A secondary separation flow measurement system based on small GLCC and ERT

By combining a small GLCC and ERT in a two-stage flow measurement system, the problems of small flow measurement range and poor generalization ability are solved, achieving higher accuracy and wider range of flow measurement, and adapting to the complex flow environment of oil fields.

CN119124294BActive Publication Date: 2026-05-12TSINGHUA SHENZHEN INTERNATIONAL GRADUATE SCHOOL
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
TSINGHUA SHENZHEN INTERNATIONAL GRADUATE SCHOOL
Filing Date
2024-07-12
Publication Date
2026-05-12

AI Technical Summary

Technical Problem

现有的单独使用GLCC或ERT方法在流量测量中存在流量测量范围小、泛化能力较差的问题,导致无法适应油田现场复杂多变的流量情况,且测量结果不准确。

Method used

Design a two-stage separation flow measurement system based on a small GLCC and ERT. Combining single-stage and two-stage separators and sensors, the flow meter results are corrected by calculating the gas-liquid void fraction using ERT. Linear projection method (LBP) is used for image reconstruction to reduce system errors and improve measurement accuracy.

Benefits of technology

It expands the flow measurement range, improves measurement accuracy and separation efficiency, reduces measurement errors, and adapts to the complex and ever-changing flow conditions in oil fields.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application relates to the technical field of multiphase flow fluid measurement, in particular to a two-stage separation flow measurement system based on a small GLCC and ERT, which can solve the problems that the existing two methods have small flow measurement ranges and poor generalization abilities when used alone, cannot adapt to complex and changeable flow conditions in oilfield sites, and the optimization of measurement results often needs complex data processing technology, which makes the measurement difficult and inaccurate. The system comprises a single-stage separator, a two-stage separator and a sensor: the single-stage separator comprises a separation chamber, the separation chamber is in a barrel type structure, the inlet of the separation chamber is connected with the system inlet, the liquid outlet of the separation chamber is connected with the system outlet, the gas outlet of the separation chamber is connected with the two-stage separator, the two-stage separator is designed based on a small GLCC, and the gas outlet and the liquid outlet of the two-stage separator are respectively connected with the system outlet; the sensor comprises a flowmeter and an ERT.
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Description

Technical Field

[0001] This application relates to the field of multiphase flow measurement technology, and more specifically, to a two-stage separation flow measurement system based on a small GLCC and ERT. Background Technology

[0002] Multiphase flow is a common phenomenon in the petrochemical industry. "Phase" refers to different physical states or different physical properties or mechanical states of the same physical state. According to the different forms of matter, substances in nature can be divided into three phases: gas, liquid and solid. Generally, a fluid system with two or more substances and a clear interface is regarded as a multiphase flow. For example, gas and water are two different substances that are incompatible. When they are mixed together, a clear interface will appear. Therefore, at room temperature, gas-water mixture can be regarded as a type of gas-liquid two-phase flow - gas-water two-phase flow.

[0003] In the field of oil extraction, containerized separators are mainly used to process the multiphase flow of oil, gas, and water generated from the wellhead. The gas-liquid cylindrical cyclone separator (GLCC) is a highly efficient gas-liquid separator suitable for gas-liquid two-phase separation and metering in onshore oil and gas fields and offshore oil and gas platforms. Compared with containerized separators, GLCC has significant advantages such as simple structure, low cost, small size, and ease of installation and operation. This makes GLCC stand out among many separators and it is widely used in major oil fields, especially in offshore oil and gas platforms. Due to limited space, the footprint and weight of the equipment need to be considered. In this regard, GLCC has a clear advantage over traditional separators. Therefore, it has shown good application prospects in new offshore gas field projects and capacity expansion and renovation of existing platforms.

[0004] The measurement of multiphase flow rates is crucial throughout the oil extraction and transportation process. In the petrochemical industry, two common methods for measuring multiphase flow rates are separation measurement and non-separation measurement.

[0005] Separation measurement involves feeding a multiphase flow into a gas-liquid separator to separate it into a gas phase flow and a liquid phase flow, and then using a single-phase flow meter to measure the flow velocity of each. One of the most critical pieces of equipment in this process is the separator. Columnar cyclone gas-liquid separators (GLCCs) are widely used in the petroleum industry due to their advantages such as small size, high separation efficiency, and ease of installation and operation.

[0006] Non-separation measurement is another method for directly measuring multiphase flows without separation, eliminating the need for separation devices. Turbine flow meters, ultrasonic flow meters, and electromagnetic flow meters are commonly used flow meters. In recent years, electro-tomography (ERT) technology has gained widespread application due to its advantages such as visualization, non-contact operation, immunity to flow field interference, and minimal environmental impact. ERT technology is a two-phase / multiphase flow measurement technique developed by combining computer application technology with modern detection technology. It can provide information about the flow characteristics of fluids, such as gas / solid, gas / liquid, and liquid / liquid two-phase flows. As an online measurement technology with advantages such as visualization, low cost, non-invasiveness, and robustness, ERT technology has become a recognized measurement technique in process applications.

[0007] However, in separation measurement methods, two factors affecting the efficiency of GLCC (Gas-Cooled Concentrate) are liquid carry-volume (LCO) and gas carry-volume (GCU). During gas-liquid separation, the phenomenon where liquid follows the gas flow and leaves from the gas outlet at the top of the separator is called LCO, while the phenomenon where gas follows the liquid towards the bottom of the separator is called GCU. Due to the influence of LCO and GCU, to ensure complete separation of gas and liquid, the separation equipment not only needs to withstand extremely high pressure, but its effective operating flow rate range will also be greatly reduced, leading to significant measurement errors. Furthermore, when the liquid phase flow rate is small and the gas phase flow rate is large, the liquid phase flow generated by the separator often contains a lot of gas, causing the differential pressure measured by the orifice plate flowmeter to be too large, resulting in a flow rate measured by the flowmeter that is larger than the actual flow rate, thus introducing a certain measurement error.

[0008] For non-separate measurements, turbine flow meters, ultrasonic flow meters, and electromagnetic flow meters are commonly used flow meters. However, these devices are easily affected by external flow fields and are large in size, requiring a high level of space for installation and measurement. The image reconstruction effect in ERT technology is greatly affected by the flow pattern of the fluid. When the fluid flow is in a stable laminar or wave flow, the image reconstruction can relatively accurately reflect the medium distribution in the pipeline. In reality, the fluid often has a high velocity and the flow pattern is often a complex slug flow or annular flow, resulting in a larger error in the image reconstruction results.

[0009] Therefore, using the above two methods alone has disadvantages such as a small flow measurement range and poor generalization ability, which makes it impossible to adapt to the complex and ever-changing flow conditions in oilfields. Optimization of measurement results often requires complex data processing techniques, which makes the measurement both difficult and inaccurate. Summary of the Invention

[0010] To address the shortcomings of existing methods, such as limited flow measurement range and poor generalization ability when used alone, which make them unsuitable for the complex and ever-changing flow conditions in oilfields, and the need for complex data processing techniques to optimize measurement results, which makes measurement both difficult and inaccurate, this application provides a two-stage separation flow measurement system based on a small GLCC and ERT.

[0011] The embodiments of this application are implemented as follows:

[0012] This application provides a two-stage flow measurement system based on a small GLCC and ERT, including a single-stage separator, a two-stage separator, and a sensor:

[0013] The single-stage separator includes a separation chamber with a cylindrical structure. The inlet of the separation chamber is connected to the system inlet, the liquid outlet of the separation chamber is connected to the system outlet, and the gas outlet of the separation chamber is connected to the secondary separator. The secondary separator is based on a small GLCC design, and the gas outlet and liquid outlet of the secondary separator are respectively connected to the system outlet.

[0014] The sensors include a flow meter and an ERT.

[0015] In one possible implementation, the liquid outlet of the single-stage separator is connected to the system outlet via a primary liquid pipeline, the liquid outlet of the secondary separator is connected to the system outlet via a secondary liquid pipeline, and the gas outlet of the secondary separator is connected to the system outlet via a gas pipeline.

[0016] In one possible implementation, sensors are installed on both the primary liquid line and the secondary liquid line.

[0017] In one possible implementation, the system inlet is tilted.

[0018] In one possible implementation, the inlet of the separation chamber is an inclined, gradually decreasing circular shape.

[0019] In one possible implementation, the ERT corrects the flow meter results by calculating the void fraction of the gas and liquid.

[0020] In one possible implementation, the ERT corrects the flow meter results by calculating the gas-liquid void fraction, further comprising:

[0021] By using appropriate image reconstruction methods, the relationship between the conductivity and grayscale values ​​of the reconstructed image can be established to visualize the conductivity distribution within the pipe cross-section.

[0022] The measurement results are corrected by calculating the void fraction.

[0023] In one possible implementation, establishing the relationship between the conductivity and grayscale values ​​of the reconstructed image using an appropriate image reconstruction method to visualize the conductivity distribution within the pipe cross-section further includes:

[0024] The voltage measurement is normalized, with the measurement when the pipe is full of water as the high calibration. The normalization formula is:

[0025] V n =(V m -V w ) / V w ;

[0026] Where Vn is the standardized voltage measurement value, Vm is the measured voltage data, and Vw is the calibration data;

[0027] The relationship between normalized voltage measurement and conductivity distribution can be expressed as:

[0028] V n =-Sσ n ;

[0029] Where S is the normalized sensitivity matrix, σn is the standardized conductivity distribution, the negative sign indicates conductivity, and the direction of change of the measured value is opposite. The equivalent voltage Vx can be assumed to be inversely proportional to the conductivity σ, i.e., x.

[0030] V x ∝1 / σ x ;

[0031] The equivalent conductivity σm is used as the input to the image reconstruction algorithm to obtain the apparent conductivity distribution.

[0032] The V n =-Sσ n Vw is measured using water filling the pipe, and σw / σm can be described as:

[0033] σ w / σ m =V m / V w ;

[0034] Therefore, combining the formula for calculating liquid volumetric flow rate based on Bernoulli's equation and V x ∝1 / σ x It can be calculated as follows:

[0035] σ m =σ w / (V n +1);

[0036] The Linear Projection Method (LBP) is applied to ERT image reconstruction. The LBP algorithm is as follows:

[0037]

[0038] Where g is the gray level of the reconstructed image, which reflects the field conductivity distribution, and μ is a unit vector, i.e., μ = [1, 1, ..., 1]T.

[0039] In one possible implementation, the step of correcting the measurement results by calculating the void fraction further includes:

[0040] Divide the pipe cross-section into different elements, and let the number of effective meshes in the pipe be represented as "n";

[0041] The gray level of the “ith” grid is represented by “x”. If the grid is filled with air (GVF = 100%), then “x” equals 0; if the grid is filled with water (GVF = 0%), then “x” equals 1.

[0042] Assuming a linear relationship between the porosity of a single grid cell and its gray level, when GVF = 60%, the gray level is 0.4. To obtain the air content throughout the entire pipe, we only need to summarize the gray levels:

[0043]

[0044] The technical solution provided in this application can achieve at least the following beneficial effects:

[0045] The two-stage separation flow measurement system based on a small GLCC and ERT provided in this application combines the advantages of both separation and non-separation measurement methods, improves measurement accuracy, expands the measurement range, and optimizes the design of the GLCC, reducing its height without compromising separation efficiency.

[0046] Furthermore, addressing the limitations of traditional GLCC separators in terms of flow range, a filter cartridge structure was added to the separator to effectively reduce LCO phenomenon. A secondary separator was added at the gas phase outlet to effectively re-separate the liquid entrained in the gas phase after single-stage separation. The improved GLCC separator effectively improves the separation efficiency of gas and liquid and expands the flow separation range, especially in complex situations where the liquid phase flow rate is low and the gas phase flow rate is high. The fluid generated by the single-stage separator has an unstable slug flow and annular flow pattern in the main liquid path pipeline, while the fluid generated by the secondary separator has a stable laminar flow pattern in the main liquid path pipeline, which facilitates subsequent flow measurement correction using ERT technology. To address the problem of inflated measurement results caused by gas entrainment in the main liquid path, the measurement error of the flow meter is corrected by calculating GVF using the ERT integrated into the system.

[0047] In summary, this study combines GLCC and ERT to design a comprehensive and accurate two-phase flow measurement system, which improves the system's separation efficiency and enhances the accuracy and precision of flow measurement. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a schematic diagram of a columnar cyclone gas-liquid separator (GLCC).

[0050] Figure 2 This is a schematic diagram of a Venturi tube structure;

[0051] Figure 3 This is a schematic diagram of the ERT sensor structure;

[0052] Figure 4 This is a schematic diagram of the computational grid for a single-pole separator;

[0053] Figure 5 This is a schematic diagram of the velocity, phase, and pressure distribution in a GLCC system.

[0054] Figure 6 A schematic diagram of the velocity distribution at the two inlet cross sections;

[0055] Figure 7 This is a schematic diagram showing the radial distribution of axial and tangential velocities at two cross sections.

[0056] Figure 8 This is a schematic diagram of the experimental procedure and equipment;

[0057] Figure 9 (a) is a schematic diagram of the two-stage separation of gas-water two-phase flow with LCO curve in the system; Figure 9 (b) is a schematic diagram of single-stage separation of the LCO curve gas-water two-phase flow in the system;

[0058] Figure 10 This is a schematic diagram showing the flow pattern of fluid in the pipe after passing through the separator, as observed in the experiment.

[0059] Figure 11 A schematic diagram of the image reconstruction results of the main fluid path pipeline over time.

[0060] Figure 12 A schematic diagram showing the gas volume flow rate entering the main liquid path pipeline;

[0061] Figure 13 This is a schematic diagram showing the measurement results of a gas-liquid two-phase flow orifice plate flowmeter and the flow correction results based on ERT technology.

[0062] Figure 14 This is a schematic diagram of the structure of a two-stage GLCC separator system illustrated in an exemplary embodiment of this application. Detailed Implementation

[0063] To make the objectives, implementation methods and advantages of this application clearer, the exemplary implementation methods of this application will be clearly and completely described below with reference to the accompanying drawings of the exemplary embodiments of this application. Obviously, the exemplary embodiments described are only some embodiments of this application, and not all embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0064] It should be noted that the brief descriptions of terms in this application are only for the purpose of facilitating the understanding of the embodiments described below, and are not intended to limit the embodiments of this application. Unless otherwise stated, these terms should be understood in their ordinary and common meaning.

[0065] The terms “first,” “second,” “third,” etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar or related objects or entities, and do not necessarily imply a specific order or sequence. Unless otherwise stated, it should be understood that such terms can be used interchangeably where appropriate.

[0066] The terms “comprising” and “having”, and any variations thereof, are intended to cover but not exclude inclusion, for example, a product or device that includes a range of components is not necessarily limited to all of the components that are clearly listed, but may include other components that are not clearly listed or that are inherent to such product or device.

[0067] To facilitate the explanation of the technical solution of this application, some concepts involved in this application will be explained first below.

[0068] Multiphase flow is a common phenomenon in the petrochemical industry. "Phase" refers to different physical states or different physical properties or mechanical states of the same physical state. According to the different forms of matter, substances in nature can be divided into three phases: gas, liquid and solid. Generally, a fluid system with two or more substances and a clear interface is regarded as a multiphase flow. For example, gas and water are two different substances that are incompatible. When they are mixed together, a clear interface will appear. Therefore, at room temperature, gas-water mixture can be regarded as a type of gas-liquid two-phase flow - gas-water two-phase flow.

[0069] In the field of oil extraction, containerized separators are mainly used to process the multiphase flow of oil, gas, and water generated from the wellhead. The gas-liquid cylindrical cyclone separator (GLCC) is a highly efficient gas-liquid separator suitable for gas-liquid two-phase separation and metering in onshore oil and gas fields and offshore oil and gas platforms. Compared with containerized separators, GLCC has significant advantages such as simple structure, low cost, small size, and ease of installation and operation. This makes GLCC stand out among many separators and it is widely used in major oil fields, especially in offshore oil and gas platforms. Due to limited space, the footprint and weight of the equipment need to be considered. In this regard, GLCC has a clear advantage over traditional separators. Therefore, it has shown good application prospects in new offshore gas field projects and capacity expansion and renovation of existing platforms.

[0070] Figure 1 This is a schematic diagram of a columnar cyclone gas-liquid separator (GLCC).

[0071] The structure of GLCC is as follows Figure 1 As shown, its main body is a vertical pipe with a tangentially inclined gas-liquid multiphase flow inlet. When the multiphase flow enters the GLCC main body from the inlet under a certain pressure, a vortex is generated, causing the fluid to rotate at high speed inside the separator. This generates centrifugal force and buoyancy that are an order of magnitude higher than gravity on the fluid. Under the combined action of gravity, centrifugal force and buoyancy, the denser liquid phase is forced to flow radially towards the pipe wall and then flows along the pipe wall to the bottom of the separator for collection; the less dense gas phase rises to the top of the separator along the center of the vortex to form a central gas column, ultimately achieving the discharge of the gas phase from the top and the flow of the liquid phase from the bottom.

[0072] To better control the liquid level and pressure in the GLCC, the separator is equipped with a liquid control valve on the liquid section and a gas control valve on the gas section. The liquid level control valve ensures proper operation under different flow conditions and eliminates or reduces liquid leakage into the gas path and gas leakage into the liquid pipeline. When the GLCC is used for metering applications, the liquid and gas components are combined in the composite section to form a multiphase metering loop.

[0073] An orifice plate flow meter is a device for measuring fluid pressure difference. Its principle for measuring fluid flow rate is based on Bernoulli's law and the continuity equation. When gas or liquid flows in the flow meter, the dynamic pressure reaches its maximum value and the static pressure reaches its minimum value at the narrowest point of the pipe (throat). Thus, a pressure difference is generated before and after the throat of the pipe. The ratio of this pressure difference to the product of the average flow velocity of the fluid flowing through that point is the flow coefficient at that point. Therefore, the flow rate and velocity of the fluid can be calculated by measuring the pressure difference and the geometric parameters of the flow meter.

[0074] Figure 2This is a schematic diagram of a Venturi tube.

[0075] like Figure 2 As shown, the flow meter is a pipe that first contracts and then gradually expands. In the figure, T represents the temperature of the fluid in the pipe, P represents the dynamic pressure, represents the differential pressure before the Venturi tube, that is, the pressure difference in the contraction section, represents the differential pressure after the Venturi tube, that is, the pressure difference in the expansion section, D represents the pipe diameter, and d represents the pipe throat diameter.

[0076] Assuming the fluid is an incompressible ideal fluid with constant density, orifice plate flowmeters can be effectively used for transient measurements. Neglecting slip between the gas and liquid phases, the formula for calculating liquid volumetric flow rate based on Bernoulli's equation is as follows:

[0077]

[0078] In the formula, ε s Let be the fluid expansion coefficient, D be the orifice flowmeter discharge coefficient, β be the ratio of throat diameter to pipe diameter, r be the throat radius, and ρ be the flow rate. s This indicates the unidirectional flow density.

[0079] ERT provides a non-invasive method to visualize the conductivity distribution of a conductive medium by measuring the voltage change between electrode pairs. The principle is that when the distribution of the conductive medium in a pipe changes, the conductivity distribution changes, which in turn leads to a change in the potential distribution in the pipe.

[0080] Figure 3 This is a schematic diagram of the ERT sensor.

[0081] like Figure 3 As shown, an ERT with a traditional 8-electrode structure is used. The electrodes and shielding layer are uniformly attached to the outer wall of the pipe. Each electrode can be configured as an excitation or detection electrode. When a pair of adjacent electrodes (as excitation electrodes) is selected for current injection, the voltage between all other combinations of adjacent electrodes (as detection electrodes) is measured. Then the next pair of electrodes is selected (for example, after selecting 1 or 2 electrode pairs first, then 2 or 3 electrode pairs), and then all other electrodes are selected. The total number of measurements for the N-electrode ERT sensor is N(N-3) / 2. The 8-electrode system used in the experiment can produce 20 independent measurement results.

[0082] For ERT, the boundary condition is that the selected electrode pair is excited by current while the other electrode pairs are grounded. In the sensitive field region of ERT, the relationship between the conductivity distribution and the potential distribution can be expressed by the following Laplace equation:

[0083]

[0084] In the formula, σ(x,y) and φ(x,y) are the spatial conductivity distribution and potential distribution of the sensitive field region, respectively. Combining the boundary conditions and formula (2), it can be deduced that the voltage between adjacent electrodes is uniquely determined. Therefore, for a certain excitation current, the conductivity distribution of the measured region can be reflected by the voltage change on the measuring electrode pair.

[0085] Gas volume fraction (GVF) in gas-liquid multiphase flow is an important parameter for measuring fluid flow. It represents the proportion of gas volume to total volume in gas-liquid two-phase flow. The ERT system can visualize the flow between different phases in multiphase flow within a pipeline and monitor the distribution of various phase media. Its application in fluid porosity measurement is one of the current research hotspots.

[0086] The measurement of multiphase flow rate is crucial from oil extraction to transportation. In the petrochemical industry, there are two common methods for measuring multiphase flow rate: separation measurement and non-separation measurement.

[0087] Separation measurement involves feeding a multiphase flow into a gas-liquid separator to separate it into a gas phase flow and a liquid phase flow. Then, a single-phase flow meter is used to measure the flow velocity of each phase. In this process, one of the most critical pieces of equipment is the separator. The columnar cyclone gas-liquid separator (GLCC) has advantages such as small size, high separation efficiency, and ease of installation and operation, and is widely used in the petroleum industry.

[0088] Non-separation measurement is another method for directly measuring multiphase flows without separation. This method does not require a separation device. Turbine flow meters, ultrasonic flow meters, and electromagnetic flow meters are commonly used flow meters. In recent years, electro-tomography (ERT) technology has been widely used due to its advantages such as visualization, non-contact operation, immunity to flow field interference, and minimal environmental impact. ERT technology is a two-phase / multiphase flow measurement technology developed by combining computer application technology with modern detection technology. It can provide information about the flow characteristics of fluids, such as gas / solid, gas / liquid, and liquid / liquid two-phase flows. As an online measurement technology with advantages such as visualization, low cost, non-invasiveness, and robustness, ERT technology has become a recognized measurement technology in process applications.

[0089] In the separation measurement method, the two factors affecting the efficiency of GLCC are liquid carry-over (LCO) and gas carry-over (GCU). During the gas-liquid separation process, the phenomenon that the liquid follows the gas flow and leaves from the gas outlet at the top of the separator is called LCO, while the phenomenon that the gas follows the liquid and is transported to the bottom of the separator is called GCU. Due to the influence of LCO and GCU, in order to ensure complete separation of gas and liquid, the separation equipment not only needs to withstand extremely high pressure, but its effective working flow rate range will also be greatly reduced, resulting in a large measurement error. In addition, when the liquid phase flow rate is small and the gas phase flow rate is large, the liquid phase flow generated by the separator often contains a lot of gas, causing the differential pressure measured by the orifice plate flow meter to be too large, resulting in the flow rate measured by the flow meter being larger than the actual flow rate, which has a certain measurement error.

[0090] For non-separate measurements, turbine flow meters, ultrasonic flow meters, and electromagnetic flow meters are commonly used flow meters. However, these devices are easily affected by external flow fields and are large in size, requiring a high level of space for installation and measurement. The image reconstruction effect in ERT technology is greatly affected by the flow pattern of the fluid. When the fluid flow is in a stable laminar or wave flow, the image reconstruction can relatively accurately reflect the medium distribution in the pipeline. In reality, the fluid often has a high velocity and the flow pattern is often a complex slug flow or annular flow, resulting in a larger error in the image reconstruction results.

[0091] Therefore, using the above two methods alone has disadvantages such as a small flow measurement range and poor generalization ability, which makes it impossible to adapt to the complex and ever-changing flow conditions in oilfields. Optimization of measurement results often requires complex data processing techniques, which makes the measurement both difficult and inaccurate.

[0092] Based on this, this application provides a two-stage separation flow measurement system based on a small GLCC and ERT. The system combines the advantages of both separation and non-separation measurement methods, improving measurement accuracy and expanding the measurement range.

[0093] Next, the technical solutions of this application and how the technical solutions of this application solve the above-mentioned technical problems will be described in detail through embodiments and in conjunction with the accompanying drawings. The embodiments can be combined with each other. The same or similar concepts or processes may not be described again in some embodiments. Obviously, the described embodiments are some embodiments of the embodiments of this application, but not all embodiments.

[0094] Figure 14 This is a schematic diagram of the structure of a two-stage GLCC separator system illustrated in an exemplary embodiment of this application.

[0095] In one exemplary embodiment, such as Figure 14As shown, a two-stage separation flow measurement system based on a small GLCC and ERT is provided. In this embodiment, the system includes a single-stage separator, a two-stage separator, and a sensor.

[0096] The single-stage separator includes a separation chamber with a cylindrical structure. The inlet of the separation chamber is connected to the system inlet, the liquid outlet of the separation chamber is connected to the system outlet, and the gas outlet of the separation chamber is connected to the secondary separator. The secondary separator is based on a small GLCC design, and the gas outlet and liquid outlet of the secondary separator are respectively connected to the system outlet.

[0097] The sensors include a flow meter and an ERT.

[0098] In one possible implementation, such as Figure 14 As shown, the system mainly consists of a single-stage separator, a two-stage separator, and sensors. The single-stage separation component includes a separation chamber connected to the inlet. The separation chamber has a cylindrical structure, with one end connected to the gas outlet of the cylindrical chamber and the other end connected to the single-stage separation liquid outlet. The inlet is an angled, reduced-size circular design. The second separator is connected to the gas outlet of the first separator and is designed based on a small GLCC. The sensors include a flow meter and an ERT. The ERT corrects the flow meter results by calculating the void fraction of the gas and liquid.

[0099] In one possible implementation, the gas-water two-phase system is a complex system due to the existence of various flow patterns. The ERT system can visualize the conductivity distribution within the pipe cross-section by establishing the relationship between the conductivity and grayscale value of the reconstructed image through appropriate image reconstruction methods. This helps to understand the mixing of the gas-water mixture and corrects the measurement results by calculating the void fraction.

[0100] In image reconstruction, to reduce systematic errors caused by finite element mesh generation, measurement circuits, experimental environment, etc., voltage measurements should be normalized. Generally, the measurement when the pipe is full of water is used as the high calibration, and the normalization formula is:

[0101] V n =(V m -V w ) / V w (3)

[0102] Where Vn is the normalized voltage measurement value, Vm is the measured voltage data, and Vw is the calibration data, the relationship between the normalized voltage measurement and the conductivity distribution

[10] can be expressed as:

[0103] V n =-Sσ n (4)

[0104] Where S is the normalized sensitivity matrix, σn is the standardized conductivity distribution, the negative sign indicates conductivity, and the direction of change of the measured value is opposite. Theoretically, the equivalent voltage Vx can be assumed to be inversely proportional to the conductivity σ, i.e., x.

[0105] V x ∝1 / σ x (5)

[0106] In this work, the equivalent conductivity σm is used as input to the image reconstruction algorithm to obtain the apparent conductivity distribution, starting from equation (4) and Vw, which is measured with the pipe full of water. σw / σm can be described as:

[0107] σ w / σ m =V m / V w (6)

[0108] Therefore, combining equations (1) and (5), we can calculate: σ m

[0109] σ m =σ w / (V n +1) (7)

[0110] Linear projection (LBP) is characterized by its simplicity and accuracy, which meets the requirements for image reconstruction. Therefore, it is applied to ERT image reconstruction. The LBP algorithm is as follows:

[0111]

[0112] Where g is the gray level of the reconstructed image, which reflects the field conductivity distribution, and μ is a unit vector, i.e., μ = [1, 1, ..., 1]T.

[0113] To calculate the air content rate of each cross section based on the gray level of the pixels captured by the ERT system, the pipe cross section is divided into different units, and the number of effective grids in the pipe is represented as "n", and the gray level of the "ith" grid is represented as "x". From the normalization in formula (5), if the grid is full of air (GVF = 100%), then "x" is equal to 0; if the grid is full of water (GVF = 0%), then "x" is equal to 1. Assuming that there is a linear relationship between the void content of a single grid and the gray level, for example, when GVF = 60%, the gray level is 0.4. To obtain the air content in the entire pipe, it is only necessary to summarize the gray levels:

[0114]

[0115] Work process:

[0116] The gas-liquid mixture first enters the system through an inclined inlet pipe, where it forms a gas-liquid stratified flow. The inclined inlet pipe connects to a vertical cylinder of the separation chamber, which has a tangential conical nozzle at the connection point. The conical nozzle accelerates the mixed liquid, and the accelerated gas-liquid mixture forms two swirling flows in the vertical cylinder of the separation chamber: a gas phase and a liquid phase. Under the combined action of centrifugal force and gravity, the liquid droplets in the gas phase are pushed against the side wall and eventually flow out of the liquid outlet. At the same time, the gas phase rotates and converges towards the central axis, forming a gas core. The gas core is then discharged from the gas outlet through a cylindrical structure, and the liquid it carries passes through a second separator for another separation.

[0117] Figure 4 This is a schematic diagram of the computational grid for a single-pole separator. Figure 5 This is a schematic diagram of the velocity, phase, and pressure distribution in a GLCC system. Figure 6 This is a schematic diagram of the velocity distribution at the two inlet cross sections. Figure 7 This is a schematic diagram showing the radial distribution of axial and tangential velocities at two cross-sections. Figure 8 This is a schematic diagram of the experimental procedure and equipment. Figure 9 (a) is a schematic diagram of the two-stage separation of gas-water two-phase flow with LCO curve in the system; Figure 9 (b) is a schematic diagram of single-stage separation of the gas-water two-phase flow in the LCO curve of the system. Figure 10 This is a schematic diagram showing the flow pattern of fluid in the pipe after passing through the separator, as observed in the experiment. Figure 11 Schematic diagram of image reconstruction results of the main fluid path pipeline over time. Figure 12 This is a schematic diagram of the gas volume flow rate entering the main liquid path pipeline. Figure 13 This is a schematic diagram showing the measurement results of the gas-liquid two-phase flow orifice plate flowmeter and the flow correction results based on ERT technology.

[0118] To verify this application, the gas-liquid two-phase flow field was simulated using the Euler multiphase model. The first phase represents the gas and the second phase represents the liquid. The diameter of the discrete liquid was set to 0.1 mm. The multiphase flow model adopted the multiphase VOF solution algorithm, which facilitated the geometric reconstruction of the two-phase interface. The simulation assumed that the gas was incompressible and isothermal.

[0119] The Euler model establishes separate conservation equations for each stage; therefore, the continuous phase equation for the q-th phase is as follows:

[0120]

[0121] Where ρ is the phase density, is The velocity vector is a volume fraction. It is the mass transfer from phase p to phase q, and the mass transfer from phase q to phase p. It is the source term, S. q

[0122] According to Newton's second law, the momentum change formula for the q-th phase in the control volume is as follows:

[0123]

[0124] In this equation, the first three terms on the right-hand side are pressure, shear, and gravity, while the fourth term is the momentum change caused by interphase mass transfer. It is an interphase interaction force that depends on friction, pressure, etc. The first term is the velocity between phases; when mass is transferred from one phase to another, the velocity of the transferring phase is taken. The fifth term is the applied interphase force. The sum of the following forces is 1: external volume force, lifting force, wall lubrication force, virtual mass force, and turbulent dissipation force.

[0125] As a centrifugal separator, the GLCC exhibits a complex three-dimensional turbulent field involving both gas and liquid phases. Typically, two turbulence models are used to simulate swirling flows: the RNG k-ε model and the RSM model. The RSM model is more suitable for robust swirling flows, while the RNG k-ε model is more suitable for milder swirling flows. wg When characterizing the swirl intensity of a GLCC, the geometric swirl intensity number () is used to describe the swirl flow field at the inlet convergence location, which can be expressed as an equation:

[0126]

[0127] In the formula, D is the cylinder diameter GLCC (mm), β is the inlet inclination angle (°), and r is the minimum radius of the nozzle (mm). In this study, since the swirl intensity of the geometric model is 4.17, the RNG k-ε model is more suitable.

[0128] A. CFD Simulation Geometry

[0129] This paper presents a numerical simulation of a single-stage separator with a cylindrical structure. To ensure the feasibility and accuracy of the simulation, the geometry needs to be appropriately simplified. The separator cylinder has an elevation of 0.5m and a diameter of 0.11m. Figure 4 The computational grid for the single-pole separator is shown.

[0130] B. Simulation conditions and parameter settings

[0131] The simulation uses a transient model with an accuracy of 10⁻³ and a time step of 0.0001, with a maximum of 100 iterations. The entire two-phase flow field adopts a fast flow scheme, and geometric modeling is performed using an unstructured mesh generation method with polyhedra. After mesh independence verification, a mesh consisting of 951,125 elements is selected as the final mesh scheme. Velocity boundaries are used at the inlet, and pressure boundaries are used at the outlet. The liquid phase outlet gauge pressure is greater than that at the gas phase outlet, and the rest of the device is enclosed by walls.

[0132] C. Simulation Verification

[0133] To evaluate the simulation accuracy, we compared the pressure drop obtained from the simulation data with the experimental pressure drop under the conditions described in the table. 2. Pressure drop is defined as the pressure difference between the inlet and the gas outlet. The experimental results show that the simulation results are in good agreement with the experimental results. It is worth noting that the viscosity and density of the oil used in the numerical simulation are different from those in the experimental setup. The numerical simulation uses engine oil, while the experiment uses white oil. Therefore, due to the change in oil properties, the difference in pressure drop is more obvious than that of water. However, the pressure drop in the simulation and the experiment show the same trend. Therefore, the simulation method described above seems to be applicable to simulating gas-liquid two-phase flow in GLCC.

[0134] Table 1 Pressure Drop (Pa)

[0135]

[0136] Displayed in the format of "Gas Flow Rate - Liquid Flow Rate", with units of m³ / h.

[0137] D. Results and Discussion

[0138] 4.1 Flow Field Characteristics

[0139] To improve our understanding of the GLCC separation process, we first conducted a flow field analysis based on CFD simulation.

[0140] Figure 5 The distributions of three key parameters in the GLCC system are described, where (a) represents the velocity distribution, (b) represents the phase-inclusive velocity distribution, and (c) represents the pressure distribution. When the two-phase mixed fluid enters through the inlet and passes through the inclined, decreasing inlet, the reduced channel inclination leads to a significant increase in velocity, resulting in downward swirling flow along the wall, such as... Figure 5 (a). As shown Figure 5 (b) shows the swirling flow formed along the wall, exhibiting clear stratification; the upper blue area represents the gas phase, while the lower red area corresponds to the liquid phase within the inlet. Furthermore... Figure 5 (c) shows the relative pressure distribution in the GLCC, indicating that the inlet pressure reaches its maximum value and gradually decreases along the wall eddies, where pressure is converted into power.

[0141] Figure 6 Radial distribution of velocity amplitude on the two cross sections: (P1) x = 37 mm; (P2) x = 165 mm. (x = 0 at the rightmost end of the inlet, air flow rate is 75-2 m3 / h)

[0142] Figure 6 The velocity distributions at two inlet cross sections are shown: P1, the non-contracting cross section, and P2, the inclined inlet cross section. Figure 6 (a) shows the velocity distribution across the cross section, indicating that the acceleration at the inclined inlet gradually increases from top to bottom. Figure 6 (b) shows the lateral distribution of two cross sections. Initially, a uniform inlet is shown. Under the influence of the gas, the liquid velocity increases, resulting in the gas and liquid velocities being close at the same cross section, but the liquid velocity is less than the gas velocity. The lateral display of the inclined inlet is not completely symmetrical, with higher velocities at the non-tangential end.

[0143] Within a GLCC, the interaction of resistance, centrifugal force on the membrane or droplets, and gravity together determine the gas-liquid flow and separation process. When the centrifugal force exceeds the radial resistance, it pushes the liquid phase toward the wall. On the other hand, if the axial resistance exceeds gravity, the liquid phase will eventually exit through the upper gas outlet. Therefore, the tangential and axial velocities of the gas are key factors affecting the gas-liquid phase separation within a GLCC.

[0144] (P3) z = 175 mm; (P4) z = 400 mm, (cylindrical) bottom z = 0, air-water flow rate is 75-2 m3 / h)

[0145] Figure 7 The diagram shows the tangential and axial velocities during gas-water two-phase separation at a flow rate of 75-2 m³ / h. The axial velocity of the gas exceeds the tangential velocity within the same cross-section. In P3, the flow field exhibits a clockwise downward eccentric swirling flow. In P4, the axial symmetry improves, and both axial and tangential velocities decrease axially. The increase in axial velocity leads to the gradual rise or carry-over of droplets or liquid films, while the increase in tangential velocity promotes the rotation of the liquid film. P3 is located below the inlet, while P4 is located above the inlet. In P3, both axial and tangential velocities are high. Driven by the high axial velocity, the film rises rapidly, and the rotation caused by the increased tangential velocity leads to film thinning. Conversely, in P4, the lower axial velocity results in a slower film rise. The decrease in tangential velocity suggests that P4, compared to P3, is more likely to form a thicker liquid film.

[0146] Therefore, the interior of a GLCC can be roughly divided into three regions: the inlet acceleration region, the swirling region (below the barrel inlet), and the escape region (above the barrel inlet).

[0147] (1) Inlet acceleration region: The gas-liquid mixture is accelerated in this region, forming a high-speed fluid.

[0148] (2) Swirl region: Located below the barrel-shaped inlet, it has high axial and radial velocities. The liquid film rotates and rises under the combined action of gas lift and gravity.

[0149] (3) Escape zone: This zone is located above the cylinder inlet. The axial and tangential velocities are low, and liquid film accumulation is likely to occur. Under a sufficiently large gas flow rate, the liquid film can be carried into the cylinder by the gas, forming a short-circuit flow.

[0150] Experimental setup and overall process

[0151] Table 2. Experimental operating conditions

[0152]

[0153]

[0154] Figure 8 The experimental setup of the multiphase flow testing laboratory is shown: in a test loop with a diameter of 50 mm, air and tap water are used as the gas phase and water phase, respectively, to simulate the pipeline of a single oil well. In the separation tank, if the liquid phase flow velocity is maintained below 20 m / s², the flow is controlled. 3 At a flow rate of / h, the gas phase velocity is maintained at 150m. 3 For flow rates below / h, the experimental operating conditions are shown in Table 2, and the experimental procedure for multiphase flow is as follows:

[0155] 1) First, start the air compressor to establish a certain amount of static pressure in the entire experimental system;

[0156] 2) Next, the air stored in the storage tank is delivered to the pipeline of the experimental apparatus by a circulating compressor pump, while water is delivered to the pipeline by a centrifugal pump.

[0157] 3) Valves and standard flow meters installed on the pipeline control and record the reference volumetric flow rates of the two single-phase fluids respectively;

[0158] 4) After air and water are mixed in the pipe, the resulting gas-liquid two-phase flow is separated into a single-phase flow after passing through the GLCC separator. The separated fluids then flow through three horizontal test pipes equipped with glass windows and multiple sensors.

[0159] 5) Finally, the fluid flowing out of the horizontal test pipe is mixed and recycled into the gas-water separator, where the mixed flow is statically separated into single-phase flow for recycling.

[0160] Experimental Results Analysis

[0161] A. Comparison of experimental results

[0162] Figure 9 This demonstrates the LCO phenomenon observed in the experiment. Figure 9 In (a), the LCO curve for the two-stage separation of gas and water phases shows a higher number of operating points, indicating superior separation performance. Figure 9 (b) shows the LCO curves for single-stage separation of the gas and aqueous phases, comparing the single-stage separation system with a two-stage separation system. Figure 9 (b) It can be seen that the LCO curve of the two-stage separation system has shifted significantly upward, which confirms that the addition of the two-stage separator significantly improves the LCO phenomenon of the entire measurement system.

[0163] Generally speaking, current flow velocity measurement systems used for gas-liquid two-phase separation are well-suited for liquid flow velocities ranging from 0.5 to 1 m / s. 3 For small oilfields with flow rates between 1 / h, higher liquid flow rates can be adjusted to lower gas flow rates.

[0164] Figure 10 The flow pattern of a two-stage separation system is demonstrated. The LCO separation curves are distinguished using images captured by a high-speed camera. After the gas phase passes through the first-stage separator, the gas phase flow is mainly annular in the pipeline, and then... Figure 10 As shown in (a) and (b), after passing through the second-stage separator, the gas phase in the pipeline mostly tends to be laminar flow, while the liquid phase, after passing through the first-stage separator, mainly exhibits stratified flow or is filled with liquid, typically only when the liquid flow velocity is 0.5 m / s. 3 Stratified flow only occurs when the flow rate is / h. After passing through a two-stage separation system, the flow state in the pipeline has greater stability, making it easier to measure the flow velocity.

[0165] B. Analysis of Image Reconstruction Results Based on ERT Technology

[0166] When the water content is high, the image reconstruction results using ERT technology can well reflect the distribution of gas-water two-phase flow in the pipeline and provide a qualitative understanding of the gas-water mixing under different flow velocities and flow ratios. Figure 11 The image reconstruction results of the gas-water two-phase flow in the main liquid path pipeline under different flow conditions are shown. In the figure, blue represents water and red represents gas. Figure 12 The volumetric flow rate of gas entering the liquid pipeline is displayed under different flow conditions.

[0167] When the water flow rate is low (Qw≤1.0m³h⁻¹), as the gas flow rate increases, the GLCC separator cannot completely separate the gas and water phases, causing some gas to enter the main liquid path. Due to gravity, water concentrates at the bottom of the pipe, while air is located at the top. As the gas flow rate increases, the volumetric flow rate of gas entering the liquid path also increases. For a single-stage separation system, when the liquid flow rate is 0.5m³h⁻¹, the maximum gas volumetric flow rate entering the main liquid path can reach 15.58m³h⁻¹, and when the liquid flow rate is 1.0m³h⁻¹, the maximum gas volumetric flow rate can reach 7.68m³h⁻¹. For a two-stage separation system, when the liquid flow rate is 0.5m³h⁻¹, the gas volumetric flow rate entering the main liquid path can reach 9.65m³h⁻¹, and when the liquid flow rate is 1.0m³h⁻¹, the gas volumetric flow rate can reach 3.42m³h⁻¹.

[0168] Figure 11 (a) shows the image reconstruction results of the two-stage separation system. Figure 11 (b) shows the image reconstruction results of the single-stage separation system. Comparing the image reconstruction results of the single-stage separator and the two-stage separator, it can be found that at a lower liquid flow rate, as the gas flow rate increases, the former has significantly more gas entering the main liquid channel than the latter. The maximum GVF of the former reaches 44.1%, while that of the latter is 29.3%. This indicates that the separation performance of the two-stage separation system is better than that of the single-stage separation system. In addition, the gas and water in the pipeline are clearly separated and do not mix with each other. Therefore, the accuracy of calculating GVF using the image reconstruction method is higher.

[0169] C. Measurement Error Analysis

[0170] The flow rate measured by the orifice plate flow meter, the flow rate corrected based on ERT technology, and the reference flow rate input to the GLCC separator were compared. Figure 13 The left side shows a comparison between the flow velocity measured experimentally using an orifice plate flow meter and a reference flow velocity. The dashed line in the figure represents the error limit. Compared with the reference data, the data obtained by the orifice plate flow meter shows good consistency. Figure 13 The right side shows the relationship between relative error and reference flow rate. Before correction, the positive error was larger when the liquid flow rate was lower and the gas flow rate was higher, and the negative error was larger when the liquid flow rate was higher and the gas flow rate was lower. After correction, the overall error of the data remained in the range of 5% to 10%, the distribution was more uniform, and the negative error was larger, which indirectly reflects the LCO phenomenon.

[0171] Based on the flow pattern analysis observed through the glass window in 3.2.5.B, under low flow conditions affected by gas (water flow rate less than 1.0 m3 / h), the pipeline exhibits a stratified flow pattern. Due to the gas entrainment in the liquid phase, this leads to an overestimation of the flow meter reading. Conversely, under high flow conditions (water flow rate greater than 2.5 m3 / h), some liquid enters the gas pipeline, causing the measured liquid value to be significantly lower than the actual value.

[0172] As can be seen, this application reduces measurement errors and expands the applicable operating conditions for flow measurement by combining GLCC and ERT. While developing a novel two-stage separation device to improve separation efficiency, it utilizes the image reconstruction function of ERT to detect the percentage of liquid volume in the pipeline to correct flow measurement errors. The main effects of this technology are as follows:

[0173] (1) Compared with single-stage separators, two-stage separators have a larger adjustable operating range. In addition, compared with the obvious slug flow in the main liquid path generated by single-stage separators, the multiphase flow generated by two-stage separators is a more stable laminar flow or full liquid flow, which makes flow measurement easier.

[0174] (2) The phase content of the liquid pipeline section is calculated using the image reconstruction function of ERT, thereby correcting the error of the flow measurement results when the liquid flow rate is small but the gas flow rate is large. The corrected error is controlled within ±10%, which meets the needs of industrial field measurement.

[0175] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0176] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A two-stage separation flow measurement system based on a small GLCC and ERT, characterized in that, Includes single-stage separators, two-stage separators, and sensors: The single-stage separator includes a separation chamber with a cylindrical structure. The inlet of the separation chamber is connected to the system inlet, the liquid outlet of the separation chamber is connected to the system outlet, and the gas outlet of the separation chamber is connected to the secondary separator. The secondary separator is based on a small GLCC design, and the gas outlet and liquid outlet of the secondary separator are respectively connected to the system outlet. The sensors include a flow meter and an ERT. The entrance to the separation chamber is an inclined, gradually decreasing circular shape; The ERT corrects the flow meter results by calculating the void fraction of the gas and liquid. The ERT corrects the flow meter results by calculating the gas-liquid void fraction, and further includes: By using appropriate image reconstruction methods, the relationship between the conductivity and grayscale values ​​of the reconstructed image can be established to visualize the conductivity distribution within the pipe cross-section. The measurement results are corrected by calculating the void fraction.

2. The two-stage separation flow measurement system based on a small GLCC and ERT as described in claim 1, characterized in that, The liquid outlet of the single-stage separator is connected to the system outlet through a primary liquid pipeline, the liquid outlet of the secondary separator is connected to the system outlet through a secondary liquid pipeline, and the gas outlet of the secondary separator is connected to the system outlet through a gas pipeline.

3. The two-stage separation flow measurement system based on a small GLCC and ERT as described in claim 2, characterized in that, Sensors are installed on both the primary liquid pipeline and the secondary liquid pipeline.

4. The two-stage separation flow measurement system based on a small GLCC and ERT as described in claim 1, characterized in that, The system entrance is set at an angle.

5. The two-stage separation flow measurement system based on a small GLCC and ERT as described in claim 1, characterized in that, The step of establishing the relationship between the conductivity and grayscale value of the reconstructed image using an appropriate image reconstruction method to visualize the conductivity distribution within the pipe cross-section further includes: The voltage measurement is normalized, with the measurement when the pipe is full of water as the high calibration. The normalization formula is: ; Among them, V n It is a standardized voltage measurement value, V m These are the measured voltage data, and V w It is calibration data; The relationship between normalized voltage measurement and conductivity distribution is expressed as follows: ; Where S is the normalized sensitivity matrix, σ n It is a standardized conductivity distribution, with the negative sign indicating conductivity, while the measured values ​​change in the opposite direction. Assuming an equivalent voltage V... x x is inversely proportional to the conductivity σ, that is: ; Wherein, the equivalent conductivity is σ m As input to the image reconstruction algorithm, the apparent conductivity distribution is obtained; The and V w σ is measured using the full volume of water in the pipe. w / σ m Described as: ; Therefore, combining the formula for calculating liquid volumetric flow rate based on Bernoulli's equation and The calculation is as follows: ; The Linear Projection Method (LBP) is applied to ERT image reconstruction. The LBP algorithm is as follows: ; Where g is the gray level of the reconstructed image, which reflects the field conductivity distribution, and μ is a unit vector, i.e., μ = [1, 1,···,1]T.

6. The two-stage separation flow measurement system based on a small GLCC and ERT as described in claim 5, characterized in that, The method of correcting the measurement results by calculating the void fraction further includes: Divide the pipe cross-section into different elements, and let the number of effective meshes in the pipe be represented as "n"; The gray level of the "ith" grid is represented by "x". If the grid is filled with air, then GVF=100%, and "x" equals 0; if the grid is filled with water, then GVF=0%, and "x" equals 1. Assuming a linear relationship between the porosity of a single grid cell and its gray level, when GVF = 60%, the gray level is 0.

4. By summarizing the gray levels, the air content in the entire pipe can be obtained. 。