Method and system for simulating plunger gas lift

Abstract

The invention discloses a method and system for simulating plunger gas lift, and the method comprises the steps: obtaining the correlation among the mass of a gas column above a plunger, the height of the plunger and the blowout flow of surface gas according to the expansion characteristics of the gas column above the plunger before the plunger ascends to a liquid slug at the top of the plunger and reaches the ground; the method comprises the following steps of: collecting reservoir fluid, determining the flowing characteristic of the reservoir fluid into an annular space based on the flowing characteristic of the reservoir fluid into an oil pipe and a casing pipe, and then constructing the correlation between the mass of the produced hydrops and the ascending speed of the plunger before the plunger continuously ascends to reach the ground; according to the expansion characteristics of the gas column at the bottom of the plunger, the correlation between the mass of the gas column at the bottom of the plunger and the blowout flow of the surface gas when the plunger stays on the ground is obtained; after the plunger descends to the liquid slug entering the bottom of the plunger, the descending speed of the plunger and the new liquid slug at the top and the new liquid slug at the bottom are respectively related. According to the invention, plunger gas lift full-period dynamic simulation is realized, and the method has good applicability and reliability.

Description

Technical Field

[0001] This invention belongs to the field of natural gas well drainage and gas production, and in particular relates to a method and system for simulating plunger gas lift. Background Technology

[0002] As natural gas extraction continues, gas reservoirs become depleted, accompanied by a gradual decrease in reservoir energy and bottom hole pressure, leading to a continuous decline in gas well production. When the gas kinetic energy is insufficient to carry the liquid produced in the gas well to the surface, it causes liquid backflow within the wellbore, forming liquid accumulation at the bottom of the well. Some gas reservoirs are water-bearing reservoirs, producing water along with gas production, and some reservoirs also produce water in the middle and later stages. Water production from gas reservoirs has adverse effects on the reservoir and wellbore. For the reservoir, intruding water will separate and block the gas layer along the permeable zone and fractures, preventing the effective extraction of large amounts of natural gas; for the wellbore, liquid accumulation will lead to corrosion and damage, reducing the economic benefits of the gas field. If the gas reservoir has sufficient energy, the high-kinetic-energy gas will generate enough drag to carry the liquid in the wellbore to the wellhead; if the gas reservoir has insufficient energy, the gas flow rate decreases, the liquid film on the inner wall of the wellbore thickens, and the gas energy is insufficient to carry all the liquid in the gas well to the wellhead. At this time, the velocity of the liquid film on the wellbore wall reverses, changing from upward to downward flow, resulting in liquid accumulation at the bottom of the well. Therefore, the treatment of water and liquid accumulation in gas wells is one of the important issues faced in the natural gas extraction process.

[0003] Among various fluid removal and gas production technologies, plunger lift is a highly efficient and flexible reciprocating pumping method that has been widely used in vertical wells, deviated wells, and cluster wells, achieving considerable economic benefits. The plunger lift system mainly consists of a plunger, surface control valve, trap, lubricator / impact spring, damper spring, and plunger sensor. A metal piston is placed in the wellbore and allowed to move freely up and down, forming an intermittent artificial lift process. Plunger lift utilizes only reservoir energy to remove accumulated fluid from the gas well, achieving intermittent and stable natural gas production. The cycle of the plunger's free up-and-down movement is controlled by the opening and closing of a wellhead electric valve. Compared to liquid slugs, the plunger, acting as a gas-liquid interface, reduces fluid backflow and gas surge, making more effective use of reservoir energy. The plunger lift process efficiently extracts liquid from the gas well, protecting the reservoir and wellbore, and effectively extending the natural gas well production cycle.

[0004] Figure 2 This is a schematic diagram illustrating the decomposition of the plunger's full-cycle motion in the prior art of this application. For example... Figure 2 (a) shows the disassembly of the plunger motion. A single-cycle plunger motion can be divided into six stages: control valve closing (I), plunger descent (II), plunger reaching the bottom of the well (III), control valve opening (IV), plunger ascent (V), and plunger reaching the wellhead (VI). During the plunger motion, the changes in process parameters and the corresponding states of the plunger and control valve are as follows: Figure 2(b) shows the trend of tubing pressure changes within a single period, and as shown in the figure. Figure 2 (c) shows the corresponding states of the valve and plunger at each stage.

[0005] Reference Figure 2 After the surface control valve is closed, the plunger lift-up cycle begins from the shut-in phase. The plunger descends from the top to the bottom of the well, first through a gas column, then through a section of fluid. Simultaneously, natural gas in the reservoir annulus and near-wellbore area creates well pressure. After the plunger reaches the bottom buffer spring (locker), the shut-in phase lasts for a period to allow fluid to flow from the reservoir to the wellbore. The plunger remains on the plunger seat, with fluid accumulating on top. Then, the control valve opens at the start of the plunger rise phase. Subsequently, due to the pressure difference between the top and bottom of the plunger, the plunger and the upper accumulating fluid move towards the surface until they reach the lubricator. The plunger provides sufficient energy to lift the fluid in the tubing and the plunger. During this period, surface productivity and tubing pressure drop sharply due to the rapid decrease in the pressure difference between the casing and tubing. Gas production reaches its peak after the accumulating fluid above the plunger is extracted. However, as casing and tubing pressures continue to decrease, the high gas production rate is unsustainable. Once the gas flow rate or tubing pressure and casing pressure drop below a critical value, the fluid will fall back and begin to accumulate at the bottom of the well again. The surface control valve closes, causing the plunger to move downwards, thus initiating another shut-in phase. Then, a new plunger lift cycle begins, and so on, forming the plunger lift production cycle.

[0006] Current technologies for plunger lift process simulation primarily rely on static and dynamic models. Static models typically use semi-empirical correlation expressions of relevant variables to describe each stage of the plunger lift process, generally only applicable to plunger lift process design and unable to perform mechanistic analysis and dynamic simulation of transient plunger production processes. Dynamic models, on the other hand, are mostly constructed based on simplifications or assumptions that deviate from reality, thus also having limited applicability. For example, existing technologies analyze high gas-liquid ratio (GLR) gas wells or plunger gas lift wells with low liquid production, proposing simplified correlations for the time-varying amount of liquid in the producing well, and using a reservoir model to simulate the plunger circulation in tight gas wells. While this model's calculation equations consider gas and liquid friction, they neglect gas leakage and liquid backflow during plunger movement. Existing technologies also divide the plunger lift process into six stages: plunger descent in the gas column, plunger descent in the liquid column, pressure accumulation, plunger rise, liquid production, and gas production. The full-cycle lifting performance of the plunger can be evaluated by running multiple cycles, thus quantitatively reproducing the typical characteristics of the plunger lifting system. However, this model oversimplifies the consideration of gas properties, does not fully account for the multiphase flow characteristics of the wellbore, and lacks uncertainty analysis of the reservoir, wellbore, and pipeline.

[0007] In actual construction sites, the production regime of most gas wells implementing plunger gas lift technology is usually determined by operational experience. This makes it difficult to accurately understand the plunger movement at depths of several thousand meters. Furthermore, because the production regime is typically fixed for extended periods, the plunger cycle time cannot be adjusted in a timely manner according to gas well production and pressure decay. Therefore, there is an urgent need for an accurate and widely applicable dynamic model of plunger gas lift to effectively simulate the dynamic behavior of gas, liquid, and plunger at different stages of the plunger lift system's cycle. This would allow for a precise understanding of the detailed movement of the plunger at different stages downhole, providing new solutions and practical evidence for cost reduction and efficiency improvement in gas wells. Summary of the Invention

[0008] To address the aforementioned problems, this invention provides a method for simulating plunger gas lift, comprising: obtaining the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate before the liquid slug at the top of the plunger reaches the surface, based on the expansion characteristics of the gas column above the plunger; determining the flow characteristics into the annulus based on the flow characteristics of reservoir fluid into the tubing and casing; then, constructing the correlation between the mass of the extracted fluid and the upward velocity of the plunger before the plunger continues to rise to the surface, thereby completing the plunger upward gas lift simulation; obtaining the correlation between the mass of the gas column at the bottom of the plunger and the surface gas flow rate when the plunger is stationary at the surface, based on the expansion characteristics of the gas column at the bottom of the plunger, thereby completing the plunger stationary gas lift simulation; and constructing the correlation between the downward velocity of the plunger and the new liquid slugs at the top and bottom after the plunger descends to the liquid slug at its bottom, thereby completing the plunger downward gas lift simulation.

[0009] Preferably, the step of obtaining the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate before the liquid slug at the top of the plunger reaches the surface includes: using the static pressure in the gas column above the plunger as the tubing pressure, obtaining a first correlation between the tubing pressure, the plunger height, and the mass of the gas column above the plunger, and a second correlation between the tubing pressure, the plunger height, and the surface gas flow rate; integrating the first correlation and the second correlation to obtain the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate.

[0010] Preferably, the first correlation and the second correlation are represented by the following expressions:

[0011]

[0012] Where, p t Indicates the oil pipe pressure, m gtt Z represents the mass of the gas column above the plunger. tR represents the gas compressibility factor, T represents the ideal gas constant, and A represents the actual gas temperature. t H represents the cross-sectional area of ​​the tubing, H represents the vertical depth of the wellbore, and X represents the cross-sectional area of ​​the tubing. p L represents the plunger height. tt M represents the length of the liquid slug at the top of the plunger. g Let represent the average molecular weight of the gas, e represent the natural constant, α represent the coefficient with respect to the gas compressibility factor, g represent the acceleration due to gravity, and d represent the average molecular weight of the gas. t Indicates the inner diameter of the oil pipe, f g q represents the gas friction coefficient. gout This indicates the flow rate of surface gas wells.

[0013] Preferably, the method further includes: obtaining the gas friction coefficient based on the Churchill formula, wherein the gas friction coefficient is calculated using the following expression:

[0014]

[0015] Where A2 and B2 represent intermediate variables, Re represents the Reynolds number, D represents the equivalent diameter, and ε represents the wall roughness.

[0016] Preferably, the method further includes: based on the force characteristics of the plunger itself and the liquid slug at the top of the plunger during the upward movement, performing momentum analysis on the upward movement of the plunger to the ground before the liquid slug at the top of the plunger reaches the ground, so as to obtain the correlation between the upward speed of the plunger and the mass of the liquid slug at the top of the plunger, thereby optimizing the upward airlift simulation of the plunger.

[0017] Preferably, the relationship between the upward velocity of the plunger and the mass of the liquid slug at the top of the plunger is expressed by the following expression:

[0018]

[0019] Among them, a t V represents the acceleration of the liquid slug at the top of the plunger. p1 The piston's upward speed is represented by t, and the upward time is represented by p. pb p represents the pressure acting on the bottom of the plunger. pt p represents the pressure acting on the plunger. fric A represents the frictional force between the inner wall of the tubing and the liquid slug at the top of the plunger. t The cross-sectional area of ​​the oil pipe is expressed in meters (m). p Indicates the plunger mass, m ltt denoted by , where represents the mass of the liquid slug at the top of the plunger, and g represents the acceleration due to gravity.

[0020] Preferably, the method further includes: obtaining the changes in gas production during the steady-state production process and the unsteady-state process based on the gas reservoir inflow relationship, so as to further optimize the plunger gas lift simulation.

[0021] Preferably, the change in gas production rate during the steady-state production process is obtained using the following expression:

[0022]

[0023]

[0024] Where A1, B1, and C1 represent intermediate variables, and Q g1 The gas production rate during steady-state production is represented by μ, gas viscosity, z, gas compressibility factor, k, gas permeability, h, and P. SC T represents the gas pressure under standard conditions, and T represents the actual gas temperature. SC Z represents the gas temperature under standard conditions. SC R represents the gas compressibility factor under standard conditions. e R represents the radius of the permeation zone. w ρ represents the radius of the oil pipe. g，SC Z represents the gas density under standard conditions, and Z represents the average gas compressibility.

[0025] Preferably, the change in gas production rate during the unsteady-state production process is obtained using the following expression:

[0026]

[0027] Among them, Q g2 p represents the amount of gas produced during a non-steady-state production process. e p represents the gas reservoir pressure. w The bottom hole flowing pressure is represented by P, the actual gas pressure is represented by t, and the production time is represented by C. t This represents the overall compression factor.

[0028] On the other hand, the present invention also provides a system for simulating plunger gas lift, the system comprising the following modules: a plunger upward gas lift simulation module, which is used to obtain the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate before the liquid slug at the top of the plunger reaches the surface, based on the expansion characteristics of the gas column above the plunger, and to determine the flow characteristics into the annulus based on the flow characteristics of the reservoir fluid into the tubing and casing, and then construct the correlation between the mass of the extracted fluid and the upward velocity of the plunger before the plunger continues to rise to the surface, thereby completing the plunger upward gas lift simulation; a plunger stationary gas lift simulation module, which is used to obtain the correlation between the mass of the gas column at the bottom of the plunger and the surface gas flow rate when the plunger is stationary at the surface, based on the expansion characteristics of the gas column at the bottom of the plunger, thereby completing the plunger stationary gas lift simulation; and a plunger downward gas lift simulation module, which is used to construct the correlation between the downward velocity of the plunger and the new liquid slugs at the top and bottom after the plunger descends to the liquid slug at its bottom, thereby completing the plunger downward gas lift simulation.

[0029] Compared with the prior art, one or more embodiments of the above solutions may have the following advantages or beneficial effects:

[0030] This invention proposes a method and system for simulating plunger gas lift. This method comprehensively considers reservoir dynamics based on classical production dynamics (e.g., IPR), taking into account the changes in plunger upward and downward velocities. First, for the plunger's upward stroke, the correlation between the gas column mass above the plunger, the plunger height, and the surface gas flow rate is obtained before the liquid slug at the top reaches the surface. Based on the flow characteristics of reservoir fluids into the tubing and casing, the flow characteristics into the annulus are determined. Then, the correlation between the produced fluid mass and the plunger's upward velocity is constructed. Next, for the gas production process, the correlation between the gas column volume at the bottom of the plunger and the surface gas flow rate is obtained. Finally, for the plunger's downward stroke, the correlation between the plunger's downward velocity and the new liquid slugs at the top and bottom are constructed. This invention achieves full-cycle dynamic simulation of plunger gas lift, exhibiting good applicability and reliability, and providing technical support for guiding the design of field drainage and gas production processes and optimizing plunger operating regimes with the goal of maximizing single-well production.

[0031] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the description, claims, and drawings. Attached Figure Description

[0032] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with the embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0033] Figure 1 This is a step diagram of a method for simulating plunger gas lift according to an embodiment of this application.

[0034] Figure 2 This is a schematic diagram of the decomposition of the plunger's full-cycle motion in the prior art of this application.

[0035] Figure 3 This is an example diagram of the plunger upward process in a method for simulating plunger air lift according to an embodiment of this application.

[0036] Figure 4 This is a block diagram of a system for simulating plunger gas lift according to an embodiment of this application. Detailed Implementation

[0037] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings and examples, so that the process of how the present invention uses technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly. It should be noted that, as long as there is no conflict, the various embodiments and features in the various embodiments of the present invention can be combined with each other, and the resulting technical solutions are all within the protection scope of the present invention.

[0038] Furthermore, the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0039] Current technologies for plunger lift process simulation primarily rely on static and dynamic models. Static models typically use semi-empirical correlation expressions of relevant variables to describe each stage of the plunger lift process, generally only applicable to plunger lift process design and unable to perform mechanistic analysis and dynamic simulation of transient plunger production processes. Dynamic models, on the other hand, are mostly constructed based on simplifications or assumptions that deviate from reality, thus also having limited applicability. For example, existing technologies analyze high gas-liquid ratio (GLR) gas wells or plunger gas lift wells with low liquid production, proposing simplified correlations for the time-varying amount of liquid in the producing well, and using a reservoir model to simulate the plunger circulation in tight gas wells. While this model's calculation equations consider gas and liquid friction, they neglect gas leakage and liquid backflow during plunger movement. Existing technologies also divide the plunger lift process into six stages: plunger descent in the gas column, plunger descent in the liquid column, pressure accumulation, plunger rise, liquid production, and gas production. The full-cycle lifting performance of the plunger can be evaluated by running multiple cycles, thus quantitatively reproducing the typical characteristics of the plunger lifting system. However, this model oversimplifies the consideration of gas properties, does not fully account for the multiphase flow characteristics of the wellbore, and lacks uncertainty analysis of the reservoir, wellbore, and pipeline.

[0040] In actual construction sites, the production regime of most gas wells implementing plunger gas lift technology is usually determined by operational experience. This makes it difficult to accurately understand the plunger movement at depths of several thousand meters. Furthermore, because the production regime is typically fixed for extended periods, the plunger cycle time cannot be adjusted in a timely manner according to gas well production and pressure decay. Therefore, there is an urgent need for an accurate and widely applicable dynamic model of plunger gas lift to effectively simulate the dynamic behavior of gas, liquid, and plunger at different stages of the plunger lift system's cycle. This would allow for a precise understanding of the detailed movement of the plunger at different stages downhole, providing new solutions and practical evidence for cost reduction and efficiency improvement in gas wells.

[0041] Therefore, to address the aforementioned problems, this invention proposes a method and system for simulating plunger gas lift. This method comprehensively considers reservoir dynamics based on classical production dynamics (e.g., IPR), taking into account the changes in plunger upward and downward velocities. First, for the plunger's upward stroke, the correlation between the gas column mass above the plunger, the plunger height, and the surface gas flow rate is obtained before the liquid slug at the top reaches the surface. Based on the flow characteristics of reservoir fluids into the tubing and casing, the flow characteristics into the annulus are determined. Then, the correlation between the produced fluid mass and the plunger's upward velocity is constructed. Next, for the gas production process, the correlation between the gas column volume at the bottom of the plunger and the surface gas flow rate is obtained. Finally, for the plunger's downward stroke, the correlation between the plunger's downward velocity and the new liquid slugs at the top and bottom are constructed. This invention achieves full-cycle dynamic simulation of plunger gas lift, exhibiting good applicability and reliability, and providing technical support for guiding the design of field drainage and gas production processes and optimizing plunger operating regimes with the goal of maximizing single-well production.

[0042] Example 1

[0043] Figure 1 This is a step diagram of a method for simulating plunger gas lift according to an embodiment of this application. See below for reference. Figure 1 This will explain each step of the method.

[0044] like Figure 1 As shown, in step S110, based on the expansion characteristics of the gas column above the plunger, the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate is obtained before the liquid slug at the top of the plunger reaches the surface. Based on the flow characteristics of the reservoir fluid into the tubing and casing, the flow characteristics into the annulus are determined. Then, the correlation between the mass of the extracted liquid and the upward velocity of the plunger is constructed before the plunger continues to rise to the surface, thereby completing the plunger upward gas lift simulation.

[0045] Specifically, this embodiment first assumes that the fluid flow between the tubing and the annulus, and between the wellbore and the reservoir, is zero at the bottom of the well during the plunger's upward movement. Based on this assumption, the following mass equation for the fluid flow during the plunger's upward movement can be obtained:

[0046] F gann =F gres -F gtub (1)

[0047] F lann =F lres -F ltub (2)

[0048] Among them, F gann F represents the mass flow rate of the ambient air gas.gres F represents the mass flow rate of reservoir gas. gtub F represents the mass flow rate of gas in the pipeline. lann F represents the mass flow rate of the annular fluid. lres F represents the mass flow rate of the reservoir fluid. ltub This indicates the mass flow rate of the fluid in the pipeline.

[0049] Figure 3 This is an example diagram illustrating the piston upward movement process in a method for simulating piston gas lift according to an embodiment of this application. (Refer to...) Figure 3 This embodiment considers the gas expansion effect when calculating the static pressure of the gas column above the plunger. It obtains the correlation between the mass of the gas column above the plunger (gas above the liquid column), the plunger height, and the surface gas well flow rate before the liquid slug (liquid column) reaches the surface. Specifically, when the surface control valve opens, the gas column above the plunger (gas above the liquid column) escapes, forming the surface gas well flow rate. Therefore, this embodiment, based on the gas expansion effect of the gas column above the plunger (gas above the liquid column) during the plunger's upward movement, uses the surface gas well flow rate to construct the correlation between the mass of the gas column above the plunger (gas above the liquid column), the plunger height, and the surface gas well flow rate.

[0050] In this embodiment, the surface gas well flow rate is calculated using the standard valve equation:

[0051]

[0052] Where, q gout C represents the surface gas well flow rate. v p represents the valve coefficient. t p represents the oil pipe pressure. l This indicates the pipeline pressure.

[0053] Meanwhile, this embodiment comprehensively considers the inflow from the bottom gas reservoir, the outflow from the wellhead, the pressure accumulation in the tubing and casing, and the bottom flow pressure balance to obtain the true bottom reservoir fluid flow rate. Combined with the fact that the reservoir fluid at the bottom of the plunger flows into the tubing and casing according to the flow characteristics represented by the mass equation during the plunger's upward movement, and under the condition that the bottom flow pressure in the tubing and the bottom flow pressure in the casing are equal (at this time, the pressure at the bottom of the tubing and the annulus is balanced, which meets the error requirements), the corresponding bottom flow pressure value is calculated to characterize the flow characteristics of the reservoir fluid from the reservoir to the annulus.

[0054] Finally, after the plunger ascends to the surface and the liquid slug (liquid column) at its top reaches the surface, the gas column above the plunger (gas above the liquid column) is completely discharged from the wellbore, with a mass of zero. Based on this, this embodiment first obtains the correlation between the mass flow rate of the produced fluid and the upward velocity of the plunger, and then uses the mass flow rate of the produced fluid as an intermediate variable to construct the correlation between the mass of the produced fluid and the upward velocity of the plunger before it continues to ascend to the surface.

[0055] In this embodiment, the relationship between the mass flow rate of the extracted fluid and the upward velocity of the plunger is expressed by the following expression:

[0056] F lout =V p1 A t ρ l (4)

[0057] Among them, F lout V represents the mass flow rate of the extracted liquid. p1 A represents the upward speed of the plunger. t ρ represents the cross-sectional area of ​​the oil pipe. l This indicates the density of the extracted liquid.

[0058] In this embodiment, the mass of the extracted fluid is the mass of the liquid slug at the top of the plunger before it reaches the ground. Therefore, the relationship between the mass of the extracted fluid and the upward velocity of the plunger is expressed by the following expression:

[0059]

[0060] Where, m ltt This indicates the mass of the liquid slug at the top of the plunger.

[0061] In the step of obtaining the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate before the liquid slug at the top of the plunger reaches the surface, the first correlation between the tubing pressure, the plunger height, and the mass of the gas column above the plunger is obtained, and the second correlation between the tubing pressure, the plunger height, and the surface gas flow rate is obtained, using the static pressure in the gas column above the plunger as the tubing pressure. Then, the first and second correlations are integrated to obtain the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate.

[0062] Specifically, in this embodiment, the static pressure in the gas column above the plunger is first used as the tubing pressure. Based on the expansion effect of the gas column above the plunger, a first correlation is constructed between the tubing pressure, plunger height, and the mass of the gas column above the plunger, as well as a second correlation between the tubing pressure, plunger height, and surface gas well flow rate. After all the correlations are constructed, the tubing pressure is used as an intermediate variable to integrate the first and second correlations, thereby obtaining the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas well flow rate.

[0063] In this embodiment of the application, the first correlation and the second correlation are represented by the following expressions:

[0064]

[0065]

[0066] Where, p t Indicates the oil pipe pressure, m gtt Z represents the mass of the gas column above the plunger. t R represents the gas compressibility factor, T represents the ideal gas constant, H represents the actual gas temperature, and X represents the wellbore vertical depth. p L represents the plunger height. tt Indicates the length of the liquid slug at the top of the plunger, M g Let Z represent the average molecular weight of the gas, e represent the natural constant, α represent the coefficient of gas compressibility, g represent the acceleration due to gravity, and d represent the average molecular weight of the gas. t Indicates the inner diameter of the oil pipe, f g This represents the coefficient of gas friction.

[0067] Next, the present invention also obtains the gas friction coefficient based on the Churchill formula, wherein the gas friction coefficient is calculated using the following expression:

[0068]

[0069] Where A2 and B2 represent intermediate variables, Re represents the Reynolds number, D represents the equivalent diameter, and ε represents the wall roughness.

[0070] Furthermore, based on the force characteristics of the plunger itself and the liquid slug at the top of the plunger during the upward movement, the present invention performs momentum analysis on the upward movement of the plunger to the ground before the liquid slug at the top of the plunger reaches the ground, so as to obtain the correlation between the upward speed of the plunger and the mass of the liquid slug at the top of the plunger, thereby optimizing the upward airlift simulation of the plunger.

[0071] Specifically, this embodiment analyzes the force state of the plunger itself and the liquid slug at its top during the upward movement of the plunger to determine the force characteristics of the plunger during this process. Then, based on these determined force characteristics, a momentum analysis is performed on the upward movement of the plunger until the liquid slug at its top reaches the ground, using the momentum balance equation. Based on this, the correlation between the acceleration and mass of the liquid slug at the top of the plunger is first obtained, followed by the correlation between the upward velocity of the plunger and the mass of the liquid slug at the top of the plunger.

[0072] In this embodiment, the relationship between the plunger's upward velocity and the mass of the liquid slug at the top of the plunger is expressed by the following expression:

[0073]

[0074] Among them, a t The acceleration of the liquid slug at the top of the plunger is represented by t, and the upward travel time is represented by p. pb p represents the pressure acting on the bottom of the plunger. pt p represents the pressure acting on the plunger. fric The frictional force, m, represents the friction between the inner wall of the tubing and the fluid slug at the top of the plunger. p Indicates the mass of the plunger.

[0075] In this embodiment, the frictional force between the inner wall of the tubing and the liquid slug at the top of the plunger is calculated using the following expression:

[0076]

[0077] Where f represents the friction factor, L s The length of the liquid slug at the top of the plunger, d t This indicates the inner diameter of the oil pipe.

[0078] In this embodiment, the flow characteristics of the reservoir fluid at the bottom of the plunger into the tubing are represented by the following expression:

[0079]

[0080] p wft =p tb +L tb ρ L g (16)

[0081] Where, m gtb L represents the mass of the gas column at the bottom of the plunger. tb p represents the length of the liquid slug below the gas column at the bottom of the plunger. tb p represents the tubing pressure at the bottom of the well. wft ρ represents the bottom hole pressure in the tubing. LThis indicates the density of the liquid passing through the plunger.

[0082] In this embodiment, the flow characteristics of the reservoir fluid at the bottom of the plunger to the casing are represented by the following expression:

[0083]

[0084] p wfa =p cb +L a ρ L g (19)

[0085] Where, p c Indicates the casing pressure, m ga Z represents the mass of the air column in the annulus. c L represents the critical compressibility factor. a p represents the length of the liquid column in the annulus. cb p represents the casing pressure at the bottom of the well. wfa This indicates the bottom hole pressure in the casing.

[0086] Furthermore, in step S120, based on the expansion characteristics of the gas column at the bottom of the plunger, the correlation between the mass of the gas column at the bottom of the plunger and the surface gas flow rate is obtained when the plunger remains at the surface, thereby completing the plunger static gas lift simulation. In practical applications, the process of the plunger reaching the surface and remaining stationary is the gas production process after the surface control valve is opened. During this process, the produced gas-liquid two-phase fluids are both produced from the reservoir. When the natural gas production is lower than the critical production level for liquid accumulation, the surface control valve is closed to terminate the current gas production process. In this embodiment, when calculating the static pressure in the gas column at the bottom of the plunger during the plunger's stationary process, the gas expansion effect is also considered, and the produced gas-liquid two-phase fluid is regarded as a corresponding single-phase fluid combination, thus obtaining the correlation between the mass of the gas column at the bottom of the plunger and the surface gas flow rate when the plunger remains at the surface.

[0087] In this embodiment, the relationship between the mass of the bottom gas column and the surface gas flow rate when the plunger is stationary on the ground is represented by the following expression:

[0088]

[0089]

[0090] In this embodiment, the mass of the gas column at the bottom of the plunger and the mass of the liquid slug at the bottom of the plunger are calculated using the following expressions:

[0091]

[0092] Among them, F gout The mass flow rate of the extracted gas is expressed in m. ltbThis indicates the mass of the liquid slug at the bottom of the plunger.

[0093] Furthermore, in step S130, after the plunger descends to the liquid sluice at its bottom, the correlation between the plunger's descent velocity and the new liquid sluices at the top and bottom is established, thereby completing the plunger descent gas lift simulation. In practical applications, after the previous natural gas extraction cycle ends, the plunger travels from the surface through the tubing to the bottom of the well. When the plunger falls into the liquid sluice formed by the accumulated fluid at the bottom of the well within the tubing, there is no gas column at the bottom of the plunger, meaning the gas mass of the gas column is zero. Therefore, this embodiment establishes the correlation between the plunger's descent velocity and the new liquid sluices at the top and bottom after the plunger descends to the liquid sluice at its bottom, thereby achieving the purpose of simulating the plunger descent gas lift.

[0094] In this embodiment, the relationship between the plunger's downward velocity and the new liquid slugs at the top and bottom is expressed by the following expressions:

[0095] m ltb1 =F ltub 1-V p3 ρ l A t (twenty four)

[0096] m ltt1 =V p3 ρ L A t (25)

[0097] Where, m ltb1 F represents the mass of the new liquid slug at the top of the plunger. ltub 1 represents the mass flow rate of the liquid in the pipeline, V p3 The velocity of the plunger as it passes through the liquid slug is expressed in m. ltt1 This indicates the mass of the new liquid slug at the bottom of the plunger.

[0098] Because of the fluid accumulation at the bottom of the well, the plunger's descent can be divided into two parts: the part through the gas column and the part through the liquid slug. Therefore, this embodiment calculates the plunger's velocity in the gas column and liquid slug sections separately. The plunger's descent acceleration is determined by the net forces on the plunger (gravity and drag). Therefore, this embodiment uses the following expression to calculate the plunger's velocity when passing through the gas column:

[0099]

[0100] Among them, V p2 C represents the velocity of the plunger as it passes through the air column. d ρ represents the traction coefficient. q A represents the density of the gas column passing through the plunger. pM represents the cross-sectional area of ​​the plunger. p Indicates the mass of the plunger.

[0101] In this embodiment, the tubing pressure and casing pressure at the bottom of the well during the plunger's downward movement are taken as the corresponding static pressures. Following a similar method to obtaining the flow characteristics of the reservoir fluid at the bottom of the plunger from the tubing to the tubing and from the bottom of the plunger to the casing during the plunger's upward movement, the corresponding flow characteristics during the plunger's downward movement are obtained. These flow characteristics are expressed using the following expressions:

[0102]

[0103] Among them, P tb1 P represents the tubing pressure at the bottom of the well during the plunger's descent. cb1 A represents the casing pressure at the bottom of the well during the plunger's descent. a This represents the cross-sectional area of ​​the annulus.

[0104] Furthermore, based on the gas reservoir inflow relationship, this invention obtains the changes in gas production during steady-state and unsteady-state processes to further optimize the plunger gas lift simulation. In practical applications, reservoir dynamics is used to display the relationship between the gas-liquid flow regime and the bottom hole flowing pressure. Since both gas and liquid phases can flow into the tubing and annulus through perforations, this embodiment utilizes IPR curves to obtain the changes in gas production during steady-state and unsteady-state processes, thereby acquiring the gas production under different production states. By incorporating gas production simulation into the current plunger gas lift simulation process, further optimization of the plunger gas lift simulation is achieved, effectively expanding the scope of application of this invention.

[0105] In this embodiment, the change in gas production rate during the steady-state production process is obtained using the following expression:

[0106]

[0107] Where A1, B1, and C1 represent intermediate variables, and Q g1 The gas production rate during steady-state production is represented by μ, gas viscosity, z, gas compressibility factor, k, gas permeability, h, and P. SC T represents the gas pressure under standard conditions, and T represents the actual gas temperature. SC Z represents the gas temperature under standard conditions. SC R represents the gas compressibility factor under standard conditions. e R represents the radius of the permeable region. w ρ represents the radius of the oil pipe. g，SC This indicates the gas density under standard conditions.

[0108] In this embodiment, the change in gas production rate during the unsteady-state production process is obtained using the following expression:

[0109]

[0110] Among them, Q g2 p represents the amount of gas produced during a non-steady-state production process. e p represents the gas reservoir pressure. w The bottom hole flowing pressure is represented by P, the actual gas pressure is represented by t, and the production time is represented by C. t This represents the overall compression factor.

[0111] Furthermore, after obtaining the gas extraction rate under different production capacity conditions, this invention converts the calculated gas extraction rate in volumetric flow rate form into mass flow rate for calculation. The conversion from volumetric flow rate to mass flow rate is achieved using the following expression:

[0112] F gres1 =ρ g,sc ·Q g (34)

[0113] Among them, Q g F represents the amount of gas produced during steady-state or unsteady-state production processes. gres1 This represents the amount of gas extracted in the form of mass flow rate.

[0114] Furthermore, the amount of gas produced or liquid produced during unsteady-state production can be obtained using the following expression:

[0115]

[0116] Among them, F lres 1 represents the extracted liquid volume in the form of mass flow rate, and GLR represents the gas-liquid ratio.

[0117] Furthermore, this invention also performs static pressure analysis on the pressure recovery process during plunger gas lift when the plunger descends to a designated position in the liquid slug (when the plunger is locked on the buffer, reservoir fluid accumulates under the plunger seat; then, when the reservoir pressure reaches a certain threshold, the bottomhole buffer will reopen, and the plunger will begin to move upward again), to complete the full-cycle simulation of plunger gas lift, thereby optimizing the simulated full-cycle plunger gas lift. During the pressure recovery process, the plunger remains stationary, and reservoir fluid enters the annulus and tubing.

[0118] Furthermore, this invention also employs a linear gradient relationship to obtain the formation temperature based on the well depth:

[0119]

[0120] Among them, Tx T0 represents the formation temperature at a depth of x, T0 represents the surface temperature, and ΔH represents the well depth.

[0121] Furthermore, this invention also achieves efficient and accurate acquisition of fluid properties during the plunger gas lift simulation process by combining a component model with a black oil model.

[0122] Furthermore, the present invention also adopts a numerical iterative solution method, which simultaneously obtains the simulation results of each complete plunger gas lift cycle by pre-setting the on / off state of the ground control valve and the plunger gas lift cycle, thus ensuring the continuity of the simulation process.

[0123] Example 2

[0124] Based on the method for simulating plunger gas lift described in Embodiment 1 above, this embodiment of the invention also provides a system for simulating plunger gas lift (hereinafter referred to as "plunger gas lift simulation system"). Figure 4 This is a block diagram of a system for simulating plunger gas lift according to an embodiment of this application.

[0125] like Figure 4 As shown, the plunger gas lift simulation system in this embodiment includes: a plunger upward gas lift simulation module 41, a plunger stationary gas lift simulation module 42, and a plunger downward gas lift simulation module 43. The plunger upward gas lift simulation module 41 is implemented according to the method described in step S110 above. It is configured to obtain the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate before the liquid slug at the top of the plunger reaches the surface, based on the expansion characteristics of the gas column above the plunger. It also determines the flow characteristics into the annulus based on the flow characteristics of the reservoir fluid into the tubing and casing. Then, it constructs the correlation between the mass of the extracted liquid and the upward velocity of the plunger before the plunger continues to rise to the surface, thereby completing the plunger upward gas lift simulation; the plunger stationary gas lift simulation module 42... The stationary gas lift simulation module 42 is implemented according to the method described in step S120 above, and is configured to obtain the correlation between the mass of the bottom gas column and the surface gas well flow rate when the plunger is stationary on the ground based on the expansion characteristics of the gas column at the bottom of the plunger, thereby completing the static gas lift simulation of the plunger; the descending gas lift simulation module 43 is implemented according to the method described in step S130 above, and is configured to construct the correlation between the descending speed of the plunger and the new liquid sluices at the top and bottom after the plunger descends to the liquid sluice at its bottom, thereby completing the descending gas lift simulation of the plunger.

[0126] This invention discloses a method and system for simulating plunger gas lift. The method comprehensively considers reservoir dynamics based on classical production dynamics (e.g., IPR), taking into account changes in plunger upward and downward velocities. First, for the plunger's upward stroke, the correlation between the gas column mass above the plunger, the plunger height, and the surface gas flow rate is obtained before the liquid slug at the top reaches the surface. Based on the flow characteristics of reservoir fluids into the tubing and casing, the flow characteristics into the annulus are determined. Then, the correlation between the produced fluid mass and the plunger's upward velocity is constructed. Next, for the gas production process, the correlation between the gas column volume at the bottom of the plunger and the surface gas flow rate is obtained. Finally, for the plunger's downward stroke, the correlation between the plunger's downward velocity and the new liquid slugs at the top and bottom are constructed. This invention achieves full-cycle dynamic simulation of plunger gas lift, exhibiting good applicability and reliability, and providing technical support for guiding the design of field drainage and gas production processes and optimizing plunger operating regimes with the goal of maximizing single-well production.

[0127] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0128] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the claims of the present invention.

[0129] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device, or fabricating them separately as individual integrated circuit modules, or fabricating multiple modules or steps as a single integrated circuit module. Thus, the present invention is not limited to any particular hardware and software combination.

[0130] While the embodiments disclosed in this invention are as described above, the content is merely for the purpose of facilitating understanding of the invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in form and detail of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A method for simulating plunger gas lift, characterized in that, include: Based on the expansion characteristics of the gas column above the plunger, the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate is obtained before the liquid slug at the top of the plunger reaches the surface. Based on the flow characteristics of reservoir fluid into the tubing and casing, the flow characteristics into the annulus are determined. Then, the correlation between the mass of the extracted liquid and the upward velocity of the plunger is constructed before the plunger continues to rise to the surface, thus completing the plunger upward gas lift simulation. Based on the expansion characteristics of the gas column at the bottom of the plunger, the correlation between the mass of the gas column at the bottom of the plunger and the surface gas flow rate when the plunger is stationary on the ground is obtained, thereby completing the simulation of the plunger static gas lift. After the plunger descends to the liquid slug at its bottom, the correlation between the plunger's descent velocity and the new liquid slugs at the top and bottom is established, thus completing the plunger descent gas lift simulation.

2. The method according to claim 1, characterized in that, The steps involved in determining the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate before the liquid slug at the top of the plunger reaches the surface include: Using the static pressure in the gas column above the plunger as the tubing pressure, a first correlation relationship is obtained between tubing pressure, plunger height, and the mass of the gas column above the plunger, and a second correlation relationship is obtained between tubing pressure, plunger height, and surface gas well flow rate. By integrating the first correlation and the second correlation, the correlation between the gas column mass above the plunger, the plunger height, and the surface gas well flow rate is obtained.

3. The method according to claim 2, characterized in that, The first correlation and the second correlation are represented by the following expressions: Where, p t Indicates the oil pipe pressure, m gtt Z represents the mass of the gas column above the plunger. t R represents the gas compressibility factor, T represents the ideal gas constant, and A represents the actual gas temperature. t H represents the cross-sectional area of ​​the tubing, H represents the vertical depth of the wellbore, and X represents the cross-sectional area of ​​the tubing. p L represents the plunger height. tt Indicates the length of the liquid slug at the top of the plunger, M g Let represent the average molecular weight of the gas, e represent the natural constant, α represent the coefficient with respect to the gas compressibility factor, g represent the acceleration due to gravity, and d represent the average molecular weight of the gas. t Indicates the inner diameter of the oil pipe, f g q represents the gas friction coefficient. gout This indicates the flow rate of surface gas wells.

4. The method according to claim 3, characterized in that, The method further includes: The gas friction coefficient is obtained based on the Churchill formula, wherein the gas friction coefficient is calculated using the following expression: Where A2 and B2 represent intermediate variables, Re represents the Reynolds number, D represents the equivalent diameter, and ε represents the wall roughness.

5. The method according to any one of claims 1 to 4, characterized in that, The method further includes: Based on the force characteristics of the plunger itself and the liquid slug at the top of the plunger during the upward movement, a momentum analysis is performed on the upward movement of the plunger until the liquid slug at the top of the plunger reaches the ground, so as to obtain the correlation between the upward velocity of the plunger and the mass of the liquid slug at the top of the plunger, thereby optimizing the upward airlift simulation of the plunger.

6. The method according to claim 5, characterized in that, The relationship between the upward velocity of the plunger and the mass of the liquid slug at the top of the plunger is expressed by the following expression: Among them, a t V represents the acceleration of the liquid slug at the top of the plunger. p1 The piston's upward speed is represented by t, and the upward time is represented by p. pb p represents the pressure acting on the bottom of the plunger. pt p represents the pressure acting on the plunger. fric A represents the frictional force between the inner wall of the tubing and the liquid slug at the top of the plunger. t The cross-sectional area of ​​the oil pipe is expressed in meters (m). p Indicates the plunger mass, m ltt denoted by , where represents the mass of the liquid slug at the top of the plunger, and g represents the acceleration due to gravity.

7. The method according to any one of claims 1 to 6, characterized in that, The method further includes: Based on the gas reservoir inflow relationship, the changes in gas production during steady-state and unsteady-state processes were obtained to further optimize the plunger gas lift simulation.

8. The method according to claim 7, characterized in that, The changes in gas production rate during the steady-state production process can be obtained using the following expression: Where A1, B1, and C1 represent intermediate variables, and Q g1 The gas production rate during steady-state production is represented by μ, gas viscosity, z, gas compressibility factor, k, gas permeability, h, and P. SC T represents the gas pressure under standard conditions, and T represents the actual gas temperature. SC Z represents the gas temperature under standard conditions. SC R represents the gas compressibility factor under standard conditions. e R represents the radius of the permeable region. w ρ represents the radius of the oil pipe. g，SC Z represents the gas density under standard conditions, and Z represents the average gas compressibility.

9. The method according to claim 8, characterized in that, The following expression can be used to obtain the changes in gas production rate during an unsteady-state production process: Among them, Q g2 p represents the amount of gas produced during a non-steady-state production process. e p represents the gas reservoir pressure. w The bottom hole flowing pressure is represented by P, the actual gas pressure is represented by t, and the production time is represented by C. t This represents the overall compression factor.

10. A system for simulating plunger gas lift, characterized in that, The system includes the following modules: The plunger-up gas lift simulation module is used to obtain the correlation between the mass of the gas column above the plunger, the plunger height, and the surface gas flow rate before the liquid slug at the top of the plunger reaches the surface, based on the expansion characteristics of the gas column above the plunger. It also determines the flow characteristics into the annulus based on the flow characteristics of the reservoir fluid into the tubing and casing. Then, it constructs the correlation between the mass of the extracted liquid and the plunger's upward velocity before the plunger continues to rise to the surface, thus completing the plunger-up gas lift simulation. The plunger static gas lift simulation module is used to obtain the correlation between the mass of the bottom gas column and the surface gas well flow rate when the plunger is stationary on the ground, based on the expansion characteristics of the gas column at the bottom of the plunger, thereby completing the plunger static gas lift simulation. The plunger downward gas lift simulation module is used to construct the correlation between the plunger's downward velocity and the new liquid slugs at the top and bottom after the plunger descends to the liquid slug at its bottom, thereby completing the plunger downward gas lift simulation.

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