A method for calculating foam drainage gas wellbore liquid holdup

Abstract

The application discloses a kind of foam drainage gas wellbore liquid holdup calculation methods, comprising: using experimental data to establish foam correction factor mapping chart;Based on foam correction factor mapping chart, the relationship between foam correction factor and dimensionless surface tension and apparent gas flow rate is fitted;The relationship between foam correction factor and dimensionless surface tension and apparent gas flow rate is used to construct foam drainage type liquid holdup coefficient relationship diagram;With foam drainage type liquid holdup coefficient relationship diagram replaces the liquid holdup coefficient relationship diagram in traditional H-B model, to obtain the modified H-B model;Foam drainage liquid holdup is predicted using the modified H-B model.The application makes that the liquid holdup prediction under foam drainage condition is more in line with the gas-liquid two-phase flow characteristics of foam system, thereby reducing the system deviation caused by directly using traditional H-B model chart, and the implementation threshold is low, and engineering landing is fast.

Description

Technical Field

[0001] This invention relates to the field of oil and gas extraction technology, and in particular to a method for calculating the liquid holdup rate of a foam drainage gas extraction wellbore. Background Technology

[0002] As gas wells enter the mid-to-late production stage, problems such as insufficient liquid carrying capacity, liquid accumulation in the wellbore, increased bottomhole back pressure, and decreased production are prone to occur in the gas-liquid two-phase flow. Foam drainage gas production technology is often used on-site, which reduces the gas-liquid interfacial tension and changes the flow pattern in the wellbore by introducing foam drainage agents to improve liquid carrying capacity.

[0003] Wellbore holdup is one of the key parameters for calculating wellbore pressure drop and flow state. In engineering, empirical models such as the Hagedorn-Brown (HB) are commonly used to calculate pressure drop in vertical / near-vertical two-phase flows, where holdup is typically solved using a graphical iterative process: [calculated using the fluid velocity...] Gas velocity number Pipe diameter Liquid viscosity number Using dimensionless parameters as the inlet, based on the liquid viscosity number Retrieve intermediate process parameters Calculate the retention coefficient And look up the liquid holdup coefficient relationship graph. Then, the liquid holdup is obtained through iteration.

[0004] However, existing HB model liquid holdup charts and coefficient relationships are mainly based on experimental data from conventional liquid systems (clear water). When the well fluid is a foam system (after adding a foaming agent), the interfacial tension is significantly reduced, and the foam structure, flow pattern characteristics, and gas-liquid slippage properties differ from those of conventional clear water systems. Directly applying traditional HB liquid holdup coefficient relationships often leads to large deviations in liquid holdup predictions under foam drainage conditions, thus affecting well pressure drop calculations and process parameter optimization.

[0005] Existing methods for bubble dissipation typically modify liquid holdup models using methods such as "concentration coefficients." However, for the HB chart iteration system, there is still a lack of a method to introduce the foam effect in an engineering-implementable, table-lookup / interpolation-based manner, while adhering to the traditional HB model chart process, and to form a reusable "bubble dissipation type liquid holdup coefficient relationship diagram." Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, this invention provides a method for calculating the liquid holdup rate of foam drainage gas production wellbores, which solves the problems of high application cost and large prediction deviation in existing technologies for measuring foam drainage liquid holdup rate.

[0007] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a method for calculating the liquid holdup rate of a foam-drained gas production wellbore, comprising: A foam correction factor mapping chart was constructed using experimental data; The relationship between the foam correction factor and dimensionless surface tension and apparent airflow velocity was fitted based on the foam correction factor mapping chart. A graph showing the relationship between the foam correction factor, dimensionless surface tension, and apparent gas flow rate was constructed to represent the liquid holdup coefficient of the bubble discharge type. The liquid holdup coefficient relationship diagram in the traditional HB model is replaced with the bubble-type liquid holdup coefficient relationship diagram to obtain the modified HB model; The modified HB model was used to predict the bubble-out liquid holdup.

[0008] Further: A foam correction factor mapping chart is constructed using experimental data, including the following steps: A1. In the vertical foam drainage wellbore simulation experimental device, under the same liquid flow rate, pressure, temperature and pipe diameter conditions, the baseline system experiment and the foam system experiment were carried out respectively; based on the given apparent gas flow rate, the liquid holdup of clear water and the liquid holdup of foam drainage were measured; among them, the baseline system is the clear water system without foam drainage agent, and the foam system is the foam system with foam drainage agent added; A2. Determine the gas-liquid surface tension corresponding to the reference system and the foam system, and calculate the dimensionless surface tension, the expression of which is:

[0009] In the formula, It is dimensionless surface tension; Let be the gas-liquid surface tension corresponding to the foam system. ; The gas-liquid surface tension corresponding to the reference system. ; A3. Calculate the bubble correction factor, its expression is:

[0010] In the formula, As a bubble correction factor; For water retention rate, ; This refers to the liquid retention rate due to foaming. ; A4. Using dimensionless surface tension as the abscissa and foam correction factor as the ordinate, establish a foam correction factor mapping chart under the same apparent airflow velocity and different dimensionless surface tensions. By changing the parameter value of the given apparent airflow rate, repeat steps A1-A4 to obtain a mapping chart of the relationship between the foam correction factor and different dimensionless surface tensions under different apparent airflow rates.

[0011] Furthermore, the relationship between the foam correction factor and dimensionless surface tension and apparent airflow velocity is as follows:

[0012] In the formula, e is the natural constant; For apparent airflow velocity, s.

[0013] Furthermore, a relationship diagram of the liquid holdup coefficient for bubble displacement type was constructed by relating the foam correction factor to dimensionless surface tension and apparent gas flow rate, including: Calculate the liquid velocity number, gas velocity number, pipe diameter number, and liquid viscosity number under average pressure and temperature conditions; Based on the liquid viscosity number, through Relationship diagrams determine intermediate process parameters The value; Intermediate process parameters are determined using a liquid holdup correction factor diagram based on gas velocity number, liquid viscosity number, and pipe diameter number. ; Based on intermediate process parameters Calculate the retention coefficient based on liquid velocity number, gas velocity number, and pipe diameter. ; Using the retention coefficient as the x-axis, Construct a graph showing the relationship between the liquid holding rate coefficients of the bubble-displacement type with the vertical axis.

[0014] Furthermore, The specific expression is: .

[0015] The beneficial effects of this invention are as follows: 1. The accuracy of predicting bubble-displacement liquid retention rate is significantly improved. This invention does not directly apply the liquid retention rate coefficient relationship diagram of the traditional HB model, but introduces dimensionless surface tension. Apparent flow rate of gas phase Two key independent variables were used to establish a foam correction factor based on measured data from foam dissipation experiments. and and The relationship between them, and by Obtain the foam retention rate Based on this, a graph showing the relationship between liquid holdup coefficients under bubble discharge conditions is generated. - Due to the reduction of gas-liquid interfacial tension under the action of foaming agents, and the decrease in gas-liquid slippage characteristics and liquid retention of the foam system, and The changes are significant. By explicitly introducing the above-mentioned effects at the diagram level, this invention makes the liquid holdup prediction results under bubble discharge conditions more consistent with the gas-liquid two-phase flow characteristics of the foam system, thereby reducing the system bias caused by directly using the traditional HB model diagram.

[0016] 2. No on-site bubble-dissipation liquid-holding rate experiment is required; the bubble-dissipation liquid-holding rate can be directly obtained through chart iteration. This invention significantly reduces testing and calculation costs by generating a graph showing the relationship between the bubble discharge and liquid retention rates. - In the engineering application phase, the iterative structure of HB's diagram can be directly followed: calculate dimensionless parameters and retrieve intermediate process parameters. Calculate the retention coefficient And directly obtained from the relationship diagram of foam discharge liquid retention coefficient Then iterate to get During the experimental phase, a foam correction relationship was established by comparing the liquid holding rates of the clear water system and the foam system. In the field application phase, it is no longer necessary to re-measure the liquid holding rate of the clear water baseline. Instead, the dimensionless parameters and retention coefficients calculated by the traditional HB model are used to directly retrieve the pre-constructed foam discharge type liquid holding rate coefficient relationship diagram, reducing the workload of experiments and field calibration and improving the replicability and scalability of the calculation process.

[0017] 3. By replacing the core liquid holdup coefficient diagram and adding a bubble-displacement correction formula, the adaptation to the bubble-displacement condition can be completed. This method is easy to implement and requires minimal system modification. The invention retains the dimensionless parameter calculation method, intermediate process parameter lookup method, retention coefficient calculation path, and iterative solution framework of the HB model. It only replaces the original traditional HB model liquid holdup coefficient diagram with a bubble-displacement type liquid holdup coefficient diagram and adds a bubble-displacement correction formula / mapping diagram to generate the diagram library, thus completing the liquid holdup calculation adaptation under the bubble-displacement condition. Compared to rebuilding the entire bubble-displacement two-phase flow model or introducing a large number of new parameters, the modification of existing programs / tables / software in this invention mainly focuses on the "diagram library replacement and retrieval," resulting in a low implementation threshold and rapid engineering deployment.

[0018] 4. Strong applicability and scalability: It can be adapted to different apparent gas flow rates. Establish corresponding bubble correction factors With dimensionless surface tension Relationship diagram, and will different The combination of patterns under certain conditions forms a bubble array pattern library. The key input of this invention is dimensionless surface tension. With apparent air velocity Both have clear physical meaning and are easily obtained: among them The surface tension of the gas-liquid system can be determined in advance or given by a database. Gas-liquid surface tension of the reference water system The calculations later yielded the following results: It can be calculated from the on-site flow rate and the cross-sectional area inside the pipe. This is achieved by establishing [a system / mechanism] during the calibration phase. It also generates a map library, enhancing the applicability and maintainability of the method.

[0019] 5. Improved computational stability: The iterative diagram format is consistent with the original HB model, facilitating control over convergence and boundary behavior. In engineering applications, this invention retains the original HB iterative structure and variable organization, only changing the (clear water) liquid holdup coefficient diagram to a bubble-displacement type. Therefore, mature iterative convergence criteria and abnormal condition handling logic can be directly applied. The bubble-displacement effect is "solidified" in the bubble-displacement liquid holdup coefficient relationship diagram, preventing the introduction of numerous additional complex coupling terms during iterative solutions in the online calculation process, thus improving numerical stability and engineering controllability. Attached Figure Description

[0020] Figure 1 A flowchart illustrating a method for calculating the liquid holdup in a foam-drained gas production wellbore, provided as an example. Figure 2 A foam correction factor mapping chart provided for the embodiment under the same apparent airflow rate and different dimensionless surface tensions; Figure 3 A mapping chart showing the relationship between the foam correction factor under different apparent airflow rates and different dimensionless surface tensions, provided for the embodiments; Figure 4 This is a graph showing the relationship between coefficient 'a' and apparent airflow velocity. Figure 5 This is a graph showing the relationship between the coefficient b and the apparent airflow velocity. Figure 6 For relational prediction A comparison chart of the measured values ​​with the experimental values; Figure 7 Provided for the embodiments Relationship diagram; Figure 8 A diagram showing the liquid holdup correction factor for the embodiments; Figure 9 This is a graph showing the relationship between the liquid holding rate coefficient and the bubble-dissipation type. Detailed Implementation

[0021] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0022] like Figure 1 As shown, in one embodiment of the present invention, a method for calculating the liquid holdup of a foam-drained gas production well includes the following steps: S1. Use experimental data to establish a foam correction factor mapping chart.

[0023] In one feasible embodiment of the present invention, the input parameters include: Wellbore structure and operating parameters: tubing inner diameter, well inclination, pressure, gas production, etc. Surface tension: Gas-liquid surface tension in conventional liquid systems (pure water) Gas-liquid surface tension in foam drainage systems (Measured experimentally or obtained on-site); Experimental measurement input: The measured baseline (clear water) liquid holdup under the same apparent gas velocity, apparent liquid velocity, pressure, temperature, pipe diameter, and inclination angle conditions. With foam retention rate .

[0024] Establishing a bubble correction factor mapping chart specifically includes the following steps: A1. In a vertical foam discharge wellbore simulation experimental device, under the same liquid flow rate, pressure, temperature, and pipe diameter (in this embodiment, the pipe diameter is 50 mm), a baseline system experiment and a foam system experiment were conducted respectively; based on a given apparent gas flow rate, the water holdup was determined. and foam retention rate The baseline system is a water system without foaming agent, and the foam system is a foam system with foaming agent added. A2. Determine the gas-liquid surface tension corresponding to the reference system and the foam system, and calculate the dimensionless surface tension, the expression of which is:

[0025] In the formula, It is dimensionless surface tension; Let be the gas-liquid surface tension corresponding to the foam system. ; The gas-liquid surface tension corresponding to the reference system. ; A3. Calculate the bubble correction factor, its expression is:

[0026] In the formula, As a bubble correction factor; For water retention rate, ; This refers to the liquid retention rate due to foaming. ;when When <1, it indicates that the wellbore liquid holdup decreases and the liquid carrying capacity increases after the foaming agent is applied.

[0027] A4. Using dimensionless surface tension as the x-axis and the foam correction factor as the y-axis, establish a mapping chart of the foam correction factor under the same apparent airflow velocity but different dimensionless surface tensions, as shown below. Figure 2 As shown.

[0028] By changing the parameter value of the given apparent airflow rate, repeat steps A1-A4 to obtain a mapping chart of the relationship between the foam correction factor and different dimensionless surface tensions under different apparent airflow rates, as shown below. Figure 3 As shown.

[0029] S2. Fitting the relationship between the foam correction factor and dimensionless surface tension and apparent airflow velocity based on the foam correction factor mapping chart. .

[0030] Depend on Figure 3 visible, The relationship with S can be characterized as an exponential function. In the formula, a and b are coefficients obtained from experimental fitting. Because a and b are to be fitted to establish... Therefore, a and b should both be related to the apparent airflow velocity. If they are related, then establish a, b and respectively. Relationship diagram as follows Figure 4 , Figure 5 As shown.

[0031] After fitting and correction, the following was obtained:

[0032]

[0033] By using the fitted formulas a and b above (where the coefficients in formulas a and b are rounded to three decimal places), the foam correction factor can be calculated. With dimensionless surface tension and apparent airflow velocity Connecting them, that is Thus obtain about , , Relationship: ; Depend on By rearranging the terms, we get: ; in, The defined bubble holdup ratio, ; Based on the baseline (clean water) liquid holdup, ; The apparent flow rate in the gas phase is... s; , The gas-liquid surface tensions are given under the bubble displacement system and the clear water system, respectively. .

[0034] The relationship between the foam correction factor and dimensionless surface tension and apparent gas flow rate is as follows: Figure 6 As shown, the specific expression is:

[0035] In the formula, e is the natural constant; For apparent airflow velocity, s.

[0036] S3. Construct a graph showing the relationship between the foam correction factor, dimensionless surface tension, and apparent gas flow rate to determine the liquid holdup coefficient of the bubble discharge type.

[0037] When it is necessary to predict the liquid retention rate of foaming at the site but it cannot be measured directly. The initial step involves calculating intermediate process parameters and retention coefficients using the traditional HB model. This method employs a traditional HB chart iterative process to solve the problem: calculating the liquid velocity number... Gas velocity number Pipe diameter Liquid viscosity number Dimensionless parameters; based on liquid viscosity Data retrieval of intermediate process parameters ; Calculate the retention coefficient Then, by referring to the relationship diagram of the subsequent replacement of the bubble discharge liquid retention rate coefficient, the following can be found: and combined with intermediate process parameters Iterative solution yields .

[0038] Specifically, it includes: Calculate the liquid velocity number, gas velocity number, pipe diameter number, and liquid viscosity number under average pressure and temperature conditions:

[0039]

[0040]

[0041]

[0042] In the formula, For liquid velocity number, For gas velocity number, For pipe diameter, These are the viscosity numbers of the liquid, and all four are dimensionless quantities. , For apparent flow rates of the gas and liquid phases, s; , These represent the densities of gas and liquid, respectively. ; For gas-liquid surface tension, ; For liquid phase viscosity, ; It is the acceleration due to gravity. ; The inner diameter of the pipe. .

[0043] Based on the liquid viscosity number, through Relationship diagrams determine intermediate process parameters The value, such as Figure 7 As shown; Calculate based on gas velocity number, liquid viscosity number, and pipe diameter number. Intermediate process parameters were determined using a liquid holdup correction coefficient diagram. ,like Figure 8 As shown; Based on intermediate process parameters The retention coefficient is calculated based on the liquid velocity number, gas velocity number, and pipe diameter number. The expression is as follows:

[0044] In the formula, Standard atmospheric pressure (0.101325). ; The average pressure in the calculated section within the wellbore. .

[0045] With retention coefficient As the x-axis, with Construct a graph showing the relationship between the liquid holding rate coefficient of the bubble displacement type on the vertical axis, such as... Figure 9 As shown.

[0046] Because the vertical axis of the liquid holdup coefficient relationship graph of the traditional HB model is... ( (for intermediate process parameters), while the present invention defines ,available:

[0047] .

[0048] According to different S and Foam correction factor under certain conditions Its ordinate is The horizontal axis uses the retention coefficient from the HB model. The new "bubble discharge type liquid retention coefficient relationship diagram" is used to predict the bubble discharge liquid retention rate. In this case, the iterative steps of the traditional HB model for predicting liquid holdup can be followed.

[0049] S4. Replace the liquid holding rate coefficient relationship diagram in the traditional HB model with the bubble-type liquid holding rate coefficient relationship diagram to obtain the modified HB model for foam systems.

[0050] S5. Predict the bubble-drainage liquid holding rate using the modified HB model.

[0051] The beneficial effects of this invention include: 1. The accuracy of predicting bubble-displacement liquid retention rate is significantly improved. This invention does not directly apply the liquid retention rate coefficient relationship diagram of the traditional HB model, but introduces dimensionless surface tension. Apparent flow rate of gas phase Two key independent variables were used to establish a foam correction factor based on measured data from foam dissipation experiments. and and The relationship between them, and by Obtain the foam retention rate Based on this, a graph showing the relationship between liquid holdup coefficients under bubble discharge conditions is generated. - Due to the reduction of gas-liquid interfacial tension under the action of foaming agents, and the decrease in gas-liquid slippage characteristics and liquid retention of the foam system, and The changes are significant. By explicitly introducing the above-mentioned effects at the diagram level, this invention makes the liquid holdup prediction results under bubble discharge conditions more consistent with the gas-liquid two-phase flow characteristics of the foam system, thereby reducing the system bias caused by directly using the traditional HB model diagram.

[0052] 2. No on-site bubble-dissipation liquid-holding rate experiment is required; the bubble-dissipation liquid-holding rate can be directly obtained through chart iteration. This invention significantly reduces testing and calculation costs by generating a graph showing the relationship between the bubble discharge and liquid retention rates. - In the engineering application phase, the iterative structure of HB's diagram can be directly followed: calculate dimensionless parameters and retrieve intermediate process parameters. Calculate the retention coefficient And directly obtained from the relationship diagram of foam discharge liquid retention coefficient Then iterate to get Therefore, during the experimental phase, a foam correction relationship was established by comparing the liquid holding rates of the clear water system and the foam system. During the field application phase, it is no longer necessary to re-measure the liquid holding rate of the clear water baseline. Instead, the dimensionless parameters and retention coefficients calculated by the traditional HB model are used to directly retrieve the pre-constructed foam discharge type liquid holding rate coefficient relationship diagram, reducing the workload of experiments and field calibration and improving the replicability and scalability of the calculation process.

[0053] 3. By replacing the core liquid holdup coefficient diagram and adding a bubble-displacement correction formula, the adaptation to the bubble-displacement condition can be completed. This method is easy to implement and requires minimal system modification. The invention retains the dimensionless parameter calculation method, intermediate process parameter lookup method, retention coefficient calculation path, and iterative solution framework of the HB model. It only replaces the original traditional HB model liquid holdup coefficient diagram with a bubble-displacement type liquid holdup coefficient diagram and adds a bubble-displacement correction formula / mapping diagram to generate the diagram library, thus completing the liquid holdup calculation adaptation under the bubble-displacement condition. Compared to rebuilding the entire bubble-displacement two-phase flow model or introducing a large number of new parameters, the modification of existing programs / tables / software in this invention mainly focuses on the "diagram library replacement and retrieval," resulting in a low implementation threshold and rapid engineering deployment.

[0054] 4. Strong applicability and scalability: It can be adapted to different apparent gas flow rates. Establish corresponding bubble correction factors With dimensionless surface tension Relationship diagram, and will different The combination of patterns under certain conditions forms a bubble array pattern library. The key input of this invention is dimensionless surface tension. With apparent air velocity Both have clear physical meaning and are easily obtained: among them The surface tension of the gas-liquid system can be determined in advance or given by a database. Gas-liquid surface tension of the reference water system The calculations later yielded the following results: It can be calculated from the on-site flow rate and the cross-sectional area inside the pipe. This is achieved by establishing [a system / mechanism] during the calibration phase. It also generates a map library, enhancing the applicability and maintainability of the method.

[0055] 5. Improved computational stability: The iterative diagram format is consistent with the original HB model, facilitating control over convergence and boundary behavior. In engineering applications, this invention retains the original HB iterative structure and variable organization, only changing the (clear water) liquid holdup coefficient diagram to a bubble-displacement type. Therefore, mature iterative convergence criteria and abnormal condition handling logic can be directly applied. The bubble-displacement effect is "solidified" in the bubble-displacement liquid holdup coefficient relationship diagram, preventing the introduction of numerous additional complex coupling terms during iterative solutions in the online calculation process, thus improving numerical stability and engineering controllability.

Claims

1. A method for calculating the liquid holdup rate in a foam-drained gas production wellbore, characterized in that, include: A foam correction factor mapping chart was constructed using experimental data; The relationship between the foam correction factor and dimensionless surface tension and apparent airflow velocity was fitted based on the foam correction factor mapping chart. A graph showing the relationship between the foam correction factor, dimensionless surface tension, and apparent gas flow rate was constructed to represent the liquid holdup coefficient of the bubble discharge type. The liquid holdup coefficient relationship diagram in the traditional HB model is replaced with the bubble-type liquid holdup coefficient relationship diagram to obtain the modified HB model; The modified HB model was used to predict the bubble-out liquid holdup.

2. The method according to claim 1, characterized in that, The following steps are included in constructing a foam correction factor mapping chart using experimental data: A1. In the vertical foam drainage wellbore simulation experimental device, under the same liquid flow rate, pressure, temperature and pipe diameter conditions, the baseline system experiment and the foam system experiment were carried out respectively; based on the given apparent gas flow rate, the liquid holdup of clear water and the liquid holdup of foam drainage were measured; among them, the baseline system is the clear water system without foam drainage agent, and the foam system is the foam system with foam drainage agent added; A2. Determine the gas-liquid surface tension corresponding to the reference system and the foam system, and calculate the dimensionless surface tension, the expression of which is: In the formula, It is dimensionless surface tension; Let be the gas-liquid surface tension corresponding to the foam system. ; The gas-liquid surface tension corresponding to the reference system. ; A3. Calculate the bubble correction factor, its expression is: In the formula, As a bubble correction factor; For water retention rate, ; This refers to the liquid retention rate due to foaming. ; A4. Using dimensionless surface tension as the abscissa and foam correction factor as the ordinate, establish a foam correction factor mapping chart under the same apparent airflow velocity and different dimensionless surface tensions. By changing the parameter value of the given apparent airflow rate, repeat steps A1-A4 to obtain a mapping chart of the relationship between the foam correction factor and different dimensionless surface tensions under different apparent airflow rates.

3. The method according to claim 2, characterized in that, The relationship between the foam correction factor and dimensionless surface tension and apparent gas flow rate is as follows: In the formula, e is the natural constant; For apparent airflow velocity, s.

4. The method according to claim 3, characterized in that, A graph showing the relationship between the foam correction factor, dimensionless surface tension, and apparent gas flow rate was constructed, including: Calculate the liquid velocity number, gas velocity number, pipe diameter number, and liquid viscosity number under average pressure and temperature conditions; Based on the liquid viscosity number, through Relationship diagrams determine intermediate process parameters The value of; where, This refers to the viscosity number of the liquid. Intermediate process parameters are determined using a liquid holdup correction factor diagram based on gas velocity number, liquid viscosity number, and pipe diameter number. ; Based on intermediate process parameters Calculate the retention coefficient based on liquid velocity number, gas velocity number, and pipe diameter. ; Using the retention coefficient as the x-axis, Construct a graph showing the relationship between the liquid holding rate coefficients of the bubble-displacement type with the vertical axis.

5. The method according to claim 4, characterized in that, The specific expression is: 。

Images