Device and method for measuring drag coefficient of a population of particles

Abstract

The application discloses a kind of drag coefficient measuring device and measuring method of group particles.The device is with stirring tank, circulating pump, transparent observation cylinder and backflow pipeline to form closed circuit circulation, a small amount of identical diameter, identical density and having unique RFID coding identification particles are mixed in base particle group, and at least three groups of annular RFID detection units are arranged along the axial direction of transparent observation cylinder.Data acquisition and processing system matches the time stamp of multiple points of the same identification particle according to unique coding, calculates segmented moving speed and screens out data with unstable speed;Then, in combination with flow, particle volume fraction and physical property parameters, the relative speed of particle, Reynolds number and group particle drag coefficient are determined.The scheme can carry out non-optical speed measurement under continuous and controllable concentration conditions, and obtain group particle drag coefficient data under different flow and particle volume fraction conditions.

Description

Technical Field

[0001] This invention relates to the fields of oil and gas engineering, multiphase flow testing, and particle dynamics parameter measurement. In particular, it addresses key engineering problems such as drilling fluid rock carrying, proppant transport and placement in fracturing operations, and calculation of bubble mass drag force in gas-liquid two-phase flow. It proposes a measuring device and method for determining the mass particle drag coefficient by using multi-point timestamp velocity measurement results of RFID-tagged particles under continuous circulation and controllable particle volume fraction conditions. Background Technology

[0002] In drilling fluid proppant transport, fracturing proppant delivery, and other solid-liquid two-phase flow processes, solid particles typically move in swarms. Hydrodynamic interactions between particles, wake disturbances, and local concentration variations alter the particle's motion relative to the fluid. Therefore, the drag coefficient obtained under single-particle conditions is difficult to directly characterize a swarm of particles with a certain volume fraction. The swarm particle drag coefficient is a crucial parameter for establishing swarm transport models and evaluating particle transport capacity.

[0003] Current methods for measuring drag coefficients mostly employ single-particle dropping or static settling methods, calculating the drag coefficient by measuring the final settling velocity of the particles. These methods are suitable for low concentrations and situations where particle interactions are weak. However, as the particle volume fraction increases, wake interference, agglomeration, and local concentration fluctuations can cause differences in the stress state of different particles, making it difficult for static settling results to represent the collective stress characteristics under continuous flow conditions.

[0004] If high-speed cameras are used to directly track the motion of multiple particles, occlusion, turbidity, and refraction in high-concentration systems will reduce the stability of particle identification and velocity matching. If the passage time of particles is recorded at only two locations, it is difficult to identify instantaneous velocity anomalies caused by local eddies, collisions with neighboring particles, or wall effects. If the velocity data obtained in this way is used for mechanical inversion without screening, local disturbances will be mistakenly included in the collective drag coefficient.

[0005] In addition, existing test systems usually do not simultaneously solve the problem of connecting particle concentration maintenance, identification of the same particle across detection locations and drag coefficient calculation: the particle concentration in the test section may change with deposition, and data from different detection locations may come from different particles, resulting in a lack of one-to-one correspondence between the measured transport velocity and the set particle volume fraction and flow conditions.

[0006] Therefore, there is a need for a device and method for measuring the population particle drag coefficient that can maintain stable circulation of particle populations, identify the multi-point passage time of particles with the same identifier under non-optical conditions, screen out unstable velocity data, and correlate effective velocity with flow rate, concentration and physical property parameters. Summary of the Invention

[0007] In view of the problems existing in the background technology, the present invention aims to solve the problems of the difficulty in stabilizing the particle population concentration under continuous flow conditions, the difficulty in reliably tracking the same particle, and the impact of local disturbance data on the drag coefficient inversion. It provides a device and method for measuring the drag coefficient of a population of particles that combines closed-loop circulation, multi-point detection with unique RFID coding, velocity consistency screening and mechanical inversion.

[0008] The technical solution provided by this invention is: a device for measuring the drag coefficient of a group of particles, comprising a mixing and supply unit, a circulating pump, a data acquisition and processing system, a transparent observation cylinder, labeled particles, and a monitoring array;

[0009] The mixing and supply unit includes a mixing tank, a stirring paddle, and a variable frequency motor. The variable frequency motor drives the stirring paddle and adjusts the stirring intensity to keep the particle group suspended and evenly distributed.

[0010] The circulating pump has its inlet connected to the bottom outlet of the mixing and supply unit via a pipeline, and its outlet connected to the lower part of the transparent observation cylinder via a pipeline. The circulating pump injects the mixed fluid into the transparent observation cylinder at a constant flow rate.

[0011] The transparent observation cylinder is a transparent vertical cylinder with a monitoring array arranged along the axial direction on its wall. The top of the transparent observation cylinder is connected to the upper part of the mixing and supply unit through a return pipeline to form a closed loop.

[0012] The aforementioned identifying particles: A small amount of identifying particles with the same diameter and density as the matrix particles are incorporated into the overall particle group of the mixed fluid, and each particle has an RFID chip with a unique code and an induction coil inside.

[0013] The monitoring array includes at least three sets of ring-shaped RFID detection units spaced apart along the axial direction of the transparent observation cylinder;

[0014] The data acquisition and processing system is connected to the monitoring array in real time. The data acquisition and processing system (3) collects the timestamps of the same identified particles with unique codes passing through different ring RFID detection units, calculates the segmented transport speed of the identified particles, and determines the group particle resistance coefficient by combining the fluid flow rate, particle volume fraction and the physical property parameters of the particles and the fluid.

[0015] The circulating pump is a variable frequency circulating pump; the transparent observation cylinder is a vertically arranged non-metallic transparent cylinder, and the axial distance between adjacent annular RFID detection units is ΔL.

[0016] The volume fraction of the labeling particles in the particle group is 0.05%, the matrix particles are spherical polyoxymethylene (POM) particles with a diameter of 5 mm, the shell of the labeling particles is made of POM, and the equivalent diameter and equivalent density of the labeling particles after assembly are the same as the diameter and density of the matrix particles, respectively.

[0017] The data acquisition and processing system can also compare the segmented transport velocities of particles with the same identifier in two adjacent measurement sections, and filter effective data for calculating the drag coefficient of the group of particles based on the relative differences in the segmented transport velocities.

[0018] The method for measuring the drag coefficient of a group of particles using the above-mentioned measuring device includes the following steps:

[0019] Step (1): Add the matrix particles and fluid with a set volume fraction ε to the mixing and supply unit, and incorporate the labeling particles;

[0020] Step (2): Start stirring and closed-loop circulation. Under the condition of stable flow rate and uniform suspension of particle population, make the mixed fluid flow upward from the bottom of the transparent observation cylinder.

[0021] Step (3): Based on the timestamps t1, t2 and t3 of at least three sets of ring RFID detection units, the segmented transport speeds U1 and U2 of two adjacent measurement sections are calculated.

[0022] Step (4): Filter valid data based on the relative difference between U1 and U2, and determine the particle transport velocity U from the valid data. s ;

[0023] Step (5): Determine the fluid velocity U based on the circulation pump displacement Q and the inner diameter D of the transparent observation cylinder. f According to U f and U s Determine the relative velocity U of the particles r and particle Reynolds number Re;

[0024] Step (6): When the segmented transport velocity of the identified particles meets the stability condition, determine the drag coefficient C of the group of particles based on the balance relationship between buoyancy, gravity and drag. d ;

[0025] Step (7): Repeat the measurement and steps (2) to (6) under different particle volume fractions ε and circulating pump displacement Q to obtain C under different operating conditions. d Re and ε data.

[0026] When the axial distance between adjacent ring RFID detection units is ΔL, U1 = ΔL / (t2-t1), U2 = ΔL / (t3-t2), and the relative difference δ = |U2-U1| / |U1|; when δ < 3%, the corresponding data is determined as valid data, and U s =(U1+U2) / 2; When δ≥3%, the corresponding data is removed.

[0027] The above U f =4Q / (πD 2 ), U r =|U f -U s |,Re=ρ l U r d / μ; where ρ l denoted as fluid density, d as particle size, and μ as fluid dynamic viscosity.

[0028] The marker particles that satisfy the stability condition are considered as spherical particles and their acceleration term is ignored, according to C d =4gd(ρ s -ρ l ) / (3ρ l U r ²) Determine the group particle drag coefficient; where g is the gravitational acceleration, ρ s To indicate the density of particles.

[0029] C obtained under different working conditions d By fitting Re and ε data, a population particle drag coefficient correlation model C applicable to the tested particle volume fraction and Reynolds number range is established. d =f(Re,ε).

[0030] In the above scheme, the monitoring array consists of at least three sets of ring-shaped RFID detection units spaced apart along the axial direction of the transparent observation cylinder. The data acquisition and processing system matches the timestamps of the same unique code in different detection units, calculates the segmented transport velocity of two adjacent sections, uses the relative difference in segmented velocity to filter valid data, and combines the flow rate, particle volume fraction, and physical property parameters to determine the relative particle velocity, Reynolds number, and collective particle drag coefficient.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] 1. The present application forms a closed-loop circulation with the mixing and supply unit, circulation pump, transparent observation cylinder and return pipeline, which helps to reduce the concentration drift caused by particle deposition and make the velocity data correspond to the set particle volume fraction.

[0033] 2. This application represents a significant improvement over existing technologies in terms of experimental conditions, detection methods, measurement accuracy, applicability, and engineering value. First, by maintaining a uniform distribution and stable concentration of the fluid and particle population through a closed-loop circulation system, the experiment can be conducted in a continuous flow environment, avoiding the clustering and uneven concentration problems commonly found in static sedimentation experiments. Therefore, the results obtained are more representative and have greater engineering applicability. Second, the combination of RFID-tagged particles and a multi-point ring detection array overcomes the shortcomings of traditional optical methods, which are susceptible to obstruction and refraction interference under high concentration and high turbidity conditions, ensuring high-precision velocity measurement data even in complex multiphase flow environments. Furthermore, this invention achieves real-time capture of the instantaneous position and velocity of the marked target through multi-point threshold detection and a timestamp algorithm. Compared to traditional sedimentation methods, this significantly improves measurement accuracy and repeatability, and can establish a complete database of population drag coefficients under different concentration and flow conditions. Empirical or semi-theoretical models of population drag coefficient variations with particle concentration and Reynolds number can be established, directly providing key data support for oil and gas engineering design.

[0034] 3. The overall device of this application is compatible with solid-liquid two-phase flow testing, covering a variety of flow states from low to high Reynolds numbers. It has good scalability and universality, and can be widely applied to different types of flow and transport studies. The Reynolds number and drag coefficient are calculated uniformly using particle relative velocity, and a Cp model is established using particle volume fraction as the data dimension. d The =f(Re, ε) correlation model enables the test results to reflect the population effect within the tested concentration range. In terms of engineering value, the experimental data on population resistance coefficients obtained by this invention can be directly applied to the study of drilling fluid rock-carrying behavior and the optimization of fracturing proppant placement, providing reliable data support and theoretical basis for optimizing key process parameters in oil and gas drilling and development. In summary, this invention is not only innovative in experimental methods and testing techniques, but also substantially improves the representativeness, data accuracy, and applicability of experimental results, providing a novel experimental platform and engineering solutions for complex flow problems in oil and gas engineering.

[0035] 4. The circulating pump displacement, particle volume fraction and monitoring point spacing of this application can all be set according to the test conditions, which makes it easy to obtain the population particle resistance coefficient data under different flow rate and concentration combinations.

[0036] 5. This application realizes the accurate measurement of the resistance coefficient of the group of particles under controlled circulation conditions, which can overcome the limitations of existing methods and form an experimental technology system with universality and engineering adaptability, providing key support for drilling fluid optimization design and fracturing proppant migration law research. Attached Figure Description

[0037] Figure 1This is a schematic diagram of the device for testing the particle drag coefficient of this application.

[0038] Figure 2 for Figure 1 A schematic diagram of the particle structure.

[0039] Figure 3 This is a flowchart of the method for testing the drag coefficient of the population particles in this application.

[0040] Figure 4 The relationship between drag coefficient and Reynolds number is given under different group volume fraction conditions. Detailed Implementation

[0041] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] Implementation examples

[0043] This embodiment uses a population of solid particles as the test object. Under continuous cycling and a set particle volume fraction, the transport state of matrix particles with the same diameter and density is characterized by identified particles with unique RFID codes, and the drag coefficient of the population particles is inverted based on valid data that has been screened for velocity consistency.

[0044] 1. Device components:

[0045] See appendix Figure 1 The measuring device includes a mixing and supply unit 1, a circulation pump 2, a data acquisition and processing system 3, a transparent observation cylinder 4, marker particles 5, and a monitoring array 6. The mixing and supply unit 1, the circulation pump 2, the transparent observation cylinder 4, and the return pipeline form a closed-loop circulation circuit; the monitoring array 6 is arranged along the axial direction of the transparent observation cylinder 4.

[0046] The mixing and supply unit 1 is a 50 L stirred tank, equipped with a stirring paddle driven by a variable frequency motor. By adjusting the stirring intensity, solid particles and fluid are fully mixed and kept suspended according to a set volume fraction, reducing particle deposition at the bottom of the tank and in the pipeline. 50 L is an example volume in this embodiment and does not constitute a limitation on the volume of the device.

[0047] The inlet of the circulating pump 2 is connected to the bottom outlet of the mixing and supply unit 1 via a pipeline, and the outlet of the circulating pump 2 is connected to the lower part of the transparent observation cylinder 4 via a pipeline. The top of the transparent observation cylinder 4 is provided with a return outlet, which is connected to the upper part of the mixing and supply unit 1 via a return pipeline. The circulating pump 2 can be a variable frequency pump, and the flow rate adjustment range in this embodiment is 0.1–2 m³ / h. The mixed fluid flows upward from the lower part of the transparent observation cylinder 4 and then returns to the mixing and supply unit 1, thereby forming a closed-loop circulation.

[0048] The transparent observation cylinder 4 is a transparent vertical cylinder that facilitates observation and sensor module arrangement. The transparent observation cylinder 4 is 2 m high and has an inner diameter of 50 cm. Three sets of ring-shaped RFID detection units are evenly arranged along the axial direction on the outer wall of the cylinder. The axial distance between adjacent detection units is ΔL = 0.30 m. The temperature is 20.0 ℃. The three sets of ring-shaped RFID detection units constitute a monitoring array 6. Each detection unit reads the unique code and records the timestamp when the identified particle 5 enters its detection area, thus forming a multi-point passage record of the same identified particle 5.

[0049] The labeling particles 5, as described Figure 2 As shown, it contains a miniature RFID chip 7 and an induction coil 8. The matrix particles used in this experiment have a diameter of 5 mm and a density of 1410 kg / m³. 3 The marker particle 5 is made of polyoxymethylene (POM) spherical particles, with the outer shell of the marker particle 5 made of POM 9. After the micro RFID chip, induction coil, and outer shell are encapsulated, the equivalent diameter and equivalent density of the marker particle 5 are the same as the diameter and density of the matrix particles, respectively, to reduce the influence of the marker structure on the flow characteristics. The particle group volume fraction ε can be set within the range where the particle group can remain uniformly suspended in a closed-loop circulation, according to the test conditions and measurement requirements, and can be changed by adjusting the amount of matrix particles added; for example, ε can be set to 1%, 2%, 5%, 10%, or 20%. The volume fraction of marker particle 5 in the particle group can be set according to the recognition capability of the monitoring array 6 and the statistical sample requirements, under the condition that the marker particle 5 can be stably identified without significantly changing the overall flow characteristics of the particle group; in this experiment, it is set to 0.05%. The above values ​​are only example conditions and do not constitute a limitation of the present invention.

[0050] The data acquisition and processing system 3 is connected to each ring RFID detection unit and acquires the circulating pump displacement Q and the particle volume fraction ε set in the experiment. The system matches the timestamps of particles 5 with the same identifier in different detection units according to the unique code, calculates the segmented transport velocity of two adjacent measurement sections; then it performs a consistency judgment on the segmented velocity, retains the data with stable velocity, and calculates the group particle resistance coefficient based on fluid flow rate, particle and fluid properties, and mechanical equilibrium relationship.

[0051] 2. Methodology Section:

[0052] like Figure 3 As shown, the method for measuring the drag coefficient of a group of particles using the above-mentioned measuring device includes the following steps:

[0053] (1) Add fluid and matrix particles with volume fractions ε of 1%, 2%, 5%, 10% and 20% respectively to the mixing and supply unit 1, and add label particles 5 with a volume fraction of 0.05%; start stirring to make the particle group uniformly suspended.

[0054] (2) Start the circulation pump 2 to make the mixed fluid flow stably in the closed circulation loop; after the circulation pump displacement Q and particle distribution are stable, the monitoring array 6 reads the unique code of the identified particle 5 point by point and records its passage time.

[0055] (3) The data acquisition and processing system 3 calculates the segmented transport speeds U1 and U2 based on the timestamps t1, t2 and t3 of the same identifier particle 5 that are matched by the unique code, and the timestamps t1, t2 and t3 of at least three sets of ring RFID detection units.

[0056] For any two adjacent detection units, the average migration velocity of the particles within the corresponding segment is:

[0057]

[0058] (4) Compare the relative differences between U1 and U2, retain the data with stable velocity, and determine the particle transport velocity U. s Calculate the fluid velocity U based on the pump displacement Q and the cylinder inner diameter D. f Then calculate the relative velocity U of the particles. r Particle Reynolds number Re and collective particle drag coefficient C d .

[0059] (5) Change the particle volume fraction ε and the circulating pump displacement Q, and repeat the above process to obtain C under different operating conditions. d We obtained Re and ε data and established a correlation model for the group particle drag coefficient applicable to the tested operating conditions.

[0060] The specific method for calculating the group resistance coefficient is as follows:

[0061] Step 1: The first detection unit records the timestamp t1:

[0062] When the first detection unit reads the unique code of the identified particle 5, the data acquisition and processing system 3 records the timestamp t1 of the identified particle 5 passing through the first detection unit.

[0063] Step 2: The second detection unit records the timestamp t2 and calculates the velocity U of the first segment. 1：

[0064] When particle 5 with the same identifier passes through the second detection unit, the system completes the matching based on the unique code and records the timestamp t2. The distance between the first and second detection units is ΔL, and the velocity U1 of the first segment is:

[0065]

[0066] The first segment velocity U1 is used for consistency comparison with the segment velocity of the next adjacent segment.

[0067] Step 3: The third detection unit records the timestamp t3 and calculates the second segment velocity U. 2：

[0068] When particle 5 with the same identifier passes through the third detection unit, the system completes the matching based on the unique code and records the timestamp t3. The distance between the second and third detection units is ΔL, and the velocity U2 of the second segment is:

[0069]

[0070] The second speed U2, together with the first speed U1, is used to determine whether the speed of the marker particle 5 is stable within the measurement section.

[0071] Step 4: Particle velocity consistency assessment and effective data screening:

[0072] Compare the relative differences between U2 and U1:

[0073]

[0074] If δ < 3%, then the velocity change of the marker particle 5 within the measurement section is considered small, and the corresponding data is taken as valid data. The particle transport velocity U is then determined using the following formula. s :

[0075]

[0076] If δ ≥ 3%, the identified particle 5 is considered to be significantly disturbed by local eddies, collisions with neighboring particles, or wall effects, and the corresponding data is discarded and not used for subsequent drag coefficient calculations. 3% is the stability threshold used in this embodiment.

[0077] Step 5: Calculate the fluid velocity U f Particle relative velocity U r and particle Reynolds number Re:

[0078] Data acquisition and processing system 3 obtains the displacement Q of the circulating pump. The inner diameter D of the transparent observation cylinder 4 is measured, and the average fluid velocity U across its cross-section is...f for:

[0079]

[0080] The relative velocity U of a particle is defined as the absolute value of the difference between the fluid velocity and the particle transport velocity. r And calculate the particle Reynolds number Re:

[0081]

[0082]

[0083] In the formula, d is the particle size, μ is the hydrodynamic viscosity, and ρ is the particle size. l Let U be the fluid density. r The absolute value of can ensure that the relative velocity and Reynolds number of the particles are non-negative in different directions of motion.

[0084] Step 6: Calculate the collective particle drag coefficient C d：

[0085] For the spherical marker particle 5 that passed the stability screening in step 4, its acceleration term is negligible relative to gravity, buoyancy, and drag. Based on the quasi-steady-state equilibrium relationship of gravity, buoyancy, and drag, the drag coefficient C of the group of particles is... d for:

[0086]

[0087] In the formula, g is the acceleration due to gravity, and ρ s The density of marker particle 5 is used. Since the marker particle 5, after encapsulation, has the same diameter and density as the matrix particles and is in the same particle volume fraction ε and flow rate conditions, its effective velocity data is used to characterize the particle resistance characteristics under the corresponding group conditions.

[0088] Step 7: Establish a drag coefficient correlation model that considers particle volume fraction:

[0089] Multiple sets of measurements were obtained by repeatedly measuring under different particle volume fractions ε and circulating pump displacement Q. d Data on Re and ε were used to establish a correlation model for the population particle drag coefficient through regression fitting or numerical optimization, such as... Figure 4 As shown:

[0090]

[0091] In the formula, ε is the particle volume fraction.

[0092] The established correlation model is applicable to the particle volume fraction, Reynolds number, and particle and fluid properties range covered by the experiment; if it exceeds this range, the model parameters should be re-determined through supplementary experiments.

[0093] 3. Experimental Results Section:

[0094] In the experiment, the volume fraction ε of the particle population was taken as 1%, 2%, 5%, 10%, and 20%, respectively; five water-glycerol mixture physical property conditions, M1 to M5, were set under each ε, and their (ρ) l μ) are respectively (1010 kg / m 3 ,2.0 mPa·s), (1030 kg / m 3 ,3.0mPa·s), (1050 kg / m 3 , 4.5 mPa·s), (1080 kg / m 3 (6.5 mPa·s) and (1110 kg / m 3 ,9.0 mPa·s).

[0095] Five marker particle passage events were recorded after 180 s of simulation stabilization for each (ε, medium) condition. The timestamps in the table use clock values ​​relative to the simulation acquisition start point T0, and list t1, t2, and t3 for the first valid sample of that condition; U s U f Re and C d The mean ± standard deviation of the effective samples selected by δ < 3% under this operating condition. To recreate the scenarios of speed fluctuations and anomaly removal, small flow rate and segmented speed disturbances were superimposed on the original data, and a small number of samples with δ ≥ 3% were set for rejection.

[0096] The following example illustrates the specific data acquisition process using a set of experimental data collection procedures. Taking the E05-M3 operating condition as an example, the particle volume fraction ε in this condition is 5%, the medium is a water-glycerol mixture, and ρ... l =1050 kg / m 3 μ = 4.5 mPa·s; particle diameter d = 5 mm; particle density ρ s =1410 kg / m 3 The axial distance between adjacent ring RFID detection units is ΔL = 0.30 m.

[0097] During the experiment, the closed-loop system was first allowed to run stably for 180 seconds. Then, the data acquisition and processing system matched the RFID tags with the same RFID code and sequentially passed through the timestamps of the first, second, and third detection units. Among the following five passing events, P01-P04 met the stability condition of δ < 3% and were used for mean calculation. P05 was discarded because δ ≥ 3% was determined to be affected by local disturbances. The results are shown in Table 1 below.

[0098] Table 1 shows the experimental results under five working conditions (M1 to M5) with a particle volume fraction ε of 5%.

[0099] sample RFID coding <![CDATA[t1 / s]]> <![CDATA[t2 / s]]> <![CDATA[t3 / s]]> <![CDATA[U1 / s]]> <![CDATA[U2 / s]]> δ / % P01 RFID-05M3-01 186.240 192.124 198.042 0.05099 0.05069 0.57 P02 RFID-05M3-02 224.730 230.632 236.504 0.05083 0.05109 0.51 P03 RFID-05M3-03 263.115 269.048 274.910 0.05056 0.05118 1.21 P04 RFID-05M3-04 305.480 311.352 317.244 0.05109 0.05092 0.34 P05 RFID-05M3-05 347.965 353.720 359.763 0.05213 0.04964 4.77

[0100] Therefore, taking the average of the four valid samples P01-P04, the particle transport velocity U s The velocity is 0.0509 m / s; the data acquisition and processing system synchronously records and converts the average fluid velocity U under this operating condition. f The relative velocity of the particle is 0.2029 m / s. Therefore, the relative velocity of the particle is U. r =|U f -U s |=0.1520 m / s. Further, according to Re=ρ l U r Calculated by d / μ, Re = 177.4; according to C d =4gd(ρ s -ρ l ) / (3ρ l Ur²) calculation, C d =0.970.

[0101] In the experiment, the volume fraction ε of the particle population was 1%, 2%, 5%, 10% and 20%, respectively; five water-glycerol mixture physical property conditions were set up under each ε, M1 to M5. The experimental methods for all these conditions were the same, and the results are shown in Table 2.

[0102] Table 2 Calculation results of the experimental dataset

[0103] Operating conditions ε % medium <![CDATA[Particle velocity U s (m / s)]]> Circulating pump displacement Q (L / s) <![CDATA[Fluid velocity U f (m / s)]]> Re <![CDATA[C d ]]> E01-M1 1 M1 0.03977 50.11 0.2552 544.1 0.558 E01-M2 1 M2 0.0440 45.55 0.2320 322.7 0.683 E01-M3 1 M3 0.0481 41.37 0.2107 189.7 0.848 E01-M4 1 M4 0.0521 37.31 0.1900 114.5 1.052 E01-M5 1 M5 0.0557 33.77 0.1720 71.7 1.308 E02-M1 2 M1 0.0415 49.66 0.2529 533.7 0.580 E02-M2 2 M2 0.0454 45.20 0.2302 317.3 0.706 E02-M3 2 M3 0.0495 41.14 0.2095 186.7 0.876 E02-M4 2 M4 0.0532 37.07 0.1888 112.6 1.087 E02-M5 2 M5 0.0574 33.58 0.1710 70.1 1.370 E05-M1 5 M1 0.0431 47.91 0.2440 507.1 0.642 E05-M2 5 M2 0.0472 43.69 0.2225 301.0 0.785 E05-M3 5 M3 0.0509 39.84 0.2029 177.4 0.970 E05-M4 5 M4 0.0551 35.95 0.1831 106.4 1.219 E05-M5 5 M5 0.0586 32.77 0.1669 66.7 1.509 E10-M1 10 M1 0.0446 44.85 0.2284 464.0 0.767 E10-M2 10 M2 0.0480 41.02 0.2089 276.3 0.932 E10-M3 10 M3 0.0526 37.48 0.1909 161.4 1.172 E10-M4 10 M4 0.0565 34.03 0.1733 97.0 1.465 E10-M5 10 M5 0.0606 31.08 0.1583 60.2 1.852 E20-M1 20 M1 0.0463 38.84 0.1978 382.6 1.128 E20-M2 20 M2 0.0500 35.76 0.1821 226.8 1.383 E20-M3 20 M3 0.0537 32.91 0.1676 132.8 1.729 E20-M4 20 M4 0.0580 30.06 0.1531 79.0 2.211 E20-M5 20 M5 0.0623 27.72 0.1412 48.6 2.845

[0104] The effective sample mean values ​​for each working condition are plotted by grouping them according to particle volume fraction, such as... Figure 4 As shown. This simulation example covers a particle Reynolds number range of approximately 49–544; at the same particle volume fraction, C d Overall, C decreases as Re increases; at similar Re values, C decreases as ε increases. d The increase indicates a trend of increased group drag as interparticle hydrodynamic interference intensifies. This trend only describes the expected output of the data processing chain in this device; the actual curve and fitting parameters should be determined from measured data.

[0105] Combining the data listed in Table 2 and Figure 4 As can be seen from the curves, this invention can obtain group particle drag coefficient data covering low, medium, and high Reynolds number ranges. Table 2 shows the U values ​​for each operating condition. s U f Re and C d There is a continuous correspondence between them. Figure 4 The curve trends of different volume fraction groups in the table corroborate each other, indicating that the data acquisition, speed screening and drag coefficient inversion process of the present invention can stably output effective results that reflect the differences in working conditions.

[0106] Based on the variation pattern, under the same particle volume fraction conditions, as Re increases, C... d The overall decrease indicates that the drag coefficient exhibits a common Reynolds number dependence characteristic when the relative motion between particles and fluid is enhanced; within a similar Re range, as the particle volume fraction ε increases, C... d The overall increase indicates that inter-particle wake interference, proximity effects, and local concentration effects enhance the drag on the particle population. This result demonstrates that the present invention can not only measure the drag coefficient under individual operating conditions, but also distinguish the combined effects of flow rate, medium properties, and particle concentration on the population drag characteristics.

[0107] Therefore, this invention maintains a set particle volume fraction through a closed-loop cycle, achieves non-optical multi-point identification of particles with the same identifier through unique RFID coding, eliminates local disturbance data through segmented velocity consistency judgment, and calculates C by combining the effective particle velocity with flow rate, particle volume fraction, and physical property parameters. d And Re. This device and method can provide a repeatable and traceable data foundation for establishing particle population resistance models in drilling fluid rock carrying, fracturing proppant migration, and other solid-liquid two-phase flow engineering.

[0108] The main technical line of this invention consists of four mutually cooperating steps: maintaining a set volume fraction of the particle population using a closed-loop circulation; performing non-optical tracking using identified particles with the same diameter and density as the matrix particles and unique RFID codes; obtaining two velocity segments using at least three detection locations and performing consistency screening; and calculating C using the effective particle relative velocity, flow rate, and physical property parameters. d The relationships between Re and ε are also considered. These steps together form a complete measurement chain, from establishing operating conditions, identifying the same particle, obtaining effective velocity, to outputting the drag coefficient.

[0109] In this embodiment, example values ​​are given for particle volume fraction, circulating pump displacement, cylinder size, monitoring point spacing, and stability threshold. Those skilled in the art can adjust the corresponding parameters based on the properties of the particles and fluid under test, while maintaining closed-loop circulation, unique coding multi-point matching, velocity consistency screening, and resistance inversion relationship unchanged.

[0110] The above are merely preferred embodiments of the present invention. Any equivalent substitutions or conventional adjustments made to the device size, flow range, particle volume fraction, number of detection units, or data processing parameters within the scope of the inventive concept should fall within the protection scope defined by the claims of the present invention.

Claims

1. A device for measuring the drag coefficient of a group of particles, characterized in that: It includes a mixing and supply unit (1), a circulation pump (2), a data acquisition and processing system (3), a transparent observation cylinder (4), marker particles (5), and a monitoring array (6); The mixing and supply unit (1) includes a mixing tank, a stirring paddle and a variable frequency motor. The variable frequency motor is used to drive the stirring paddle and adjust the stirring intensity so that the particle group remains suspended and evenly distributed. The circulation pump (2): The inlet end of the circulation pump (2) is connected to the bottom outlet of the mixing and supply unit (1) through a pipeline, and the outlet end of the circulation pump (2) is connected to the lower part of the transparent observation cylinder (4) through a pipeline; the circulation pump (2) injects the mixed fluid into the transparent observation cylinder (4) at a constant flow rate. The transparent observation cylinder (4) is a transparent vertical cylinder, and a monitoring array (6) is arranged along the axial direction on the cylinder wall of the transparent observation cylinder (4); the top of the transparent observation cylinder (4) is connected to the upper part of the mixing and supply unit (1) through a return pipeline to form a closed loop. The identification particles (5): A small amount of identification particles (5) with the same diameter and density as the matrix particles are incorporated into the overall particle group of the mixed fluid, and the particles are equipped with an RFID chip (7) with a unique code and an induction coil (8). The monitoring array (6) includes at least three sets of ring-shaped RFID detection units spaced apart along the axial direction of the transparent observation cylinder (4); The data acquisition and processing system (3) is connected to the monitoring array (6) in real time. The data acquisition and processing system (3) collects the timestamps of the same identified particles (5) with unique codes matching through different ring RFID detection units, calculates the segmented transport speed of the identified particles (5), and determines the group particle resistance coefficient by combining the fluid flow rate, particle volume fraction and the physical properties of the particles and fluid.

2. The measuring device according to claim 1, characterized in that: The circulating pump (2) is a variable frequency circulating pump; the transparent observation cylinder (4) is a vertically arranged non-metallic transparent cylinder, and the axial distance between adjacent annular RFID detection units is ΔL.

3. The measuring device according to claim 1, characterized in that: The volume fraction of the labeling particle (5) in the particle group is 0.05%, the matrix particle is a polyoxymethylene (POM) spherical particle with a diameter of 5 mm, the shell of the labeling particle (5) is made of polyoxymethylene (9), and the equivalent diameter and equivalent density of the labeling particle (5) after encapsulation are the same as the diameter and density of the matrix particle, respectively.

4. The measuring device according to claim 1, characterized in that: The data acquisition and processing system (3) can also compare the segmented transport speeds of the same labeled particles (5) in two adjacent measurement sections, and filter effective data for calculating the drag coefficient of the group particles based on the relative differences in the segmented transport speeds.

5. A method for measuring the drag coefficient of a group of particles using the measuring device according to any one of claims 1 to 4, characterized in that, Includes the following steps: Step 1: Add the matrix particles and fluid with a set volume fraction ε to the mixing and supply unit (1), and incorporate the labeling particles (5). Step 2: Start stirring and closed-loop circulation. Under the condition of stable flow rate and uniform suspension of particle population, make the mixed fluid flow upward from the bottom of the transparent observation cylinder (4). Step 3: Based on the timestamps t1, t2 and t3 of at least three sets of ring RFID detection units, calculate the segmented transport speeds U1 and U2 of two adjacent measurement sections according to the same identifier particle (5) matched by the unique code; Step 4: Filter valid data based on the relative difference between U1 and U2, and determine the particle transport velocity U from the valid data. s ; Step 5: Determine the fluid velocity U based on the circulation pump displacement Q of the circulation pump (2) and the inner diameter D of the transparent observation cylinder (4). f According to U f and U s Determine the relative velocity U of the particles r and particle Reynolds number Re; Step 6: When the segmented transport velocity of the identified particle (5) meets the stability condition, determine the drag coefficient C of the group of particles based on the balance relationship between buoyancy, gravity and drag. d ; Step 7: Repeat steps (2) to (6) under different particle volume fractions ε and circulating pump displacement Q to obtain C under different operating conditions. d Re and ε data.

6. The method for measuring the collective particle drag coefficient according to claim 5, characterized in that: When the axial distance between adjacent ring RFID detection units is ΔL, U1 = ΔL / (t2-t1), U2 = ΔL / (t3-t2), and the relative difference δ = |U2-U1| / |U1|; when δ < 3%, the corresponding data is determined as valid data, and U s =(U1+U2) / 2; When δ≥3%, the corresponding data is removed.

7. The method for measuring the collective particle drag coefficient according to claim 5, characterized in that: And f =4Q / (πD 2 ),And r =|U f -U s |,Re=ρ l And r d / μ; Where, ρ l denoted as fluid density, d as particle size, and μ as fluid dynamic viscosity.

8. The method for measuring the collective particle drag coefficient according to claim 7, characterized in that: The marker particle (5) that satisfies the stability condition is considered as a spherical particle and its acceleration term is ignored, according to C d =4gd(ρ s -ρ l ) / (3ρ l U r ²) Determine the group particle drag coefficient; where g is the gravitational acceleration, ρ s The density of particles (5) is used to identify the density of particles.

9. The method for measuring the collective particle drag coefficient according to claim 8, characterized in that: C obtained under different working conditions d By fitting Re and ε data, a population particle drag coefficient correlation model C applicable to the tested particle volume fraction and Reynolds number range is established. d =f(Re,ε).

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