A perforating cable weak point failure calculation method based on energy method

Abstract

The application discloses a perforating cable weak point failure calculation method based on an energy method, first, a reasonable assumption is made to a cable weak point-pipe column system based on engineering practice and a dynamic model is established; subsequently, a system energy balance equation is constructed, impact kinetic energy, cable weak point elastic energy and fluid damping energy consumption are calculated respectively; then, a cable weak point fracture criterion is established based on energy balance; finally, system energy response characteristics are obtained through numerical solution, and cable weak point failure risk assessment is completed. The application realizes accurate quantitative calculation of cable weak point failure under impact load generated by perforation, and provides reliable guarantee for safe design of perforation engineering.

Description

Technical Field

[0001] This invention relates to the field of oil and gas well perforation engineering technology, specifically to a method for calculating the weakness failure of perforation cables based on the energy method. Background Technology

[0002] During perforation operations in oil and gas wells, impact loads trigger complex dynamic responses in cable weaknesses. Differences in wire diameter and material uniformity within the cable's weak points mean that, during downhole operations, the impact loads generated by perforation exceed the cable's ultimate load capacity, yet the cable does not break. This is because the dynamic behavior of the cable-string system is influenced by multiple factors, including elastic deformation and fluid damping. Traditional calculation methods do not fully consider the system's energy transfer and dissipation patterns, making it difficult to accurately quantify the breakage risk of the cable weaknesses. Existing technologies for analyzing cable weakness failures often lack a systematic consideration of energy balance relationships and have not established a calculation system combining piecewise elastic modeling and fluid damping effects, failing to meet the precise requirements of engineering safety design. Therefore, there is an urgent need for an energy-based method for calculating cable weakness failure during perforation, enabling accurate assessment of the cable weakness failure risk under the impact loads generated by perforation. (Invention Content)

[0003] The purpose of this invention is to provide a method for calculating the weak point failure of perforated cables based on the energy method, so as to overcome the defects of the prior art. Through segmented elastic modeling and energy balance analysis, it can achieve accurate quantification of the risk of cable weak point failure, and provide technical support for the safe construction of joint projects.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for calculating the weakness failure of perforated cables based on the energy method includes the following steps:

[0006] Step 1: Establish the dynamic model of the cable weakness-pipe system: Based on the modeling assumptions, the cable weakness-pipe system is simplified into a single-degree-of-freedom segmented elastic system;

[0007] Step 2: Construct the system energy balance equation: Determine the calculation methods for impact kinetic energy, elastic energy at cable weak points, and fluid damping energy dissipation, and establish the system energy balance relationship;

[0008] Step 3: Establish criteria for cable weakness fracture: Set the criteria for determining cable weakness fracture based on energy balance.

[0009] Step 4: Numerical Solution and Failure Assessment: The dynamic equations are numerically solved using a specified solver to obtain the system energy response characteristics. Based on the cable weakness fracture criterion, the cable weakness failure risk assessment is completed.

[0010] Traditional methods use load limits as failure criteria, failing to consider the energy transfer and dissipation laws of the system and the coupling effects of multiple factors. They lack system energy balance analysis, and the modeling does not combine piecewise elasticity and fluid damping, making it difficult to accurately quantify fracture risk. This application overcomes the above shortcomings by constructing a complete energy balance equation and scientific criteria through four assumptions and piecewise elastic modeling. Combined with a high-precision solver, it achieves quantitative evaluation and outputs a visualized energy curve, providing reliable support for engineering safety design.

[0011] Furthermore, the dynamic model of the cable weakness-pipeline system established in step one is as follows:

[0012]

[0013] In the formula, is the first derivative of displacement x with respect to time, in m / s; v is the axial velocity of the tubing, in m / s; ν is the axial acceleration of the tubular column, the first derivative of velocity v with respect to time, in m / s². The axial time-varying external load on the tubing is expressed in N. The nonlinear drag damping force exerted by the fluid on the cable is expressed in N. This represents the number of segments in the entire cable, without units. λ is the axial stiffness of a single cable segment, in N / m; x is the axial displacement of the pipe column relative to its equilibrium position, in meters. The lumped mass of the tubular column is expressed in kg.

[0014] Furthermore, the modeling assumptions in step one specifically include:

[0015] Concentrated mass assumption: Cable weak points whose mass accounts for less than or equal to one-twentieth of the system mass are regarded as "massless elastic bodies" that only provide elastic restoring force and damping force. The mass of the pipe column is concentrated at the end of the cable weak point, and the system is simplified to a single-degree-of-freedom system.

[0016] Segmented elasticity assumption: The cable's weak points are uniformly divided into n segments, each of which is considered a homogeneous linear elastic spring. The whole structure is a series structure and follows Hooke's Law.

[0017] Square damping assumption: When the cable's weak point moves in the mud, it is in a turbulent state, and the damping force is proportional to the square of the velocity;

[0018] The stress-strain linearity assumption is that the stress follows Hooke's law when it does not exceed the proportional limit, and remains constant when it exceeds the proportional limit but does not reach the ultimate stress.

[0019] In step one, the modeling method is improved to break through the limitations of traditional overall modeling. The segmented discrete modeling method is used to realize the quantitative characterization of local characteristics of weaknesses and avoid the homogenization effect of local weakness features in traditional models. Four core assumptions are proposed to achieve full-condition mechanical response coverage of cable weaknesses from elastic deformation to near fracture.

[0020] Furthermore, the system energy balance equation constructed in step two is as follows:

[0021]

[0022] In the formula, Impact kinetic energy, measured in J; The weak elasticity of the cable is expressed in J. Energy consumed by fluid damping, in J; Plastic deformation energy, in J, is the energy generated before the material reaches its yield strength. .

[0023] Furthermore, (1) the method for calculating the impact kinetic energy is as follows:

[0024]

[0025] In the formula, Impact kinetic energy, measured in J; The mass of the cable string at the weak point is expressed in kg. The velocity of the tube string is expressed in m / s.

[0026] (2) The calculation method for the weak elastic properties of the cable is as follows:

[0027]

[0028] In the formula, The weak elasticity of the cable is expressed in J. The weak point stiffness of a single cable segment, in N / M. E represents the weak point elastic modulus of the cable, in Pa. This refers to the cross-sectional area of ​​the cable's weak point, in units of... ; The weak point length of a single cable segment, in meters (m). is the maximum displacement under load, in meters; n is the number of uniformly divided weak points in the cable, dimensionless.

[0029] (3) The calculation method for the fluid damping energy consumption is as follows:

[0030]

[0031] In the formula, Energy consumed by fluid damping, in J; Work done by fluid damping force, measured in J; The instantaneous fluid damping force is expressed in N, and a quadratic damping model is used. , For drilling fluid density, in units , This is the fluid resistance coefficient; The windward area of ​​a single cable segment's weak point, in units ; Instantaneous velocity, unit: m / s; The total impact time is expressed in seconds (s).

[0032] In step two, the elastic energy of the cable's weak point is characterized as an independent energy component. Based on the cross-sectional parameters of the cable's weak point, its stiffness and elastic energy are solved separately to accurately capture the local energy accumulation effect.

[0033] Furthermore, the cable weakness fracture criterion established in step three is specifically as follows:

[0034] It will break

[0035] No breakage will occur

[0036] In the formula Impact kinetic energy, measured in J; The weak elasticity of the cable is expressed in J. Energy consumed by fluid damping, in J;

[0037] In step three, the limitations of traditional overall stress criteria are broken through. The criteria are combined with the energy of cable weaknesses. Based on the energy balance relationship, the energy overload fracture of the weakness is determined, the fracture risk is quantified, and concrete decision support is provided for the precise optimization of construction parameters.

[0038] Furthermore, the specified solver in step four is a fourth- to fifth-order adaptive step-size Runge-Kutta ordinary differential equation solver, with a relative accuracy of 10 during the solution process. -6 Absolute precision is 10 -8 Ensure that the displacement calculation error is less than 10. -8 m, velocity solution error less than 10 -8 m / s. The time history curves of the system's kinetic energy, elastic energy, and damping energy dissipation are obtained by solving the problem. Based on the cable weakness fracture criterion, a cable weakness failure risk assessment is completed.

[0039] In step four, a multi-dimensional energy time history curve is output, presenting the dynamic evolution process of cable weakness energy. The output results are clear and concise, accurately locating high-risk periods and providing visual support for risk management.

[0040] Compared with the prior art, the present invention has the following beneficial technical effects:

[0041] Step 1 of this invention involves segmenting and simplifying the cable weakness-pipe system to construct a dedicated dynamic model adapted to the impact load conditions generated by perforation, providing reliable model support for subsequent failure risk calculations. Step 2 involves constructing a comprehensive energy balance equation, systematically quantifying the three core components of impact kinetic energy, cable elastic energy, and fluid damping energy dissipation, and improving the energy transfer and dissipation analysis system, laying a solid foundation for establishing fracture criteria. Step 3 involves establishing cable weakness fracture criteria based on the energy balance principle, achieving accurate quantitative assessment of fracture risk, and providing core reference for the safety design of perforation projects. Step 4 involves completing the entire calculation process using a high-precision solver, which can quickly output energy history curves and failure assessment results, efficiently supporting engineering decisions and providing strong protection for the construction safety of joint projects. Attached Figure Description

[0042] Appendix Figure 1 This is a flowchart illustrating a specific embodiment of the present invention;

[0043] Appendix Figure 2 This is a field measurement data illustration of a specific embodiment of the present invention, including the X, Y, and Z axis accelerations of the perforation tube string;

[0044] Appendix Figure 3 This is a data illustration of the maximum displacement of a cable weakness under load, according to a specific embodiment of the present invention.

[0045] Appendix Figure 4 This is a schematic diagram showing the calculation results of the time history curves of the system's kinetic energy, elastic energy, and damping energy dissipation in a specific embodiment of the present invention. Detailed Implementation

[0046] Example 1:

[0047] A method for calculating the weakness failure of perforated cables based on the energy method, such as... Figure 1 As shown, it includes the following steps:

[0048] Step 1: Establish the dynamic model of the cable weakness-pipe system: Based on the modeling assumptions, the cable weakness-pipe system is simplified into a single-degree-of-freedom segmented elastic system;

[0049] Step 2: Construct the system energy balance equation: Determine the calculation methods for impact kinetic energy, elastic energy at cable weak points, and fluid damping energy dissipation, and establish the system energy balance relationship;

[0050] Step 3: Establish criteria for cable weakness fracture: Set the criteria for determining cable weakness fracture based on energy balance.

[0051] Step 4: Numerical Solution and Failure Assessment: The dynamic equations are numerically solved using a specified solver to obtain the system energy response characteristics. Based on the cable weakness fracture criterion, the cable weakness failure risk assessment is completed.

[0052] The dynamic model of the cable weakness-pipe system established in step one:

[0053]

[0054] In the formula, is the first derivative of displacement x with respect to time, in m / s; v is the axial velocity of the tubing, in m / s; The axial acceleration of the tubular column is given by the first derivative of velocity v with respect to time, in m / s². 2 ; The axial time-varying external load on the tubing is expressed in N. The nonlinear drag damping force exerted by the fluid on the cable is expressed in N. This represents the number of segments in the entire cable, without units. λ is the axial stiffness of a single cable segment, in N / m; x is the axial displacement of the pipe column relative to its equilibrium position, in meters. The lumped mass of the tubular column is expressed in kg.

[0055] The modeling assumptions in step one specifically include:

[0056] Concentrated mass assumption: Cable weak points whose mass accounts for less than or equal to one-twentieth of the system mass are regarded as "massless elastic bodies" that only provide elastic restoring force and damping force. The mass of the pipe column is concentrated at the end of the cable weak point, and the system is simplified to a single-degree-of-freedom system.

[0057] Segmented elasticity assumption: The cable's weak points are uniformly divided into n segments, each of which is considered a homogeneous linear elastic spring. The whole structure is a series structure and follows Hooke's Law.

[0058] Square damping assumption: When the cable's weak point moves in the mud, it is in a turbulent state, and the damping force is proportional to the square of the velocity;

[0059] The stress-strain linearity assumption is that the stress follows Hooke's law when it does not exceed the proportional limit, and remains constant when it exceeds the proportional limit but does not reach the ultimate stress.

[0060] The system energy balance equation constructed in step two is as follows:

[0061]

[0062] In the formula, Impact kinetic energy, measured in J; The weak elasticity of the cable is expressed in J. Energy consumed by fluid damping, in J; Plastic deformation energy, in J, is the energy generated before the material reaches its yield strength. .

[0063] The method for calculating the impact kinetic energy is as follows:

[0064]

[0065] In the formula, Impact kinetic energy, measured in J; The mass of the cable string at the weak point is expressed in kg. The velocity of the tube string is expressed in m / s.

[0066] The method for calculating the weak elastic properties of the cable is as follows:

[0067]

[0068] In the formula, The weak elasticity of the cable is expressed in J. The weak point stiffness of a single cable segment, in N / M. E represents the weak point elastic modulus of the cable, in Pa. This refers to the cross-sectional area of ​​the cable's weak point, in units of... ; The weak point length of a single cable segment, in meters (m). is the maximum displacement under load, in meters; n is the number of uniformly divided weak points in the cable, dimensionless.

[0069] The calculation method for the fluid damping energy dissipation is as follows:

[0070]

[0071] In the formula, Energy consumed by fluid damping, in J; Work done by fluid damping force, measured in J; The instantaneous fluid damping force is expressed in N, and a quadratic damping model is used. , For drilling fluid density, in units , This is the fluid resistance coefficient; The windward area of ​​a single cable segment's weak point, in units ; Instantaneous velocity, unit: m / s; The total impact time is expressed in seconds (s).

[0072] The cable weakness fracture criterion established in step three is as follows:

[0073] It will break

[0074] No breakage will occur

[0075] In the formula Impact kinetic energy, measured in J; The weak elasticity of the cable is expressed in J. Energy consumed by fluid damping, in J;

[0076] The solver specified in step four is a fourth- to fifth-order adaptive step-size Runge-Kutta ordinary differential equation solver, with a relative accuracy of 10 during the solution process. -6 Absolute precision is 10 -8 Ensure that the displacement calculation error is less than 10. -8 m, velocity solution error less than 10 -8 m / s.

[0077] Example 2:

[0078] A method for calculating the weakness failure of perforated cables based on the energy method is presented in this embodiment, which is further illustrated with a specific case based on Embodiment 1.

[0079] I. Establishing a dynamic model of the cable weakness-pipeline system

[0080] The cable-pipe system is simplified according to the four core assumptions set forth in this invention: Cable weaknesses, whose mass percentage is less than or equal to one-twentieth of the system mass, are treated as "massless elastic bodies," providing only elastic restoring force and damping force; the pipe mass is concentrated at the cable end, simplifying the distributed mass system to a single-degree-of-freedom system; based on the cable's aspect ratio characteristics and the requirements for local deformation analysis, the cable weaknesses are uniformly divided into 10 segments, each considered a homogeneous linear elastic spring, and the entire system is modeled using a series structure; based on the cable's motion flow field in the drilling fluid, a square damping model is used to describe the fluid damping effect; and following the assumption of a linear stress-strain relationship, the mechanical response laws for different stress ranges are clarified.

[0081] II. Required Calculation Parameters

[0082] The required parameters are shown in the table below:

[0083]

[0084] III. Constructing the energy balance equation and calculating each energy component

[0085] 1. Impact kinetic energy calculation: The tubing mass is 400 kg. (The calculation is based on the following information:) Figure 2 The Z-axis acceleration of the middle tube string determines the time-varying velocity of the tube string. The impact kinetic energy calculation formula is used, and the impact kinetic energy is calculated by substituting the parameters.

[0086] 2. Calculation of cable's weak elastic modulus: Based on the cable's weak elastic modulus of 57.2 GPa and cross-sectional area of ​​5.0265 × 10⁻⁶... -5 m 2 Calculate the stiffness of a single cable segment based on its weak point length and the number of weak point segments. Figure 3 The maximum displacement of a cable weakness under load is calculated using the elastic energy calculation formula, which is the energy stored during the elastic deformation of the cable weakness.

[0087] 3. Fluid damping energy consumption calculation: based on drilling fluid density of 1000 A model of instantaneous fluid damping force is established by considering the fluid damping coefficient and the windward area of ​​a single cable segment's weak point. The damping power is integrated over time using a solver to obtain the total dissipated energy of fluid damping during the impact process. This energy is the heat dissipation converted from the work done by the damping force.

[0088] IV. Failure Assessment Based on Fracture Criteria

[0089] After calculating the impact kinetic energy, the elastic energy of the cable weakness, and the energy dissipation due to fluid damping, the fracture risk of the cable weakness is assessed based on the energy balance fracture criterion established in this invention: the impact kinetic energy is compared with the sum of the cable weakness's elastic energy and the fluid damping energy dissipation. If the impact kinetic energy is greater than the sum of the two, the cable weakness is determined to have a fracture risk; if the impact kinetic energy is less than the sum of the two, the cable weakness is determined not to fracture. This criterion enables a quantitative assessment of the cable weakness failure risk, providing a direct basis for engineering safety decisions.

[0090] V. Results Analysis

[0091] The time history curves of the system's kinetic energy, elastic energy, and damping energy dissipation are obtained through numerical solutions, and the variation patterns of each energy are analyzed.

[0092] Appendix Figure 4 The energy evolution during the movement of the tube string is shown: the impact kinetic energy reaches its maximum value of 2.2 × 10⁻⁶ when the tube string begins to move. 5 J exhibits a multi-peak fluctuating downward trend, with multiple energy fluctuations occurring during this period. These fluctuations originate from the "energy storage-release" cycle of the cable's elastic deformation. After the elastic energy accumulates to a certain level, it is converted back into kinetic energy, forming energy oscillations. The change in elastic potential energy lags behind the peak value of kinetic energy, with a maximum value of 8.7 × 10⁻⁶. 5 J, the elastic potential energy gradually decreases with energy oscillation; the total damping energy dissipation, being the integral of the work done by the damping force over time, exhibits a continuous linear increase, reaching a maximum value of 2.1 × 10⁻⁶ in the final stage of the tube string motion. 5 J, during this stage, the damping energy dissipation trend remains stable, indicating that regardless of the increase or decrease in the tube string velocity, the fluid damping continuously dissipates energy; Appendix Figure 4 The following are the calculation results for the impact kinetic energy, cable weak point elastic energy, and fluid damping energy dissipation during the pipe string movement process, attached. Figure 4 At any given moment, the sum of the elastic energy of the cable's weak point and the energy dissipated by fluid damping is greater than the impact kinetic energy. Based on the established criterion for cable weakness fracture, it is concluded that the cable's weak point will not fracture under this load.

Claims

1. A method for calculating the weakness failure of perforated cables based on the energy method, characterized in that, Includes the following steps: Step 1: Establish the dynamic model of the cable weakness-pipe system: Based on the modeling assumptions, the cable weakness-pipe system is simplified into a single-degree-of-freedom segmented elastic system; Step 2: Construct the system energy balance equation: Determine the calculation methods for impact kinetic energy, elastic energy at cable weak points, and fluid damping energy dissipation, and establish the system energy balance relationship; The system energy balance equation constructed in step two is as follows: ； In the formula, Impact kinetic energy, measured in J; The weak elasticity of the cable is expressed in J. Energy consumed by fluid damping, in J; Plastic deformation energy, in J, is the energy generated before the material reaches its yield strength. ; The method for calculating the impact kinetic energy is as follows: ； In the formula, Impact kinetic energy, measured in J; The mass of the cable string at the weak point is expressed in kg. The velocity of the tube string is expressed in m / s. The method for calculating the weak elastic properties of the cable is as follows: ； In the formula, The weak elasticity of the cable is expressed in J. The weak point stiffness of a single cable segment, in N / M. E represents the weak point elastic modulus of the cable, in Pa. This refers to the cross-sectional area of ​​the cable's weak point, in units of... ; The length of a single cable segment with a weak point, in meters (m). is the maximum displacement under load, in meters; n is the number of uniformly divided weak points in the cable, dimensionless. The calculation method for the fluid damping energy dissipation is as follows: ； In the formula, Energy consumed by fluid damping, in J; Work done by fluid damping force, measured in J; The instantaneous fluid damping force is expressed in N, and a quadratic damping model is used. , For drilling fluid density, in units , This is the fluid resistance coefficient; The windward area of ​​a single cable segment's weak point, in units ; Instantaneous velocity, unit: m / s; The total impact time is expressed in seconds (s). Step 3: Establish criteria for cable weakness fracture: Set the criteria for determining cable weakness fracture based on energy balance. The cable weakness fracture criterion established in step three is as follows: It will break No breakage will occur In the formula, Impact kinetic energy, measured in J; The weak elasticity of the cable is expressed in J. Energy consumed by fluid damping, in J; Step 4: Numerical Solution and Failure Assessment: The dynamic equations are numerically solved using a specified solver to obtain the system energy response characteristics. Based on the cable weakness fracture criterion, the cable weakness failure risk assessment is completed.

2. The energy-based method for calculating the weakness failure of perforated cables according to claim 1, characterized in that, The dynamic model of the cable weakness-pipe system established in step one is as follows: ； In the formula, is the first derivative of displacement x with respect to time, in m / s; v is the axial velocity of the tubing, in m / s; ν is the axial acceleration of the tubular column, the first derivative of velocity v with respect to time, in m / s². The axial time-varying external load on the tubing is expressed in N. The nonlinear drag damping force exerted by the fluid on the cable is expressed in N. This represents the number of segments in the entire cable, without units. λ is the axial stiffness of a single cable segment, in N / m; x is the axial displacement of the pipe column relative to its equilibrium position, in meters. The lumped mass of the tubular column is expressed in kg.

3. The energy-based method for calculating the weakness failure of perforated cables according to claim 1, characterized in that, The modeling assumptions in step one specifically include: Concentrated mass assumption: Cable weak points whose mass accounts for less than or equal to one-twentieth of the system mass are regarded as "massless elastic bodies" that only provide elastic restoring force and damping force. The mass of the pipe column is concentrated at the end of the cable weak point, and the system is simplified to a single-degree-of-freedom system. Segmented elasticity assumption: The cable's weak points are uniformly divided into n segments, each of which is considered a homogeneous linear elastic spring. The whole structure is a series structure and follows Hooke's Law. Square damping assumption: When the cable's weak point moves in the mud, it is in a turbulent state, and the damping force is proportional to the square of the velocity; The stress-strain linearity assumption is that the stress follows Hooke's law when it does not exceed the proportional limit, and remains constant when it exceeds the proportional limit but does not reach the ultimate stress.

4. The energy-based method for calculating the weakness failure of perforated cables according to claim 1, characterized in that, The solver specified in step four is a fourth- to fifth-order adaptive step-size Runge-Kutta ordinary differential equation solver, with a relative accuracy of 10 during the solution process. -6 Absolute precision is 10 -8 Ensure that the displacement calculation error is less than 10. -8 m, velocity solution error less than 10 -8 m / s.

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