step seven. When the relative consistency error exceeds 5%, the mass normalization coefficient is first corrected according to equation (15), and the surface update in step five is re-executed. If the relative consistency error still exceeds 5% after correction by the preset maximum number of iterations, step four is returned to check the smoothing integral retention, parameter domain interpolation, material density, normal direction, and node update amount, and the degraded surface is regenerated. When the dangerous peak is retained or the circumferential periodic continuity does not meet the requirements, step four is also returned to adjust the smoothing constraint. The E95 surface that passes the check enters the main contact analysis, and the E90 and E99 surfaces enter the uncertainty boundary analysis.

[0087] For example, in step seven, the verified three-dimensional degenerate surface is directly constructed as the ball seat contact surface, and a contact model between the fracturing ball and the ball seat contact surface is established. Positive contact pressure records are extracted in the neighborhood of the theoretical sealing zone, and candidate contact records are screened based on the area-weighted quantile reference pressure and the lowest effective contact pressure. Connectivity components are identified for the candidate contact records, and effective contact patches are retained according to area contribution or load contribution. The effective contact area is divided into circumferential partitions, and the pressure-weighted contact center trajectory, area-weighted average contact pressure, contact stress, local effective contact width, and circumferential coverage are calculated. The contact center offset is calculated from the pressure-weighted contact center trajectory.

[0088] Specifically, the three-dimensional degenerate surface verified in step six contains non-axisymmetric degenerate features that vary with both axial and circumferential parameters. To enable these features to be transferred to the seal evaluation, this embodiment directly constructs the three-dimensional degenerate surface as the ball seat contact surface, without compressing it into an axial generatrix or generating an axisymmetric solid by rotating it through the axial generatrix.

[0089] Specifically, a three-dimensional model of the fracturing ball that mates with the ball seat is established, and the fracturing ball is placed in the reduced-diameter sealing area of ​​the ball seat. The initial ball seat and the three-dimensional degenerate ball seat use the same fracturing ball size, material parameters, constraint methods, contact algorithms, and load application methods, only replacing the ball seat contact geometry, thus making the contact results in the two states comparable. This embodiment uses a surface-to-surface contact algorithm for contact solving, dividing the ball seat contact surface into contact surface elements corresponding to the parameter nodes of the degenerate surface. The discrete size of the contact surface element is 1 mm, and the friction coefficient between the fracturing ball and the ball seat is 0.1. The above contact algorithm, discrete size of the contact surface element, and friction coefficient are only used to illustrate the contact solving process of this embodiment and do not constitute a necessary limitation of this method.

[0090] In this embodiment, 10MPa, 30MPa, and 50MPa were used as verification pressure differentials to perform three-dimensional contact calculations on the initial ball seat, the E90 degenerate surface, the E95 degenerate surface, and the E99 degenerate surface. The E95 degenerate surface corresponds to three main verification conditions, the E90 and E99 degenerate surfaces correspond to six uncertainty boundary conditions, and the initial ball seat corresponds to three baseline conditions, forming a total of 12 contact comparison conditions. The aforementioned verification pressure differentials are only used to illustrate the contact evaluation process of this embodiment and do not constitute a necessary limitation on the applicable pressure differentials of this method. The axial load acting on the fracturing ball is calculated based on the upstream and downstream pressure differentials of the ball seat: (16) In the formula, F ΔP This represents the axial load generated by the pressure difference; Δ P This indicates the pressure difference between the upstream and downstream sides of the ball seat; A seal Proj represents the region enclosed by the theoretically sealed closure curve. ez This represents the projection along the axis of the ball seat; A p This represents the axial projected area of ​​the theoretical sealing region.

[0091] After the contact solution is completed, the contact results are organized as follows: (17) In the formula, C Represents the set of three-dimensional contact results; c l Indicates the first l Data records for each contact node or contact surface element; yl Indicates its three-dimensional position; a l This indicates the area of ​​contact. p l Indicates contact pressure; σ l Indicates the equivalent stress or specified contact stress in the contact area; i l This represents the circumferential angle of the contact point after mapping to the ball seat parameter domain; N c This indicates the total number of contact nodes or contact surface elements.

[0092] In this embodiment, the minimum effective contact pressure p req Take 1.2 times the corresponding verification pressure difference ΔP, that is, take 12MPa, 36MPa and 60MPa respectively under verification pressure differences of 10MPa, 30MPa and 50MPa; initial effective sealing bandwidth b c0 The effective contact width of the ball seat is determined by the contact results of the initial ball seat under the reference working conditions. Specifically, for the reference working conditions of the initial ball seat under the verification pressure difference of 10MPa, 30MPa and 50MPa, the local effective contact width of each circumferential zone is calculated according to formula (20). The average value of the local effective contact width along the circumference under each pressure difference working condition is taken as the initial effective sealing bandwidth under that pressure difference. b c0 , b c0 The theoretical sealing band neighborhood width used in equation (18) d n And the allowable contact center offset in step eight d lim .

[0093] To exclude nodes with minimal contact pressure, non-sealing contact points far from the theoretical sealing zone, and numerical noise, this embodiment employs a combination of robust pressure threshold, theoretical sealing zone neighborhood, and topological connectivity to screen effective contact areas. First, contact records with positive contact pressure within the theoretical sealing zone neighborhood are extracted, forming a neighborhood pressure set. P b Then calculate the area-weighted quantile reference pressure of the neighborhood pressure set. p ref Finally, based on the minimum effective contact pressure p req and relative pressure threshold c pref The larger value in the selection is used to filter candidate contact records, forming a candidate contact set C0, which is specifically calculated according to formula (18): (18) In the formula, Pb This represents the positive contact pressure within the neighborhood of the theoretical sealing strip. and their corresponding contact area The set that constitutes; d n This represents the theoretical sealing band neighborhood width; in this embodiment, the initial effective sealing band width is used. b c0 Initial effective sealing bandwidth b c0 The mean value of the local effective contact width along the circumferential direction is taken from the initial ball seat reference working condition calculated by formula (20); d g ( y l ,Γ seal ) indicates the contact position y l To the theoretical sealing closure curve Γ seal The geodesic distance on the wall; C 0 represents the set of candidate contacts that simultaneously satisfy both the pressure condition and the theoretical sealing zone neighborhood condition; This indicates that the weighting is based on the contact area. Quantile operations; p ref This represents the robust reference pressure (i.e., the area-weighted quantile reference pressure) within the neighborhood of the theoretical sealing zone. This represents the pressure screening quantile, which is 0.95 in this embodiment; c This represents the relative pressure screening coefficient, which is set to 0.20 in this embodiment. p req This represents the minimum effective contact pressure, the value of which is determined according to the verification pressure difference and pressure safety factor mentioned above in this step; Γ seal This represents the theoretically sealed closed curve determined by the initial geometry; the meanings of the other symbols are the same as those described above.

[0094] The pressure condition in equation (18) is used to eliminate low-pressure contact records that do not meet the minimum sealing pressure requirement, and the spatial neighborhood condition is used to eliminate non-sealing contact records far from the theoretical sealing zone. The area-weighted quantile reference pressure does not directly depend on a single maximum contact pressure; therefore, a single abnormally high-pressure node will not directly raise the screening threshold for all candidate contact records. When there is no positive contact pressure record within the neighborhood of the theoretical sealing zone, C Set 0 to an empty set and mark the corresponding operating condition as having no effective contact.

[0095] To distinguish between continuous load-bearing contact patches and isolated numerical points, the contact mesh topology is used to... C 0. Perform connected component identification: (19) In the formula, CC(·) represents the connected component identification operation; P m Indicates the first m One candidate contact plaque; N p Indicates the number of candidate contact plaques; A m Indicates the first m The contact area of ​​each patch; Lm Indicates the first m The normal contact load borne by each patch; A 0 and L 0 represents the total area and total contact load of all candidate patches, respectively; or Ac and or Lc These represent the area contribution threshold and the load contribution threshold, respectively; Ω c This represents the effective three-dimensional contact area (i.e., effective contact patch) retained after screening. In this embodiment, the area contribution threshold... or Ac and load contribution threshold or Lc The value is set to 0.01, meaning that if the contact area or normal contact load of a candidate contact patch accounts for no less than 1% of the total corresponding amount of all candidate patches, the candidate contact patch is retained. The above values ​​are parameters for this embodiment and do not constitute necessary limitations.

[0096] Pressure conditions and spatial neighborhood conditions are used to screen individual contact records for candidates, while topological connectivity is used to determine whether candidate contact records form contact patches with spatial continuity. These three conditions are applied sequentially. Contact surface elements with common edges, common nodes, or periodic correspondences on both sides of the circumferential 0° and 360° are treated as adjacent surface elements. Candidate connected components should contain at least two mutually adjacent contact surface elements; a single isolated contact surface element is not directly determined as a valid contact patch. Based on satisfying the topological connectivity condition, valid contact patches are retained according to the area contribution condition or load contribution condition of equation (19).

[0097] The effective contact area is divided into multiple circumferential zones according to circumferential parameters. C k Calculate the pressure-weighted contact center, area-weighted average contact pressure, and local effective contact width at each circumferential location: (20) In the formula, C k Indicates the first k The set of effective contact points within a circumferential partition; c p ( ik This indicates the pressure-weighted contact center at that circumferential location; Indicates the first k An angular interval of each circumferential partition; i k This indicates the representative circumferential position of the circumferential partition; all. c p ( i k After sequential connection, a pressure-weighted contact center trajectory is formed; This represents the area-weighted average contact pressure at that circumferential location; b c ( i k () indicates the local effective contact width; l k This represents the arc length of the theoretical sealing curve within that circumferential partition; e p and e l This indicates a small positive number that prevents the denominator from being zero.

[0098] For the k A circumferential partition, pressure-weighted contact center c p ( i k The three-dimensional position is obtained by weighting each effective contact position within the partition; the pressure-weighted contact centers are connected in ascending order of circumferential parameters to form the pressure-weighted contact center trajectory. Local effective contact width. b c ( i k The effective contact area within the circumferential zone is used in conjunction with the arc length of the theoretical sealing curve zone. l k The ratio calculation is used to characterize the equivalent width of the contact area after unfolding along the normal direction of the theoretical sealing curve. When there is no effective contact record in the circumferential zone, or l k When it is zero, b c ( i k The area-weighted average contact pressure is set to zero, and the pressure-weighted contact center is marked as a vacancy, without interpolating across vacancy between adjacent contact centers.

[0099] Equation (20) outputs the contact center trajectory, circumferential pressure distribution, and local contact width. To evaluate whether the sealing strip provides a continuous seal throughout the entire circumference and to identify local pressure concentrations, further calculations are performed: (twenty one) In the formula,C θ Indicates the circumferential coverage of the effective contact area; | C k | indicates the first k The number of effective contact points within each circumferential zone; This represents the average contact pressure across the entire effective contact area. F p ( u ) represents the area-weighted cumulative distribution function of contact pressure within the effective contact area; P 95 This represents the area-weighted 95th percentile contact pressure. D c This represents the root mean square offset of the pressure-weighted contact center trajectory relative to the theoretical sealing curve. W k Indicates the first k The contact load borne by each circumferential zone.

[0100] For the first [item] where effective contact exists k Each circumferential partition is used to calculate the pressure-weighted contact center. c p ( i k ) to the theoretical sealing closure curve Γ seal The local contact center offset is obtained from the geodesic distance of the wall surface. d c,k .Will d c,k Mapped to the risk assessment parameter unit within the corresponding circumferential partition, denoted as d c , jk The root mean square offset is obtained by weighting all local contact center offsets according to the circumferential zone contact load. D c .in, d c , jk Used in step eight to construct a localized sealed risk field. D c It is used to characterize the overall offset of the contact center trajectory under the current operating conditions.

[0101] Peripheral coverage C θ Calculated based on the ratio of the angle occupied by the circumferential zone with effective contact patches to the complete circumferential angle. When each circumferential zone is set at equal intervals, C θIt equals the ratio of the number of circumferential partitions with valid contact records to the total number of circumferential partitions; when the circumferential partitions are set at unequal intervals, the weighted calculation is performed according to the corresponding circumferential angle. The circumferential 0° and 360° are determined for connectivity based on the periodic boundary, but the coverage angle is not counted repeatedly.

[0102] The offset of the pressure-weighted contact center trajectory relative to the theoretical sealing curve is determined according to the contact load borne by each circumferential zone. W k Weighting is applied, and the root mean square offset is further calculated. D c Circumferential zones without effective contact are not included in the average calculation of contact center offset, but are included in the comprehensive risk assessment in step eight through the circumferential coverage deficiency item.

[0103] For example, in step eight, for each parameter unit, the ratio of normal degradation depth to allowable normal degradation depth, insufficient contact pressure, excessive contact stress, and pressure-weighted contact center offset are normalized respectively. The insufficient contact pressure is determined by the area-weighted average contact pressure, the excessive contact stress is determined by the contact stress, and the pressure-weighted contact center offset is determined by the contact center offset. The normalized values ​​are combined with the risk weights for normal degradation depth, insufficient pressure, excessive stress, and contact center offset to obtain a local sealing risk value. All local sealing risk values ​​are arranged according to the parameter domain to form a three-dimensional sealing risk field. A three-dimensional comprehensive sealing risk index is synthesized by weighting the area-weighted average risk, the area-weighted high quantile risk, and the insufficient circumferential contact coverage. The insufficient circumferential contact coverage is determined by the circumferential coverage rate. The three-dimensional comprehensive sealing risk index determines the sealing reliability index and risk level.

[0104] Specifically, for parameter elements without valid contact records, their effective contact pressure and effective contact stress are set to zero, and they are marked as locations with missing circumferential contact. Since this parameter element lacks a calculable pressure-weighted contact center, its contact center offset and contact center offset risk component are set to zero; the lack of contact risk for this parameter element is characterized by insufficient pressure risk and insufficient circumferential contact coverage risk. For parameter elements with multiple contact records, the area-weighted average contact pressure and area-weighted average contact stress are calculated based on the representative contact area.

[0105] In this embodiment, allowable stress s allow Choose the material with the lower yield strength between the ball seat material and the fracturing ball material. s s 0.6 times; allowable contact center offset d lim Take the initial effective sealing bandwidth bc0 0.5 times, of which b c0 The effective contact width is determined according to the local conditions of the initial ball seat reference working condition in step seven.

[0106] In this embodiment, the normal degradation depth is allowed. h lim Take 0.5 mm; continue using the minimum effective contact pressure determined in step seven. p req ; h lim The value of the normal degradation depth used to characterize the allowable normal degradation depth of the ball seat wall is determined based on the ball seat size, allowable wear amount, or product inspection requirements. p req To characterize the minimum effective contact pressure required to maintain the current verification pressure differential, this embodiment uses a pressure safety factor of 1.2; s allow The stress that the contact area can withstand is used to characterize the stress, and its value is determined based on the lower yield strength and stress safety factor of the ball seat material and fracturing ball material. d lim The value is used to characterize the permissible offset of the pressure-weighted contact center relative to the theoretical sealing band, and its value is determined based on the initial effective sealing band width. The above values ​​are evaluation parameters for this embodiment and do not constitute limitations on other materials, dimensions, or differential pressure conditions.

[0107] Regarding the ( j , k ) parameter units are used to construct the local sealing risk value: (twenty two) In the formula, Indicates the ( j , k The local sealing risk value of each parameter zone; x ] + =max( x ,0); clip( x (,0,1) indicates that the value is restricted to the range of 0 to 1; h jk Indicates the depth of normal degradation; h lim Indicates the allowed normal degradation depth or the reference normal degradation depth; This represents the average contact pressure mapped to the partition of this parameter; p req Indicates the minimum effective contact pressure; This represents the average equivalent stress (i.e., contact stress) of the parameter partition. s allow Indicates the allowable stress of the ball seat material;d c,jk This indicates a shift in the contact center; d lim Indicates the allowable contact center offset distance; β h , β p , β σ and β d These represent the weights of each risk component.

[0108] In this embodiment, the weights of the risks of normal degradation depth, insufficient pressure, excessive stress, and contact center offset are... β h , β p , β σ and β d We take values ​​of 0.30, 0.35, 0.20, and 0.15 respectively, and the sum of the four values ​​is 1.

[0109] In equation (22), the greater the normal degradation depth, the more severe the wall thinning, the more significant the weakening of the bearing and deformation capacity of the sealing surface, and the higher the corresponding degradation risk; when the contact pressure is lower than the minimum effective contact pressure, the sealing specific pressure is insufficient to maintain an effective seal, increasing the probability of forming a leakage channel; when the contact stress exceeds the allowable stress of the material, the sealing surface is at risk of yielding or failure; when the pressure-weighted contact center deviates from the theoretical sealing zone, the actual sealing position of the fracturing ball and the ball seat drifts, possibly deviating from the designed sealing area. All local sealing risk values ​​are calculated according to ( z , i The parameters are arranged to form a three-dimensional sealed risk field.

[0110] To simultaneously reflect the overall risk, local high risk, and circumferential contact interruption of the sealed area, area-weighted average risk and area-weighted high quantile risk are calculated: (twenty three) In the formula, This represents the area-weighted average risk of the sealed area. This represents the area-weighted high quantile risk value of the risk field; q r Indicates risk quantiles; R 3D This represents the comprehensive risk index of three-dimensional sealing. C θ Indicates circumferential contact coverage; α 1. α 2 and α 3 represents the comprehensive risk weight, and it is preferred that the sum of the three factors is 1;I seal This represents the three-dimensional seal reliability index; the closer its value is to 1, the higher the seal reliability under the current degradation state. In this embodiment, the weights of area-weighted average risk, area-weighted high quantile risk, and circumferential insufficient contact coverage risk are... α 1. α 2 and α 3. The values ​​are 0.40, 0.40, and 0.20 respectively, and the sum of the three is 1; Risk quantile. q r A value of 0.95 is used to calculate the area-weighted 95th percentile risk value of the three-dimensional sealing risk field. The comprehensive risk index of the three-dimensional sealing is calculated according to equation (23). R 3D and in accordance with I seal =1- R 3D Obtain the three-dimensional sealing reliability index.

[0111] Area-weighted average risk is used to characterize the overall sealing condition; area-weighted high quantile risk is used to prevent local dangerous areas from being masked by the average value; circumferential contact coverage deficiency is used to identify situations where effective contact patches have not formed a complete sealing ring.

[0112] Risk level is determined based on comprehensive risk indicators: (twenty four) In the formula, G Indicates the risk level; G 1. G 2 and G 3 represents the risk levels from low to high; t 1 and t 2 represents the risk grading threshold; in this embodiment, the risk grading threshold is... t 1 is 0.30. t 2 is 0.60. When R 3D When the value is less than 0.30, the risk level G is low risk; when R 3D When the value is not less than 0.30 and less than 0.60, the risk level G is medium risk; when R 3D When the value is not less than 0.60, the risk level G is high risk.

[0113] When the input data contains registration surface metadata corresponding to multiple erosion time periods, the three-dimensional degradation surface reconstruction steps one through six are performed for each erosion time period. The degradation surface at each stage accumulates the normal degradation depth in the order of erosion time under the same spherical base reference coordinate system, forming a degradation surface sequence that evolves with erosion time. For the initial spherical base and the three-dimensional degradation spherical bases corresponding to different erosion times, calculations are performed under the same pressure differential conditions. R 3D , I seal and G This forms a sequence for evaluating the reliability of the seal as it changes over time. If the consistency check or smoothing constraint check fails to meet the requirements, the return path specified in step six is ​​followed.

[0114] For the same verification pressure difference, the corresponding E95 degenerate surface R 3D , I seal and G As the primary evaluation result, the smaller and larger reliability indices from the corresponding evaluation results of the E90 and E99 degraded surfaces are used as the lower and upper boundaries of the reliability evaluation, respectively, and the minimum and maximum values ​​of the corresponding comprehensive risk indicators are used as the range of risk uncertainty. The initial spherical seat result is used as the baseline result under the same verification pressure difference. Thus, for each verification pressure difference, the baseline result, the primary evaluation result, and the uncertainty boundary result are output.

[0115] After meeting all verification requirements, the system outputs the three-dimensional degradation surface, effective contact patch, pressure-weighted contact center trajectory, local effective contact width, circumferential contact coverage, three-dimensional sealing risk field, sealing reliability index, and risk level under the current erosion time and differential pressure conditions, forming a ball seat erosion degradation and contact seal reliability evaluation report. This evaluation report guides the ball seat erosion status assessment and seal maintenance decisions: when the risk level is high or the sealing reliability index is below the preset lower limit, it is determined that the current ball seat is close to or has reached the erosion degradation seal failure state, suggesting that the ball seat be replaced or the fracturing operation parameters be adjusted before subsequent fracturing operations to reduce erosion aggravation; when the risk level is medium, the remaining seal life is predicted by combining the sealing reliability evaluation sequence that changes with erosion time, and the next ball seat inspection node is scheduled.

[0116] Based on the same inventive concept as the above method, this application embodiment also provides a ball seat erosion surface reconstruction and contact seal reliability evaluation system, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of the above-described ball seat erosion surface reconstruction and contact seal reliability evaluation method.

[0117] This application embodiment improves the accuracy of ball seat erosion degradation surface reconstruction and contact seal reliability evaluation by establishing an axial-period circumferential parameter domain and driving three-dimensional peak smoothing and normal reconstruction with area-weighted quantile envelope, and then combining the contact model with three-dimensional sealing risk field evaluation.

[0118] By uniformly converting 3D surface element erosion data into erosion rate and deleting records with non-physical area, coordinates, or rate, the consistency and effectiveness of wall surface element data are improved, avoiding unit inconsistencies and outliers from interfering with subsequent degenerate surface reconstruction.

[0119] By registering the wall surface elements to the spherical reference coordinate system and establishing an overlapping joint statistical window using the periodic angular distance, the continuity of axial and circumferential neighborhood partitioning is improved, avoiding artificial statistical discontinuities caused by circumferential start and end seams and curvature changes.

[0120] By constructing an area-weighted quantile erosion envelope with the actual area of ​​the surface element as the weight, the retention capacity of dangerous erosion areas is improved, and the excessive influence of small-area high-value surface elements on the statistical envelope is avoided, making the erosion degradation characterization more consistent with the actual material removal distribution.

[0121] By establishing a smooth objective function with axial, circumferential and coupling penalty terms in the normalized parameter domain and setting constraints for maintaining dangerous peaks and periodic continuity, the smoothness and fidelity of the erosion surface are improved, non-physical oscillations are suppressed while maintaining dangerous peaks and periodic continuity.

[0122] By using a three-dimensional peak-preserving constrained smooth surface as the erosion rate surface and calculating the normal degradation depth along the real wall normal, and then using reinterpolation and area Jacobian thresholding to prevent folding, the spatial position accuracy and geometric effectiveness of the degradation surface are improved.

[0123] By calculating the material removal mass from the original surface erosion data and the difference in solid volume before and after degradation, and performing consistency verification and iterative correction, the consistency of material removal between the reconstructed degradation geometry and the original erosion data is improved, ensuring the credibility of subsequent evaluations.

[0124] By directly constructing the three-dimensional degenerate surface as the contact surface and using robust pressure thresholds, theoretical sealing zone neighborhoods, and topological connectivity to screen effective contact patches, the accuracy of effective contact area identification is improved, while isolated numerical points and non-sealing contacts far from the sealing zone are excluded.

[0125] By normalizing and weighting the normal degradation depth, contact pressure, contact stress, and contact center offset to construct a three-dimensional sealing risk field, and combining the insufficient circumferential coverage to form a reliability index, the comprehensiveness and reliability of the risk assessment of erosion-degraded ball seat seals are improved.

[0126] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0127] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal, characterized in that, Includes the following steps: Step 1: Obtain three-dimensional surface erosion data of the wall surface to be evaluated on the spherical seat, and establish a set of wall surface data including spatial coordinates, surface area and erosion rate; Step 2: Establish an axial-periodic circumferential spherical ball seat wall parameter domain for the wall surface data set, and obtain the parameter partition surface element set using an overlapping joint statistical window; Step 3: Construct an area-weighted quantile erosion envelope for the parameter partitioned face set using the actual area of ​​the face as the weight; Step four: The area-weighted quantile erosion envelope is smoothed with dangerous peak preservation and periodic continuity constraints to obtain a three-dimensional peak-preserving constrained smooth surface. Step 5: Calculate the current wall normal vector and normal degradation depth based on the three-dimensional peak-preserving constraint smooth surface, update the spherical seat wall along the normal, and obtain the three-dimensional degradation surface; Step 6: Verify the consistency of material removal amount and geometric volume change of the three-dimensional degraded surface, correct the quality normalization coefficient, and obtain the three-dimensional degraded surface that passes the verification. Step 7: Establish a contact model between the fracturing ball and the verified three-dimensional degenerate surface, screen effective contact patches, calculate the pressure-weighted contact center trajectory, area-weighted average contact pressure, contact stress, local effective contact width and circumferential coverage, and obtain the contact center offset from the pressure-weighted contact center trajectory. Step 8: Construct a three-dimensional sealing risk field based on the normal degradation depth, the area-weighted average contact pressure, the contact stress, the contact center offset, and the circumferential coverage, and output the sealing reliability index and risk level.

2. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, In step one, three-dimensional surface erosion data of the wall surface to be evaluated on the spherical seat is obtained, and a one-to-one correspondence record of spatial coordinates, surface area, and erosion rate is established for each surface element. The erosion rate represents the amount of material mass loss per unit wall area per unit time. When the input data uses mass loss, volume loss, or normal degradation depth as the erosion characterization quantity, the erosion characterization quantity is converted into the erosion rate according to the corresponding surface area, action time, and spherical seat material density. A set of wall surface data containing spatial coordinates, surface area, and erosion rate is established, and non-physical records with an area not greater than zero, invalid coordinates, and negative erosion rates are deleted.

3. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, In step two, the wall surface data is registered to the spherical reference coordinate system, and a wall parameter domain consisting of axial parameters and periodic circumferential parameters is established. The axial and circumferential parameters of each surface element are calculated, and axial and circumferential output nodes are set in the wall parameter domain. An axial and circumferential overlapping joint statistical window is established with each output node as the center. The circumferential direction uses the periodic angular distance to measure the head-to-tail connection relationship, so that surface elements located near 0° and 360° enter the same statistical neighborhood, forming a parameter partitioned surface element set.

4. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, Step three, which involves constructing an area-weighted quantile erosion envelope using the actual area of ​​the face cells as the weight, includes: For each joint statistical window, the erosion rate and area of ​​effective surface elements are extracted, and they are arranged in ascending order of erosion rate. The proportion of the cumulative area of ​​surface elements not exceeding any erosion rate threshold to the total area of ​​all effective surface elements within the window is calculated. The area-weighted quantile erosion rate and area-weighted average erosion rate are determined using the area-weighted cumulative distribution, and the E90, E95, and E99 quantile erosion rate surfaces are constructed, which are the area-weighted quantile erosion envelopes. Confidence weights are set according to the number of effective surface elements and the effective coverage area of ​​the window for subsequent smoothing and fitting.

5. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, Step four, the smoothing process with dangerous peak retention and periodic continuity constraints, includes: The axial and circumferential parameters are normalized, and the confidence weight is used as the data fitting weight. The area-weighted quantile erosion envelope is used as the fitting object. A smoothing objective function is established, which includes data fitting terms, axial second-order variation penalty terms, circumferential second-order variation penalty terms, and axial-circumferential coupling variation penalty terms. During the smoothing process, dangerous peak preservation constraints, area integral preservation constraints, different quantile surface order preservation constraints, and circumferential function value and periodic derivative continuity constraints are set to obtain a three-dimensional peak-preserving constrained smooth surface.

6. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, In step five, the three-dimensional peak-preserving constraint smooth surface is used as the erosion rate surface. The unit normal vector pointing to the interior of the spherical seat entity is calculated based on the tangent vectors of the current three-dimensional wall surface to the axial and circumferential parameters, which is the current wall surface normal vector. The mass normalization coefficient is calculated under the condition that the area integral of the erosion rate surface in the parameter domain is consistent with the erosion integral of the original surface element, and the erosion rate surface is converted into the normal degradation depth. The wall nodes are updated along the current wall normal to obtain a temporary degradation surface. Then, the three-dimensional degradation surface is obtained by re-interpolating the surface while maintaining the circumferential periodic continuity, and the surface folding is prevented by a local area Jacobian threshold.

7. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, In step six, the first material removal mass is obtained by integrating the original wall surface erosion data, and the second material removal mass is obtained by the volume difference of the spherical seat before and after degradation. The relative consistency error between the first and second material removal masses is calculated. When the relative consistency error exceeds the preset consistency threshold, the mass normalization coefficient is updated according to the correction formula, the normal degradation depth is recalculated, and the surface update in step five is performed. When the relative consistency error does not exceed the preset consistency threshold and the geometric validity meets the requirements, a verified three-dimensional degradation surface is obtained.

8. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, In step seven, the verified three-dimensional degenerate surface is directly constructed as the ball seat contact surface, and a contact model between the fracturing ball and the ball seat contact surface is established. Positive contact pressure records are extracted in the neighborhood of the theoretical sealing zone, and candidate contact records are screened based on the area-weighted quantile reference pressure and the lowest effective contact pressure. Connectivity components are identified for the candidate contact records, and effective contact patches are retained according to area contribution or load contribution. The effective contact area is divided into circumferential partitions, and the pressure-weighted contact center trajectory, area-weighted average contact pressure, contact stress, local effective contact width, and circumferential coverage are calculated. The contact center offset is calculated from the pressure-weighted contact center trajectory.

9. The method for reconstructing the eroded surface of a ball seat and evaluating the reliability of the contact seal according to claim 1, characterized in that, In step eight, for each parameter unit, the ratio of normal degradation depth to allowable normal degradation depth, insufficient contact pressure, excessive contact stress, and pressure-weighted contact center offset are normalized respectively. The insufficient contact pressure is determined by the area-weighted average contact pressure, the excessive contact stress is determined by the contact stress, and the pressure-weighted contact center offset is determined by the contact center offset. The normalized values ​​are combined with the risk weights for normal degradation depth, insufficient pressure, excessive stress, and contact center offset to obtain the local sealing risk value. All local sealing risk values ​​are arranged according to parameter domains to form a three-dimensional sealing risk field; a three-dimensional sealing comprehensive risk index is synthesized by weighting area-weighted average risk, area-weighted high quantile risk and insufficient circumferential contact coverage, wherein insufficient circumferential contact coverage is determined by the circumferential coverage rate, and the sealing reliability index and risk level are determined by the three-dimensional sealing comprehensive risk index.

10. A ball seat erosion surface reconstruction and contact seal reliability evaluation system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the ball seat erosion surface reconstruction and contact seal reliability evaluation method as described in any one of claims 1 to 9.

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