CN111948020B - Complex stratum directional well pipe column running capability evaluation method based on virtual contact point - Google Patents
Complex stratum directional well pipe column running capability evaluation method based on virtual contact point Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B7/00—Special methods or apparatus for drilling
- E21B7/20—Driving or forcing casings or pipes into boreholes, e.g. sinking; Simultaneously drilling and casing boreholes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0076—Hardness, compressibility or resistance to crushing
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/06—Indicating or recording means; Sensing means
- G01N2203/067—Parameter measured for estimating the property
- G01N2203/0682—Spatial dimension, e.g. length, area, angle
Abstract
A complex stratum directional well pipe column running capability evaluation method based on virtual contact points comprises the following steps: aiming at the characteristics of a directional well and a pipe column thereof in a complex stratum, a vertical and horizontal bending beam model which is relatively close to reality and can contain virtual contact points is established; analyzing whether the contact point is a real contact point or a virtual contact point based on an incremental displacement approximation method of the virtual spring, and solving the position and the contact force of the contact point of the tubular column and the well wall; the friction coefficient is inversely calculated according to different parameters aiming at different working conditions of sliding drilling and rotary drilling by utilizing field logging data; calculating the friction force according to the contact force and the friction coefficient at the real contact point; and analyzing the influence factors of the running friction of the bent well section pipe column by using a model, and carrying out simulation and comparative analysis on the running resistance of the high-rigidity drifting drill column and the thick-wall casing pipe.
Description
Technical Field
The invention relates to the technical field of oil and gas well engineering, in particular to a method for evaluating the running capability of a directional well pipe column of a complex stratum based on a virtual contact point.
Background
In the process of petroleum drilling, creep shrinkage of a brine-gypsum section in a complex formation can cause the size of a borehole to be smaller than the size of a drill bit; after cementing is complete, it may cause the casing to collapse. Thus, it is often necessary to drill in a timely manner to prevent the wellbore from being reduced in diameter while drilling in a brine section, and it is often necessary to use a thickened casing to prevent the casing from collapsing. No matter the diameter of the borehole is reduced or the wall thickness of the casing is increased, the rigid contact force between the pipe column and the wall of the borehole is increased, and the smooth running of the pipe column is influenced. In order to improve and improve the efficiency and effect of the pipe column running construction, pipe column running simulation analysis research needs to be carried out.
At present, a hard model is often needed for predicting the friction resistance torque of a horizontal well pipe column, different solving methods aiming at the hard model are presented due to the very complicated solving of the hard model, such as a finite element method, a Ho H-S method, a longitudinal and transverse bending beam method and the like, but the finite element method is complicated in calculation process and poor in stability, and the Ho H-S method is partially unreasonable in assumption and is greatly different from the actual situation, so that the Ho H-S method is not widely applied on site. The crossbar bending beam method is gaining more and more acceptance because of its clear physical meaning and relatively simple algorithm. However, the traditional longitudinal and transverse bending beam method needs to designate the contact point of the pipe column and the well wall, once the designated contact point is unreasonable, the contact point can be eliminated through multiple trial calculation, and the more unreasonable contact points are, the greater the difficulty of elimination is, and even the situation that a calculation result cannot be obtained can occur. Because of this, the conventional longitudinal and transverse bending beam method is generally cautious when specifying contact points, the specified contact points are few, but the actual contact points are necessarily missed, and the contact points need to be found according to whether the deflection of the pipe column between the two contact points exceeds the gap between the pipe column and the well wall, and when the number of the newly added contact points is more, the calculation process is more troublesome, and even a calculation result cannot be obtained.
Disclosure of Invention
Aiming at the problems occurring in the solving process of different models, the invention provides a complex stratum directional well pipe column running capability evaluation method based on virtual contact points.
The invention relates to a complex stratum directional well pipe column running capability evaluation method based on virtual contact points, which comprises the following steps:
and 4, analyzing influence factors of the running friction of the bent well section pipe column by using the model, and carrying out comparative analysis on the running resistance of the high-rigidity drifting drill column and the thick-wall casing.
The step 1 comprises the following steps:
step 11, in order to facilitate analysis and calculation, certain simplifying assumptions are made for the directional well string running of the complex stratum:
1) The pipe column is a small elastic deformation system;
2) The well wall is a rigid body, the well hole is a bending cylinder taking the axis of the well hole as the center, the inner diameter of the cylinder is kept constant in sections, and the size of the cylinder does not change along with time;
3) The method comprises the following steps of taking convex points of joints, couplings, centralizers and the like on a pipe column and appointed points at intervals of a certain length as constraint points, wherein the constraint points can be real contact points or virtual contact points which are not in contact with a well wall;
4) The influence of vibration is not taken into account.
And step 12, designating the parts with relatively large diameters on the pipe columns such as joints, couplings, centralizers and the like as contact points, and establishing a pipe column longitudinal and transverse bending continuous beam model containing virtual contact points.
The step 2 comprises the following steps:
step 21, establishing a three-dimensional coordinate system, and solving initial relative displacement of each constraint point in a well deviation plane P and an azimuth plane Q;
step 22, calculating the deflection and the end corner of the lower beam under the combined action of the axial load and the transverse load;
step 23, calculating initial additional corners generated by initial relative displacement of two ends of each span beam, and solving a three-bending-moment equation set of the tubular column;
step 24, judging a new contact point, and calculating the contact force and the frictional resistance at the constraint point and the relative displacement of the constraint point in the next iteration;
and 25, judging whether the constraint point is a real contact point or not, and calculating the frictional resistance of the pipe column.
The step 21 includes:
1) Establishing a three-dimensional coordinate system with the bottom of the tubular column as an origin
The center of a borehole section of the well depth where the drill bit or the guide shoe is located is taken as a coordinate origin o, the tangential direction of the borehole axis at the drill bit or the guide shoe is taken as the x-axis direction (the direction to the well mouth is positive), the direction perpendicular to the x-axis on a vertical plane passing through the x-axis is taken as the z-axis direction (the direction to the well mouth is positive), and the y-axis and the positive direction thereof are determined by the right-hand rule.
Unit vector of positive x-axis direction
Comprises the following steps:
in the formula, alpha b 、φ b The well inclination angle and the azimuth angle at the drill bit or the guide shoe respectively;
unit vectors in the directions of the vertical down, north and east coordinates, respectively.
Unit vector in z-axis direction
Comprises the following steps:
unit vector of y-axis direction
Comprises the following steps:
with the unit vectors of the three coordinate axes of the bottom coordinate system in the wellhead coordinate system, a coordinate conversion matrix [ T ] for converting the vector in the wellhead coordinate system into the vector in the bottom coordinate system can be obtained G ]：
Coordinates of each point in the wellhead coordinate system in the bottom coordinate system are as follows:
in the formula, H b 、N b 、E b Respectively an H coordinate, an N coordinate and an E coordinate at the drill bit or the guide shoe in a wellhead coordinate system; H. n, E is respectively the H coordinate, N coordinate and E coordinate of any point in the wellhead coordinate system; and x, y and z are respectively the x coordinate, the y coordinate and the z coordinate of the corresponding point in the bottom coordinate system.
2) Calculating the initial relative displacement of each constraint point in the P, Q plane
If the pipe column has n +1 constraint points, and the length from each constraint point to the drill bit or the guide shoe is Li (i =0to n), the initial relative displacement deltaz of the ith constraint point on the pipe column on the P, Q plane i 0 、δy i 0 Respectively as follows:
δz i 0 ＝z i (6)
δy i 0 ＝y i (7)
said step 22 comprises:
1) Deflection and end corner calculation of beam on P plane under combined action of transversely uniformly distributed load and axial load
On the P plane, withA left support of the span beam is used as a coordinate system origin O, the connection line direction of the left support and the right support is used as the xi axis direction, the xi axis direction is rotated by 90 degrees anticlockwise (upward direction) and used as the eta axis direction, and a P plane local coordinate system O xi eta is established. If the span beam acts with a load q uniformly distributed in the transverse direction in the P plane P (the positive direction of the eta axis is defined to be positive) and the axial load P (the axial load for pressing the beam is defined to be positive, the axial load on the P, Q plane is the same, and the actual axial load of the beam is adopted), the flexural line equation of the beam on the P plane under the joint action of the two loads is as follows:
wherein E is the modulus of elasticity of the beam material; i is the beam bending stiffness; l is 0 Is the span length of the beam;
derivation is performed on both sides of equation (8), and xi =0 and xi = L are respectively set 0 The corners of the left and right ends of the beam on the P plane can be obtained
And &>
As can be seen from the mechanics of materials, the first factor in the formulas (9) and (10) is that the left end and the right end of the beam on the P plane rotate when only transversely uniformly distributed load acts (P = 0)Angle, the second factor being the coefficient of influence of axial load on the beam-end corner, if any
Then there are:
in the plane P, the deflection and the beam end corner under the combined action of the transverse distribution load and the axial load P are in a nonlinear relation, and when the P is not changed, the deflection and the beam end corner and the axial load are in a nonlinear relation with the transverse distribution load q P And has a linear relationship.
2) Deflection and end corner calculation of beam on P plane under combined action of transverse concentrated load and axial load
By adopting a processing method similar to that of the transverse distributed load, the transverse concentrated load Q on the P plane can be obtained P (the positive direction of the eta axis is defined as positive) and the axial load P:
in the formula, L Q For concentrating the load Q P Distance of the point of action on the beam to the origin of coordinates.
Derivatives are obtained on both sides of equation (13), and xi =0 and xi = L respectively 0 The corners of the left and right ends of the beam on the P plane can be obtained
And &>
In the plane P, the deflection and the beam end corner under the combined action of the transverse concentrated load and the axial load P are in a nonlinear relation, and when the P is not changed, the P and the transverse concentrated load Q are all in a nonlinear relation P And has a linear relationship.
3) Deflection and end corner calculation of beam on P plane under combined action of end force couple and axial load
The couple at the right end on the P plane can be obtained by adopting a similar processing method to the first two loads
(the point on the beam section where η is large is specified to be compressed to be positive) and the axial load P:
derivatives are obtained on both sides of equation (16), and xi =0 and xi = L respectively 0 The corners of the left and right ends of the beam on the P plane can be obtained
And &>
By material mechanicsIt is noted that the first factor in the expressions (17) and (18) is the right and left end turning angles of the beam when only the right end force couple acts (P = 0), and the second factor is the influence coefficient of the axial load on the end turning angles of the beam, if the order is given
Then there are: />
The left end couple on the P plane can be obtained by the same method
(the point on the beam section where η is large is specified to be compressed to be positive) and the axial load P, the bending line equation and the end corner of the beam under the combined action:
in the plane P, the deflection and the beam end corner under the combined action of the end force couple and the axial load P are in a non-linear relationship, and when the P is not changed, the deflection and the beam end corner and the axial load P are in a linear relationship with the end force couple.
On a Q plane, a left support of the span is taken as a coordinate system origin o, a connecting line direction of the left support and the right support is taken as a xi axis direction, a xi axis direction is taken as a zeta axis direction, a direction (upward direction) of counterclockwise rotation of the xi axis by 90 degrees is taken as a zeta axis direction, and a Q plane local coordinate system o xi zeta is established. By applying the same analysis method in the P plane, a calculation formula of a deflection line equation and an end corner under the joint action of various transverse loads and axial loads in the Q plane can be obtained.
On the P plane or the Q plane, all transverse loads are only in coupling relation with axial loads, and deflection and end corners under the combined action of the transverse loads and the axial loads are in linear relation with all transverse loads, so that deflection and end corners of a beam under the coupling action of the axial loads and all transverse loads are obtained, and total deflection and end corners of the beam under the action of all loads can be calculated through superposition.
The step 23 includes:
1) Calculating initial additional rotation angle generated by initial relative displacement of two ends of each span beam
The foregoing formula for the rotation angle of the beam end is only the rotation angle of the single-span straight beam relative to the local coordinate system o ξ η (or o ξ ζ), and in the P-plane coordinate system oxz (or Q-plane coordinate system oxy), the rotation angles of the two ends of the straight beam are the sum of the rotation angle of the beam in the local coordinate system and the rotation angle of the local coordinate system relative to the P (or Q) -plane coordinate system.
In the P plane, the initial additional corner generated by the initial relative displacement of the supports at the two ends of the ith span beam
Comprises the following steps:
in the formula, x i-1 、x i And the coordinate values of the left and right supports of the ith span beam on the x axis are respectively.
In the Q plane, the initial additional corner generated by the initial relative displacement of the supports at the two ends of the ith span beam
Comprises the following steps:
2) Solving three bending moment equation set of tubular column
For the ith support in the P plane, the left side and the right side of the ith support are respectively the ith span beam and the (i + 1) th span beam, and according to the continuity condition that the corners of the beams at the two sides of the support are equal, the three bending moment equation set of the bottom drilling tool assembly in the P plane can be obtained as follows:
in the formula, M i，p The internal bending moment of the beam at the ith support on the plane P; I.C. A i Moment of inertia for the ith span;
the additional corner is calculated by the relative displacement of the supports at the two ends of the ith span beam on the P plane; theta T,P The projection angle of the included angle between the axis direction of the well hole at the upper tangent point and the x direction in the bottom coordinate system on the P plane; Δ L i Is the length of the ith span, Δ L i ＝L i -L i-1 ；
P i Representing the average axial force in the ith span
q i，P For a component in the P-plane of the load distributed transversely of the i-th cross beam>
α i Representing the well angle at the ith bearing; w is a i The weight of the ith span beam per meter in the slurry; the meaning of the rest parameters is analogized or the same as before.
Depending on the boundary conditions at the drill bit or guide and at the point of tangency on the P-plane, there may be:
M 0,P ＝0 (27)
M n,P ＝E·I n ·k αT (28)
in the formula, k αT Is the rate of change of the well deviation at the tangent point.
When equations (27) and (28) are substituted into the equation set (26), the equation set (26) has n unknowns M in total i，P (i =1to n-1) and L n Exactly n equations exist, so that the bending moment M at each support on the P plane can be solved i，P (i =1to n-1) and the length of the last span L n 。
For the ith support in the Q plane, the left side and the right side of the ith support are respectively provided with an ith span beam and an (i + 1) th span beam, and a three bending moment equation set of the bottom drilling tool assembly in the Q plane can be obtained according to the continuity condition that the corners of the two side beams of the support are equal. Due to the distribution of the load q i，Q =0, last span length L n Calculated at the P plane, the system of three bending moments equations for the bottom hole assembly in the Q plane can be simplified as follows:
in the formula, the subscript of the parameter is changed from P to Q, and then the corresponding parameter on the Q plane is shown, and the other parameters have the same meanings as before.
Depending on the boundary conditions at the drill bit and at the tangent point on the Q plane, there may be:
M 0,Q ＝0 (30)
M n,Q ＝E·I n ·k φT sinα T (31)
in the formula, k φT Is the azimuth rate of change at the tangent point; alpha is alpha T Is the angle of the well at the tangent point.
When equations (30) and (31) are substituted into equation set (29), equation set (29) has n-1 unknowns M in total i，P (i =1to n-1), there are exactly n-1 equations, so that the bending moment M at the respective support on the Q plane can be solved i，Q (i＝1 to n-1)。
Said step 24 comprises:
1) Determination of new contact points
In a span beam, the place with the largest deflection is the place which is firstly contacted with the well wall, once the maximum deflection of the beam column between two supports exceeds the maximum range, a new contact point is formed, and a support is required to be added for calculation again.
Because the stress conditions are different, the place with the largest deflection in a span beam is difficult to calculate, and when the method is actually applied, the straight beam takes the midpoint of the span beam as the place with the largest deflection, so that approximate calculation with enough precision can be given.
Maximum deflection eta in P plane for ith straight beam i,m And maximum deflection ζ on Q plane i,m Can be calculated according to equations (32) and (33), respectively:
judging whether the pipe column and the well wall generate new contact, and checking whether the maximum deflection of the beam column between the two supports exceeds the maximum range, therefore, the criterion for generating the new contact point is as follows:
in the formula, R is the average curvature radius of the well section where the span beam is located; omega is the angle which the xoz plane rotates to the inclined plane circular arc plane of the well section where the span beam is located by taking the x coordinate axis as the rotating shaft.
Once a new contact point is generated, a new constraint point needs to be added to start the calculation from the first step again.
2) Calculation of contact force and frictional resistance at constraint points
After the magnitude of the bending moment of the beam at each support on the P, Q plane is obtained, the magnitude of the supporting force at each support can be calculated according to the equations (35) and (36).
3) Calculation of next iteration constraint point relative displacement
According to the calculated supporting force of each support on the P, Q plane, the relative displacement of the constraint point of the next iteration can be obtained:
δz i j ＝δz i j-1 -N i,P /K s (37)
δy i j ＝δy i j-1 -N i,Q /K s (38)
wherein Ks is the spring rate of the dummy spring, N/m.
The step 25 comprises:
1) Judging whether the constraint point is a real contact point
If the outer diameter of the tubular column at the ith constraint point is assumed to be SD i Borehole diameter of D w (L i ) Then when
Indicating that the pipe column at the constraint point is contacted with the well wall in the direction with large z value,
when/is>
Represents that the tubular column at the constraint point is in contact with the well wall in the direction with the small z value and is in the or-the-well direction>
When/is>
Represents that the pipe column at the constraint point is contacted with the well wall in the direction with the large y value>
And when>
Represents that the pipe column at the closing point is contacted with the well wall in the direction with small y value>
If all the constraint points are either contact force zero or contact with the well wall, ending the iteration process; otherwise, the calculation is started from the first step according to the new tie point position.
2) Calculation of frictional resistance of pipe string
If all the constraint points are in contact with the well wall or the contact force is zero, and no new contact point exists, the positive pressure N at each constraint point can be calculated according to the formulas (39) and (40) i Harmonic frictional resistance F i ：
F i ＝μ(L i )·N i (40)
And calculating new axial force distribution in the casing string according to the frictional resistance at each constraint point, calculating again until the calculation results of two adjacent times are within a given error range, finally obtaining the frictional resistance at each constraint point, and accumulating to obtain the frictional resistance of the whole pipe column.
The step 3 comprises the following steps:
step 32, removing transition points and problem points between the two modes;
step 33, calculating the friction coefficient reversely according to the bit pressure and the hook load aiming at the sliding drilling working condition; and (4) aiming at the rotary drilling working condition, reversely calculating the friction coefficient according to the torque of the drill bit and the torque of the wellhead.
The method for evaluating the running capability of the directional well pipe column of the complex stratum based on the virtual contact point has the greatest advantage that whether the point is a real contact point or not is not considered when the contact point is specified, so that parts with larger relative diameters on the pipe columns such as a joint, a coupling, a centralizer and the like can be specified as the contact point, and non-real contact points can be considered according to the virtual contact point, so that the application and the solution of a model are more convenient and feasible.
Drawings
FIG. 1 is a pipe string crossbar bending continuous beam model with virtual contact points;
FIG. 2 is a graph of the change of the friction coefficient with the well depth during the sliding drilling of the well A;
FIG. 3 is a graph of the change of the friction coefficient with the well depth during the rotary drilling of the well A;
FIG. 4 is the relationship between the running friction resistance of three casings in a 0-30 degree bending well section and the curvature of a well bore
FIG. 5 is the relationship between the lowering friction of three casings in the curved well section of 30-60 degrees and the curvature of the well hole;
FIG. 6 is the relationship between the running friction resistance of three casings in a 60-90 degree bending well section and the curvature of a well bore;
FIG. 7 is the relationship of the running friction resistance of three casings in a 0-90 degree bending well section along with the curvature of a well bore;
FIG. 8 shows the variation of the lowering friction resistance of three casings along with the hole diameter expansion rate in a bent well section of 30-60 degrees;
FIG. 9 is the results of the A well 12-1/4 "wellbore casing run-in calculation;
FIG. 10 is a comparison of the run in friction of the casing string and the drifting drilling assembly in the A well 12-1/4 wellbore.
FIG. 11 is a flow chart of the complex formation directional well string running capability evaluation method based on virtual contact points according to the invention.
Detailed Description
The complex stratum directional well pipe column running capability evaluation method based on the virtual contact point is described in detail below by combining specific embodiments.
Examples
The present embodiment mainly comprises the following steps:
1) In order to facilitate analysis and calculation, certain simplifying assumptions are made for the directional well string running of the complex stratum:
a. the pipe column is a small elastic deformation system;
b. the well wall is a rigid body, the well hole is a bending cylinder taking the axis of the well hole as the center, the inner diameter of the cylinder is kept constant in sections, and the size of the cylinder does not change along with time;
c. the method comprises the following steps of taking convex points of joints, couplings, centralizers and the like on a pipe column and appointed points at intervals of a certain length as constraint points, wherein the constraint points can be real contact points or virtual contact points which are not in contact with a well wall;
d. the effect of the vibration is not taken into account.
2) The parts with relatively large diameters on the pipe columns such as joints, couplings, centralizers and the like can be designated as contact points, and a pipe column longitudinal and transverse bending continuous beam model containing virtual contact points is established.
1) Establishing a three-dimensional coordinate system, and solving initial relative displacement of each constraint point in a well deviation plane P and an azimuth plane Q;
a. establishing a three-dimensional coordinate system with the bottom of the tubular column as an origin
The center of a borehole section of the depth of the drill bit or the guide shoe is taken as a coordinate origin o, the tangential direction of the borehole axis at the drill bit or the guide shoe is taken as the x-axis direction (the direction to the well head is positive), the direction perpendicular to the x-axis on a vertical plane passing through the x-axis is taken as the z-axis direction (the direction to the upper is positive), and the y-axis and the positive direction thereof are determined by the right-hand rule.
Unit vector of positive x-axis direction
Comprises the following steps:
in the formula (1), α b 、φ b The inclination angle and the azimuth angle of the drill bit or the guide shoe respectively;
unit vectors in the directions of the vertical down, north and east coordinates, respectively.
Unit vector in z-axis direction
Comprises the following steps:
unit vector of y-axis direction
Comprises the following steps:
with the unit vectors of the three coordinate axes of the bottom coordinate system in the wellhead coordinate system, a coordinate conversion matrix [ T ] for converting the vector in the wellhead coordinate system into the vector in the bottom coordinate system can be obtained G ]：
Coordinates of each point in the wellhead coordinate system in the bottom coordinate system are as follows:
in the formula (5), H b 、N b 、E b Respectively an H coordinate, an N coordinate and an E coordinate at the drill bit or the guide shoe in a wellhead coordinate system; H. n, E is respectively the H coordinate, N coordinate and E coordinate of any point in the wellhead coordinate system; x, y, z are the x, y and z coordinates of the corresponding point in the bottom coordinate system, respectively.
b. Calculating the initial relative displacement of each constraint point in the P, Q plane
If the pipe column has n +1 constraint points, and the length from each constraint point to the drill bit or the guide shoe is Li (i =0to n), the initial relative displacement deltaz of the ith constraint point on the pipe column on the P, Q plane i 0 、δy i 0 Respectively as follows:
δz i 0 ＝z i (6)
δy i 0 ＝y i (7)
2) Calculating the deflection and the end corner of the lower beam under the combined action of the axial load and the transverse load;
a. deflection and end corner calculation of beam on P plane under combined action of transversely uniformly distributed load and axial load
On the P plane, a left support of the span is taken as a coordinate system origin O, the connection line direction of the left support and the right support is taken as a xi axis direction, the xi axis is rotated counterclockwise by 90 degrees (upward direction) and taken as an eta axis direction, and a P plane local coordinate system O xi eta is established. If the span beam acts with a load q uniformly distributed in the transverse direction in the P plane P (the positive direction of the eta axis is defined to be positive) and the axial load P (the axial load for pressing the beam is defined to be positive, the axial load on the P, Q plane is the same, and the actual axial load of the beam is adopted), the deflection line equation of the beam on the P plane under the joint action of the two loads is as follows:
in the formula (8), E is the elastic modulus of the beam material; i is the beam bending stiffness; l is 0 Is the span length of the beam;
the derivatives are obtained on both sides of the equation (8), and xi =0 and xi = L are respectively set 0 The corners of the left end and the right end of the beam on the P plane can be obtained
And &>
According to the mechanics of materials, the first factor in the formulas (9) and (10) is the corner of the left end and the right end of the beam on the P plane when only the transversely uniformly distributed load acts (P = 0), the second factor is the influence coefficient of the axial load on the corner of the beam end, and if the angle is equal to the angle, the angle is equal to the angle
Then there are:
in the plane P, the deflection and the beam end corner under the combined action of the transverse distribution load and the axial load P are in a nonlinear relation, and when the P is not changed, the deflection and the beam end corner and the axial load P are in a nonlinear relation with the transverse distribution load q P And has a linear relationship.
b. Deflection and end corner calculation of beam on P plane under combined action of transverse concentrated load and axial load
By adopting a processing method similar to that of the transverse distributed load, the transverse concentrated load Q on the P plane can be obtained P (the positive direction of the eta axis is defined as positive) and the axial load P:
in the formula (13), L Q For concentrating the load Q P Distance of the point of action on the beam to the origin of coordinates.
Derivatives are obtained on both sides of equation (13), and xi =0 and xi = L respectively 0 The corners of the left end and the right end of the beam on the P plane can be obtained
And &>
In the plane P, the deflection and the beam end corner under the combined action of the transverse concentrated load and the axial load P are in a nonlinear relation, and when the P is not changed, the P and the transverse concentrated load Q are in a nonlinear relation P And has a linear relationship.
c. Deflection and end corner calculation of beam on P plane under combined action of end force couple and axial load
The couple at the right end on the P plane can be obtained by adopting a similar processing method to the first two loads
(the point on the beam section where η is large is specified to be compressed to be positive) and the axial load P:
derivatives are obtained on both sides of equation (16), and xi =0 and xi = L respectively 0 The corners of the left and right ends of the beam on the P plane can be obtained
And &>
As can be seen from the mechanics of materials, the first factor in the equations (17) and (18) is the corner at the left and right ends of the beam when only right end force couple acts (P = 0), and the second factor is the influence coefficient of axial load on the corner at the beam end, if order
Then there are:
the left end couple on the P plane can be obtained by the same method
(the point on the beam section where η is large is specified to be compressed to be positive) and the axial load P, the bending line equation and the end corner of the beam under the combined action:
in the plane P, the deflection and the beam end corner under the combined action of the end force couple and the axial load P are in a non-linear relationship, and when the P is not changed, the deflection and the beam end corner and the axial load P are in a linear relationship with the end force couple.
On a Q plane, a left support of the span is taken as a coordinate system origin o, a connecting line direction of the left support and the right support is taken as a xi axis direction, a xi axis direction is taken as a zeta axis direction, a direction (upward direction) of counterclockwise rotation of the xi axis by 90 degrees is taken as a zeta axis direction, and a Q plane local coordinate system o xi zeta is established. By applying the same analysis method in the P plane, a calculation formula of a deflection line equation and an end corner under the joint action of various transverse loads and axial loads in the Q plane can be obtained.
On the P plane or the Q plane, all transverse loads are only in coupling relation with axial loads, and deflection and end corners under the combined action of the transverse loads and the axial loads are in linear relation with all transverse loads, so that deflection and end corners of a beam under the coupling action of the axial loads and all transverse loads are obtained, and total deflection and end corners of the beam under the action of all loads can be calculated through superposition.
3) Calculating initial additional corners generated by initial relative displacement of two ends of each span beam, and solving a three-bending-moment equation set of the tubular column;
a. calculating initial additional rotation angle generated by initial relative displacement of two ends of each span beam
The foregoing formula for the rotation angle of the beam end is only the rotation angle of the single-span straight beam relative to the local coordinate system o ξ η (or o ξ ζ), and in the P-plane coordinate system oxz (or Q-plane coordinate system oxy), the rotation angles of the two ends of the straight beam are the sum of the rotation angle of the beam in the local coordinate system and the rotation angle of the local coordinate system relative to the P (or Q) -plane coordinate system.
In the P plane, the initial additional corner generated by the initial relative displacement of the supports at the two ends of the ith span beam
Comprises the following steps:
in the formula, x i-1 、x i And the coordinate values of the left and right supports of the ith span beam on the x axis are respectively.
In the Q plane, the initial additional corner generated by the initial relative displacement of the supports at the two ends of the ith span beam
Comprises the following steps:
b. solving three bending moment equation set of tubular column
For the ith support in the P plane, the left side and the right side of the ith support are respectively the ith span beam and the (i + 1) th span beam, and according to the continuity condition that the corners of the two side beams of the support are equal, the three bending moment equation set of the bottom drilling tool assembly in the P plane can be obtained as follows:
in the formula, M i，p The internal bending moment of the beam at the ith support on the P plane is set; i is i Moment of inertia for the ith span;
an additional corner is calculated by relative displacement of supports at two ends of the ith span beam on the plane P; theta T,P The projection angle of the included angle between the axial direction of the well hole at the upper tangent point and the x direction in the bottom coordinate system on the P plane; Δ L i Is the length of the ith span, Δ L i ＝L i -L i-1 ；
P i Representing the average axial force in the ith span
q i，P For a component in the P-plane of the load distributed transversely of the i-th cross beam>
α i Representing the well angle at the ith bearing; w is a i The weight of the ith span beam per meter in the slurry; the meaning of the rest parameters is analogized or the same as before.
Depending on the boundary conditions at the drill bit or guide and at the point of tangency on the P-plane, there may be:
M 0,P ＝0 (27)
M n,P ＝E·I n ·k αT (28)
in the formula, k αT Is the rate of change of the well deviation at the tangent point.
When equations (27) and (28) are substituted into the equation set (26), the equation set (26) has n unknowns M in total i，P (i =1to n-1) and L n Exactly n equations exist, so that the bending moment M at each support on the P plane can be solved i，P (i =1to n-1) and the length L of the last span n 。
For the ith support in the Q plane, the left side and the right side of the ith support are respectively provided with an ith span beam and an (i + 1) th span beam, and a three bending moment equation set of the bottom drilling tool assembly in the Q plane can be obtained according to the continuity condition that the corners of the two side beams of the support are equal. Due to the distribution of the load q i，Q =0, last span length L n Calculated at the P plane, the system of three bending moments equations for the bottom hole assembly in the Q plane can be simplified as follows:
in the formula, the subscript of the parameter is changed from P to Q, and then the corresponding parameter on the Q plane is shown, and the other parameters have the same meanings as before.
Depending on the boundary conditions at the drill bit and at the point of tangency on the Q-plane, there may be:
M 0,Q ＝0 (30)
M n,Q ＝E·I n ·k φT sinα T (31)
in the formula, k φT Is the azimuth rate of change at the tangent point; alpha is alpha T Is the angle of the well at the tangent point.
When equations (30) and (31) are substituted into equation set (29), equation set (29) has n-1 unknowns M in total i，P (i =1to n-1), there are exactly n-1 equations, so that the bending moment M at each support on the Q plane can be solved i，Q (i＝1 to n-1)。
4) Judging a new contact point, and calculating the contact force and the frictional resistance at the constraint point and the relative displacement of the constraint point in the next iteration;
a. determination of new contact point
In a span beam, the place with the largest deflection is the place which is firstly contacted with the well wall, once the maximum deflection of the beam column between two supports exceeds the maximum range, a new contact point is formed, and a support is required to be added for calculation again.
Because the stress conditions are different, the place with the largest deflection in a span beam is difficult to calculate, and when the method is actually applied, the straight beam takes the midpoint of the span beam as the place with the largest deflection, so that approximate calculation with enough precision can be given.
Maximum deflection eta in P plane for ith straight beam i,m And maximum deflection ζ on Q plane i,m Can be calculated according to equations (32) and (33), respectively:
judging whether the pipe column and the well wall generate new contact, and checking whether the maximum deflection of the beam column between the two supports exceeds the maximum range, therefore, the criterion for generating the new contact point is as follows:
in the formula, R is the average curvature radius of the well section where the span beam is located; omega is the angle which the xoz plane rotates to the inclined plane circular arc plane of the well section where the span beam is located by taking the x coordinate axis as the rotating shaft.
Once a new contact point is generated, a new constraint point needs to be added to start the calculation from the first step again.
b. Calculation of contact force and frictional resistance at constraint points
After the magnitude of the bending moment of the beam at each support on the P, Q plane is obtained, the magnitude of the supporting force at each support can be calculated according to the equations (35) and (36).
c. Calculation of next iteration constraint point relative displacement
According to the calculated supporting force of each support on the P, Q plane, the relative displacement of the constraint point of the next iteration can be obtained:
δz i j ＝δz i j-1 -N i,P /K s (37)
δy i j ＝δy i j-1 -N i,Q /K s (38)
wherein Ks is the spring rate of the dummy spring, N/m.
5) And judging whether the constraint point is a real contact point or not, and calculating the frictional resistance of the pipe column.
a. Judging whether the constraint point is a real contact point
If the outer diameter of the tubular column at the ith constraint point is assumed to be SD i Borehole diameter of D w (L i ) Then when
Indicating that the pipe column at the constraint point is contacted with the well wall in the direction with large z value,
when/is>
Represents that the pipe column at the constraint point is contacted with the well wall in the direction with small z value, and is pressed against the well wall>
When/is>
Represents that the pipe column at the constraint point is contacted with the well wall in the direction with the large y value>
And when>
Represents that the pipe column at the closing point is contacted with the well wall in the direction with small y value>
If all the constraint points are either contact force zero or contact with the well wall, ending the iteration process; otherwise, the calculation is started from the first step according to the new tie point position.
b. Calculation of frictional resistance of pipe string
If all the constraint points are in contact with the well wall or the contact force is zero, and no new contact point exists, the positive pressure N at each constraint point can be calculated according to the formulas (39) and (40) i Harmonic frictional resistance F i ：
F i ＝μ(L i )·N i (40)
And calculating new axial force distribution in the casing string according to the frictional resistance at each constraint point, calculating again until the calculation results of two adjacent times are within a given error range, finally obtaining the frictional resistance at each constraint point, and accumulating to obtain the frictional resistance of the whole pipe column.
1) Sliding drilling friction coefficient of A well
By reading drilling engineering parameters of the well A, which change along with the well depth, including well body track, drilling tool combination, bit pressure, bit torque, drilling fluid density and other data, data points with the rotating speed of a turntable being zero and the torque of a well head being zero or less than 3 KN.m are selected as the sliding drilling section data of the well, the friction coefficient of each point of the sliding drilling section of the well is calculated back, and a graph 2 shows the change relation of the friction coefficient along with the well depth.
As can be seen from FIG. 2, the friction coefficient of sliding drilling in the deflecting process of 4410 m-4537 m of the well A is relatively large and reaches up to 0.65. In summary, when the well is not clean, the apparent friction coefficient obtained by the reverse calculation of the friction torque model can reach 0.65 at most, but under normal conditions, the friction coefficient is about 0.35 at most.
2) Coefficient of friction resistance of rotary drilling for well A
By reading the drilling engineering parameters of the A well along with the change of the well depth, selecting data points with the rotating speed of the turntable greater than zero and the wellhead torque greater than 3 KN.m as the data of the rotary drilling section of the well, calculating the friction coefficient of each point of the rotary drilling section of the well, and obtaining the relation between the friction coefficient and the change of the well depth as shown in figure 3.
As can be seen from FIG. 3, the rotary drilling friction coefficient of the well A between 4615m and 5000m is relatively large and exceeds 0.65 at most, but the rotary drilling friction coefficient of the well A between 5000m and 5135m is lower than 0.35.
And 4, analyzing the influence factors of the running friction of the bent well section pipe column by using the model, and carrying out comparative analysis on the running friction of the high-rigidity drifting drill column and the thick-wall casing pipe.
1) Analysis of main influence factors of running friction resistance of bent well section pipe column
The bending well section is a dangerous well section through which a pipe column is put, the main influence factors of the friction resistance in the bending well section are cleared, and the method has very important significance for the selection of the curvature of the well bore and the selection of the pipe column entering the well in the track design. Various factors influencing the running friction of the pipe column are various, such as friction coefficient, pipe column weight, average well deviation angle and the like, but for a bending well section, well bore curvature, pipe column bending rigidity, annular space between the pipe column and the well wall and the like have important influence on the running friction in addition to the factors.
a. Wellbore curvature and string stiffness
FIGS. 4, 5 and 6 show the variation of the friction resistance of different casing strings in a 30-degree bent section with different average well deviation angles according to the curvature of the well bore. When calculating the friction resistance, other parameters are as follows: the diameter of a borehole is 311.1mm, the friction coefficient is 0.35, and the density of the drilling fluid is 1.2g/cm 3 。
It can be seen from the calculation results that as the curvature of the borehole increases, the change rule of the casing running friction resistance is different along with the difference of the average well deviation angle of the bent well section: when the bending section is a well section of 0-30 degrees (the average well inclination angle is 15 degrees), the downward friction resistance changes little along with the curvature of the well when the curvature of the well is small, when the curvature of the well exceeds 30 degrees/100 m, the downward friction resistance is rapidly increased along with the increase of the curvature of the well, and the pipe column with higher rigidity is increased more rapidly; when the bending section is a well section of 30-60 degrees (the average well inclination angle is 45 degrees), the running friction resistance is reduced along with the increase of the well curvature when the well curvature is smaller, and the running friction resistance is rapidly increased along with the increase of the well curvature when the well curvature exceeds 30 degrees/100 m, and the pipe column with higher rigidity is increased more quickly; when the bending section is a 60-90-degree well section (the average well inclination angle is 75 degrees), the lowering friction resistance is rapidly reduced along with the increase of the well curvature when the well curvature is smaller, the lowering friction resistance is rapidly increased along with the increase of the well curvature when the well curvature exceeds 30 degrees/100 m, and the pipe column with higher rigidity is increased more rapidly. The reduction in tubular run-in friction with increasing wellbore curvature occurs when the average angle of inclination is larger and the wellbore curvature is smaller because the smaller the wellbore curvature, the longer the curved wellbore section of the same angle, the heavier the total weight of the tubular string, and the greater the weight is converted into friction at larger angles of inclination. Therefore, it is preferable that the borehole curvature is 30 °/100m in view of the friction resistance.
The greater the bending stiffness of the casing, the greater the casing running friction through the same angle of the curved section of the wellbore, and the greater the wellbore curvature, the more significant the effect of the bending stiffness.
FIG. 7 is the relationship between the friction resistance of different casing strings running in the 0-90 degree bending section and the curvature of the well bore, and other parameters are the same as before when the friction resistance is calculated. The change relation of the running friction resistance of the inner casing pipe in the 0-90-degree bent well section along with the curvature of the well hole is basically the same as that in the 30-60-degree bent well section, but the numerical values are different.
b. Annular space gap between pipe column and well wall
Because the annular space between the pipe column and the well wall is related to the hole diameter expansion rate and the outer diameter of the pipe column centralizer, the hole diameter expansion rate is used for replacing the annular space for convenient analysis. FIG. 8 shows the variation of casing running friction with hole diameter enlargement rate. The calculation conditions used in the calculation of the entering friction resistance are as follows: the curvature of the well bore is 30 degree/100m, the bending well section of 30 degree-60 degree, the diameter of the well bore is 311.1mm, the friction coefficient is 0.35, the density of the drilling fluid is 1.2g/cm 3 。
As can be seen from fig. 8, the running friction of the pipe string in the curved section decreases linearly with the increase in the hole diameter expansion rate, and the pipe string decreases faster the greater the rigidity. The effect of the hole diameter size considered here on the running friction resistance is mainly considered from the viewpoint that the change in the hole diameter affects the stress and deformation of the string in the borehole, and the mechanical resistance due to the reduction or expansion is not considered.
c. Other parameters
The factors such as the curvature of a well bore, the rigidity of a pipe column, the size of a well diameter and the like have important influence on the running resistance of the pipe column of the bent well section; the main influence factors of the running resistance of the pipe column at the inclined and straight well section, such as friction coefficient, average well inclination angle, pipe column weight and the like, also influence the running resistance of the pipe column at the bent well section, and the influence relationship is the same as that of the inclined and straight section, namely: the larger the friction coefficient, the larger the average well inclination angle and the heavier the pipe column weight, the larger the pipe column running friction is, and the pipe column basically and linearly increases.
Comparing the impact of different factors on the running resistance of the pipe string in the bent well section shows that most parameters such as the well diameter expansion rate, the friction coefficient, the average well inclination angle, the weight of the pipe string and the running friction of the pipe string are in a linear relationship, but the impact of the well curvature and the pipe string size on the running friction of the pipe string is nonlinear and very large, so that the well curvature and the pipe string size are required to be carefully selected when the track design and the pipe string are selected.
2) Casing run-in simulation analysis in a wellbore
Simulation analysis was performed for casing run in the 12-1/4 "wellbore from well A.
FIG. 9 shows the results of the downhole friction analysis of a 10-3/4 "+ 9-5/8" composite casing in a 12-1/4 "wellbore in a well A.
As can be seen in fig. 9, the wellhead hook load is much greater than zero, indicating that the composite casing string can be made to run downhole smoothly from a mere downhole friction drag perspective. It can also be seen that where bending stresses are high, the frictional resistance of the string increases rapidly, indicating that for thick walled casing the effect of the stiffness forces in the bent wellbore on the run-in frictional resistance must be taken into account.
3) Comparative analysis of running resistance of large-rigidity drifting drill column and thick-wall casing
Comparison of running friction resistance of casing and last drifting drilling tool combination in A well 12-1/4 well
Combining the sleeves: phi 273.05mm TP140 cannula (wall thickness 26.24 mm). Times. 243.09m + phi 244.5mm VM140 cannula (wall thickness 11.99 mm). Times.4476 m.
And finally, drifting combination: a phi 311.1mm drill bit, a phi 311.1mm centralizer, 1 phi 203.2mm drill collar, 3 phi 311.1mm centralizer and 3 phi 203.2mm drill collars.
FIG. 10 shows the comparative results of the run-in friction of the casing string and the drift assembly in the 12-1/4' borehole of the A-well.
As can be seen from figure 10, the drift assembly has a higher run-in friction than the casing, seen from the bottom 50m of the string alone, which means that the average contact force generated by the drift assembly is higher than that of the casing, i.e. that in the same case the drift assembly suffers a higher mechanical friction than the casing. Thus, as long as there is no problem with running the drifting drilling assembly in, it indicates that there is no problem with running the thick walled casing.
The above examples are only for illustrating the present invention and are not intended to limit the present invention.
Claims (4)
1. A complex stratum directional well string running capability evaluation method based on virtual contact points is characterized by comprising the following steps:
step 1, establishing a longitudinal and transverse bending beam model containing virtual contact points according to the types, motion states and stress conditions of a complex stratum directional well and a pipe column thereof;
step 2, analyzing whether the contact point is a real contact point or a virtual contact point based on the incremental displacement approximation method of the virtual spring, further solving the position and the contact force of the contact point between the pipe column and the well wall,
the step 2 comprises the following steps:
step 21, establishing a three-dimensional coordinate system by taking the bottom of the pipe column as an origin, taking the center of a well bore section of the well depth where the drill bit or the guide shoe is located as an origin of coordinates O, taking the tangential direction of the well bore axis at the drill bit or the guide shoe as the x-axis direction and pointing to the well mouth as positive, taking the direction vertical to the x-axis on a vertical plane passing through the x-axis as the z-axis direction and pointing upwards as positive, determining the y-axis and the positive direction thereof by a right-hand rule, and solving initial relative displacement of each constraint point in a well inclination plane P and an azimuth plane Q;
step 22, calculating the deflection and the end corner of the lower beam under the combined action of the axial load and the transverse load;
step 23, calculating initial additional corners generated by initial relative displacement of two ends of each span beam, and solving a three-bending-moment equation set of the tubular column;
step 24, judging a new contact point, and calculating the contact force and the frictional resistance of the constraint point and the relative displacement of the next iteration constraint point;
step 25, judging whether the constraint point is a real contact point, and calculating the frictional resistance of the pipe column;
the step 21 includes:
1) Establishing a three-dimensional coordinate system with the bottom of the tubular column as an origin,
obtaining a coordinate conversion matrix [ T ] for converting the vector in the wellhead coordinate system into the vector in the bottom coordinate system according to the unit vector of the three coordinate axes of the bottom coordinate system in the wellhead coordinate system G ]：
In the formula (1), α b 、
The well inclination angle and the azimuth angle at the drill bit or the guide shoe respectively;
coordinates of each point in the wellhead coordinate system in the bottom coordinate system are as follows:
in the formula (2), H b 、N b 、E b Respectively an H coordinate, an N coordinate and an E coordinate at the drill bit or the guide shoe in a wellhead coordinate system; H. n, E is respectively the H coordinate, N coordinate and E coordinate of any point in the wellhead coordinate system; x, y and z are respectively the x coordinate, the y coordinate and the z coordinate of the corresponding point in the bottom coordinate system;
2) The initial relative displacement of each constraint point in the P, Q plane is calculated,
if the pipe column has n +1 constraint points, and the length from each constraint point to the drill bit or the guide shoe is Li (i =0to n), the initial relative displacement deltaz of the ith constraint point on the pipe column on the P, Q plane i 0 、δy i 0 Respectively as follows:
δz i 0 ＝z i (3)
δy i 0 ＝y i (4)
thereby calculating the initial relative displacement of each constraining point in the P, Q plane;
the step 22 includes:
1) Calculating the deflection and the end corner of the beam on the P plane under the combined action of the transversely uniformly distributed load and the axial load,
on a P plane, taking a left support of the span as a coordinate system origin O, taking a connecting line direction of the left support and the right support as a xi axis direction, taking the xi axis anticlockwise rotating by 90 degrees, namely an upward direction as an eta axis direction, establishing a P plane local coordinate system xi eta, and if the span acts on a P plane with a load q uniformly distributed transversely P And axial load P, respectively setting the positive direction of the eta axis as positive and the axial load of Liang Shouya as positive, wherein the axial loads on the P, Q plane are the same, and adopting the actual axial loads of the beam, the flexural line equation of the beam on the P plane under the combined action of the two loads is as follows:
in the formula (5), E is the elastic modulus of the beam material; i is the beam bending stiffness; l is a radical of an alcohol 0 Is a span of a beamLength;
let xi =0, xi = L respectively 0 Obtaining the corners of the left and right ends of the beam on the P plane
And &>
In the plane P, the deflection and the beam end corner under the combined action of the transverse distribution load and the axial load P are in a nonlinear relation, and when the P is not changed, the deflection and the beam end corner and the axial load P are in a nonlinear relation with the transverse distribution load q P A linear relationship;
2) Calculating the deflection and the end corner of the beam on the P plane under the combined action of the transverse concentrated load and the axial load,
transverse concentrated load Q on P plane P Equation of the beam's deflection line under the combined action of axial load P, where Q P The positive direction of the eta axis is defined as positive:
in the formula (8), L Q For concentrating the load Q P The distance of the point of action on the beam to the origin of coordinates,
xi =0 and xi = L 0 The corners of the left and right ends of the beam on the P plane can be obtained
And &>
In the plane P, the deflection and the beam end corner under the combined action of the transverse concentrated load and the axial load P are in a nonlinear relation, and when the P is not changed, the P and the transverse concentrated load Q are in a nonlinear relation P A linear relationship;
3) Calculating the deflection and the end corner of the beam on the P plane under the combined action of the end force couple and the axial load,
couple of right and upper ends of P plane
The equation for the beam's deflection line under the combined action of axial load P specifies that the point on the beam section where η is large is pressurized to be positive:
let xi =0, xi = L respectively 0 The corners of the left and right ends of the beam on the P plane can be obtained
And &>
Left end couple on P plane
The bending line equation and the end corner of the beam under the combined action of the axial load P specify that the point with a large eta value on the beam section is compressed to be positive:
in the plane P, the deflection and the beam end corner under the combined action of the end force couple and the axial load P are in a nonlinear relation, and when the P is not changed, the deflection and the beam end corner and the axial load P are in a linear relation with the end force couple;
on a Q plane, taking a left support of the span as a coordinate system origin O, taking the connection direction of the left support and the right support as a xi axis direction, rotating the xi axis counterclockwise by 90 degrees, namely, taking the upward direction as a zeta axis direction, establishing a Q plane local coordinate system xi zeta, and obtaining a deflection line equation and an end corner calculation formula under the combined action of various transverse loads and axial loads in the Q plane by applying the same analysis method in a P plane;
the step 23 includes:
1) Calculating initial additional rotation angles generated by initial relative displacement of two ends of each bridge,
in a P plane coordinate system oxz or a Q plane coordinate system oxy, the two end corners of the straight beam are taken as the sum of the corner of the beam in a local coordinate system and the corner of the local coordinate system relative to the P or Q plane coordinate system, wherein in the P plane, the initial additional corner generated by the initial relative displacement of the supports at the two ends of the ith cross beam
Comprises the following steps:
in the Q plane, the initial additional corner generated by the initial relative displacement of the supports at the two ends of the ith span beam
Comprises the following steps:
in the formulae (17) and (18), x i-1 、x i Respectively are coordinate values of the ith span beam left and right supports on the x axis;
2) Solving a three-bending-moment equation set of the tubular column,
for the ith support in the P plane, the left side and the right side of the ith support are respectively an ith span beam and an (i + 1) th span beam, and according to the continuity condition that the corners of the two side beams of the support are equal, the three bending moment equation set of the bottom drilling tool assembly in the P plane is obtained as follows:
in formula (19), M i，p The internal bending moment of the beam at the ith support on the plane P;I i moment of inertia for the ith span;
the additional corner is calculated by the relative displacement of the supports at the two ends of the ith span beam on the P plane; theta T,P The projection angle of the included angle between the axis direction of the well hole at the upper tangent point and the x direction in the bottom coordinate system on the P plane is shown; Δ L i Is the length of the ith span, Δ L i ＝L i -L i-1 ；
P i Representing the average axial direction within the ith span,
q i，P for a component in the P-plane of the load distributed transversely of the i-th cross beam>
α i Representing the well angle at the ith bearing; w is a i The weight of the ith span beam per meter in the slurry; the meaning of the other parameters is analogized or the same as before;
according to the boundary conditions of the drill bit or the guide shoe and the upper tangent point on the P plane, the following conditions are provided:
M 0,P ＝0 (20)
M n,P ＝E·I n ·k αT (21)
in the formula (21), k αT The rate of change of well deviation at the tangent point;
equation set (19) has a total of n unknowns M i，P (i =1to n-1) and L n There are n equations to solve the bending moment M of each support on the P plane i，P (i =1to n-1) and the length of the last span L n ；
For the ith support in the Q plane, the left side and the right side of the support are also dividedObtaining a three bending moment equation set of the bottom drilling tool assembly in the Q plane according to the continuity condition that the rotation angles of the two side beams of the support are equal; due to the distributed load q i ， Q =0, the system of three bending moments equations for the bottom hole assembly in the Q plane is therefore simplified as:
in the formula, the meaning of the parameters is analogized or the same as that of the parameters;
depending on the boundary conditions at the drill bit and at the point of tangency on the Q-plane, there are:
M 0,Q ＝0 (23)
M n,Q ＝E·I n ·k φT sinα T (24)
in formula (24), k φT Is the rate of change of orientation at the tangent point; alpha is alpha T Is the well angle at the tangent point;
then the system of equations (19) has n-1 unknowns M in total i，P (i =1to n-1) with n-1 equations, solving the bending moment M at each support on the Q plane i，Q (i＝1to n-1)；
Said step 24 comprises:
1) The judgment of the new contact point is carried out,
for the ith straight spanning beam, the maximum deflection eta on the P plane i,m And maximum deflection ζ on Q plane i,m Calculated according to equations (25) and (26), respectively:
judging whether the pipe column and the well wall generate new contact, and checking whether the maximum deflection of the beam column between the two supports exceeds the maximum range, wherein the criterion of the new contact point is as follows:
in the formula, R is the average curvature radius of the well section where the span beam is located; omega is the angle which the plane rotates to the inclined plane circular arc plane of the well section where the span beam is located by taking the x coordinate axis as a rotating shaft, and if a new contact point is generated, a new constraint point is added to start calculation from the first step again;
2) The calculation of the contact force and the frictional resistance at the constraint points,
after the magnitude of the bending moment of the beam at each support on a P, Q plane is obtained, the magnitude of the supporting force at each support is calculated as follows:
3) The next iteration is to calculate the relative displacement of the constraint points,
according to the calculated supporting force of each support on the P, Q plane, the relative displacement of the constraint point of the next iteration can be obtained:
δz i j ＝δz i j-1 -N i,P K s (30)
δy i j ＝δy i j-1 -N i,Q K s (31)
in the formulas (30) and (31), ks is the elastic stiffness of the virtual spring, N/m;
the step 25 comprises:
1) It is determined whether the constraining point is a true contact point,
if the outer diameter of the tubular column at the ith constraint point is assumed to be SD i Borehole diameter of D w (L i ) Then when
Indicating that the pipe column at the constraint point is contacted with the well wall in the direction with large z value,
when/is>
Represents that the pipe column at the constraint point is contacted with the well wall in the direction with small z value, and is pressed against the well wall>
When/is>
Represents that the pipe column at the constraint point is contacted with the well wall in the direction with the large y value>
And when>
Represents that the pipe column at the constraint point is contacted with the well wall in the direction with small y value>
/>
If all the constraint points are either contact force zero or contact with the well wall, ending the iteration process; otherwise, calculating from the first step according to the position of the new constraint point;
2) The calculation of the frictional resistance of the pipe column,
if all the constraint points are in contact with the well wall or the contact force is zero and no new contact point exists, calculating the positive pressure N at each constraint point i Harmony frictional resistance F i ：
F i ＝μ(L i )·N i (33)
Calculating new axial force distribution in the casing string according to the frictional resistance at each constraint point, calculating again until the calculation results of two adjacent times are within a given error range, finally obtaining the frictional resistance at each constraint point, and obtaining the frictional resistance of the whole pipe column after accumulation;
step 3, utilizing field logging data, and reversely calculating friction coefficient according to different parameters aiming at different working conditions of sliding drilling and rotary drilling;
and 4, analyzing influence factors of the running friction of the bent well section pipe column by using the model, and performing comparative analysis on the running resistance of the high-rigidity drifting drill column and the thick-wall casing.
2. The method of claim 1, wherein step 1 comprises:
step 11, making a simplifying assumption on the descending of the directional well string in the complex stratum;
and step 12, designating the part with the relatively larger diameter on the tubular column as a contact point, and establishing a tubular column longitudinal and transverse bending continuous beam model containing a virtual contact point.
3. The method of claim 2, wherein the simplifying assumption of step 11 comprises:
1) The pipe column is a small elastic deformation system;
2) The well wall is a rigid body, the well hole is a bending cylinder taking the axis of the well hole as the center, the inner diameter of the cylinder is kept constant in sections, and the size of the cylinder does not change along with time;
3) Using each part with larger relative diameter on the pipe column and appointed points at intervals of a certain length as constraint points, wherein the constraint points are real contact points and/or virtual contact points which are not in contact with the well wall, and the parts with larger relative diameter comprise joints, couplings and centralizers;
4) The effect of the vibration is not taken into account.
4. The method of claim 1, wherein step 3 comprises:
step 31, determining whether an analysis point is data in a sliding drilling mode or data in a rotary drilling mode according to whether the rotating speed parameter is zero or not and whether the wellhead torque is less than 3 kN.m or not;
step 32, removing transition points and problem points between the two modes;
step 33, calculating the friction coefficient reversely according to the bit pressure and the hook load aiming at the sliding drilling working condition; and (4) aiming at the rotary drilling working condition, reversely calculating the friction coefficient according to the torque of the drill bit and the torque of the wellhead.
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