Quantitative test method for stress condition of sucker rod string of coal-bed gas well

Abstract

The invention discloses a quantitative testing method for the stress condition of a sucker rod string of a coal-bed gas well, and belongs to the technical field of coal-bed gas well top drive screw pump lifting systems. Comprising the steps that a mechanical analysis model under the static load strength of the sucker rod string is established, stress types in all directions are analyzed, and the stress types and directions are determined; establishing a mathematical model according to the established mechanical model; the stress of the sucker rod under the alternating stress condition is calculated and whether the stress meets the safety coefficient or not is calculated; the overall safety performance of the sucker rod is determined through the safety coefficients under the two different conditions; according to the method, the stress main control factors are obtained through analysis, quantitative design and check optimization work of the rod string are achieved, the breakage fault of the sucker rod is reduced or even avoided, and the problems that at present, judgment on the stress condition of the sucker rod string of the coal-bed gas well is fuzzy, and actual production cannot be guided by theoretical results are solved.

Description

Technical Field

[0001] This invention belongs to the technical field of top-drive screw pump lifting systems for coalbed methane wells, specifically a quantitative inspection method for the stress condition of sucker rod strings in coalbed methane wells; it can prevent sucker rod string fractures in a comprehensive, multi-angle, and quantitative manner. Background Technology

[0002] In recent years, top-drive screw pump drainage gas production technology has become increasingly prominent among various coalbed methane drainage methods, becoming one of the main mechanical lifting methods. Currently, in field development, the stress conditions of the sucker rod string are unclear, mainly due to reliance on experience and analogy for selection, lacking specific methods and deviating from the actual engineering parameters of the target well. This results in a high failure rate of sucker rods and an inability to quantitatively and accurately describe the impact of various factors on the load strength of the sucker rod string. Although some scholars have conducted similar research, it has remained at the theoretical level, failing to consider calculations under different operating conditions, and the calculation results cannot guide actual production.

[0003] With single-branch horizontal wells becoming the mainstream development well type in the industry, top-drive screw pump systems have become the main lifting system for this well type, accounting for over 85%, due to their advantages such as strong coal powder carrying capacity, simple daily maintenance, and low operating costs. However, with large-scale application, sucker rod breakage has become frequent. Statistics from over 3,000 single-branch horizontal wells show that rod breakage accounts for as high as 42%, making it the primary constraint affecting the continuous and stable production of coalbed methane wells. Clearly, traditional methods relying on field experience to select pump type, sucker rod model, and rotation speed cannot meet the current higher production requirements. Therefore, it is urgent to deeply analyze the stress types and main controlling factors of the sucker rod and establish a quantitative stress analysis method to achieve quantification across multiple stages of the sucker rod process, from initial design to mid-term management and optimization. Summary of the Invention

[0004] This invention overcomes the shortcomings of existing technologies by proposing a quantitative verification method for the stress condition of sucker rod strings in coalbed methane wells. It calculates the stress magnitude of the sucker rod string in a top-drive screw pump system under static load and fatigue strength conditions, and analyzes the main stress-controlling factors to achieve quantitative design, verification, and optimization of the rod string, reducing or even preventing sucker rod fracture failures. This solves the problems of ambiguity in current assessments of the stress condition of sucker rod strings in coalbed methane wells and the inability of theoretical results to guide actual production.

[0005] This invention is achieved through the following technical solution:

[0006] A quantitative method for verifying the stress condition of a pumping rod string in a coalbed methane well includes the following steps:

[0007] Step 1: Establish a mechanical analysis model of the sucker rod string under static load strength, analyze the force types in each direction, and determine the types and directions of the forces.

[0008] Step 2: Based on the established mechanical model, establish a mathematical model and calculate the force values ​​in each direction: including the calculation of axial load, circumferential load, and composite stress of the sucker rod; determine the magnitude of the force on the sucker rod under static load strength and whether it meets the safety factor.

[0009] Step 3: Calculate the magnitude of the force on the sucker rod under alternating stress and whether it meets the safety factor.

[0010] Step 4: Determine the overall safety performance of the sucker rod using safety factors under two different conditions.

[0011] Preferably, in step one, the force analysis is based on the following formula:

[0012] Axial load: F=F g +F a -F f ;

[0013] In the formula, F is the load force on the sucker rod shaft, in N; F g The force F represents the weight of the screw pump and sucker rod, in N. a F represents the axial torque generated by the pressure difference between the inlet and outlet of the screw pump, in Nm. f The buoyancy force, in N, acts on the screw pump and sucker rod.

[0014] Sucker rod circumferential load: M c =M p +M y +M f ;

[0015] In the formula M C For the circumferential load on the sucker rod, N; M P My is the load generated by the pressure difference between the pump inlet and outlet, in N; My is the load generated by the friction of the rod fluid, in N; M f The torque generated by friction between the rotor and stator, in N.

[0016] Preferably, in step two, the axial load on the sucker rod is calculated according to the following formula:

[0017] Axial load on sucker rod: F = F g +F a -F f ;

[0018] Screw pump and sucker rod gravity: F g = gL+G 泵 ;

[0019] In the formula G is the linear density of the sucker rod, kg / m, L is the length of the sucker rod, m; 泵 Let be the weight of the screw pump, in N;

[0020] Axial force generated by the pressure difference between the inlet and outlet of the screw pump: F a =4eD3 P +π(D3) 2 -D1 2 P / 4;

[0021] In the formula, e is the rotor eccentricity, mm; D3 is the screw pump rotor diameter, mm; P is the pressure difference between the pump inlet and outlet, expressed in MPa; P is the pump outlet pressure, expressed in MPa.

[0022] The buoyancy force on the screw pump and sucker rod: F f =πD3 2 P h / 4;

[0023] In the formula P h The static pressure at the pump inlet is MPa.

[0024] Preferably, in step two, the circumferential load on the sucker rod is calculated according to the following formula:

[0025] Sucker rod circumferential load: M c =M p +M y +M f ;

[0026] Load generated by the pressure difference between the pump inlet and outlet: M p = ;

[0027] In the formula, r is the rotational speed, r / min; Q is the daily water production, m³; and H is the pump hanging depth, m. The density of the extracted water;

[0028] Load generated by rod-fluid friction: M y =2π 2 D1 2 D2 2 rL*10 -6 / (D2 2 -D1 2 );

[0029] In the formula, D1 is the diameter of the sucker rod, mm; D2 is the inner diameter of the sucker tube, mm; The fluid viscosity is given in MPa·s; L is the length of the sucker rod; and r is the rotational speed.

[0030] Load generated by friction between pump rotor and stator: Mf =1.02*(91.3* -r 0.45 +46.2;

[0031] In the formula is the initial interference fit of the pump, in mm; r is the rotational speed.

[0032] Preferably, in step two, the combined stress of the sucker rod is calculated according to the following formula:

[0033] Normal stress on the cross section of the sucker rod: =F / A=4F / πD1 2 ;

[0034] Shear stress in the cross section of the sucker rod:

[0035] The composite stress was calculated using the fourth strength theory: ;

[0036] = ≥1.5;

[0037] In the formula For composite stress, MPa; Let be the allowable stress of the sucker rod, in MPa.

[0038] Preferably, in step three, the magnitude of the force on the sucker rod under alternating stress is determined according to the following formula:

[0039] Fatigue limit under symmetrical cyclic conditions: = ;

[0040] Average stress magnitude = ;

[0041] Stress amplitude: =12E*D1*tan / L 弯曲段长 ;

[0042] ≥1.5;

[0043] In the formula The effective stress concentration factor; This is a size factor; Surface dimension factor; is the sensitivity coefficient; E is the elastic modulus, GPa.

[0044] Preferably, in step four, the overall safety performance includes evaluating pump depth, water volume, speed, and rod diameter parameters to ensure that the rod operates within a reasonable range.

[0045] The beneficial effects of this invention compared to the prior art are as follows:

[0046] This invention achieves quantitative design and verification of the sucker rod string by quantitatively calculating the stress changes of the sucker rod in a top-drive screw pump system. By establishing a mechanical and mathematical calculation model of the sucker rod string, quantitative calculations are performed under two different conditions: static load strength and fatigue strength. This determines the magnitude of various forces and the yield strength of sucker rods of different models and sizes, thus establishing a safety factor. Furthermore, based on the calculation results, the main stress-controlling factors can be analyzed, corresponding measures can be formulated, and integrated with actual project production. Comprehensive optimization can be achieved from aspects such as drainage control intensity, pump hanger design, sucker rod selection, and operating speed, improving the stability of the top-drive screw pump system well and extending the pump inspection cycle. This invention solves the problems of ambiguity in judging the stress conditions of the sucker rod string in coalbed methane wells and the inability of theoretical results to guide actual production. Attached Figure Description

[0047] Figure 1 The variation of circumferential torque under different rotational speeds and water volumes;

[0048] Figure 2 The variation of circumferential torque at different rotational speeds for different types of sucker rods;

[0049] Figure 3 A recommended rotational speed for sucker rods with different water volumes and rod diameters. Detailed Implementation

[0050] To make the technical problems to be solved, the technical solutions, and the beneficial effects of this invention clearer, the invention will be further described in detail with reference to the embodiments and accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. The technical solutions of this invention are described in detail below with reference to the embodiments and accompanying drawings, but the scope of protection is not limited thereto.

[0051] This embodiment proposes a quantitative verification method for the stress condition of the sucker rod string in a coalbed methane well. By quantitatively calculating the stress changes of the sucker rod in the top drive screw pump system, it enables the quantitative design and verification of the rod string and the analysis of the main stress-controlling factors.

[0052] The specific implementation steps are as follows:

[0053] Step 1: Establish a mechanical analysis model of the sucker rod string under static load strength and analyze the force types in each direction. The sucker rod string is subjected to complex forces, including both axial loads and circumferential torque loads. The analysis is calculated based on the following formula:

[0054] (a) Axial load: F = F g +F a -F f

[0055] In the formula, F is the load force on the sucker rod shaft, in N; F g The force F represents the weight of the screw pump and sucker rod, in N. a F represents the axial torque generated by the pressure difference between the inlet and outlet of the screw pump, in Nm. f The buoyancy force, in N, is the force exerted on the screw pump and sucker rod.

[0056] (b) Circumferential load on the sucker rod: M c =M p +M y +M f

[0057] In the formula M C For the circumferential load on the sucker rod, N; M P My is the load generated by the pressure difference between the pump inlet and outlet, in N; My is the load generated by the friction of the rod fluid, in N; M f The torque generated by friction between the rotor and stator, in N.

[0058] Step 2: Based on the established mechanical model, establish a mathematical model and calculate the force values ​​in each direction:

[0059] 2.1 Calculation of Axial Load on Sucker Rod

[0060] (c) Axial load on the sucker rod: F = F g +F a -F f

[0061] (d) Gravity of screw pump and sucker rod: F g = gL+G 泵

[0062] In the formula G is the linear density of the sucker rod, kg / m, L is the length of the sucker rod, m; 泵 Let be the weight of the screw pump, in N.

[0063] (e) Axial force generated by the pressure difference between the inlet and outlet of the screw pump: F a =4eD3 P +π(D3) 2 -D1 2 P / 4

[0064] In the formula, e is the rotor eccentricity, mm; D3 is the screw pump rotor diameter, mm; P is the pressure difference between the pump inlet and outlet, in MPa; P is the pump outlet pressure, in MPa.

[0065] (f) Buoyancy force on the screw pump and sucker rod: F f =πD3 2 Ph / 4

[0066] In the formula P h The static pressure at the pump inlet is MPa.

[0067] 2.2 Calculation of circumferential load on sucker rod

[0068] (g) Sucker rod circumferential load: M c =M p +M y +M f

[0069] (h) Load generated by the pressure difference between the pump inlet and outlet: M p =

[0070] In the formula, r is the rotational speed, r / min; Q is the daily water production, m³; and H is the pump hanging depth, m. This refers to the density of the extracted water.

[0071] (i) Load generated by rod-fluid friction: M y =2π 2 D1 2 D2 2 rL*10 -6 / (D2 2 -D1 2 )

[0072] In the formula, D1 is the diameter of the sucker rod, mm; D2 is the inner diameter of the sucker tube, mm; is the fluid viscosity, mPa·s; L is the sucker rod length; r is the rotational speed.

[0073] (j) Load generated by friction between the pump rotor and stator: M f =1.02*(91.3* -r 0.45 +46.2

[0074] In the formula The initial interference fit of the pump is in mm.

[0075] 2.3 Calculation of Composite Stress in Sucker Rod

[0076] (k) Normal stress on the cross section of the sucker rod: =F / A=4F / πD1 2

[0077] (l) Shear stress in the cross section of the sucker rod:

[0078] (m) The composite stress is calculated using the fourth strength theory:

[0079] (n) = ≥1.5

[0080] In the formula For composite stress, MPa; Let be the allowable stress of the sucker rod, in MPa.

[0081] Step 3: Calculate the magnitude of the force on the sucker rod under alternating stress and whether it meets the safety factor.

[0082] Field practice shows that under alternating stress, even if the stress does not exceed the strength limit, the sucker rod will fracture instantaneously after a long period of alternating stress. This type of fracture is called fatigue fracture.

[0083] (o) Fatigue limit under symmetrical cyclic conditions: =

[0084] (p) Magnitude of average stress =

[0085] (q) Stress amplitude: =12E*D1*tan / L 弯曲段长

[0086] (r) ≥1.5;

[0087] In the formula The effective stress concentration factor; This is a size factor; Surface dimension factor; is the sensitivity coefficient; E is the elastic modulus, GPa.

[0088] Based on the above steps, the type and direction of the force can be determined first. According to the formula (c)-(n) in step two, the magnitude of the force on the sucker rod under static load strength and whether it meets the safety factor can be calculated. According to the formula (o)-(r) in step three, the magnitude of the force on the sucker rod under alternating stress and whether it meets the safety factor can be calculated. Thus, the overall safety performance of the sucker rod can be determined by the safety factor under two different conditions. The dynamic parameters involved are as follows: pump depth, water volume, rotation speed, rod diameter, etc., to ensure that the rod operates within a reasonable range.

[0089] Specifically in this embodiment:

[0090] (1) Compile the parameters of the production well, such as daily water production, rotation speed, bottom hole flowing pressure, coal powder content, pump type, rod diameter, pump inclination depth, pump vertical depth, and dogleg angle, and refer to Table 1:

[0091] ;

[0092] (2) Calculate the axial torque, circumferential torque, composite stress, torsional safety factor and yield safety factor under static load conditions step by step according to the above formulas, and evaluate whether the stress under static load strength conditions is reasonable. See Table 2.

[0093] ;

[0094] (3) Calculate the fatigue limit, average stress, stress amplitude, and fatigue limit safety factor under fatigue strength conditions, and evaluate whether the stress under fatigue strength conditions is reasonable. See Table 3.

[0095] ;

[0096] (4) Based on the calculation results, determine which direction of force caused the safety factor, and based on the analysis results, propose targeted optimization from a single direction or a combination of directions, such as pump mounting depth, rod diameter, rotational speed, and daily water production, to improve the safety factor and reduce the risk of rod breakage; specifically:

[0097] (4.1) Comprehensive assessment: The safety factors for yield strength and fatigue strength are both less than 1.5, making it relatively easy for the rod to break.

[0098] (4.2) Suggestions for optimizing this assignment:

[0099] With the water volume unchanged, the speed of the larger pump is stable at 15-30 rpm, the torsional safety factor is 2.02, the yield strength safety factor is 1.57, and the fatigue strength safety factor is 1.48. Except for the fatigue strength safety factor, it basically meets the requirements.

[0100] After replacing the sucker rod with a φ25mm rod, the safety factors are 2.73, 2.25, and 1.55, which fully meet the requirements.

[0101] (4.3) Current progress: After the above optimization suggestions were adopted, the well has been operating stably since March and no rod breakage has occurred.

[0102] (5) Effect verification:

[0103] Through a year of practical testing on more than 60 wells, the results were significant, with a quantitative assessment and optimization success rate of over 70%. See the table below for data: ;

[0104] This calculation method was tested in two main scenarios this year. One scenario involved calculating the stress levels of wells after rod breakage, which were previously designed based on experience, and then optimizing the rods accordingly. The calculation results showed a very high degree of agreement with actual field conditions. Furthermore, this method was used to quantitatively calculate and optimize the structure of these wells with broken rods, and so far, no rod breaks have occurred (the longest run has been 9 months). The other scenario involved using dynamic parameters to calculate and predict whether rod breaks would occur in wells that have not yet experienced rod breaks. Two wells have already experienced rod breaks; the others are being monitored. See [link to relevant documentation]. Figures 1 to 3 .

[0105] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the protection scope of this invention.

[0106] To provide the public with a thorough understanding of the present invention, specific details have been described in detail in the above preferred embodiments. However, those skilled in the art can fully understand the invention even without these detailed descriptions. Several improvements and modifications can be made without departing from the principles of the invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A quantitative method for verifying the stress condition of a pumping rod string in a coalbed methane well, characterized in that, Includes the following steps: Step 1: Establish a mechanical analysis model of the sucker rod string under static load strength, analyze the force types in each direction, and determine the types and directions of the forces. Step 2: Based on the established mechanical model, establish a mathematical model and calculate the force values ​​in each direction: including the calculation of axial load, circumferential load, and composite stress of the sucker rod; determine the magnitude of the force on the sucker rod under static load strength and whether it meets the safety factor. Step 3: Calculate the magnitude of the force on the sucker rod under alternating stress and whether it meets the safety factor. Step 4: Determine the overall safety performance of the sucker rod using safety factors under two different conditions.

2. The quantitative testing method for the stress condition of a coalbed methane well sucker rod string according to claim 1, characterized in that, In step one, the force analysis is based on the following formula: Axial load on sucker rod: F = F g +F a -F f ; In the formula, F is the load force on the sucker rod shaft, in N; F g The force F represents the weight of the screw pump and sucker rod, in N. a F represents the axial torque generated by the pressure difference between the inlet and outlet of the screw pump, in Nm. f The buoyancy force, in N, acts on the screw pump and sucker rod. Sucker rod circumferential load: M c =M p +M y +M f ; In the formula M C The circumferential load on the sucker rod is N; M P My is the load generated by the pressure difference between the pump inlet and outlet, in N; My is the load generated by the friction of the rod fluid, in N; M f The torque generated by friction between the rotor and stator, in N.

3. The quantitative testing method for the stress condition of a coalbed methane well sucker rod string according to claim 1, characterized in that, In step two, the axial load on the sucker rod is calculated according to the following formula: Axial load on sucker rod: F = F g +F a -F f ; Screw pump and sucker rod gravity: F g = gL+G 泵 ; In the formula G is the linear density of the sucker rod, kg / m, L is the length of the sucker rod, m; 泵 Let be the weight of the screw pump, in N; Axial force generated by the pressure difference between the inlet and outlet of the screw pump: F a =4eD3 P +π(D3) 2 -D1 2 P / 4; In the formula, e is the rotor eccentricity, mm; D3 is the screw pump rotor diameter, mm; P is the pressure difference between the pump inlet and outlet, expressed in MPa; P is the pump outlet pressure, expressed in MPa. The buoyancy force on the screw pump and sucker rod: F f =πD3 2 P h / 4; In the formula P h The static pressure at the pump inlet is MPa.

4. The quantitative testing method for the stress condition of a coalbed methane well sucker rod string according to claim 1, characterized in that, In step two, the circumferential load on the sucker rod is calculated according to the following formula: Sucker rod circumferential load: M c =M p +M y +M f ; Load generated by the pressure difference between the pump inlet and outlet: M p = ; In the formula, r is the rotational speed, r / min; Q is the daily water production, m³; and H is the pump hanging depth, m. The density of the extracted water; Load generated by rod-fluid friction: M y =2π 2 D1 2 D2 2 rL*10 -6 / (D2 2 -D1 2 ); In the formula, D1 is the diameter of the sucker rod, mm; D2 is the inner diameter of the sucker tube, mm; The fluid viscosity is given in MPa·s; L is the length of the sucker rod; and r is the rotational speed. Load generated by friction between pump rotor and stator: M f =1.02*(91.3* -r 0.45 +46.2; In the formula is the initial interference fit of the pump, in mm; r is the rotational speed.

5. A quantitative testing method for the stress condition of a coalbed methane well sucker rod string according to claim 1, characterized in that, In step two, the combined stress of the sucker rod is calculated according to the following formula: Normal stress on the cross section of the sucker rod: =F / A=4F / πD1 2 ; Shear stress in the cross section of the sucker rod: ; The composite stress was calculated using the fourth strength theory: ; = ≥1.5； In the formula For composite stress, MPa; Let be the allowable stress of the sucker rod, in MPa.

6. The quantitative testing method for the stress condition of a coalbed methane well sucker rod string according to claim 1, characterized in that, In step three, the magnitude of the force on the sucker rod under alternating stress is determined by the following formula: Fatigue limit under symmetrical cyclic conditions: = ; Average stress magnitude = ; Stress amplitude: =12E*D1*tan / L 弯曲段长 ; ≥1.5； In the formula The effective stress concentration factor; This is a size factor; Surface dimension factor; is the sensitivity coefficient; E is the elastic modulus, GPa.

7. A quantitative testing method for the stress condition of a coalbed methane well sucker rod string according to claim 1, characterized in that, In step four, overall safety performance includes assessing pump depth, water volume, speed, and rod diameter parameters to ensure the rod operates within a reasonable range.

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