Study and Analysis on the Influence Degree of Particle Settlement Factors in Pipe Transportation of Backfill Slurry

Abstract

In this study, we developed a pipeline transport model to investigate the influence of particle sedimentation factors on slurry transportation through pipelines. The particle tracking module of the software was used to simulate the transport process, and the influences on the sedimentation rate were analyzed considering the slurry concentration, particle size, and flow velocity. The established model exhibited small calculation errors. In addition, the results revealed that the proposed model is reliable for calculating the degree of influence of various factors on particle sedimentation. The effect of the particle sedimentation rate on the pipeline slurry was explored considering the particle size, slurry concentration, and flow velocity. The sedimentation rate was positively related to particle size and adversely related to the slurry concentration and flow velocity. Indeed, study on the sedimentation rate requires considering a reasonable range of particle sizes, preparing a slurry with an appropriate concentration, and adjusting an appropriate flow velocity. Numerical simulations were performed using the filling data as the background for a sample mining area. The experimental results showed optimal slurry concentration and particle size of 60% and 25.25 µm, respectively.

1. Introduction

In recent years, pipeline filling technology has been widely used while the mining depth has been gradually increased [1,2,3]. Therefore, both the rules of sedimentation and influence on the pipeline transportation must be determined [4,5,6]. The production capacity of a mine can be increased by selecting an appropriate technology of particle sedimentation, and avoiding pipe blocking to reduce the failure rates in mine pipelines [7,8,9].

There are many methods to study particle sedimentation: the bottom suction pipe method based on the Oden theory [10,11], repetition depth pipette method based on the McLaughlin formula [12,13], and sand sink method to study the effect of flow turbulence on the particle settling rate [14,15,16]. Some studies were conducted to perform sedimentation tests on a sediment suspension in a sedimentation cylinder, and formulae for the sedimentation rate were obtained [17,18]. Other studies analyzed experimental data to design a conical settlement cylinder and establish a settlement rate formula for nonuniform sand groups [19]. Some study results have shown that both sediment concentration and particle size are important factors affecting the sedimentation rate [20].

Foreign research is more advanced. Debadutta Das et al. studied the surface activity of the natural surfactant A. auriculiformis isolated by a chemical and aqueous extraction method by calculating its critical micellar concentration (CMC) on the basis of surface tension measurement. The stability of fly ash slurry was determined from its rheological parameters, dispersant concentration, and stabilization mechanism. The stabilization of high-concentration fly ash slurry has been studied through its rheological behavior by variation of temperature and dispersant and ash concentration [21,22]. Anupama Routray et al. researched the flow behavior of coal water slurry (CWS) characterized with a mixture of non-ionic surfactant saponin from shikakai and a cationic surfactant di-docyl ammonium bromide (DDAB) at different coal loadings, pH, and dispersant dosages. A suitable mechanism of interaction between the mixture of saponin and DDAB on coal surfaces was given on the basis of zeta potential measurement [23]. Subrata Narayan Das et al. reported the stabilization of various types of slurries (particularly iron ore slurry) with their rheological behaviors and CFD analysis for economic pipeline transportation [24].

In this study, we established a filling pipeline model using COMSOL software to simulate the flow regime of slurry in pipelines and to determine the degree of influence of various factors on particle sedimentation [25,26,27]. This will provide a theoretical basis for improving the stability of mine filling pipeline transportation.

Therefore, we analyzed the factors that affect particle settlement in the slurry and obtained the influence degree of each factor, which provides a reference for the calculation of pipeline transportation parameters. COMSOL software has noticeable advantages in the simulation of particle settlement experiments, simple calculations, and a high visualization degree [28,29,30].

2. Materials and Methods

This experiment refers to the “Technical Specification for the Total Tailings Paste Backfill” standard (GB/T 39489-2020).

2.1. Test Material

The tailings of the test material were chosen from the Iron Mine of Gao Guan Ying. It was ground by the ore powder grinding machine of our laboratory (YGM130). The density of tailings was determined to be 2620 kg/m³. The contents of TFe, SiO₂, CaO, MgO, and Al₂O₃ in the tailings were 6.00, 67.58, 4.04, 5.60, and 7.30%, respectively. A NKT6100-D (Haixinrui Technology, Beijing, China) laser particle size analyzer was used to detect the particle size composition. The volume proportion and cumulative proportion of particle size are shown in

Table 1. Particle size, volume proportion, and cumulative proportion.

No.	Size	Volume %	Accumulation %	No.	Size	Volume %	Accumulation %	No.	Size	Volume %	Accumulation %
	µm				µm				µm
1	0.36	0.01	0.01	13	2.53	2.72	14.67	25	17.84	6.43	65.84
2	0.42	0.02	0.03	14	2.98	2.75	17.42	26	20.99	6.67	72.51
3	0.5	0.03	0.06	15	3.50	2.81	20.23	27	24.70	6.60	79.11
4	0.59	0.09	0.15	16	4.12	2.93	23.16	28	29.06	6.15	85.26
5	0.69	0.19	0.34	17	4.85	3.14	26.30	29	34.20	5.34	90.60
6	0.81	0.42	0.76	18	5.71	3.53	29.83	30	40.24	4.17	94.77
7	0.95	0.76	1.52	19	6.72	4.01	33.84	31	47.36	2.87	97.64
8	1.12	1.25	2.77	20	7.91	4.42	38.26	32	55.73	1.65	99.29
9	1.32	1.78	4.55	21	9.30	4.72	42.98	33	65.58	0.66	99.95
10	1.55	2.22	6.77	22	10.95	5.02	48.00	34	77.17	0.05	100.00
11	1.83	2.51	9.28	23	12.88	5.44	53.44
12	2.15	2.67	11.95	24	15.16	5.97	59.41

and Figure 1a,b.

According to Table 1, weighted average particle size, $d_{av}={{\displaystyle \sum }}_{i=1}^n{d}_i{G}_i/100=15.05\mathsf{\mu }\mathrm{m}$; uniformity coefficient, $K_0=\frac{d_{60}}{d_{10}}=7.16$; and curvature coefficient, $C_c=\frac{d_{30}^2}{d_{60}\times d_{10}}=1.76$, where $d_i$ represents the particle size of tailings, $G_i$ represents the weight of tailings, $d_{60}$ is the particle size less than 60%, and $d_{30}$ and $d_{10}$ are 30 and 10%, respectively.

According to the development status of domestic mining science, in the process of tailings cementing, filling and the pipe gravity transport filling times line is typically not more than 5–6; thus, the concentration of filling slurry should be reduced or a method of increasing the pressure should be adopted when the filling timeline is extremely large. The filling timeline of the test was 2.5 and the diameter of the pipe was 200 mm. Viscosity, slurry stability, and pressure are the most important parameters to explain the flow behaviors. Viscosity is a physical and chemical property of a substance. Due to the action of viscosity, the object is subject to friction resistance and differential pressure resistance when moving in the fluid, resulting in the loss of mechanical energy. The stability of slurry is affected by many factors, the most important of which are its concentration and flow velocity. Appropriate concentration and velocity will make the slurry flow steadily and the flow state will not change greatly. In a broad sense, pressure pipes refer to all pipes subjected to internal or external pressure, regardless of the medium in the pipe. The pressure pipeline is a part of the pipeline; the pipeline is used for transportation, distribution, mixing, separation, discharge, metering, control, and stopping the flow of fluid by pipes, pipe fittings, flanges, bolt connections, gaskets, valves, other components, or compression parts and supporting parts of the assembly.

Pipeline transportation is a complex process; therefore, the results of the test can be affected by the pipe diameter, pipe wall, flow velocity, particle size, concentration, temperature, height, friction, and other factors. The optimal value of each factor was calculated by the resistance loss experiment, and the concentration range was 50–60%; the particle size range was 20–60 μm, the flow rate was not more than 2.5 m/s, and the number of experiments in each group was less than 10.

To obtain the test data more scientifically and reduce redundant work, the degree of influence of each factor on sedimentation was explored considering the concentration, particle size, and velocity (

Table 2. Simulation test plan parameters.

Number	Concentration %	Particle Size (µm)	Flow Velocity (m/s)
1	60	15.05	2.0
2	55	30.25	2.2
3	50	50.95	2.4

). Orthogonal experimental design is an experimental design method of multiple factors and multiple levels. According to the orthogonality, some representative points are selected from the comprehensive test to carry out the test. These representative points have the characteristics of uniform dispersion and uniform comparability. Orthogonal experimental design is the main method of fractional factorial design. Orthogonal assistant software was used to obtain the experimental scheme and plan. The details are presented in

Table 3. Factor and level chart.

Number	1	2	3
Name	Concentration %	Particle Size (µm)	Flow Velocity (m/s)
Level 1	60	15.05	2.0
Level 2	55	30.25	2.2
Level 3	50	50.95	2.4

and

Table 4. Experimental plan.

Factor	Concentration %	Particle Size (µm)	Flow Velocity (m/s)
Test 1	60	15.05	2.0
Test 2	60	30.25	2.2
Test 3	60	50.95	2.4
Test 4	55	15.05	2.2
Test 5	55	30.25	2.4
Test 6	55	50.95	2.0
Test 7	50	15.05	2.4
Test 8	50	30.25	2.0
Test 9	50	50.95	2.2

.

After drying the material, the particle sizes were separated, the attrition treatment was performed, and the particle size was measured. Three kinds of tailings with average weighted particle sizes of 15.05, 30.25, and 50.95 µm were selected, whereas the cement–sand ratio of the test samples was 1:6. The concentrations of 60, 55, and 50% were prepared for the three types of tailings, respectively, as shown in

Table 5. Tailings test scheme parameters.

Concentration	Cement–Sand Ratio	Quality1 (g)	Quality2 (g)	Quality3 (g)
60%	1:6	25.71	154.29	300
55%	1:6	23.57	141.43	300
50%	1:6	21.43	128.57	300

.

Mixing the cement with tailings: The tailings slurry was prepared according to the ratios listed in Table 5. Slag Portland cement was used in this test. The prepared slurry of each group was placed in the rheometer. The rheological characteristic curve of the slurry was obtained using a HAAKES series rheometer manufactured by Thermo Fisher Scientific Company (Shanghai, China), USA. A four-blade pulp rotor (FL16SK01140438, Thermo Fisher Scientific Company, Shanghai, China) was used in the test. The type of sleeve used for filling the slurry was L13092 (Thermo Fisher Scientific Company, Shanghai, China), with an inner sleeve diameter of 26.20 mm and an outer diameter of 30.00 mm. Filling slurries were prepared with particle sizes of 15.05, 30.25, and 50.95 μm, and mass concentrations of 60, 55, and 50%. The rheological characteristic curves of filling slurries with different particle sizes and mass concentrations were obtained by controlling the shear rate (the CR method). Compared with the test method of controlling shear stress (the CS method), the rheological characteristic curve of the slurry tested using the CR method is more comprehensive, which can reflect the rheological characteristics of the slurry during the entire process from the low-speed to the high-speed state. The test was carried out at room temperature (22 °C) to avoid the influence of temperature changes on the test results.

The test parameters are presented in

Table 6. Rheological characteristics of the tailings.

Concentration	Cement–Sand Ratio	Particle Size (µm)	Yield Stress (Pa)	Plastic Viscosity (Pa·s)
60%	1:6	15.05	50.05	0.513
60%	1:6	30.25	51.23	0.522
60%	1:6	50.95	52.34	0.568
55%	1:6	15.05	20.58	0.339
55%	1:6	30.25	21.36	0.348
55%	1:6	50.95	22.59	0.362
50%	1:6	15.05	15.33	0.248
50%	1:6	30.25	16.47	0.269
50%	1:6	50.95	17.26	0.297

. The fluid flow can be characterized by many physical quantities, among which the Reynolds number has been used frequently [31,32,33]. The linear dimension of pipe diameter was used in determining the Reynolds number. The Reynolds numbers of the materials used in this experiment were all less than 2300 and belonged to the laminar flow state; they were calculated using $R_e=\rho vd/\mu$.

2.2. Geometric Modeling and Meshing

First, we made the following assumptions: The size of slurry particles is uniform. The fluid in the pipeline is a single-phase laminar homogeneous body, and the particles rebound when the fluid flows to the pipeline wall. There is no heat exchange phenomenon inside the pipeline; thus, the influence of water viscosity on particle and interference sedimentations on the particle sedimentation velocity are ignored.

In this test, COMSOL software was used to conduct a simulation on the filling pipeline, which was used to build a model of the filling elbow pipe, as shown in Figure 2. As the pipeline had an axisymmetric model, the physical structure of the pipeline could be sufficiently reflected by a two-dimensional model. Therefore, an “L”-shaped geometric model was drawn, and the filling timeline of the test was 2.5. The height of the standpipe part, outer diameter of the elbow pipe, inner diameter of the elbow pipe, and length of the horizontal straight pipe were 1.0, 1.0, 0.8, and 4.0 m, respectively. Particles follow the flow, with the inlet and outlet at the top and bottom of the pipe, respectively. COMSOL software (Multiphysics 5.5., Shanghai, China.)includes a mesh division tool, which can edit the modularized physical model. The mesh division was based on the laminar flow and FPT modules, as shown in Figure 3. A contour of the flow pattern of particle deposition and the pressure result are shown in Figure 4 and Figure 5.

Laminar flow module conditions:

(1)

Fluid properties: density 1680 (kg/m³), dynamic viscosity 0.513 (Pa·s).

(2)

Initial values: both are 0.

(3)

Wall: Wall condition—no slip.

(4)

Gravity: x axis is “0”, y axis is “g_const”.

(5)

Inlet: Normal speed is 2.0 m/s, 2.2 m/s, 2.4 m/s.

(6)

Outlet: Pressure condition is “0” Pa.

Fluid particle tracking module:

(1)

Particle properties: Particle density is 2620 (kg/m³). Particle diameter is 15.05 μm, 30.25 μm, 50.95 μm

(2)

Entrance: Release time—range (0, 0.05, 10), number of particles released each time n = 20.

The unit size was selected to be ultrafine, and the sequence type was the physical field control network. Finally, the partition results contained 5194 domain units and 566 boundary elements. The minimum cell mass of the mesh was 0.4462, average cell mass of the mesh was 0.8112, unit area ratio was 0.2884, and the time step of the fluid flow was in the range (0, 0.05, 10). This meant release every 0.05 s from 0 to 10 s.

3. Results

The resistance of particles in the pipeline can be expressed as follows:

$$F_D=C_D\frac{\rho u_0^2}{2}{A}_D=C_D\frac{\rho u_0^2}{2}\frac{\pi d^2}{4}$$

(1)

where $\rho$ is the slurry density and $C_D$ is the coefficient of resistance, which varies with Reynolds number $R_e$ and ranges from 0.01 to 10⁵. The coefficient of resistance can be expressed as

$$C_D=2{\left(1.84R_e^{-0.31}+0.293R_e^{-0.06}\right)}^{3.45}$$

(2)

According to Newton second law, the forces of the particles in the pipeline are gravity, buoyancy, and drag, which can be expressed as follows:

$$F_g-F_b-F_D=m\frac{d_u}{d_t},$$

(3)

where $F_g=mg$, $F_b=\frac{m}{{\rho }_p}\rho g$, and d is the diameter. $F_b$ is lift force, which is not significant in this test.

The differential equation of motion of particles can be expressed as

$$\frac{d_u}{d_t}=\left(\frac{{\rho }_p-\rho }{{\rho }_p}\right)g-\frac{3C_D}{4d}\frac{\rho }{{\rho }_p}{u}^2$$

(4)

where ${\rho }_p$ is the solid density and $d_u/d_t=0$. The relative rate of particle-free sedimentation can be written as follows:

$$u=\sqrt{\frac{4\left({\rho }_p-\rho \right)gd}{3\rho C_D}}$$

(5)

According to the corresponding relationship between the coefficient of resistance and Reynolds number, the free sedimentation velocity in a laminar flow can be expressed as

$$u=\frac{\left({\rho }_p-\rho \right)g{d}^2}{18\mu },$$

(6)

where $\mu$ is the coefficient of viscosity, ${\rho }_p$ is the particle density, $\rho$ is the slurry density, and d is the particle size.

The density of the particles is high and some forces need to be taken into account such as added mass. In actual transportation, particles are moving in groups. Collision and friction will inevitably occur between particles and the pipe wall. At this time, if you want to accelerate the movement, this will cause the surrounding fluid to accelerate the movement. Because the fluid has inertia, it acts as a reaction force on the particles. At this point, the force pushing the particle will be greater than the inertial force of the particle itself, as if the particle mass had increased. The force greater than the inertial force of the particle itself is called the additional mass force.

$$F=\left(m+\delta \right)a$$

(7)

where $\delta$ is mass force; a is accelerated velocity.

The sedimentation velocity of the particles cannot be affected when the slurry flows horizontally. The solid particle sizes are in a wide range in the slurry transported by the mine pipelines. The effect of water viscosity on sedimentation is ignored. In addition, when $d_i\le 0.3a$, the sedimentation velocity of particles in a laminar flow can be calculated using a simplified Stokes formula as follows [34]:

$$\left\{\begin{array}{c}a=\sqrt[3]{0.0001+\left({\rho }_g-1\right)}\\ {\mathrm{V}}_{\mathrm{s}}=5450d_i^2\left({\rho }_g-1\right)\end{array}\right\}$$

(8)

The calculation results using Equation (8) were compared with the numerical simulation results to verify the reliability of COMSOL software in the numerical simulation of slurry particle settlement. The details are presented in

Table 7. Results of experimental simulation and actual calculation.

No.	Concentration %	Particle Size µm	Flow Velocity m/s	Simulation Speed cm/s	Calculation Speed cm/s	Relative Error %
1	50%	15.05	2.0	0.0182	0.0199	8.54
2	50%	30.25	2.2	0.0759	0.0807	5.95
3	50%	50.95	2.4	0.2193	0.2291	4.28
4	55%	15.05	2.2	0.0175	0.0199	12.06
5	55%	30.25	2.4	0.0724	0.0807	10.29
6	55%	50.95	2.0	0.2135	0.2291	6.81
7	60%	15.05	2.4	0.0166	0.0199	16.58
8	60%	30.25	2.0	0.0701	0.0807	13.14
9	60%	50.95	2.2	0.2099	0.2291	8.38

.

SPSS software (Beijing Netnumber Times Technology, Beijing, China) was used to analyze the correlation between the simulation and calculation results (

Table 8. Correlation between the simulation and actual calculation results.

Name	Simulation Speed (cm/s)			Calculation Speed (cm/s)
	Pearson Correlation	Sig. (Double Tail)	Case Number	Pearson Correlation	Sig. (Double Tail)	Case Number
Simulation speed (cm/s)	1	0	9	0.999437	1.3948388027 × 10−11	9
Calculation speed (cm/s)	0.999437	1.3948388027 × 10−11	9	1	0	9

). As shown in Table 8, the value of Sig. (double tail) was less than 0.01, confirming a significant correlation between the simulation and calculation results. Additionally, the correlation coefficient between the simulation and calculation results is 0.999437, which is close to 1, confirming an extreme correlation [35,36,37].

As shown in Table 7, the relative error between the calculated results of Equation (1) and those of the numerical simulation is less than 20%, indicating that the numerical model of tailing particle sedimentation established in this experiment is relatively reliable.

The range analysis method was adopted to examine the influence degree of slurry concentration, particle size, and flow velocity on the particle sedimentation velocity.

Table 9. Degree of influence of each factor on the sedimentation velocity.

Range	Test Factor
	Concentration %	Particle Size (µm)	Flow Velocity (m/s)
$K_1$	0.3134	0.0523	0.3018
$K_2$	0.3034	0.2184	0.3033
$K_3$	0.2966	0.6427	0.3083
$\overline{K_1}$	0.1045	0.0174	0.1006
$\overline{K_2}$	0.1011	0.0728	0.1011
$\overline{K_3}$	0.0989	0.2142	0.1028
$R$	0.0056	0.1968	0.0022

shows the degree of influence of each factor on the sedimentation velocity. Software was used to establish the regression equation of sedimentation velocity with respect to the three factors. The regression equation can be expressed as follows:

Y = 2.811 − 4.654x₁ + 7.153 × 10⁻³x₂ − 1.482x₃ − 1.752 × 10⁻²x₁x₂ + 2.407x₁x₃ + 3.943 × 10⁻³x₂x₃,

where Y is the sedimentation velocity, x₁ is the concentration, x₂ is the particle size, and x₃ is the flow velocity. The correlation coefficients of this regression equation before and after adjustment were R = 0.99365 and Ra = 0.97433, respectively. Therefore, the regression equation is significant and its reliability is high.

In Table 9, K₁, K₂, and K₃ are the sums of ranges for each factor; $\overline{K_1}$, $\overline{K_2}$, $\overline{K_3}$ are the mean ranges of each factor at each level.

The pipeline circulation monitoring system designed and built by our research group in the laboratory was used to verify the above model. The experimental platform is shown as Figure 6. The platform is composed of transparent pipe, ITS detector, mixing tank, pressure pump, etc. Among them, the ITS mainly collects the data of the front and rear sections and transmits them to the computer. Finally, the results were analyzed, as shown in the table below. According to the data in

Table 10. Results of simulation and experiment.

	Concentration %	Particle Size µm	Flow Velocity m/s	Simulation Speed cm/s	Experimental Speed cm/s	Relative Error %
1	50%	15.05	2.0	0.0182	0.0198	8.08
2	50%	30.25	2.2	0.0759	0.0805	5.71
3	50%	50.95	2.4	0.2193	0.2293	4.36
4	55%	15.05	2.2	0.0175	0.0195	10.26
5	55%	30.25	2.4	0.0724	0.0809	10.51
6	55%	50.95	2.0	0.2135	0.2289	6.73
7	60%	15.05	2.4	0.0166	0.0194	14.43
8	60%	30.25	2.0	0.0701	0.0802	12.59
9	60%	50.95	2.2	0.2099	0.2288	8.26

, the relative errors are within 20% and the model established by the software has certain reliability.

4. Discussion

4.1. Analysis of the Influence Degree

The obtained results confirm that the particle size has a significant influence on the slurry particle sedimentation process.

In addition, the particle density affected the sedimentation velocity, which had a certain influence on the degree of settlement [38]. Particles in the slurry with a larger apparent density presented a higher difference between the density of the particles and filling slurry, resulting in a greater sedimentation tendency.

In this study, ultrafine unclassified tailings were used as the experimental material, whereas the weighted mean particle size was 15.05 μm. Both the apparent and bulk densities are approximately the same [39,40,41,42]. Experimental materials were treated with extremely fine and approximately uniform shapes. The densities of each sample group were approximately equal, ranging from 2620.2 to 2620.5 kg/m³. In the future, we will conduct a thorough study on the factors influencing the particle density.

The grading of tailings in the filling pipeline is crucial. Filling slurries prepared with coarse, fine, or ultrafine tailings have different influences on the entire filling process. Finer tailings are easier to prepare from approximately homogeneous fluids, which makes the flow smoother. When the particle size remains the same, slurry of different concentrations affects the sedimentation velocity of particles and the flow pattern. When the concentration is low, the slurry flows and settles at the same time, and becomes thin when it reaches the stope, which influences the filling effect. However, when the concentration is high, the viscosity of the slurry increases so that the filling speed slows down, the pumping pressure increases, and even excessive sedimentation leads to silting. In serious cases, pipes burst, resulting in serious accidents. When only the influence of velocity is considered, as the particle is affected by the drag force in the fluid, the faster velocity produces a larger drag force, pulling the particle forward; hence, it is not easy to settle.

In conclusion, particle size, slurry concentration, and flow velocity have a certain influence on the sedimentation of the filling slurry. Therefore, it is crucial to study the degree of influence of the three factors on particle sedimentation for the entire filling system. A three-dimensional direct view is shown in Figure 7.

4.2. Effect of Particle Size on the Sedimentation Velocity

When the slurry is transported by a mine filling pipeline, the size of the solid particles is distributed over a wide range. In the filling slurry of fine tailings, the particle size of one stage can be selected as the basis for the sedimentation velocity calculations. Because particle size and shape are the key factors affecting particle sedimentation, we assumed that the shape of tailings was approximately the same after refining treatment; hence, the correction coefficient of the sedimentation velocity of non-spherical particles was not considered. In addition, an increase in the particle size generates a certain head effect. The influence of particle size on sedimentation velocity is shown in Figure 8. As shown, with an increase in particle size, the sedimentation velocity gradually increases. Under the conditions of the same particle size and different concentrations, the sedimentation law is roughly the same; however, the sedimentation velocity gradually decreases with an increase in the concentration. The sedimentation of a single particle causes the movement of the surrounding water in the fluid, which considerably affects the sedimentation velocity. However, solid particles in the filling pipeline are distributed in clusters, the resistance of the nearby water increases when a single particle settles down, and the viscosity reduces its sedimentation velocity. When a group of particles settles down, the surrounding water rises, and the sedimentation velocity increases.

4.3. Effect of Concentration on the Sedimentation Velocity

Concentration is not only an important parameter affecting the hydraulic gradient but is also a key factor in the reasonable operation of the entire filling system. An appropriate slurry concentration can not only guarantee stable transportation of the filling pipeline but also avoid pipe blocking accidents caused by the concentration problem. A low concentration of slurry causes the center point of the slurry to move up; thus, the speed of all sides is larger at the top and smaller at the bottom; therefore, the bottom of the pipeline can readily produce siltation, or even pipe blocking, causing serious accidents that affect production. The influence of concentration on the sedimentation velocity is shown in Figure 9. As shown, there is an adverse relationship between the concentration and sedimentation velocity. When different types of tailings are selected to prepare the slurry with the same concentration, the larger the content of large particles, the easier is the settlement, and the faster is the sedimentation velocity. When concentration increases, the sedimentation velocity of the slurry with a small particle size remains unchanged. When the pipe diameter is constant and the concentration is extremely high, the conveying resistance increases accordingly so that the horizontal direction speed in the pipe decreases, and the free sedimentation velocity of the particles in the vertical direction increases. When the concentration was minimal, the particles in the slurry appeared to be suspended. The resistance loss in the horizontal direction was slight; thus, the slurry flow in the pipeline was smooth, and the vertical direction of the sedimentation velocity was reduced, indicating a state of stable flow.

4.4. Effect of Flow Velocity on the Sedimentation Velocity

The calculation of the hydraulic gradient is significant in the hydraulic transport of solid materials. Many factors affect the hydraulic gradient, whereas the flow velocity has the highest influence. Solid–liquid mixtures are usually divided into structural, Newtonian, homogeneous, and heterogeneous flows. In general, cream-body fill belongs to the category of structural flow. In practical production, however, Newtonian flow is frequently used for gravity flow conveying. A heterogeneous fluid is affected by the drag force of the fluid to produce a forward force when it flows in a pipeline. The particles in the fluid do not easily undergo sedimentation if the flow velocity is considerably fast, and the drag force is significantly large. Otherwise, the flow velocity is moderate, and the sedimentation velocity is swift. The influence of the concentration on the sedimentation velocity is shown in Figure 10. With an increase in the slurry velocity, the sedimentation velocity exhibits a slight downward trend. The faster the flow velocity of the slurry in the pipeline, the slower the sedimentation velocity. The particles are subjected to a drag force in the horizontal direction, and the vertical direction of the sedimentation velocity decreases; thus, an adverse relationship exists. As shown in Figure 7, under the same flow velocity, the larger the particle size, the faster the sedimentation velocity. When the particle size varies from 30.25 to 50.95 µm, the sedimentation velocity presents a step change. We cannot set the flow velocity more widely during the process of actual transportation. A film was formed between the precipitated particles and the pipe wall. If the flow velocity is extremely high, the friction between the slurry and the pipe wall is aggravated. It is easy to wear the pipe wall, which causes the slurry to settle and hoard. In long-term operations, it may also lead to serious leakage and plugging accidents, causing vast economic losses.

4.5. Case Study and Analysis

The mining area is an underground mine, and waste tailings need to enter the filling station for secondary utilization. They are conveyed to the underground goaf by a pipeline to maintain the stress balance of the stope. The system adopts the entire tailings cemented filling technology. The ground station is equipped with a slurry at a concentration range of 55–60%, and a particle size range of 18.25 to 32.25 µm. A large flow rate in a pipeline with an inner diameter of 200 mm was selected, in which the straight pipe part, horizontal, vertical, slope angle, and the flow rate per unit time were approximately 2000 m, 1500 m, 500 m, 45°, and 120–160 m³/h, respectively. The filling system is shown in Figure 11.

To restore the scene, the sedimentation velocity of the slurry in the pipe during the conveying process of the filling system was calculated, and a geometric model with a model size of 1:1 was established. A slurry with a concentration of 55% was selected according to the actual filling conditions. Simultaneously, based on the analysis of the three influencing factors, the optimal parameters were selected for verification, and the tailings of particle sizes of 18.25, 25.25, and 32.25 µm were screened for comparison with those of the concentration of 60%, as shown in Figure 12.

The figure shows that when filling is carried out in accordance with an engineering practice, the particle sedimentation velocity in the pipeline is faster. The sedimentation velocity of the particles decreases with an increase in the concentration. To avoid the risk of pipe plugging caused by sedimentation, a larger concentration range can be selected; however, it is necessary to balance the resistance loss caused by high concentrations. This is shown in

Table 11. Case analysis data.

	Concentration	Particle Size	Flow Velocity	Sedimentation Velocity	Resistance Loss
	%	µm	m/s	cm/s	Pa/m
1	55%	18.25	2.0	0.0256	4532.6
2	55%	25.25	2.0	0.0618	4705.7
3	55%	32.25	2.0	0.1393	4932.4
4	60%	18.25	2.0	0.0248	5087.5
5	60%	25.25	2.0	0.0601	5365.2
6	60%	32.25	2.0	0.1154	5736.6

below. The larger the particle size, the greater the resistance loss will be. In addition, the larger the particle size, the faster the sedimentation rate. This will lead to the formation of a slip layer or even a settlement area in the pipe, which will affect the transportation of the whole pipe and lead to greater resistance loss. Although a small particle size is helpful for pipeline transportation, too small a particle size will affect the formation of the early strength of the backfill. The transport resistance of the filling pipeline increases rapidly with the increase in slurry concentration. When the slurry concentration is less than 60%, the energy loss in the slurry pipeline transportation can be greatly reduced, and the risk of pipe blocking and pipe explosion can also be reduced. Considering the strength demand of the filling structure in the mine, in order to effectively improve the mine production efficiency and reduce the water seepage, the concentration of the filling body should not be lower than 60%.

Therefore, the optimal concentration for this experiment was 60%. As the particle size of the tailings is variable, screening procedures are added to classify the tailings. Therefore, the larger the particle size, the greater the sedimentation velocity; thus, the selection of tailings slurry with small particle size is the best choice. Nevertheless, an extremely small particle size is not conducive to increase the viscosity of the slurry. Thus, a moderate particle size of 25.25 µm can be selected. Consequently, the optimal parameters of this project were a concentration of 60% and particle size of 25.25 µm. In addition, when the pipe diameter is less than or equal to 200 mm, the optimal flow rate can be calculated using the Durard formula ($v=F_l\sqrt{2gD\frac{{\rho }_g-{\rho }_1}{{\rho }_1}}$), where $F_l$ is the correlation coefficient, g is gravitational acceleration, D is pipe diameter, ${\rho }_g$ is the density of the mixture, and ${\rho }_1$ is the density of the slurry. In our experiment, the optimal flow rate was 1.44 m/s.

5. Conclusions

In this study, we established a pipeline transport model to investigate the influence of particle sedimentation factors on slurry transportation. The following conclusions can be drawn:

• The simulation transport process model of the filling slurry pipeline was established and verified using COMSOL software. Comparing the simulation results with those obtained using a simplified Stokes formula and ignoring the influence of medium viscosity on sedimentation velocity yielded a relative error in the range 4–17%, which proved the reliability of the proposed model.
• Under different conditions, the model was used to calculate the variation characteristics of the sedimentation velocity. The sedimentation velocity was positively related to the particle size and adversely related to the concentration and flow velocity. Setting a reasonable range of particle sizes, preparing a slurry with a reasonable concentration, and adjusting an appropriate flow velocity are key factors in examining the sedimentation velocity. Therefore, this study provides a theoretical basis for investigating the sedimentation law.
• Using the range analysis method showed that the degree of influence on the sedimentation velocity is as follows: particle size > concentration > flow velocity. In a sample mining area, the optimal slurry concentration and particle size were 60% and 25.25 µm, respectively. Consequently, finding optimal parameters is significantly important in reducing the sedimentation velocity of particles and improving the efficiency of pipeline transportation.