A method and device for calculating friction torque of a horizontal well

Abstract

The present application relates to the technical field of oil and gas drilling engineering, and particularly relates to a horizontal well friction torque calculation method and device. The method comprises the following steps: based on the pipe string-borehole data of each unit after the pipe string in the target well is discretized, a dynamic contact longitudinal-lateral curved beam finite element model corresponding to each unit is constructed; the contact normal pressure corresponding to each dynamic contact longitudinal-lateral curved beam finite element model is calculated; based on the dynamic contact longitudinal-lateral curved beam finite element model and the pipe string-borehole data, a dynamic friction coefficient calculation model corresponding to each unit is constructed; based on the contact normal pressure corresponding to all dynamic contact longitudinal-lateral curved beam finite element models and the dynamic friction coefficient calculation model, a target well friction torque calculation model is constructed; and the friction torque of the target well is calculated based on the target well friction torque calculation model. The present application introduces a multi-physical model and a buckling correction coefficient, quantifies the additional friction caused by buckling, and improves the prediction accuracy under deep wells and complex borehole trajectories.

Description

Technical Field

[0001] This invention relates to the field of oil and gas drilling engineering technology, and in particular to a method and apparatus for calculating the friction torque of horizontal wells. Background Technology

[0002] In drilling and completion operations of horizontal and extended reach wells, the contact relationship between the tubing string and the wellbore is complex, and predicting frictional torque is a core aspect of ensuring safe and efficient operations. Chinese Patent CN 105701299 A discloses a method that uses a real-time interaction model between the drill bit and the rock as the lower boundary condition of the tubing string. This method comprehensively considers the dynamic behavior characteristics of the tubing string's three-dimensional longitudinal and transverse torsional coupling, treating the contact between the tubing string and the wellbore as part of the tubing string's dynamic motion process. The existing technology has the following main shortcomings: 1. Limitations of pre-defined contact points: Traditional longitudinal and transverse bending beam methods require pre-specifying contact points, which can easily lead to calculation errors or non-convergence due to unreasonable assumptions; some methods use virtual contact points, but they do not adequately consider the dynamic evolution of the contact state and stiffness coupling.

[0003] 2. Staticizing the friction coefficient: Most models treat the friction coefficient as a constant, ignoring its dynamic changes with wellbore curvature, tubing stiffness, cuttings bed and drilling fluid rheological parameters.

[0004] 3. Insufficient coupling between buckling and friction: Existing friction models do not adequately characterize the additional contact force and friction increment caused by sinusoidal buckling and helical buckling of the tubing string, resulting in low prediction accuracy for deep wells, ultra-deep wells and complex wellbore trajectories.

[0005] 4. Insufficient coverage of all working conditions: Differentiated calculation models and parameter identification methods for different working conditions such as sliding drilling, rotary drilling, and string running in / out need to be improved.

[0006] To address the aforementioned issues, there is an urgent need to propose a method for calculating friction torque based on dynamic contact and multi-physics coupling, in order to improve prediction accuracy and engineering applicability. Summary of the Invention

[0007] To address the above problems, this invention provides a method and apparatus for calculating the frictional torque of horizontal wells. The technical solution provided by this invention is as follows: This invention provides a method for calculating the frictional torque of a horizontal well, the method comprising: The tubing string in the target well is discretized into several units, and the tubing string-wellbore data for each unit is obtained; Based on the tubing-wellbore data of each unit, a finite element model of the longitudinal and transverse bending beams with dynamic contact corresponding to each unit is constructed. Calculate the contact normal force corresponding to the longitudinal and transverse bending beam finite element model for each dynamic contact; Based on the finite element model of the longitudinal and transverse bending beams in dynamic contact and the tubing-wellbore data, a dynamic friction coefficient calculation model is constructed for each unit. Based on the calculation model of contact normal force and dynamic friction coefficient corresponding to the finite element model of all dynamically contacting longitudinal and transverse bending beams, a calculation model of friction torque for the target well is constructed. The friction torque of the target well is calculated based on the target well friction torque calculation model.

[0008] Furthermore, the tubing-wellbore data includes wellbore trajectory data, tubing structure parameters, drilling fluid parameters, and formation parameters, among which... The collected wellbore trajectory data includes well depth, inclination angle, azimuth angle, and wellbore curvature; The structural parameters of the tubular column include the steel grade of the tubular column, the wall thickness of the tubular column, the length of the tubular column, and the joint size; Drilling fluid parameters include density, viscosity, and rheological model; Formation parameters include wellbore roughness and cuttings bed thickness.

[0009] Furthermore, the contact normal force corresponding to the longitudinal and transverse bending beam finite element model for each dynamic contact is calculated, including: Based on the column stiffness parameters, the displacement vectors of each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam are calculated. Based on the displacement vectors of each element in the finite element model of the longitudinal and transverse bending beam in dynamic contact, it is determined whether the tubing of each element in the finite element model of the longitudinal and transverse bending beam in dynamic contact is in contact with the well wall. When the tubing of each unit comes into contact with the well wall, calculate the normal contact reaction force of the virtual spring of that unit; Based on the wellbore curvature, the type of tubing buckling is determined, including linear or no buckling, sinusoidal buckling, and helical buckling. Based on the buckling type of the tubular column, obtain the buckling-inducing contact force corresponding to each element; The normal contact reaction force of the virtual spring in each element and the buckling-induced contact force of each element are summed to obtain the contact normal force of each element in the finite element model of the longitudinal and transverse bending beam in dynamic contact.

[0010] Furthermore, based on the column stiffness parameters, the displacement vectors corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beams are calculated, including: Based on the stiffness parameters of the tubular column, the mechanical equilibrium equations corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam are established. Based on the aforementioned mechanical equilibrium equations, the displacement vectors corresponding to each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam are calculated.

[0011] Furthermore, the calculation formulas for the mechanical equilibrium equations corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam are as follows:

[0012] In the formula, Let be the stiffness matrix corresponding to the i-th element; Let i be the displacement vector corresponding to the i-th element; This is the external load vector corresponding to the i-th element; Let be the contact reaction force vector of the well wall corresponding to the i-th unit.

[0013] Furthermore, based on the displacement vectors corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam, it is determined whether the tubing of each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam is in contact with the well wall, including: when When there is actual contact, the virtual spring is activated; when At this time, it is a virtual contact, and the virtual spring fails; In the formula: Let i be the displacement vector corresponding to the i-th element; The radius of the wellbore; This refers to the outer diameter of the tubular column.

[0014] Furthermore, when the tubing of each unit comes into contact with the wellbore, the formula for calculating the normal contact reaction force of the virtual spring in that unit is as follows:

[0015] In the formula: This represents the normal contact reaction force of the virtual spring corresponding to the i-th unit; This is the virtual spring stiffness coefficient; Let be the deflection penetration amount corresponding to the i-th unit, which is when in actual contact. When virtual contact occurs = 0.

[0016] Furthermore, when K i < At this time, the buckling type of the tubing is linear or the tubing does not buckle, and buckling induces contact forces. N i,cr = 0; When K cr ≤K i < At that time, the buckling type of the tubular column is sinusoidal buckling, and buckling induces contact forces. N i,cr = (1.1~1.3) ; When K i ≥ At that time, the buckling type of the tubular string was helical buckling, and buckling induced contact forces. N i,cr = (1.5~2.0) , in,

[0017] In the formula, K i Let be the wellbore curvature corresponding to the i-th unit. Let be the critical buckling curvature corresponding to the i-th unit; Let be the stiffness of the i-th unit column; The buoyancy per unit length of the tubing; Let be the length of the pipe column corresponding to the i-th unit.

[0018] Furthermore, the dynamic friction coefficient calculation model is expressed as follows:

[0019] In the formula: The dynamic friction coefficient corresponding to the i-th unit; The reference friction coefficient is denoted as K; a, b, c, and d are the working condition fitting coefficients; K i Let be the wellbore curvature corresponding to the i-th unit; As the reference curvature; Let be the stiffness of the i-th unit column; As the reference stiffness; Density of drilling fluid; The base drilling fluid density; The thickness of the rock cuttings bed.

[0020] Furthermore, the target well friction torque calculation model includes sub-models for calculating axial loads at different depths, torque loads at different depths, and friction forces at different depths. The axial load calculation sub-model is represented as follows:

[0021] The torque load calculation sub-model is represented as follows:

[0022] The friction calculation sub-model is represented as follows:

[0023] in,

[0024]

[0025] In the formula, For axial load, For torque load, For frictional resistance, This is a mapping from depth sounding D to element ordinal number. This is the buoyancy coefficient of the tubing steel in the drilling fluid. Let the mass of the i-th unit be... For drilling speed, This refers to the drill string rotation speed. Let i be the frictional force of the i-th unit; Let the friction torque be the torque of the i-th unit; Let be the dynamic friction coefficient of the i-th unit; For the contact normal force of the i-th unit, ; Let be the frictional force of the i-th unit.

[0026] Furthermore, the method also includes optimizing the friction torque calculation model, specifically: When the wellbore is being slidably drilled into the wellbore, the friction coefficient of the slid drilling is calculated back based on the drilling pressure and the axial load at the maximum depth. The formula for calculating the friction coefficient of sliding drilling is as follows:

[0027] In the formula, Axial loads at different depths; WOB is drill pressure; The coefficient of friction in sliding drilling; For the contact normal pressure of the i-th unit; and / or, When the wellbore is rotary drilled into the wellbore, the friction coefficient of rotary drilling is calculated based on the wellhead torque and drill bit torque. The formula for calculating the friction coefficient of rotary drilling is as follows:

[0028] In the formula, This refers to the wellhead torque. This refers to the drill bit torque. The coefficient of friction in rotary drilling is denoted as . The total contact normal force of the i-th unit, The outer radius of the i-th element is divided by the equivalent contact radius. The friction coefficients of sliding drilling and / or rotary drilling are re-introduced into the dynamic friction coefficient calculation model corresponding to each unit for iterative calculation. Axial loads and torque loads at different depths are calculated until the axial load error between two adjacent iterations is ≤1% and the torque load error is ≤0.5%. The iteration terminates, and the friction torque of the target well is output. The friction torque is the frictional resistance. and torque load .

[0029] A horizontal well friction torque calculation device is also provided, the device comprising, The acquisition unit is used to discretize the tubing string in the target well into several units and acquire the tubing string-wellbore data for each unit; The first building unit is used to construct the finite element model of the longitudinal and transverse bending beams corresponding to each unit based on the tubing-wellbore data of each unit. The first calculation unit is used to calculate the contact normal force corresponding to the finite element model of each dynamically contacting longitudinal and transverse bending beam. The second building unit is used to build a dynamic friction coefficient calculation model for each unit based on the finite element model of the longitudinal and transverse bending beams in dynamic contact and the tubing-wellbore data. The third building unit is used to construct the target well friction torque calculation model based on the contact normal pressure and dynamic friction coefficient calculation model corresponding to the finite element model of all dynamically contacting longitudinal and transverse bending beams. The second calculation unit is used to calculate the friction torque of the target well based on the target well friction torque calculation model.

[0030] The technical effects and advantages of this invention are as follows: (1) More accurate dynamic contact: The virtual contact point and incremental displacement approximation method avoid the limitations of the preset contact point and truly reflect the contact evolution process between the tubing and the well wall.

[0031] (2) More complete buckling coupling: Introducing multi-physics models and buckling correction coefficients to quantify the additional friction caused by buckling and improve the prediction accuracy of deep wells and complex wellbore trajectories.

[0032] (3) Strong adaptability to all working conditions: Differentiated parameter identification and calculation processes are established for different working scenarios, covering core working conditions such as sliding drilling and rotary drilling.

[0033] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention can be realized and obtained by means of the structures pointed out in the description and the drawings. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method for calculating horizontal well friction and torque provided in an embodiment of this application; Figure 2 This is a diagram illustrating the implementation process of calculating horizontal well friction and torque according to an embodiment of this application; Figure 3 This is a contact determination diagram of the finite element model of the longitudinal and transverse bending beam provided in the embodiments of this application. Detailed Implementation

[0035] 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.

[0036] To address the shortcomings of existing technologies, this invention discloses a method for calculating the friction and torque of horizontal wells, such as... Figure 1 and 2 As shown, the method includes, Step 1: Discretize the tubing string in the target well into several units and obtain the tubing string-wellbore data for each unit; Step 2: Based on the tubing-wellbore data of each unit, construct the finite element model of the longitudinal and transverse bending beams with dynamic contact for each unit; Step 3: Calculate the contact normal force corresponding to the finite element model of the longitudinal and transverse bending beams for each dynamic contact; Step 4: Based on the finite element model of the longitudinal and transverse bending beams in dynamic contact and the tubing-wellbore data, construct the dynamic friction coefficient calculation model corresponding to each unit; Step 5: Based on the calculation models of contact normal force and dynamic friction coefficient corresponding to the finite element models of all dynamically contacting longitudinal and transverse bending beams, construct the target well friction torque calculation model; Step 6: Calculate the friction torque of the target well based on the target well friction torque calculation model.

[0037] In a specific embodiment of the present invention, step 1 is as follows: Acquiring tubing-wellbore data includes wellbore trajectory data, tubing structure parameters, drilling fluid parameters, and formation parameters. Wellbore trajectory data includes well depth, inclination angle, azimuth angle, and wellbore curvature. Well depth, inclination angle, and azimuth angle are used to calculate the wellbore curvature K. i The tubing string structural parameters include the tubing steel grade, tubing wall thickness, tubing length, and joint dimensions (including the tubing cross-sectional radius r or diameter Dp); drilling fluid parameters include density, viscosity, and rheological model. For example, the viscosity and rheological model are used to calculate the reference drilling fluid density. Formation parameters include wellbore roughness, cuttings bed thickness, and, for example, the friction coefficient μ. i The calculation requires the thickness of the cuttings bed.

[0038] For example, wellbore trajectory data (well depth, inclination angle, azimuth angle, curvature), tubing structure parameters (steel grade, wall thickness, length, joint size), drilling fluid parameters (density, viscosity, rheological model), and formation parameters (well wall roughness, cuttings bed thickness) are collected to construct a structured database.

[0039] In a specific embodiment of the present invention, for step 2, based on the tubing-wellbore data of each unit, a finite element model of the dynamic contact longitudinal and transverse bending beams corresponding to each unit is constructed, specifically as follows: like Figure 3 As shown, based on three-dimensional wellbore trajectory data, the tubing string is discretized into several units. Each unit contains wellbore trajectory data at the corresponding well depth, tubing string structural parameters, drilling fluid parameters, and formation parameters. A finite element model of a longitudinal and transverse bending beam with virtual contact points is established, allowing the contact points to dynamically evolve with tubing string deformation and wellbore curvature. For example, the finite element model of the longitudinal and transverse bending beam with virtual contact points is a tubing string segmented using the finite element method, i.e., the tubing string is segmented according to a fixed step size, and has no inherent formula. After segmentation, deflection calculation, contact state determination, and contact force calculation are performed on each segment.

[0040] In a specific embodiment of the present invention, for step 3, calculating the contact normal force corresponding to the finite element model of each dynamically contacting longitudinal and transverse bending beam includes: Step 301: Combining Figure 2 Based on the column stiffness parameters, the displacement vectors corresponding to each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam are calculated; specifically: Step 3011: Based on the stiffness parameters of the tubing string, establish the mechanical equilibrium equations corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam. For example, by introducing the stiffness parameters of the tubing string and distinguishing between three physical models—soft rod (stiffness ignored), rigid rod (stiffness considered), and continuous beam (lower drill string assembly)—the calculation formulas for the mechanical equilibrium equations corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam are as follows:

[0041] In the formula, Let be the stiffness matrix corresponding to the i-th element; Let i be the displacement vector corresponding to the i-th element; This is the external load vector corresponding to the i-th element; Let be the wellbore contact reaction force vector corresponding to the i-th unit. Where, These are structural parameters of the tubular column, and are related to the steel grade, wall thickness, length, and joint dimensions of the tubular column. It is the sum of the axial components of the gravity of all elements below the i-th element, and belongs to the structural parameters of the tube column, which are related to the tube column steel grade, tube column wall thickness and tube column length. The component of the gravity acting on the i-th element in the normal direction of the contact surface is a structural parameter of the pipe column, along with the pipe column steel grade, pipe column wall thickness, and pipe column length.

[0042] Step 3012: Based on the mechanical equilibrium equation, calculate and obtain the displacement vectors corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam.

[0043] Step 302: Based on the displacement vectors corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam, determine whether the tubing of each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam is in contact with the well wall. Specifically: Contact state determination rules: when When there is actual contact, the virtual spring is activated; when At this time, it is a virtual contact, and the virtual spring fails; In the formula: Let i be the displacement vector corresponding to the i-th element; The radius of the wellbore; This refers to the outer diameter of the tubular column.

[0044] Step 303: When the tubing of each unit comes into contact with the wellbore, calculate the normal contact reaction force of the virtual spring in that unit; the formula for calculating the normal contact reaction force of the virtual spring in that unit is:

[0045] In the formula: This represents the normal contact reaction force of the virtual spring corresponding to the i-th unit; This is the virtual spring stiffness coefficient; Let be the deflection penetration amount corresponding to the i-th unit, which is when in actual contact. When virtual contact occurs = 0.

[0046] Step 304: Based on the wellbore curvature, determine the type of tubing buckling, which includes linear or no buckling, sinusoidal buckling, and helical buckling.

[0047] For example, based on the normal contact reaction force of the virtual spring in step 303, the buckling is corrected, and the friction torque of each unit is calculated by combining the dynamic friction coefficient. The friction torque distribution at each depth of the tubing is calculated by accumulating it segment by segment from the drill bit to the wellhead.

[0048] A buckling correction factor is introduced to determine the buckling type of the tubing based on the wellbore curvature and axial load, namely linear (no buckling), sinusoidal buckling, and helical buckling, and to calculate the additional contact force caused by buckling.

[0049] Step 305: Based on the buckling type of the tubular column, obtain the buckling-inducing contact force corresponding to each element; where, (1) Formula for calculating critical buckling curvature: ; In the formula: Where E is the critical curvature; and E is the elastic modulus. Let i be the moment of inertia of the tubing corresponding to the i-th unit. Let be the stiffness of the i-th unit column; The buoyancy per unit length of the tubing; Let be the length of the pipe column corresponding to the i-th unit.

[0050] (2) Calculation of additional contact force during buckling: Calculate wellbore curvature: In the formula: This represents the total angle variation (dogleg angle) of the adjacent well segments in the i-th unit. The depth difference between two adjacent measuring points in the i-th unit is used to calculate the unit length.

[0051] When K i < At this time, the buckling type of the tubing is linear or the tubing does not buckle, and buckling induces contact forces. N i,cr = 0; When K cr ≤K i < At that time, the buckling type of the tubular column is sinusoidal buckling, and buckling induces contact forces. N i,cr = (1.1~1.3) ; When K i ≥ At that time, the buckling type of the tubular string was helical buckling, and buckling induced contact forces. N i,cr = (1.5~2.0) .

[0052] Step 306: Summing the normal contact reaction force of the virtual spring in each element and the buckling-induced contact force in each element yields the contact normal force of each element in the finite element model of the longitudinal and transverse bending beam in dynamic contact. The formula is: .

[0053] In a specific embodiment of the present invention, for step 4, based on the finite element model of the dynamically contacting longitudinal and transverse bending beams and the tubing-wellbore data, a dynamic friction coefficient calculation model is constructed for each unit; wherein... The dynamic friction coefficient calculation model is expressed as follows:

[0054] In the formula: The dynamic friction coefficient corresponding to the i-th unit; The reference friction coefficient is denoted as K; a, b, c, and d are the working condition fitting coefficients; K i Let be the wellbore curvature corresponding to the i-th unit; As the reference curvature; Let be the stiffness of the i-th unit column; As the reference stiffness; Density of drilling fluid; The base drilling fluid density; The thickness of the rock cuttings bed.

[0055] In a specific embodiment of the present invention, for step 5, based on the calculation model of contact normal force and dynamic friction coefficient corresponding to the finite element model of all dynamically contacting longitudinal and transverse bending beams, a calculation model for the friction torque of the target well is constructed. For example, Based on three physical models—flexible rod, rigid rod, and continuous beam—mathematical equations for axial load, torque load, and friction force are established to synthesize a target well friction torque calculation model. The target well friction torque calculation model includes sub-models for calculating axial loads at different depths, torque loads at different depths, and friction forces at different depths. The axial load calculation sub-model is represented as follows:

[0056] The torque load calculation sub-model is represented as follows:

[0057] The friction calculation sub-model is represented as follows:

[0058] in,

[0059]

[0060] In the formula, For axial load, For torque load, For frictional resistance, This is a mapping from depth sounding D to element ordinal number. This is the buoyancy coefficient of the tubing steel in the drilling fluid. Let the mass of the i-th unit be... For drilling speed, This refers to the drill string rotation speed. Let i be the frictional force of the i-th unit; Let the friction torque be the torque of the i-th unit; Let be the dynamic friction coefficient of the i-th unit; For the contact normal force of the i-th unit, ; Let be the frictional force of the i-th unit.

[0061] In one specific embodiment of the present invention, the method further includes optimizing the friction torque calculation model, specifically by: inputting on-site measured data and dividing the calculation scenarios according to the working conditions (sliding drilling / rotary drilling): (1) When the wellbore is being slidably drilled into the wellbore, the friction coefficient of the slid drilling is calculated back based on the drilling pressure and the axial load at the maximum depth, where, The formula for calculating the friction coefficient of sliding drilling is as follows:

[0062] In the formula, Axial loads at different depths; WOB is drill pressure; The coefficient of friction in sliding drilling; For the contact normal pressure of the i-th unit; and / or, (2) When the wellbore is being drilled into the wellbore using rotary drilling, the friction coefficient of rotary drilling is calculated based on the wellhead torque and the drill bit torque. The formula for calculating the friction coefficient of rotary drilling is as follows:

[0063] In the formula, This refers to the wellhead torque. This refers to the drill bit torque. The coefficient of friction in rotary drilling is denoted as . The total contact normal force of the i-th unit, The outer radius of the i-th element is divided by the equivalent contact radius. The friction coefficients of sliding drilling and / or rotary drilling are re-introduced into the dynamic friction coefficient calculation model corresponding to each unit for iterative calculation. Axial loads and torque loads at different depths are calculated until the axial load error between two adjacent iterations is ≤1% and the torque load error is ≤0.5%. The iteration terminates, and the friction torque of the target well is output. The friction torque is the frictional resistance. and torque load .

[0064] (3) Verify the model accuracy using field measured data (wellhead hook load, torque, tubing strain), and calculate the relative error using the following formula: ,in, This is relative error; For calculated values; The value is the true value, and the error is required to be ≤5%.

[0065] It outputs friction torque curves, contact force distribution, and safety factor assessment results to guide the design of tubing and the optimization of operating parameters.

[0066] The present invention also provides a horizontal well friction torque calculation device, the device comprising, The acquisition unit is used to discretize the tubing string in the target well into several units and acquire the tubing string-wellbore data for each unit; The first building unit is used to construct the finite element model of the longitudinal and transverse bending beams corresponding to each unit based on the tubing-wellbore data of each unit. The first calculation unit is used to calculate the contact normal force corresponding to the finite element model of each dynamically contacting longitudinal and transverse bending beam. The second building unit is used to build a dynamic friction coefficient calculation model for each unit based on the finite element model of the longitudinal and transverse bending beams in dynamic contact and the tubing-wellbore data. The third building unit is used to construct the target well friction torque calculation model based on the contact normal pressure and dynamic friction coefficient calculation model corresponding to the finite element model of all dynamically contacting longitudinal and transverse bending beams. The second calculation unit is used to calculate the friction torque of the target well based on the target well friction torque calculation model.

[0067] Regarding the apparatus in the above embodiments, the specific manner in which each unit performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0068] The technical solution of the present invention will be further described below with reference to specific embodiments.

[0069] This embodiment uses a horizontal well (A1) in a certain block of an oil and gas field as the calculation object. The well has a total drilled depth of 3200m, a vertical depth of 2000m, a 600m build-up section, and an 800m horizontal section. The maximum local wellbore curvature in the horizontal section is 4.5° / 30m. During drilling, a stable cuttings bed exists in the horizontal section, resulting in high sliding drilling friction. The method described in this invention is used to calculate the friction torque of the entire well section. The specific implementation steps are as follows: Step 1: String Discretization and String-Wellbore Data Acquisition The entire well string was discretized into 320 computational units along the well depth direction at 10m increments. Four types of parameters—wellbore trajectory, string structure, drilling fluid, and formation—were matched to each unit to construct a unit-level structured database. Specific parameters are as follows: ① Wellbore trajectory data Vertical well section (0~1600m): well inclination angle 0°, azimuth angle 0°, wellbore curvature 0° / 30m; The build-up section (1600~2200m): the well inclination angle increases from 0° to 90°, the average build-up rate is 5° / 30m, and the maximum curvature is 6° / 30m; Horizontal section (2200~3000m): Well inclination angle 89.5°~90.5°, average curvature 1.2° / 30m, local maximum curvature 4.5° / 30m; The diameter of the entire wellbore is uniformly 215.9 mm, and the wellbore radius Rb = 107.95 mm.

[0070] ② Pipe column structural parameters The main body uses Φ127mm S135 steel grade drill pipe with a wall thickness of 9.19mm, a pipe string outer diameter Dp=127mm, a unit length mass in air of 29.02kg / m, an elastic modulus E=2.06×10¹¹Pa, a drill pipe joint outer diameter of 165mm, and a single length of 9.6m.

[0071] The lower drilling assembly includes a Φ172mm screw drill bit and a Φ215.9mm PDC drill bit, with a designed drilling pressure of 120kN. The operating parameters are: mechanical drilling speed of 8m / h during sliding drilling and rotary table speed of 80r / min during rotary drilling.

[0072] ③ Drilling fluid parameters A water-based drilling fluid system was used, with a density ρm = 1.25 g / cm³ and a plastic viscosity of 25 mPa. s, the rheological model is the Bingham model; the baseline drilling fluid density ρ is calculated. ref= 1.0 g / cm³.

[0073] ④ Formation parameters The wellbore roughness of the vertical section is 0.05 mm, and the cuttings bed thickness hc=0; the wellbore roughness of the directional section is 0.08 mm, and the cuttings bed thickness hc=5 mm; the wellbore roughness of the horizontal section is 0.1 mm, and the cuttings bed thickness hc=15 mm.

[0074] Step 2: Construct a finite element model of a dynamically contacting longitudinal and transverse bending beam. For each discrete element, a spatial longitudinal and transverse bending beam finite element is established based on the spatial node coordinates of the three-dimensional wellbore trajectory. The element nodes contain six degrees of freedom: axial displacement, transverse deflection in two directions, and corresponding rotation angle. A virtual contact spring is set in the annular gap between the tubing and the wellbore. The spring is initially in an inactive state, and the contact point position is not pre-fixed. It dynamically evolves with the deformation of the tubing under stress, without the need to pre-set the contact point.

[0075] The equilibrium equations of a single element are uniformly expressed as: k i ·δ i =F i +N i In the formula, k i The stiffness matrix of the spatial beam element is δ, which is calculated from the elastic modulus of the column, the moment of inertia of the section, and the element length; i Let F be the displacement vector of the i-th element node; i N is the external load vector of the i-th element, containing the spatial components of the element's buoyancy, axial load, and centrifugal force;i Let be the contact reaction force vector of the well wall in the i-th unit, provided by the virtual contact spring.

[0076] Step 3: Calculate the normal contact force of each unit. Following the process of "displacement solution—contact identification—basic contact force calculation—buckling correction—total contact force synthesis," the contact normal force is calculated element by element. The 180th element of the inclined section (well depth 1800m, element length L) is used as an example. 180 =10m, wellbore curvature K 180 Taking 5° / 30m as an example, the calculation process is as follows: ① Solve for the element displacement vector Substituting the stiffness parameters of the unit column and the boundary conditions of the axial load at the lower end, the mechanical equilibrium equations are established and solved to obtain the maximum lateral displacement δ of the column center within the unit. 180 =48mm.

[0077] ② Contact state determination The annular clearance between the tubing string and the wellbore (the maximum distance the center of the tubing string can move) is: (R b -D p ) / 2 = (215.9 - 127) / 2 = 44.45 mm Due to δ 180 =48mm>44.45mm, which is considered a real contact, and the virtual contact spring is activated.

[0078] ③ Calculate the normal contact reaction force of the virtual spring. Take the virtual spring stiffness coefficient k spring =2×10 7 N / m, deflection penetration is: Δδ 180 =δ 180 -(R b -D p ) / 2 = 48 - 44.45 = 3.55 mm = 0.00355 m The basic normal contact reaction force provided by the virtual spring: =2×10 7 ×0.00355=71000N=71kN ④ Determine the buckling type and calculate the additional buckling contact force. First, calculate the critical buckling curvature K of the element. 180,cr : The buoyancy weight per unit length of the tubing is q: Taking the density of steel as 7.85 g / cm³, the buoyancy coefficient k = 1 - ρm / ρsteel ≈ 0.8408, therefore, q=29.02×9.81×0.8408≈239.2N / m Substitute into the critical curvature formula:

[0079] The critical curvature K of the element was calculated. 180,cr =2° / 30m.

[0080] Because of K 180 =5° / 30m≥2×K 180,cr The tubing was determined to have experienced helical buckling, and the additional contact force due to buckling was adjusted by a factor of 1.8. N 180,cr =1.8×N 180,0 =1.8 × 71 = 127.8 kN ⑤ Total contact normal force synthesis =127.8 + 71 = 198.8 kN All 320 units in the well were calculated according to the above process, and the distribution curve of the contact positive pressure of each unit along the well depth was obtained. The lower part of the build-up section and the root of the horizontal section are the peak contact force areas.

[0081] Step 4: Construct a dynamic friction coefficient calculation model A dynamic friction coefficient calculation model with multiple coupled factors is adopted, and the formula is as follows: In the formula, the reference friction coefficient μ0 = 0.3; the working condition fitting coefficients a = 0.25, b = 0.15, c = 0.2, and d = 0.006 mm. - ¹; Reference curvature K ref =3° / 30m; Reference stiffness EI ref =1.2×10 6 N m²; reference drilling fluid density ρ ref =1.0g / cm³.

[0082] Taking unit 180 above as an example, substitute the parameters for calculation: K 180 / K ref =5 / 3≈1.667, EI 180 / EI ref =1.47×10 6 / (1.2×10 6 )=1.225, ρ m / ρ ref =1.25, hc=5mm μ 180 =0.3×(0.25×1.667+0.15×1.225+0.2×1.25+0.006×5)≈0.264 Similarly, calculate the 250th unit (K) of the horizontal segment. 250 =3° / 30m, h c The dynamic friction coefficient of the wellbore (15mm) is approximately 0.232, reflecting the dynamic variation characteristics of the friction coefficient with parameters such as wellbore curvature and cuttings bed thickness.

[0083] The dynamic friction coefficient for each unit is obtained by following the above calculation process.

[0084] Step 5: Construct a calculation model for the friction torque of the target well. Based on the contact normal pressure N of each unit in the whole well i With dynamic friction coefficient μ i Three calculation sub-models were constructed for axial load, torque load, and frictional resistance, and the calculations were performed unit by unit from the bottom of the well to the wellhead.

[0085] The basic calculation formulas for unit friction force and unit friction torque are as follows:

[0086]

[0087] In the formula, D p The equivalent contact radius of the tubing string is 0.127m, and the drill pipe body is taken as 0.127m.

[0088] Taking rotary drilling as an example, the resultant velocity component of the axial velocity and the circumferential linear velocity is used to allocate the proportion of axial friction: Axial drilling speed v axial =8m / h≈0.00222m / s Circumferential linear velocity v of the drill string rotate ≈0.532m / s Axial friction component coefficient: ≈0.00417 After summing up each unit, the preliminary calculation yields: Wellhead axial load (hook load): =2185kN Total wellhead torque: =38.2kN m Total frictional resistance of the entire well: =287kN Step 6: Model Iteration Optimization and Result Output By introducing on-site measured data for working condition inversion and iterative optimization, the accuracy of calculations can be improved.

[0089] ① Inversion and Iteration of Sliding Drilling Conditions The measured drilling pressure (WOB) during sliding drilling was 120 kN, and the wellhead hook load was F. axial =2210kN. The sum of the contact normal pressures of all well elements, ∑N i =6530kN, substituting into the inverse calculation formula:

[0090] The back-calculated friction coefficient was substituted into the dynamic friction coefficient model, and the fitting coefficients were corrected before recalculating the contact normal pressure and friction torque of the entire well. After the first iteration, the axial load at the wellhead was 2205 kN, with an error of 0.23% compared to the measured value; after the second iteration, the error was 0.08%, satisfying the convergence condition of axial load error ≤1%, and the iteration was terminated.

[0091] ② Rotary drilling condition inversion and iteration Field measurement of wellhead torque T during rotary drilling surf =39kN m, drill bit torque T bit =10kN m. Total well ∑(N) i r i )≈414.7kN m, substituting into the inverse calculation formula: =(39-10) / 414.7≈0.070 Substituting into the dynamic model iteration, the wellhead torque after the second iteration is 38.9 kN. The error between m and the measured value is 0.26%, which meets the convergence condition of torque load error ≤ 0.5%.

[0092] ③Final output results After iterative convergence, the calculation results of the total well friction torque are output: Sliding drilling conditions: maximum frictional resistance throughout the well is 298 kN, hook load at the wellhead is 2208 kN, and the relative error between the calculated and measured values ​​is 0.09%. Rotary drilling conditions: Total well friction torque 29.1 kN m, total torque at the wellhead 39.1kN m, the relative error between the calculated value and the measured value is 0.26%; The peak contact positive pressure of the entire well is located in the lower part of the build-up section, with a maximum contact positive pressure of 212kN per unit, corresponding to the helical buckling section.

[0093] The results of this embodiment show that, compared with the traditional soft rod calculation model with a fixed friction coefficient, the relative error of friction torque calculation using the dynamic contact and dynamic friction coupling method of the present invention is reduced from the conventional 8%~12% to less than 1%. It can accurately characterize the additional friction caused by tubing buckling and is suitable for accurate prediction of friction torque in horizontal wells with large curvature and extended reach wells.

[0094] It should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the frictional torque of a horizontal well, characterized in that, The method includes, The tubing string in the target well is discretized into several units, and the tubing string-wellbore data for each unit is obtained; Based on the tubing-wellbore data of each unit, a finite element model of the longitudinal and transverse bending beams with dynamic contact corresponding to each unit is constructed. Calculate the contact normal force corresponding to the longitudinal and transverse bending beam finite element model for each dynamic contact; Based on the finite element model of the longitudinal and transverse bending beams in dynamic contact and the tubing-wellbore data, a dynamic friction coefficient calculation model is constructed for each unit. Based on the calculation model of contact normal force and dynamic friction coefficient corresponding to the finite element model of all dynamically contacting longitudinal and transverse bending beams, a calculation model of friction torque for the target well is constructed. The friction torque of the target well is calculated based on the target well friction torque calculation model.

2. The method for calculating the friction torque of a horizontal well according to claim 1, characterized in that, Tubing-wellbore data includes wellbore trajectory data, tubing structure parameters, drilling fluid parameters, and formation parameters, among which... The collected wellbore trajectory data includes well depth, inclination angle, azimuth angle, and wellbore curvature; The structural parameters of the tubular column include the steel grade of the tubular column, the wall thickness of the tubular column, the length of the tubular column, and the joint size; Drilling fluid parameters include density, viscosity, and rheological model; Formation parameters include wellbore roughness and cuttings bed thickness.

3. The method for calculating the friction torque of a horizontal well according to claim 1, characterized in that, Calculate the contact normal force corresponding to the longitudinal and transverse bending beam finite element model for each dynamic contact, including: Based on the column stiffness parameters, the displacement vectors of each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam are calculated. Based on the displacement vectors of each element in the finite element model of the longitudinal and transverse bending beam in dynamic contact, it is determined whether the tubing of each element in the finite element model of the longitudinal and transverse bending beam in dynamic contact is in contact with the well wall. When the tubing of each unit comes into contact with the well wall, calculate the normal contact reaction force of the virtual spring of that unit; Based on the wellbore curvature, the type of tubing buckling is determined, including linear or no buckling, sinusoidal buckling, and helical buckling. Based on the buckling type of the tubular column, obtain the buckling-inducing contact force corresponding to each element; The normal contact reaction force of the virtual spring in each element and the buckling-induced contact force of each element are summed to obtain the contact normal force of each element in the finite element model of the longitudinal and transverse bending beam in dynamic contact.

4. The method for calculating the friction torque of a horizontal well according to claim 3, characterized in that, Based on the column stiffness parameters, the displacement vectors corresponding to each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam are calculated as follows: Based on the stiffness parameters of the tubular column, the mechanical equilibrium equations corresponding to each element in the finite element model of the dynamically contacting longitudinal and transverse bending beam are established. Based on the aforementioned mechanical equilibrium equations, the displacement vectors corresponding to each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam are calculated.

5. The method for calculating the friction torque of a horizontal well according to claim 4, characterized in that, The formulas for calculating the mechanical equilibrium equations for each element in the finite element model of a dynamically contacting longitudinally and transversely bending beam are as follows: In the formula, Let be the stiffness matrix corresponding to the i-th element; Let i be the displacement vector corresponding to the i-th element; This is the external load vector corresponding to the i-th element; Let be the contact reaction force vector of the well wall corresponding to the i-th unit.

6. The method for calculating the friction torque of a horizontal well according to claim 3, characterized in that, Based on the displacement vectors of each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam, determine whether the tubing of each element in the finite element model of a dynamically contacting longitudinal and transverse bending beam is in contact with the well wall, including: when When there is actual contact, the virtual spring is activated; when At this time, it is a virtual contact, and the virtual spring fails; In the formula: Let i be the displacement vector corresponding to the i-th element; The radius of the wellbore; This refers to the outer diameter of the tubular column.

7. The method for calculating the friction torque of a horizontal well according to claim 3, characterized in that, When the tubing of each unit comes into contact with the wellbore, the formula for calculating the normal contact reaction force of the virtual spring in that unit is as follows: In the formula: This represents the normal contact reaction force of the virtual spring corresponding to the i-th unit; This is the virtual spring stiffness coefficient; Let be the deflection penetration amount corresponding to the i-th unit, which is when in actual contact. When virtual contact occurs = 0.

8. The method for calculating the friction torque of a horizontal well according to claim 3, characterized in that, When K i < At this time, the buckling type of the tubing is linear or the tubing does not buckle, and buckling induces contact forces. N i,cr = 0; When K cr ≤K i < At that time, the buckling type of the tubular column is sinusoidal buckling, and buckling induces contact forces. N i,cr = (1.1~1.3) ; When K i ≥ At that time, the buckling type of the tubular string was helical buckling, and buckling induced contact forces. N i,cr = (1.5~2.0) , in, In the formula, K i Let be the wellbore curvature corresponding to the i-th unit. The critical buckling curvature corresponding to the i-th unit; Let be the stiffness of the i-th unit column; The buoyancy per unit length of the tubing; Let be the length of the pipe column corresponding to the i-th unit.

9. The method for calculating the friction torque of a horizontal well according to claim 3, characterized in that, The dynamic friction coefficient calculation model is expressed as follows: In the formula: The dynamic friction coefficient corresponding to the i-th unit; The reference friction coefficient is denoted as K; a, b, c, and d are the working condition fitting coefficients; K i Let be the wellbore curvature corresponding to the i-th unit; As the reference curvature; Let be the stiffness of the i-th unit column; As the reference stiffness; Density of drilling fluid; The base drilling fluid density; The thickness of the rock cuttings bed.

10. The method for calculating the friction torque of a horizontal well according to claim 3, characterized in that, The target well friction torque calculation model includes sub-models for calculating axial loads at different depths, torque loads at different depths, and friction forces at different depths. The axial load calculation sub-model is represented as follows: The torque load calculation sub-model is represented as follows: The friction calculation sub-model is represented as follows: in, In the formula, For axial load, For torque load, For frictional resistance, This is a mapping from depth sounding D to element ordinal number. This is the buoyancy coefficient of the tubing steel in the drilling fluid. Let the mass of the i-th unit be... For drilling speed, This refers to the drill string rotation speed. The frictional force is the frictional force of the i-th element. The friction torque of the i-th unit; Let be the dynamic friction coefficient of the i-th unit; For the contact normal force of the i-th unit, ; Let be the frictional force of the i-th unit.

11. The method for calculating the friction torque of a horizontal well according to claim 1, characterized in that, The method also includes optimizing the friction torque calculation model, specifically: When the wellbore is being slidably drilled into the wellbore, the friction coefficient of the slid drilling is calculated back based on the drilling pressure and the axial load at the maximum depth. The formula for calculating the friction coefficient of sliding drilling is as follows: In the formula, Axial loads at different depths; WOB is drill pressure; The coefficient of friction in sliding drilling; For the contact normal pressure of the i-th unit; and / or, When the wellbore is rotary drilled into the wellbore, the friction coefficient of rotary drilling is calculated based on the wellhead torque and drill bit torque. The formula for calculating the friction coefficient of rotary drilling is as follows: In the formula, This refers to the wellhead torque. This refers to the drill bit torque. The coefficient of friction in rotary drilling is denoted as . The total contact normal force of the i-th unit, The outer radius of the i-th element is divided by the equivalent contact radius. The friction coefficients of sliding drilling and / or rotary drilling are re-introduced into the dynamic friction coefficient calculation model corresponding to each unit for iterative calculation. Axial loads and torque loads at different depths are calculated until the axial load error between two adjacent iterations is ≤1% and the torque load error is ≤0.5%. The iteration terminates, and the friction torque of the target well is output. The friction torque is the frictional resistance. and torque load .

12. A horizontal well friction torque calculation device, characterized in that, The device includes, The acquisition unit is used to discretize the tubing string in the target well into several units and acquire the tubing string-wellbore data for each unit; The first building unit is used to construct the finite element model of the longitudinal and transverse bending beams corresponding to each unit based on the tubing-wellbore data of each unit. The first calculation unit is used to calculate the contact normal force corresponding to the finite element model of each dynamically contacting longitudinal and transverse bending beam. The second building unit is used to build a dynamic friction coefficient calculation model for each unit based on the finite element model of the longitudinal and transverse bending beams in dynamic contact and the tubing-wellbore data. The third building unit is used to construct the target well friction torque calculation model based on the contact normal pressure and dynamic friction coefficient calculation model corresponding to the finite element model of all dynamically contacting longitudinal and transverse bending beams. The second calculation unit is used to calculate the friction torque of the target well based on the target well friction torque calculation model.

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