A method of determining a position of nonlinear contact of a drill string with a wellbore wall

Abstract

This invention discloses a method for determining the nonlinear contact position between the drill string and the wellbore. The connection point between two adjacent elements is considered a node. The finite element dynamic equations of the drill string at the current moment are transformed into a relationship between the effective stiffness matrix of the drill string, the displacement matrices of all nodes of the drill string, and the effective load matrix. The method divides the equations into blocks according to the two-element, three-node relationship. Matrix operations are performed on each sub-expression to obtain the radial displacement matrix expression for each intermediate node. If the radial displacement is greater than the gap between the wellbore and the drill string, the radial displacement of the node is set to the gap value, and matrix multiplication is performed again to obtain a new effective load sub-matrix. This process is repeated to calculate the radial displacement of all nodes until all are within the gap between the wellbore and the drill string. The radial displacement of the drill string at the current moment is then combined to obtain the node displacements at all times. Finally, it is determined whether the radial displacements of all nodes at all times are equal to the gap between the wellbore and the drill string to determine the nonlinear contact position between the drill string and the wellbore.

Description

Technical Field

[0001] This invention relates to the field of oilfield drilling and production technology, specifically to a method for determining the nonlinear contact position between the drill string and the wellbore. Background Technology

[0002] In oil drilling, the drill string comes into contact with the wellbore within the wellbore. Due to the complexity of the wellbore trajectory and the ultra-long, slender characteristics of the drill string, the contact position between the drill string and the wellbore is difficult to determine. Currently, the mechanical characteristics of the drill string within the wellbore can only be calculated using numerical methods, commonly including the global matrix method and the modal method. However, the global matrix method, based on the overall stiffness matrix and stress characteristics of the drill string, cannot reflect the nonlinear characteristics of the contact between the drill string and the wellbore. The modal method, based on the superposition of mode shapes, performs simple corrections when the calculated mode shapes extend beyond the wellbore, failing to reflect the true contact state.

[0003] In fact, the contact between the ultra-slender drill string and the well wall is not only affected by the flexural characteristics of the wellbore trajectory and the wellbore size, but also by the ultra-long and slender characteristics of the drill string. There are multiple contact points between the drill string and the well wall, and these points change with the load, making it a nonlinear contact boundary problem.

[0004] The handling of nonlinear contact between the drill string and the wellbore is very complex. Currently, there is no accurate method to determine the nonlinear contact position between the drill string and the wellbore, and therefore no means to help engineers understand the true state of the drill string downhole. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for determining the nonlinear contact position between the drill string and the well wall, which uses the idea of ​​node iterative loop to calculate and determine the nonlinear contact position between the drill string and the well wall.

[0006] This invention is achieved through the following technical solution:

[0007] A method for determining the nonlinear contact position between the drill string and the wellbore includes the following steps:

[0008] Step 1: First, divide the drill string into elements, with the connection between two adjacent elements being a node. Then, transform the finite element dynamic equation of the drill string at the current moment downhole into the relationship between the effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix.

[0009] Step 2: Divide the relational expression described in Step 1 into several sub-relative expressions by forming a sub-relative expression with two units. In each sub-relative expression, the effective stiffness sub-matrix of the three nodes corresponding to the two units is arranged on one side of the equal sign, and the effective load sub-matrix of the three nodes corresponding to the two units is arranged on the other side. Perform matrix multiplication and transformation on each sub-expression to obtain the displacement matrix expression corresponding to each intermediate node.

[0010] Step 3: First, solve one of the displacement matrix expressions obtained in Step 2 to obtain the radial displacement of the node corresponding to the expression. If the obtained radial displacement is greater than the gap between the wellbore and the drill string, set the radial displacement of the node as the gap between the wellbore and the drill string. Then, substitute the gap value into the sub-relationship in Step 2 to perform matrix multiplication to obtain a new effective load sub-matrix.

[0011] Step 4: Using the new effective load submatrix, calculate the radial displacement of all nodes cyclically according to the calculation process described in Step 3 until the radial displacement of all nodes is within the gap between the wellbore and the drill string. Combine the radial displacement of each node of the drill string to obtain the radial displacement of the drill string at the current moment.

[0012] Step 5: Using steps 1 to 4, obtain the node displacements of the drill string at all times. The radial displacement of the node corresponding to all node displacements is the nonlinear contact position between the drill string and the well wall.

[0013] Preferably, in step 1, the drill bit and stabilizer of the drill string are considered as a single point. The effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix include the outer diameter, weight, elastic modulus, and Poisson's ratio of the drill bit and stabilizer.

[0014] Preferably, the nodes mentioned in step 1 include drill bit, stabilizer, drill pipe joint, and drill collar joint.

[0015] Preferably, the length of each unit in step 1 is 3m or 9m.

[0016] Preferably, the effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix mentioned in step 1 all use the global coordinate system, with the gravity direction as the coordinate system. The axis is based on the geographical direction of due north. The axis, due east is The transformation relationship between the global coordinate system and the local coordinate system fixed on the wellbore axis of the i-th unit is as follows:

[0017]

[0018] In the formula, α i , Let x, y, and z be the inclination angle and azimuth angle of the i-th unit, respectively. Let x, y, and z be the coordinate axes in the local coordinate system. Let the wellbore extension direction be the x-axis, the wellbore elevation direction be the y-axis, and the z-axis be determined according to the right-hand screw rule.

[0019] Furthermore, the relationships between the effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix mentioned in step 1 are as follows:

[0020]

[0021] in Let u be the effective load matrix, and let u be the displacement matrix of all nodes in the drill string. Let be the effective stiffness matrix of the drill string. The expressions for the effective stiffness matrix and the effective load matrix of the drill string are as follows: (a) and (b).

[0022]

[0023]

[0024] In equation (a), M, K, and C are the overall mass matrix, overall stiffness matrix, overall damping matrix, and overall load matrix of the drill string in the global coordinate system, respectively. In equation (b), u t-Δt Let be the displacement matrix of all nodes of the drill string at the previous moment. Let be the velocity matrix of all nodes of the drill string at the previous moment. Let be the acceleration matrix of all nodes of the drill string at the previous moment, and Δt be the time interval. In equations (a) and (b), δ and η are variable values ​​in the Newmark method.

[0025] Preferably, the gap between the wellbore and the drill string in step 4 is obtained by the following expression:

[0026] In the formula D w D is the inner diameter of the wellbore, in meters (m). p The outer diameter of the drill string is in meters (m).

[0027] Preferably, in step 4, the radial displacement of all nodes is calculated cyclically, first in order of increasing node number, then in order of decreasing node number, and finally in order of decreasing node number to increasing node number.

[0028] Preferably, step 5 combines the node displacement, node velocity, and node acceleration of the drill string at the first moment, as well as the processing methods of steps 1 to 4, and obtains the node displacement of the drill string at all moments according to the recursive formula of the Newmark numerical integration method.

[0029] Furthermore, step 5 obtains the nodal displacements of the drill string at all times as follows:

[0030] Step 5a: First, the node displacement, node velocity, and node acceleration of the drill string at the first moment are all 0. Then, the node displacement of the drill string at the second moment is obtained according to the method of Steps 1 to 4. According to the recursive formula of Newmark numerical integration method, the node velocity and node acceleration at the second moment are calculated from the node displacement at the second moment and the node displacement, node velocity, and node acceleration at the first moment. Then, the node displacement of the drill string at the third moment is obtained according to the method of Steps 1 to 4.

[0031] Step 5b: Calculate the node displacements of the drill string at all subsequent moments using the recursive calculation method established in step 5a.

[0032] Compared with the prior art, the present invention has the following beneficial technical effects:

[0033] This invention provides a method for determining the nonlinear contact position between the drill string and the wellbore. It considers the ultra-long, slender structure of the drill string and the nonlinear contact characteristics between the drill string and the wellbore. Based on the finite element dynamics equations of the drill string, unlike the global matrix method, it utilizes an iterative node calculation to determine the contact position. After correcting the effective load submatrix of the drill string and the radial displacement of the nodes, the next calculation is performed. This process is repeated cyclically, with the difference decreasing until a stable result is reached. This process continues until the calculation result is stable, and all node radial displacements are within the gap between the wellbore and the drill string, ultimately reflecting the true contact state between the drill string and the wellbore downhole, thus determining the contact position. This invention accurately tracks the contact nodes between the drill string and the wellbore and corrects the load submatrix at the point of contact. This method better reflects actual drilling conditions and provides a foundation for understanding the working state of the drill string downhole. Attached Figure Description

[0034] Figure 1a This refers to a local coordinate system fixed on the wellbore axis within the well section where a certain drill string unit is located, as described in this invention.

[0035] Figure 1b This is a schematic diagram illustrating the relationship between the local coordinate system and the global coordinate system described in this invention.

[0036] Figure 2 This is a schematic diagram of the two-unit, three-node model described in this invention.

[0037] Figure 3 This is a diagram of the iterative calculation process described in this invention.

[0038] Figure 4 This is an example of the contact state diagram between the drill string and the well wall at the 5th second and the 10th second, respectively, according to the present invention. Detailed Implementation

[0039] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0040] This invention provides a method for determining the nonlinear contact position between the drill string and the wellbore, comprising the following steps:

[0041] Step 1: The drill string consists of a drill bit, multiple drill pipes, multiple drill collars, and multiple stabilizers. For any given drill string, the dimensions, weight, elastic modulus, and Poisson's ratio of the drill bit, each drill pipe, each drill collar, and each stabilizer can be obtained by consulting the drilling manual.

[0042] The drill bit and stabilizer are usually considered as a single point, taking only the outer diameter into account while retaining their weight, elastic modulus, and Poisson's ratio. The length of each drill rod and drill collar is typically 9m.

[0043] Step 2: Based on the finite element theory, the drill string given in Step 1 is divided into elements. Since the drill string is an ultra-long and slender structure, conforming to the Euler-Bernoulli beam theory, the length of each element can be set to 3m or 9m. Each element includes the dimensions, weight, elastic modulus, and Poisson's ratio determined in Step 1. The connection between two adjacent elements is recorded as a node. At the same time, the drill bit, stabilizer, drill pipe joint, and drill collar joint are also determined as nodes of the elements. The uppermost wellhead is recorded as the first node, and the lowermost drill bit is recorded as the Nth node.

[0044] Step 3, Figure 1a This diagram illustrates a single unit and a local coordinate system fixed to the wellbore axis of the section containing that unit. Specifically, the wellbore extension direction is defined as the x-axis, the wellbore elevation direction as the y-axis, and the z-axis is determined using the right-hand rule. M in the diagram... ix M iy M iz F represents the torque in the x, y, and z directions at the i-th node. ix F iy F iz Let u represent the forces in the x, y, and z directions at the i-th node, respectively. jx u jy u jz Let θ represent the displacements in the x, y, and z directions at the j-th node, respectively. jx θ jy θ jz These represent the rotation angles in the x, y, and z directions at the j-th node, respectively. The arrows in the diagram indicate the vector directions of force, torque, displacement, and rotation angle.

[0045] Figure 1b This illustrates the correspondence between the local and global coordinate systems, with the axes of the global coordinate system distinguished by horizontal lines above the corresponding letters. The direction of gravity is used as the reference point. The axis is based on the geographical direction of due north. The axis, due east is Establish a global coordinate system using axes.

[0046] The following step, step 4, uses the global coordinate system. The transformation relationship between the local coordinate system and the global coordinate system is as follows:

[0047]

[0048] In the formula, α i , These are the well inclination angle and azimuth angle of the i-th unit, respectively.

[0049] Step 4: Based on the finite element dynamics equations of the drill string, the finite element dynamics equations of the drill string are iteratively calculated using the idea of ​​nodal iteration to obtain the nonlinear contact position between the drill string and the wellbore. This specifically includes the following steps:

[0050] Step 41, the finite element dynamic equation of the drill string at a certain moment downhole is:

[0051]

[0052] In the formula, M, K, C, and F are the overall mass matrix, overall stiffness matrix, overall damping matrix, and overall load matrix of the drill string in the global coordinate system, respectively, which are derived from the mass matrix of each element. Stiffness matrix Damping matrix and load matrix It is formed by stacking.

[0053] Element mass matrix for:

[0054]

[0055] In the formula, ρ is the element density, A is the element cross-sectional area, l is the element length, and I is the element density. x Let ρ be the moment of inertia of the cross section about the x-axis. To make formula (3) easier to display, the element mentioned in this paragraph is the i-th element, ρ, A, l and I. x Subscripts are omitted in all cases, and the same applies to subsequent cases.

[0056] Element stiffness matrix for

[0057]

[0058] In the formula, E is the element's elastic modulus, A is the element's cross-sectional area, l is the element's length, G is the element's shear modulus, and J is the element's moment of inertia. For Poisson's ratio, I y and I zThese are the moments of inertia of the element section about the y and z axes, respectively.

[0059] Element damping matrix C e For M e and K e linear combination

[0060]

[0061] In the formula, γ is the proportionality constant, and in engineering, two natural frequency values ​​ω are usually selected. i ω j and the corresponding damping ratio ξ i ξ j Calculated γ:

[0062]

[0063]

[0064] Damping ratio The value of γ can be obtained through experimental testing, but in engineering, it is generally difficult to obtain the specific value of the damping ratio as a function of frequency. Therefore, ξ is usually set as ξ. i =ξ j =ξ0, typically the damping ratio in mud drilling. γ is 0.02 to 0.10.

[0065] Element load matrix F e for:

[0066]

[0067] In the formula, α i These are the well inclination angles of the i-th unit, Let be the buoyancy of the i-th beam element. represent Figure 1a Torque in represent Figure 1a The force in the middle, Figure 1a The torque and force indicated are just symbols, not specific values ​​or formulas.

[0068] u is the displacement matrix of all nodes of the drill string that needs to be calculated. The elements in the displacement matrix are... Figure 1a The displacement and rotation mentioned in the text are the quantities that need to be solved. Let be the velocity matrix of all nodes in the drill string. Let be the acceleration matrix of all nodes in the drill string. Using the Newmark method, equation (2) can be written as:

[0069]

[0070] In the formula, The effective stiffness matrix;

[0071]

[0072] For the payload matrix

[0073]

[0074] In the formula, u t-Δt Let be the displacement matrix of all nodes of the drill string at the previous moment. Let be the velocity matrix of all nodes of the drill string at the previous moment. Let Δt be the acceleration matrix of all nodes of the drill string at the previous moment, where Δt is the time interval. The displacement, velocity, and acceleration at the first moment are generally given as 0, i.e., at rest. When δ≥0.5, η≥0.25(0.5+δ) 2 At this time, the Newmark method is unconditionally stable, meaning that the magnitude of the time step Δt does not affect the stability of the solution.

[0075] In step 42, when solving equation (9) in step 41, the matrix on both sides of the equality in equation (9) needs to be divided into blocks in order to perform iterative calculations using the idea of ​​node iteration and obtain the nonlinear contact position between the drill string node and the well wall.

[0076] Any two adjacent elements on the drill string, such as Figure 2 As shown. Where k represents the element number, k = 1, 2, ..., m; A, E, l represent the element cross-sectional area, element elastic modulus, and element length, respectively. Poisson's ratio is not listed. These four quantities can express the mass matrix, stiffness matrix, and damping matrix of each element for easy explanation; two elements include three nodes, and the subscript i is used to represent the node number, i = 1, 2, ..., n.

[0077] for Figure 2 The drill rod shown is divided into two units. Equation (9) in step 41 is divided into blocks, and the expression form of two units and three nodes is separated out, as follows:

[0078]

[0079] In the formula, The effective stiffness submatrix corresponding to node i (the common node of element k and element k+1) is denoted as KB. i That is, equation (10). The matrix corresponding to u i The effective stiffness submatrix for the location; each element represents a 6×6 matrix. KB iThe specific elements of the matrices to the left and right of the matrix in the same row cannot be written out because... K, M, and C are all integral matrices assembled from unit matrices. These cannot be derived manually using formulas; the derivation process is extremely tedious and complex. Instead, computers directly input data, perform matrix multiplication, and then add the results at the corresponding positions.

[0080] Then perform matrix multiplication to obtain F. i Then equation (12) can be written as

[0081]

[0082] Then the displacement matrix u of node i i It can be represented by the displacements of nodes i-1 and i+1. Therefore, by transforming equation (13), we can obtain equation (14). In equation (14), the subscripts of the corresponding matrices are omitted in the brackets. Specifically,

[0083]

[0084] Step 43, the calculation process of the node iteration loop

[0085] The displacement u of node i is obtained according to equation (14). i Then, if the radial displacement u of that node ir If the distance between the wellbore and the drill string exceeds the limit, the radial displacement of the node will be directly limited to the range of the wellbore and drill string clearance.

[0086]

[0087] In the formula: u ir Let be the radial displacement of node i, in meters (m). D is the gap between the wellbore and the drill string, measured in meters (m). w D is the inner diameter of the wellbore, in meters (m). p The outer diameter of the drill string is in meters (m).

[0088] The restricted displacement u ir Replace the radial displacement of node i in equation (12) and recalculate the effective load matrix F using equation (12). i .

[0089] Then, following a similar approach, select nodes i, i+1, and i+2 to continue calculating the displacement of node i+1. For the entire drill string, the calculation must proceed forward from node 1 to node N, then backward from node N back to node 1, and so on, as follows: Figure 3As shown, the calculation is repeated until the radial displacement of all nodes is within the gap between the wellbore and the drill string. The radial displacement of each node of the drill string is combined to obtain the radial displacement of the drill string at the current moment. Based on the radial displacement, it can be determined whether each node of the drill string is in contact with the well wall inside the wellbore.

[0090] The above steps are used to obtain the nodal displacements of the drill string at all times. The radial displacements of the nodes corresponding to all nodal displacements are the nonlinear contact positions between the drill string and the wellbore. Specifically, combining the nodal displacements, nodal velocities, and nodal accelerations of the drill string at the first moment, and the processing method described above, the nodal displacements of the drill string at all times are obtained according to the recursive formula of the Newmark numerical integration method. That is, given that the nodal displacements, nodal velocities, and nodal accelerations of the drill string at the first moment are all 0, the nodal displacements of the drill string at the second moment are obtained according to the above steps. According to the recursive formula of the Newmark numerical integration method, the nodal velocities and nodal accelerations at the second moment are calculated from the nodal displacements at the second moment and the nodal displacements, nodal velocities, and nodal accelerations at the first moment. Then, the nodal displacements of the drill string at the third moment are obtained according to the above steps. Following this recursive calculation method, the nodal displacements of the drill string at all subsequent moments are calculated.

[0091] Example 1

[0092] The drill string structure of a certain well is as follows:

[0093] Φ311.2mm PDC drill bit + Φ228.6mm drill collar × 18m + Φ306mm stabilizer + Φ228.6mm drill collar × 9m + Φ308mm stabilizer + Φ228.6mm drill collar × 54m + Φ203.2mm drill collar × 27m + Φ127mm drill rod × 4392m.

[0094] Each unit is 3m long, with a well inclination angle of 2°, an azimuth angle of 180°, a drilling pressure of 100kN, a drilling speed of 90r / min, and a drilling fluid density of 1.2g / cm³. 3 .

[0095] Based on step 4, the finite element dynamic equations of the drill string downhole are first formed. In the equation, M, C, K, and F are calculated from equations (3) to (6), and their equivalent equations are obtained according to equation (9). Then, the equation (14) is iteratively solved, with 5000 iterations at each moment. It is found that the calculated radial displacements of the drill string nodes are all within the wellbore constraint range. The radial displacements of each node of the drill string at the 5th and 10th seconds in the global coordinate system are taken as follows: Figure 4As shown in the figure. By comparing whether the radial displacement and the gap value of the well wall are the same, the contact condition between the drill string and the cylindrical well wall is obtained. The contact node depth between the drill string and the well wall at any two moments (such as the 5th second and the 10th second) is shown in Table 1. Because the lateral displacement of the drill string is very small relative to its length, the lateral displacement is enlarged to a certain scale for ease of observation when plotting.

[0096] Table 1. Contact positions between drill string and wellbore at different times

[0097]

[0098] This embodiment illustrates that the nonlinear contact calculation method between the drill string and the wellbore based on node iterative cycles can obtain the actual contact state between the drill string and the wellbore downhole.

Claims

1. A method for determining the nonlinear contact position between the drill string and the wellbore, characterized in that, Includes the following steps: Step 1: First, divide the drill string into elements, with the connection between two adjacent elements being a node. Then, transform the finite element dynamic equation of the drill string at the current moment downhole into the relationship between the effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix. Step 2: Divide the relational expression described in Step 1 into several sub-relative expressions by forming a sub-relative expression with two units. In each sub-relative expression, the effective stiffness sub-matrix of the three nodes corresponding to the two units is arranged on one side of the equal sign, and the effective load sub-matrix of the three nodes corresponding to the two units is arranged on the other side. Perform matrix multiplication and transformation on each sub-expression to obtain the displacement matrix expression corresponding to each intermediate node. Step 3: First, solve one of the displacement matrix expressions obtained in Step 2 to obtain the radial displacement of the node corresponding to the expression. If the obtained radial displacement is greater than the gap between the wellbore and the drill string, set the radial displacement of the node as the gap between the wellbore and the drill string. Then, substitute the gap value into the sub-relationship in Step 2 to perform matrix multiplication to obtain a new effective load sub-matrix. Step 4: Using the new effective load submatrix, calculate the radial displacement of all nodes cyclically according to the calculation process described in Step 3 until the radial displacement of all nodes is within the gap between the wellbore and the drill string. Combine the radial displacement of each node of the drill string to obtain the radial displacement of the drill string at the current moment. Step 5: Using steps 1 to 4, obtain the node displacements of the drill string at all times. The radial displacement of the node corresponding to all node displacements is the nonlinear contact position between the drill string and the well wall.

2. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 1, characterized in that, In step 1, the drill bit and stabilizer of the drill string are considered as a single point. The effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix include the outer diameter, weight, elastic modulus, and Poisson's ratio of the drill bit and stabilizer.

3. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 1, characterized in that, The nodes mentioned in step 1 include the drill bit, stabilizer, drill pipe joint, and drill collar joint.

4. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 1, characterized in that, In step 1, the length of each unit is 3m or 9m.

5. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 1, characterized in that, The effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix mentioned in step 1 all use the global coordinate system, with the gravity direction as the coordinate system. The axis is defined with due north as the y-axis and due east as the y-axis. The transformation relationship between the global coordinate system and the local coordinate system fixed on the wellbore axis of the i-th unit is as follows: In the formula, α i , Let x, y, and z be the inclination angle and azimuth angle of the i-th unit, respectively. Let x, y, and z be the coordinate axes in the local coordinate system. Let the wellbore extension direction be the x-axis, the wellbore elevation direction be the y-axis, and the z-axis be determined according to the right-hand screw rule.

6. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 5, characterized in that, The relationships between the effective stiffness matrix of the drill string, the displacement matrix of all nodes of the drill string, and the effective load matrix mentioned in step 1 are as follows: in Let u be the effective load matrix, and let u be the displacement matrix of all nodes in the drill string. Let be the effective stiffness matrix of the drill string. The expressions for the effective stiffness matrix and the effective load matrix of the drill string are as follows: (a) and (b). In equation (a), M, K, and C are the overall mass matrix, overall stiffness matrix, overall damping matrix, and overall load matrix of the drill string in the global coordinate system, respectively. In equation (b), u t-Δt Let be the displacement matrix of all nodes of the drill string at the previous moment. Let be the velocity matrix of all nodes of the drill string at the previous moment. Let be the acceleration matrix of all nodes of the drill string at the previous moment, and Δt be the time interval. In equations (a) and (b), δ and η are variable values ​​in the Newmark method.

7. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 1, characterized in that, The gap between the wellbore and the drill string in step 4 is obtained by the following expression: In the formula D w D is the inner diameter of the wellbore, in meters (m). p The outer diameter of the drill string is in meters (m).

8. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 1, characterized in that, Step 4: First, calculate the radial displacement of all nodes in the order of increasing node number, then in the order of decreasing node number, and finally in the order of decreasing node number to increasing node number.

9. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 1, characterized in that, Step 5 combines the node displacement, node velocity, and node acceleration of the drill string at the first moment, as well as the processing methods in steps 1 to 4, and obtains the node displacement of the drill string at all moments according to the recursive formula of the Newmark numerical integration method.

10. The method for determining the nonlinear contact position between the drill string and the wellbore according to claim 9, characterized in that, Step 5 obtains the nodal displacements of the drill string at all times as follows: Step 5a: First, the node displacement, node velocity, and node acceleration of the drill string at the first moment are all 0. Then, the node displacement of the drill string at the second moment is obtained according to the method of Steps 1 to 4. According to the recursive formula of Newmark numerical integration method, the node velocity and node acceleration at the second moment are calculated from the node displacement at the second moment and the node displacement, node velocity, and node acceleration at the first moment. Then, the node displacement of the drill string at the third moment is obtained according to the method of Steps 1 to 4. Step 5b: Calculate the node displacements of the drill string at all subsequent moments using the recursive calculation method established in step 5a.

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