CN115324538A - Perforation pipe string dynamic system and analysis method for oil and gas exploration - Google Patents
Perforation pipe string dynamic system and analysis method for oil and gas exploration Download PDFInfo
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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
- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
- E21B43/11—Perforators; Permeators
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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
- E21B17/00—Drilling rods or pipes; Flexible drill strings; Kellies; Drill collars; Sucker rods; Cables; Casings; Tubings
-
- 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
- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
- E21B43/11—Perforators; Permeators
- E21B43/116—Gun or shaped-charge perforators
- E21B43/117—Shaped-charge perforators
-
- 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
- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
- E21B43/11—Perforators; Permeators
- E21B43/119—Details, e.g. for locating perforating place or direction
- E21B43/1195—Replacement of drilling mud; decrease of undesirable shock waves
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
- G01L5/14—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring the force of explosions; for measuring the energy of projectiles
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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
- G01N3/30—Investigating strength properties of solid materials by application of mechanical stress by applying a single impulsive force, e.g. by falling weight
- G01N3/313—Investigating strength properties of solid materials by application of mechanical stress by applying a single impulsive force, e.g. by falling weight generated by explosives
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- 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
- G01N2203/0676—Force, weight, load, energy, speed or acceleration
-
- 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
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention discloses a perforation tubular column dynamic system and an analysis method for oil-gas exploration, wherein the system comprises an oil pipe hanger, a double male short section, a telescopic joint, an oil pipe, a safety joint, a packer, a sieve tube and a perforation gun; the packer is anchored on the inner wall of the casing and used for packing off the reservoir stratum; the perforating gun is suspended below the packer through an oil pipe and faces the reservoir layer in the position, and is used for launching the shaped perforating bullet inside the perforating gun. The perforating string system can be used for simulating and analyzing the influence of different factors on the safety performance of a perforating pipeline, so that risks are avoided in the actual exploitation process, the damage of instruments is avoided, and the service life of equipment is prolonged; the perforating string system and the analysis method are used for simulating the exploitation in special environments such as ultra-deep wells or tight shale gas wells, the parameters of the equipment can be adjusted in real time according to the simulation result to obtain the optimal configuration, the configuration of the equipment can be carried out by referring to the simulation parameters in actual engineering, and the exploitation efficiency is improved.
Description
Technical Field
The invention relates to the field of oil-gas exploration, in particular to a perforation tubular column dynamic system and an analysis method for oil-gas exploration.
Background
In recent years, as petroleum and natural gas resources are gradually lacked, the difficulty of exploitation is getting greater and greater, and the focus of oil and gas exploration gradually turns to unconventional and deep water. The perforation operation is called as 'near-door one-foot' in the field of petroleum and natural gas exploration and development, and the improvement and perfection of the perforation technology have a self-evident significance for the efficient exploitation of oil and gas reservoirs. Under the action of explosive charge, the downhole tubular column and the testing instrument can generate strong impact vibration. After detonating the index detonation charge, the formed jet penetrates the formation, and about 60-70% of the detonation energy is released to a narrow and long region of the well bore, loads the perforating gun in the form of impact load and causes the perforating string to vibrate. Energy is firstly transmitted upwards along the tubular column through the end part of the perforating gun, is transmitted to the packer after being buffered by the shock absorber, and is enhanced in reflection at the constraint part. When the energy generated by the high explosive in the gun is large enough, the perforating string can be violently vibrated and even plastically deformed. The large load at the packer may cause unsetting failure of the packer, and continued upward transmission of vibration may cause damage to the test instrument, resulting in inaccurate or even unavailable data acquisition. With the marching of oil and gas field development towards ultra-deep wells and dense shale gas wells, the perforating guns with longer length, higher density and larger loading capacity are required to be adopted, so that the working environment of the perforating string is more and more severe, and even buckling, fracture, separation and packer damage of the perforating string can be caused seriously. Whether the string is unstable, buckling breaks, the packer is unset, or the test instrument is damaged, the loss to production from the well is significant.
The prior art has the following technical problems:
(1) In the process of oil and gas field exploitation, the explosive action of the perforating bullet impacts the perforating gun, so that the perforating string is easy to deform;
(2) When the perforating string is exploited in special environments such as hard geology, deeper positions and the like, the common perforating string cannot bear the impact of perforating charges with larger dosage.
Disclosure of Invention
In order to solve the technical problems, the invention provides a perforation string dynamic system and an analysis method for oil and gas exploration.
The invention provides a perforating string dynamic system for oil-gas exploration, which comprises an oil pipe hanger, double male short joints, telescopic joints, an oil pipe, a safety joint, a packer, a sieve pipe and a perforating gun, wherein the oil pipe hanger is connected with the double male short joints; the packer is anchored on the inner wall of the casing and used for packing off the reservoir stratum; the perforating gun is suspended below the packer through an oil pipe and faces the reservoir layer in the position, and is used for launching the energy-collecting perforating bullet inside the perforating gun.
Furthermore, the perforating pipe column and the shaft are both circular in cross section, the axis of the perforating pipe column at the initial moment is coincident with the axis of the shaft, and an initial annular space exists between the perforating pipe column and the shaft.
The perforating string is further characterized by being a three-dimensional elastic beam, and the material and the geometric characteristics of the perforating string are uniform.
The shock absorber is a spring with rigidity and damping without mass and is used for bearing the axial and transverse impact loads of the perforating string.
The invention also provides a perforation pipe column dynamics analysis method for oil and gas exploration, which comprises the following steps:
s1, establishing a geodetic coordinate system and a local coordinate system of a perforating string, and calculating a dynamic equation of a three-dimensional space beam unit under the local coordinate system;
s2, converting the dynamic equation of the lower three-dimensional space beam unit with local coordinates into a beam unit dynamic equation under a geodetic coordinate system, and assembling the motion equations of all the beam units to obtain the motion equation of the whole perforating string;
s3, calculating detonation loads of the perforating string, and giving a detonation load at the position of each perforating charge and the bottom of the perforating gun according to an actual detonation sequence at a time interval of 0.0001S;
s4, calculating boundary conditions of the perforating string, including a top boundary condition, a bottom boundary condition and an initial condition, and taking the boundary conditions as initial values input into a perforating string dynamic system;
and S5, adding the impact and friction influence, and calculating the displacement, the transverse acceleration and the longitudinal acceleration of the perforating string by using a bending drill string dynamic system.
Further, step S1 includes the following substeps:
s101, dispersing the perforating string into n units, wherein each unit is provided with two nodes (n +1 nodes in total), each node has six degrees of freedom, and the six degrees of freedom comprise three translational degrees of freedom (u, v, w) and three rotational degrees of freedom (theta) x ，θ y ，θ z ) Establishing a geodetic coordinate system by taking a wellhead as an origin, a borehole axis as an x-axis and a downward direction as a positive direction;
s102, establishing a local coordinate system of the perforating string by taking the axis of the perforating string as an x axis and taking two transverse directions as a y axis and a z axis respectively;
s103, under the action of detonation load, based on Green-Lagrange strain and neglecting high-order small terms, and considering the collision between the perforating string and the inner wall of the casing pipe caused by the small annular space between the perforating string and the casing pipe, obtaining a dynamic equation of the beam unit:
wherein M is e Is a beam element mass matrix, C e Is a Rayleigh damping matrix, K e Matrix of cell stiffness, F e In the form of a force matrix of the unit nodes,
and
respectively the nodal velocity and acceleration, U, of the beam element e Is the nodal displacement of the beam element.
Further, step S2 includes the following substeps:
s201, converting a beam unit dynamic equation under a three-dimensional local coordinate into a beam unit dynamic equation under a geodetic coordinate system:
s202, assembling the motion equations of all the beam units to obtain the power equation of the whole perforating string:
wherein
U and F 'are matrix of speed, acceleration, displacement and external force of all nodes of the perforating string respectively, and M', C 'and K' are matrix of total mass, matrix of total damping and matrix of total displacement of the perforating string respectively.
Further, the step S3 of calculating the detonation load includes the following substeps:
s301, on the basis of an empirical formula of transient pressure peak value of shock wave formed by TNT explosion in an infinite water area, considering the actual working condition of bottom hole explosion of a perforating charge, performing LS-DANA numerical simulation, and improving to obtain a distribution function P (R, t) of perforating detonation pressure in a shaft
S302, calculating detonation load F through a distribution function c (t)：
Wherein F cL (t) and F cT (t) axial and transverse detonation loads, A 1 And A 2 The cross-sectional area of the gun and the area of the perforation hole are respectively.
Further, the boundary conditions in step S4 are:
top:
bottom:
at the initial moment, the perforating string is elongated under its own weight:
initial conditions:
wherein Q is the weight of the pipe column per unit length, and A is the sectional area of the pipe column.
Further, in the step S5, the calculation of the perforating string dynamics system uses a generalized- α method (an improved Newmark method which takes calculation accuracy and stability into consideration), and calculates the displacement, lateral acceleration and longitudinal acceleration of the perforating string, and includes the following sub-steps:
s501, calculating a global stiffness matrix K ', a mass matrix M ' and a damping matrix C ' of the perforating string in the geodetic coordinate system;
s502, inputting the displacement d0, the speed v0 and the approximate value a0 of the acceleration of the boundary condition initial value perforating string;
s503, setting a time step (less than or equal to 0.0001S), and calculating an integral constant C k 、C 0 、C 1 、C 2 、C 3 、C 4 、C 5 ；
S504, calculating an effective stiffness matrix by using an integral constant
S505, calculating the effective load vector at the t + delta t moment
S506, utilizing the rigidity matrix
And payload vector
Calculating the displacement d at the time t + delta t n+ 1：
S507, utilizing the displacement d at the moment of t + delta t n+1 Calculating the acceleration a at the time t + Deltat n+1 And velocity v n+1 ：
v n+1 ＝v n +(1-γ 2 )Δta n +γ 2 Δta n+1
Wherein beta is 2 And gamma 2 Are parameters of the generalized-alpha algorithm.
The invention has the beneficial effects that:
(1) The perforating string system can be used for simulating and analyzing the influence of different factors on the safety performance of a perforating pipeline, so that risks are avoided in the actual exploitation process, the damage of instruments is avoided, and the service life of equipment is prolonged;
(2) The perforation pipe column system and the analysis method are used for simulating the exploitation in special environments such as ultra-deep wells or tight shale gas wells, the equipment parameters can be adjusted in real time according to the simulation result to obtain the optimal configuration, the equipment configuration can be carried out in actual engineering by referring to the simulation parameters, and the exploitation efficiency is improved.
Drawings
FIG. 1 is a schematic diagram of a perforating string system;
FIG. 2 is a schematic diagram of node force and node displacement coordinates of a three-dimensional space beam unit in a local coordinate system;
FIG. 3 is a schematic diagram of a perforating string spacer;
FIG. 4 is a schematic illustration of detonation loading applied to a perforating string;
FIG. 5 is a graph comparing simulation results and actual measurement results;
FIG. 6 is a time history of longitudinal displacement and axial force of the tubing at different locations for different perforating gun lengths of example 2;
FIG. 7 is a graph of the movement traces of the oil pipe under different lengths of perforating guns in the embodiment 2;
FIG. 8 is a graph showing the maximum impact force of the tubing at different gun lengths according to example 2;
FIG. 9 is a schematic representation of the maximum buckling deformation of the tubing at different perforating gun lengths of example 2;
FIG. 10 is the maximum equivalent stress of the tubing at the length of the perforating gun in example 2;
the reference numbers in the figures illustrate: 1-oil pipe hanger, 2-double male short section, 3-expansion joint, 4-oil pipe, 5-safety joint, 6-packer, 7-sieve pipe, 8-shock absorber and 9-perforating gun.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, which is a schematic diagram of a perforation string dynamic system, the perforation string comprises a tubing hanger 1, a double male short joint 2, an expansion joint 3, an oil pipe 4, a safety joint 5, a packer 6, a sieve tube 7, a shock absorber 8 and a perforation gun 9; the packer 6 is anchored on the inner wall of the casing and used for packing off the reservoir stratum; the perforating gun 9 is suspended below the packer 6 through the oil pipe 4 and faces the reservoir layer in the opposite direction, and is used for launching the shaped perforating bullet inside the perforating gun.
The set-up of a perforating string system requires following assumptions:
(1) The tubular column and the shaft are both circular sections;
(2) The perforating string is regarded as a three-dimensional elastic beam, and the material and the geometric characteristics of the perforating string are uniform;
(3) The axis of the pipe column at the initial moment is coincident with the axis of the shaft, and an initial annular space exists between the pipe column and the shaft;
(4) Neglecting the effect of temperature on the stiffness of the pipe string. The steps of establishing the system are as follows:
s1, establishing a geodetic coordinate system and a local coordinate system of the perforating string, and calculating a dynamic equation of the three-dimensional space beam unit under the local coordinate system.
Because the length of the perforating pipe column reaches hundreds of meters, the outer diameter of the perforating pipe column is only about 0.1m, and the perforating pipe column bears axial and transverse impact loads. Thus, for such a large aspect ratio and buckling load bearing string, the perforating string is discretized into n cells using the Bernoulli-Euler assumption, using the finite element method, where the shock absorber is considered to be a spring with stiffness, damping and no mass. Each unit has two nodes (n +1 nodes in total), each node has six degrees of freedom including three translational degrees of freedom (u, v, w) and three rotational degrees of freedom (theta) x ，θ y ，θ z ). And establishing a geodetic coordinate system by taking the well mouth as an origin, the well axis as an x-axis and the downward direction as a positive direction. And establishing a local coordinate system of the perforating string by taking the axis of the perforating string as an x axis and taking the two transverse directions as a y axis and a z axis respectively. The node force and node displacement coordinates of the three-dimensional space beam unit in the local coordinate system are shown in FIG. 2.
The movement of the perforating string can be represented by the nodal displacement of the beam elements: u shape e ＝Nd e
Wherein d is e For nodal displacement vectors:
d e ＝[u i ,v i ,w i ,θ ix ,θ iy ,θ iz ,u j ,v j ,w j ,θ jx ,θ jy ,θ jz ] T
n is Hermitian shape function matrix:
wherein ξ is represented as
l e Is the beam element length.
Under the action of detonation load, based on Green-Lagrange strain and neglecting high-order small terms, the generalized strain of the beam unit is obtained:
generalized strain epsilon includes linear strain epsilon L And nonlinear strain epsilon NL Two parts are as follows:
ε＝ε L +ε NL
linear part B of its kinematic relation matrix L And non-linearity part B NL Respectively as follows:
linear stiffness matrix of beam unit
And a geometric stiffness matrix
Can be expressed as:
wherein L is the length of the perforating string, F c For detonation loads, D is the elastic matrix:
wherein E and G are respectively the modulus of elasticity and shear modulus of the beam, I z 、I y And I p The moments of inertia in the y and z planes, and the polar moments of inertia in the x plane, respectively.
Because the annular space between the perforating string and the casing is small, the perforating string is susceptible to collision with the casing when vibrated. The gap elements are introduced here to characterize the collision of the perforating string with the inner wall of the casing, as shown in fig. 3, which is a schematic diagram of the gap elements of the perforating string, the local coordinate system of the gap elements coinciding with the local coordinate system of the beam elements.
The gap element is a two-dimensional unit, and the displacement of the gap element is the transverse displacement of the beam element. The displacement vector of the gap element at any position x of the beam unit is as follows:
u G ＝[v x ,w x ] T ＝N G d e
wherein N is G Is a shape function matrix of the gap elements,
the transverse displacement U of the gap element at any position G And a direction angle theta G Comprises the following steps:
θ G ＝kπ+arctan(v x /w x )
in the event of a collision, the casing imparts a contact reaction force to the perforating string:
wherein D i Is the inner diameter of the casing, D o Is the outer diameter of the perforating string G k Is the elastic contact stiffness. The stiffness matrix of the interstitial element
Can be expressed as:
the contact reaction force inevitably causes frictional resistance and frictional resistance torque:
wherein
And
respectively a circumferential friction force and an axial friction force,
and
respectively circumferential and axial friction torque, mu 1 And mu 2 The circumferential dynamic friction coefficient and the axial dynamic friction coefficient are respectively.
Additional nodal force generated by contact impact
Can be expressed as:
the beam element's equation of force can be expressed as:
wherein M is e Is a beam element mass matrix, C e As a damping matrix, K e A matrix of cell stiffness values is generated,
is an additional stiffness matrix caused by gravity; f e In the form of a force matrix of the unit nodes,
the equivalent nodal force caused by detonation loads,
for the additional nodal force caused by gravity,
And S2, converting the dynamic equation of the lower three-dimensional space beam unit of the local coordinate into a beam unit dynamic equation under a geodetic coordinate system, and assembling the motion equations of all the beam units to obtain the motion equation of the whole perforating string.
The local coordinate system and the natural coordinate system of the three-dimensional space beam unit have the following relations:
if Tr is a conversion matrix, then
Each beam unit comprises two nodes, and each node comprises three translational displacements and three rotational displacements; thus, the overall transformation matrix of a beam element can be expressed as:
the mass matrix, stiffness matrix, damping matrix and resultant force matrix of the beam element in the geodetic coordinate system can then be expressed as:
[M e ′]＝[Trans][M e ]
[K e ′]＝[Trans][K e ]
[C e ′]＝[Trans][C e ]
[F e ′]＝[Trans][F e ]
the beam unit balance equation under the geodetic coordinate system is:
assembling the motion equations of all the beam units to obtain the motion equation of the whole perforating string:
wherein
U and F 'are matrix of speed, acceleration, displacement and external force of all nodes of the perforating string respectively, and M', C 'and K' are matrix of total mass, matrix of total damping and matrix of total displacement of the perforating string respectively.
And S3, calculating the detonation load of the perforating string, and giving a detonation load at the position of each perforating charge and the bottom of the perforating gun according to the actual detonation sequence at a time interval of 0.0001S.
On the basis of an empirical formula of a transient pressure peak value of shock waves formed by TNT explosion in an infinite water area, the practical working condition of bottom hole explosion of a perforating bullet is considered, LS-DANA numerical simulation is used for improvement, and a distribution function of perforating detonation pressure in a shaft is obtained:
wherein
C 0 Is the sound velocity in standing water, W is the TNT explosion equivalent, W 0 ＝0.809W。
The detonation load can be expressed as:
wherein F cL (t) and F cT (t) axial and transverse detonation loads, A 1 And A 2 The cross-sectional area of the gun and the area of the perforation hole are respectively. And a detonation load is given to the position of each perforating charge and the bottom of the perforating gun according to the actual detonation sequence at a time interval of one time step (0.0001 s). FIG. 4 provides a schematic illustration of the detonation load applied at a phase angle of 90.
And S4, calculating boundary conditions of the perforating string, including a top boundary condition, a bottom boundary condition and an initial condition, and taking the boundary conditions as initial values input into a perforating string dynamic system.
The top of a conventional perforating string is sealed by a packer, while the bottom hangs freely. The boundary conditions can therefore be written as:
top:
bottom:
at the initial moment, the perforating string is elongated under its own weight:
initial conditions:
wherein Q is the weight of the column per unit length and A is the cross-sectional area of the column.
And S5, taking the collision and friction factors into consideration, and calculating the displacement, the transverse acceleration and the longitudinal acceleration of the perforating string by using a perforating string dynamic system.
From the above conditions, it can be seen that the perforating string dynamics system for detonation loading is a complex nonlinear system that needs to be solved numerically. In a complex structure well bore, the perforating string often collides with the lower well bore under detonation loads, generating axial and tangential friction forces. In order to obtain better convergence, a generalized-alpha method, namely an improved Newmark method which has both calculation precision and stability, is introduced to calculate the bending drill string system by taking collision and friction factors into consideration.
The basic form of the generalized-alpha method:
v n+1 ＝v n +[(1-γ 2 )a n +γ 2 a n+1 ]Δt
d 0 ＝d
v 0 ＝v
a 0 ＝M′ -1 (F′(0)-C′v-K′d)
d n ,v n and a n Respectively representing approximate values of the displacement, the speed and the acceleration of the perforating string; Δ t represents the time step, s; the subscript n denotes the number of time steps. Algorithm parameters
γ 2 And beta 2 The relationship of (a) to (b) is as follows:
in the formula (I), the compound is shown in the specification,
represents the limiting spectral radius, here taken to be 1/2.
From the above equation we can get:
the detailed calculation procedure of the generalized- α method is as follows:
s501, calculating a global stiffness matrix K ', a mass matrix M ' and a damping matrix C ' of the perforating string in the geodetic coordinate system.
S502, inputting the initial values of the boundary conditions, namely the displacement d0, the velocity v0 and the approximate value a0 of the acceleration of the perforating string
S503, setting a time step (0.0001S or less), and calculating an integration constant:
c 2 ＝Δtc 0 ,
s504, calculating an effective rigidity matrix:
and S505, calculating the payload vector at the t + delta t moment:
s506, calculating the displacement at time t + Δ t:
and S507, calculating the acceleration and the speed at the moment t + delta t:
v n+1 ＝v n +(1-γ 2 )Δta n +γ 2 Δta n+1
the system is used for predicting the transverse acceleration and the longitudinal acceleration of a perforating string of a highly-deviated well in an oil field X1:
taking a certain oil field X1 highly-deviated well as an example, axial and radial acceleration data of an X1 well pipe column under the action of perforation detonation are obtained by installing a storage type sensor at the top of a perforating gun on site. The perforation string structure and perforation parameters for the X1 well are shown in Table 1. Fig. 5 is a calculation result according to the system, and the result is basically consistent when fig. 5 is compared with the data actually measured on site in table 1.
TABLE 1
The impact of perforating gun length on safety performance was analyzed using a system [ example 2 ]:
for oil and gas wells with thick oil layers and multiple thin oil layers, perforation is usually completed at one time by prolonging a perforating gun in order to reduce cost. FIG. 6 is a time-course plot of longitudinal displacement and axial force at different locations of the tubing for different gun lengths. The motion tracks, the maximum collision force and the maximum buckling deformation of the oil pipe under different perforating gun lengths are shown in the figures 7, 8 and 9. FIG. 10 shows the maximum equivalent stress of the tubing for a length of perforating gun; as can be seen from FIG. 6, the longer the perforating gun, the smaller the displacement amplitude and the axial force amplitude of the oil pipe, and the larger the vibration period; as can be seen from fig. 7, 8 and 9, the longer the perforating gun is, the smaller the trajectory area of the oil pipe is, the smaller the contact length and contact force between the oil pipe and the casing are, and the weaker the buckling deformation degree of the oil pipe is; as can be seen from fig. 10, the longer the perforating gun, the less the equivalent stress of the tubing, which is due to the fact that the overall mass of the perforating gun increases with the length of the perforating gun, meaning that the work done by the detonation load on the perforating string is more converted into kinetic energy of the perforating gun, the energy applied to the tubing decreases, and the shock absorber acts to further attenuate the impact applied to the tubing. It can therefore be concluded that the use of longer perforating guns can improve the safety of the tubing.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A perforating string dynamic system for oil-gas exploration is characterized by comprising a tubing hanger (1), a double male short joint (2), an expansion joint (3), an oil pipe (4), a safety joint (5), a packer (6), a sieve tube (7) and a perforating gun (9); the packer (6) is anchored on the inner wall of the casing and used for packing off the reservoir stratum; the perforating gun (9) is suspended below the packer (6) through an oil pipe (4) and faces the reservoir layer at the position, and is used for launching the shaped perforating bullet inside the perforating gun.
2. A perforating string dynamics system for oil and gas exploration as claimed in claim 1, characterized in that the perforating string and the wellbore are circular in cross section, and the axis of the perforating string at the initial moment coincides with the wellbore axis, there being an initial annular space between the perforating string and the wellbore.
3. The perforating string dynamics system for hydrocarbon exploration as claimed in claim 1 wherein the perforating string is a three dimensional elastic beam with uniform material and geometric properties.
4. Perforating string dynamics system for oil and gas exploration according to claim 1 characterized by further comprising shock absorbers (8) for axial and transversal shock loads of the perforating string, said shock absorbers being springs with stiffness, damping and no mass.
5. A perforation string dynamics analysis method for oil and gas exploration is characterized by comprising the following steps:
s1, establishing a geodetic coordinate system and a local coordinate system of a perforating string, and calculating a dynamic equation of a three-dimensional space beam unit under the local coordinate system;
s2, converting the dynamic equation of the lower three-dimensional space beam unit with local coordinates into a beam unit dynamic equation under a geodetic coordinate system, and assembling the motion equations of all the beam units to obtain the motion equation of the whole perforating string;
s3, calculating detonation loads of the perforating pipe column, and giving a detonation load at the position of each perforating charge and the bottom of the perforating gun according to an actual detonation sequence at a time interval of 0.0001S;
s4, calculating boundary conditions of the perforating string, including a top boundary condition, a bottom boundary condition and an initial condition, and taking the boundary conditions as initial values input into a perforating string dynamic system;
and S5, taking the collision and friction factors into consideration, and calculating the displacement, the transverse acceleration and the longitudinal acceleration of the perforating string by using a perforating string dynamic system.
6. A perforating string dynamics analysis method for oil and gas exploration according to claim 5, characterized by the fact that step S1 comprises the following sub-steps:
s101, dispersing the perforating string into n units, wherein each unit is provided with two nodes (n +1 nodes in total), each node has six degrees of freedom, and the six degrees of freedom comprise three translational degrees of freedom (u, v, w) and three rotational degrees of freedom (theta) x ，θ y ，θ z ) Establishing a geodetic coordinate system by taking a wellhead as an origin, a borehole axis as an x-axis and a downward direction as a positive direction;
s102, establishing a local coordinate system of the perforating string by taking the axis of the perforating string as an x axis and taking two transverse directions as a y axis and a z axis respectively;
s103, under the action of detonation load, based on Green-Lagrange strain and neglecting high-order small terms, and considering the collision between the perforating string and the inner wall of the casing pipe caused by the small annular space between the perforating string and the casing pipe, obtaining a dynamic equation of the beam unit:
wherein M is e Is a beam element mass matrix, C e Is a Rayleigh damping matrix, K e Matrix of cell stiffness, F e In the form of a force matrix of the unit nodes,
and
respectively the nodal velocity and acceleration, U, of the beam element e Is the nodal displacement of the beam element.
7. A perforating string dynamics analysis method for oil and gas exploration according to claim 5, characterized by the step S2 comprising the following sub-steps:
s201, converting a beam unit dynamic equation under a three-dimensional space local coordinate into a beam unit dynamic equation under a geodetic coordinate system:
s202, assembling the motion equations of all the beam units to obtain the power equation of the whole perforating string:
wherein
U and F 'are matrix of speed, acceleration, displacement and external force of all nodes of the perforating string respectively, and M', C 'and K' are matrix of total mass, matrix of total damping and matrix of total displacement of the perforating string respectively.
8. A perforating string dynamics analysis method for oil and gas exploration according to claim 5, characterized in that the calculation of detonation loads of step S3 comprises the following sub-steps:
s301, on the basis of an empirical formula of a transient pressure peak value of shock waves formed by TNT explosion in an infinite water area, considering the actual working condition of explosion of a perforating bullet at the bottom of a well, performing LS-DANA numerical simulation, and improving to obtain a distribution function P (R, t) of the perforating detonation pressure in a shaft
S302, calculating detonation load F through a distribution function c (t)：
Wherein F cL (t) and F cT (t) axial detonation loads respectivelyLoad and transverse detonation load, A 1 And A 2 The cross-sectional area of the gun and the area of the perforation hole are respectively.
9. The perforating string dynamics analysis method for hydrocarbon exploration as claimed in claim 5, wherein the boundary conditions in step S4 are:
top:
bottom:
at the initial moment, the perforating string is elongated under its own weight:
initial conditions:
wherein Q is the weight of the column per unit length and A is the cross-sectional area of the column.
10. The perforating string dynamics analysis method for oil and gas exploration according to claim 5, wherein the perforating string dynamics system in step S5 uses a generalized-alpha method (a modified Newmark method with both calculation accuracy and stability), and calculates the displacement, lateral acceleration and longitudinal acceleration of the perforating string, comprising the sub-steps of:
s501, calculating a global stiffness matrix K ', a mass matrix M ' and a damping matrix C ' of the perforating string in the geodetic coordinate system;
s502, inputting the displacement d0, the speed v0 and the approximate value a0 of the acceleration of the boundary condition initial value perforating string;
s503, setting a time step (less than or equal to 0.0001S), and calculating an integral constant C k 、C 0 、C 1 、C 2 、C 3 、C 4 、C 5 ；
S504, calculating effectiveness by using integral constantRigidity matrix
S505, calculating the effective load vector at the t + delta t moment
S506, utilizing the rigidity matrix
And payload vector
Calculating the displacement d at the time t + Deltat n+1 ：
S507, utilizing the displacement d at the time of t + delta t n+1 Calculating the acceleration a at the time t + Deltat n+1 And velocity v n+1 ：
v n+1 ＝v n +(1-γ 2 )Δta n +γ 2 Δta n+1
Wherein beta is 2 And gamma 2 Are parameters of the generalized-alpha algorithm.
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