Gas storage injection and production well completion pipe string transverse vibration analysis method and device

Abstract

The invention relates to a gas storage injection-production well completion pipe string transverse vibration analysis method and device. The method comprises the steps of determining kinetic energy of an infinitesimal section of a well completion pipe string in a transverse bending vibration process and total potential energy of the well completion pipe string according to the cross sectional area of the well completion pipe string, the mass of the well completion pipe string per unit length, the flexural rigidity of the well completion pipe string, parameters related to fluid flowing through the well completion pipe string and pressure borne by the well completion pipe string; according to the kinetic energy of the infinitesimal section of the well completion pipe string in the transverse bending vibration process, the total potential energy of the well completion pipe string and the boundary conditions of the well completion pipe string, a transverse fluid-solid coupling vibration equation of the well completion pipe string is constructed; solving to obtain the inherent frequency of each order; and the string vibration frequency corresponding to the gas injection and production is simulated, and the critical gas production and gas injection of the completion string are determined. According to the method, the damage of transverse vibration to the injection-production well completion pipe string is reduced through injection-production measures for avoiding resonance gas flow, and the method has important significance on transverse vibration diagnosis and evaluation of injection-production well completion pipe string operation.

Description

Technical Field

[0001] This manual relates to the field of unconventional oil and gas production enhancement technology, especially the method and device for analyzing the lateral vibration of the completion tubing in gas storage injection and production wells. Background Technology

[0002] Underground gas storage facilities are currently the most important method for natural gas storage and peak shaving. When considering well completion processes, gas storage facilities must not only fully utilize the production capacity of injection and production wells and ensure the emergency peak shaving capacity of the gas storage facilities, but also ensure safe and efficient injection and production.

[0003] Because of the complex composition of natural gas and the complex structure of the injection / production / completion tubing, the movement of natural gas within the tubing is also complex. This is especially true when high-pressure natural gas flows through curved sections and areas of variable cross-section in the tubing, exerting forces on it. Due to fluctuations in natural gas volume and pressure, these complex operating conditions during injection and production activities in gas storage facilities can easily lead to lateral vibration of the injection / production / completion tubing. Furthermore, due to the uncertainty of formation production and human intervention such as well opening / closing and production adjustments, the flow rate and pressure of natural gas are in a pulsating state. This is equivalent to natural gas applying a dynamic load to the injection / production / completion tubing, thus inducing lateral vibration. When the natural gas volume is large, this dynamic load increases further.

[0004] Lateral bending vibrations can cause bending deformation in injection and production completion tubing, which not only exacerbates friction between the completion tubing and casing, leading to fatigue wear of the tubing, but can even induce fatigue fracture of the completion tubing. Furthermore, when the frequency generated by the natural gas flow within the injection and production completion tubing is close to the natural frequency of the completion tubing itself, resonance can easily occur, potentially causing safety accidents in the gas storage facility. Therefore, lateral resonance of the completion tubing must be avoided during natural gas injection and production in gas storage facilities, and the maximum lateral vibration displacement should be minimized as much as possible. Summary of the Invention

[0005] To address the problem of lateral vibration in injection and production well completion tubing in existing technologies, this specification provides a method and apparatus for analyzing lateral vibration of gas storage injection and production well completion tubing.

[0006] This specification provides a method for analyzing the lateral vibration of completion strings in gas storage injection and production wells. The method includes: determining the kinetic energy of a small segment of the completion string and the total potential energy of the completion string during lateral bending vibration based on the cross-sectional area of ​​the completion string, the mass per unit length of the completion string, the bending stiffness of the completion string, parameters related to the fluid flowing through the completion string, and the pressure exerted on the completion string; constructing the lateral fluid-structure interaction vibration equation of the completion string based on the kinetic energy of the small segment of the completion string during lateral bending vibration, the total potential energy of the completion string, and the boundary conditions of the completion string; solving the lateral fluid-structure interaction vibration equation of the completion string and calculating the natural frequencies of each order of fluid-structure interaction of the completion string; and determining the relative value of the amplitude of the lateral fluid-structure interaction vibration of the completion string based on the natural frequencies.

[0007] According to one aspect of the embodiments of this specification, determining the kinetic energy of a micro-segment of the completion string and the total potential energy of the completion string during lateral bending vibration includes: determining the lateral vibration velocity of the completion string, the horizontal component and the vertical component of the fluid velocity within the completion string, based on the cross-sectional area of ​​the completion string, the mass per unit length of the completion string, the bending stiffness of the completion string, parameters related to the fluid flowing through the completion string, and the pressure exerted on the completion string; and determining the kinetic energy of a micro-segment of the completion string and the total potential energy of the completion string during lateral bending vibration based on the lateral vibration velocity of the completion string and the horizontal component and the vertical component of the fluid velocity within the completion string.

[0008] According to one aspect of the embodiments of this specification, the kinetic energy of a small segment of the completion string and the total potential energy of the completion string during lateral bending vibration are determined based on the lateral vibration velocity of the completion string, the horizontal component and the vertical component of the fluid velocity inside the completion string, including:

[0009] The kinetic energy of a small segment of the completion string during lateral bending vibration is determined using the following formula: in, y represents the lateral vibration velocity of the completion string; v represents the fluid velocity inside the completion string; y represents the lateral vibration displacement of the completion string. x Indicates the horizontal component; v y The vertical component is represented by y′; y′ represents the slope of the completion string axis; t represents time; m p Indicates the mass per unit length of the completion string; A i Let represent the cross-sectional area of ​​the completion string in the i-th infinitesimal segment, ρ represent the fluid density, and dx represent the infinitesimal segment of the completion string. The total potential energy of the completion string in the infinitesimal segment is determined according to the following formula: Where EI represents the bending stiffness of the completion string, F represents the axial force on the completion string, and p i p represents the internal pressure of the i-th micro-element segment of the completion string. ip represents the internal pressure within the i-th micro-element of the completion string. o A represents the annular pressure of the completion string. i Let A0 represent the cross-sectional area of ​​the completion string in the i-th infinitesimal segment, y′ represent the axial slope of the completion string, and y″ represent the rate of change of the axial slope of the completion string.

[0010] According to one aspect of the embodiments of this specification, the lateral fluid-structure interaction vibration equation of the completion string is constructed based on the kinetic energy of the micro-segment of the completion string during lateral bending vibration, the total potential energy of the completion string, and the boundary conditions of the completion string. This includes: transforming the kinetic energy of the micro-segment of the completion string during lateral bending vibration and the total potential energy of the completion string into variational equations according to Hamilton's principle; and constraining the variational equations using the boundary conditions of the completion string to obtain the lateral fluid-structure interaction vibration equation of the completion string.

[0011] According to one aspect of the embodiments of this specification, solving the lateral fluid-structure interaction vibration equation of the completion string includes: determining the spatial mode shape of the lateral fluid-structure interaction vibration equation of the completion string based on the lateral fluid-structure interaction vibration equation of the completion string, wherein the spatial mode shape is a linear combination of sine and cosine functions; substituting the linear combination of sine and cosine functions into the lateral fluid-structure interaction vibration equation of the completion string to obtain a set of linear second-order equations corresponding to the lateral fluid-structure interaction vibration equation of the completion string; and solving the set of linear second-order equations.

[0012] According to one aspect of the embodiments of this specification, the lateral vibration velocity of the completion string, the horizontal component and the vertical component of the fluid velocity inside the completion string are determined by the following formulas: in, y represents the lateral vibration velocity of the completion string; v represents the fluid velocity inside the completion string; y represents the lateral vibration displacement of the completion string. x The horizontal component representing the fluid velocity within the completion string; v y y' represents the vertical component of the fluid velocity within the completion string; y′ represents the slope of the completion string axis; and t represents time.

[0013] According to one aspect of the embodiments of this specification, simulating the string vibration frequency corresponding to the gas injection / production volume, and determining the gas production volume and gas injection volume of the completion string when the string vibration frequency reaches the natural frequency, includes: simulating a first string vibration frequency under different gas injection volumes and a second string vibration frequency under different gas production volumes; and determining the gas production volume and gas injection volume corresponding to the completion string when the first string vibration frequency and the second string vibration frequency respectively reach the natural frequency.

[0014] This specification also provides an embodiment of a device for analyzing the lateral vibration of a completion string in a gas storage injection-production well. The device includes: a first determining unit, used to determine the kinetic energy of a micro-segment of the completion string and the total potential energy of the completion string during lateral bending vibration based on the cross-sectional area of ​​the completion string, the mass per unit length of the completion string, the bending stiffness of the completion string, parameters related to the fluid flowing through the completion string, and the pressure exerted on the completion string; an equation constructing unit, used to construct the lateral fluid-structure coupling vibration equation of the completion string based on the kinetic energy of the micro-segment of the completion string during lateral bending vibration, the total potential energy of the completion string, and the boundary conditions of the completion string; a calculation unit, used to solve the lateral fluid-structure coupling vibration equation of the completion string and calculate the natural frequencies of each order of fluid-structure coupling of the completion string; and a second determining unit, used to simulate the string vibration frequency corresponding to the injection / production gas volume, and when the string vibration frequency reaches the natural frequency, to determine the critical production gas volume and injection gas volume of the completion string.

[0015] This specification also provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for analyzing the lateral vibration of the completion tubing of the gas storage injection and production well.

[0016] This specification also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for analyzing the lateral vibration of the completion tubing in the gas storage injection and production wells.

[0017] This invention analyzes the maximum lateral displacement of injection and completion tubing under different gas volumes and the impact of different gas volumes on the vibration frequency of the completion tubing. It determines the resonant injection / production gas volume and reduces the damage to the injection / production completion tubing caused by lateral vibration by implementing injection / production measures that avoid resonant gas volumes. This invention is of great significance for the diagnosis, assessment, and safety precautions of lateral vibration during on-site injection / production completion tubing operations. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 The diagram shown is a flowchart of a method for analyzing the lateral vibration of the completion tubing in a gas storage injection-production well, as described in this specification.

[0020] Figure 2The diagram shown is a flowchart of a method for determining the kinetic energy of a micro-segment of a completion string and the total potential energy of the completion string during lateral bending vibration, according to an embodiment of this specification.

[0021] Figure 3 The diagram shown is a flowchart of a method for constructing the transverse fluid-structure interaction vibration equation of a well completion string according to an embodiment of this specification.

[0022] Figure 4 The diagram shown is a flowchart of a method for solving the transverse fluid-structure interaction vibration equation of a well completion string according to an embodiment of this specification.

[0023] Figure 5 The diagram shown is a flowchart of a method for determining the gas extraction volume and the gas injection volume according to an embodiment of this specification.

[0024] Figure 6 The diagram shown is a schematic diagram of the lateral vibration analysis device for the completion tubing of a gas storage injection-production well, according to an embodiment of this specification.

[0025] Figure 7A The diagram shown is a schematic diagram of the vibration frequency and natural frequency of the well completion string under the gas production conditions in the embodiments of this specification.

[0026] Figure 7B The diagram shown is a schematic diagram of the vibration frequency and natural frequency of the completion tubing under the gas injection condition in the embodiments of this specification.

[0027] Figure 7C The figure shown is a schematic diagram of the lateral vibration dynamics model of a well completion string according to an embodiment of this specification;

[0028] Figure 8A The diagram shown illustrates the relationship between the maximum lateral vibration displacement of the well completion string and time when the gas production rate is 1.05 million cubic meters per day, as described in the embodiments of this specification.

[0029] Figure 8B The diagram shown illustrates the relationship between the maximum lateral vibration displacement of the well completion string and time when the gas injection rate is 800,000 cubic meters per day, as described in the embodiments of this specification.

[0030] Figure 9A The diagram shown is a schematic of the longitudinal vibration displacement of the completion string at a distance of 400m from the packer under different gas production rates in this manual.

[0031] Figure 9B The diagram shown is a schematic of the longitudinal vibration displacement of the completion string at a distance of 400m from the packer under different gas injection volumes in this manual.

[0032] Figure 10 The diagram shown is a structural schematic of a computer device according to an embodiment of this specification.

[0033] Explanation of symbols in the attached drawings:

[0034] 601. First Determined Unit;

[0035] 602. Equation building unit;

[0036] 603. Calculation Unit;

[0037] 604. Second Determined Unit;

[0038] 1002. Computer equipment;

[0039] 1004, Processor;

[0040] 1006. Memory;

[0041] 1008. Drive mechanism;

[0042] 1010. Input / Output Module;

[0043] 1012. Input devices;

[0044] 1014. Output devices;

[0045] 1016. Presentation device;

[0046] 1018. Graphical User Interface;

[0047] 1020. Network interface;

[0048] 1022. Communication link;

[0049] 1024. Communication bus. Detailed Implementation

[0050] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this specification.

[0051] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, apparatus, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0052] This specification provides the operational steps of the methods described in the embodiments or flowcharts, but based on conventional or non-inventive labor, more or fewer operational steps may be included. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only possible execution order. In actual system or device products, the methods shown in the embodiments or drawings can be executed sequentially or in parallel.

[0053] It should be noted that the lateral vibration analysis method for completion tubing of gas storage injection and production wells in this manual can be used in the field of unconventional oil and gas production enhancement and transformation technology, as well as in the field of oil and gas field exploration and development. This manual does not limit the application field of the lateral vibration analysis method and device for completion tubing of gas storage injection and production wells.

[0054] During oil and gas well extraction, when the frequencies of various vibration sources approach the natural frequencies of the completion tubing, the completion tubing will resonate, exacerbating its damage. When natural gas is transported within the completion tubing, the force exerted by the natural gas on the tubing is a variable load. When the frequency of the natural gas flow excitation force couples with a certain natural frequency of the completion tubing, resonance will occur. This is one of the main causes of tubing breakage or rupture during natural gas extraction.

[0055] When gas or liquid flows through the completion string, the changes in flow velocity and the fluctuations in pressure acting on the completion string will induce vibrations in the oil completion string. Resonance will be particularly severe when the frequency of the excitation force is close to a natural frequency of the completion string.

[0056] Lateral vibration of the completion string poses a significant hazard, often being a major cause of wear and subsequent fracture, thus drastically shortening its fatigue life. Lateral vibration is a forced vibration resulting from the combined effects of internal and external fluids, axial forces, and internal and external pressures within the completion string.

[0057] Figure 1The diagram shown is a flowchart of a method for analyzing the lateral vibration of a gas storage injection-production well completion string, according to an embodiment of this specification. The method specifically includes the following steps:

[0058] Step 101: Based on the cross-sectional area of ​​the completion string, the mass per unit length of the completion string, the bending stiffness of the completion string, the parameters related to the fluid flowing through the completion string, and the pressure on the completion string, determine the kinetic energy of the micro-segment of the completion string during the transverse bending vibration process and the total potential energy of the completion string.

[0059] In this specification, the completion string is a crucial channel for fluid production from the formation and for surface working fluid injection into the formation. The completion string includes components such as tubing, variable thread couplings, packers, screens, various valves, and perforating guns. The main vibration modes of the completion string can be categorized into longitudinal and lateral vibrations, and these two vibration modes often couple, exacerbating fatigue failure of the completion string. During operation, the completion string will buckle and deform under the influence of various factors such as axial force, internal and external pressure, and temperature. Changes in the flow velocity of gas or liquid flowing through the completion string and fluctuations in the pressure acting on it will induce vibrations in the completion string.

[0060] In this specification, fluid flowing through the completion string has a certain velocity, and the parameters related to the fluid flowing through the completion string include: fluid velocity, fluid density, etc. The pressures on the completion string specifically include: internal pressure within the completion string, annular pressure, and axial force on the completion string. Annular pressure represents the pressure between the annular spaces of each casing layer during drilling, and further includes hydrostatic pressure and dynamic pressure. Lateral vibration of the completion string is a forced vibration resulting from the combined effects of fluids inside and outside the completion string, axial force, and internal and external pressures.

[0061] In the embodiments of this specification, firstly, based on data such as the cross-sectional area of ​​the completion string, the mass per unit length of the completion string, the bending stiffness of the completion string, the fluid velocity flowing through the completion string, the fluid density, and the internal pressure, annular pressure, and axial force of the completion string, the lateral vibration velocity of the completion string, and the horizontal and vertical components of the fluid velocity within the completion string are calculated. The lateral vibration velocity of the completion string can be understood as the velocity of the completion string in the direction perpendicular to the axis. Further, based on the lateral vibration velocity and the fluid velocity within the completion string, the kinetic energy of each micro-segment of the completion string during the lateral bending vibration process is calculated, and the total potential energy of the completion string is also calculated.

[0062] like Figure 7C The diagram shown is a schematic representation of the lateral vibration dynamics model of a completion string according to an embodiment of this specification. To illustrate the characteristics of the lateral vibration of the completion string and the influence of internal natural gas flow on the vibration, the completion string is idealized as an elastic tube with a uniform cross-section and hinged supports at both ends, as shown below. Figure 7CAs shown in the figure. The span length of the completion string is L, and the mass per unit length of the string is m. p The bending stiffness of the tubular column is EI, and the inner and outer diameters of the tubular column are D and D, respectively. i D o The fluid density is ρ f The cross-sectional area A of the pipe flows through it at a constant velocity V. The lateral deflection of the pipe column is y(z,t), and the axial coordinate of the pipe column is z.

[0063] In this manual, the completion string works inside the casing. When the amplitude of the completion string is large, the outer wall of the completion string will continuously collide with the inner wall of the casing, resulting in bidirectional wear between the tubing and the casing. The coupling is a protruding part in the completion string system, so wear will first occur at the coupling.

[0064] Wear can lead to coating failure, reduced strength, and even penetration of the casing wall on the completion string surface. On the other hand, friction between the casing and tubing generates a large amount of heat, which can reduce the hardness and other mechanical properties of the completion string material. Therefore, wear has an extremely detrimental effect on the completion string. The downhole completion string is composed of individual tubing segments connected by threads. These threads are the weakest part of the completion string system. Prolonged excessive vibration can cause fatigue fracture at the threads and loosening of the threads, affecting the connection and sealing of the completion string and causing leaks. Lateral resonance increases the bending stress of the completion string, accelerating fatigue failure and wear between the tubing coupling and the casing. Therefore, lateral resonance in the completion string assembly should be avoided during design.

[0065] Step 102: Based on the kinetic energy of the micro-segment of the completion string during the transverse bending vibration process, the total potential energy of the completion string, and the boundary conditions of the completion string, construct the transverse fluid-structure coupling vibration equation of the completion string.

[0066] In this specification, based on Hamilton's principle, the kinetic energy of the infinitesimal segment of the completion string during lateral bending vibration and the total potential energy of the completion string are transformed to obtain a variational equation. Further processing of the variational equation using the boundary conditions of the completion string yields the lateral fluid-structure interaction vibration equation for the completion string. For a detailed description of constructing the lateral fluid-structure interaction vibration equation for the completion string, please refer to [link to documentation]. Figure 3 describe.

[0067] In the embodiments described in this specification, the completion string is hinged at both ends, and packers are located at both ends of the completion string, with the positions of the packers fixed. Based on this, boundary conditions for the completion string can be set. Specifically, the boundary conditions are: as time changes, the displacement of the starting end of the completion string is 0, and the displacement of the ending end of the completion string is 0.

[0068] In this step, the equations representing the boundary conditions of the completion string are substituted into the formulas for the kinetic energy of a small segment of the completion string during lateral bending vibration and the total potential energy of the completion string. This yields the differential equations representing the lateral fluid-structure interaction vibration of the completion string. These differential equations encompass the influence of the fluid within the completion string, the axial force within the completion string, the injection pressure within the completion string, and the annular pressure on the vibration of the completion string.

[0069] Step 103: Solve the transverse fluid-structure interaction vibration equation of the completion string and calculate the natural frequencies of each order of fluid-structure interaction of the completion string.

[0070] In this step, the method of separation of variables can be used to transform the transverse fluid-structure interaction vibration equation of the completion string, converting it into a linear combination of spatial mode shapes with sine and cosine modes. This allows for the solution of the transverse fluid-structure interaction vibration equation of the completion string, calculating the natural frequencies and amplitudes of each order of the fluid-structure interaction vibration of the completion string.

[0071] Step 104: Simulate the tubing vibration frequency corresponding to the gas injection / production volume. When the tubing vibration frequency reaches the natural frequency, determine the critical gas production volume and gas injection volume of the completion tubing.

[0072] When the frequency generated by the fluid flow within the well completion string is close to the natural frequency of the completion string itself, the resulting gas production and injection volumes will cause resonance in the completion string. Therefore, in this step, by simulating the first vibration frequency of the string under different injection volumes and the second vibration frequency of the string under different production volumes, the critical production and injection volumes corresponding to the completion string when the first vibration frequency and the second vibration frequency of the string reach the natural frequency are determined. Therefore, when injecting and producing natural gas in a gas storage facility, operations should avoid using these production and injection volumes to prevent lateral resonance in the completion string and to minimize the maximum lateral vibration displacement.

[0073] Figure 2 The diagram shown is a flowchart illustrating a method for determining the kinetic energy of a micro-segment of a completion string and the total potential energy of the completion string during lateral bending vibration, according to an embodiment of this specification. The method specifically includes the following steps:

[0074] Step 201: Based on the cross-sectional area of ​​the completion string, the mass per unit length of the completion string, the bending stiffness of the completion string, the parameters related to the fluid flowing through the completion string, and the pressure on the completion string, determine the lateral vibration velocity of the completion string, the horizontal component and the vertical component of the fluid velocity inside the completion string.

[0075] In the embodiments of this specification, a transverse fluid-structure interaction vibration model of the injection-production completion string is first established. This model considers the influence of fluid inside the completion string, axial force of the completion string, injection pressure inside the completion string, and annular pressure on the transverse vibration of the injection-production completion string.

[0076] Assuming the completion string is a continuous system with distributed mass and distributed elasticity, its vibration is elastic, conforming to the basic assumptions of an elastic body, namely, obeying Hooke's law and exhibiting homogeneity and isotropy. The completion string does not contact the casing, thus friction between the tubing and casing is negligible. The fluid is an ideal fluid, inviscid and incompressible.

[0077] In the embodiments described in this specification, the packer of the completion string can be considered as a hinged structure, with hinged supports at both ends of the completion string. Fluid is injected into the completion string, flowing through it at a certain velocity. The fluid density is denoted as ρ, and the fluid flow velocity is denoted as v. The cross-sectional area of ​​the completion string, the internal pressure within the completion string, the annular pressure, the axial force, the mass per unit length of the completion string, and the bending stiffness of the completion string are obtained. The flow direction of the fluid within the completion string is tangent to the axis of the completion string.

[0078] Based on the cross-sectional area of ​​the completion string, the mass per unit length of the completion string, the bending stiffness of the completion string, the fluid velocity, the fluid density, and the internal pressure, annular pressure, and axial force on the completion string obtained as described above, the lateral vibration velocity of the completion string and the horizontal and vertical components of the fluid velocity inside the completion string are determined using the following formulas:

[0079]

[0080]

[0081] in, y represents the lateral vibration velocity of the completion string; v represents the fluid velocity inside the completion string; y represents the lateral vibration displacement of the completion string. x The horizontal component representing the fluid velocity within the completion string; v y y' represents the vertical component of the fluid velocity within the completion string; y′ represents the slope of the completion string axis; and t represents time.

[0082] Step 202: Based on the lateral vibration velocity of the completion string and the horizontal and vertical components of the fluid velocity inside the completion string, determine the kinetic energy of the micro-segment of the completion string during the lateral bending vibration process and the total potential energy of the completion string.

[0083] In the embodiments described in this specification, the kinetic energy of a micro-segment of the completion string during lateral bending vibration is expressed by the following formula:

[0084]

[0085] Where dT represents the kinetic energy of a certain infinitesimal segment of the completion string during lateral bending vibration. y represents the lateral vibration velocity of the completion string; v represents the fluid velocity inside the completion string; y represents the lateral vibration displacement of the completion string. x Indicates the horizontal component; v y The vertical component is represented by y′, the slope of the completion string axis is represented by y″, and t represents time (m). p Indicates the mass per unit length of the completion string; A i Let dx represent the cross-sectional area of ​​the completion string in the i-th infinitesimal segment, ρ represent the fluid density, and dx represent the infinitesimal segment of the completion string.

[0086] In the embodiments described in this specification, the total potential energy of this micro-element segment of the completion string is expressed by the following formula:

[0087]

[0088] Where dU represents the potential energy of a micro-element of the completion string, EI represents the bending stiffness of the completion string, F represents the axial force on the completion string, and p i p represents the internal pressure of the i-th micro-element segment of the completion string. o A represents the annular pressure of the completion string. i Let A0 represent the cross-sectional area of ​​the completion string in the i-th infinitesimal segment, y′ represent the axial slope of the completion string, y″ represent the rate of change of the axial slope of the completion string, and dx represent the infinitesimal segment.

[0089] Based on the above formula, the kinetic energy of the completion string during the lateral bending vibration process and the total potential energy of the completion string can be determined.

[0090] Figure 3 The diagram shown is a flowchart of a method for constructing the transverse fluid-structure interaction vibration equation of a well completion string according to an embodiment of this specification, which specifically includes the following steps:

[0091] Step 301: Based on Hamilton's principle, the kinetic energy of the infinitesimal segment of the completion string during the transverse bending vibration process and the total potential energy of the completion string are transformed to obtain the variational equation.

[0092] In this specification, Hamilton's principle is expressed by the following formula: δ(TU)=0; (5)

[0093] Where T represents the kinetic energy of the completion string and U represents the total potential energy of the completion string.

[0094] according to Figure 1The kinetic energy of the infinitesimal segment of the completion string during the lateral bending vibration process, calculated in the previous step, and the potential energy of the infinitesimal segment of the completion string, are substituted into Hamilton's principle formula to obtain the following formula:

[0095] (6),

[0096] Where EI represents the bending stiffness of the completion string, F represents the axial force on the completion string, and p i p represents the internal pressure of the i-th micro-element segment of the completion string. o A represents the annular pressure of the completion string. i Let A0 represent the cross-sectional area of ​​the completion string in the i-th infinitesimal segment. y′ represents the lateral vibration velocity of the completion string, dx represents the slope of the completion string axis, dt represents the infinitesimal segment, y″ represents the infinitesimal variable with time t as the variable, and y″ represents the slope of the completion string axis.

[0097] By performing variational rearrangement on the above formula (6), we obtain formula (7):

[0098]

[0099] Formula (7) Where x1 and x2 represent two different abscissas, t1 and t2 represent two different time points, y′ represents the slope of the completion string axis, y″ represents the rate of change of the slope of the completion string axis, and m p A represents the mass per unit length of the completion string. i dx represents the cross-sectional area of ​​the i-th micro-element of the completion string; ρ represents the fluid density, and dx represents the micro-element. The lateral vibration velocity of the completion string is represented by F, the axial force on the completion string is represented by P0, and the annulus pressure is represented by P. i A represents the internal pressure within the completion string. i Let A0 represent the cross-sectional area of ​​the i-th micro-element of the completion string, EI represent the bending stiffness of the completion string, and dx represent the micro-element.

[0100] Step 302: Using the boundary conditions of the completion string to constrain the variational equation, the transverse fluid-structure interaction vibration equation of the completion string is obtained.

[0101] In the embodiments described in this specification, the boundary conditions of the completion string are expressed as formulas, as follows:

[0102]

[0103] The variational formula (7) after deformation is constrained by the boundary conditions of the completion string. Where y represents the longitudinal displacement of the completion string, L represents the length of the completion string, t represents time, and the boundary conditions of the completion string include a quadratic differential equation.

[0104] Since δy is arbitrary, the necessary and sufficient condition for the integral to be 0 is that the integrand is equal to 0, thus we can further obtain formula (9):

[0105] This yields the lateral fluid-structure interaction vibration equation for the completion string. Where EI represents the bending stiffness of the completion string, F represents the axial force on the completion string, and p... i p represents the internal pressure of the i-th micro-element segment of the completion string. o A represents the annular pressure of the completion string. i Let A0 represent the cross-sectional area of ​​the completion string in the i-th infinitesimal segment, dx represent the infinitesimal segment, ρ represent the fluid density, y represent the lateral vibration displacement of the completion string, and t represent time, m. p Indicates the mass per unit length of the completion string; A i Let represent the cross-sectional area of ​​the completion string in the i-th infinitesimal segment. Equation (9) is the fourth-order partial differential equation for the transverse fluid-structure interaction vibration of the completion string. The equation includes the effects of the fluid inside the completion string, the axial force of the completion string, the injection pressure inside the completion string, and the annular pressure on the vibration of the completion string.

[0106] Specifically, the first term in the formula For stiffness, the second term These are inertial terms, both independent of fluid flow, and are two terms that always exist. The third term... This indicates the effect of the inertial force of the injected fluid on the vibration of the completion string, reflecting the fluid-structure interaction between the fluid and the completion string, and is a manifestation of the coupled vibration between the fluid inside the pipe and the completion string. (The last item...) This represents the force required for fluid to change its flow direction when the completion string bends.

[0107] Figure 4 The diagram shown is a flowchart of a method for solving the transverse fluid-structure interaction vibration equation of a well completion string according to an embodiment of this specification, which specifically includes the following steps:

[0108] Step 401: Based on the transverse fluid-structure coupling vibration equation of the completion string, determine the spatial mode shape of the transverse fluid-structure coupling vibration equation of the completion string. The spatial mode shape is a linear combination of sine and cosine functions.

[0109] In this step, the fourth-order partial differential equation (8) of the transverse fluid-structure interaction vibration of the completion string is solved using the method of separation of variables. Specifically, both sides of equation (9) are divided by EI, and parameters are introduced to simplify the formula.

[0110] The introduced parameters a, b, and c are expressed as shown in formula (10):

[0111]

[0112] Where EI represents the bending stiffness of the completion string, m p P represents the mass per unit length of the completion string. i The value represents the internal pressure within the completion string, F represents the axial force on the completion string, P0 represents the annular pressure, a, b, and c are parameters, and A0 represents the cross-sectional area of ​​the well completion string. i Let represent the cross-sectional area of ​​the completion string for the i-th infinitesimal segment.

[0113] Then formula (10) can be simplified and rearranged to obtain formula (11):

[0114]

[0115] Where a, b, and c represent different parameters, x and y represent coordinates in a two-dimensional coordinate system, and t represents time.

[0116] Let F'(x,t) be the force and Proportional, equation (11) can be transformed into:

[0117]

[0118] Where a, b, and c represent different parameters, x and y represent coordinates in a two-dimensional coordinate system, t represents time, and F'(x,t) represents the force exerted by the injected fluid on the tubing string at time t with a lateral displacement of x. In this specification, the influence of the injected fluid on the tubing string vibration reflects the fluid-structure interaction between the fluid and the completion tubing string, and is a manifestation of the coupled vibration between the fluid inside the tubing and the tubing string.

[0119] Because the differential equation for the lateral fluid-structure interaction vibration of the completion string contains mixed partial derivative terms. The presence of this element means that the mode shape of the completion string is a linear combination of spatial mode shapes with sine and cosine characteristics, as shown below:

[0120]

[0121] Where i = 1, 2, ..., n, w represents the natural frequency of the completion string, and y i Let A represent the mode shape of the i-th segment of the completion string. 2n-1Let A represent the amplitude at the (2n-1)th point. 2k This represents the amplitude at the 2kth point.

[0122] In the embodiments of this specification, mode shape refers to the motion pattern or shape exhibited by an object or system when it vibrates, which can be used to analyze and understand the vibration characteristics of complex systems.

[0123] According to formula (13), the mode shapes of the transverse vibration system of the completion string in the gas storage injection-production well in this specification can be represented or approximately described by a combination of multiple sine and cosine functions. The superposition of multiple sine and cosine functions can form complex mode shapes, which may contain vibration modes with multiple frequencies and amplitudes. Each function represents a specific vibration mode or frequency. The mode shapes and natural frequencies of the completion string can be determined through modal analysis. These parameters are very important for evaluating the stability and safety of the structure.

[0124] Step 402: Substitute the linear combination of the sine and cosine functions into the transverse fluid-structure interaction vibration equation of the completion string to obtain the linear second equation set corresponding to the transverse fluid-structure interaction vibration equation of the completion string.

[0125] Substituting equation (13) into equation (12), we can obtain the mixed partial derivative terms. The coefficients of the corresponding terms include as well as and These two terms can be expanded into a Fourier series of a sine function:

[0126]

[0127]

[0128] Where n and k both represent positive integers, and l represents a non-zero real number; H 2n-1 and H 2k All of these are coefficients in the Fourier series expansion.

[0129] Where H 2k and H 2n-1 This can be obtained through the orthogonality relationship of trigonometric functions, as shown below:

[0130]

[0131] Step 403: Solve the linear second-order equations to obtain the natural frequencies of each order of fluid-structure interaction of the completion tubing.

[0132] After the transformation of equation (15), all terms in the transverse fluid-structure interaction vibration equation (9) of the completion string contain sinω. t t or cosωt t will contain sinω t t and cosω t The terms of t are combined together. To make the lateral fluid-structure interaction vibration equation of the completion string zero, the coefficients of both terms must also be zero. This leads to the following about A. 2n-1 and A 2k The system of linear equations.

[0133]

[0134] The system of equations (16) can be represented in matrix form:

[0135]

[0136] Among them, w i Let A represent the i-th natural frequency, K represent the coefficient matrix, I represent the identity matrix, and G represent the constant matrix.

[0137] In the above formula (16):

[0138]

[0139] The necessary and sufficient condition for the system of equations (17) to have non-zero solutions is that the determinant of its coefficient matrix is ​​equal to zero:

[0140]

[0141] Equation (20) is the frequency equation for the fluid-structure interaction lateral vibration of the completion string. This equation can be used to calculate the natural frequencies of each order of fluid-structure interaction in the completion string. Substituting the obtained frequencies into equations (15) and (16), the relative values ​​of the amplitudes of the fluid-structure interaction lateral vibration of the completion string can be obtained. Substituting the obtained amplitudes into equation (13), the expression for the mode shape function of the fluid-structure interaction lateral vibration of the completion string can be obtained.

[0142] Figure 5 The diagram shown is a flowchart of a method for determining the gas extraction volume and gas injection volume according to an embodiment of this specification, which specifically includes the following steps:

[0143] Step 501: Simulate the first vibration frequency of the tubing string under different gas injection rates and the second vibration frequency of the tubing string under different gas production rates. Based on the measured data of a certain study well (see Table 1, Basic Parameter Table of Study Well), the dynamics of the tubing string under injection and production conditions are evaluated and analyzed, mainly including the vibration frequency, displacement, velocity, acceleration, axial force of the tubing string, and VonMises stress analysis.

[0144] Specifically, different gas injection and gas extraction volumes are simulated, and the first vibration frequency of the tubing corresponding to each gas injection volume and the second vibration frequency of the tubing corresponding to each gas extraction volume are calculated.

[0145] Table 1 Basic parameters of the study well

[0146]

[0147] Step 502: When the first vibration frequency and the second vibration frequency of the tubing string reach the natural frequency, determine the critical gas production rate and gas injection rate corresponding to the completion tubing string.

[0148] In the embodiments described in this specification, when the frequency of the excitation force is close to a certain natural frequency of the completion string, the completion string will vibrate violently. Excessive impact load can cause tools on the completion string and other tubing strings to break directly. Therefore, it is determined that when the first and second vibration frequencies of the tubing string reach the natural frequency of the tubing string, resonance will occur. To avoid resonance during injection and production, the corresponding critical production and injection rates need to be avoided in actual production operations.

[0149] like Figure 6 The diagram shown is a structural schematic of a lateral vibration analysis device for a gas storage injection-production well completion string according to an embodiment of this specification. The diagram illustrates the basic structure of the device. The functional units and modules can be implemented using software, or using general-purpose or specific chips to perform lateral vibration analysis of the gas storage injection-production well completion string. The device specifically includes:

[0150] The first determining unit 601 is used to determine the kinetic energy of the micro-segment of the completion string and the total potential energy of the completion string during the transverse bending vibration process based on the cross-sectional area of ​​the completion string, the mass of the completion string per unit length, the bending stiffness of the completion string, the parameters related to the fluid flowing through the completion string, and the pressure on the completion string.

[0151] Equation building unit 602 is used to build the transverse fluid-structure coupling vibration equation of the completion string based on the kinetic energy of the micro-segment of the completion string during the transverse bending vibration process, the total potential energy of the completion string, and the boundary conditions of the completion string.

[0152] The calculation unit 603 is used to solve the transverse fluid-structure interaction vibration equation of the completion string and calculate the natural frequencies of each order of fluid-structure interaction of the completion string.

[0153] The second determining unit 604 is used to simulate the tubing vibration frequency corresponding to the gas injection and production volume. When the tubing vibration frequency reaches the natural frequency, the critical gas production volume and gas injection volume of the completion tubing are determined.

[0154] By observing the longitudinal vibration displacement, velocity, and acceleration curves of the completion string at different locations from the packer under gas production and injection conditions, it can be observed that the longitudinal vibration displacement, velocity, and acceleration of the completion string change over time at different distances from the packer. The farther away from the packer, the greater the displacement, velocity, and acceleration of the vibration within the completion string. At a distance of 400m from the packer, the vibration displacement, velocity, and acceleration of the completion string reach their maximum. As the distance continues to increase, the vibration displacement, velocity, and acceleration within the completion string gradually decrease. Within the first 1.5 seconds of vibration, the amplitude of the completion string fluctuation is relatively large, and subsequently, the amplitude remains stable with periodic variations. Therefore, during injection and production, the maximum values ​​of the vibration displacement, velocity, and acceleration of the completion string are mainly concentrated in the 300–500m section above the packer, where collision with the wellbore is most likely to occur.

[0155] Figure 7A The diagram shown is a schematic of the vibration frequency and natural frequency of the well completion string under the gas production conditions in the embodiments of this specification.

[0156] from Figure 7A It can be seen that under gas production conditions, when the gas production rate is 1.85 million cubic meters / day and 3.7 million cubic meters / day, the vibration frequency of the tubing above the packer is equal to the natural frequency. The tubing exhibits first-order and second-order resonances, respectively.

[0157] Figure 7B The diagram shown is a schematic of the vibration frequency and natural frequency of the well completion string under the gas injection condition in the embodiment of this specification.

[0158] from Figure 7B It can be seen that under the gas injection condition, when the gas injection volume is 1.72 million cubic meters / day and 3.5 million cubic meters / day, the vibration frequency of the tubing above the packer is equal to the natural frequency, and the tubing undergoes first-order and second-order resonance respectively.

[0159] Under resonance conditions, the vibration displacement, velocity, and acceleration of the tubing will increase significantly. Therefore, resonance should be avoided during injection and production. It is recommended that the gas production volume should be avoided to the extent possible at 1.85 million cubic meters per day and 3.7 million cubic meters per day, and the gas injection volume should be avoided to the extent possible at 1.72 million cubic meters per day and 3.5 million cubic meters per day.

[0160] Figure 7C The diagram shown is a schematic representation of the lateral vibration dynamics model of a completion string according to an embodiment of this specification. In the diagram, the span length of the completion string is L, and the mass per unit length of the string is m. p The bending stiffness of the tubular column is EI, and the inner and outer diameters of the tubular column are D and D, respectively. i D o The fluid density is ρ f The cross-sectional area A of the pipe flows through it at a constant velocity V. The lateral deflection of the pipe column is y(z,t), and the axial coordinate of the pipe column is z.

[0161] Figure 8A The diagram shows the relationship between the maximum lateral vibration displacement of the completion string and time under a gas production condition of 1.05 million cubic meters per day, as described in an embodiment of this specification. As can be seen from the diagram, the lateral vibration displacement of the completion string fluctuates significantly within the first 1.5 seconds of the gas production operation, and then maintains a stable amplitude that changes periodically.

[0162] When producing gas at a rate of 1.05 million cubic meters per day, the maximum lateral vibration displacement of the completion string was 12.2 mm. The maximum lateral vibration displacement did not reach the 20.24 mm gap between the oil casing and the casing, indicating that the lateral vibration of the completion string did not collide with the well wall.

[0163] Figure 8B The diagram shown illustrates the relationship between the maximum lateral vibration displacement of the completion string and time under a gas injection condition of 800,000 cubic meters per day, as described in one embodiment of this specification. The maximum lateral vibration displacement of the completion string under gas production and injection conditions is shown below. Figure 8A and Figure 8B As shown in the figure, during the first 1.5 seconds of vibration in the gas injection condition, the amplitude of the lateral vibration displacement of the completion tubing is relatively large, and the amplitude remains stable and changes periodically thereafter.

[0164] When injecting gas at a rate of 800,000 cubic meters per day, the maximum lateral vibration displacement of the completion string was 10.2 mm. The maximum lateral vibration displacement did not reach the 20.24 mm gap between the oil casing and the casing, indicating that the lateral vibration of the completion string did not collide with the well wall.

[0165] Figure 9A The diagram shown is a schematic of the longitudinal vibration displacement of the completion string at a distance of 400m from the packer under different gas production rates in this manual. Figure 9B The diagram shows the longitudinal vibration displacement of the completion string at a distance of 400m from the packer under different gas injection volumes as described in this manual.

[0166] Based on the dynamic analysis results of the completion string under gas production and injection conditions, a dynamic sensitivity analysis of the completion string was further conducted to study the impact of production rate on the dynamic behavior of the completion string. The relationship between the vibration displacement of the completion string at 400m from the packer and time under different gas volumes is shown in the figure. Figure 9A and Figure 9B As shown in the figure, the vibration displacement of the completion string gradually increases with the increase of gas volume until it collides with the wellbore, at which point the maximum lateral vibration displacement of the completion string no longer increases. The critical gas volumes for gas production and injection are 2 million cubic meters per day and 2.5 million cubic meters per day, respectively.

[0167] Analysis results indicate that 1.85 × 10⁻⁶ should be avoided in the study well under injection-production conditions. 6 m 3 / d gas production and 1.72×10 6m 3 The gas injection rate should be 2.00 × 10⁶ / day, and the gas extraction rate should preferably not exceed 2.00 × 10⁶ / day. 6 m 3 / day, the gas injection volume should not exceed 2.50×10 6 m 3 / d. By avoiding the aforementioned gas injection and production measures, the damage to the injection and production tubing caused by lateral vibration can be effectively reduced. These results are of great significance for the diagnosis, assessment, and safety precautions regarding lateral vibration during on-site injection and production tubing operations.

[0168] like Figure 10 The diagram illustrates a computer device provided in an embodiment of this specification. The lateral vibration analysis method for completion tubing in gas storage injection and production wells described in this application can be applied to this computer device. The computer device 1002 may include one or more processors 1004, such as one or more central processing units (CPUs), each of which can implement one or more hardware threads. The computer device 1002 may also include any memory 1006 for storing any kind of information, such as code, settings, data, etc. Non-limitingly, for example, the memory 1006 may include any type of RAM, any type of ROM, flash memory, hard disk, optical disk, etc. More generally, any memory can use any technology to store information. Further, any memory can provide volatile or non-volatile retention of information. Further, any memory can represent a fixed or removable component of the computer device 1002. In one case, when the processor 1004 executes associated instructions stored in any memory or combination of memories, the computer device 1002 can perform any operation of the associated instructions. The computer device 1002 also includes one or more drive mechanisms 1008 for interacting with any memory, such as a hard disk drive mechanism, an optical disk drive mechanism, etc.

[0169] Computer device 1002 may also include an input / output module 1010 (I / O) for receiving various inputs (via input device 1012) and providing various outputs (via output device 1014). A specific output mechanism may include a presentation device 1016 and an associated graphical user interface (GUI) 1018. In other embodiments, the input / output module 1010 (I / O), input device 1012, and output device 1014 may be omitted, and the device may function solely as a computer device within a network. Computer device 1002 may also include one or more network interfaces 1020 for exchanging data with other devices via one or more communication links 1022. One or more communication buses 1024 couple the components described above together.

[0170] The communication link 1022 can be implemented in any way, such as via a local area network, a wide area network (e.g., the Internet), a point-to-point connection, or any combination thereof. The communication link 1022 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc., governed by any protocol or combination of protocols.

[0171] Corresponding to Figures 1 to 6 In addition to the methods described above, embodiments of this specification also provide a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the methods described above.

[0172] This specification also provides computer-readable instructions, wherein when a processor executes the instructions, the program therein causes the processor to perform the following... Figures 1 to 6 The method shown.

[0173] It should be understood that in the various embodiments of this specification, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this specification.

[0174] It should also be understood that, in the embodiments of this specification, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this specification generally indicates that the preceding and following related objects have an "or" relationship.

[0175] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this specification can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this specification.

[0176] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0177] In the several embodiments provided in this specification, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through some interfaces, devices, or units, or they may be electrical, mechanical, or other forms of connection.

[0178] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments described in this specification, depending on actual needs.

[0179] Furthermore, the functional units in the various embodiments of this specification can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0180] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this specification, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this specification. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0181] This specification uses specific embodiments to illustrate the principles and implementation methods of this specification. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this specification. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this specification. Therefore, the content of this specification should not be construed as a limitation of this specification.

Claims

1. A method for analyzing lateral vibration of a gas storage injection-production well completion pipe string, characterized in that, The method comprises: determining kinetic energy of a microelement section of the well completion string in lateral bending vibration process and total potential energy of the well completion string according to cross-sectional area of the well completion string, mass per unit length of the well completion string, bending stiffness of the well completion string, parameters related to fluid flowing through the well completion string and pressure borne by the well completion string; constructing lateral fluid-structure coupling vibration equation of the well completion string according to kinetic energy of the microelement section of the well completion string in lateral bending vibration process, total potential energy of the well completion string and boundary conditions of the well completion string; solving the lateral fluid-structure coupling vibration equation of the well completion string to obtain natural frequency of each order of fluid-structure coupling of the well completion string; simulating vibration frequency of the string corresponding to injection and production gas volume, determining critical production gas volume and injection gas volume of the well completion string when the string vibration frequency reaches the natural frequency.

2. The method of claim 1, wherein, The determination of the kinetic energy of the microelement section of the well completion string in the lateral bending vibration process and the total potential energy of the well completion string comprises: determining lateral vibration velocity of the well completion string, horizontal component and vertical component of fluid velocity in the well completion string according to cross-sectional area of the well completion string, mass per unit length of the well completion string, bending stiffness of the well completion string, parameters related to fluid flowing through the well completion string and pressure borne by the well completion string; determining kinetic energy of a microelement section of the well completion string in lateral bending vibration process and total potential energy of the well completion string according to cross-sectional area of the well completion string, mass per unit length of the well completion string, bending stiffness of the well completion string, parameters related to fluid flowing through the well completion string and pressure borne by the well completion string; 3. The method of claim 2, wherein, The determination of the kinetic energy of the microelement section of the well completion string in the lateral bending vibration process and the total potential energy of the well completion string according to the lateral vibration velocity of the well completion string, the horizontal component and the vertical component of the fluid velocity in the well completion string comprises: determining kinetic energy of a microelement section of the well completion string in lateral bending vibration process and total potential energy of the well completion string according to cross-sectional area of the well completion string, mass per unit length of the well completion string, bending stiffness of the well completion string, parameters related to fluid flowing through the well completion string and pressure borne by the well completion string; wherein dT represents the kinetic energy of a certain microelement section of the completion string during lateral bending vibration, represents the lateral vibration velocity of the completion string; v represents the fluid velocity in the completion string, y represents the lateral vibration displacement of the completion string, v x represents the horizontal component; v y represents the vertical component; y' represents the axis slope of the completion string, t represents time, m p represents the mass of the completion string per unit length; A i represents the cross-sectional area of the completion string of the i-th microelement section, p represents the fluid density, dx represents the microelement section of the completion string; determining kinetic energy of a microelement section of the well completion string in lateral bending vibration process and total potential energy of the well completion string according to cross-sectional area of the well completion string, mass per unit length of the well completion string, bending stiffness of the well completion string, parameters related to fluid flowing through the well completion string and pressure borne by the well completion string; wherein dU represents the total potential energy of the micro-element section of the completion string; EI represents the bending stiffness of the completion string, F represents the axial force of the completion string, p i represents the internal pressure of the i-th micro-element section of the completion string, p i represents the internal pressure of the i-th micro-element section of the completion string, p o represents the annular pressure of the completion string, A i represents the cross-sectional area of the i-th micro-element section of the completion string, A0 represents the cross-sectional area of the well completion string, y' represents the slope of the axis of the completion string, and y" represents the rate of change of the slope of the axis of the completion string.

4. The method of claim 3, wherein, The construction of the lateral fluid-structure coupling vibration equation of the well completion string according to the kinetic energy of the microelement section of the well completion string in the lateral bending vibration process, the total potential energy of the well completion string and the boundary conditions of the well completion string comprises: transforming the kinetic energy of the microelement section of the well completion string in the lateral bending vibration process and the total potential energy of the well completion string according to Hamilton principle to obtain a variational equation; constraining the variational equation by the boundary conditions of the well completion string to obtain the lateral fluid-structure coupling vibration equation of the well completion string.

5. The method of claim 4, wherein, The solving of the lateral fluid-structure coupling vibration equation of the well completion string comprises: determining spatial vibration mode of the lateral fluid-structure coupling vibration equation of the well completion string according to the lateral fluid-structure coupling vibration equation of the well completion string, the spatial vibration mode being linear combination of sine function and cosine function; substituting the linear combination of the sine function and the cosine function into the lateral fluid-structure coupling vibration equation of the well completion string to obtain linear second-order equation set corresponding to the lateral fluid-structure coupling vibration equation of the well completion string; solving the linear second-order equation set to obtain natural frequency of each order of fluid-structure coupling of the well completion string.

6. The method of claim 5, wherein, The determination of the lateral vibration velocity of the well completion string, the horizontal component and the vertical component of the fluid velocity in the well completion string is according to the following formula: wherein, represents the lateral vibration velocity of the completion string; v represents the fluid velocity within the completion string, y represents the lateral vibration displacement of the completion string, v x represents the horizontal component of the fluid velocity within the completion string; v y represents the vertical component of the fluid velocity within the completion string; y' represents the axis slope of the completion string, t represents time.

7. The method of claim 6, wherein, The method comprises the following steps: The method comprises the following steps: When the first vibration frequency and the second vibration frequency reach the natural frequency, the critical gas production rate and the critical gas injection rate of the well completion string are determined.

8. A device for analyzing lateral vibration of a gas storage well completion string, characterized in that, The device comprises: The first determining unit is configured to determine kinetic energy of a microelement section of the well completion string in a lateral bending vibration process and total potential energy of the well completion string according to a cross-sectional area of the well completion string, a mass per unit length of the well completion string, a bending stiffness of the well completion string, a parameter related to a fluid flowing through the well completion string, and a pressure borne by the well completion string. The equation constructing unit is configured to construct a lateral fluid-structure coupling vibration equation of the well completion string according to the kinetic energy of the microelement section of the well completion string in the lateral bending vibration process, the total potential energy of the well completion string, and a boundary condition of the well completion string. The computing unit is configured to solve the lateral fluid-structure coupling vibration equation of the well completion string to obtain the natural frequency of each order of the fluid-structure coupling of the well completion string. The second determining unit is configured to simulate a vibration frequency of the well completion string corresponding to a gas injection rate and a gas production rate, and determine the critical gas production rate and the critical gas injection rate of the well completion string when the vibration frequency of the well completion string reaches the natural frequency.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the method in any one of claims 1 to 7 when executing the computer program.

10. A computer readable storage medium characterized by, The computer readable storage medium stores the computer program, and the computer program is executed by the processor to implement the method in any one of claims 1 to 7.

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