Perforation section tubular column strength safety analysis method

Abstract

The invention relates to the technical field of oil-gas exploration and development, in particular to a perforation section tubular column strength safety analysis method, which comprises the following steps of: obtaining a tubular column dynamic response result at a corresponding time point by utilizing a tubular column dynamic response model, performing curve analysis on the tubular column dynamic response result, and determining the strength safety of a perforation section tubular column in combination with a perforation section tubular column strength safety evaluation standard. And obtaining a perforation section pipe column strength safety evaluation result, and determining that pipe column vibration bending and vibration breaking are easy to occur at a section close to the packer. On the basis of accurately analyzing detonation parameters and based on the reflection principle, a casing and perforation fluid interface reflection parameter analysis method is perfected, and the detonation parameters are calculated through a pressure pulsation calculation model. The problem that perforation fluid pressure pulsation and oil casing string damage under deep wells, high initial pressure and long and narrow boundaries are difficult to solve by the existing shallow-layer, low-initial-pressure and free-boundary underwater explosion theory is solved. Meanwhile, a perforation section tubular column strength safety analysis method is formed according to the tubular column dynamic response model, and the adaptability and precision of solving the perforation detonation problem are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas exploration and development, and is a method for analyzing the strength and safety of a perforated section string. Background Art

[0002] Deep and ultra-deep oil and gas resources have become an important replacement field for increasing reserves and production in domestic oil and gas exploration and development. Well testing is the "last kick" in the process of oil exploration and development, and well testing after completion of ultra-deep wells over 7000m has gradually become the new normal. Perforating and testing combined operation is the most common process for improving testing efficiency in high-pressure ultra-deep wells. However, under high detonation pressure, high hydrostatic pressure, high confining pressure, and narrow boundaries, accidents and complexities such as pipe string breakage and sticking are likely to occur during perforating and testing combined operation. For example, in wells such as TW1 in Xinjiang Oilfield, JT1 in Southwest Oil and Gas Field, and DN2-27 in Tarim Oilfield, packer mandrels broke and tubing fractured during perforating, causing serious economic losses. The mechanical analysis and evaluation of the perforated section string under perforating detonation involve complex processes such as explosion mechanics, fluid dynamics, underwater explosion theory, phase change theory, and fluid-structure interaction. Domestic relevant scholars have developed simulation test experimental devices for the problem of dynamic response of the perforated section string to explosion shock, and established theoretical prediction methods for perforating pressure pulsation and dynamic impact load, but there are approximations and assumptions in the algorithms and designs, and the analysis and prediction accuracy is low.

[0003] In the Chinese patent document with the publication number CN115324538A, a perforating string dynamics system and analysis method for oil and gas exploration are given. The system includes a tubing hanger, double-male nipple, expansion joint, tubing, safety joint, packer, screen pipe, and perforating gun, which are used to simulate and analyze the effects of different factors on the safety performance of the perforated section string. Since this system is a similarity experimental system established according to size ratios, it cannot truly simulate the downhole high-temperature and high-pressure working conditions and cannot obtain real experimental data.

[0004] In the Chinese patent document with the publication number CN116411931, a perforating detonation analysis method and device for testing completion string are given, which consists of four parts: a geometric generation module for testing completion string, a task creation module for perforating detonation analysis, a module for perforating detonation analysis, and a structural module for perforating detonation analysis. Since this device is a similarity experimental system according to size ratios, and the influence of factors such as the instantaneous fall of perforating fluid during perforating detonation on the pipe string load is not considered in the analysis method, and this result has not been seen in actual production.

[0005] Therefore, in the strength and safety analysis of the perforated section string, new methods need to be studied to solve the problem of large analysis result errors caused by approximations and assumptions in traditional algorithms and designs, and improve the analysis and calculation accuracy. Summary of the Invention

[0006] The present invention provides a method for analyzing the strength and safety of a perforated section string, overcoming the deficiencies of the above-mentioned prior art, and effectively solving the problems of large errors in the analysis results and low analysis and calculation accuracy caused by approximations and assumptions in the existing traditional algorithms and designs for the strength and safety analysis of perforated section strings during oil exploration and development.

[0007] One of the technical solutions of the present invention is achieved by the following measures: A method for analyzing the strength and safety of a perforated section string is carried out according to the following method:

[0008] First, using the pipe string dynamic response model, the pipe string dynamic response results at corresponding time points are obtained. Among them, the pipe string dynamic response results include the axial displacement change curve at the bottom end of the pipe string, the axial velocity change curve at the bottom end of the pipe string, the axial acceleration at the bottom end of the pipe string, and the equivalent stress change curve of the pipe string at the packer under axial load. The pipe string dynamic response model is as follows:

[0009] Displacement:

[0010] Velocity:

[0011] Acceleration:

[0012] Stress:

[0013] Among them, E is the elastic modulus, MPa; v is the velocity of the perforating fluid, m / s; c is the viscous friction, m 2 / s; 1 is the length of the perforated section, m; x is the coordinate of a certain point on the pipe string, m; t is a certain moment, s; λ and β are calculation constants, dimensionless;

[0014] Then, curve analysis is carried out on the pipe string dynamic response results, and combined with the strength and safety evaluation criteria of the perforated section string, the strength and safety evaluation results of the perforated section string are obtained. Among them, the strength and safety evaluation criteria of the perforated section string include that in the equivalent stress change curve of the pipe string at the packer under axial load, the maximum perforated section string peak stress point is found, and this point is the point closest to the packer. At this point, the pipe string of the perforated section is prone to pipe string vibration bending and vibration breaking phenomena;

[0015] The following is a further optimization or / and improvement of one of the above-mentioned technical solutions of the invention:

[0016] The above construction of the pipe string dynamic response model includes:

[0017] The first step is to apply the Michelson equation and the average specific heat capacity method, introduce the maximum degree of heat release coefficient, correct the calculation formulas of the explosion volume, heat of explosion, and explosion temperature, and analyze and calculate the detonation pressure and detonation velocity by applying the maximum energy release principle and the Kamelet method;

[0018] Step 2: Based on the detonation wave parameters and Tait equation in the continuity of the phase change interface shock wave, establish an initial shock wave pressure analysis model. Combining the detonation pressure and detonation velocity, based on the initial shock wave pressure analysis model, reflection principle, and classical explosion experimental data, analyze and obtain the shock wave pressure calculation model under different pulsation stages of the direct wave and reflected wave superposition, as follows:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] p(t) = p 0 (t 0 ) + p 1 (t 1 ) + p 2 (t 2 ) + p 3 (t 3 ) + p 4 (t 4 )

[0025] Among them, P ro is the reflected pressure of the No. 0 bullet, MPa; θ is the time decay constant, θ = 12,3 μs; P ai is the reflected wave pressure value of the No. i bullet, MPa;

[0026] Step 3: Based on the shock wave pressure calculation model under different pulsation stages, apply the vibrating cantilever beam theory of vibration mechanics. Combining the vibration differential equations under the three impact loads of axial, transverse, and torsional of the pipe string, and obtaining the respective derivatives, the dynamic response model of the pipe string is obtained, as follows:

[0027] Displacement:

[0028] Velocity:

[0029] Acceleration:

[0030] Stress:

[0031] Among them, E is the elastic modulus, MPa; v is the velocity of the perforating fluid, m / s; c is the viscous friction, m 2 / s; 1 is the perforation section length, m; x is the coordinate of a certain point on the pipe string, m; t is a certain moment, s; λ and β are calculation constants, dimensionless.

[0032] In the above first step, the calculation method of the detonation wave parameters is as follows:

[0033] D = A(1 + Bρ)ψ 1 / 2

[0034] P = 1.558ρ 2 ψ

[0035]

[0036] Among them, P is the detonation pressure, GPa; D is the detonation velocity, km / s, A = 1.01, B = 1.3; N is the number of moles of gas products per 1 kg of explosive, mol / kg; ρ is the explosive density, g / cm 3 ; is the molar average mass of the gas components; Qmax is the maximum possible detonation heat value, kcal / kg.

[0037] In the above second step, a shock wave pressure calculation model under different pulsation stages is constructed, including:

[0038] S1. Based on the shock wave continuity at the phase change interface and the Tait equation, an initial shock wave pressure calculation model in the perforating fluid is obtained as follows:

[0039]

[0040] Among them, P is the initial shock wave pressure in the perforating fluid, GPa; ρ c is the detonation product density, g / cm 3 ; is ρ oc is the density of the perforating fluid in front of the shock wave front, g / cm 3 ; A is an experimentally determined parameter, A = 307.7 MPa; m is an experimentally determined parameter, m = 7.15;

[0041] S2. According to the LS-DYNA analysis of the attenuation law of the detonation pressure along the axis, an analytical expression for the variation of the shock wave pressure peak with the detonation distance is obtained as follows:

[0042] p m = p 0 + p x e -0.031(R-1 / 3r)

[0043] Among them, P m is the pressure peak at the detonation distance R, GPa; P x is the initial shock wave pressure, GPa; P 0is the initial static liquid column pressure of the perforating fluid, MPa; R is the detonation distance, m; r is the scaled distance, dimensionless;

[0044] S3. Based on the reflection principle and combining the reflection law of the perforating fluid shock wave at the casing interface, the calculation formula for the shock wave pressure propagating in the reverse direction in the perforating fluid is obtained as follows:

[0045] p r = p A - p B

[0046] where Pr is the reflected shock wave pressure, GPa; PA is the initial shock wave pressure at a certain point, GPa; PB is the reflected wave pressure, GPa;

[0047] S4. Based on the fact that the detonation shock wave will produce an inclined collision near the midpoint between adjacent charges and superimpose on each other, the calculation formula for the superimposed pressure of the shock wave between charges is obtained as follows:

[0048] p a = 0.6 × 2p r = 1.2p r

[0049] where Pa is the superimposed shock wave pressure, GPa; Pr is the shock wave pressure generated by the explosion of a single perforating charge, GPa;

[0050] S5. According to the pressure pulsation characteristics of the explosion shock wave and the interface reflection law, combining the initial shock wave pressure calculation model in the perforating fluid, the analytical expression of the shock wave pressure peak varying with the detonation distance, the calculation formula for the shock wave pressure propagating in the reverse direction in the perforating fluid, and the calculation formula for the superimposed pressure of the shock wave between charges, the shock wave pressure calculation model in different pulsation stages is obtained as follows:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] p(t) = p 0 (t 0 ) + p 1 (t 1 ) + p 2 (t 2 ) + p 3 (t 3 ) + p 4 (t4 )

[0057] Among them, P ro is the reflection pressure of the No. 0 bullet, MPa; θ is the time decay constant, θ = 12.3 μs; P ai is the reflected wave pressure value of the i-th bullet, MPa.

[0058] In the above-mentioned third step, a dynamic response model of the pipe string is constructed, including:

[0059] S1, based on the on-site perforation-test joint pipe string system, combined with the axial, lateral, and torsional impact loads on the perforated pipe string, and regarding the packer as the fixed end of the pipe string, the bottom end of the pipe string is free, and the perforated pipe string is a cantilever beam. Dynamic models under the three loads are established respectively;

[0060] S2, according to D'Alembert's principle, the axial vibration equation of the perforated pipe string is obtained as follows:

[0061] Vibration equilibrium equation:

[0062] Vibration element equation:

[0063] Boundary conditions:

[0064] Initial conditions:

[0065] Displacement response equation:

[0066] Among them, is the inertial force on the element, N; is the internal force of the cross-section, N; E is the elastic modulus of the pipe string material, Pa; ρ is the density of the pipe material, kg / m 3 ; FN is the axial force of the cross-section, N; A is the cross-sectional area, m 2 ; I is a positive integer; Τ is the time integration variable;

[0067] S3, according to D'Alembert's inertial principle, the lateral vibration equation of the perforated pipe string is obtained as follows:

[0068]

[0069] Among them, E is the elastic modulus, Pa; I is the moment of inertia, mm 4 ; ρ is the density of the pipe material, kg / m 3 ; A is the cross-sectional area / m 2 ; y(x, t) is the lateral displacement of the cross-section at x from the origin at time t, m; f(x, t) is the unit lateral load / N / m;

[0070] S4. According to D'Alembert's principle, the torque vibration equation of the perforated section string is obtained as follows:

[0071]

[0072] where, is the angular displacement of the string cross-section at x from the origin at time t, °; G is the shear modulus of elasticity, Pa; ρ is the density of the pipe material, kg / m 3 ; IP is the polar moment of inertia of the cross-section, mm 4 ; f(x, t) is the unit torsional load / N / m;

[0073] S5. After taking the derivatives of the axial vibration of the perforated section string, the dynamic response model of the string is obtained as follows:

[0074] Displacement:

[0075] Velocity:

[0076] Acceleration:

[0077] Stress:

[0078] where, E is the modulus of elasticity, MPa; v is the velocity of the perforating fluid, m / s; c is the viscous friction, m 2 / s; l is the length of the perforated section, m; x is the coordinate of a point on the string, m; t is a certain moment, s; λ and β are calculation constants, dimensionless.

[0079] The second technical solution of the present invention is achieved by the following measures: An apparatus applying the method for analyzing the strength and safety of a perforated section string includes:

[0080] An evaluation data acquisition unit, which uses the dynamic response model of the string to obtain the dynamic response results of the string at corresponding time points. The dynamic response results of the string include the axial displacement change curve at the bottom end of the string, the axial velocity change curve at the bottom end of the string, the axial acceleration change at the bottom end of the string, and the equivalent stress change curve of the string at the packer under the axial load. The dynamic response model of the string is as follows:

[0081] Displacement;

[0082] Acceleration:

[0083] Acceleration:

[0084] Stress:

[0085] Among them, E is the elastic modulus, in MPa; v is the perforating fluid velocity, in m / s; c is the viscous friction, in m 2 / s; l is the length of the perforating section, in m; x is the coordinate of a certain point on the pipe string, in m; t is a certain moment, in s; λ and β are calculation constants, dimensionless;

[0086] For the safety evaluation unit, curve analysis is carried out on the dynamic response results of the pipe string, and combined with the strength safety evaluation standard of the perforating section pipe string, the strength safety evaluation result of the perforating section pipe string is obtained. Among them, the strength safety evaluation standard of the perforating section pipe string includes finding the maximum peak stress point of the perforating section pipe string in the curve of the equivalent stress change of the pipe string at the packer under the axial load. Then, this point is the point closest to the packer, and the pipe string section at this point is prone to pipe string vibration and breakage.

[0087] Based on the accurate analysis of detonation parameters, the present invention improves the analysis method of reflection parameters at the interface between the casing and the perforating fluid based on the reflection principle, and solves the problems of perforating fluid pressure pulsation and oil casing string damage in deep wells, high initial pressure, and narrow boundaries that are difficult to solve by the existing underwater explosion theory of shallow layers, low initial pressure, and free boundaries through a pressure pulsation calculation model; at the same time, according to the pipe string dynamic response model, a strength safety analysis method for the perforating section pipe string is formed, improving the adaptability and accuracy of solving perforating detonation problems. Brief Description of the Drawings

[0088] Attached Figure 1 is the diagram of the pressure pulsation law of the explosion shock wave in the present invention.

[0089] Attached Figure 2 is the system diagram of the on-site perforating-test joint pipe string in the present invention.

[0090] Attached Figure 3 is the axial vibration dynamics model diagram of the perforating pipe string under the impact load and pressure pulsation excitation in the present invention.

[0091] Attached Figure 4 is the radial vibration dynamics model diagram of the perforating pipe string under the impact load and pressure pulsation excitation in the present invention.

[0092] Attached Figure 5 is the torque vibration dynamics model diagram of the perforating pipe string under the impact load and pressure pulsation excitation in the present invention.

[0093] Attached Figure 6 is the numerical model diagram of the pipe string dynamic response of the perforating pipe string under the impact load and pressure pulsation excitation in the present invention.

[0094] Attached Figure 7 is the curve diagram of the energy change of the perforating fluid between perforating charges during the instant of perforating detonation in the present invention.

[0095] Attached Figure 8This is the curve graph of the vibration velocity and acceleration of the perforating fluid and the perforating string in the present invention.

[0096] Appendix Figure 9 This is the curve graph of the stress of the perforating string and the pressure of the perforating fluid between charges in the present invention.

[0097] Appendix Figure 10 This is the schematic diagram of the monitoring string structure for the downhole parameters of the perforating test in a certain well in the present invention.

[0098] Appendix Figure 11 This is the curve graph of the measured downhole string vibration acceleration of the perforating test string in a certain well in the present invention.

[0099] Appendix Figure 12 This is the curve graph of the annulus pressure change below the packer of the perforating test in a certain well in the present invention. Detailed implementation manners

[0100] The present invention is not limited by the following embodiments, and the specific implementation manners can be determined according to the technical solution of the present invention and the actual situation.

[0101] The present invention will be further described below in conjunction with embodiments:

[0102] Embodiment 1: The method for analyzing the strength safety of the perforating section string is carried out according to the following method:

[0103] First, using the string dynamic response model, the string dynamic response results at corresponding time points are obtained. Among them, the string dynamic response results include the axial displacement change curve at the bottom end of the string, the axial velocity change curve at the bottom end of the string, the axial acceleration at the bottom end of the string, and the equivalent stress change curve of the string at the packer under the axial load. The string dynamic response model is as follows:

[0104] Displacement:

[0105] Velocity:

[0106] Acceleration:

[0107] Stress:

[0108] Among them, E is the elastic modulus, MPa; v is the velocity of the perforating fluid, m / s; c is the viscous friction, m 2 / s; l is the length of the perforating section, m; x is the coordinate of a certain point on the string, m; t is a certain moment, s; λ and β are calculation constants, dimensionless;

[0109] Then, perform a curve analysis on the dynamic response results of the pipe string. Combining with the evaluation criteria for the strength safety of the pipe string in the perforation section, obtain the evaluation results for the strength safety of the pipe string in the perforation section. Among them, the evaluation criteria for the strength safety of the pipe string in the perforation section include finding the maximum peak stress point of the pipe string in the perforation section in the equivalent stress change curve of the pipe string at the packer under axial load. Then, this point is the point closest to the packer, and the pipe string in the perforation section at this point is prone to pipe string vibration and bending and vibration breakage phenomena.

[0110] Based on the pipe string dynamic response model of the present invention, apply AUTODYN software to establish a transient model. Use the Euler-Multimaterial model to describe the large-deformation perforating fluid and the perforating charge that undergoes solid-liquid-gas phase changes, simulate the fluid-structure interaction, analyze and calculate the pressure pulsation of the perforating fluid and the displacement, velocity, acceleration, and stress values of the pipe string, establish a pressure pulsation calculation model and a pipe string dynamic response model, thereby obtaining a method for analyzing the strength safety of the pipe string in the perforation section, and further explaining the phenomenon that the perforating test pipe string is often damaged near the packer, and verifying the applicability and accuracy of the theoretical algorithm.

[0111] Example 2: As an optimization of the above example, construct a pipe string dynamic response model, including:

[0112] In the first step, apply the Michelson equation and the average specific heat capacity method, introduce the maximum heat release achievement coefficient, correct the calculation formulas for the explosion volume, heat release, and explosion temperature, and analyze and calculate the detonation pressure and detonation velocity using the maximum energy release principle and the Kamelet method;

[0113] In the second step, based on the detonation wave parameters and the Tait equation in the shock wave continuity at the phase change interface, establish an initial shock wave pressure analysis model. Combining the detonation pressure and detonation velocity, based on the initial shock wave pressure analysis model, the reflection principle, and the classical explosion experimental data, analyze and obtain the shock wave pressure calculation model under different pulsation stages of the superposition of the direct wave and the reflected wave, as follows:

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] p(t) = p 0 (t 0 ) + p 1 (t 1 ) + p 2 (t 2 ) + p3 (t 3 )+p 4 (t 4 )

[0120] where P ro is the reflection pressure of the No. 0 bullet, MPa; θ is the time decay constant, θ = 12.3 μs; P ai is the reflected wave pressure value of the No. i bullet, MPa;

[0121] Step 3: Based on the shock wave pressure calculation model under different pulsation stages, applying the vibrating cantilever beam theory of vibration mechanics, combining the vibration differential equations under the three impact loads of axial, transverse, and torsional of the pipe string, and obtaining the dynamic response model of the pipe string after taking the derivatives of each order, as follows:

[0122] Displacement:

[0123] Velocity:

[0124] Acceleration:

[0125] Stress:

[0126] where E is the elastic modulus, MPa; v is the velocity of the perforating fluid, m / s; c is the viscous friction, m 2 / s; l is the length of the perforated section, m; x is the coordinate of a certain point on the pipe string, m; t is a certain moment, s; λ and β are calculation constants, dimensionless.

[0127] Example 3: As an optimization of the above example, in the first step, the calculation method of the detonation wave parameters is as follows:

[0128] D = A(1 + Bρ)ψ 1 / 2

[0129] P = I.558ρ 2 ψ

[0130]

[0131] where P is the detonation pressure, GPa; D is the detonation velocity, km / s, A = 1.01, B = 1.3; N is the number of moles of gas products per 1 kg of explosive, mol / kg; ρ is the density of the explosive, g / cm 3 ; is the molar average mass of the gas components; Qmax is the maximum possible detonation heat value, kcal / kg.

[0132] Example 4: As an optimization of the above example, in the second step, constructing the shock wave pressure calculation model under different pulsation stages includes:

[0133] S1. Based on the continuity of the shock wave at the phase change interface and the Tait equation, the calculation model for the initial shock wave pressure in the perforating fluid is obtained as follows:

[0134]

[0135] where P is the initial shock wave pressure in the perforating fluid, in GPa; ρ c is the density of the detonation products, in g / cm 3 ; ρ oc is the density of the perforating fluid in front of the shock wave front, in g / cm 3 ; A is an experimentally determined parameter, A = 307.7 MPa; m is an experimentally determined parameter, m = 7.15;

[0136] S2. According to the law of attenuation of the detonation pressure along the axis analyzed by LS - DYNA, the analytical expression for the variation of the peak shock wave pressure with the detonation distance is obtained as follows:

[0137] p m = p 0 + p x e -0.031(R-1 / 3r)

[0138] where P m is the peak pressure at the detonation distance R, in GPa; P x is the initial shock wave pressure, in GPa; P 0 is the initial hydrostatic pressure of the perforating fluid, in MPa; R is the detonation distance, in m; r is the scaled distance, dimensionless;

[0139] S3. Based on the reflection principle and combined with the reflection law of the shock wave of the perforating fluid at the casing interface (as Figure 1 shown), the calculation formula for the shock wave pressure propagating in the reverse direction in the perforating fluid is obtained as follows:

[0140] p r = p A - p B

[0141] where Pr is the reflected shock wave pressure, in GPa; PA is the initial shock wave pressure at a certain point, in GPa; PB is the reflected wave pressure, in GPa;

[0142] S4. Based on the fact that the detonation shock wave will produce an inclined collision and superposition near the mid - point between adjacent two charges, the calculation formula for the superposition pressure of the shock wave between charges is obtained as follows:

[0143] p a = 0.6×2p r = 1.2p r

[0144] Among them, Pa is the pressure of the superimposed shock wave, in GPa; Pr is the pressure of the shock wave generated by the explosion of a single perforating charge, in GPa.

[0145] S5. According to the characteristics of the explosion shock wave pressure pulsation and the law of interface reflection, combined with the initial shock wave pressure calculation model in the perforating fluid, the analytical expression of the change of the shock wave pressure peak with the detonation distance, the calculation formula of the shock wave pressure propagating in the reverse direction in the perforating fluid, and the calculation formula of the superimposed pressure of the shock waves between charges, a shock wave pressure calculation model under different pulsation stages is obtained as follows:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] p(t) = p 0 (t 0 ) + p 1 (t 1 ) + p 2 (i 2 ) + p 3 (t 3 ) + p 4 (t 4 )

[0152] Among them, P ro is the reflected pressure of the No. 0 charge, in MPa; θ is the time decay constant, θ = 12.3 μs; P ai is the reflected wave pressure value of the i-th charge, in MPa.

[0153] Example 5: As an optimization of the above example, in the third step, a dynamic response model of the string is constructed, including:

[0154] S1. Based on the on-site perforating-test joint string system (as Figure 2 shown), combined with the axial, lateral, and torsional impact loads on the perforating string section, and regarding the packer as the fixed end of the string, the bottom end of the string is free, and the perforating string section is a cantilever beam, dynamic models under the three loads are established respectively (as Figures 3 to 5 shown);

[0155] S2. According to D'Alembert's principle, the axial vibration equation of the perforating string section is obtained as follows:

[0156] Vibration balance equation:

[0157] Vibration micro-element equation:

[0158] Boundary conditions:

[0159] Initial conditions:

[0160] Displacement response equation:

[0161] Wherein, is the inertial force on the micro-element, N; is the internal force of the cross-section, N; E is the elastic modulus of the pipe column material, Pa; ρ is the density of the pipe material, kg / m 3 ; FN is the axial force of the cross-section, N; A is the cross-sectional area, m 2 ; I is a positive integer; Τ is the time integral variable;

[0162] S3. According to D'Alembert's inertial principle, the transverse vibration equation of the perforated pipe column is obtained as follows:

[0163]

[0164] Wherein, E is the elastic modulus, Pa; I is the moment of inertia, mm 4 ; ρ is the density of the pipe material, kg / m 3 ; A is the cross-sectional area / m 2 ; y(x, t) is the transverse displacement of the cross-section at a distance x from the origin at time t, m; f(x, t) is the unit transverse load / N / m;

[0165] S4. According to D'Alembert's principle, the torsional vibration equation of the perforated pipe column is obtained as follows:

[0166]

[0167] Wherein, is the angular displacement of the pipe column cross-section at a distance x from the origin at time t, °; G is the shear elastic modulus, Pa; ρ is the density of the pipe material, kg / m 3 ; IP is the polar moment of inertia of the cross-section, mm 4 ; f(x, t) is the unit torsional load / N / m;

[0168] S5. After taking the derivatives of the axial vibration of the perforated pipe column of each order, the dynamic response model of the pipe column is obtained as follows:

[0169] Displacement:

[0170] Velocity:

[0171] Acceleration:

[0172] Stress:

[0173] Among them, E is the elastic modulus, MPa; v is the perforating fluid velocity, m / s; c is the viscous friction, m 2 / s; l is the length of the perforating section, m; x is the coordinate of a certain point on the pipe string, m; t is a certain moment, s; λ and β are calculation constants, dimensionless.

[0174] Example 6: The device for analyzing the strength and safety of the pipe string in the perforating section includes:

[0175] An evaluation data acquisition unit, using the pipe string dynamic response model, obtains the pipe string dynamic response results at corresponding time points. Among them, the pipe string dynamic response results include the axial displacement change curve at the bottom end of the pipe string, the axial velocity change curve at the bottom end of the pipe string, the axial acceleration change at the bottom end of the pipe string, and the equivalent stress change curve of the pipe string at the packer under the axial load. The pipe string dynamic response model is as follows:

[0176] Displacement:

[0177] Acceleration:

[0178] Acceleration:

[0179] Stress:

[0180] Among them, E is the elastic modulus, MPa; v is the perforating fluid velocity, m / s; c is the viscous friction, m 2 / s; l is the length of the perforating section, m; x is the coordinate of a certain point on the pipe string, m; t is a certain moment, s; λ and β are calculation constants, dimensionless;

[0181] A safety evaluation unit analyzes the curve of the pipe string dynamic response results, and combines with the strength and safety evaluation standard of the pipe string in the perforating section to obtain the strength and safety evaluation result of the pipe string in the perforating section. Among them, the strength and safety evaluation standard of the pipe string in the perforating section includes finding the maximum peak stress point of the pipe string in the perforating section in the equivalent stress change curve of the pipe string at the packer under the axial load. Then, this point is the point closest to the packer, and the pipe string section at this point is prone to pipe string vibration and bending and vibration and breakage phenomena.

[0182] Example 7: Taking Well DN2-25 as an example, the implementation process is as follows:

[0183] First, establish a numerical analysis model: A combination of a Φ73.02mm×7.82mm P110 tubing string and a Φ177.80mm×12.65mm TP140 casing is used, with a total length of 11m. The length from the top of the perforation section to the packer is 5m, 16 perforating charges are arranged, the phase angle is 60°, the length is 1m, the length below the perforation section is 5m, the axial distance between charges is 62.5mm, and spherical charge HMX with a charge of 45g and a density of 1.3g / cm 3 is used, with a radius of 20.2mm. Six different observation points are set in the model (as Figure 6 shown).

[0184] The coordinate at the lower end of the packer is (0, 0), and the coordinate at the bottom end of the tubing string is (11000, 0). The boundary at (0, 0) is set as "Flow out" where matter and energy can freely exchange, and the displacement is set as a fixed boundary; the boundary at (0, 11000) is set as a "rigid boundary". The length of the detonating cord is 80mm, and the detonation velocity of the RDX explosive in the detonating cord is between 7000m / s and 8500m / s, so the detonation interval between adjacent charges is 10μs. The number of casing nodes is 4513, and the number of elements is 3408; the number of tubing string nodes is 1612, and the number of elements is 988; the number of perforating fluid nodes is 12224, and the number of elements is 12121. The coordinates and positions of the specific elements and nodes are shown in Table 1.

[0185] Then, analyze the energy change during the detonation instant (as Figure 7 shown): In the first 3.7μs, the energy value at point 5 is relatively low, remaining at about 0.3×10 5 J / kg, and the energy values at points 4 and 6 remain at about 4.0×10 6 J / kg, which is about 10 times that of point 5. Point 5 is in the detonation center area, but the energy is the lowest, indicating that the detonation gas instantaneously fills the cavity in the perforating gun, causing an energy "vacuum zone".

[0186] Next, analyze the vibration velocity and acceleration of the perforating fluid and the perforating tubing string (as Figure 8 shown): The velocities at points 15, 16, and 17 on the axis of the perforating tubing string continuously increase, with a peak velocity of about 30m / s; the velocities at points 15, 16, and 17 in the radial direction of the perforating tubing string oscillate symmetrically, with a peak velocity of about 15m / s; for the axial velocity fluctuation of the perforating fluid, the peak upward velocity at point 4 is about 480m / s, the velocity at point 5 hardly changes, and the peak downward velocity at point 6 is about 1500m / s.

[0187] Analysis shows that there is a time difference in the sequentially detonated perforating charges. The last perforating charge at the bottom is detonated at 6.3 μs, and the detonation wave generated by the previously detonated perforating charges also reaches this point. After superposition, the peak velocity is achieved; this is the radial velocity fluctuation of the perforating fluid, and the peak velocity at 6.3 μs is about 266 m / s; the magnitude and direction of the axial acceleration of the perforating string show a periodic change with a period of 3 ms. At 4 ms, the positive peak acceleration at the 17th point is 463 m / s 2 or so; the radial acceleration of the perforating string has a reverse peak acceleration of 564 m / s at the 17th point at 7 ms 2 or so.

[0188] Finally, the stress of the perforating string and the pressure pulsation of the perforating fluid between the charges are analyzed (as Figure 9 shown): The stress of the perforating string continuously increases, and peak stresses of 288 MPa, 279 MPa, and 218 MPa appear at the 15th, 16th, and 17th points successively. According to the magnitude of the stress and the position law, it can be seen that the closer to the packer, the greater the stress value. If the string is damaged under the combined action of the impact load and the pulsating pressure of the perforating fluid, it should occur near the packer, that is, the string near the packer is prone to vibration bending and vibration fracture; the pressure pulsation conditions at different positions. At the initial stage of detonation, the detonation products have not yet diffused, and the peak pressure at the 5th point is 865 MPa. As the gas rapidly diffuses, the pressure drops suddenly by about 46 MPa, and the peak pressures at the 4th and 6th points are about 606 and 528 MPa. At 6.2 ms, the pressure fluctuations at each point increase, and the pressure at the 5th point increases by about 110 MPa.

[0189] Analysis shows that when the detonation gas expands to a certain limit value, the perforating fluid falls back due to gravity and continuously squeezes the gas, resulting in an increase in pressure.

[0190] Therefore, it can be known that under the combined action of the impact load and the pulsating pressure of the perforating fluid, the stress value on the string near the packer is greater. Combining the results that the energy and density are also greater near the packer as described above, it can be known that the string near the packer is prone to vibration bending and vibration fracture.

[0191] Example 8: A downhole tester for perforating fluid pressure pulsation and string vibration is lowered into the perforating - testing combined string in a certain well. By analyzing the data actually measured on - site, the law of perforating fluid pressure pulsation and the dynamic response mechanism of the perforating string section are further revealed.

[0192] According to the structure of the perforating - testing string in this well (as Figure 10 shown), an upper vibration tester (1012 m), a lower vibration tester (4500 m), and a perforating tester (4914 m) are respectively lowered. The acceleration threshold values of the string vibration tester are shown in Table 2, and the brief situation of the well - testing operation in this well is shown in Table 3.

[0193] After pulling out the perforating test string, the monitoring data of 3 testers were replayed, and the analysis results are as follows:

[0194] Vibration response of the perforating string: The vibration at 1012 m of the upper string was not obvious and did not reach the threshold value of the acceleration setting. The axial and radial vibration accelerations monitored at 4500 m of the lower vibration tester were both within 2.5 g, with the radial being 1.33 g and the axial being 2.46 g (as shown in (a) below), and the extreme values of the acceleration change are shown in Table 4. At 4914 m of the perforating tester, the maximum X-direction acceleration was 18.2 g and the maximum reverse acceleration was 18.4 g (as shown in (b) below), the maximum Y-direction acceleration was 22.7 g and the maximum reverse acceleration was 17.8 g (as shown in (c) below), and the maximum Z-direction acceleration was 21.3 g and the maximum reverse acceleration was 26.5 g (as shown in (d) below). Figure 11 At 4914 m of the perforating tester, the maximum X-direction acceleration was 18.2 g and the maximum reverse acceleration was 18.4 g (as shown in (b) below), the maximum Y-direction acceleration was 22.7 g and the maximum reverse acceleration was 17.8 g (as shown in (c) below), and the maximum Z-direction acceleration was 21.3 g and the maximum reverse acceleration was 26.5 g (as shown in (d) below). Figure 11 At 4914 m of the perforating tester, the maximum Y-direction acceleration was 22.7 g and the maximum reverse acceleration was 17.8 g (as shown in (c) below), and the maximum Z-direction acceleration was 21.3 g and the maximum reverse acceleration was 26.5 g (as shown in (d) below). Figure 11 At 4914 m of the perforating tester, the maximum Z-direction acceleration was 21.3 g and the maximum reverse acceleration was 26.5 g (as shown in (d) below). Figure 11 In summary, based on the accurate analysis of detonation parameters, the present invention improves the analysis method of reflection parameters at the interface between the casing and the perforating fluid based on the reflection principle, and solves the problems of perforating fluid pressure pulsation and damage to the oil casing string in deep wells, high initial pressures, and narrow boundaries that are difficult to solve by the existing underwater explosion theories for shallow layers, low initial pressures, and free boundaries through a pressure pulsation calculation model; at the same time, a method for analyzing the strength safety of the perforating section string is formed according to the pipe string dynamic response model, improving the adaptability and accuracy of solving perforating detonation problems.

[0195] Variation of the perforating fluid pressure in the annulus at 4914 m: The maximum annulus pressure was 174.8 MPa, and the time interval between the wave peak and the wave trough was 0.56 seconds. Downhole measurements showed that the peak pressure of the perforating fluid could reach about 3 times the hydrostatic pressure (as shown below), and due to the "backfill" of the perforating fluid to the perforating gun, a local "negative pressure" would be formed, and at this time, the downward load generated by the pipe string would be transmitted to the central pipe of the packer. Figure 12 In summary, based on the accurate analysis of detonation parameters, the present invention improves the analysis method of reflection parameters at the interface between the casing and the perforating fluid based on the reflection principle, and solves the problems of perforating fluid pressure pulsation and damage to the oil casing string in deep wells, high initial pressures, and narrow boundaries that are difficult to solve by the existing underwater explosion theories for shallow layers, low initial pressures, and free boundaries through a pressure pulsation calculation model; at the same time, a method for analyzing the strength safety of the perforating section string is formed according to the pipe string dynamic response model, improving the adaptability and accuracy of solving perforating detonation problems.

[0196] The above technical features constitute the embodiments of the present invention, which have strong adaptability and implementation effects. Non-essential technical features can be added or subtracted according to actual needs to meet the requirements of different situations.

[0197] The above technical features constitute the embodiments of the present invention, which have strong adaptability and implementation effects. Non-essential technical features can be added or subtracted according to actual needs to meet the requirements of different situations.

[0198] Table 1

[0199]

[0200]

[0201] Table 2

[0202]

[0203] Table 3

[0204]

[0205] Table 4

[0206] Bottom-hole vibration perforation X direction Y direction Z direction Maximum value / g 2.46 2.47 2.46 Minimum value / g -1.33 -2.50 -2.50

Claims

1. A method for analyzing the strength safety of a perforating section pipe string, characterized in that Proceed as follows: First, the dynamic response model of the tubing string is used to obtain the dynamic response results of the tubing string at the corresponding time point. The dynamic response results of the tubing string include the axial displacement change curve at the bottom of the tubing string, the axial velocity change curve at the bottom of the tubing string, the axial acceleration change at the bottom of the tubing string, and the equivalent stress change curve of the tubing string at the packer under axial load. The dynamic response model of the tubing string is shown as follows: Displacement: speed: Acceleration: stress: Where E is the elastic modulus, MPa; v is the perforating fluid velocity, m / s; c is the viscous friction, m 2 / s; l is the length of the perforation section, m; x is the coordinate of a point in the string, m; t is a moment, s; λ and β are calculation constants, dimensionless; Then, a curve analysis was performed on the dynamic response results of the tubing string, and the strength safety evaluation results of the perforating section tubing string were obtained in combination with the strength safety evaluation standard of the perforating section tubing string. The strength safety evaluation standard of the perforating section tubing string included finding the maximum peak stress point of the perforating section tubing string in the equivalent stress change curve of the tubing string at the packer under axial load. This point is the point closest to the packer, and the perforating section tubing string at this point is prone to tubing string vibration bending and vibration breaking.

2. The method for analyzing the strength safety of a perforating section pipe string according to claim 1 is characterized in that Construct a string dynamic response model, including: The first step is to apply the Michaelisson equation and the average specific heat method, introduce the maximum explosion heat realization degree coefficient, modify the explosion capacity, explosion heat and explosion temperature calculation formulas, and apply the maximum energy release principle and Kamelet method to analyze and calculate the detonation pressure and detonation velocity; In the second step, based on the detonation wave parameters and Tait equation in the continuity of the phase change interface shock wave, the initial shock wave pressure analysis model is established. Combining the detonation pressure and detonation velocity, based on the initial shock wave pressure analysis model, reflection principle and classical explosion experimental data, the shock wave pressure calculation model under different pulsation stages of the superposition of direct waves and reflected waves is analyzed and obtained, as shown below: p(t)=p0(t0)+p1(t1)+p2(t2)+p3(t3)+p4(t4) Among them, P ro is the reflection pressure of No. 0 bullet, MPa; θ is the time decay constant, θ=12.3μs; P ai is the reflected wave pressure value of the i-th bullet, MPa; The third step is to obtain the dynamic response model of the pipe string based on the shock wave pressure calculation model at different pulsation stages, apply the cantilever beam theory of vibration dynamics, combine the vibration differential equations under the three impact loads of axial, lateral and torsional loads of the pipe string, and calculate the derivatives of each order, as shown below: Displacement: speed: Acceleration: stress: Where E is the elastic modulus, MPa; v is the perforating fluid velocity, m / s; c is the viscous friction, m 2 / s; l is the length of the perforation section, m; x is the coordinate of a point in the string, m; t is a moment, s; λ and β are calculation constants and are dimensionless.

3. The method for analyzing the strength safety of a perforation section pipe string according to claim 2, characterized in that In the first step, the calculation method of the detonation wave parameters is as follows: D=A(1+Bρ)ψ 1 / 2 P=1.558ρ 2 ψ Where P is the detonation pressure, GPa; D is the detonation velocity, km / s, A = 1.01, B = 1.3; N is the number of moles of gas products per kg of explosive, mol / kg; ρ is the density of explosive, g / cm 3 ; is the average molar mass of the gas component; Qmax is the maximum possible explosion heat value, kcal / kg.

4. The method for analyzing the strength safety of a perforation section pipe string according to claim 2 or 3, characterized in that In the second step, a shock wave pressure calculation model is constructed at different pulsation stages, including: S1, based on the continuity of the phase change interface shock wave and the Tait equation, the calculation model of the initial shock wave pressure in the perforating fluid is obtained as follows: Where P is the initial shock wave pressure in the perforating fluid, GPa; ρ c is the density of detonation products, g / cm 3 ; is ρ oc is the density of the perforating fluid before the shock wave front, g / cm 3 ; A is the experimental measurement parameter, A = 307.7MPa; m is the experimental measurement parameter, m = 7.15; S2, according to the LS-DYNA analysis of the detonation pressure attenuation law along the axial direction, the analytical expression of the shock wave pressure peak value changing with the explosion distance is obtained, as shown below: pp m =p0+p x have been -0.031(R-1 / 3r) Among them, P m is the peak pressure at the explosion distance R, GPa; P x is the initial pressure of the shock wave, GPa; P0 is the initial static column pressure of the perforating fluid, MPa; R is the explosion distance, m; r is the proportional distance, dimensionless; S3, based on the reflection principle and combined with the reflection law of the perforating fluid shock wave at the casing interface, the calculation formula for the shock wave pressure propagating in the reverse direction in the perforating fluid is obtained as follows: p r =p A -p B Among them, P r is the reflected shock wave pressure, GPa; P A is the initial shock wave pressure at a certain point, GPa; P B is the reflected wave pressure, GPa; S4, based on the fact that the detonation shock wave will produce an oblique collision near the midpoint of two adjacent bombs and superimpose each other, the calculation formula for the superposition pressure of the shock wave between bombs is obtained as follows: p a =0.6×2p r =1.2p r Among them, P a is the superimposed shock wave pressure, GPa; P r is the shock wave pressure generated by a single perforating charge explosion, GPa; S5, according to the pulsation characteristics of the explosion shock wave pressure and the law of interface reflection, combined with the calculation model of the initial shock wave pressure in the perforating fluid, the analytical expression of the shock wave pressure peak value changing with the explosion distance, the calculation formula of the reverse propagation shock wave pressure in the perforating fluid, and the calculation formula of the superposition pressure of the shock wave between bullets, the calculation model of the shock wave pressure at different pulsation stages is obtained, as shown below: p(t)=p0(t0)+p1(t1)+p2(t2)+p3(t3)+p4(t4) Among them, P ro is the reflection pressure of No. 0 bullet, MPa; θ is the time decay constant, θ=12.3μs; P ai is the reflected wave pressure value of the i-th bullet, MPa.

5. The method for analyzing the strength safety of a perforation section pipe string according to claim 2, 3 or 4, characterized in that In the third step, the string dynamic response model is constructed, including: S1, based on the field perforating-testing combined string system, combined with the axial, lateral and torsional impact loads on the perforating section string, and considering the packer as the fixed end of the string, the bottom end of the string is free, and the perforating section string is a cantilever beam, the dynamic models under the three loads are established respectively; S2, based on the D'Alembert principle, the equation for the axial vibration of the perforating section string is obtained as follows: Vibration equilibrium equation: Vibration differential equation: Boundary conditions: Initial conditions: Displacement response equation: in, is the inertial force on the microelement, N; is the cross-sectional internal force, N; E is the elastic modulus of the pipe string material, Pa; ρ is the pipe density, kg / m 3 ; FN is the axial force of the cross section, N; A is the cross-sectional area, m 2 ; I is a positive integer; Τ is the time integral variable; S3, based on the D'Alembert inertia principle, the equation for the lateral vibration of the perforating section string is obtained as follows: Where, E is the elastic modulus, Pa; I is the moment of inertia, mm 4 ; ρ is the pipe density, kg / m 3 ; A is the cross-sectional area / m 2 ; y(x, t) is the lateral displacement of the section at the origin x at time t, m; f(x, t) is the unit lateral load / N / m; S4, based on the D'Alembert principle, the torque vibration equation of the perforating section string is obtained as follows: in, is the angular displacement of the pipe section at the origin x at time t, °; G is the shear elastic modulus, Pa; ρ is the pipe density, kg / m 3 ; IP is the polar moment of inertia of the cross section, mm 4 ; f(x, t) is the unit torsional load / N / m; S5, after calculating the derivatives of each order of the axial vibration of the tubing string in the perforation section, the dynamic response model of the tubing string is obtained, as shown below: Displacement: speed: Acceleration: stress: Where E is the elastic modulus, MPa; v is the perforating fluid velocity, m / s; c is the viscous friction, m 2 / s; l is the length of the perforation section, m; x is the coordinate of a point in the string, m; t is a moment, s; λ and β are calculation constants and are dimensionless.

6. A perforation section string strength safety analysis device using the method as claimed in any one of claims 1 to 5, characterized in that include: The evaluation data acquisition unit uses the tubing dynamic response model to obtain the tubing dynamic response results at the corresponding time points, wherein the tubing dynamic response results include the axial displacement change curve at the bottom of the tubing, the axial velocity change curve at the bottom of the tubing, the axial acceleration change at the bottom of the tubing, and the equivalent stress change curve of the tubing at the packer under axial load. The tubing dynamic response model is as follows: Displacement: speed: Acceleration: stress: Where E is the elastic modulus, MPa; v is the perforating fluid velocity, m / s; c is the viscous friction, m 2 / s; l is the length of the perforation section, m; x is the coordinate of a point in the string, m; t is a moment, s; λ and β are calculation constants, dimensionless; The safety evaluation unit performs curve analysis on the dynamic response results of the tubing string, and obtains the strength safety evaluation results of the tubing string of the perforating section in combination with the strength safety evaluation standard of the tubing string of the perforating section. The strength safety evaluation standard of the tubing string of the perforating section includes finding the maximum peak stress point of the tubing string of the perforating section in the equivalent stress variation curve of the tubing string at the packer under axial load. This point is the point closest to the packer, and the tubing string section at this point is prone to tubing string vibration bending and vibration breaking.

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