Flow visualization simulation of cemented tailings backfill slurry by particle tracking technology

Pipeline flow visualization of cemented tailings backfill slurry (CTBS) improves the safety and stability of transportation. High turbidity and low resolution make it difficult for conventional methods to monitor the particle distribution state of CTBS in a short period of time. Particle tracking technology (PTT) is used to simulate and investigate the flow characteristics of CTBS pipeline, combine with theoretical analysis to construct a CTBS pipeline visualization model, elaborate the particle distribution state when CTBS flows in the pipeline, and explore the effects of pipe diameter (PD), flow velocity (FV) and tailings gradation (TG) on the particle distribution. The results show that particle tracking technology is better applied to investigate the particle transport distribution characteristics of CTBS tailings. Three concepts of particle accumulated gravity Ga, static friction angle θ and diameter dividing line are defined, and the transport pipe is divided into light wear zone, medium wear zone and heavy wear zone. The increase in pipe diameter increases the content of fine particles at the pipe wall and the thickness of the lubrication layer becomes larger, which improves the safety and stability of CTBS transport. The increased flow velocity reduces the settling phenomenon of large size particles and improves the transport efficiency, which increases the pipeline transport resistance. Under good tailings grading conditions, a wide range of tailings grading is more suitable as backfill material. The results of the study illustrate the flow characteristics of the backfill slurry in the pipeline from the particle perspective and provide a theoretical basis for pipeline transportation research.

backfill slurry CTBS is crucial, and it is the primary factor affecting the efficiency of the filling operation. As two parameters of CTBS pipeline transport, pipe transport resistance and slurry flow velocity are the key indicators to evaluate whether the pipeline system design is economic and reasonable. 5,6 Recently, safety problems occur frequently when the CTBS flows in the pipeline, which is manifested by accidents such as wear and pipeline failure due to excessive resistance to pipe transport, too fast flow velocity as well as blockage and pipe burst inside the pipeline due to slower flow velocity, 7,8 which greatly hinders the smooth implementation of the back-filling method, brings serious safety hazards and affects the economic benefits of mining enterprises. Due to the fact that the liquidity of CTBS in the pipeline is an important evaluation factor affecting the productivity and economic efficiency of the back-filling method, it is crucial to investigate the nature of its flow in the pipeline, and the need to improve the flow theory of CTBS pipeline is significant. CTBS is mainly prepared from tailings and cementitious materials with the addition of a certain proportion of water. 9 The fluidity of CTBS depends on the duration of freshness and rheological properties. 10,11 The factors affecting the freshness of CTBS mainly include ash-sand ratio, mass concentration, external additives, type of filling material, and so forth. 12,13 Under certain conditions, the addition of anti-hardening agent could enhance the duration of freshness of CTBS, which is beneficial to the transport of CTBS, but not conducive to the hardening of CTBS to form compressive strength. 14,15 CTBS flow process is complex and there are more models to describe its mobility. The Bingham model or Herschel-Bulkley model is generally used to investigate the flowability of CTBS to derive the rheological properties, pipe transport resistance, and velocity field distribution of CTBS, [16][17][18] and fruitful results have been obtained. However, it is still difficult to determine the location of the CTBS transport process plugging and pipe bursting accidents. To overcome this challenge, researchers have explored a rapid and accurate method for locating the location of CTBS blockage by using electrical resistance tomography (ERT) imaging system as a technical driver, and reliable results have been obtained. [19][20][21] However, the above studies only considered the flow characteristics of CTBS from macroscopic point of view, without analyzing from fine point of view, and failed to investigate the pipe transport resistance and flow path of CTBS flow process based on the tailings particle level, which could not make an in-depth analysis of CTBS flow mechanism.
Pipeline visualization technology (PVT) realizes the visual monitoring of the pipeline interior, grasps the flow status of the fluid in the pipeline in real time, locates the location of the pipeline accident in time, reduces the economic loss caused by delayed processing, and improves the stability and safety of the transmission to a certain extent. [22][23][24] Pipeline visualization technology possesses a wide range of applications in pipeline materials, 25 fluid flow characteristics [26][27][28][29][30] pipeline sensitivity assessment, 31,32 risk assessment, 33 welding flaw exploration, [34][35][36] and subsurface corrosion detection. 37,38 The cemented tailing sand filling slurry CTBS is fouling in nature and the particle distribution state is not as clearly discernible as in aqueous solutions. Therefore, it is difficult to achieve a real physical visualization in the pipeline in a short time. Nowadays, numerical simulation software has gradually matured, and the simulation results are able to maintain a better consistency with the data measured by physical tests with a high degree of confidence. However, there are few reports on the use of numerical simulation methods to investigate the flow characteristics of CTBS based on the tailings particle perspective.
This paper investigates the flow characteristics of CTBS in the pipeline based on COMSOL numerical simulation software, combined with particle tracking technology model, to visualize the flow of CTBS pipeline. To construct a pipeline transport visualization model from the perspective of fine view (tailings particle) and analyze the particle distribution state, flow path, pipeline transport resistance and pipeline wear characteristics during the flow of CTBS. Delineate the wear zone for the transport pipeline and propose the basis for the delineation. The effects of pipe diameter (PD), flow velocity (FV), tailings gradation (TG) on CTBS pipeline resistance and pipe wear are investigated.

Tailings and binder
Tailings from Sijiaying iron ore mine in Hebei Province, China, were selected as shown in Figure 1. The NKT6100-D laser particle size analyzer was used to analyze the particle size of a variety of tailings. Figure 2 shows the NKT6100-D laser particle size analyzer. Figure 3 shows the cumulative content curves of various types of waste tailings particle sizes. Table 1 shows some physical properties of various types of tailings. In general, when the average particle size of tailing  Note: D x represents the value of x% tailings particle diameter by volume fraction less than D x μm. C c coefficient of curvature (C c = D 30 × D 30 /(D 10 × D 60 )). C u Coefficient of uniformity (C u = D 60 /D 10 ).
sand is less than 300 μm, it is called fine tailing sand; when the average particle size of tailing sand is less than 19 μm, it is called ultra-fine tailing sand; otherwise, it is coarse tailing sand. The binder material is P.S 42.5 slag silicate cement.

Cemented tailings backfill slurry
Based on the backfill scheme currently in use at this mine, municipal domestic water was selected to formulate CTBS in the laboratory under a variety of tailings grading conditions. The rheological tests were conducted by laboratory Thermo Scientific HAKKES rheometer on a variety of CTBS with different tailings gradation types to investigate the flow deformation characteristics and obtain the rheological parameters (yield stress and plastic viscosity) which provided reliable numerical support for the numerical simulation tests. Figure 4 shows the Thermo Scientific HAKKES rheometer. Table 2 shows the properties associated with the CTBS for different tailings types.

Physical model
The back-filling pipeline system of this iron ore mine could be approximated as consisting of multiple sets of L-shaped transport pipelines. Figure 5 illustrates the backfilling operating procedure in this mine. This paper constructed a Backfilling system sketch simplified model of the pipeline transport link in the backfilling system of this mine based on COMSOL numerical simulation software, as shown in Figure 6. Among them, the horizontal pipe is 9 m, the vertical pipe is 3 m, and the stowing gradient is 4. In this paper, fluid flow model and particle tracking model were selected for coupling analysis. Gravity and drag force were added to the fluid flow particle-tracking module to characterize the flow process in a realistic scenario. The transient study was chosen to facilitate the acquisition of the particle distribution characteristics of the CTBS under different time points. The released particle method selected the value function release. The release time is 3 s, and the release step is 0.05 s. To improve the accuracy of the experiment calculation, the simulation model is meshed more minutely. The relative tolerance of the experiment results was set to 1 × 10 −5 . The transient solver performs a three-part separated solution. The calculation results of tailings position and tailings radius in the fluid flow particle-tracking module were divided into one solving step. The calculation results of the flow velocity field and pressure in the fluid flow module were divided into another solving step. Finally, the results of the particle velocity calculation were stored in the last solving step.

2.2.2
Mathematical model CTBS is a Bingham plastic fluid. 39,40 The energy conservation equation (Bernoulli's principle), the momentum equation, the continuity equation and the equation of state of particle motion could be derived by introducing different constitutive relation calculations which are consistent with the CTBS. [41][42][43][44] (as shown in Equations 1-4) Where z 1 , z 2 is the height of different positions of CTBS. p 1 , p 2 is the pressure under different positions of the cemented tailing sand filling slurry. is the CTBS volumetric weight. g is the gravitational acceleration. v is the CTBS flow velocity. p is the pressure on CTBS. F is the mass force on the CTBS. 0 is the CTBS plastic viscosity. ⋅ ⃑ v is the velocity divergence.
p is the particle density in CTBS. p is the CTBS density. C is the resistance coefficient. A is the tailings particle area correction constant. Experimental parameters The simulation experimental variables include the tailings particle size, slurry density, plastic viscosity, yield stress, flow velocity, and pipe diameter. Table 2 has shown some of the parameters of the CTBS, only remaining flow velocity and pipe diameter are not listed. In this paper, the flow velocity of CTBS is selected as 1.6, 1.9, 2.2, and 2.5 m/s. The pipe diameter is selected as 320, 360, 400, and 440 mm.

Model verification
Model verification is to ensure that the simulation model has high reliability. 45,46 In this paper, the resistance loss of the simulated flow process is calculated by setting the same test parameters as the physical experiment. The reliability of the developed simulation model is analyzed by comparing it with the physical experimental measurement results. Numerical simulation software is used to perform calculations using the iterative method, comparing the error of two adjacent calculation results. 47,48 When the error value is less than the set relative tolerance, the calculation is considered to be converged and the calculation result is accurate and reliable. Table 3 shows the parameters related to the model verification and the computational results. Figure 7 shows the residual convergence curves of the computed results. Figure 7A shows that the relative average error between the resistance loss measured by the physical experiment and calculated by the simulation experiment is 4.19%. The errors for each group of experimental conditions are 5.30%, 5.36%, 7.55, 1.51%, and 0.018%. Figure 7B shows that the computational error is 9.4 × 10 −6 when iterating 81 times, which is less  than the set relative tolerance of 1 × 10 −5 . The above analysis shows that the calculation results are convergent and usable, and the simulation model is reliable and feasible.

Visualization of CTBS particle distribution
This paper used numerical simulation software to investigate the state of particles distribution inside the pipe for different types of tailings under different transport parameters. Figures 8 and 9 show the solid phase particle flow paths in the bend and horizontal pipes under different flow times. Figure 8 shows that the particles are mainly concentrated under the bend pipe when the CTBS flows into the bend pipe from the vertical pipe at an accelerated velocity. Affected by gravity, the velocity direction of tailings particles changes when flowing from the bend pipe to the horizontal pipe. In this process, some of the tailing's particles would collide with the bottom of the bend pipe, which would have an impact effect on the pipe. Also, some small size tailings particles would form a small thickness lubrication layer along the bottom of the pipe. The lubrication layer could reduce the impact of large-size particles on the bottom of the bend pipe, and also decrease the frictional resistance between the large-size particles and the bottom of the bend pipe, which could play the role of protecting the bend pipe. However, when the tailings particle size is excessively small and the mass concentration of the CTBS is too high, the probability of pipe blockage accident may increase at this location as the flow of CTBS proceeds. Figure 9 illustrates that when the slurry flows from the bend pipe to the horizontal pipe, it first flows into the bottom of the horizontal pipe. A certain empty area may exist at the top position of the pipe, which forms a dissatisfied pipe flow pattern. In this case, the frictional effect is relatively high at the bottom of the pipe and the resistance loss is higher than that at the top of the pipe. The cross-sectional position at the connection between the bend pipe and the horizontal pipe, the flow velocity increases in steps from the top of the pipe to the bottom of the pipe. The above visualization results show that, by taking the diameter parallel to the y-axis direction in the horizontal pipe as the dividing line, the frictional resistance loss caused by tailings particles in the part of the pipe above the diameter dividing line is less than that in the part below it. And, there is also a different degree of frictional resistance below of the diameter dividing line, as shown in Figure 10. Figure 10 shows that the tailings particles are subjected to forces of different magnitudes in different locations of the pipe. Below the diameter dividing line, the tailings particles are subject to a variety of forces such as gravity, pipe wall support, drag force between slurry flow layers, and shear force. 49,50 Among them, the shear force and drag force depend on the relative flow velocity between the slurry and the tailings particle, the physical properties of the tailings and other multi-factors, which is one of the reasons for the resistance loss of the flow of the CTBS. The gravitational effect of the tailings particles in the pipe depends not only on their own gravity, but also on the pressure brought by other tailings particles. Therefore, this gravity is called accumulative gravity. The accumulative gravity and the size of the pipe wall support force have different magnitudes in different locations. In Figure 10, the accumulative gravity in different locations below the diameter dividing line is denoted as G a1 , G a2 , and G a . Due to the gravitational influence of other tailings particles, their relationship in size is G a2 > G a > G a1 . The gravity on the tailings particles in different locations above the diameter dividing line and in contact with the pipe wall is G a3 , G a4 . Their size depends on the self-weight of the particles. Below the diameter dividing line, the accumulative gravity G a could be decomposed in the Cartesian system of coordinates into a component G ax in the positive direction of the x 1 axis and a component G ay in the negative direction of the y 1 axis. Defining the angle between G ax and G a as the static friction angle, the relationship between the support and static friction forces with the accumulative gravity is: The static friction angle varies with the position of the tailings particles, and the variation range is 0-90 • . When the tailings particles are located on the diameter dividing line, = 0 • . When the tailings particles are located on the bottom of the pipe, = 90 • . The force analysis shows that G ay is the main force, which causes the frictional loss between the tailing's particles and the inner wall of the pipe. From the diameter dividing line to the bottom of the pipe, the static friction angle increases continuously. Sin is a monotonically increasing function in this interval. Therefore, G ay increases continuously and the degree of pipe wear increases gradually. Due to the fact that the CTBS does not cause more intense pipe friction when flowing in the pipe because of static friction, it is possible to classify the static friction as a beneficial force. When the component of accumulative gravity is larger in the x 1 axis, the beneficial force (static friction) is larger than the harmful force that generates friction loss. The pipe friction is relatively low in this case, and this zone is defined as the medium friction zone. When the component of accumulative gravity in the x 1 axis is low, the beneficial force (static friction) is lower than the harmful force that generates friction loss. The friction between the tailings particles and the pipe wall is more F I G U R E 10 Diagram of pipe wear zone during the flow of cemented tailings backfill slurry intense in this case, and this zone is defined as the heavy friction zone. When the accumulative gravity produces equal components in the x 1 and y 1 axes, it is defined as the dividing line between the two friction zones. When Equations (7) and (8) are equal, the static friction angle could be found (see Equation 9). G ax = G ay (7) G a cos = G a sin (8) cos = sin (9) The horizontal line where the static friction angle = 45 • is located is the dividing line between the medium friction zone and the heavy friction zone. The accumulative gravity is no longer the main effect of the frictional resistance between the tailing's particles and the pipe wall in the position above the diameter dividing line. It is the main force that causes the shearing interaction between the flow layers of the CTBS and the collision and extrusion of the tailing's particles. Therefore, the wear degree in this zone is less than the zone below the diameter dividing line, and this zone is defined as light friction zone.

Effect of pipe diameter and flow velocity on the distribution of tailings particles
Pipe diameter and flow velocity are crucial parameters affecting the transport of CTBS, especially for the bend pipe part and horizontal pipe part of the pipeline transport system. They could change the transport efficiency of CTBS, transport stability, and affect the economic benefits of mining enterprises to a certain extent. It is possible to reduce the impact of the CTBS in the bend pipe and decrease the frictional resistance of the horizontal pipe by reasonably selecting the transport parameters and weighting the constraint relationship between pipe diameter and flow velocity. This paper obtains the distribution of tailings particles in the bend pipe and horizontal pipe under different pipe diameters based on the numerical simulation calculation results. The results are shown in Figure 11. Figure 11 shows that when the pipe diameter is 320-360 mm, the number of tailings particles inside the bend pipe is the largest. When the pipe diameter is 320 mm, the largest number of large-size particles in the pipe are 2825, 3413, 2262, and 2079. In Figure 11A-C, the percentage of small particles size tailings shows a good consistency. The percentage of small particle size tailings increases and then decreases with the increase of pipe diameter. The highest percentage of the pipe diameter is 400 mm. In Figure 11D, the percentage of small particle size tailings decreases and then increases. The highest percentage of small particle size tailings is achieved when the pipe diameter reaches 440 mm. The above results show that, within a certain range, increasing the pipe diameter could improve the reliability of transport. Specifically, by increasing the pipe diameter, the content of small particle size tailings increases, and the formation length and thickness of the lubrication layer at the bottom of the pipe are enhanced. To a certain extent, the environment of CTBS transportation has been improved. The frictional heat between the large size tailings particles and the pipe is reduced, which leads to a decrease in resistance losses during pipeline transportation.
The particle transport paths are plotted by classifying the particles under different scales in the pipe, and the results are shown in Figure 12. Figure 12 indicates that the flow path of the CTBS gradually tends to be turbulent with the increase of flow velocity. In Figure 12A, the large-size particles in the CTBS produce irregular flow with increasing flow velocity. When the flow velocity reaches 2.2-2.5 m/s, large particles will collide with the inner wall of the pipe to form a jet. This could cause a more severe shock to the pipeline. In Figure 12B, the flow paths of the tailings particles with different particle size classifications exhibit dissimilarity. When the flow velocity is 1.6-1.9 m/s, the flow process of large-size tailings particles is prone to sedimentation. When the flow velocity gets to 2.2-2.5 m/s, the sedimentation phenomenon decreases, but does not disappear completely. This indicates that with increasing flow velocity, the chances of pipe blockage accidents are reduced. In the bend pipe and horizontal pipe, the flow path of small particle size tailings has a certain degree of consistency. With a low flow velocity, a lubrication layer is preferentially formed on the inner wall of the pipe. When the flow velocity increases to a certain value, the flow path of small particle size tailings will gradually tend to turbulence, and part of the lubrication layer is destroyed.

Effect of tailings gradation on particle distribution
The beneficiation technology of mines has gradually improved, and the particle size of waste tailings continues to decrease. This has resulted in an increasing range of tailings grain sizes. Therefore, it is of significance to study the effect of tailings gradation on slurry pipeline transportation. According to particle size classification of the soil mechanics sand grains (as shown in Table 4), the different types of tailings are divided into two types of large and small particles. For ultra-fine tailings fine tailings, the size particle separation particle size is 0.1 mm. For unclassified tailings and coarse tailings, the size particle separation particle size is 0.25 mm. The paper calculates the flow distribution states of tailings particles of different gradation types in bend pipe and horizontal pipe through simulation experiments, as shown in Tables 5 and 6. Table 5 shows that in the bend pipe, the specific gravity ratio of large and small size particles of different tailings gradations are ranked as unclassified tailings, ultra-fine tailings, fine tailings and coarse tailings. Table 6 shows that in the horizontal pipe, the specific gravity ratio of large and small size particles of different tailings gradations are ranked as unclassified tailings, fine tailings, ultra-fine tailings and coarse tailings in order. The high proportion of large-size particles would lead to increased wear of the pipeline, which would seriously affect the service life of the pipeline and reduce the production efficiency of the mine, considering the problem of pipeline resistance loss. Moreover, severe wear and tear conditions also pose a transport safety hazard. Therefore, it is unfavorable to use only coarse tailings as backfill material. TA B L E 4 Classification of waste tailings particle size It is appropriate to use ultra-fine tailings, fine tailings and unclassified tailings as backfill aggregates for slurry pipeline transportation.

CONCLUSIONS
This paper explored the flow characteristics of the CTBS in the pipeline based on the particle tracking technology, and visualized the flow of the CTBS in the theoretical perspective. The main conclusions are as follows: 1. The angle between the accumulative gravity and the particle static friction in the opposite direction of the line is , called the static friction angle. The static friction angle size is related to the location of the tailing's particles with the variation range of 0-90 • . With smaller static friction angle , the tendency of particles to slip toward the bottom of the pipe is greater. Based on the visualization of the CTBS, the transport pipeline can be divided into three wear zones: light wear zone, medium wear zone, and heavy wear zone. 2. Increasing the pipe diameter could enhance the thickness of the lubrication layer on the inner wall of the pipe, and the reliability of the CTBS pipe is improved. Low flow velocity could lead the tailings particles tend to sedimentation phenomenon, which increases the chance of pipe blockage accidents. High flow velocity could lead the sedimentation phenomenon diminishes but not disappear and the flow efficiency then increases. However, the pipe wear becomes more intense. 3. Tailings gradation affects the reliability of the CTBS transportation. The wider the range of particle size gradation and the smaller the ratio of the number of large and small particle size tailings, the more suitable the tailings would be as backfill aggregate. Coarse tailings are not suitable as backfill aggregate alone. Fine tailings, ultra-fine tailings and unclassified tailings are relatively suitable and unclassified tailings are the most suitable.
In this paper, the distribution state of tailings particles in the pipeline is obtained. Based on this, the change characteristics of the pipe transport resistance in mine filling can be analyzed to provide some theoretical guidance. However, only the particle distribution state is analyzed. In future research, the authors would investigate the characteristics of