CN105239944A - Method for additionally installing centralizer for complex borehole trajectory - Google Patents

Abstract

The invention discloses a complex borehole trajectory centralizer installing method, which comprises the following steps: applying a cubic spline interpolation calculation method, and taking a preset interpolation step length to carry out interpolation calculation on the actually measured track data of a well section to obtain a well inclination angle and an azimuth angle of any well depth on the well section; determining the configuration interval of the centralizer based on the inclination angle and the azimuth angle of any well depth on the well section; and determining the mounting positions and the number of the centralizers on the sucker rod based on the configuration intervals of the centralizers. The invention reduces the using amount of the centralizers to the maximum extent, fully protects the oil pipe and the sucker rod, effectively prolongs the pump inspection period of the oil well and reduces the operation cost.

Description

Method for additionally installing centralizer for complex borehole trajectory

Technical Field

The invention relates to the technical field of crude oil exploitation, in particular to a method for additionally installing a centralizer for a complex well track.

Background

With the continuous deepening of the exploration and development of oil fields and the continuous improvement of the drilling technical level, the development of directional wells and horizontal wells becomes an important trend for efficiently developing oil and gas resources, the oil pumping unit rod pump oil extraction mode is generally adopted in land oil fields in China, and good economic benefits and good development prospects are displayed.

The mechanical behavior of the sucker rod string in a well bore of the directional well is more complex than that in a vertical well bore due to the fact that the directional well and the horizontal well have larger well inclination angle and full angle change rate, the sucker rod string in the directional well moves up and down along with a suspension point of a pumping unit, meanwhile, the sucker rod string and an oil pipe are in contact friction, and meanwhile, the problems of eccentric wear and breaking of the sucker rod string are serious along with transverse bending, spiral coupling deformation and the like, the stability of the system is greatly reduced, and the pump detection period is shortened.

Aiming at the eccentric wear problem of the sucker rod and the oil pipe, the prior art mainly adopts the mode that a hoop type or an injection molding type centralizer is arranged at a specific position of the sucker rod, so that the sucker rod is prevented from contacting the oil pipe to the maximum extent, and the purpose of protecting the sucker rod and the oil pipe is achieved. The design method of the installation position of the sucker rod centralizer mainly adopts two design methods at present:

the method adopts a compression bar stable Euler formula to calculate, determines the installation position of the sucker rod string centralizer according to the load at the bottom end of the sucker rod string, ensures that the sucker rod string has equal bending rigidity and is not unstable when being pressed, but aims at preventing the sucker rod from being bent when being pressed between the centralizers, technically obtains the dense installation space of the centralizers, has over-safe design, increases the installation quantity of the centralizers, increases the uplink and downlink frictional resistance of the rod string and the liquid flow resistance of produced liquid in an oil pipe, increases the load of the rod string and shortens the service life of the rod string.

Secondly, a method for designing the position of a centralizer of a sucker rod string of a directional well (patent application No. 201110196790.1) is characterized in that the method adopts a finite element node iteration method to calculate the configuration of the three-dimensional space of the sucker rod string in a well bore, and the possible contact point position is calculated to be used as the position of the centralizer; the method adopts a finite element iterative calculation method, the solution of node displacement is complex, meanwhile, the mechanical equation is only based on the whole load of the indicator diagram of the sucker rod and the three-dimensional characteristics of the well track, the influence of the neutral point at the lower part of the rod column on the change of the spatial form of the rod column is not considered, the calculated contact area of the sucker rod and the oil pipe has deviation from the actual contact position, and the eccentric wear prevention effect of the centralizer is influenced to a certain extent.

Disclosure of Invention

The embodiment of the application provides a complex well track centralizer installing method, according to well track measured data and the axial and radial load of a rod string, consider the bending that the rod string produced by well track change, consider the instability below the neutral point of rod string descending simultaneously, receive the contact that the oil pipe restraint produced, and combine the actual length of sucker rod to carry out the design of the reasonable distribution point position of centralizer, furthest reduces the use quantity of centralizer, fully protects oil pipe and sucker rod, effectively prolongs the oil well pump inspection cycle, and reduces the operating cost.

The application provides a complex borehole trajectory centralizer installing method, which comprises the following steps:

applying a cubic spline interpolation calculation method, and taking a preset interpolation step length to carry out interpolation calculation on the actually measured track data of a well section to obtain a well inclination angle and an azimuth angle at any well depth on the well section;

determining the configuration interval of the centralizer based on the well inclination angle and the azimuth angle of any well depth on the well section;

and determining the mounting positions and the number of the centralizers on the sucker rod based on the configuration intervals of the centralizers.

Preferably, the applying a cubic spline interpolation calculation method, which performs interpolation calculation on measured trajectory data of a well section by using a preset interpolation step length, to obtain a well angle and an azimuth angle at any well depth on the well section, includes:

setting a group of orderly measuring points on a certain section [ a, b ] of a known directional well;

well depth: a ═ x₀＜x₁＜x₂.......＜x_N＝b；

Corresponding angle α₀,α₁,α₂,......α_N；

The corresponding azimuth angle is:

constructing cubic splines of the well inclination angle and the azimuth angle:

$\mathrm{\α}\left(x\right)=\frac{M_{k-1}{\left(x_k-x\right)}^3}{6L_k}+\frac{M_k{\left(x-x_{k-1}\right)}^3}{6L_k}+\left(\frac{{\mathrm{\α}}_k}{L_k}-\frac{M_k{L}_k}{6}\right)\left(x-x_{k-1}\right)+\left(\frac{{\mathrm{\α}}_{k-1}}{L_k}-\frac{M_{k-1}{L}_k}{6}\right)\left(x_k-x\right)$

wherein k is 1, 2, 3 … …, N, the measurement point number;

L_kmeasuring the length of the segment, L_k＝x_k-x_k-1；

x is the well depth at the interpolation point, which is also a preset difference step length;

n is the number of measuring points;

x_k,x_k-1-the well depth of two adjacent measuring points;

α_k,α_k-1-the well inclination angle of two adjacent measuring points;

-azimuth angle of two adjacent measurement points;

establishing M_K、m_kThe system of linear equations of:

M_k＝α"(x_k)

$\left[\begin{array}{ccccccc}2& {\mathrm{\λ}}_0& 0& 0& \mathrm{...}& 0& 0\\ {\mathrm{\μ}}_1& 2& {\mathrm{\λ}}_1& 0& \mathrm{...}& 0& 0\\ 0& {\mathrm{\μ}}_2& 2& {\mathrm{\λ}}_2& \mathrm{...}& 0& 0\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ 0& 0& 0& {\mathrm{\μ}}_{N-1}& \mathrm{...}& 2& {\mathrm{\λ}}_{N-1}\\ 0& 0& 0& 0& \mathrm{...}& {\mathrm{\μ}}_N& 2\end{array}\right]\left[\begin{array}{c}{M}_0\\ M_1\\ M_2\\ .\\ .\\ .\\ M_{N-1}\\ M_N\end{array}\right]=\left[\begin{array}{c}{D}_0\\ D_1\\ D_2\\ .\\ .\\ .\\ D_{N-1}\\ D_N\end{array}\right]$

$\left[\begin{array}{ccccccc}2& {\mathrm{\λ}}_0& 0& 0& \mathrm{\Λ}& 0& 0\\ {\mathrm{\μ}}_1& 2& {\mathrm{\λ}}_1& 0& \mathrm{\Λ}& 0& 0\\ 0& {\mathrm{\μ}}_2& 2& {\mathrm{\λ}}_2& \mathrm{\Λ}& 0& 0\\ \mathrm{\Λ}& \mathrm{\Λ}& \mathrm{\Λ}& 2& \mathrm{\Λ}& \mathrm{\Λ}& \mathrm{\Λ}\\ 0& 0& 0& {\mathrm{\μ}}_{N-1}& \mathrm{\Λ}& 2& {\mathrm{\λ}}_{N-1}\\ 0& 0& 0& 0& \mathrm{\Λ}& {\mathrm{\μ}}_N& 2\end{array}\right]\left[\begin{array}{c}{m}_0\\ m_1\\ m_3\\ L\\ m_{N-1}\\ m_N\end{array}\right]=\left[\begin{array}{c}{d}_0\\ d_1\\ d_2\\ L\\ d_{N-1}\\ d_N\end{array}\right]$

$D_k=6\left(\frac{\frac{{\mathrm{\α}}_{k+1}-{\mathrm{\α}}_k}{L_{k+1}}-\frac{{\mathrm{\α}}_k-{\mathrm{\α}}_{k-1}}{L_k}}{L_k+L_{k+1}}\right)$

solving by adopting a catch-up method, and solving the solution M_i,m_i(i ═ o, 1, … …, N) are substituted into α (x) and α (x) respectivelyIn the expression of (1), find [ a, b ]]Angle of inclination and azimuth at any well depth on the interval.

Preferably, the determining the configured interval of the centralizer based on the inclination angle and the azimuth angle of any well depth on the well section comprises:

determining the bending deformation of the sucker rod column section on the dog-leg plane of the shaft based on the well inclination angle and the azimuth angle of any well depth on the well section;

determining the bending deformation of the sucker rod column section in a plane perpendicular to the plane of the dog leg on the basis of the well inclination angle and the azimuth angle of any well depth on the well section;

determining the bending deformation of the sucker rod column section in three dimensions based on the bending deformation of the sucker rod column section in a dog leg plane of a shaft and the bending deformation of the sucker rod column section in a plane perpendicular to the dog leg plane;

and determining the configuration interval of the centralizer based on the bending deformation of the sucker rod column section in three dimensions.

Preferably, the determining the bending deformation of the sucker rod column section in the dog-leg plane of the well bore based on the inclination angle and the azimuth angle of any well depth on the well section comprises:

the bending deformation of the sucker rod column section on the dog leg plane of the shaft: ${\mathrm{\δ}}_{dp}=\left(\frac{N_{dp}{L}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)\left(\frac{u^2}{2}-\frac{u\·chu-u}{shu}\right)$

in the formula, $u=\sqrt{\frac{{\mathrm{FL}}^2}{4EJ}}$

N_dp＝q'_rLcosγ_n+2Fsin(β/2)；

f is the axial force of the lower end of the sucker rod string;

γ_n-the angle between the shaft principal normal direction and the gravity vector;

beta-the rate of change of the angle;

l is the configuration interval of the centralizer;

e-modulus of elasticity of steel;

qr-weight of sucker rod in liquid per unit length;

$\sin \frac{\mathrm{\β}}{2}=\sqrt{{\sin }^2\left(\frac{{\mathrm{\α}}_{i+1}-{\mathrm{\α}}_i}{2}\right)+{\sin }^2\left(\frac{{\mathrm{\φ}}_{i+1}-{\mathrm{\φ}}_i}{2}\right){\mathrm{sin\α}}_i{\mathrm{sin\α}}_{i+1}};$

${\mathrm{cos\γ}}_n=\sin \left(\frac{{\mathrm{\α}}_{i+1}-{\mathrm{\α}}_i}{2}\right)\sin \left(\frac{{\mathrm{\α}}_{i+1}+{\mathrm{\α}}_i}{2}\right)/\sin \left(\frac{\mathrm{\β}}{2}\right);$

α_i、φ_i-the angle of inclination and azimuth of the upper end of the rod string;

α_i+1、φ_i+1-the lower end of the rod string is in angle and azimuth;

i＝0、1、2、3……N。

preferably, the determining the bending deformation of the sucker rod column section in the plane perpendicular to the dogleg plane based on the inclination angle and the azimuth angle of any well depth on the well section comprises:

the bending deformation of the sucker rod column section in the plane perpendicular to the plane of the dog leg:

${\mathrm{\δ}}_p=\left(\frac{N_p{L}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)\left(\frac{u^2}{2}-\frac{u\·chu-u}{shu}\right)$

in the formula, N_p＝q'_rLcosγ₀

γ o is the angle between the double normals of the wellbore curve and the gravity vector;

${\mathrm{cos\γ}}_0=\frac{{\mathrm{sin\α}}_i{\mathrm{sin\α}}_{i+1}sin({\mathrm{\φ}}_{i+1}-{\mathrm{\φ}}_i)}{\sin \mathrm{\β}};$

e-modulus of elasticity of steel;

j-the inertia distance of the cross section area of the sucker rod to the mandrel.

Preferably, the determining the bending deformation of the sucker rod string section in three dimensions based on the bending deformation of the sucker rod string section in the dog leg plane of the well bore and the bending deformation of the sucker rod string section in the plane perpendicular to the dog leg plane comprises:

the bending deformation in three dimensions is: ${\mathrm{\δ}}_i=\sqrt{{\mathrm{\δ}}_{dp}^2+{\mathrm{\δ}}_p^2}=\left(\frac{{\mathrm{NL}}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)\left(\frac{u^2}{2}-\frac{u\·chu-u}{shu}\right)$

in the formula, $N=\sqrt{N_{dp}^2+N_p^2}.$

preferably, the determining the configuration interval of the centralizer based on the bending deformation of the sucker rod string section in three dimensions comprises:

based on inequalityL obtained by solving is the configuration space of the centralizers of different well sections;

in the formula (d)_g-tubing diameter;

d_r-sucker rod diameter.

Preferably, the determining the installation positions and the number of the centralizers on the sucker rod based on the configuration intervals of the centralizers comprises:

in the well section with L less than 4m, each sucker rod is additionally provided with 3 centralizers, and two ends and the middle of the sucker rod are respectively additionally provided with 1 centralizer;

in the well section with the length of L being more than 4m and less than 8m, each sucker rod is additionally provided with 2 centralizers, and two ends of each sucker rod are respectively additionally provided with 1 centralizer;

in the well section with the L being more than 8m and less than 16m, 1 centralizer is additionally arranged on each sucker rod, and a centralizer is additionally arranged near a sucker rod coupling;

in the well section with L more than 16m, 2 centralizers are additionally arranged every other sucker rod;

the weight rods are matched below the neutral point, and a centralizing short section is additionally arranged between every two weight rods.

One or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:

1. in the embodiment of the application, the interval of the actually measured well track data is generally 30 meters, the actual length of the sucker rod is about 8 meters, the actually measured well track data cannot accurately describe each sucker rod, the interpolation step length can be defined by a cubic spline interpolation method, the track parameters of the sucker rod in a three-dimensional space can be accurately calculated, and the calculation errors of the axial load and the radial load are reduced.

2. In the embodiment of the application, the spatial form of the sucker rod in the well track is described by using a minimum curvature method, the deformation of the sucker rod in a curve inclined plane and an orthogonal inclined plane is obtained, the maximum deformation of the sucker rod is considered to be smaller than the constraint radius of a pipe column, the solving result is more practical, and the compression bar stable Euler method is based on the premise that the sucker rod column is not unstable, and the placement position of the centralizer is more dense.

3. In this application embodiment, centralizer configuration interval design, the influence of considering the sucker rod coupling is installed the position design additional to the centralizer comparatively rationally, comparatively coincide with the reality.

4. In the embodiment of the application, the calculation equation is a linear equation, and compared with a finite element kinetic equation, the calculation complexity is low and the calculation efficiency is high.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.

FIG. 1 is a flow chart of a method for installing a complex wellbore trajectory centralizer according to an embodiment of the present application;

FIG. 2 is a graph of wellbore trajectory space in an embodiment of the present application;

FIG. 3 is a schematic view of each sucker rod with 3 centralizers;

FIG. 4 is a schematic view of an embodiment of the present application in which 2 centralizers are added to each sucker rod;

FIG. 5 is a schematic view of the embodiment of the present application in which 1 centralizer is added to each sucker rod.

Detailed Description

The embodiment of the application provides a complex well track centralizer installing method, according to well track measured data and the axial and radial load of a rod string, consider the bending that the rod string produced by well track change, consider the instability below the neutral point of rod string descending simultaneously, receive the contact that the oil pipe restraint produced, and combine the actual length of sucker rod to carry out the design of the reasonable distribution point position of centralizer, furthest reduces the use quantity of centralizer, fully protects oil pipe and sucker rod, effectively prolongs the oil well pump inspection cycle, and reduces the operating cost.

In order to better understand the technical solution, the technical solution will be described in detail with reference to the drawings and the specific embodiments.

The embodiment provides a method for installing a centralizer for a complex borehole trajectory, as shown in fig. 1, including:

step S101: and (3) applying a cubic spline interpolation calculation method, and taking a preset interpolation step length to perform interpolation calculation on the measured track data of a well section to obtain the well inclination angle and the azimuth angle of any well depth on the well section.

Specifically, the detailed procedure of step S101 is as follows:

a certain section [ a, b ] of the known directional well is provided with a group of ordered measuring points:

well depth: a ═ x₀＜x₁＜x₂.......＜x_N＝b

The corresponding ground well inclination angle and azimuth angle are:

angle of inclination α₀,α₁,α₂,......α_N

Azimuth angle:

constructing cubic splines of the well inclination angle and the azimuth angle:

$\mathrm{\α}\left(x\right)=\frac{M_{k-1}{\left(x_k-x\right)}^3}{6L_k}+\frac{M_k{\left(x-x_{k-1}\right)}^3}{6L_k}+\left(\frac{{\mathrm{\α}}_k}{L_k}-\frac{M_k{L}_k}{6}\right)\left(x-x_{k-1}\right)+\left(\frac{{\mathrm{\α}}_{k-1}}{L_k}-\frac{M_{k-1}{L}_k}{6}\right)\left(x_k-x\right)$

wherein k is 1, 2, 3 … …, N, the measurement point number;

L_kmeasuring the length of the segment, L_k＝x_k-x_k-1；

x is the well depth at the interpolation point, which is also the difference step length;

n is the number of measuring points;

x_x,x_k-1-well depth of two adjacent measuring points, unit: rice;

α_k,α_k-1-the well inclination angle of two adjacent measuring points;

-azimuth angle of two adjacent measuring points.

Establishing M_K、m_kThe system of linear equations of:

M_k＝α"(x_k)

$\left[\begin{array}{ccccccc}2& {\mathrm{\λ}}_0& 0& 0& \mathrm{...}& 0& 0\\ {\mathrm{\μ}}_1& 2& {\mathrm{\λ}}_1& 0& \mathrm{...}& 0& 0\\ 0& {\mathrm{\μ}}_2& 2& {\mathrm{\λ}}_2& \mathrm{...}& 0& 0\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ 0& 0& 0& {\mathrm{\μ}}_{N-1}& \mathrm{...}& 2& {\mathrm{\λ}}_{N-1}\\ 0& 0& 0& 0& \mathrm{...}& {\mathrm{\μ}}_N& 2\end{array}\right]\left[\begin{array}{c}{M}_0\\ M_1\\ M_2\\ .\\ .\\ .\\ M_{N-1}\\ M_N\end{array}\right]=\left[\begin{array}{c}{D}_0\\ D_1\\ D_2\\ .\\ .\\ .\\ D_{N-1}\\ D_N\end{array}\right]$

$\left[\begin{array}{ccccccc}2& {\mathrm{\λ}}_0& 0& 0& \mathrm{\Λ}& 0& 0\\ {\mathrm{\μ}}_1& 2& {\mathrm{\λ}}_1& 0& \mathrm{\Λ}& 0& 0\\ 0& {\mathrm{\μ}}_2& 2& {\mathrm{\λ}}_2& \mathrm{\Λ}& 0& 0\\ \mathrm{\Λ}& \mathrm{\Λ}& \mathrm{\Λ}& 2& \mathrm{\Λ}& \mathrm{\Λ}& \mathrm{\Λ}\\ 0& 0& 0& {\mathrm{\μ}}_{N-1}& \mathrm{\Λ}& 2& {\mathrm{\λ}}_{N-1}\\ 0& 0& 0& 0& \mathrm{\Λ}& {\mathrm{\μ}}_N& 2\end{array}\right]\left[\begin{array}{c}{m}_0\\ m_1\\ m_3\\ L\\ m_{N-1}\\ m_N\end{array}\right]=\left[\begin{array}{c}{d}_0\\ d_1\\ d_2\\ L\\ d_{N-1}\\ d_N\end{array}\right]$

$D_k=6\left(\frac{\frac{{\mathrm{\α}}_{k+1}-{\mathrm{\α}}_k}{L_{k+1}}-\frac{{\mathrm{\α}}_k-{\mathrm{\α}}_{k-1}}{L_k}}{L_k+L_{k+1}}\right)$

wherein, α'₀、α′_NAndis determined by the boundary conditions, where fixed boundary conditions are chosen. Solving the above equation set type diagonal equation set by pursuit method_i,m_i(i ═ o, 1, … …, N) are substituted into α (x) and α (x) respectivelyIn the expression of (1), the value of [ a, b ] can be obtained]Angle of inclination and azimuth at any well depth on the interval.

Step S102: and determining the configuration interval of the centralizer based on the well inclination angle and the azimuth angle of any well depth on the well section.

Specifically, step S102 specifically includes:

determining the bending deformation of the sucker rod column section on the dog-leg plane of the shaft based on the well inclination angle and the azimuth angle of any well depth on the well section;

determining the bending deformation of the sucker rod column section in a plane perpendicular to the plane of the dog leg on the basis of the well inclination angle and the azimuth angle of any well depth on the well section;

determining the bending deformation of the sucker rod column section in three dimensions based on the bending deformation of the sucker rod column section in a dog leg plane of a shaft and the bending deformation of the sucker rod column section in a plane perpendicular to the dog leg plane;

and determining the configuration interval of the centralizer based on the bending deformation of the sucker rod column section in three dimensions.

In more detail, in a three-dimensional borehole, axial force causes the sucker rod to bend and deform in an inclined spatial plane, and the bending caused by the weight of the sucker rod column always faces downwards, the bending deformation of the sucker rod column section is formed by two vectors of bending deformation of a dogleg plane of a shaft and bending deformation of a plane perpendicular to the dogleg plane, and the bending deformation is respectively caused by the axial force and the gravity of the sucker rod column (as shown in figure 2).

(1) The bending deformation of the sucker rod column section on the dog leg plane of the shaft:

${\mathrm{\δ}}_{dp}=\left(\frac{N_{dp}{L}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)\left(\frac{u^2}{2}-\frac{u\·chu-u}{shu}\right)$

in the formula, $u=\sqrt{\frac{{\mathrm{FL}}^2}{4EJ}}$

N_dp＝q'_rLcosγ_n+2Fsin(β/2)；

f is axial force of the lower end of the sucker rod string, unit: newton;

γ_n-the angle between the shaft principal normal direction and the gravity vector;

beta-the rate of change of the angle;

l is the configuration interval of the centralizer;

e is the elastic modulus of steel, 2.06 multiplied by 10^11 Pa;

qr-weight of sucker rod in liquid per unit length, unit: newton/m;

$\sin \frac{\mathrm{\β}}{2}=\sqrt{{\sin }^2\left(\frac{{\mathrm{\α}}_{i+1}-{\mathrm{\α}}_i}{2}\right)+{\sin }^2\left(\frac{{\mathrm{\φ}}_{i+1}-{\mathrm{\φ}}_i}{2}\right){\mathrm{sin\α}}_i{\mathrm{sin\α}}_{i+1}}$

${\mathrm{cos\γ}}_n=\sin \left(\frac{{\mathrm{\α}}_{i+1}-{\mathrm{\α}}_i}{2}\right)\sin \left(\frac{{\mathrm{\α}}_{i+1}+{\mathrm{\α}}_i}{2}\right)/\sin \left(\frac{\mathrm{\β}}{2}\right)$

alpha i and phi i are the angle of inclination and the azimuth angle of the upper end of the sucker rod string;

alpha i +1 and phi i +1, namely the well inclination angle and the azimuth angle at the lower end of the sucker rod string;

i＝0、1、2、3……N。

(2) the bending deformation of the sucker rod column section in the plane perpendicular to the plane of the dog leg:

${\mathrm{\δ}}_p=\left(\frac{N_p{L}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)\left(\frac{u^2}{2}\right)\left(\frac{u\·chu-u}{shu}\right)$

in the formula, N_p＝q'_rLcosγ₀

γ o is the angle between the double normals of the wellbore curve and the gravity vector;

${\mathrm{cos\γ}}_0=\frac{{\mathrm{sin\α}}_i{\mathrm{sin\α}}_{i+1}sin({\mathrm{\φ}}_{i+1}-{\mathrm{\φ}}_i)}{\sin \mathrm{\β}};$

e is the elastic modulus of steel, 2.06 multiplied by 10^11 Pa;

j-the inertia distance of the cross section area of the sucker rod to the mandrel;

alpha i and phi i are the angle of inclination and the azimuth angle of the upper end of the sucker rod string;

alpha i +1 and phi i +1, namely the well inclination angle and the azimuth angle at the lower end of the sucker rod string;

i＝0、1、2、3……N。

in three-dimensional well bores, the sucker rod string section is bent and deformed by_dpAnd_psuperimposed, since the two are perpendicular to each other, the bending deformation in three dimensions is:

${\mathrm{\δ}}_i=\sqrt{{\mathrm{\δ}}_{dp}^2+{\mathrm{\δ}}_p^2}=\left(\frac{{\mathrm{NL}}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)\left(\frac{u^2}{2}-\frac{u\·chu-u}{shu}\right)$

in the formula $N=\sqrt{N_{dp}^2+N_p^2};$

In order to ensure that the sucker rod string and the oil pipe are not contacted, the bending deformation of the sucker rod string between the two centralizers is less than the radial clearance between the sucker rod string and the wall of the oil pipe,

namely: ${\mathrm{\δ}}_t\≤\frac{1}{2}(d_g-d_r)$

in the formula d_g-tubing diameter, mm;

d_r-sucker rod diameter, mm.

L obtained by solving according to the inequality is the configuration space of the centralizers of different well sections, and the configuration space of the centralizers is also unequal due to different bending deformation and stress of the rod columns of different well sections.

Step S103: and determining the mounting positions and the number of the centralizers on the sucker rod based on the configuration intervals of the centralizers.

Specifically, the centralizer is additionally designed according to the L obtained through calculation. The length of each sucker rod is 8-9 meters, the sucker rods are connected by a coupling, the mounting position of the centralizer is influenced by the coupling, and the coupling is a main abrasion part of the rod pipe, so the actual mounting position of the centralizer is mainly in the middle of the rod body between the two couplings and the vicinity of the coupling, and the configuration of the centralizer needs to be reasonably designed by combining a calculation result and well track parameters.

In the well section with L less than 4m, each sucker rod is additionally provided with 3 centralizers, and two ends and the middle of the sucker rod are respectively additionally provided with 1 centralizer; (as shown in FIG. 3);

in the well section with the length of L being more than 4m and less than 8m, each sucker rod is additionally provided with 2 centralizers, and two ends of each sucker rod are respectively additionally provided with 1 centralizer; (as shown in FIG. 4);

in the well section with the L being more than 8m and less than 16m, 1 centralizer is additionally arranged on each sucker rod, and a centralizer is additionally arranged near a sucker rod coupling; (as shown in FIG. 5);

in the well section with L more than 16m, 2 centralizers are additionally arranged every other sucker rod;

the supporting weight bars below the neutral point, and a centralizing short section is additionally arranged between every two weight bars.

Taking a certain well as an example, the three-dimensional wellbore trajectory parameters are shown in fig. 2, and the fluid production amounts are as follows: 32m/d, pump depth: 1600m, pole combination: h-stage phi 25mm × 360+ phi 22mm × 1040m + phi 28mm × 100m, pump diameter: 44mm, stroke: 6m, stroke frequency: 2.7 times/min.

Step S101: and (3) applying a cubic spline interpolation calculation method, and taking a preset interpolation step length to perform interpolation calculation on the measured track data of a well section to obtain the well inclination angle and the azimuth angle of any well depth on the well section.

The actual measurement data are shown in table 1.

TABLE 1

② interpolation data, step length 2m, the calculation result is shown in table 2.

TABLE 2

Step S102: and determining the configuration interval of the centralizer based on the well inclination angle and the azimuth angle of any well depth on the well section, wherein the specific data is shown in a table 3.

TABLE 3

Step S103: based on the configuration interval of the centralizers, the mounting positions and the number of the centralizers on the sucker rod are determined, and specific data are shown in table 4.

TABLE 4

The core of the method for installing the complex well track centralizer can be summarized into the following points:

(1) the parameter calculation of the well track adopts a spline interpolation method, and the change trend of the sucker rod string in the well is the same as the change of the well track.

(2) The centralizer configuration interval is calculated by adopting a method of dividing the sucker rod into micro-element sections in a three-dimensional space, calculating the spatial deformation of each micro-element section in a well track, and calculating the centralizer configuration interval by considering the contact distance of the sucker rod in an oil pipe.

(3) The centralizer configuration design considers the influence of the sucker rod coupling according to the calculation interval, and determines the actual position of the sucker rod installation centralizer.

The technical scheme in the embodiment of the application at least has the following technical effects or advantages:

1. in the embodiment of the application, the interval of the actually measured well track data is generally 30 meters, the actual length of the sucker rod is about 8 meters, the actually measured well track data cannot accurately describe each sucker rod, the interpolation step length can be defined by a cubic spline interpolation method, the track parameters of the sucker rod in a three-dimensional space can be accurately calculated, and the calculation errors of the axial load and the radial load are reduced.

2. In the embodiment of the application, the spatial form of the sucker rod in the well track is described by using a minimum curvature method, the deformation of the sucker rod in a curve inclined plane and an orthogonal inclined plane is obtained, the maximum deformation of the sucker rod is considered to be smaller than the constraint radius of a pipe column, the solving result is more practical, and the compression bar stable Euler method is based on the premise that the sucker rod column is not unstable, and the placement position of the centralizer is more dense.

3. In this application embodiment, centralizer configuration interval design, the influence of considering the sucker rod coupling is installed the position design additional to the centralizer comparatively rationally, comparatively coincide with the reality.

4. In the embodiment of the application, the calculation equation is a linear equation, and compared with a finite element kinetic equation, the calculation complexity is low and the calculation efficiency is high.

While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (8)

1. A complex borehole trajectory centralizer installing method is characterized by comprising the following steps:

applying a cubic spline interpolation calculation method, and taking a preset interpolation step length to carry out interpolation calculation on the actually measured track data of a well section to obtain a well inclination angle and an azimuth angle at any well depth on the well section;

determining the configuration interval of the centralizer based on the well inclination angle and the azimuth angle of any well depth on the well section;

and determining the mounting positions and the number of the centralizers on the sucker rod based on the configuration intervals of the centralizers.

2. The method of claim 1, wherein said applying a cubic spline interpolation method to interpolate trace measured data for a well interval at a predetermined interpolation step size to obtain a borehole angle and an azimuth at any depth on said well interval comprises:

setting a group of orderly measuring points on a certain section [ a, b ] of a known directional well;

well depth: a ═ x₀＜x₁＜x₂.......＜x_N＝b；

Corresponding angle α₀,α₁,α₂,......α_N；

The corresponding azimuth angle is:

constructing cubic splines of the well inclination angle and the azimuth angle:

$\mathrm{\α}\left(x\right)=\frac{M_{k-1}{(x_k-x)}^3}{6L_k}+\frac{M_k{(x-x_{k-1})}^3}{6L_k}+(\frac{{\mathrm{\α}}_k}{L_k}-\frac{M_k{L}_k}{6})(x-x_{k-1})+(\frac{{\mathrm{\α}}_{k-1}}{L_k}-\frac{M_{k-1}{L}_k}{6})(x_k-x)$

wherein k is 1, 2, 3 … …, N, the measurement point number;

L_kmeasuring the length of the segment, L_k＝x_k-x_k-1；

x is the well depth at the interpolation point, which is also a preset difference step length;

n is the number of measuring points;

x_k,x_k-1-the well depth of two adjacent measuring points;

α_k,α_k-1-the well inclination angle of two adjacent measuring points;

-azimuth angle of two adjacent measurement points;

establishing M_K、m_kThe system of linear equations of:

M_k＝α"(x_k)

$\left[\begin{array}{ccccccc}2& {\mathrm{\λ}}_0& 0& 0& ...& 0& 0\\ {\mathrm{\μ}}_1& 2& {\mathrm{\λ}}_1& 0& ...& 0& 0\\ 0& {\mathrm{\μ}}_2& 2& {\mathrm{\λ}}_2& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& {\mathrm{\μ}}_{N-1}& ...& 2& {\mathrm{\λ}}_{N-1}\\ 0& 0& 0& 0& ...& {\mathrm{\μ}}_N& 2\end{array}\right]\left[\begin{array}{c}{M}_0\\ M_1\\ M_2\\ .\\ .\\ .\\ M_{N-1}\\ M_N\end{array}\right]=\left[\begin{array}{c}{D}_0\\ D_1\\ D_2\\ .\\ .\\ .\\ D_{N-1}\\ D_N\end{array}\right]$

$\left[\begin{array}{ccccccc}2& {\mathrm{\λ}}_0& 0& 0& \mathrm{\Λ}& 0& 0\\ {\mathrm{\μ}}_1& 2& {\mathrm{\λ}}_1& 0& \mathrm{\Λ}& 0& 0\\ 0& {\mathrm{\μ}}_2& 2& {\mathrm{\λ}}_2& \mathrm{\Λ}& 0& 0\\ \mathrm{\Λ}& \mathrm{\Λ}& \mathrm{\Λ}& 2& \mathrm{\Λ}& \mathrm{\Λ}& \mathrm{\Λ}\\ 0& 0& 0& {\mathrm{\μ}}_{N-1}& \mathrm{\Λ}& 2& {\mathrm{\λ}}_{N-1}\\ 0& 0& 0& 0& \mathrm{\Λ}& {\mathrm{\μ}}_N& 2\end{array}\right]\left[\begin{array}{c}{m}_0\\ m_1\\ m_3\\ L\\ m_{N-1}\\ m_N\end{array}\right]=\left[\begin{array}{c}{d}_0\\ d_1\\ d_2\\ L\\ d_{N-1}\\ d_N\end{array}\right]$

$D_k=6\left(\frac{\frac{{\mathrm{\α}}_{k+1}-{\mathrm{\α}}_k}{L_{k+1}}-\frac{{\mathrm{\α}}_k-{\mathrm{\α}}_{k-1}}{L_k}}{L_k+L_{k+1}}\right)$

solving by adopting a catch-up method, and solving the solution M_i,m_i(i ═ o, 1, … …, N) are substituted into α (x) and α (x) respectivelyIn the expression of (1), find [ a, b ]]Angle of inclination and azimuth at any well depth on the interval.

3. The method of claim 2, wherein determining the configured spacing of the centralizers based on the angle of inclination and the azimuth at any well depth on the wellbore interval comprises:

determining the bending deformation of the sucker rod column section on the dog-leg plane of the shaft based on the well inclination angle and the azimuth angle of any well depth on the well section;

determining the bending deformation of the sucker rod column section in a plane perpendicular to the plane of the dog leg on the basis of the well inclination angle and the azimuth angle of any well depth on the well section;

determining the bending deformation of the sucker rod column section in three dimensions based on the bending deformation of the sucker rod column section in a dog leg plane of a shaft and the bending deformation of the sucker rod column section in a plane perpendicular to the dog leg plane;

and determining the configuration interval of the centralizer based on the bending deformation of the sucker rod column section in three dimensions.

4. The method of claim 3, wherein said determining the flexural deformation of the sucker rod string section in the dogleg plane of the wellbore based on the angle of inclination and azimuth at any well depth on said well section comprises:

the bending deformation of the sucker rod column section on the dog leg plane of the shaft: ${\mathrm{\δ}}_{dp}=\left(\frac{N_{dp}{L}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)(\frac{u^2}{2}-\frac{u\·chu-u}{shu})$

wherein, $u=\sqrt{\frac{{\mathrm{FL}}^2}{4EJ}}$

N_dp＝q'_rLcosγ_n+2Fsin(β/2)；

f is the axial force of the lower end of the sucker rod string;

γ_n-the angle between the shaft principal normal direction and the gravity vector;

beta-the rate of change of the angle;

l is the configuration interval of the centralizer;

e-modulus of elasticity of steel;

qr-weight of sucker rod in liquid per unit length;

$\sin \frac{\mathrm{\β}}{2}=\sqrt{{\sin }^2\left(\frac{{\mathrm{\α}}_{i+1}-{\mathrm{\α}}_i}{2}\right)+{\sin }^2\left(\frac{{\mathrm{\φ}}_{i+1}-{\mathrm{\φ}}_i}{2}\right){\mathrm{sin\α}}_i{\mathrm{sin\α}}_{i+1}};$

${\mathrm{cos\γ}}_n=sin\left(\frac{{\mathrm{\α}}_{i+1}-{\mathrm{\α}}_i}{2}\right)sin\left(\frac{{\mathrm{\α}}_{i+1}+{\mathrm{\α}}_i}{2}\right)/sin\left(\frac{\mathrm{\β}}{2}\right);$

α_i、φ_i-the angle of inclination and azimuth of the upper end of the rod string;

α_i+1、φ_i+1-the lower end of the rod string is in angle and azimuth;

i＝0、1、2、3……N。

5. the method of claim 4, wherein said determining the flexural deformation of the sucker rod string section in a direction plane perpendicular to the dogleg plane based on the angle of inclination and azimuth at any well depth on said well section comprises:

the bending deformation of the sucker rod column section in the plane perpendicular to the plane of the dog leg:

${\mathrm{\δ}}_p=\left(\frac{N_p{L}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)(\frac{u^2}{2}-\frac{u\·chu-u}{shu})$

wherein N is_p＝q'_rLcosγ₀

γ o is the angle between the double normals of the wellbore curve and the gravity vector;

${\mathrm{cos\γ}}_0=\frac{{\mathrm{sin\α}}_i{\mathrm{sin\α}}_{i+1}sin({\mathrm{\φ}}_{i+1}-{\mathrm{\φ}}_i)}{\sin \mathrm{\β}};$

e-modulus of elasticity of steel;

j-the inertia distance of the cross section area of the sucker rod to the mandrel.

6. The method of claim 5, wherein determining the flexural deformation of the sucker rod string section in three dimensions based on the flexural deformation of the sucker rod string section in a dogleg plane of the wellbore and the flexural deformation of the sucker rod string section in a direction perpendicular to the dogleg plane comprises:

the bending deformation in three dimensions is: ${\mathrm{\δ}}_t=\sqrt{{\mathrm{\δ}}_{dp}^2+{\mathrm{\δ}}_p^2}=\left(\frac{{\mathrm{NL}}^3}{384EJ}\right)\left(\frac{24}{u^4}\right)(\frac{u^2}{2}-\frac{u\·chu-u}{shu})$

wherein, $N=\sqrt{N_{dp}^2+N_p^2}.$

7. the method of claim 6, wherein determining the deployed spacing of the centralizers based on the bending deformation of the sucker rod string in three dimensions comprises:

based on inequalityL obtained by solving is the configuration space of the centralizers of different well sections;

wherein d is_g-tubing diameter;

d_r-sucker rod diameter.

8. The method of claim 7, wherein determining the installed locations and number of centralizers on a sucker rod based on the configured spacing of the centralizers comprises:

in the well section with L less than 4m, each sucker rod is additionally provided with 3 centralizers, and two ends and the middle of the sucker rod are respectively additionally provided with 1 centralizer;

in the well section with the length of L being more than 4m and less than 8m, each sucker rod is additionally provided with 2 centralizers, and two ends of each sucker rod are respectively additionally provided with 1 centralizer;

in the well section with the L being more than 8m and less than 16m, 1 centralizer is additionally arranged on each sucker rod, and a centralizer is additionally arranged near a sucker rod coupling;

in the well section with L more than 16m, 2 centralizers are additionally arranged every other sucker rod;

the weight rods are matched below the neutral point, and a centralizing short section is additionally arranged between every two weight rods.