Design method of steel sleeve crack arrestor for dense-phase carbon dioxide pipeline

Abstract

The invention discloses a design method of a steel sleeve crack arrestor for a dense-phase carbon dioxide pipeline, which comprises the following steps: S1, selecting a sample steel pipe, and determining the steady-state expansion speed of cracks in the steel pipe; s2, establishing a finite element model: simulating the geometric dimension of a real pipeline, dividing the pipeline, and adopting a cohesion unit as a crack propagation path; s3, calculating the saturation pressure of the carbon dioxide component, and applying the pressure to the tip of the crack; s4, determining cohesion parameters, and taking the cohesion parameters as finite element model parameters; s5, determining pressure distribution after the cracks enter the crack arresters; s6, a non-contact algorithm is established, and the constraint force of the crack arresters on crack propagation is evaluated through the algorithm; and S7, the crack steady-state expansion speed is obtained, and design of the steel sleeve crack arrestor is completed. According to the design method of the steel sleeve crack arrestor for the dense-phase carbon dioxide pipeline, the problem that crack arrest cannot be conducted in time after the dense-phase carbon dioxide pipeline with the small caliber OD508 or below cracks is solved.

Description

Technical Field

[0001] This invention belongs to the field of carbon dioxide pipeline fracture control technology, specifically relating to the design method of steel sleeve fracture arrestor for dense phase carbon dioxide pipelines. Background Technology

[0002] China has proposed to peak carbon emissions by 2030 and achieve carbon neutrality by 2060. To achieve this goal, at least tens of millions of tons of carbon dioxide need to be stored annually, making dense-phase carbon dioxide pipeline transportation an essential approach.

[0003] Compared to natural gas, dense-phase carbon dioxide exhibits a long decompression plateau (saturation pressure), preventing pressure release at the crack tip and allowing for long-range crack propagation, leading to significant personal and property damage. Once a dense-phase carbon dioxide pipeline cracks, the high-pressure gas inside cannot be immediately vented. Instead, a decompression wave is generated on each side of the fracture point and propagates to distant locations. Because the gas decompression wave velocity is lower than the steady-state crack propagation velocity, the crack tip remains under continuous high stress, causing the crack to continue propagating at a high speed, resulting in long-range ductile crack propagation in the gas pipeline. Long-range crack propagation in dense-phase carbon dioxide pipelines can cause enormous disasters and losses; therefore, it is crucial to ensure timely crack arrest once a pipeline cracks. Existing full-scale burst test results indicate that for CO2 pipelines with high design coefficients, it is difficult to rely on their own toughness to arrest cracks. This has become a serious bottleneck problem threatening pipeline safety and restricting the application of carbon dioxide pipelines. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for a steel sleeve crack arrestor for dense phase carbon dioxide pipelines, which solves the problem that small-diameter dense phase carbon dioxide pipelines of OD508 and below cannot stop cracking in time.

[0005] The technical solution adopted in this invention is a design method for a steel sleeve crack arrester for dense phase carbon dioxide pipelines, comprising the following steps:

[0006] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0007] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0008] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0009] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0010] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0011] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0012] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0013] The invention is further characterized by:

[0014] The specific process of S1 is as follows:

[0015] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0016] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0017] v = d / (t2-t1) (1).

[0018] In S2, ABAQUS software is used to simulate the actual geometry of the pipe for modeling. In the mesh module, shell elements are used to divide the pipe. The refinement of the shell elements is increased in the region near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The code of the finite element model uses the explicit integration algorithm code based on the central difference method. The crack propagation path uses cohesive elements with a size of less than 2mm.

[0019] The calculation of the saturation pressure of carbon dioxide components in S3 is specifically as follows: the GERG08 equation of state is used to calculate the saturation pressure of carbon dioxide components.

[0020] The specific process of S4 is as follows: The general program uses the ABAQUS software Explicit explicit solver module to perform three-dimensional dynamic elastoplastic finite element analysis. Saturation pressure is applied to the crack tip, the cohesive element parameters are continuously adjusted, the steady-state crack propagation rate under the specified crack tip pressure is calculated, and compared with the steady-state crack propagation rate obtained by the experiment in S1 until the two are equal. The cohesive element parameters at this time are selected as the finite element model parameters.

[0021] The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to equation (2);

[0022]

[0023] Where G: cohesive energy; σ mδ: The maximum traction force when the cohesive unit is damaged; c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 .

[0024] In S5, the pressure distribution after the crack enters the crack arrester is divided into three regions: Region 1: pressure region at the crack tip; Region 2: pressure distribution region from the edge of the crack arrester to the crack tip; Region 3: pressure distribution region outside the edge of the crack arrester.

[0025] The pressure distribution in Region 1 was calculated using a shock tube model and the GERG08 equation of state.

[0026] The pressure distribution in region 2 is calculated using equation (3);

[0027] P2 = 0.8 P s +0.002222222X (3);

[0028] Where P2: pressure in region two; X: distance from the crack tip to the crack apex;

[0029] The pressure distribution in region 3 is calculated using equation (4);

[0030]

[0031] Specifically, when θ < 5, C = 0.0408θ + 0.4867, n = -0.314lnθ + 2.7489, C1 = -0.0197θ + 0.0367; when 5 < θ < 90, C = 0.0058θ + 0.5931, n = 0.0103θ + 1.9522, C1 = 0; when 90 < θ < 180, C = 1.0, n = 1.0, C1 = 0.

[0032] The specific process of S6 is as follows:

[0033] S6.1. The total circumferential length Lp of the deformed outer surface of the pipe before the crack enters the crack arrester is directly extracted by finite element model calculation. The total circumferential length Lp is the sum of the length of the steel pipe after deformation and the crack opening amount COD.

[0034] S6.2 Calculate the equivalent circumferential strain δ according to equation (5). e ;

[0035]

[0036] Where, δ e : Equivalent circumferential strain; σup : Tensile strength of steel pipe; σ ua : Tensile strength of crack arrester; t p : Steel pipe wall thickness; t a Crack arrester wall thickness; L p : Total circumferential length of the outer surface of the deformed pipe; L A Circumferential length of the crack arrester;

[0037] S6.3 Calculate the corresponding annular stress t by using the stress corresponding to the equivalent strain in the actual stress-strain curve of the crack arrester;

[0038] S6.4 For each element, tensile stress t is applied to the element edge, i.e. the edge aligned with the longitudinal element direction, which is the bisector of the angle between the element under consideration and the circumferential adjacent element. The equivalent pressure p is calculated according to Equation (6) by vector summation of the virtual force F generated from the tensile stress.

[0039]

[0040] Where A: unit area; F: virtual force.

[0041] The specific process of S7 is as follows: the constraint of the steel sleeve crack arrester on the steel pipe is equivalent to the externally applied stress p. The steady-state crack propagation rate is calculated by the finite element model. When the steady-state crack propagation rate is 0 within the range of action of the crack arrester, the design of the steel sleeve crack arrester is completed.

[0042] The beneficial effects of this invention are:

[0043] The present invention provides a design method for a steel sleeve crack arrester for dense phase carbon dioxide pipelines. The steel sleeve crack arrester designed by this method has been verified by full-scale burst test to achieve the crack arrest function for high-speed propagation cracks. Attached Figure Description

[0044] Figure 1 This is a flowchart of the design method for a steel sleeve crack arrester for dense phase carbon dioxide pipelines according to the present invention;

[0045] Figure 2 This is a schematic diagram of the finite element modeling of the present invention;

[0046] Figure 3 This is a schematic diagram illustrating the calculation of saturation pressure according to the present invention;

[0047] Figure 4 This is a schematic diagram of the bilinear traction force-separation curve of the present invention;

[0048] Figure 5 This is a schematic diagram comparing the calculated and experimental values ​​of the crack steady-state propagation rate according to the present invention;

[0049] Figure 6 This is a pressure distribution diagram after a crack enters the crack arrester of the present invention.

[0050] Figure 7 This is a schematic diagram of the steel pipe deformation according to the present invention;

[0051] Figure 8 This is a stress-strain curve diagram of the crack arrester of the present invention;

[0052] Figure 9 This is a schematic diagram illustrating the calculation of the constraint force of the crack arrester on the steel pipe according to the present invention.

[0053] Figure 10 This is a schematic diagram comparing the calculated and experimental values ​​of the crack steady-state propagation rate in Embodiment 9 of the present invention; Detailed Implementation

[0054] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0055] Example 1

[0056] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0057] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0058] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0059] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0060] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0061] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0062] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0063] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0064] Example 2

[0065] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0066] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0067] The specific process of S1 is as follows:

[0068] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0069] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0070] v = d / (t2-t1) (1);

[0071] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0072] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0073] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0074] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0075] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0076] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0077] Example 3

[0078] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0079] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0080] The specific process of S1 is as follows:

[0081] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0082] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0083] v = d / (t2-t1) (1).

[0084] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0085] In S2, ABAQUS software is used to model the actual pipe geometry. In the mesh module, shell elements are used to divide the pipe, with the refinement of the shell elements increasing near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The finite element model code uses an explicit integration algorithm based on the central difference method, such as... Figure 2 As shown, the crack propagation path uses cohesive elements, and the size of the cohesive elements is less than 2 mm;

[0086] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0087] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0088] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0089] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0090] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0091] Example 4

[0092] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0093] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0094] The specific process of S1 is as follows:

[0095] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0096] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0097] v = d / (t2-t1) (1).

[0098] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0099] In S2, ABAQUS software is used to model the actual pipe geometry. In the mesh module, shell elements are used to divide the pipe, with the refinement of the shell elements increasing near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The finite element model code uses an explicit integration algorithm based on the central difference method, such as... Figure 2 As shown, the crack propagation path uses cohesive elements, and the size of the cohesive elements is less than 2 mm;

[0100] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0101] The specific calculation of the saturation pressure of carbon dioxide components is as follows: Figure 3 As shown, the saturation pressure of carbon dioxide components is calculated using the GERG08 equation of state;

[0102] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0103] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0104] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0105] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0106] Example 5

[0107] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0108] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0109] The specific process of S1 is as follows:

[0110] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0111] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0112] v = d / (t2-t1) (1).

[0113] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0114] In S2, ABAQUS software is used to model the actual pipe geometry. In the mesh module, shell elements are used to divide the pipe, with the refinement of the shell elements increasing near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The finite element model code uses an explicit integration algorithm based on the central difference method, such as... Figure 2 As shown, the crack propagation path uses cohesive elements, and the size of the cohesive elements is less than 2 mm;

[0115] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0116] The specific calculation of the saturation pressure of carbon dioxide components is as follows: Figure 3 As shown, the saturation pressure of carbon dioxide components is calculated using the GERG08 equation of state;

[0117] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0118] The specific process of S4 is as follows: The general program uses the ABAQUS software's Explicit solver module to perform three-dimensional dynamic elastoplastic finite element analysis. Saturation pressure is applied at the crack tip, and the cohesive element parameters are continuously adjusted. The steady-state crack propagation rate under the specified crack tip pressure is calculated and compared with the experimentally obtained crack steady-state propagation rate in S1 until the two are equal. Figure 4 , 5 As shown, the cohesive element parameters at this time are selected as the parameters of the finite element model.

[0119] The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to equation (2);

[0120]

[0121] Where G: cohesive energy; σ m δ: The maximum traction force when the cohesive unit is damaged; c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0122] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0123] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0124] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0125] Example 6

[0126] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0127] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0128] The specific process of S1 is as follows:

[0129] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0130] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0131] v = d / (t2-t1) (1).

[0132] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0133] In S2, ABAQUS software is used to model the actual pipe geometry. In the mesh module, shell elements are used to divide the pipe, with the refinement of the shell elements increasing near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The finite element model code uses an explicit integration algorithm based on the central difference method, such as... Figure 2As shown, the crack propagation path uses cohesive elements, and the size of the cohesive elements is less than 2 mm;

[0134] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0135] The specific calculation of the saturation pressure of carbon dioxide components is as follows: Figure 3 As shown, the saturation pressure of carbon dioxide components is calculated using the GERG08 equation of state;

[0136] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0137] The specific process of S4 is as follows: The general program uses the ABAQUS software's Explicit solver module to perform three-dimensional dynamic elastoplastic finite element analysis. Saturation pressure is applied at the crack tip, and the cohesive element parameters are continuously adjusted. The steady-state crack propagation rate under the specified crack tip pressure is calculated and compared with the experimentally obtained crack steady-state propagation rate in S1 until the two are equal. Figure 4 , 5 As shown, the cohesive element parameters at this time are selected as the parameters of the finite element model.

[0138] The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to equation (2);

[0139]

[0140] Where G: cohesive energy; σ m δ: The maximum traction force when the cohesive unit is damaged; c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0141] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0142] In S5, such as Figure 6 As shown, the pressure distribution after the crack enters the crack arrester is divided into three regions: Region 1: pressure region at the crack tip; Region 2: pressure distribution region from the edge of the crack arrester to the crack tip; Region 3: pressure distribution region outside the edge of the crack arrester.

[0143] The pressure distribution in Region 1 was calculated using a shock tube model and the GERG08 equation of state.

[0144] The pressure distribution in region 2 is calculated using equation (3);

[0145] P2 = 0.8 P s +0.002222222X (3);

[0146] Where P2: pressure in region two; X: distance from the crack tip to the crack apex;

[0147] The pressure distribution in region 3 is calculated using equation (4);

[0148]

[0149] Specifically, when θ < 5, C = 0.0408θ + 0.4867, n = -0.314lnθ + 2.7489, C1 = -0.0197θ + 0.0367; when 5 < θ < 90, C = 0.0058θ + 0.5931, n = 0.0103θ + 1.9522, C1 = 0; when 90 < θ < 180, C = 1.0, n = 1.0, C1 = 0.

[0150] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0151] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0152] Example 7

[0153] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0154] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0155] The specific process of S1 is as follows:

[0156] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0157] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0158] v = d / (t2-t1) (1).

[0159] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0160] In S2, ABAQUS software is used to model the actual pipe geometry. In the mesh module, shell elements are used to divide the pipe, with the refinement of the shell elements increasing near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The finite element model code uses an explicit integration algorithm based on the central difference method, such as... Figure 2 As shown, the crack propagation path uses cohesive elements, and the size of the cohesive elements is less than 2 mm;

[0161] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0162] The specific calculation of the saturation pressure of carbon dioxide components is as follows: Figure 3 As shown, the saturation pressure of carbon dioxide components is calculated using the GERG08 equation of state;

[0163] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0164] The specific process of S4 is as follows: The general program uses the ABAQUS software's Explicit solver module to perform three-dimensional dynamic elastoplastic finite element analysis. Saturation pressure is applied at the crack tip, and the cohesive element parameters are continuously adjusted. The steady-state crack propagation rate under the specified crack tip pressure is calculated and compared with the experimentally obtained crack steady-state propagation rate in S1 until the two are equal. Figure 4 , 5 As shown, the cohesive element parameters at this time are selected as the parameters of the finite element model.

[0165] The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to equation (2);

[0166]

[0167] Where G: cohesive energy; σ m δ: The maximum traction force when the cohesive unit is damaged; c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0168] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0169] In S5, such as Figure 6As shown, the pressure distribution after the crack enters the crack arrester is divided into three regions: Region 1: pressure region at the crack tip; Region 2: pressure distribution region from the edge of the crack arrester to the crack tip; Region 3: pressure distribution region outside the edge of the crack arrester.

[0170] The pressure distribution in Region 1 was calculated using a shock tube model and the GERG08 equation of state.

[0171] The pressure distribution in region 2 is calculated using equation (3);

[0172] P2 = 0.8 P s +0.002222222X (3);

[0173] Where P2: pressure in region two; X: distance from the crack tip to the crack apex;

[0174] The pressure distribution in region 3 is calculated using equation (4);

[0175]

[0176] Specifically, when θ < 5, C = 0.0408θ + 0.4867, n = -0.314lnθ + 2.7489, C1 = -0.0197θ + 0.0367; when 5 < θ < 90, C = 0.0058θ + 0.5931, n = 0.0103θ + 1.9522, C1 = 0; when 90 < θ < 180, C = 1.0, n = 1.0, C1 = 0.

[0177] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0178] The specific process of S6 is as follows:

[0179] S6.1, such as Figure 7 As shown, the total circumferential length Lp of the deformed outer surface of the pipe before the crack enters the crack arrester is directly extracted by the finite element model calculation. The total circumferential length Lp is the sum of the length of the steel pipe after deformation and the crack opening amount COD.

[0180] S6.2 Calculate the equivalent circumferential strain δ according to equation (5). e ;

[0181]

[0182] Where, δ e : Equivalent circumferential strain; σ up : Tensile strength of steel pipe; σ ua : Tensile strength of crack arrester; t p : Steel pipe wall thickness; t a Crack arrester wall thickness; Lp : Total circumferential length of the outer surface of the deformed pipe; L A Circumferential length of the crack arrester;

[0183] S6.3, such as Figure 8 As shown, the corresponding annular stress t is calculated by using the stress corresponding to the equivalent strain in the actual stress-strain curve of the crack arrester.

[0184] S6.4, such as Figure 9 As shown, for each element, tensile stress t is applied to the element edge, i.e. the edge aligned with the longitudinal element direction, which is the bisector of the angle between the element under consideration and the circumferential adjacent element. The equivalent pressure p is calculated according to Equation (6) by vector summation of the virtual force F generated from the tensile stress.

[0185]

[0186] Where A: unit area; F: virtual force;

[0187] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0188] Example 8

[0189] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0190] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0191] The specific process of S1 is as follows:

[0192] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0193] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1);

[0194] v = d / (t2-t1) (1).

[0195] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0196] In S2, ABAQUS software is used to model the actual pipe geometry. In the mesh module, shell elements are used to divide the pipe, with the refinement of the shell elements increasing near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The finite element model code uses an explicit integration algorithm based on the central difference method, such as... Figure 2 As shown, the crack propagation path uses cohesive elements, and the size of the cohesive elements is less than 2 mm;

[0197] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0198] The specific calculation of the saturation pressure of carbon dioxide components is as follows: Figure 3 As shown, the saturation pressure of carbon dioxide components is calculated using the GERG08 equation of state;

[0199] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0200] The specific process of S4 is as follows: The general program uses the ABAQUS software's Explicit solver module to perform three-dimensional dynamic elastoplastic finite element analysis. Saturation pressure is applied at the crack tip, and the cohesive element parameters are continuously adjusted. The steady-state crack propagation rate under the specified crack tip pressure is calculated and compared with the experimentally obtained crack steady-state propagation rate in S1 until the two are equal. Figure 4 , 5 As shown, the cohesive element parameters at this time are selected as the parameters of the finite element model.

[0201] The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to equation (2);

[0202]

[0203] Where G: cohesive energy; σ m δ: The maximum traction force when the cohesive unit is damaged; c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0204] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0205] In S5, such as Figure 6As shown, the pressure distribution after the crack enters the crack arrester is divided into three regions: Region 1: pressure region at the crack tip; Region 2: pressure distribution region from the edge of the crack arrester to the crack tip; Region 3: pressure distribution region outside the edge of the crack arrester.

[0206] The pressure distribution in Region 1 was calculated using a shock tube model and the GERG08 equation of state.

[0207] The pressure distribution in region 2 is calculated using equation (3);

[0208] P2 = 0.8 P s +0.002222222X (3);

[0209] Where P2: pressure in region two; X: distance from the crack tip to the crack apex;

[0210] The pressure distribution in region 3 is calculated using equation (4);

[0211]

[0212] Specifically, when θ < 5, C = 0.0408θ + 0.4867, n = -0.314lnθ + 2.7489, C1 = -0.0197θ + 0.0367; when 5 < θ < 90, C = 0.0058θ + 0.5931, n = 0.0103θ + 1.9522, C1 = 0; when 90 < θ < 180, C = 1.0, n = 1.0, C1 = 0.

[0213] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0214] The specific process of S6 is as follows:

[0215] S6.1, such as Figure 7 As shown, the total circumferential length Lp of the deformed outer surface of the pipe before the crack enters the crack arrester is directly extracted by the finite element model calculation. The total circumferential length Lp is the sum of the length of the steel pipe after deformation and the crack opening amount COD.

[0216] S6.2 Calculate the equivalent circumferential strain δ according to equation (5). e ;

[0217]

[0218] Where, δ e : Equivalent circumferential strain; σ up : Tensile strength of steel pipe; σ ua : Tensile strength of crack arrester; t p : Steel pipe wall thickness; t a Crack arrester wall thickness; Lp : Total circumferential length of the outer surface of the deformed pipe; L A Circumferential length of the crack arrester;

[0219] S6.3, such as Figure 8 As shown, the corresponding annular stress t is calculated by using the stress corresponding to the equivalent strain in the actual stress-strain curve of the crack arrester.

[0220] S6.4, such as Figure 9 As shown, for each element, tensile stress t is applied to the element edge, i.e. the edge aligned with the longitudinal element direction, which is the bisector of the angle between the element under consideration and the circumferential adjacent element. The equivalent pressure p is calculated according to Equation (6) by vector summation of the virtual force F generated from the tensile stress.

[0221]

[0222] Where A: unit area; F: virtual force;

[0223] S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

[0224] The specific process is as follows: the constraint of the steel sleeve crack arrester on the steel pipe is equivalent to the externally applied stress p. The steady-state crack propagation rate is calculated by the finite element model. When the steady-state crack propagation rate is 0 within the range of action of the crack arrester, the design of the steel sleeve crack arrester is completed.

[0225] Example 9

[0226] The steel sleeve crack arrester design method for dense-phase carbon dioxide pipelines proposed in this embodiment includes the following steps:

[0227] S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test;

[0228] The specific process is as follows:

[0229] S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0230] S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation velocity v = 263 m / s in the steel pipe according to formula (1);

[0231] v = d / (t2-t1) (1);

[0232] S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths;

[0233] In S2, ABAQUS software is used to simulate the actual pipe geometry for modeling. In the mesh module, shell elements are used to divide the pipe. The refinement of the shell elements is increased in the region near the upper generatrix. Crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The code of the finite element model uses the explicit integration algorithm code based on the central difference method. The crack propagation path uses cohesive elements with a size of less than 2mm.

[0234] S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip;

[0235] The specific calculation of the saturation pressure of carbon dioxide components is as follows: Figure 3 As shown, the saturation pressure of carbon dioxide components is calculated using the GERG08 equation of state;

[0236] S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters;

[0237] The specific process is as follows: The general program uses the ABAQUS software's Explicit solver module to perform three-dimensional dynamic elastoplastic finite element analysis. Saturation pressure is applied at the crack tip, and the cohesive element parameters are continuously adjusted. The steady-state crack propagation rate under the specified crack tip pressure is calculated and compared with the steady-state crack propagation rate obtained experimentally in S1 until the two are equal. Figure 10 As shown in Table 1, the parameters of the cohesive elements at this time are selected as the parameters of the finite element model.

[0238] Table 1. Cohesive Parameters

[0239]

[0240] The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to equation (2);

[0241]

[0242] Where G: cohesive energy; σ m δ: The maximum traction force when the cohesive unit is damaged; c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0243] S5. Determine the pressure distribution after the crack enters the crack arrester;

[0244] In S5, the pressure distribution after the crack enters the crack arrester is divided into three regions: Region 1: pressure region at the crack tip; Region 2: pressure distribution region from the edge of the crack arrester to the crack tip; Region 3: pressure distribution region outside the edge of the crack arrester.

[0245] The pressure distribution in Region 1 was calculated using a shock tube model and the GERG08 equation of state.

[0246] The pressure distribution in region 2 is calculated using equation (3);

[0247] P2 = 0.8 P s +0.002222222X (3);

[0248] Where P2: pressure in region two; X: distance from the crack tip to the crack apex;

[0249] The pressure distribution in region 3 is calculated using equation (4);

[0250]

[0251] Specifically, when θ < 5, C = 0.0408θ + 0.4867, n = -0.314lnθ + 2.7489, C1 = -0.0197θ + 0.0367; when 5 < θ < 90, C = 0.0058θ + 0.5931, n = 0.0103θ + 1.9522, C1 = 0; when 90 < θ < 180, C = 1.0, n = 1.0, C1 = 0.

[0252] S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm;

[0253] The specific process is as follows:

[0254] S6.1, such as Figure 7 As shown, the total circumferential length Lp of the deformed outer surface of the pipe before the crack enters the crack arrester is directly extracted by the finite element model calculation. The total circumferential length Lp is the sum of the length of the steel pipe after deformation and the crack opening amount COD.

[0255] S6.2 Calculate the equivalent circumferential strain δ according to equation (5). e ;

[0256]

[0257] Where, δ e : Equivalent circumferential strain; σ up : Tensile strength of steel pipe; σua : Tensile strength of crack arrester; t p : Steel pipe wall thickness; t α Crack arrester wall thickness; L p : Total circumferential length of the outer surface of the deformed pipe; L A Circumferential length of the crack arrester;

[0258] S6.3, such as Figure 8 As shown, the corresponding annular stress t is calculated by using the stress corresponding to the equivalent strain in the actual stress-strain curve of the crack arrester.

[0259] S6.4, such as Figure 9 As shown, for each element, tensile stress t is applied to the element edge, i.e. the edge aligned with the longitudinal element direction. These edges are the bisectors of the angle between the element under consideration and the circumferential adjacent elements. The equivalent pressure p = 100 N is calculated according to Equation (6) by vector summation of the virtual force F generated from the tensile stress.

[0260]

[0261] Where A: unit area; F: virtual force;

[0262] S7. Equivalent the constraint force to the externally applied stress to obtain the steady-state crack propagation rate and complete the design of the steel sleeve crack arrester.

[0263] The specific process is as follows: the constraint of the steel sleeve crack arrester on the steel pipe is equivalent to the externally applied stress p. The steady-state crack propagation rate is calculated by the finite element model. When the steady-state crack propagation rate is 0 within the range of action of the crack arrester, the design of the steel sleeve crack arrester is completed.

Claims

1. A design method for a steel sleeve crack arrester used in dense phase carbon dioxide pipelines, characterized in that, Includes the following steps: S1. Select a sample steel pipe and determine the steady-state crack propagation rate in the sample steel pipe through DWTT test; S2. Establish a finite element model: simulate the actual pipe geometry, use shell elements to divide the pipe, and use cohesive elements for crack propagation paths; S3. Calculate the saturation pressure of the carbon dioxide component and apply the pressure to the crack tip; S4. Use a general program to perform three-dimensional dynamic elastoplastic finite element analysis, determine the cohesive force parameters, and use the cohesive force parameters as finite element model parameters; S5. Determine the pressure distribution after the crack enters the crack arrester; S6. Establish a non-contact algorithm and evaluate the constraint force of the crack arrester on crack propagation through the algorithm; S7. Equivalent the constraint force to the externally applied stress to obtain the crack propagation rate and complete the design of the steel sleeve crack arrester.

2. The design method for a steel sleeve crack arrester for dense-phase carbon dioxide pipelines according to claim 1, characterized in that, The specific process of S1 is as follows: S1.1 Select a steel pipe, conduct a DWTT test, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography; S1.2 Determine the linear time intervals t1 and t2 of the steel pipe, determine the crack propagation distance d during the time interval t1 to t2 using high-speed imaging, and calculate the steady-state crack propagation rate v in the steel pipe according to formula (1); v = d / (t2-t1) (1).

3. The design method for a steel sleeve crack arrester for dense-phase carbon dioxide pipelines according to claim 1, characterized in that, In step S2, ABAQUS software is used to simulate the actual geometric dimensions of the pipe for modeling. In the mesh module, shell elements are used to divide the pipe. The refinement of the shell elements increases in the region near the upper generatrix, and crack propagation is applied in this region. The average side length of the shell elements is 100mm-10mm. The code of the finite element model uses explicit integration algorithm code based on the central difference method. The crack propagation path uses cohesive elements, and the size of the cohesive elements is less than 2mm.

4. The design method for a steel sleeve crack arrester for dense-phase carbon dioxide pipelines according to claim 1, characterized in that, The calculation of the saturation pressure of carbon dioxide components described in S3 specifically involves using the GERG08 equation of state to calculate the saturation pressure of carbon dioxide components.

5. The design method for a steel sleeve crack arrester for dense-phase carbon dioxide pipelines according to claim 1, characterized in that, The specific process of S4 is as follows: the general program uses the ABAQUS software Explicit explicit solver module to perform three-dimensional dynamic elastoplastic finite element analysis, applies saturation pressure at the crack tip, continuously adjusts the cohesive element parameters, calculates the steady-state crack propagation rate under the specified crack tip pressure, compares it with the steady-state crack propagation rate obtained experimentally in S1, until the two are equal, and selects the cohesive element parameters at this time as the finite element model parameters. The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to equation (2); Where G: cohesive energy; σ m δ: The maximum traction force when the cohesive unit is damaged; c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 .

6. The design method for a steel sleeve crack arrester for dense-phase carbon dioxide pipelines according to claim 1, characterized in that, In S5, the pressure distribution after the crack enters the crack arrester is divided into three regions: Region 1: pressure region at the crack tip; Region 2: pressure distribution region from the edge of the crack arrester to the crack tip; Region 3: pressure distribution region outside the edge of the crack arrester. The pressure distribution in Region 1 was calculated using a shock tube model and the GERG08 equation of state. The pressure distribution in region two is calculated using equation (3); P2=0.8 P s +0.002222222X (3); Where P2: pressure in region two; X: distance from the crack tip to the crack apex; The pressure distribution in region three is calculated using equation (4); Specifically, when θ < 5, C = 0.0408θ + 0.4867, n = -0.314lnθ + 2.7489, C1 = -0.0197θ + 0.0367; when 5 < θ < 90, C = 0.0058θ + 0.5931, n = 0.0103θ + 1.9522, C1 = 0; when 90 < θ < 180, C = 1.0, n = 1.0, C1 = 0.

7. The design method for a steel sleeve crack arrester for dense-phase carbon dioxide pipelines according to claim 1, characterized in that, The specific process of S6 is as follows: S6.

1. The total circumferential length Lp of the deformed outer surface of the pipe before the crack enters the stable propagation stage is directly extracted by finite element model calculation. The total circumferential length Lp is the sum of the length of the steel pipe after deformation and the crack opening amount COD. S6.2 Calculate the equivalent circumferential strain δ according to equation (5). e ; Where, δ e : Equivalent circumferential strain; σ up : Tensile strength of steel pipe; σ ua : Tensile strength of crack arrester; t p : Steel pipe wall thickness; t α Crack arrester wall thickness; L p : Total circumferential length of the outer surface of the deformed pipe; L A Circumferential length of the crack arrester; S6.3 Calculate the corresponding annular stress t by using the stress corresponding to the equivalent strain in the actual stress-strain curve of the crack arrester; S6.4 For each element, tensile stress t is applied to the element edge, i.e. the edge aligned with the longitudinal element direction, which is the bisector of the angle between the element under consideration and the circumferential adjacent element. The equivalent pressure p is calculated according to Equation (6) by vector summation of the virtual force F generated from the tensile stress. Where A: unit area; F: virtual force.

8. The design method for a steel sleeve crack arrester for dense-phase carbon dioxide pipelines according to claim 1, characterized in that, The specific process of S7 is as follows: the constraint of the steel sleeve crack arrester on the steel pipe is equivalent to the externally applied stress p. The steady-state crack propagation rate is calculated by the finite element model. When the steady-state crack propagation rate is 0 within the range of action of the crack arrester, the design of the steel sleeve crack arrester is completed.

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