A tubing string design method based on material strain

Abstract

The application discloses a kind of oil pipe column design methods based on material strain, it is related to oil and gas production technology field, solve the technical problem that existing super deep well oil pipe column design is difficult, including determining basic parameters;Determine the working condition information of oil pipe column;The temperature and pressure distribution of the inner and outer wall of oil pipe column are calculated;The strain distribution of oil pipe column is calculated;Determine the strain safety factor threshold of oil pipe column;The oil pipe column is checked.The application breaks through the research direction of conventional pipeline design criterion, studies the working condition of super deep well, and based on research findings, the application combines the temperature distribution and pressure distribution of oil pipe column, and then calculates stress according to load, obtains strain based on stress, and then determines the steel grade of oil pipe column according to the comparison between strain and allowable strain, which increases the design window of super deep oil well, reduces the design difficulty, and provides scientific theoretical support for the selection of super deep well pipe column material and the optimization of pipe column combination.

Description

Technical Field

[0001] This invention relates to the field of oil and gas production technology, specifically to a tubing string design method based on material strain, and more specifically to the safety verification of tubing strings. Background Technology

[0002] As oil and gas well depths increase, the conventional tubing string design method based on allowable stress currently used in my country has limited application scenarios. It cannot completely and effectively solve all tubing string design problems in gas wells, especially for ultra-deep gas wells with depths exceeding 7,000 meters. Therefore, in order to improve the safety and smoothness of ultra-deep gas well production, it is essential to research tubing string design methods specifically for ultra-deep gas wells.

[0003] Currently, there are three main design criteria for the strength of metal tubing: conventional tubing string design criteria based on allowable stress, design criteria based on plastic failure, and design criteria based on strain. Among these, the conventional tubing string design criteria based on allowable stress is the most widely used design criterion in oil and gas well engineering. Its design window specifies that the load borne by the tubing string cannot exceed the yield strength of the tubing material used. Specifically, for example… Figure 1 As shown. The design criterion based on plastic failure is mainly used in the field of pressure vessel engineering. Its design window specifies that the load borne by the metallic material cannot exceed its tensile strength, such as... Figure 2 As shown. The strain-based design principle is mainly used in pipeline design engineering. Its design window stipulates that when the pipe material is subjected to a certain load, its strain range cannot exceed the material's ultimate strain.

[0004] The working conditions for tubing string design in ultra-deep gas wells are special and the design is difficult. The three design methods mentioned above all have their own defects and none of them can be fully applied to the tubing string design of ultra-deep gas wells. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned technical problems by providing a tubing string design method based on material strain. As well depth increases, the load on the tubing string gradually increases, leading to a narrowing of the stress-based plastic design window. This significantly increases the difficulty of tubing string design in ultra-deep gas wells. Consequently, even with higher-strength tubing steel grades, it is difficult to find a matching tubing string combination that meets the safety factor requirements and the high load-bearing demands of ultra-deep gas wells under design criteria based on plastic failure. On the other hand, research has found that the tubing string elongation rate used in ultra-deep wells does not decrease significantly, and its deformation capacity is significantly improved. Furthermore, creep can offset the stress borne by the tubing string.

[0006] The above discovery, based on the unconventional technical angle, the inventors found that the present application breaks through the conventional relationship between load and yield limit of pipe material, the relationship between load and tensile limit of pipe material, and the relationship between strain and limit strain of pipe material caused by load, and proposes a new tubing string design method based on material strain for ultra-deep gas wells: determining strain distribution based on load, and determining safety factor based on strain distribution. This method effectively overcomes the influence of the special working state of the tubing string in the ultra-deep well on the design, increases the design window of the tubing string in the ultra-deep well, reduces the design difficulty, provides a new scientific design method for the selection of tubing string materials and the optimization of tubing string combination in the ultra-deep well, provides scientific support for the checking of the tubing string in the ultra-deep well, thereby providing a guidance basis for the production of the tubing string in the ultra-deep well, and further improving the service life of the tubing string in the ultra-deep well, reducing the related maintenance cost, and ensuring the smooth operation of the related operation.

[0007] In order to achieve the above-mentioned purpose, the present application specifically adopts the following technical solutions:

[0008] A tubing string design method based on material strain, comprising the following contents:

[0009] S1, determining basic parameters: determining well structure, tubing string steel grade, reservoir and fluid physical property parameters;

[0010] S2, determining the working condition information of the tubing string in the initial stage, and further determining the temperature and pressure of the fluid when entering the tubing string;

[0011] S3, based on the temperature and pressure of the fluid when entering the tubing string as boundary conditions, calculating the temperature and pressure distribution of the inner and outer walls of the tubing string under the corresponding working condition;

[0012] S4, based on the data information in S1-S3, calculating the load borne by the tubing string under the corresponding working condition, and obtaining the strain distribution of the tubing string according to the calculation result;

[0013] S5, determining the strain safety factor threshold of the tubing string based on the strain distribution of the tubing string;

[0014] S6, checking the tubing string based on the strain safety factor threshold.

[0015] The well structure includes: vertical depth TVD of the well, deviation depth MD, azimuth angle AZ, tubing and casing combination program, packer position PD, and safety valve position SD.

[0016] The tubing and casing combination program includes pipe string length h i , outer diameter OD, inner diameter ID, and wire weight W.

[0017] The reservoir and fluid physical property parameters include: reservoir pressure Pres , reservoir temperature T res , fluid density p, fluid specific heat c p .

[0018] The working condition includes a stimulation stage and a production stage;

[0019] When the working condition is the production stage, the temperature of the fluid when entering the tubing string needs to consider the bottom hole temperature rise caused by the Joule-Thomson effect of the fluid from the formation to the bottom hole;

[0020] The bottom hole temperature rise caused by the Joule-Thomson effect is calculated by the following formula:

[0021]

[0022] Where, μ J-T is the Joule-Thomson coefficient;

[0023] T-fluid temperature, K;

[0024] p-fluid density, kg / m 3 ;

[0025] c p -fluid specific heat, J / (kg.K);

[0026] The bottom hole temperature T wf is:

[0027] T wf =T res -△Pμ J-T (2)

[0028] Where, △P is the production pressure difference of the tubing string.

[0029] The working condition information of the stimulation stage includes: construction pump pressure P p , construction displacement Q p , injection fluid viscosity v i , injection fluid density p i ;

[0030] The working condition information of the production stage includes: wellhead pressure P wh , wellhead temperature T wh , wellhead flow rate Q wh .

[0031] The temperature and pressure distribution of the tubing string in and out of S3 are calculated by the following formula:

[0032]

[0033]

[0034] Coupling formula (3) and formula (4) to solve the temperature and pressure distribution in the pipe column. Wherein,

[0035] T f - fluid temperature, ℃;

[0036] T ei - formation temperature, ℃;

[0037] r to - tubing column outer diameter, m;

[0038] U mul - annulus heat transfer coefficient, J / (s·m 2 ·℃);

[0039] k e - formation thermal conductivity;

[0040] w- fluid mass change per unit time, kg / s;

[0041] m- fluid mass per unit length, kg / m;

[0042] c p - specific heat capacity of fluid, J / (kg·℃);

[0043] C J - Joule-Thomson coefficient of natural gas in the tubing column, m·℃·s 2 ;T D - dimensionless time;

[0044] z- well depth, mg G - geothermal gradient, ℃ / m;

[0045] v- fluid flow rate, m / s;

[0046] C T - heat storage coefficient, decimal;

[0047] θ- inclination angle, °;

[0048] g- acceleration of gravity, 9.80 m / s 2 .

[0049] In the S4, the load on the tubing column is calculated by the following method:

[0050]

[0051]

[0052]

[0053] Wherein,

[0054] σ1 Tubing string axial stress, MPa;

[0055] σ2 Tubing string circumferential stress, MPa;

[0056] σ3 Tubing string radial stress, MPa;

[0057] P in Tubing string internal pressure, MPa;

[0058] P ou Tubing string external pressure, MPa;

[0059] r to Tubing string outer diameter, m;

[0060] r ti Tubing string inner diameter, m;

[0061] P A Tubing string and casing annulus pressure;

[0062] r Point to tubing string center axis distance;

[0063] r c Tubing string inner diameter after deformation, m;

[0064] F c Tubing string axial force.

[0065] In the S5, the strain distribution of the tubing string is calculated by the following method:

[0066] The circumferential strain ε θ of the tubing string is:

[0067]

[0068] The radial strain ε r of the tubing string is:

[0069]

[0070] Wherein, ε s is the strain at the midpoint of the inner wall and the outer wall of the tubing.

[0071] The specific method for determining the safety factor threshold of the tubing string based on the strain distribution is:

[0072] The strain design of the tubing string will allow the tubing string to occur plastic deformation, and the design criterion is the maximum uniform elongation of the pipe material, and the n% of the uniform elongation of the tubing string material is the allowable strain [ε] of the tubing string:

[0073] [ε] = δ × n% (10)

[0074] Wherein, δ is the maximum elongation of the pipe material.

[0075] The strain safety factor threshold of the tubing string is:

[0076]

[0077] The working strain of the tubing string is: ∑

[0078]

[0079] Wherein,

[0080] Delta L is the elongation of the tubing string;

[0081] L0 is the original gauge length;

[0082] The working strain of the tubing string is:

[0083] The working strain of the tubing string is: Σ The working strain of the tubing string is:

[0084] The working strain safety factor of the tubing string is:

[0085]

[0086] The safety factor threshold is based on the tubing string, including: the working strain safety factor of the selected tubing string is compared with the strain safety factor threshold, if the working strain safety factor of the selected tubing string is not less than the strain safety factor threshold, the selected tubing string meets the requirements; if the working strain safety factor of the selected tubing string is less than the strain safety factor threshold, the selected tubing string does not meet the requirements, the tubing string steel grade is improved to recheck, until the working strain safety factor of the selected tubing string is not less than the strain safety factor threshold.

[0087] The beneficial effects of the present application are as follows:

[0088] The present application breaks through the research direction of the conventional pipeline design criterion, and studies the working condition of the ultra-deep well, so that the special working condition of the ultra-deep well is found, that is, the extension rate of the tubing string used in the working condition of the ultra-deep well is not significantly reduced, and the deformation ability is significantly improved, and the stress borne by the tubing string can also be offset by creep; then based on this, the present application provides a new tubing string design method based on material strain, which combines the temperature distribution and pressure distribution of the tubing string, and then calculates the stress according to the load, obtains the strain based on the stress, and then determines the steel grade of the tubing string according to the comparison between the strain and the allowable strain, which increases the design window of the ultra-deep well, reduces the design difficulty, and provides scientific theoretical support for the selection of the tubing string material of the ultra-deep well and the optimization of the tubing string combination. BRIEF DESCRIPTION OF DRAWINGS

[0089] Figure 1 ​is a schematic diagram of an ultra-deep well structure;

[0090] Figure 2 is a temperature distribution under different working conditions;

[0091] Figure 3 is a pressure distribution under different working conditions;

[0092] Figure 4 is a flowchart of the present application. DETAILED DESCRIPTION

[0093] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations.

[0094] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0095] Embodiment 1

[0096] As shown in the following table, the present embodiment provides a specific implementation of a tubing string design method based on material strain. Figures 1 to 4

[0097] A certain well has a drilled depth of 6390.00 m, a vertical depth of 5510.00 m, a formation pressure of 76.9 MPa, a formation temperature of 152℃, a pressure coefficient of 1.75, and a production condition of natural gas production of 80×10 4 m 3 / d and a production pressure difference of 30 MPa.

[0098] The parameter information of the tubing string is as follows:

[0099]

[0100] Table 1. Parameter information table of the tubing string

[0101] Based on the above information, the following processing is performed:

[0102] ​S1, determining well structure, tubing string steel grade, reservoir and fluid physical property parameters; well depth structure includes: well TVD, MD, AZ, casing program, packer position PD, safety valve position SD; wherein, the casing program includes tubing string length h i , outer diameter OD, inner diameter ID, line weight W; reservoir and fluid physical property parameters include: reservoir pressure P res , reservoir temperature T res , fluid density p, fluid specific heat c p ;

[0103] S2, determining the working condition information of the tubing string in the initial stage, and further determining the temperature and pressure of the fluid when entering the tubing string;

[0104] bottom hole pressure P wf =P res -△P;

[0105] △P is determined by existing formula;

[0106] The working condition includes stimulation stage and production stage;

[0107] The working condition information of the stimulation stage includes: construction pump pressure P p , construction displacement Q p , injection fluid viscosity v i , injection fluid density p i ;

[0108] The working condition information of the production stage includes: wellhead pressure P wh , wellhead temperature T wh , wellhead flow rate Q wh ;

[0109] When the working condition is the production stage, the temperature of the fluid when entering the tubing string needs to consider the bottom hole temperature rise caused by the Joule-Thomson effect of the fluid from the formation to the bottom hole;

[0110] The bottom hole temperature rise caused by the Joule-Thomson effect is calculated by the following formula:

[0111]

[0112] Wherein, μ J-T is the Joule-Thomson coefficient;

[0113] T-fluid temperature, K;

[0114] p-fluid density, kg / m 3 ;

[0115] c p -fluid specific heat, J / (kg.K)

[0116] Wellbore temperature T wf is:

[0117] T wf = T res -△Pμ J-T (2)

[0118] wherein,△P is the production pressure difference of the tubing string.

[0119] S3, based on the temperature and pressure of the fluid when entering the tubing string as the boundary condition, calculating the temperature and pressure distribution of the inner and outer wall of the tubing string under the corresponding working condition;

[0120] The temperature and pressure distribution of the inner and outer wall of the tubing string is calculated by the following formula:

[0121]

[0122]

[0123] Coupling formula (3) and formula (4) to solve the temperature and pressure distribution in the tubing string, the temperature distribution of this tubing string under the two working conditions of the stimulation modification stage and the production stage is as shown in Figure 2 ; The corresponding pressure distribution is as shown in Figure 3 .

[0124] wherein,

[0125] T f - fluid temperature, ℃;

[0126] T ei - formation temperature, ℃;

[0127] r to - tubing string outer diameter, m;

[0128] U mul - annulus heat transfer coefficient, J / (s·m 2 ·℃);

[0129] k e - formation thermal conductivity;

[0130] w- fluid mass change per unit time, kg / s;

[0131] m- fluid mass per unit length, kg / m;

[0132] c p - specific heat capacity of fluid, J / (kg·℃);

[0133] C J - Joule-Thomson coefficient of natural gas in the tubing string, m·℃·s2 ;

[0134] T D - dimensionless time;

[0135] z - well depth, m

[0136] g G - geothermal gradient, °C / m;

[0137] v - fluid flow rate, m / s;

[0138] C T - thermal storage coefficient, decimal;

[0139] θ - inclination angle, °;

[0140] g - gravity acceleration, 9.80 m / s 2 .

[0141] S4, based on the data information in S1-S3, calculating the load on the tubing string under the corresponding working condition, and calculating the strain distribution of the tubing string according to the calculation result;

[0142] The load on the tubing string is calculated by the following method:

[0143]

[0144]

[0145]

[0146] wherein,

[0147] σ1 - axial stress of the tubing string, MPa;

[0148] σ2 - circumferential stress of the tubing string, MPa;

[0149] σ3 - radial stress of the tubing string, MPa;

[0150] P in internal pressure of the tubing string pipe wall, MPa;

[0151] P ou external pressure of the tubing string pipe wall, MPa;

[0152] r to outer diameter of the tubing string, m;

[0153] r ti inner diameter of the tubing string, m;

[0154] P A tubing string and casing annulus pressure;

[0155] r distance from the solution point to the center axis of the tubing string;

[0156] r c The inner diameter of the tubing string after deformation, m;

[0157] F c is the axial force of the tubing string.

[0158] S5, determining a strain safety factor threshold of the tubing string based on the strain distribution of the tubing string;

[0159] The strain distribution of the tubing string is calculated by the following method:

[0160] The circumferential strain ε θ of the tubing string is:

[0161]

[0162] The radial strain ε r of the tubing string is:

[0163]

[0164] wherein ε s is the strain at the midpoint of the inner and outer walls of the tubing.

[0165] The specific method for determining the safety factor threshold of the tubing string based on the strain distribution is:

[0166] The strain design of the tubing string will allow the tubing string to undergo plastic deformation, and the design criterion is the maximum uniform elongation of the pipe material, and the allowable strain [ε] of the tubing string is taken as 80% of the uniform elongation of the tubing string material:

[0167] [ε] = δ × 80% (10)

[0168] wherein δ is the maximum elongation of the pipe material.

[0169] The strain safety factor threshold of the tubing string is:

[0170]

[0171] Based on the above information, the minimum safety factor of the tubing string is calculated, as shown in the following table:

[0172]

[0173]

[0174] Table 2. Minimum safety factor of the tubing string under each working condition

[0175] The position 1 / 2 / 3 of the oil pipe string in the oil pipe string refers to a weak position of stress concentration on the oil pipe string; the minimum safety factor in the oil pipe string refers to a safety factor corresponding to the weak position of the oil pipe string in operation, that is, the minimum safety factor of the whole oil pipe string.

[0176] The working strain of the oil pipe string is ∑ :

[0177]

[0178] Wherein,

[0179] The working strain is also called engineering strain; the stress is obtained based on the load, and the strain is obtained based on the stress and the area ratio of deformation;

[0180] △L is the elongation of the oil pipe string;

[0181] L0 is the original gauge length;

[0182] The working strain of the oil pipe string satisfies:

[0183] ε ∑ ≤[ε]=δ×80% (12)

[0184] Therefore, the working strain safety factor of the oil pipe string is:

[0185]

[0186] S6, the oil pipe string is checked based on the strain safety factor threshold value: the working strain safety factor of the selected oil pipe string is compared with the strain safety factor threshold value, if the working strain safety factor of the selected oil pipe string is not less than the strain safety factor threshold value, the selected oil pipe string meets the requirements; if the working strain safety factor of the selected oil pipe string is less than the strain safety factor threshold value, the selected oil pipe string does not meet the requirements, the steel grade of the oil pipe string is improved to recheck, until the working strain safety factor of the selected oil pipe string is not less than the strain safety factor threshold value.

[0187] In summary, the application breaks through the research direction of the conventional pipeline design criterion, studies the working condition of the ultra-deep well, and finds that the special working condition of the ultra-deep well is that the pipe string elongation used in the working condition of the ultra-deep well is not significantly reduced, and the deformation capacity is significantly improved, and the stress borne by the pipe string can also be offset by creep; then based on this, the application provides a new oil pipe string design method based on material strain, which combines the temperature distribution and pressure distribution of the oil pipe string, and then calculates the stress according to the load, obtains the strain based on the stress, and then determines the steel grade of the oil pipe string according to the comparison between the strain and the allowable strain, which increases the design window of the ultra-deep oil well, reduces the design difficulty, and provides scientific theoretical support for the selection of the pipe string material of the ultra-deep well and the optimization of the pipe string combination.

[0188] The above merely provides the preferred embodiment of the present application, and not intended to limit the present application. Accordingly, any modification, equivalent replacement, and improvement made without departing from the spirit and principle of the present application shall fall in the scope of protection of the present application.

Claims

1. A tubing string design method based on material strain, characterized in that, Includes the following: S1. Determine basic parameters: Determine wellbore structure, tubing string steel grade, reservoir and fluid properties; S2. Determine the operating conditions of the tubing string in the initial stage, and further determine the temperature and pressure of the fluid when it enters the tubing string; S3. Based on the temperature and pressure of the fluid entering the tubing string as boundary conditions, calculate the temperature and pressure distribution on the inner and outer walls of the tubing string under the corresponding operating conditions. S4. Based on the data information in S1 to S3, calculate the load on the tubing string under the corresponding working conditions, and obtain the strain distribution of the tubing string based on the calculation results. S5. Determine the strain safety factor threshold of the tubing string based on the strain distribution of the tubing string; S6. Verify the tubing string based on the strain safety factor threshold; The temperature and pressure distribution on the inner and outer walls of the tubing string in S3 is calculated using the following formula: (1) (2) The temperature and pressure distribution inside the tubular column can be obtained by coupling Equation (1) and Equation (2) to solve the problem. Among them, T f - Fluid temperature, °C; T ei - Formation temperature, °C; r to -Outer diameter of tubing string, in meters; U mul - Annular heat transfer coefficient, J / (s·m2·℃); k e - Thermal conductivity of the formation; w - Change in fluid mass per unit time, kg / s; m - mass of fluid per unit length, kg / m; c p - Specific heat capacity of the fluid, J / (kg·℃); C J - Joule-Thomson coefficient of natural gas in tubing string, m·℃·s2; T D - Dimensionless time; z-well depth, m g G - Geothermal gradient, °C / m; v - fluid velocity, m / s; C T - Thermal storage coefficient, decimal; θ - Inclination angle, degrees; g - gravitational acceleration, 9.80 m / s² 2 ; In step S4, the load on the tubing string is calculated using the following method: (3) (4) (5) Where σ1 is the axial stress of the tubing string, in MPa; σ2 - Circumferential stress in the tubing string, MPa; σ3 - Radial stress of the tubing string, MPa; P in - Pressure inside the tubing string wall, MPa; P ou - External pressure on the tubing string wall, MPa; r to -Outer diameter of tubing string, in meters; r ti - Inner diameter of tubing string, in meters; P A -Annular pressure between tubing string and casing; r - Distance from the solution point to the center axis of the tubular column; r c -Inner diameter of the tubing string after deformation, in meters; F c - Axial force on the tubing string.

2. The tubing string design method based on material strain according to claim 1, characterized in that, The wellbore structure includes: vertical depth (TVD), inclination depth (MD), azimuth angle (AZ), casing and tubing assembly program, packer position (PD), and safety valve position (SD).

3. The tubing string design method based on material strain according to claim 2, characterized in that, The casing assembly procedure includes a tubing string length h. i Outer diameter OD, inner diameter ID, line weight W.

4. The tubing string design method based on material strain according to claim 1, characterized in that, The reservoir and fluid properties include: reservoir pressure P res Reservoir temperature T res Fluid density ρ, fluid specific heat c p .

5. The tubing string design method based on material strain according to claim 1, characterized in that, The operating conditions include the production expansion and modification phase and the production phase; When the operating condition is in the production stage, determining the temperature of the fluid when it enters the tubing string requires taking into account the temperature rise at the bottom of the well caused by the Joule-Thomson effect of the fluid from the formation to the bottom of the well. The temperature rise at the bottom of the well caused by the Joule-Thomson effect is calculated using the following formula: (6) Where, μ J-T The Joule-Thomson coefficient; T - Fluid temperature, K; ρ - fluid density, kg / m³; c p - Specific heat of fluid, J / (kg·K); Bottom hole temperature T wf for: T wf =T res -△Pμ J-T (7) Where △P is the production pressure differential of the tubing string.

6. The tubing string design method based on material strain according to claim 5, characterized in that, The operating condition information during the production expansion and modification phase includes: construction pump pressure P. p Construction displacement Q p Injected fluid viscosity ν i Injected fluid density ρ i ; The operating condition information during the production stage includes: wellhead pressure P wh Wellhead temperature T wh Wellhead flow rate Q wh .

7. The tubing string design method based on material strain according to claim 1, characterized in that, In S5, the strain distribution of the tubing string is calculated using the following method: Circumferential strain ε of tubing string θ for: (8) Radial strain ε of tubing string r for: (9) Where, ε s The strain is at the midpoint between the inner and outer walls of the tubing. The specific method for determining the safety factor threshold of the tubing string based on strain distribution is as follows: The strain design of the tubing string will allow for plastic deformation. The design criterion is the maximum uniform elongation of the tubing material. Taking n% of the uniform elongation of the tubing material as the allowable strain [ε] of the tubing string, the following is given: (10) Where δ is the maximum elongation of the pipe; The strain safety factor threshold for the tubing string is: (11) The working strain ε of the tubing string ∑ for: (12) Where △L is the tubing string elongation and L0 is the original gauge length; Working strain ε of tubing string ∑ The allowable strain [ε] should satisfy: (13) Therefore, the working strain safety factor of the tubing string is: (14)。 8. The tubing string design method based on material strain according to claim 1, characterized in that, The verification of the tubing string based on the safety factor threshold includes: comparing the working strain safety factor of the selected tubing string with the strain safety factor threshold; if the working strain safety factor of the selected tubing string is not less than the strain safety factor threshold, then the selected tubing string meets the requirements; if the working strain safety factor of the selected tubing string is less than the strain safety factor threshold, then the selected tubing string does not meet the requirements, and the steel grade of the tubing string is increased for re-verification until the working strain safety factor of the selected tubing string is not less than the strain safety factor threshold.

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