A method for calculating the downward velocity of a plunger used in plunger gas lift in a horizontal wellbore
By dividing the three stages in the plunger drop process and establishing the motion equation, the problem of inaccurate prediction of the plunger downward velocity in the prior art is solved, scientific calculation and accurate prediction of the plunger downward velocity are achieved, and the efficiency of gas lifting and drainage of the horizontal well plunger is optimized.
Patent Information
- Application Number
- CN202210258752.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-16
- Publication Date
- 2025-05-23
- Estimated Expiration
- 2042-03-16
AI Technical Summary
The prior art is difficult to accurately predict the downward speed of the plunger in the horizontal well bore, resulting in inaccurate plunger drop position, affecting the efficiency of gas lifting, drainage and gas extraction of horizontal well plunger.
By dividing the three stages of the plunger's drop process (downward in the gas column, impact in the incoming water and downward in the liquid column), and establishing the motion equation based on the stress analysis, calculate the downward velocity and acceleration of the plunger in each stage, and deducing the equilibrium velocity of the plunger's downward equilibrium velocity.
The scientific calculation of the downward speed of the plunger in the horizontal well bore is achieved, the prediction accuracy is improved, and the gas lifting and drainage gas extraction process of the horizontal well plunger is optimized.
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Figure CN114611429B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of gas well plunger gas lift drainage and gas production, and in particular to a method for calculating the downward velocity of a plunger used for plunger gas lift in a horizontal wellbore. Background Art
[0002] Plunger gas lift is one of the most widely used liquid drainage and gas production processes. Using the plunger as a solid sealing interface can effectively separate the gas column and the liquid column, reduce liquid fallback, and improve liquid lifting efficiency. When using plunger gas lift to drain water and produce gas in horizontal wells, it is hoped that the plunger can go down to a deeper position as much as possible to discharge the liquid in the wellbore to the greatest extent, restore the gas well production capacity, and ensure stable production of the gas well.
[0003] The plunger descending speed is a key parameter for accurately predicting the plunger's falling position in the horizontal wellbore. At present, the plunger descending speed mainly adopts the empirical value or field test value of domestic and foreign scholars. For example, Foss & Gaul gave the plunger's descending speed in gas and liquid in a vertical well as 10.18m / s and 0.874m / s respectively. The plunger descending speed in the gas column in a vertical well tested in Weiyuan Gas Field in my country was 0.85m / s. The mechanical state is constantly changing during the plunger's descent. From the perspective of the horizontal wellbore trajectory, the plunger needs to go through the vertical section and the inclined section to fall. From the perspective of the fluid type, the plunger needs to go through the gas column and the liquid column to fall. Therefore, the use of a single average speed cannot accurately characterize the plunger's descending process in the horizontal wellbore.
[0004] To this end, the present invention has established a method for calculating the downward velocity of the plunger in the horizontal wellbore based on the mechanical analysis of the plunger falling process, which can predict the falling position of the plunger in the horizontal well and provide theoretical and technical support for the development of horizontal well plunger gas lift drainage and gas production technology. Summary of the invention
[0005] The purpose of the present invention is to provide a method for calculating the downward speed of a plunger used for plunger gas lift in a horizontal wellbore, explore the law of the plunger's downward movement, predict the final stop position of the plunger, and promote the development of horizontal well plunger gas lift theory, which has great practical significance for optimizing the horizontal well plunger gas lift water drainage and gas production process.
[0006] A method for calculating the downward velocity of a plunger for plunger gas lift in a horizontal wellbore comprises the following steps:
[0007] Step 1: Divide the plunger's falling movement stages in the horizontal well. According to the type of fluid encountered by the plunger during its descent in the wellbore of the horizontal well, the descent process is divided into three stages: descent in the gas column, water impact, and descent in the liquid column.
[0008] Step 2: Calculate the downward speed of the plunger in the gas column and the liquid column. The plunger falls in a single fluid both in the gas column and in the liquid column, so the motion law is the same, the calculation method is the same, and only the parameter values are different. Under a single well inclination angle, the plunger speed gradually changes from the initial value to the equilibrium speed, and descends at a constant speed at the equilibrium speed. The initial velocity of the plunger falling in the vertical section of the gas column is 0, while the initial velocity in the liquid column is calculated by step three. From the wellbore trajectory, the plunger needs to go through a vertical section and an inclined section when falling, both of which can be characterized by the well inclination angle θ: the well inclination angle of the vertical section is 0°, and the well inclination angle of the inclined section is 0° to 90°.
[0009] The force analysis of the plunger falling at any well inclination angle θ is carried out. The plunger is subject to its own gravity, buoyancy, support force, friction force and falling resistance. The motion equation of the plunger is derived as follows:
[0010] F 重力 cosθ-F 浮力 cosθ-F 摩擦力 -F 阻力 =ma (1)
[0011] where F 重力 is the plunger gravity, N; θ is the well inclination, the angle between the central axis of the oil pipe and the plumb line of the earth, °; F 浮力 is the buoyancy of the fluid on the plunger, N; F 摩擦力 F is the friction force exerted on the plunger by the tube wall, N; 阻力 is the resistance encountered by the plunger as it falls in the fluid, N.
[0012] Substituting the specific expressions of each force into equation (1) and sorting it out, we get:
[0013] mg cosθ-ρgπr 2 L cosθ-f(mg sinθ-ρgπr 2 L sinθ)-0.5Cρπr 2 v 2 =ma (2)
[0014] Where m is the plunger weight, N; g is the acceleration of gravity, N / kg; θ is the well inclination, the angle between the central axis of the tubing and the earth's plumb line, °; ρ is the density of the fluid, kg / m 3 ; π is pi, dimensionless; r is plunger radius, m; L is plunger length, m; f is friction coefficient, dimensionless; C is resistance coefficient, dimensionless; v is plunger velocity, m / s; a is plunger acceleration, m / s 2 .
[0015] According to formula (2), the calculation formula for the acceleration of the plunger downward can be obtained:
[0016]
[0017] After transforming the acceleration a and integrating equation (3), we can derive the expression for the distance the plunger moves with variable acceleration:
[0018]
[0019] Where y is the distance the plunger moves with variable acceleration, m; v is the distance the plunger moves with variable acceleration, m; 0 is the initial velocity of the plunger undergoing variable acceleration motion, m / s.
[0020] When the plunger acceleration is 0, the plunger reaches a balanced state and begins to move downward at a constant speed. The equilibrium speed calculation formula for the downward movement of the plunger can be obtained as follows:
[0021]
[0022] where v 平衡 is the equilibrium velocity of the falling plunger, m / s.
[0023] Step 3: Analyze the speed change of the plunger during the impact of water and determine the initial speed of the plunger in the liquid column. The plunger hits the liquid surface at the final speed of the plunger in the gas column. Since the density of the liquid is much greater than the density of the gas, the resistance of the plunger to displace the fluid increases significantly, resulting in the resultant external force on the plunger being opposite to the direction of the speed, and the plunger begins to decelerate; while the downward resistance of the plunger is positively correlated with the square of the plunger speed, which will decrease significantly as the plunger speed decreases, and the acceleration also decreases accordingly. Therefore, in this process, the plunger performs a deceleration movement with decreasing acceleration. There may be three situations when both the plunger speed and acceleration are decreasing: (i) The speed decreases to zero before the acceleration. At this time, the acceleration direction is still upward along the tangent direction of the oil pipe, and the plunger will move upward along the oil pipe. During the experimental test, the plunger did not move in the opposite direction to the wellhead, so this condition does not hold; (ii) The acceleration decreases to zero before the speed, and the plunger reaches a state of equilibrium and descends at a uniform speed; (iii) The acceleration and speed decrease to zero at the same time, and the plunger stops. The third case is an extreme case of the second case. Due to the high density of the liquid, the instantaneous resistance generated by the impact on the liquid surface is extremely large. The water impact process is extremely short, and the impact distance is much smaller than the length of the horizontal wellbore. Therefore, the distance of the plunger's water impact process is ignored, and the plunger speed is instantly reduced to the equilibrium speed, which is the initial velocity of the plunger going down in the liquid column, and can be calculated by formula (5).
[0024] The advantages of the present invention are:
[0025] Based on the plunger downward force analysis, a method for calculating the plunger downward velocity in the horizontal wellbore is established, which is more scientific than the empirical method and has great practical significance for optimizing the plunger drainage and gas production process in horizontal wells. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] Figure 1It is a schematic diagram of the force analysis of the plunger falling at any well inclination angle;
[0027] Figure 2 This is a schematic diagram of the analysis of the velocity and acceleration changes during the plunger's impact into water;
[0028] Figure 3 It is a schematic diagram of the wellbore trajectory of a horizontal well;
[0029] Figure 4 It is a graph showing the change in plunger falling speed versus depth in a horizontal well. DETAILED DESCRIPTION
[0030] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the method of the present invention is further described in detail below with reference to examples and drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
[0031] Step 1: Divide the plunger's falling movement stages in the horizontal well. According to the type of fluid encountered by the plunger during its descent in the wellbore of the horizontal well, the descent process is divided into three stages: descent in the gas column, water impact, and descent in the liquid column.
[0032] Step 2: Calculate the plunger's downward velocity in the gas column. From the wellbore trajectory, the plunger needs to go through a vertical section and an inclined section, both of which can be represented by the well inclination angle θ: the vertical section well inclination angle is 0°, and the inclined section well inclination angle is 0° to 90°. Figure 1 As shown in the figure, the force analysis of the plunger falling at any well inclination angle θ is carried out. The plunger is subjected to its own gravity, buoyancy, support force, friction force and falling resistance, and the motion equation of the plunger is derived:
[0033] F 重力 cosθ-F 浮力 cosθ-F 摩擦力 -F 阻力 =ma (1)
[0034] Among them, F 重力 is the plunger gravity, N; θ is the well inclination, the angle between the central axis of the oil pipe and the plumb line of the earth, °; F 浮力 is the buoyancy of the fluid on the plunger, N; F 摩擦力 F is the friction force exerted on the plunger by the tube wall, N; 阻力 is the resistance encountered by the plunger as it falls in the fluid, N.
[0035] Substituting the specific expressions of each force into equation (1) and sorting it out, we get:
[0036] mg cosθ-ρgπr 2 L cosθ-f(mg sinθ-ρgπr 2 L sinθ)-0.5Cρπr2 v 2 =ma (2)
[0037] Where m is the plunger weight, N; g is the acceleration of gravity, N / kg; θ is the well inclination, the angle between the central axis of the tubing and the plumb line of the earth, °; ρ is the density of the fluid, kg / m 3 ; π is pi, dimensionless; r is plunger radius, m; L is plunger length, m; f is friction coefficient, dimensionless; C is resistance coefficient, dimensionless; v is plunger velocity, m / s; a is plunger acceleration, m / s 2 .
[0038] According to formula (2), the calculation formula for the acceleration of the plunger downward can be obtained:
[0039]
[0040] After transforming the acceleration a and integrating equation (3), we can derive the expression for the distance the plunger moves with variable acceleration:
[0041]
[0042] Where y is the distance the plunger moves with variable acceleration, m; v is the distance the plunger moves with variable acceleration, m; 0 is the initial velocity of the plunger undergoing variable acceleration motion, m / s.
[0043] When the plunger acceleration is 0, the plunger reaches a balanced state and begins to move downward at a constant speed. The equilibrium speed calculation formula for the downward movement of the plunger can be obtained as follows:
[0044]
[0045] where v 平衡 is the equilibrium velocity of the falling plunger, m / s.
[0046] Formula (4) is used to calculate the velocity change of the plunger in the gas column at each single well inclination angle during the variable acceleration motion process, and formula (5) is used to calculate the equilibrium velocity reached by the plunger at each single well inclination angle in the gas column, where the initial velocity of the vertical section is zero, and the initial velocity of each well inclination angle in the inclined section is the final velocity of the plunger falling at the previous well inclination angle.
[0047] Step 3: Analyze the change in the speed of the plunger during the impact process and determine the initial speed of the plunger in the liquid column. Figure 2As shown in the figure, the plunger hits the liquid surface at the final speed of the downward movement in the gas column. Since the density of the liquid is much greater than the density of the gas, the resistance of the plunger to displace the fluid increases significantly, resulting in the resultant external force on the plunger being opposite to the direction of the speed, and the plunger begins to decelerate; while the downward resistance of the plunger is positively correlated with the square of the plunger speed, and will be greatly reduced as the plunger speed decreases, and the acceleration also decreases accordingly. Therefore, in this process, the plunger performs a deceleration movement with decreasing acceleration. When both the plunger speed and acceleration are decreasing, three situations may occur: (i) the speed decreases to zero before the acceleration. At this time, the acceleration direction is still upward along the tangent direction of the tubing, and the plunger will move upward along the tubing. During the experimental test, the plunger did not move in the opposite direction to the wellhead, so this condition does not hold; (ii) the acceleration decreases to zero before the speed, and the plunger reaches a state of equilibrium and descends at a uniform speed; (iii) the acceleration and speed decrease to zero at the same time, and the plunger stops. The third situation is an extreme case of the second situation. Due to the high density of the liquid, the instantaneous resistance generated by the impact on the liquid surface is extremely large. The water impact process is extremely short, and the impact distance is much smaller than the length of the horizontal wellbore. Therefore, the distance of the plunger's water impact process is ignored, and the plunger speed is instantly reduced to the equilibrium speed, which is the initial velocity of the plunger going down in the liquid column, and can be calculated by formula (5).
[0048] Step 4: Calculate the speed of the plunger going down in the liquid column. The plunger falling in the gas column and in the liquid column is falling in a single fluid, so the motion law is the same, the calculation method is the same, and only the parameter values are different. Use formula (4) to calculate the speed change of the plunger in the liquid column at each single well inclination angle during the variable acceleration motion process, and use formula (5) to calculate the equilibrium speed reached by the plunger at each single well inclination angle in the liquid column. The initial speed of the plunger going down in the liquid column is the equilibrium speed reached during the water impact process, and the initial speed of the plunger falling at each subsequent well inclination angle in the liquid column is the final speed of the plunger falling at the previous well inclination angle.
[0049] The wellbore trajectory of a horizontal well is as follows Figure 3 As shown, the depth of the inclination point of the well is 3153m, the inclination angle of the inclination point is 8.67°, the depth of target point A is 3600m, the inclination angle of target point A is 97.93°, the depth of target point B is 4920m, the inclination angle of target point B is 92°, the liquid level depth is 2900m, and the liquid level well inclination is 4.83°.
[0050] The specific values of each parameter are: plunger mass m = 3.18 kg, plunger radius r = 0.024 m, plunger length L = 0.38 m, pi = 3.14, gravitational acceleration g = 9.8 N / kg, air column density ρ = 112.77 kg / m 3 , the resistance coefficient of falling in the air column is C = 11.55, the friction coefficient of falling in the air column is f = 0.46, and the density of the liquid column is ρ = 1000kg / m 3 , the falling resistance coefficient in the liquid column is C=550, and the falling friction coefficient in the liquid column is f=0.31.
[0051] Use the above steps to simulate and calculate the change in the speed of the plunger as it falls in the horizontal well. Figure 4 As shown in the figure, in the vertical well section, the plunger speed increases rapidly to 5m / s in a short distance. As the well depth increases, the well inclination changes slightly, and the plunger speed fluctuates to a certain extent, but the change is not large. When the plunger falls to a measured depth of 2900m and hits the liquid surface, the speed instantly decreases to 0.2m / s, and then the plunger continues to descend. As the well inclination gradually increases, the falling speed gradually decreases to zero, and the plunger finally stops at a measured depth of 3461m and a well inclination of 75.7°.
[0052] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
Claims
1. A method for calculating the downward velocity of a plunger used in plunger gas lift in a horizontal wellbore, It is characterized in that The steps include: Step 1: Divide the falling movement stages of the plunger in the horizontal well; Step 2: Calculate the downward speed of the plunger in the gas column and liquid column; Step 3: Analyze the speed change of the plunger during the water impact process to determine the initial downward speed of the plunger in the liquid column; Step 4: Calculate the speed of the plunger moving downward in the liquid column. The step 1 of dividing the plunger's falling movement stages in the horizontal well is specifically as follows: according to the type of fluid encountered by the plunger during its descending process in the wellbore of the horizontal well, the descending process is divided into three stages: descending in the gas column, impacting in water, and descending in the liquid column; The step 2 of calculating the downward speed of the plunger in the gas column and the liquid column is specifically: The plunger falls in a single fluid when it falls in a gas column or a liquid column, so the motion law and calculation method are the same, only the parameter values are different; the plunger speed gradually changes from the initial value to the equilibrium speed under a single well inclination angle, and descends at a uniform speed at the equilibrium speed; the initial speed of the plunger falling in the vertical section of the gas column is 0, while the initial speed of the plunger falling in the liquid column is calculated by step three; from the wellbore trajectory, the plunger needs to go through the vertical section and the inclined section, both of which are characterized by the well inclination angle θ: the vertical section well inclination angle is 0°, and the inclined section well inclination angle is 0° to 90°; The force analysis of the plunger falling at any well inclination angle θ is carried out. The plunger is subject to its own gravity, buoyancy, support force, friction force and falling resistance. The motion equation of the plunger is derived as follows: F 重力 cosθ-F 浮力 cosθ-F 摩擦力 -F 阻力 =ma(1) where F 重力 is the plunger weight, N; θ is the well inclination, the angle between the central axis of the oil pipe and the earth's plumb line, °; F 浮力 is the buoyancy of the fluid on the plunger, N; F 摩擦力 F is the friction force exerted on the plunger by the tube wall, N; 阻力 is the resistance of the plunger falling in the fluid, N; m is the mass of the plunger; a is the acceleration of the plunger, m / s 2 ; Substituting the specific expressions of each force into equation (1) and sorting it out, we get: mgcosθ-ρgπr 2 Lcosθ-f(mgsinθ-ρgπr 2 Lsinθ)-0.5Cρπr 2 v 2 =ma(2) Where m is the mass of the plunger, N; g is the acceleration of gravity, N / kg; θ is the well inclination, the angle between the central axis of the tubing and the plumb line of the earth, °; ρ is the density of the fluid, kg / m 3 ; π is pi, dimensionless; r is plunger radius, m; L is plunger length, m; f is friction coefficient, dimensionless; C is resistance coefficient, dimensionless; v is plunger velocity, m / s; a is plunger acceleration, m / s 2 ; According to formula (2), the calculation formula of the acceleration of the plunger downward is obtained: After transforming the acceleration a, we integrate equation (3) and derive the expression of the distance the plunger moves with variable acceleration: Where y is the distance the plunger moves with variable acceleration, m; v is the distance the plunger moves with variable acceleration, m; 0 is the initial velocity of the plunger doing variable acceleration motion, m / s; When the plunger acceleration is 0, the plunger reaches a balanced state and begins to move downward at a constant speed. The calculation formula for the equilibrium speed of the plunger is: where v 平衡 is the equilibrium velocity of the plunger falling, m / s; Among them, the step three analyzes the speed change of the plunger in the water impact process, and determines that the initial speed of the plunger going down in the liquid column is specifically: The plunger hits the liquid surface at the final speed of the downward movement in the gas column. Since the density of the liquid is greater than the density of the gas, the resistance of the plunger to displace the fluid increases, resulting in the resultant external force on the plunger being opposite to the direction of the speed, and the plunger begins to decelerate. The downward resistance of the plunger is positively correlated with the square of the plunger speed, which will decrease as the plunger speed decreases, and the acceleration also decreases accordingly. Therefore, in this process, the plunger performs a deceleration motion with decreasing acceleration. Both the plunger speed and acceleration are decreasing, and three situations occur: (a) The speed decreases to zero before the acceleration. At this time, the acceleration direction is still upward along the tangent direction of the oil pipe, and the plunger will move upward along the oil pipe. The experimental test process There is no reverse movement of the plunger toward the wellhead in the process, so this condition does not hold; (ii) the acceleration decreases to zero before the speed, the plunger reaches a balanced state and moves downward at a uniform speed; (iii) the acceleration and speed decrease to zero at the same time, the plunger stops, and the third case is the extreme case of the second case. Since the density of the liquid is greater than the density of the gas, the resistance generated by the impact on the liquid surface increases, the time of the water impact process is shortened, and the impact distance is less than the length of the horizontal wellbore. Therefore, the distance of the plunger's water impact process is ignored, and the plunger speed is instantly reduced to the equilibrium speed, which is the initial speed of the plunger in the liquid column, calculated by formula (5); The step 4 of calculating the downward speed of the plunger in the liquid column is specifically: Formula (4) is used to calculate the speed change of the plunger in the liquid column at each single well inclination angle during the variable acceleration motion process, and formula (5) is used to calculate the equilibrium speed reached by the plunger at each single well inclination angle in the liquid column; the initial speed of the plunger falling in the liquid column is the equilibrium speed reached in the water impact process, and the initial speed of the plunger falling at each subsequent well inclination angle in the liquid column is the final speed of the plunger falling at the previous well inclination angle.