Gas well effusion displacement measuring method

Abstract

The invention relates to a gas well accumulated liquid displacement measuring method. The method comprises the steps that 1, a stress state model of an intelligent plunger in an underground critical state and a stress state model in the dynamic change process are established; 2, the leakage amount related to a liquid column in the upward movement process of the intelligent plunger is determined, and a relation model between the liquid column height and the initial liquid column height in the nth time period is constructed based on the leakage amount; 3, on the basis of the stress state model in the dynamic change process established in the step 1, constructing an upward movement distance equation of the plunger and the liquid column above in each time period in the step 2; 4, solving the upward movement distance equation of the plunger and the liquid column above the plunger in each time period constructed in the step 3 to obtain each section of movement distance; and 5, according to the solution value of each section of movement distance in the step 4, substituting the solution value into the relational model of the liquid column height and the initial liquid column height in the nth time period in the step 2 to obtain the liquid discharge height in the last time period. The method can be used for accurately obtaining the accumulated liquid displacement when the device moves to the wellhead.

Description

Technical Field

[0001] The invention relates to a method for measuring water discharge, and in particular to a method for measuring water discharge of liquid accumulation in a gas well. Background Art

[0002] The plunger-based gas well drainage and gas production process has significantly increased the production capacity of older natural gas wells. Traditional plungers are typically located at a bottomhole retainer during the process. The pressure differential between the plunger and its upper and lower parts at the moment of well opening drives the plunger from the bottom of the well to the wellhead, discharging excess liquid from the bottom of the well and increasing gas production. To address the problem of traditional plungers located at a bottomhole retainer, which can easily lead to liquid overload and well plugging, the intelligent plunger is designed with a fixed drainage height, allowing the device to hover at a fixed position below the bottomhole liquid, thus avoiding the risk of liquid overload.

[0003] However, in the drainage gas production process using a smart plunger as a carrier, the drainage rate is usually set based on well parameters such as the wellhead and bottomhole conditions. With the help of gas well energy recovery, the smart plunger itself and the accumulated liquid above it are driven to move to the wellhead and discharge the accumulated liquid. Because gas wells are located in underground spaces and are invisible, it is necessary to measure the drainage rate of the accumulated liquid in the gas well. The drainage rate of each working cycle during the production process must be verified and compared with the expected drainage rate set in advance to determine the accuracy of the drainage rate design process. Therefore, determining the drainage rate of gas well accumulated liquid is a key step in the gas well production stimulation process. Based on the existing needs, it is necessary to design a gas well accumulated liquid drainage rate measurement method. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a method for measuring the drainage volume of liquid accumulation in a gas well.

[0005] The above-mentioned purpose of the present invention is achieved through the following technical solutions:

[0006] A method for measuring the drainage volume of liquid accumulation in a gas well comprises the following steps:

[0007] Step 1: Establish a stress state model of the intelligent plunger in the critical state downhole and a stress state model during the dynamic change process;

[0008] Step 2: determining the amount of leakage of the liquid column during the upward movement of the smart plunger, and constructing a relationship model between the height of the liquid column in the nth time period and the initial liquid column height based on the leakage;

[0009] Step 3: Based on the force state model during the dynamic change process established in step 1, construct the equation for the upward movement distance of the plunger and the upper liquid column in each time period in step 2;

[0010] Step 4: Solve the equation for the upward movement distance of the plunger and the upper liquid column in each time period constructed in step 3 to obtain the movement distance of each section;

[0011] Step 5: Based on the solution value of each movement distance obtained in step 4, substitute it into the relationship model between the liquid column height in the nth time period and the initial liquid column height in step 2 to obtain the drainage height in the last time period.

[0012] Furthermore, step 1 includes:

[0013] 1.1. When the smart plunger is suspended at a fixed position below the liquid level in the gas well, the force analysis is performed with the moment of well opening but before the smart plunger moves as the initial critical state. The resultant force state at the moment of well opening is:

[0014] F0=P0A s -Mg-F f

[0015] Among them, F0 is the initial state resultant force at the moment of well opening, P0 is the pressure difference between the upper and lower surfaces of the plunger and the upper liquid column, A s is the cross-sectional area of the gas well, M is the total mass of the plunger and the liquid column above it, g is the acceleration of gravity, and F f It is the static friction force in the opposite direction of subsequent movement at the moment of well opening;

[0016] 1.2. After the plunger and the liquid column above it begin to move, the resultant force state during the dynamic change process is:

[0017]

[0018] in, is the net external force that changes with the state of motion, is the pressure difference that changes with the motion state, is the friction force that changes with the state of motion; pressure difference It can be expressed as:

[0019]

[0020] Among them, P c is the pressure value at the position of the plunger, P y is the pressure value at the ground oil pipeline;

[0021] Friction that varies with the state of motion It can be expressed as:

[0022]

[0023] Among them, λ lis the dimensionless liquid friction coefficient, ρ is the density of the liquid above the plunger, v is the upward velocity of the plunger and the liquid column above it, d is the diameter of the gas well, is the height of the liquid column above the plunger that changes with movement; then It can be simplified as:

[0024]

[0025] The resultant force state in the above dynamic change process is:

[0026]

[0027] Furthermore, step 2 includes:

[0028] The amount of liquid loss is a linear function of the plunger's upward velocity FB, then:

[0029] FB=0.00378K B (v up -V0)

[0030] Among them, FB is the liquid loss per unit time, K B is the slope of the leakage curve, V0 is the velocity intercept, v up is the rising rate of the smart plunger;

[0031] The above formula is converted to:

[0032] FB=k loss sh0A s

[0033] Among them, k loss is the liquid loss coefficient, usually 1 / (m·s) / 100, h0 is the length of the initial liquid section above the plunger, and s is the upward movement distance;

[0034] The relationship between the height of the liquid column in different time periods and the amount of liquid loss per unit time is:

[0035]

[0036] Among them, h n With h n+1 is the height of the liquid section at different times;

[0037] The relationship between the initial height and the height of the liquid column in the first time period is:

[0038]

[0039] Then the relationship between the height of the liquid column in the nth time period and the initial liquid column height is:

[0040]

[0041] Furthermore, step 3 includes:

[0042] The resultant force state formula in the dynamic change process in step 1 is applied to the general case and can be expressed as:

[0043]

[0044] According to Newton's second law of mechanics, the formula for the net external force can generally be expressed as:

[0045]

[0046] Among them, the relationship between acceleration and movement distance in each time period is expressed as:

[0047]

[0048] The formula for the total external force can be expressed as:

[0049]

[0050] The above formula can be simplified as:

[0051]

[0052] Among them, the coefficients K1, K2, and K3 are:

[0053]

[0054] The above formula can be converted into a definite solution of a second-order ordinary differential equation, which is expressed as follows:

[0055]

[0056] Furthermore, step 4 includes:

[0057] First, the second-order ordinary differential equation is converted into an initial value solution problem of a first-order differential equation system by variable substitution, and then solved by the Jung-Kutta method; in the reduced-order variable substitution, let q = s', then q' = s", and the second-order ordinary differential equation system in step 3 is converted to:

[0058]

[0059] Let e be the search step length, then:

[0060]

[0061] The coefficients are expressed as:

[0062]

[0063] Finally, the solution is obtained through the Hamming method loop, and the loop process is:

[0064]

[0065] The advantages and positive effects of the present invention are:

[0066] It can be seen from the above technical solution that due to the invisibility of the underground space where the gas well is located and the need to measure the discharge volume of the bottom hole accumulated liquid during the production process, the present invention discloses a method for measuring the drainage volume of the gas well accumulated liquid, which uses the built-in sensor of the intelligent plunger to obtain the movement information of the intelligent plunger during its own working process. Combined with force analysis and fluid dynamics analysis, a force state model of the intelligent plunger itself and the accumulated liquid above it in the critical state underground is established, a force state model in the dynamic change process is established, a liquid column height segmentation model based on the leakage amount is established, the movement distance equation is solved, and finally the drainage volume of the accumulated liquid when moving to the wellhead is obtained, providing a data basis for the adjustment of the subsequent production system. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a schematic diagram of force analysis of the intelligent plunger of the present invention when it is suspended in a fixed position below the liquid level in a gas well. DETAILED DESCRIPTION

[0068] The structure of the present invention will be further described below with reference to the accompanying drawings and through examples. It should be noted that the present examples are descriptive rather than restrictive.

[0069] A method for measuring the drainage volume of liquid accumulation in gas wells, see Figure 1 , the invention point is that it comprises the following steps:

[0070] Step 1: Establish a stress state model of the intelligent plunger in the critical state underground and the stress state model during the dynamic change process.

[0071] The smart plunger is suspended at a fixed position below the liquid level of the gas well. The force analysis is carried out at the initial critical state when the well is opened but the smart plunger has not yet achieved movement. Figure 1 shown.

[0072] At the moment of well opening, the smart plunger and the upper liquid column move upward under the action of their own gravity, the upward support force generated by the upper and lower pressure differences, and the downward friction force. The resultant force state at the moment of well opening is:

[0073] F0=P0A s -Mg-F f

[0074] Among them, F0 is the initial state resultant force at the moment of well opening, P0 is the pressure difference between the upper and lower surfaces of the plunger and the upper liquid column, A sis the cross-sectional area of the gas well, M is the total mass of the plunger and the liquid column above it, g is the acceleration of gravity, and F f It is the static friction force in the opposite direction to the subsequent movement at the moment of well opening.

[0075] After the plunger and the liquid column above it begin to move, the resultant force in the above formula, the pressure difference between the upper and lower surfaces of the plunger and the liquid column above it, and the friction force during the movement all change. The resultant force state during the dynamic change process is:

[0076]

[0077] in, is the net external force that changes with the state of motion, is the pressure difference that changes with the motion state, is the friction force that changes with the state of motion. Pressure difference It can be expressed as:

[0078]

[0079] Among them, P c is the pressure value at the position of the plunger, P y is the pressure value at the ground oil pipeline.

[0080] Friction that varies with the state of motion It can be expressed as:

[0081]

[0082] Among them, λ l is the dimensionless liquid friction coefficient, ρ is the density of the liquid above the plunger, v is the upward velocity of the plunger and the liquid column above it, d is the diameter of the gas well (usually 62 mm), is the height of the liquid column above the plunger that changes with movement. It can be simplified as:

[0083]

[0084] The resultant force state in the above dynamic change process is:

[0085]

[0086] Step 2: Determine the amount of liquid column leakage during the upward movement of the smart plunger. Based on the leakage, construct a relationship model between the liquid column height in the nth time period and the initial liquid column height, where n = 1, 2, 3, etc.:

[0087] As the smart plunger moves upward, the liquid above it will leak along the inner wall of the gas well as the plunger moves upward. The amount of leakage directly determines the height of the liquid column above the plunger. Usually, the liquid leakage is a linear function of the plunger's upward speed FB, so:

[0088] FB=0.00378K B (v up -V0)

[0089] Among them, FB is the liquid loss per unit time, K B is the slope of the leakage curve, V0 is the velocity intercept, v up is the rising rate of the smart plunger.

[0090] The above formula is converted into the following after introducing the leakage coefficient, movement distance, liquid column height and cross-sectional area parameters in the initial state:

[0091] FB=k loss sh0A s

[0092] Among them, k loss is the liquid loss coefficient (usually 1 / (m·s) / 100), h0 is the length of the initial liquid section above the plunger, and s is the upward movement distance.

[0093] The relationship between the height of the liquid column in different time periods and the amount of liquid loss per unit time is:

[0094]

[0095] Among them, h n With h n+1 is the height of the liquid section at different times.

[0096] Taking the initial height and the height of the first time period as an example, the relationship between the liquid column heights in the two time periods is:

[0097]

[0098] Wherein, s1 is the distance that the smart plunger moves upward during the first time period.

[0099] Applied in general form, the relationship between the height of the liquid column in the nth time period and the initial liquid column height is:

[0100]

[0101] Among them, s i is the distance the smart plunger moves upward during the i-th period, i = 1, 2, L, n.

[0102] Step 3: Based on the force state model during the dynamic change process established in step 1, construct the equation for the upward movement distance of the plunger and the upper liquid column in each time period in step 2

[0103] The resultant force formula in step 1 is applied to the general case and can be expressed as:

[0104]

[0105] According to Newton's second law of mechanics, the formula for the net external force can generally be expressed as:

[0106]

[0107] Among them, the relationship between acceleration and movement distance in each time period is expressed as:

[0108]

[0109] The formula for the total external force can be expressed as:

[0110]

[0111] The above formula can be simplified as:

[0112]

[0113] Among them, the coefficients K1, K2, and K3 are:

[0114]

[0115] The above formula can be converted into a definite solution of a second-order ordinary differential equation, which is expressed as follows:

[0116]

[0117] Step 4: Solve the equation for the upward movement distance of the plunger and the upper liquid column in each time period constructed in step 3 to obtain the movement distance s for each period i

[0118] The equation in step 3 is nonlinear and cannot be solved analytically, so a numerical solution is used. First, the second-order ordinary differential equation is converted to an initial value problem for a system of first-order differential equations by variable substitution, and then solved using the Jung-Kutta method. In the reduced variable substitution, let q = s', then q' = s", and the second-order ordinary differential equation system in step 3 is converted to:

[0119]

[0120] Let e be the search step length, we have:

[0121]

[0122] The coefficients are expressed as:

[0123]

[0124] Finally, the solution is obtained through the Hamming method loop, and the loop process is:

[0125]

[0126] Step 5: Calculate the height h of the discharged liquid column n

[0127] According to step 4, for each movement distance s i The solution value is substituted into the relationship model between the liquid column height in the nth time period and the initial liquid column height in step 2 to obtain the drainage height h in the last time period. n .

[0128] Example:

[0129] The method for measuring drainage volume from liquid accumulation in gas wells, described in this paper, was tested in gas wells in the Sulige region. Three different drainage heights were set, and five repeatability tests were conducted at each height. The results are shown in Table 1.

[0130] Table 1 Displacement (height) settings and final measurement results (rounded off)

[0131]

[0132]

[0133] As can be seen from Table 1, the method for measuring the drainage volume of liquid accumulation in a gas well according to the present invention meets the requirements in the field application example.

[0134] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will understand that various replacements, changes and modifications are possible without departing from the spirit of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for measuring the amount of liquid discharge from a gas well, characterized by: The steps include: Step 1: Establish a stress state model of the intelligent plunger in the critical state downhole and a stress state model during the dynamic change process; Step 2: determining the amount of leakage of the liquid column during the upward movement of the smart plunger, and constructing a relationship model between the height of the liquid column in the nth time period and the initial liquid column height based on the leakage; Step 3: Based on the force state model during the dynamic change process established in step 1, construct the equation for the upward movement distance of the plunger and the upper liquid column in each time period in step 2; Step 4: Solve the equation for the upward movement distance of the plunger and the upper liquid column in each time period constructed in step 3 to obtain the movement distance of each section; Step 5: Based on the solution value of each movement distance obtained in step 4, substitute it into the relationship model between the liquid column height in the nth time period and the initial liquid column height in step 2 to obtain the drainage height in the last time period.

2. The method for measuring the amount of liquid discharge from a gas well according to claim 1, wherein: Step 1 includes: 1.

1. When the smart plunger is suspended at a fixed position below the liquid level in the gas well, the force analysis is performed with the moment of well opening but before the smart plunger moves as the initial critical state. The resultant force state at the moment of well opening is: F0=P0A s -Mg-F f Among them, F0 is the initial state resultant force at the moment of well opening, P0 is the pressure difference between the upper and lower surfaces of the plunger and the upper liquid column, A s is the cross-sectional area of the gas well, M is the total mass of the plunger and the liquid column above it, g is the acceleration of gravity, and F f It is the static friction force in the opposite direction of subsequent movement at the moment of well opening; 1.

2. After the plunger and the liquid column above it begin to move, the resultant force state during the dynamic change process is: in, is the net external force that changes with the state of motion, is the pressure difference that changes with the motion state, is the friction force that changes with the state of motion; pressure difference It can be expressed as: Among them, P c is the pressure value at the position of the plunger, P y is the pressure value at the ground oil pipeline; Friction that varies with the state of motion It can be expressed as: Among them, λ l is the dimensionless liquid friction coefficient, ρ is the density of the liquid above the plunger, v is the upward velocity of the plunger and the liquid column above it, d is the diameter of the gas well, is the height of the liquid column above the plunger that changes with movement; then It can be simplified as: The resultant force state in the above dynamic change process is:

3. The method for measuring the amount of liquid discharge from a gas well according to claim 2, wherein: Step 2 includes: The amount of liquid loss is a linear function of the plunger's upward velocity FB, then: FB=0.00378K B (v up -V0) Among them, FB is the liquid loss per unit time, K B is the slope of the leakage curve, V0 is the velocity intercept, v up is the rising rate of the smart plunger; The above formula is converted to: FB=k loss sh0A s Among them, k loss is the liquid loss coefficient, usually 1 / (m·s) / 100, h0 is the length of the initial liquid section above the plunger, and s is the upward movement distance; The relationship between the height of the liquid column in different time periods and the amount of liquid loss per unit time is: Among them, h n With h n+1 is the height of the liquid section at different times; The relationship between the initial height and the height of the liquid column in the first time period is: Then the relationship between the height of the liquid column in the nth time period and the initial liquid column height is:

4. The method for measuring the amount of liquid discharge from a gas well according to claim 3, wherein: Step 3 includes: The resultant force state formula in the dynamic change process in step 1 is applied to the general case and can be expressed as: According to Newton's second law of mechanics, the formula for the net external force can generally be expressed as: Among them, the relationship between acceleration and movement distance in each time period is expressed as: The formula for the total external force can be expressed as: The above formula can be simplified as: Among them, the coefficients K1, K2, and K3 are: The above formula can be converted into a definite solution of a second-order ordinary differential equation, which is expressed as follows:

5. The method for measuring the amount of liquid discharge from a gas well according to claim 1, wherein: Step 4 includes: First, the second-order ordinary differential equation is converted into an initial value solution problem of a first-order differential equation system by variable substitution, and then solved by the Jung-Kutta method; in the reduced-order variable substitution, let q = s', then q' = s", and the second-order ordinary differential equation system in step 3 is converted to: Let e be the search step length, then: The coefficients are expressed as: Finally, the solution is obtained through the Hamming method loop, and the loop process is:

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