Method for calculating drag force of casing running in horizontal well considering buckling effect

Abstract

The present application belongs to the technical field of drilling engineering, and discloses a horizontal well three-dimensional wellbore casing running friction calculation method considering buckling effect. According to the well trajectory parameters, the pipe string combination conditions and the boundary conditions, the well pipe string is divided into n units with the well trajectory measuring points as nodes, the unit length pipe string unit upper end axial force is equal to the lower end axial force, the contact force of the pipe string unit is calculated, the axial force is recalculated with the contact force, the contact force is calculated again with the axial force, the contact force and the corresponding axial force meeting the accuracy are obtained through iterative calculation, and then the casing buckling or not is combined to calculate the friction value of the unit length pipe string unit, and each pipe string unit is calculated in turn until the end. The method of the present application takes into account the influence of casing buckling deformation, continuously corrects the results in the iteration process, can calculate the friction size and distribution of the casing at specific positions of the whole well section more accurately according to the calculation results of the complex well trajectory, and the calculation results are closer to the engineering practice.

Description

Technical Field

[0001] This invention belongs to the field of drilling engineering technology, specifically relating to a method for calculating the friction of running three-dimensional well casing in horizontal wells considering buckling effects. Background Technology

[0002] Downhole tubing friction is a crucial factor that receives significant attention in the design and operation of horizontal well projects. Pre-drilling tubing friction analysis provides a scientific basis for selecting or upgrading drilling rigs and is an important foundation for optimizing wellbore profile design. Post-drilling tubing friction analysis provides a scientific basis for selecting the optimal casing running operation plan. Comparing predicted and measured values ​​of tubing friction can effectively monitor the degree of wellbore cleaning and diagnose complex downhole conditions and accidents.

[0003] Traditional methods for calculating casing string friction rely on classical casing mechanics to establish a comprehensive stress model of the casing string. However, the calculated friction deviates significantly from actual engineering conditions, failing to meet on-site construction expectations and providing inadequate guidance for drilling operations. Furthermore, the complexity of three-dimensional wellbore trajectories and the high instability of drilling conditions mean that traditional casing string friction calculation methods are overly idealistic in their application of principles and simplification of conditions. Consequently, the calculated friction magnitude and distribution cannot reflect the true stress state of the casing string.

[0004] In the prior art, patent document CN109869132A discloses a method for calculating the friction coefficient of casing. This method includes: S1, obtaining the length of each casing segment, well inclination angle, casing linear weight, steel density, and drilling fluid density when the casing is run to a predetermined well depth; S2, real-time monitoring and recording of the hook load data during the casing run to the predetermined well depth; S3, determining the type and number of friction coefficients based on the type and location of the centralizers in the casing string, and selecting the same number of time points as the number of friction coefficients to collect the hook load data and corresponding casing string data at each time point; S4, based on the hook load data and corresponding casing string data at each time point, listing the hook load calculation formulas to obtain a set of equations; S5, solving the set of equations to obtain the friction coefficient value. This technical solution can accurately calculate the friction coefficient of different types of centralizers, is simple and easy to implement, and can provide reliable technical guidance for casing running operations. However, its calculation results do not consider the influence of buckling effects.

[0005] Patent document CN105545260A discloses a casing string running method and apparatus. The method includes: performing a stress analysis on the casing string to obtain a casing string friction calculation equation; calculating the hook load corresponding to different floating lengths based on the casing string friction calculation equation; taking the floating length corresponding to the largest hook load as the optimal floating length, based on satisfying preset load conditions; setting a floating coupling at the position corresponding to the optimal floating length of the casing string, and performing the casing string running operation. This invention applies the principle of floating casing running, performs mechanical analysis on the casing string, establishes a floating casing running mechanical model, and forms an optimized scheme for calculating the casing floating length, thereby determining the optimal floating section length, placing the floating coupling at the optimal well depth, maximizing the remaining running load, ensuring the casing string is successfully run into position, providing technical support for floating casing running, and thus successfully completing well completion operations. However, this technical solution still does not consider the influence of helical buckling effect on friction.

[0006] The paper "Research on Calculation Method of Casing Friction Considering the Influence of Centralizers" (You Yao, Journal of Yangtze University, January 2014) discloses that during cementing operations in horizontal and extended reach wells, a certain number of casing centralizers are often installed in the high-angle and horizontal sections to ensure cementing quality. During the running of multi-centralizer casing strings in curved wells, the spatial bending effect of the wellbore and the increased stiffness of the casing string due to the centralizers increase the wellbore support force and friction, making it prone to hard jamming and self-locking, thus increasing the difficulty of running the casing. To address this issue, the paper studies the friction problem of multi-centralizer casing strings during the running process in curved wells from a mechanical perspective. However, the paper only considers the influence of the centralizers on friction, without considering the influence of buckling effect on casing friction.

[0007] The paper "Calculation of Horizontal Well Casing Friction and Analysis of Run-in Feasibility" (Zhang Yang, Southwest Petroleum University, June 2015) discloses that: due to the influence of factors such as the self-weight of the casing string and wellbore curvature, the casing string will come into contact with the well wall during the running-in process. Therefore, the stress on the casing string during the running-in process is relatively complex. It is necessary to analyze and calculate the friction and load of the casing string during the running-in process to provide a theoretical basis for safe casing running construction. In addition, the solution process of the friction mechanical model requires the use of wellbore trajectory survey data such as well inclination angle and azimuth angle, while the field survey data are discrete points. To minimize errors in measurement data, it is necessary to first smooth the data and perform cubic spline interpolation. The interpolated inclination data is then used to solve the frictional resistance model. This paper mainly analyzes and calculates the frictional resistance and axial force of casing in horizontal wells, based on the research of domestic and foreign scholars on the frictional resistance model of casing downhole. It comprehensively considers factors affecting frictional resistance such as mud viscosity resistance, differential pressure resistance, dynamic load, casing and wellbore size, and wellbore trajectory parameters. However, it also does not consider the influence of buckling effect on casing frictional resistance.

[0008] Buckling deformation frequently occurs during the running of horizontal well casing. Buckling under pressure alters the contact state between the casing and the wellbore, changing the magnitude of the contact load. This buckling increases the contact force and running friction between the casing and the wellbore. Therefore, developing a method for calculating the running friction of horizontal well casing in three-dimensional boreholes, considering the additional contact force and friction caused by casing buckling, is a challenging problem that needs to be solved. Summary of the Invention

[0009] This invention aims to address the problems existing in the prior art by providing a method for calculating the frictional resistance of casing during three-dimensional horizontal wellbore running, considering the buckling effect. Based on traditional casing frictional resistance calculation methods, this method incorporates the influence of casing buckling deformation on frictional resistance and continuously refines the calculation results during the iterative process. The method of this invention can accurately calculate the magnitude and distribution of frictional resistance at specific locations throughout the wellbore based on the calculation results of complex wellbore trajectories, providing theoretical guidance for optimizing wellbore structure design and selecting the best casing running operation method.

[0010] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0011] A method for calculating the frictional resistance of running a three-dimensional casing in a horizontal well considering the buckling effect, the method comprising the following steps:

[0012] Step S101: Based on the wellbore trajectory parameters, tubing combination conditions, and boundary conditions, divide the downhole tubing into n tubing units, with the wellbore trajectory measuring points as nodes. The tubing between any two adjacent measuring points is a tubing unit. Start the calculation from the initial tubing unit i=1 at the bottom of the tubing and input the initial conditions.

[0013] Step S102: Calculate the average well inclination angle, average azimuth angle, vertical component of the unit normal vector, and vertical component of the unit sub-normal vector for the tubing unit.

[0014] Step S103: Assign an initial value to the axial force at the upper end of the tubular unit, setting the axial force T1 per unit length of the upper end of the tubular unit to be... i Equal to the axial force at the lower end of a unit length of tubular column element Right now

[0015] Step S104: Calculate the contact force per unit length of the tubular column element.

[0016]

[0017] in,

[0018]

[0019]

[0020]

[0021]

[0022] In the above formula, Let N be the contact force per unit length of the tubular column element; The total contact force per unit length of the column element in the full-angle plane, in N; The total contact force per unit length of the column element perpendicular to the full-angle plane is expressed in N. T1 represents the length of the tubular unit, in meters (m). i The axial force at the upper end of a unit length of tubular column unit, in N; θ is the axial force at the lower end of a unit length tubular column, in N; i For the full angular variation of a unit length tubular column element; This represents the vertical component of the normal vector of the column element; q is the vertical component of the binormal vector of the tubular element; i The weight per unit length of the tubular column unit; The inclination angle at the top of the unit length of the tubing string; The inclination angle at the lower end of a unit length of tubing string; The azimuth angle of the upper end of the unit length of the tubular column; The azimuth angle of the lower end of the unit length column element; i = 1, 2, ..., n, representing the i-th column element.

[0023] Step S105: Contact force per unit length of the tubular column element calculated according to step S104. Recalculate the axial force T1 at the upper end of the unit length tubular column element. i The calculation formula is as follows:

[0024]

[0025] In the above formula, T1 i The axial force at the upper end of a unit length of tubular column unit, in N; The axial force at the lower end of a unit length of tubular column, in N; θ is the length of the tubular element, in meters; i The total angle variation per unit length of the tubular column element; q i The weight per unit length of the tubular column element; α i The average well inclination angle per unit length of tubing unit; μ is the friction coefficient;

[0026] Step S106: Calculate the axial force T1 at the upper end of the unit length tubular column unit based on step S105. i Substitute the values ​​into the calculation formula in step S104 to back-calculate the contact force per unit length of the column element.

[0027] Step S107: Calculate the contact force per unit length of the tubular column element in step S104. Contact force with the unit length of the tubular column element in step S106 The difference between the two is determined, and it is judged whether the absolute value of the difference is less than the allowable error ε.

[0028] like Then the axial force T1 at the upper end of the unit length tubular unit, recalculated in step S105, is used. i As the updated value, return to steps S104-S106 to re-iterate and calculate, correcting the calculation result F. n (i)′ ;

[0029] like Then at this time The axial force at the upper end of the corresponding unit length tubular element is used as the final calculated axial force T1 at the upper end of the unit length tubular element. i Proceed to the next step, S108;

[0030] Step S108: Based on the axial force T1 at the upper end of the unit length tubular unit calculated in step S107.i Determine whether the casing has buckled; calculate the final contact force per unit length of the tubing unit based on the determination result. If the cannula buckles, then The additional contact force due to casing buckling is taken into account; if the casing does not buckle, then... Additional contact forces due to casing buckling are not included in the calculation.

[0031] Step S109: Based on the calculation in step S108 Calculate the friction value per unit length of the tubular column element:

[0032]

[0033] In the formula, F t is the frictional resistance between a unit length of tubing string and the wellbore, in N; μ is the coefficient of friction between a unit length of tubing string and the wellbore.

[0034] Step S110: Based on the fact that the axial force at the lower end of the next tubing unit is equal to the axial force at the upper end of the previous tubing unit, repeat steps S102-S109 to calculate the contact force, axial force, and friction value of the next tubing unit i = i+1. Iterate in this way until the contact force, axial force, and friction value of the nth tubing unit are calculated. At this point, the calculation of all tubing units in the entire well casing is completed, and the calculation ends. The axial force, contact force, and friction value of the entire tubing from the top to the bottom of the well are summarized, as well as the distribution law of the axial force, contact force, and friction value in the entire well casing.

[0035] Furthermore, the following steps are included before step S101:

[0036] Step S100: Obtain the actual drilling and logging data of the target well, number the measuring points of the wellbore trajectory sequentially from the wellhead down to n, calculate the wellbore trajectory parameters using the minimum curvature method, and store the calculation results in an array variable for future reference.

[0037] The actual drilling and logging data include well inclination angle, azimuth angle, and depth measurement.

[0038] The measuring points include a series of data points consisting of depth, well inclination angle, and azimuth angle.

[0039] Furthermore, in step S100, the wellbore trajectory parameters are calculated using the minimum curvature method, specifically including:

[0040] Calculate the northward displacement variation rate N1′, the eastward displacement variation rate E1′, and the vertical well depth variation rate V1′ of the measuring points on a unit length of tubing string:

[0041]

[0042]

[0043] V1′=cosα i-1

[0044] In the above formula, α i-1 The well inclination angle at the measuring point on a unit length of tubing string; The azimuth angle of the measuring point on a unit length of tubular column;

[0045] Calculate the northward displacement variation rate N2′, the eastward displacement variation rate E2′, and the vertical well depth variation rate V2′ of the measuring points under the unit length of the tubing string:

[0046]

[0047]

[0048] V2′=cosα i

[0049] In the above formula, α i The well inclination angle at the measuring point per unit length of tubing unit; The azimuth angle of the measuring point per unit length of the tubular column;

[0050] Calculate the depth variation ΔL and total angle variation θ per unit length of the tubular column element. i cosine, wellbore curvature K i :

[0051] ΔL=L i -L i-1

[0052] cosθ i =N1′N2′+E1′E2′+V1′V2′

[0053] K i =θ i ΔL

[0054] In the above formula, L i For depth measurement at the measuring point under a unit length of tubular column; L i-1 For depth measurement at measuring points on a unit length of tubular column;

[0055] Calculate the northward displacement N of a unit length tubular element. i Eastward displacement E i , vertical well depth V i and horizontal displacement H i :

[0056]

[0057]

[0058]

[0059]

[0060] In the above formula, N i-1 E represents the northward displacement of the measuring point on a unit length of tubular column element. i-1 V represents the eastward displacement of the measuring point on a unit length of tubular column unit; i-1 θ represents the vertical well depth of the measuring point per unit length of tubing unit; i For the full angular variation of a unit length tubular column element;

[0061] And following the above method, the wellbore curvature K of each tubing unit is calculated iteratively for i = 1, 2, ..., n. i , depth change ΔL, displacement in the due north direction N i Displacement E in the due east direction i , vertical well depth V i and horizontal displacement H i Thus, the wellbore trajectory parameters are obtained.

[0062] Further, in step S101, the tubing assembly conditions include the dimensions and steel grades of each assembled casing segment, and the boundary conditions are the loads on the initial tubing unit at the bottom of the tubing column. The initial conditions include the outer diameter, inner diameter, elastic modulus, and Poisson's ratio of the tubing unit.

[0063] Further, in step S108, the axial force T1 at the upper end of the unit length tubular unit, calculated in step S107, is used... i To determine whether the cannula has buckled, the specific steps are as follows:

[0064] If T1 i If the load is less than or equal to the critical load for helical buckling, helical buckling will occur.

[0065] If the critical load of helical buckling <T1 i If the load is less than or equal to the critical load for sinusoidal buckling, then sinusoidal buckling will occur.

[0066] If T1 i If the critical load for sinusoidal buckling is reached, buckling will not occur.

[0067] Furthermore, in step S108, if the sleeve undergoes helical buckling, then F n (i)″ Additional contact force F due to helical buckling of the casing nhel ,Right now:

[0068] F n (i)″ =F n (i)′+F nhel ;

[0069]

[0070] If the bushing undergoes sinusoidal buckling, then Additional contact force F due to sinusoidal buckling of the casing ns i n ,Right now:

[0071] F n (i)″ =F n (i)′ +F nsin

[0072]

[0073] If the cannula does not buckle, then The additional contact force due to casing buckling is not taken into account, that is:

[0074] F n (i)″ =F n (i)′

[0075] In the above formula, E is the elastic modulus; I is the moment of inertia of the cross section; and r is the gap between the casing and the wellbore.

[0076] Further, in step S110, the process iterates sequentially until the contact force, axial force, and friction of the nth tubular unit are calculated, specifically including:

[0077] The operation is determined based on whether the iteration loop condition i = i + 1 is greater than n.

[0078] If i>n is not true, repeat steps S102-S109 to calculate the contact force, axial force and friction value of the next tubular unit.

[0079] If i>n holds true, the calculation ends, and the values ​​of axial force, contact force, and frictional resistance of the entire casing string from top to bottom of the well are summarized, as well as the distribution of axial force, contact force, and frictional resistance throughout the casing string.

[0080] This invention provides a method for calculating the frictional resistance of a three-dimensional casing run-down in a horizontal well considering buckling effects. First, the wellbore trajectory parameters are calculated using the minimum curvature method. Then, the casing string is divided into several units, with the axial force at the upper end of each unit equal to the axial force at the lower end. The contact force of each unit is calculated, and the axial force is then used to back-calculate the contact force. The calculated axial force is then used to recalculate the contact force of the casing unit. It is then determined whether buckling has occurred in the casing. The frictional resistance value per unit length of the casing unit is calculated. This process is repeated for each casing unit until the end.

[0081] Compared with the prior art, the beneficial effects of the present invention are:

[0082] Based on existing methods for calculating casing running friction, this method incorporates the influence of casing buckling deformation and continuously corrects the calculation results during the iteration process. It can also accurately calculate the magnitude and distribution of friction at specific locations of the casing throughout the well section based on the calculation results of complex wellbore trajectory parameters, making the calculation results closer to engineering reality. This has important guiding significance for optimizing wellbore structure design and selecting the best casing running operation scheme. Attached Figure Description

[0083] Figure 1 This is a flowchart illustrating the method for calculating the frictional resistance of horizontal well casing running in a three-dimensional wellbore, taking into account the buckling effect, in an embodiment of the present invention. Detailed Implementation

[0084] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] Example 1

[0086] The target well XX61 in the embodiment provided by this invention has a three-dimensional wellbore trajectory. The drilling process involved azimuth adjustments. The well depth is 5876m, the maximum inclination angle is 90.6°, the maximum dogleg angle is 7.555° / 30m, and the horizontal displacement is 2055m. The casing size is 127mm, the casing wall thickness is 11.1mm, the casing steel grade is TP125V, and 532 casing sections are connected to the well. The oil layer casing structure is shown in Table 1.

[0087] Table 1. Casing Structure of Oil Layer in Well XX61

[0088]

[0089] This invention provides a method for calculating the frictional resistance of a horizontal well casing during three-dimensional casing lowering, considering the buckling effect. This method is used to calculate the magnitude and distribution of frictional resistance throughout the casing section during the lowering process of the target well, XX61. Figure 1 As shown, the method mainly includes the following steps:

[0090] Step S100: Obtain the actual drilling and logging data of the target well, number the measuring points of the wellbore trajectory sequentially from the wellhead down to n, calculate the wellbore trajectory parameters using the minimum curvature method, and store the calculation results in an array variable for future reference.

[0091] The actual drilling and logging data include well inclination angle, azimuth angle, and depth measurement.

[0092] The measuring points are a series of data points consisting of depth, well inclination angle, and azimuth angle.

[0093] The wellbore trajectory parameters specifically include the wellbore curvature K, depth change, northward displacement N, eastward displacement E, vertical well depth V, and horizontal displacement H for each tubing unit i = 1, 2, ..., n.

[0094] The wellbore trajectory parameters are calculated using the minimum curvature method, specifically as follows:

[0095] Calculate the northward displacement variation rate N1′, the eastward displacement variation rate E1′, and the vertical well depth variation rate V1′ of the measuring points on a unit length of tubing string:

[0096]

[0097]

[0098] V1′=cosα i-1 (3)

[0099] In equations (1)-(3) above, α i-1 The well inclination angle at the measuring point on a unit length of tubing string; The azimuth angle of the measuring point on a unit length of tubular column;

[0100] Calculate the northward displacement variation rate N2′, the eastward displacement variation rate E2′, and the vertical well depth variation rate V2′ of the measuring points under the unit length of the tubing string:

[0101]

[0102]

[0103]

[0104] In equations (4)-(6) above, α i The well inclination angle at the measuring point per unit length of tubing unit; The azimuth angle of the measuring point per unit length of the tubular column;

[0105] Calculate the depth variation ΔL and total angle variation θ per unit length of the tubular column element. i cosine, wellbore curvature K i :

[0106] ΔL=L i -L i-1 (7)

[0107] cosθ i=N1′N2′+E1′E2′+V1′V2′ (8)

[0108] K i =θ i / ΔL (9)

[0109] In the above formula, L i For depth measurement at the measuring point under a unit length of tubular column; L i-1 For depth measurement at measuring points on a unit length of tubular column;

[0110] Calculate the northward displacement N of a unit length tubular element. i Eastward displacement E i , vertical well depth V i and horizontal displacement H i :

[0111]

[0112]

[0113]

[0114]

[0115] In equations (10)-(13) above, N i-1 E represents the northward displacement of the measuring point on a unit length of tubular column element. i-1 V represents the eastward displacement of the measuring point on a unit length of tubular column unit; i-1 θ represents the vertical well depth of the measuring point per unit length of tubing unit; i For the full angular variation of a unit length tubular column element;

[0116] And following the above method, the wellbore curvature K of each tubing unit is calculated iteratively for i = 1, 2, ..., n. i , depth change ΔL, displacement in the due north direction N i Displacement E in the due east direction i , vertical well depth V i and horizontal displacement H i .

[0117] Step S101: Based on the wellbore trajectory parameters, tubing combination conditions, and boundary conditions, divide the downhole tubing into n tubing units, with the wellbore trajectory data points as nodes. The tubing between any two adjacent data points is a tubing unit. Start the calculation from the initial tubing unit i=1 at the bottom of the tubing and input the initial conditions.

[0118] The wellbore trajectory parameters are calculated in step S100. The tubing combination conditions include the dimensions and steel grades of each section of the casing. The boundary conditions are the loads on the initial tubing unit at the bottom of the tubing string. The initial conditions include the outer diameter, inner diameter, elastic modulus, and Poisson's ratio of the tubing unit.

[0119] Step S102: Calculate the average well inclination angle, average azimuth angle, vertical component of the unit normal vector, and vertical component of the unit sub-normal vector for the tubing unit.

[0120] Step S103: Assign an initial value to the axial force at the upper end of the tubular unit, setting the axial force T1 per unit length of the upper end of the tubular unit to be... i Equal to the axial force at the lower end of a unit length of tubular column element Right now During the initial casing lowering process, the bottom axial force is 0, i.e.

[0121] Step S104: Calculate the contact force per unit length of the tubular column element.

[0122] In a 3D wellbore, the total contact force per unit length of tubing string is the vector sum of the total contact force in the full-angle plane of the tubing string and the total contact force perpendicular to the full-angle plane of the tubing string; since they are perpendicular to each other, the contact force per unit length of tubing string is... The calculation formula is:

[0123]

[0124] in,

[0125]

[0126]

[0127]

[0128]

[0129] In equations (14)-(18) above, Let N be the contact force per unit length of the tubular column element; The total contact force per unit length of the column element in the full-angle plane, in N; The total contact force per unit length of the column element perpendicular to the full-angle plane is expressed in N. T1 represents the length of the tubular unit, in meters (m). i The axial force at the upper end of a unit length of tubular column unit, in N; θ is the axial force at the lower end of a unit length tubular column, in N; iFor the full angular variation of a unit length tubular column element; This represents the vertical component of the normal vector of the column element; q is the vertical component of the binormal vector of the tubular element; i The weight per unit length of the tubular column unit; The inclination angle at the top of the unit length of the tubing string; The inclination angle at the lower end of a unit length of tubing string; The azimuth angle of the upper end of the unit length of the tubular column; The azimuth angle of the lower end of the unit length column element; i = 1, 2, ..., n, representing the i-th column element.

[0130] Step S105: Contact force per unit length of the tubular column element calculated according to step S104. Recalculate the axial force T1 at the upper end of the unit length tubular column element. i The calculation formula is as follows:

[0131]

[0132] In equation (19) above, T1 i The axial force at the upper end of a unit length of tubular column unit, in N; L represents the axial force at the lower end of a unit length tubular column element, expressed in N. i s θ is the length of the tubular element, in meters; i The total angle variation per unit length of the tubular column element; q i The weight per unit length of the tubular column element; α i denoted as the average well inclination angle per unit length of tubing string; μ is the friction coefficient.

[0133] Step S106: Calculate the axial force T1 at the upper end of the unit length tubular column unit based on step S105. i Substitute the values ​​into the calculation formula in step S104 to back-calculate the contact force per unit length of the column element.

[0134] Step S107: Calculate the contact force per unit length of the tubular column element in step S104. Contact force with the unit length of the tubular column element in step S106 The difference between the two is determined, and it is judged whether the absolute value of the difference is less than the allowable error ε.

[0135] like Then the axial force T1 at the upper end of the unit length tubular unit, recalculated in step S105, is used. i As the updated value, return to steps S104-S106 to re-iterate and calculate, correcting the calculation results.

[0136] like Then at this time The axial force T1 at the upper end of the corresponding unit length tubular column unit i The axial force T1 at the upper end of the unit length tubular element is used for the final calculation. i Proceed to the next step, S108.

[0137] Step S108: Based on the axial force T1 at the upper end of the unit length tubular unit calculated in step S107. i Determine whether the casing has buckled; calculate the final contact force per unit length of the tubing unit based on the determination result. If the cannula buckles, then The additional contact force due to casing buckling is taken into account; if the casing does not buckle, then... Additional contact forces due to casing buckling are not included in the calculation.

[0138] Specifically: if T1 i If the load is less than or equal to the critical load for helical buckling, then helical buckling will occur. Additional contact force F due to helical buckling of the casing nhel ,Right now:

[0139]

[0140]

[0141] If the critical load of helical buckling <T1 i If the load is less than or equal to the critical load for sinusoidal buckling, then sinusoidal buckling will occur. Additional contact force F due to sinusoidal buckling of the casing nsin ,Right now:

[0142]

[0143]

[0144] If T1 i If the critical load for sinusoidal buckling is reached, buckling will not occur. The additional contact force due to casing buckling is not taken into account, that is:

[0145]

[0146] In the above formulas (20)-(24), E is the elastic modulus; I is the moment of inertia of the cross section; and r is the gap between the casing and the wellbore.

[0147] Step S109: Based on the calculation in step S108 Calculate the friction value per unit length of the tubular column element:

[0148]

[0149] In equation (25), F t is the frictional resistance between a unit length of tubing string and the wellbore, in N; μ is the coefficient of friction between a unit length of tubing string and the wellbore.

[0150] Step S110: Based on the fact that the axial force at the lower end of the next tubular unit is equal to the axial force at the upper end of the previous tubular unit, repeat steps S102-S109 to calculate the contact force, axial force, and friction value of the next tubular unit i = i + 1. Iterate in this way until the contact force, axial force, and friction value of the nth tubular unit are calculated. That is, the operation is judged based on whether i = i + 1 is greater than n according to the iteration loop condition.

[0151] If i>n is not true, repeat steps S102-S109 to calculate the contact force, axial force and friction value of the next tubular unit.

[0152] If i>n holds true, then the calculation of all tubing units in the entire well casing is completed, the calculation ends, and the axial force, contact force, and friction values ​​of the entire tubing from the top to the bottom of the well are summarized, as well as the distribution law of axial force, contact force, and friction values ​​in the entire well casing.

[0153] The above description is merely an embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the frictional resistance of running a three-dimensional casing in a horizontal well considering buckling effects, characterized in that, The method includes the following steps: Step S101: Based on the wellbore trajectory parameters, tubing combination conditions, and boundary conditions, divide the downhole tubing into n tubing units, with the wellbore trajectory measuring points as nodes. The tubing between any two adjacent measuring points is a tubing unit. Start the calculation from the initial tubing unit i=1 at the bottom of the tubing and input the initial conditions. Step S102: Calculate the average well inclination angle, average azimuth angle, vertical component of the unit normal vector, and vertical component of the unit sub-normal vector for the tubing unit. Step S103: Assign an initial value to the axial force at the upper end of the tubular unit, setting the axial force T1 per unit length of the upper end of the tubular unit to be... i Equal to the axial force at the lower end of a unit length of tubular column element Right now Step S104: Calculate the contact force per unit length of the tubular column element. in, In the above formula, Let N be the contact force per unit length of the tubular column element; The total contact force per unit length of the column element in the full-angle plane, in N; The total contact force per unit length of the column element perpendicular to the full-angle plane is expressed in N. T1 represents the length of the tubular unit, in meters (m). i The axial force at the upper end of a unit length of tubular column unit, in N; θ is the axial force at the lower end of a unit length tubular column, in N; i For the full angular variation of a unit length tubular column element; This represents the vertical component of the normal vector of the column element; q is the vertical component of the binormal vector of the tubular element; i The weight per unit length of the tubular column unit; The inclination angle at the top of the unit length of the tubing string; The inclination angle at the lower end of a unit length of tubing string; The azimuth angle of the upper end of the unit length of the tubular column; The azimuth angle of the lower end of the unit length column element; i = 1, 2, ..., n, representing the i-th column element; Step S105: Contact force per unit length of the tubular column element calculated according to step S104. Recalculate the axial force T1 at the upper end of the unit length tubular column element. i The calculation formula is as follows: In the above formula, T1 i The axial force at the upper end of a unit length of tubular column unit, in N; The axial force at the lower end of a unit length of tubular column, in N; θ is the length of the tubular element, in meters; i The total angle variation per unit length of the tubular column element; q i The weight per unit length of the tubular column element; α i The average well inclination angle per unit length of tubing unit; μ is the friction coefficient; Step S106: Calculate the axial force T1 at the upper end of the unit length tubular column unit based on step S105. i Substitute the values ​​into the calculation formula in step S104 to back-calculate the contact force per unit length of the column element. Step S107: Calculate the contact force per unit length of the tubular column element in step S104. Contact force with the unit length of the tubular column element in step S106 The difference between the two is determined, and it is judged whether the absolute value of the difference is less than the allowable error ε. like Then the axial force T1 at the upper end of the unit length tubular unit, recalculated in step S105, is used. i As the updated value, return to steps S104-S106 to re-iterate and calculate, correcting the calculation results. like Then at this time The axial force at the upper end of the corresponding unit length tubular element is used as the final calculated axial force T1 at the upper end of the unit length tubular element. i Proceed to the next step, S108; Step S108: Based on the axial force T1 at the upper end of the unit length tubular unit calculated in step S107. i Determine whether the casing has buckled; calculate the final contact force per unit length of the tubing unit based on the determination result. If the cannula buckles, then The additional contact force due to casing buckling is taken into account; if the casing does not buckle, then... Additional contact forces due to casing buckling are not included in the calculation. Step S109: Based on the calculation in step S108 Calculate the friction value per unit length of the tubular column element: In the formula, F t is the frictional resistance between a unit length of tubing string and the wellbore, in N; μ is the coefficient of friction between a unit length of tubing string and the wellbore. Step S110: Based on the fact that the axial force at the lower end of the next tubing unit is equal to the axial force at the upper end of the previous tubing unit, repeat steps S102-S109 to calculate the contact force, axial force, and friction value of the next tubing unit i = i+1. Iterate in this way until the contact force, axial force, and friction value of the nth tubing unit are calculated. At this point, the calculation of all tubing units in the entire well casing is completed, and the calculation ends. The axial force, contact force, and friction value of the entire tubing from the top to the bottom of the well are summarized, as well as the distribution law of the axial force, contact force, and friction value in the entire well casing.

2. The method according to claim 1, characterized in that, The following steps are included before step S101: Step S100: Obtain the actual drilling and logging data of the target well, number the measuring points of the wellbore trajectory sequentially from the wellhead down to n, calculate the wellbore trajectory parameters using the minimum curvature method, and store the calculation results in an array variable for future reference. The actual drilling and logging data include well inclination angle, azimuth angle, and depth measurement. The measuring points include a series of data points consisting of depth, well inclination angle, and azimuth angle.

3. The method according to claim 2, characterized in that, In step S100, the wellbore trajectory parameters are calculated using the minimum curvature method, specifically including: Calculate the northward displacement variation rate N1′, the eastward displacement variation rate E1′, and the vertical well depth variation rate V1′ of the measuring points on a unit length of tubing string: V′1=cosα i-1 In the above formula, α i-1 The well inclination angle at the measuring point on a unit length of tubing string; The azimuth angle of the measuring point on a unit length of tubular column; Calculate the northward displacement variation rate N2′, the eastward displacement variation rate E2′, and the vertical well depth variation rate V2′ of the measuring points under the unit length of the tubing string: V2′=cosα i In the above formula, α i The well inclination angle at the measuring point per unit length of tubing unit; The azimuth angle of the measuring point per unit length of the tubular column; Calculate the depth variation ΔL and total angle variation θ per unit length of the tubular column element. i cosine, wellbore curvature K i : ΔL=L i -L i-1 cosθ i =N1′N2′+E1′E2′+V1′V2′ K i =θ i / ΔL In the above formula, L i For depth measurement at the measuring point under a unit length of tubular column; L i-1 For depth measurement at measuring points on a unit length of tubular column; Calculate the northward displacement N of a unit length tubular element. i Eastward displacement E i , vertical well depth V i and horizontal displacement H i : In the above formula, N i-1 E represents the northward displacement of the measuring point on a unit length of tubular column element. i-1 V represents the eastward displacement of the measuring point on a unit length of tubular column unit; i-1 θ represents the vertical well depth of the measuring point per unit length of tubing unit; i For the full angular variation of a unit length tubular column element; And following the above method, the wellbore curvature K of each tubing unit is calculated iteratively for i = 1, 2, ..., n. i , depth change ΔL, displacement in the due north direction N i Displacement E in the due east direction i , vertical well depth V i and horizontal displacement H i Thus, the wellbore trajectory parameters are obtained.

4. The method according to claim 1, characterized in that, In step S101, the tubing assembly conditions include the dimensions and steel grades of each assembled casing segment, and the boundary conditions are the loads on the initial tubing unit at the bottom of the tubing column. The initial conditions include the outer diameter, inner diameter, elastic modulus, and Poisson's ratio of the tubing unit.

5. The method according to claim 1, characterized in that, In step S108, the axial force T1 at the upper end of the unit length tubular unit is calculated based on the final calculation in step S107. i To determine whether the cannula has buckled, the specific steps are as follows: If T1 i If the load is less than or equal to the critical load for helical buckling, helical buckling will occur. If the critical load of helical buckling <T1 i If the load is less than or equal to the critical load for sinusoidal buckling, then sinusoidal buckling will occur. If T1 i If the critical load for sinusoidal buckling is reached, buckling will not occur.

6. The method according to claim 5, characterized in that, In step S108, if the sleeve undergoes helical buckling, then Additional contact force F due to helical buckling of the casing nhel ,Right now: If the bushing undergoes sinusoidal buckling, then Additional contact force F due to sinusoidal buckling of the casing nsin ,Right now: If the cannula does not buckle, then The additional contact force due to casing buckling is not taken into account, that is: F n (i)” =F n (i)’ In the above formula, E is the elastic modulus; I is the moment of inertia of the cross section; and r is the gap between the casing and the wellbore.

7. The method according to claim 1, characterized in that, In step S110, the process iterates sequentially until the contact force, axial force, and friction of the nth tubular unit are calculated. Specifically, this includes: The operation is determined based on whether the iteration loop condition i = i + 1 is greater than n. If i>n is not true, repeat steps S102-S109 to calculate the contact force, axial force and friction value of the next tubular unit. If i>n holds true, the calculation ends, and the values ​​of axial force, contact force, and frictional resistance of the entire casing string from top to bottom of the well are summarized, as well as the distribution of axial force, contact force, and frictional resistance throughout the casing string.

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