Experimental determination method for debris settling velocity of irregular-shaped bridge plug

Abstract

The invention belongs to the technical field of oil and gas field development, and particularly relates to an experimental determination method for the debris settling velocity of an irregular-shaped bridge plug. The method comprises the following steps: collecting bridge plug scraps flowback on site, classifying and testing the volume and density of the bridge plug scraps according to the material of the bridge plug scraps, measuring the shape parameters of the bridge plug scraps by using an image processing method, combining five bridge plug scrap shape characterization parameters of roundness, aspect ratio, radius ratio, sphericity and equivalent diameter, and taking a correlation coefficient R2 as an evaluation index, the correlation among the shape parameters of the bridge plug chippings is compared, the aspect ratio, the radius ratio and the roundness are determined to serve as main parameter characteristic parameters of follow-up calculation, the settling speed of the bridge plug chippings is measured through a static settling experiment, and a drag coefficient model suitable for the bridge plug chippings in the irregular shape is established on the basis of a spherical drag coefficient model. The model is fitted by using the measured settling velocity data, and theoretical support is provided for the design of the debris flowback flow parameters of the bridge plug of the shale gas horizontal well.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas field development, and in particular relates to an experimental determination method for the sedimentation velocity of irregular-shaped bridge plug debris. Background Art

[0002] The efficient development of shale gas reservoirs relies on horizontal well volume fracturing technology. After segmented bridge plug perforation and sand fracturing, continuous tubing is used to drill and sweep the wellbore bridge plug to establish a complete reservoir gas flow channel. However, the horizontal section of a shale gas horizontal well is generally more than 1,500 meters long, and bridge plug debris is prone to deposition, remaining in the wellbore and affecting the later production of the gas well. Therefore, in the early stage of gas well production, high-speed return fluid is used to remove the residual bridge plug debris in the wellbore to ensure the smooth flow of the gas wellbore and the safe operation of ground equipment, which has become an important measure for the efficient and stable production of shale gas wells.

[0003] Accurate calculation of the flow velocity of debris carrying bridge plugs is the key to the design of flowback flow parameters of debris carrying bridge plugs in shale gas horizontal wells. The core is the calculation of the settling velocity of bridge plug debris based on the drag force model. The existing drag force calculation model is mainly aimed at the movement research of nearly spherical regular shaped particles. For example, through a large amount of experimental test data, the influencing factors of particle settling velocity are clarified, the drag force coefficient is continuously improved, and the particle settling velocity is calculated. In order to improve the calculation accuracy of the flow velocity of debris carrying bridge plugs and meet the needs of field applications, it is still necessary to establish a drag force coefficient model suitable for irregular shaped bridge plug debris on site. The invention patent (CN116578813A) uses the deviation between the Reynolds number of irregular particles and the initial Reynolds number to calculate their sedimentation velocity in Newtonian fluids, but this method only comprehensively considers the shape factors of the long, medium and short axes and volume composition of the particles; the invention patent (CN114166728A) calculates the drag coefficients of different non-spherical particles in real time to fit the drag coefficient model of non-spherical particles in stable motion, but the particle characteristic parameters considered in the model include sphericity, flatness, Reynolds number, and circularity, and fails to compare and screen the selected characteristic parameters, which is inefficient when processing a large amount of particle data; the invention patent (CN104089859A) uses the measured sedimentation velocity to obtain a more accurate effective sedimentation particle size through iterative calculation, but its iterative process is cumbersome and has a high dependence on the initial value.

[0004] To this end, the present invention provides an experimental determination method for the settling velocity of irregular-shaped bridge plug debris. By collecting basic data of bridge plug debris, analyzing and calculating its characteristic parameters, targeted bridge plug debris settling experiments are carried out to test the settling velocity of bridge plug debris. Based on the drag force calculation method of spherical particles, the aspect ratio, radius ratio, roundness, sphericity and equivalent diameter of the bridge plug debris are considered, representative characteristic parameters are determined through correlation comparison, experimental test data are introduced, and a bridge plug debris drag coefficient model is established, and then the settling velocity applicable to irregular-shaped bridge plug debris is calculated, providing theoretical support for the design of flowback flow parameters of bridge plug debris in shale gas horizontal wells. Summary of the invention

[0005] The present invention provides an experimental determination method for the settling velocity of irregular-shaped bridge plug debris. The method collects on-site flowback bridge plug debris, statistically analyzes the material, density and composition ratio of the bridge plug debris, calculates the aspect ratio, radius ratio, roundness, sphericity and equivalent diameter of the bridge plug debris, and performs characteristic analysis to determine representative characteristic parameters. A targeted static settling experiment is carried out to calculate the settling velocity. A drag coefficient model suitable for irregular-shaped bridge plug debris is established based on a spherical drag coefficient model. The model is fitted using the measured settling velocity data, thereby providing theoretical support for the design of flowback flow parameters for bridge plug debris in shale gas horizontal wells.

[0006] To achieve the above-mentioned purpose, the specific steps of the experimental determination method of the settling velocity of irregular-shaped bridge plug debris described in the present invention are as follows: Step 1: Classification of bridge plug debris and measurement of some parameters: Collect the bridge plug debris returned from the site and classify them into rubber, cement, black stone, white stone and plastic according to their materials. Measure the volume and density of each type of bridge plug debris and calculate their composition ratio. Among them, the method for measuring the volume of bridge plug debris is the drainage method. The required tools include a large and a small beaker and an electronic scale. The specific operation process is: fill the beaker with water, then immerse the bridge plug debris of a certain material in the beaker, and measure the volume of the discharged water.

[0007] Step 2: Use image processing method to measure the shape parameters of bridge plug debris: Place the bridge plug debris neatly and take photos, and use noise processing, image binarization, and boundary recognition methods to obtain the shape parameters of the bridge plug debris; The tools required for the image processing method include A4 paper, camera, and image processing program. The specific operation process is as follows: Arrange the bridge plug debris in a matrix from large to small on A4 paper with a spacing of 2 to 3 cm; To obtain images, use a bracket to make the camera parallel to the shooting plane. To reduce the interference of shadows on photo processing, use parallel light in a dark space to take three views of the bridge plug debris. Noise processing: import the captured photos into the program, select the threshold value according to the color distribution characteristics of the read image, enhance the image contrast, highlight the small noise points, and use color replacement to remove the noise points; Image binarization, constantly adjusting the binarization threshold to convert color images into black and white images to facilitate boundary recognition; Boundary recognition: select five commonly used boundary detection methods, namely Roberts, Sobel, Prewitt, Log, and Canny. Choose different boundary detection methods for different photos. Characteristic parameter calculation, identifying interrelated data points, calculating the centroid position, area and perimeter of the bridge plug debris in different views and outputting them to Excel tables; Different types of bridge plug debris have their own shape characteristics. Therefore, the physical parameters of roundness, aspect ratio, radius ratio, sphericity and equivalent diameter are selected to quantitatively characterize the differences in the shapes of bridge plug debris. The specific formula is: (1); (2); (3); (4); (5); In the formula, R r is the roundness of the bridge plug debris, dimensionless; S is the plane perimeter of the bridge plug debris, m; A is the plane area of ​​the bridge plug debris, m 2 ; R d is the aspect ratio of the bridge plug debris, dimensionless; d 1 is the major axis of the ellipse equivalent to the bridge plug debris, m; d 2 is the minor axis of the ellipse equivalent to the bridge plug debris, m; R z is the radius ratio of the bridge plug debris, dimensionless; r 1 is the maximum distance from the center point of the bridge plug debris to the boundary, m; r 2 is the minimum distance from the center point of the bridge plug debris to the boundary, m; is the sphericity, dimensionless; d eq is the equivalent diameter, m; V is the volume of bridge plug debris, m 3 ; The present invention takes into account the parameter range and quantity of bridge plug debris. To reduce the additional influence of the physical properties of bridge plug debris on each other during the flow process, the absolute difference between the radius ratio, aspect ratio, roundness, sphericity and equivalent diameter is within 10%.

[0008] Step 3: Determine the characteristic parameters: Combine the five bridge plug debris shape characterization parameters of roundness, aspect ratio, radius ratio, sphericity and equivalent diameter, and use the correlation coefficient R 2 As evaluation indexes, the correlation between the shape parameters of the bridge plug debris tested in step 2 was compared, and the roundness, aspect ratio, and radius ratio were selected as the main parameters for subsequent calculations; The five characteristic parameters are matched with each other, the relationship curve between the characteristic parameters is drawn, and the linear relationship curve between the two is fitted. R 2 Characterizes the correlation between two characteristic parameters, R 2 The larger it is, the greater the correlation between the two feature parameters; Comparative verification shows that there is a strong correlation between roundness and sphericity, equivalent diameter and radius ratio, and aspect ratio. Representative roundness, aspect ratio, and radius ratio are selected as the main parameters for subsequent calculations.

[0009] Step 4: Experimentally measure the settling velocity of the bridge plug debris: Conduct a static settling experiment in water on the selected bridge plug debris to measure the settling velocity of the bridge plug debris; The tools used in the static sedimentation experiment include transparent glass tubes, high-speed cameras, whiteboards, and computers. The specific operation process is as follows: A simple sedimentation experimental device was built, and a transparent glass tube with an inner diameter of 15 cm and a length of 2 m was selected. A high-speed camera (960 frames / second) was used for shooting during the experiment. After the experiment was completed, the experimental photos were extracted on the computer to calculate the sedimentation velocity. To facilitate the observation and calculation of the sedimentation velocity, a ruler was placed next to the plexiglass to understand the position of the bridge plug debris in the pipe column. In order for the camera to clearly capture the stable sedimentation process, the distance between the camera and the plexiglass tube was adjusted before the experiment. Due to the irregular shape of the bridge plug debris and the large differences between different bridge plug debris, the sedimentation velocities of different bridge plug debris were accurately obtained, and the sedimentation acceleration distance was observed through a test experiment.

[0010] Step 5: Establish a drag coefficient model for bridge plug debris: Based on the spherical drag coefficient model, the shape of the bridge plug debris is divided into near-spherical and non-spherical shapes by using the ratio of the middle axis to the short axis of the bridge plug debris, and a drag coefficient model suitable for irregular-shaped bridge plug debris is established. The settling velocity data measured in step 4 is used to fit the parameters to be fitted in the model; During the settlement of bridge plug debris, the most important force acting on the bridge plug debris is the force opposite to the movement direction of the bridge plug debris, that is, the drag force.F D , defined as: (6); In the formula, r f is the fluid density, kg / m 3 ; C D is the drag coefficient of the bridge plug debris, dimensionless; A f is the reference area related to the size of bridge plug debris, m 2 ; v p is the speed of bridge plug debris, m / s; v f is the fluid velocity, m / s; is the vector form of the bridge plug debris velocity, m / s; is the vector form of fluid velocity, m / s; The fluid in the static experiment is the static fluid in the tube. v f = 0m / s, derive the drag coefficient C D The formula is as follows: (7); (8); In the formula, g is the acceleration due to gravity, m 2 / s; L s is the characteristic length considering the rolling condition, m; r p is the density of bridge plug debris, kg / m 3 ; r f is the fluid density, kg / m 3 ; d m is the center axis of the bridge plug debris, m; C 1 is the coefficient to be fitted, dimensionless; A is the area of ​​bridge plug debris, m 2 ; d s is the minor axis of the bridge plug debris, m; d l is the long axis of the bridge plug debris, m.

[0011] Irregular shaped bridge plug debris is classified and calculated by shape: When the ratio of the minor axis to the median axis Assuming that the bridge plug debris is nearly spherical, the drag coefficient is related to density and viscosity. Combined with formula (7), the drag coefficient is used C D and the dimensionless shape constant N In the form of multiplication, the sedimentation velocity can be calculated and the simplified formula is as follows: (9); (10); In the formula, m f is the liquid viscosity, Pa·s; N is the shape factor constant, dimensionless; s is the surface tension of water, N / m; when When the bridge plug debris is considered to be non-spherical, the roundness, aspect ratio, and radius ratio of the bridge plug debris need to be considered comprehensively, and the following formula is used for fitting: (11); (12); In the formula, k N is the roughness coefficient of the sphere, dimensionless; ψ is the bridge plug debris shape factor, dimensionless; C 2 is the coefficient to be fitted, dimensionless. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A technical roadmap for experimental determination of the settling velocity of debris from an irregularly shaped bridge plug. DETAILED DESCRIPTION

[0013] In order to make the purpose and calculation process of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings to highlight the advantages of the present invention.

[0014] Example 1: Figure 1 As shown, Figure 1 The present invention provides a method for experimentally determining the settling velocity of irregular-shaped bridge plug debris, by collecting on-site backflow bridge plug debris, statistically analyzing the material, density and composition ratio of the bridge plug debris, calculating the aspect ratio, radius ratio, roundness, sphericity and equivalent diameter of the bridge plug debris and performing characteristic analysis, determining representative characteristic parameters, conducting targeted static settling experiments, calculating the settling velocity, establishing a drag coefficient model suitable for irregular-shaped bridge plug debris based on the spherical drag coefficient model, fitting the model using the measured settling velocity data, and providing theoretical support for the design of flow parameters for backflow of bridge plug debris in shale gas horizontal wells.

[0015] To achieve the above-mentioned purpose, the specific steps of the experimental determination method of the settling velocity of irregular-shaped bridge plug debris described in the present invention are as follows: Step 1: Classification of bridge plug debris and measurement of some parameters: Collect the bridge plug debris returned from the site and classify them into rubber, cement, black stone, white stone and plastic according to their materials. Measure the volume and density of each type of bridge plug debris and calculate their composition ratio. Among them, the method for measuring the volume of bridge plug debris is the drainage method. The required tools include a large and a small beaker and an electronic scale. The specific operation process is: fill the beaker with water, then immerse the bridge plug debris of a certain material in the beaker, and measure the volume of the discharged water.

[0016] Step 2: Use image processing method to measure the shape parameters of bridge plug debris: Place the bridge plug debris neatly and take photos, and use noise processing, image binarization, and boundary recognition methods to obtain the shape parameters of the bridge plug debris; The tools required for the image processing method include A4 paper, camera, and image processing program. The specific operation process is as follows: Arrange the bridge plug debris in a matrix from large to small on A4 paper with a spacing of 2 to 3 cm; To obtain images, use a bracket to make the camera parallel to the shooting plane. To reduce the interference of shadows on photo processing, use parallel light in a dark space to take three views of the bridge plug debris. Noise processing: import the captured photos into the program, select the threshold value according to the color distribution characteristics of the read image, enhance the image contrast, highlight the small noise points, and use color replacement to remove the noise points; Image binarization, constantly adjusting the binarization threshold to convert color images into black and white images to facilitate boundary recognition; Boundary recognition: select five commonly used boundary detection methods, namely Roberts, Sobel, Prewitt, Log, and Canny. Choose different boundary detection methods for different photos. Characteristic parameter calculation, identification of interrelated data points, calculation of the centroid position, area and perimeter of the bridge plug debris in different views and output to Excel.

[0017] Different types of bridge plug debris have their own shape characteristics. Therefore, the physical parameters of roundness, aspect ratio, radius ratio, sphericity and equivalent diameter are selected to quantitatively characterize the differences in the shapes of bridge plug debris. The specific formula is: (1); (2); (3); (4); (5); In the formula, R r is the roundness of the bridge plug debris, dimensionless; S is the plane perimeter of the bridge plug debris, m; A is the plane area of ​​the bridge plug debris, m 2 ; R d is the aspect ratio of the bridge plug debris, dimensionless; d 1 is the major axis of the ellipse equivalent to the bridge plug debris, m; d 2 is the minor axis of the ellipse equivalent to the bridge plug debris, m; R z is the radius ratio of the bridge plug debris, dimensionless; r 1 is the maximum distance from the center point of the bridge plug debris to the boundary, m; r 2 is the minimum distance from the center point of the bridge plug debris to the boundary, m; is the sphericity, dimensionless; d eq is the equivalent diameter, m; V is the volume of bridge plug debris, m 3 ; The present invention takes into account the parameter range and quantity of bridge plug debris. To reduce the additional influence of the physical properties of bridge plug debris on each other during the flow process, the absolute difference between the radius ratio, aspect ratio, roundness, sphericity and equivalent diameter is within 10%.

[0018] Step 3: Determine the characteristic parameters: Combine the five bridge plug debris shape characterization parameters of roundness, aspect ratio, radius ratio, sphericity and equivalent diameter, and use the correlation coefficient R 2 As evaluation indexes, the correlation between the shape parameters of the bridge plug debris tested in step 2 was compared, and the roundness, aspect ratio, and radius ratio were selected as the main parameters for subsequent calculations; The five characteristic parameters are matched with each other, the relationship curve between the characteristic parameters is drawn, and the linear relationship curve between the two is fitted. 2 Characterizes the correlation between two characteristic parameters, R 2 The larger it is, the greater the correlation between the two feature parameters; Comparative verification shows that there is a strong correlation between roundness and sphericity, equivalent diameter and radius ratio, and aspect ratio. Representative roundness, aspect ratio, and radius ratio are selected as the main parameters for subsequent calculations.

[0019] Step 4: Experimentally measure the settling velocity of the bridge plug debris: Conduct a static settling experiment in water on the selected bridge plug debris to measure the settling velocity of the bridge plug debris; The tools used in the static sedimentation experiment include transparent glass tubes, high-speed cameras, whiteboards, and computers. The specific operation process is as follows: A simple sedimentation experimental device was built, and a transparent glass tube with an inner diameter of 15 cm and a length of 2 m was selected. A high-speed camera (960 frames / second) was used for shooting during the experiment. After the experiment was completed, the experimental photos were extracted on the computer to calculate the sedimentation velocity. To facilitate the observation and calculation of the sedimentation velocity, a ruler was placed next to the plexiglass to understand the position of the bridge plug debris in the pipe column. In order for the camera to clearly capture the stable sedimentation process, the distance between the camera and the plexiglass tube was adjusted before the experiment. Due to the irregular shape of the bridge plug debris and the large differences between different bridge plug debris, the sedimentation velocities of different bridge plug debris were accurately obtained, and the sedimentation acceleration distance was observed through a test experiment.

[0020] Step 5: Establish a drag coefficient model for bridge plug debris: Based on the spherical drag coefficient model, the shape of the bridge plug debris is divided into near-spherical and non-spherical shapes by using the ratio of the middle axis to the short axis of the bridge plug debris, and a drag coefficient model suitable for irregular-shaped bridge plug debris is established. The settling velocity data measured in step 4 is used to fit the parameters to be fitted in the model; During the settlement of bridge plug debris, the most important force acting on the bridge plug debris is the force opposite to the movement direction of the bridge plug debris, that is, the drag force. F D , defined as: (6); In the formula, r f is the fluid density, kg / m 3 ; C D is the drag coefficient of the bridge plug debris, dimensionless; A f is the reference area related to the size of bridge plug debris, m 2 ; v p is the speed of bridge plug debris, m / s; v f is the fluid velocity, m / s; is the vector form of the bridge plug debris velocity, m / s; is the vector form of fluid velocity, m / s; The fluid in the static experiment is the static fluid in the tube. v f = 0m / s, derive the drag coefficient C D The formula is as follows: (7); (8); In the formula, g is the acceleration due to gravity, m 2 / s; L s is the characteristic length considering the rolling condition, m; r p is the density of bridge plug debris, kg / m 3 ; r f is the fluid density, kg / m 3 ; d m is the center axis of the bridge plug debris, m; C 1 is the coefficient to be fitted, dimensionless; A is the area of ​​bridge plug debris, m 2 ; d s is the minor axis of the bridge plug debris, m; d l is the long axis of the bridge plug debris, m.

[0021] Irregular shaped bridge plug debris is classified and calculated by shape: When the ratio of the minor axis to the median axis Assuming that the bridge plug debris is nearly spherical, the drag coefficient is related to density and viscosity. Combined with formula (7), the drag coefficient is used C D and the dimensionless shape constant N In the form of multiplication, the sedimentation velocity can be calculated and the simplified formula is as follows: (9); (10); In the formula, m f is the liquid viscosity, Pa·s; N is the shape factor constant, dimensionless; s is the surface tension of water, N / m; when When the bridge plug debris is considered to be non-spherical, the roundness, aspect ratio, and radius ratio of the bridge plug debris need to be considered comprehensively, and the following formula is used for fitting: (11); (12); In the formula, k N is the roughness coefficient of the sphere, dimensionless; ψis the bridge plug debris shape factor, dimensionless; C 2 is the coefficient to be fitted, dimensionless.

[0022] Compared with the shortcomings and deficiencies of the prior art, the present invention has the following beneficial effects: 1) Based on the shape characteristics of irregular bridge plug debris, the image processing method is used to more carefully characterize the irregular shape of bridge plug debris, providing data support for the establishment of the drag coefficient model of bridge plug debris; 2) Static sedimentation experiments were carried out to calculate the sedimentation velocity. A drag coefficient model suitable for irregular-shaped bridge plug debris was established based on the spherical drag coefficient model. The model was fitted using the sedimentation velocity data measured in step 4 to provide theoretical support for the design of flowback flow parameters for bridge plug debris in shale gas horizontal wells. Obviously, the above is only the research idea of ​​the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An experimental method for determining the settling velocity of irregular shaped bridge plug debris, characterized in that: The following steps are involved: Step 1: Classification of bridge plug debris and measurement of some parameters: Collect the bridge plug debris returned from the site and classify them into rubber, cement, black stone, white stone and plastic according to their materials. Measure the volume and density of each type of bridge plug debris and calculate their composition ratio. Step 2: Use image processing method to measure the shape parameters of bridge plug debris: Place the bridge plug debris neatly and take photos, and use noise processing, image binarization, and boundary recognition methods to obtain the shape parameters of the bridge plug debris; Step 2.1: The specific operation process of the image processing method is: Arrange the bridge plug debris in a matrix from large to small on A4 paper with a spacing of 2 to 3 cm; obtain the image, use a bracket to make the camera parallel to the shooting plane, illuminate with parallel light in a dark space to reduce the interference of shadows on photo processing, and take three views of the bridge plug debris; noise processing, import the photographed photos into the program, select the threshold according to the color distribution characteristics of the read image, enhance the image contrast, highlight the small noise, and use color substitution to remove the noise; image binarization, continuously adjust the binarization threshold, convert the color image into a black and white image, and facilitate boundary recognition; boundary recognition, select five existing commonly used boundary detection methods, namely Roberts, Sobel, Prewitt, Log, and Canny, and select different boundary detection methods for different photos; Characteristic parameter calculation, identifying interrelated data points, calculating the centroid position, area and perimeter of the bridge plug debris in different views and outputting them to Excel tables; Step 3: Determine the characteristic parameters: Combine the five bridge plug debris shape characterization parameters of roundness, aspect ratio, radius ratio, sphericity and equivalent diameter, and use the correlation coefficient R 2 As evaluation indexes, the correlation between the shape parameters of the bridge plug debris tested in step 2 was compared, and the roundness, aspect ratio, and radius ratio were selected as the main parameters for subsequent calculations; Step 4: Experimentally measure the settling velocity of the bridge plug debris: Conduct a static settling experiment in water on the selected bridge plug debris to measure the settling velocity of the bridge plug debris; Step 5: Establish a drag coefficient model for bridge plug debris: Based on the spherical drag coefficient model, the shape of the bridge plug debris is divided into near-spherical and non-spherical shapes using the ratio of the mid-axis to the short axis of the bridge plug debris. A drag coefficient model suitable for irregularly shaped bridge plug debris is established, and the parameters to be fitted in the model are fitted using the sedimentation velocity data measured in step 4.

2. The method for experimentally determining the settling velocity of irregular-shaped bridge plug debris according to claim 1, characterized in that: In step 5, a drag coefficient model suitable for irregular-shaped bridge plug debris is established. The specific process is as follows: During the settlement of bridge plug debris, the most important force acting on the bridge plug debris is the force opposite to the movement direction of the bridge plug debris, that is, the drag force. F D , defined as: In the formula, ρ f is the fluid density, kg / m 3 ; C D is the drag coefficient of the bridge plug debris, dimensionless; A f is the reference area related to the size of bridge plug debris, m 2 ; v p is the speed of bridge plug debris, m / s; v f is the fluid velocity, m / s; is the vector form of the bridge plug debris velocity, m / s; is the vector form of fluid velocity, m / s; The fluid in the static experiment is the static fluid in the tube. v f = 0m / s, derive the drag coefficient C D The formula is as follows: In the formula, g is the acceleration due to gravity, m 2 / s; L s is the characteristic length considering the rolling condition, m; ρ p is the density of bridge plug debris, kg / m 3 ; ρ f is the fluid density, kg / m 3 ; d m is the center axis of the bridge plug debris, m; C 1 is the coefficient to be fitted, dimensionless; A is the area of ​​bridge plug debris, m 2 ; d s is the minor axis of the bridge plug debris, m; d l is the long axis of the bridge plug debris, m; Irregular shaped bridge plug debris is classified and calculated by shape: When the ratio of the minor axis to the median axis It is considered that the bridge plug debris is nearly spherical. Since the drag coefficient is related to density and viscosity, the drag coefficient formula is used. C D and the dimensionless shape constant N In the form of multiplication, the sedimentation velocity can be calculated and the simplified formula is as follows: In the formula, μ f is the liquid viscosity, Pa·s; N is the shape factor constant, dimensionless; σ is the surface tension of water, N / m; when When the bridge plug debris is considered to be non-spherical, the roundness, aspect ratio, and radius ratio of the bridge plug debris need to be considered comprehensively, and the following formula is used for fitting: In the formula, k N is the roughness coefficient of the sphere, dimensionless; ψ is the bridge plug debris shape factor, dimensionless; R r is the roundness of the bridge plug debris, dimensionless; R d is the aspect ratio of the bridge plug debris, dimensionless; R z is the radius ratio of the bridge plug debris, dimensionless; C 2 is the coefficient to be fitted, dimensionless.

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