Numerical Study on Deposition Behavior of Micron-Sized Suspended Solids in Broken Rock Mass within a Goaf Based on Coupled CFD-DEM Method

Abstract

After coal mine wastewater is artificially injected into a groundwater reservoir transformed from a goaf, micron-sized suspended matter in the wastewater is purified by the broken rock mass in the goaf. Existing studies can only analyze the macroscopic changes in the content of suspended solids during the purification process, and it is difficult to explain the microscopic deposition mechanism of the suspended solids in broken rock. This paper studied the microscopic deposition behavior of micron-sized suspended solids inside the broken rock mass via numerical simulation using a coupled CFD-DEM method. In addition, indoor model tests were carried out to verify the accuracy and reliability of the model in comparison. The study results show that suspended solids’ deposition behavior varies significantly under broken rock masses’ different pore sizes (0.47 mm, 1.14 mm, 3.00 mm, and 5.33 mm). Within the goaf, the adsorption of suspended solids by the broken rock mass plays a dominant role. At the same time, suspended particles are mostly collected in the inlet area, and the difference in the number of deposited particles can reach 74% when comparing the first 50 mm range as well as the 50–100 mm range. The number of deposited particles at a flow rate of 0.02 m/s is 14% more than that at a flow rate of 0.06 m/s. This work offers new ideas for studying the purification mechanism of coal mine wastewater within a goaf.

1. Introduction

As a major coal-producing region, the western mining areas in China have exhibited increasing coal production yearly [1,2]. However, the increase in coal production has brought more severe ecological and environmental problems, the most prominent of which is the challenge of water resource utilization in coal-producing areas [3]. The goaf is an abandoned area left after coal seam mining, filled with broken rock from the upper collapse inside. Studies have shown that underground reservoirs constructed using abandoned space created after coal mining can store and purify the lost wastewater from the coal mine [4]. These studies provide a new idea to solve water utilization challenges in western mining areas [5,6]. Currently, underground water reservoirs have been practically applied in the Shendong region of China. The Daliuta coal mine is the first coal mine in China with a three-dimensional spatial network of groundwater resource recycling systems [7]. Including the Daliuta coal mine, 32 underground water reservoirs have been built in 13 mines in the Shendong region, obtaining 27 million cubic meters of water storage [8]. The empirical results show that underground reservoirs can efficiently use underground waste space in coal mines and the storage of coal mine wastewater, which is an effective way to solve the problem of water resource utilization in goafs.

Contaminants such as water-soluble chemical elements, organic matter, and insoluble suspended solids are commonly found in coal mine wastewater [9]. Underground reservoirs can purify the coal mine wastewater of contaminants during the storage of coal mine wastewater. Studies and field projects have shown that after the coal mine wastewater flows into the underground reservoir, the insoluble suspended solids in the coal mine wastewater are trapped and adsorbed by the broken coal rock mass in the goaf [10], as shown in Figure 1. Soluble chemical elements and organic matter react with the coal rock mass and are separated from the coal mine wastewater [11,12]. These two effects achieve the purification of coal mine wastewater via the broken coal and rock mass. After purification, the pollutants in the coal mine wastewater are significantly reduced, and the water quality can meet the mine’s industrial and domestic water standards [3]. The current research on the purification process only explores the variation in different pollutants in coal mine wastewater from a macroscopic perspective. Most of them are laboratory-scale model experiments [11,13] or direct measurements of in situ water samples that explain the mechanism of coal mine wastewater purification by comparing the changes in the content of pollutants in the water before and after purification [12]. However, the microscopic deposition and distribution patterns of contaminants are not clear due to the difficulty of directly observing the microscopic movement behavior of contaminants.

Coal mine wastewater can be classified into four categories according to the characteristics of contaminants: coal mine wastewater containing suspended solids, highly mineralized coal mine wastewater, acid coal mine wastewater, and coal mine wastewater with unique contaminants [14]. Most coal mine wastewater in China contains suspended solids [14,15]. During the purification process of suspended coal mine wastewater by broken rock masses, the suspended solids are retained and adsorbed by the broken rock masses [10]. The strength of this interception and adsorption depends on the rocks’ properties and the pore channels between the rocks [16,17], while factors such as rock shape and grain size can affect the pore structure and permeability characteristics [18,19,20]. The migration patterns of fluids and fine particles are very different under different pore-size conditions [21,22], which in turn affects the deposition of suspended material inside the broken rock. However, it is difficult to directly observe the migration distribution process of suspended solids in the broken rock mass due to the closed area inside the goaf. With the continuous development of computer technology, many scholars have begun to use numerical simulation methods to study the scientific problems inside the goaf [23,24,25,26], which provides new ideas for studying the microscopic migration patterns of suspended solids there.

The CFD-DEM method is a numerical simulation method to simulate particle–fluid interaction [27,28,29]. This coupling method is based on the simplified N-S equation for numerical modeling and the Euler–Lagrange reference system to study particle and flow field motion under different operating conditions [30]. The accuracy of the numerical model can also be verified by simulating indoor tests in the numerical simulation model [27]. The CFD-DEM method has been used in many applications in the field of fluid–solid coupling in geotechnical engineering. It has proved to be highly accurate in explaining the microscopic motion patterns of particles in the flow field. Zhang et al. [31] used the coupled CFD-DEM method to simulate the motion of broken rock masses in the goaf. However, only the microscopic motion behavior of millimeter-scale broken rock masses was discussed. In the goaf, the particle size of suspended solids in coal mine wastewater is in the submicron-to-micron range [32,33], and the particle size of broken coal rock can reach a scale from millimeters to meters [34]. The particle size affects the pore size distribution inside the broken coal rock mass, and if the pore size of the broken coal rock mass is too large, the deposition of suspended solids will not even occur. Therefore, the microscopic deposition behavior of micron-sized suspended solids under different pore conditions must be studied according to the actual conditions within the goaf.

In this paper, the coupled CFD-DEM simulation method is used to study the deposition behavior of micron-sized suspended solids inside the broken rock mass in the goaf, revealing the microscopic deposition mechanism and the migration characteristics of suspended solids in the broken rock mass, which are difficult to observe experimentally. The numerical model is appropriately simplified according to the actual geological conditions of the goaf. The simulation analyzes the microscopic deposition behavior of suspended solids under different pore conditions, and the mechanisms of different influencing factors on the microscopic motion of suspended solids are illustrated.

2. Methodology and Theoretical Background

2.1. Control Equations

In this study, the coupled CFD-DEM method is used to study the microscopic deposition behavior of suspended solids. CFD and DEM are coupled through the Euler–Lagrange Model, in which CFD simulates the continuous fluid phase while DEM simulates the discrete particle phase.

2.1.1. Fluid Control Equations

The fluid control equation, derived based on the law of mass conservation, is called the fluid continuity equation. Suppose the fluid is set up with a computational unit cell. In that case, the continuity equation can be formulated as the difference in mass flowing into and out of the unit cell per unit time equals the change in mass within the unit cell [27].

$$\frac{\mathsf{\partial }\left(\epsilon {\rho }_{\mathrm{f}}\right)}{\mathsf{\partial }t}=\nabla ·\left(\epsilon {\rho }_{\mathrm{f}}{\mathit{u}}_{\mathrm{f}}\right)$$

(1)

where ρ_f is the fluid density, u_f is the fluid motion velocity, ε is the solid unit’s void ratio, and ∇ is the Laplace operator.

The fluid control equation derived from Newton’s second law is called the momentum equation, and the control equation is as follows [27].

$$\frac{\mathsf{\partial }\left(\epsilon {\rho }_{\mathrm{f}}\right)}{\mathsf{\partial }t}=\nabla ·\left(\epsilon {\rho }_{\mathrm{f}}{\mathit{u}}_{\mathrm{f}}{\mathit{u}}_{\mathrm{f}}\right)-\epsilon \nabla ·\left({\mu }_{\mathrm{f}}\nabla {\mathit{u}}_{\mathrm{f}}\right)=-\nabla p-{\mathit{F}}_{\mathrm{f},\mathrm{p}}+\epsilon {\rho }_{\mathrm{f}}g$$

(2)

where p is the fluid pressure, μ_f is the viscosity coefficient, and F_f,p is the particle–fluid interaction force. g is the gravitational acceleration.

2.1.2. Particle–Fluid Interaction Forces

The study of the motion of particles within a fluid usually simplifies the interaction forces with a small degree of influence. The average particle size of suspended particles is small, and the primary interaction forces considered are the traction force F_d and the pressure gradient force F_b. The effect of other forces on the particle motion state is not in the same order of magnitude as the main forces and can usually be neglected. Thus, lift force, virtual mass force, and other interaction forces are neglected. Therefore, the equation for the particle–fluid interaction force can be written as

$${\mathit{F}}_{\mathrm{f},\mathrm{p}}={\mathit{F}}_{\mathrm{d}}+{\mathit{F}}_{\mathrm{b}}$$

(3)

where the pressure gradient force F_b is expressed by equations as follows [34]:

$${\mathit{F}}_{\mathrm{b}}=-V_P\nabla p$$

(4)

V_p is the particle volume. The traction force F_d is expressed as follows [35]:

$${\mathit{F}}_{\mathrm{d}}=\frac{\beta V_P}{1-\epsilon }\left({\mathit{u}}_{\mathrm{f}}-{\mathit{u}}_{\mathrm{p}}\right)$$

(5)

u_p is the velocity of particle motion. β is the momentum transfer coefficient, and the expression is [36]

$$\beta =\left\{\begin{array}{c}150\frac{{\mu }_{\mathrm{f}}{\left(1-\epsilon \right)}^2}{\epsilon d_{\mathrm{p}}^2}+1.75\left(1-\epsilon \right)\frac{{\rho }_{\mathrm{f}}}{d_{\mathrm{P}}}\left|{\mathit{u}}_{\mathrm{f}}-{\mathit{u}}_{\mathrm{p}}\right|\left(\epsilon \le 0.8\right)\\ \frac{3}{4}{\mathit{C}}_{\mathrm{d}}\frac{\epsilon \left(1-\epsilon \right)}{d_{\mathrm{P}}}{\rho }_{\mathrm{f}}{\epsilon }^{-1.65}\left|{\mathit{u}}_{\mathrm{f}}-{\mathit{u}}_{\mathrm{p}}\right|\left(\epsilon >0.8\right)\end{array}\right.$$

(6)

$${\mathit{C}}_{\mathrm{d}}=\left\{\begin{array}{c}\frac{24}{{\mathrm{Re}}_{\mathrm{P}}}\left(1+0.15{\mathrm{Re}}_{\mathrm{p}}^{0.687}\right)\left({\mathrm{Re}}_{\mathrm{P}}\le 1000\right)\\ 0.44\left({\mathrm{Re}}_{\mathrm{P}}>1000\right)\end{array}\right.$$

(7)

where C_d is the trapping coefficient, d_p is the particle diameter, and Re_p is the particle Reynolds number, expressed as [27,37]

$${\mathrm{Re}}_{\mathrm{P}}=\frac{\epsilon {\rho }_{\mathrm{f}}{d}_{\mathrm{P}}\left|{\mathit{u}}_{\mathrm{f}}-{\mathit{u}}_{\mathrm{p}}\right|}{{\mu }_{\mathrm{f}}}$$

(8)

2.1.3. Particle Control Equation

The DEM calculates the state of motion of each particle. The equations of motion of the particles, established through Newton’s second law, to which the forces between the fluid and the particles are added, lead to the particle control equations [38].

$$m_i\frac{\mathrm{d}{u}_i}{\mathrm{d}t}={\displaystyle \sum }_{j=1}^{n_i}{\mathit{F}}_{ij}+{\mathit{F}}_{\mathrm{f},\mathrm{p},i}+{\mathit{F}}_{\mathrm{G},i}$$

(9)

$$I_i\frac{\mathrm{d}{\omega }_i}{{\mathrm{d}}_t}={\displaystyle \sum }_{j=1}^{n_i}{M}_{ij}$$

(10)

where u_i is the velocity of particle i, F_ij is the contact force on particle i, F_G,i is the gravitational force on particle i, I_i is the rotational inertia of the particle; ω_i is the rotational angular velocity of particle i, and M_ij is the rotational moment of particle i by particle j or the wall.

The contact model defines the calculation of interparticle contact forces. This paper uses the Hertz–Mindlin and JKR contact models [39]. The Hertz–Mindlin contact model is based on the Hertzian contact theory [40] with the Middlin–Deresiewicz tangential force model [41], which has high computational efficiency in dealing with the contact interaction of conventional particles. The JKR contact model is derived based on the Hertz theory, which increases the cohesion between particles. It can simulate the strong viscous interaction between particles and adds the effect of van der Waals forces on particle motion, which is very suitable for the numerical simulation of powdery or wet particles. When calculating the forces between wet particles, the JKR contact model considers the two controlling factors of liquid surface tension γ_s and wetting angle.

$${\mathit{F}}_{\mathrm{w},\mathrm{p}}=-2\pi {\gamma }_s\cos \left(\mathsf{\theta }\right)\sqrt{R_i{R}_j}$$

(11)

where R_i and R_j are the radii of the contact particles i, j.

The object of study in this paper is the suspended solids in the coal mine wastewater and the broken rock mass in the underground reservoir, both of which are wet particles. The diameter of suspended solids in coal mine wastewater can reach a micron level, and the influence of van der Waals force on the particle motion state should be considered. With the addition of interparticle cohesion, the JKR contact model can simulate the adsorption of suspended solids by the broken rock mass. Therefore, the JKR contact model is well suited for the study in this paper.

2.2. CFD-DEM Coupling Process

The computational data are updated between CFD and DEM during the coupling process according to the time step. The CFD solves the flow field information and transforms it into particle–fluid interaction forces for transmission to the DEM, which updates the particle position, volume, velocity, and other parameter information. The particle information is then submitted to the CFD and matched with the fluid cells, after which the flow field calculation is performed in the next step. This data exchange is recurring throughout the coupled calculation process until the calculation is completed, as shown in Figure 2. The coupling process of CFD-DEM is implemented here using FLUENT and EDEM, and the EDEM (2021) and FLUENT (2021) software pass information through an application programming interface (API) [42].

2.3. Model Simplification

At the microscopic scale, the structure, geometry, and size distribution of the broken rock are the significant parameters that influence the deposition behavior of suspended particles. The geometry of broken rock can be simplified, or the rock can be scanned directly to obtain a realistic geometry [43]. A sphere is the most straightforward 3D representation of a single broken rock mass, and choosing a real geometry requires a higher computational cost. At larger scales, when considering the distribution of particles over a specific range, combinations of non-homogeneous geometries [44] or spheres [31] with fixed, regular [45], or random distribution in the model [29,30]. For computational efficiency, randomly distributed spheres are used in this paper to represent the broken rock mass, which is considered an isotropic porous medium, as shown in Figure 3.

The pore size of the coal rock mass is another significant parameter affecting fine particles’ deposition behavior [21,22]. The PPTR represents the fine particle size (d) ratio to the large particle pore size (D). The movement behavior of particles with different values of PPTR varies greatly, as shown in Figure 4. If d > D, the fine particles are directly intercepted by the pore space. If d < D and the difference between particle size and pore throat size is insignificant, bridging blockage occurs. If d << D and the particle size is much smaller than the pore size, the fine particles directly penetrate the medium. In addition, if d < D and the particles are adsorbed on the surface of the medium due to surface forces, adsorption mainly occurs. When d < D, there is a critical value for the PPTR, which can distinguish between different motility behaviors. Oort et al. [46] argued that when D/d > 7, the particles penetrate directly into the media segment without clogging. Oyeneyin et al. [47] concluded that the clogging effect begins to appear in particles when (0.1 < d/D). Bagrezaie et al. [48] concluded that the bridging mechanism begins to appear when (0.1 < d/D < 0.6).

The size of suspended solids in coal mine wastewater is in the submicron to micron range [32,33]. If the pore size of the broken rock mass is too large, the suspended solids will directly penetrate the broken rock mass, so a suitable pore size of broken rock mass needs to be selected for the study. Due to the complexity of the pores of the broken rock mass, the average pore diameter D_pore can be used instead of the pore diameter D [47], and the average pore diameter D_pore can be obtained according to the following equation [47]:

$${\mathrm{D}}_{\mathrm{pore}}=\frac{{\mathrm{D}}_{50}\cdot \epsilon }{3\left(1-\epsilon \right)}$$

(12)

where ε is the void fraction of the broken rock mass and D₅₀ is the median particle size of the broken rock mass.

After the roof rock’s collapse, the goaf’s interior is closed, making it difficult to make practical measurements. The void ratio and the particle size distribution of the broken rock inside the goaf can be determined using theoretical settlement and numerical simulation [49,50,51], and then the pore size of the broken rock can be determined. The data show that the void ratio inside the goaf ranges from 0.1 to 0.4 [49,50]. The diameter of broken coal rock particles in the goaf can reach a scale from millimeters to meters [34,52]. Too large a particle size can lead to excessive pore size, affecting suspended solids’ migration patterns. Meanwhile, the computational efficiency will be greatly reduced if the actual particle size gradation is used in the numerical simulation. Therefore, in this paper, the particle size grading of the broken coal rock mass is simplified by selecting the suitable broken coal rock particle size in combination with the critical value of the PPTR and the particle filling model with uniform particle size. After simplification, the median particle size D₅₀ of the broken rock mass in Equation (12) is equal to the particle diameter d_p, while the following equation can calculate the void ratio ε:

$$\epsilon =1-\frac{V_{\mathrm{p}}}{V_{\mathrm{m}}}$$

(13)

where V_p is the total particle volume, and V_m is the total model volume.

After coal mining, the collapse of the top rock layer in the goaf leads to the settlement of the upper strata. The stratigraphic stress is disturbed and redistributed, showing different stress distribution characteristics in different areas of the goaf [53,54,55]. This stress distribution affects the degree of compaction of the broken rock mass, which in turn affects the broken coal rock’s particle size distribution and pore size.

It can be seen from Figure 5 that the rock formation above the legacy coal pillar forms a long cantilever beam structure after the collapse of the upper part of the rock layer in the goaf [56]. The broken rock mass near the leftover coal pillar bears the lower upper load, so the compaction degree of the broken rock mass is low. The broken rock mass in the middle area of the goaf directly bears the load of the upper collapsed strata, and the compaction degree of the broken rock mass is significant. Due to the degree of compaction difference, the pore space between the rock blocks in different areas of the goaf differs. However, at the same time, the broken coal rock masses in the same area have some similarities. Therefore, if the deposition behavior of suspended solids under different values of PPTR can be obtained, the deposition behavior of suspended solids in different areas of goaf can be deduced based on the PPTR. Furthermore, the law of suspended solids deposition in the goaf can be deduced.

2.4. Granular Domain Settings

This paper studies suspended material’s microscopic deposition behavior within the goaf’s broken rock mass. Different pore size conditions are simulated by varying the filler particles’ particle size and the void ratio. Therefore, three models of different sizes are created in this paper to calculate the deposition process of suspended solids within the unit body. The model sizes are 0.1 m × 0.1 m × 0.1 m, 0.3 m × 0.2 m × 0.15 m, and 0.5 m × 0.1 m × 0.1 m, and the models are shown in Figure 6.

According to the critical value of the PPTR, it is known that the suspended material will directly penetrate the broken rock mass under the condition of too large pore size [47,48], so a suitable pore size needs to be selected. According to Equation (12), the factors affecting the pore size of the broken rock mass include void ratio and particle size. The void ratio of the broken rock mass in the goaf is in the range of 0.1–0.4 [49,50], and the range of the void ratio is selected to be 0.26–0.4 in combination with the accumulation of particles. Concerning the existing laboratory-scale experimental and simulation settings and critical values of the PPTR [23,30,31,57,58], the particle sizes of the broken rock mass were set to 4 mm, 8 mm, 16 mm, and 24 mm. The corresponding mean pore sizes D_pore were 0.47 mm, 1.14 mm, 3.00 mm, and 5.33 mm. Eighty-eight percent of the suspended solids in the coal mine wastewater have an average particle size of less than 50 µm [59], so the suspended solids’ size was set to 50 µm. The suspended solids particle size ratios to the average pore size of the broken rock were 0.11, 0.04, 0.02, and 0.01.

In the particle filling phase, the Hertz–Mindlin contact model is first used to allow the natural accumulation of broken rock particles in the unitary model to form the base model. By setting up a downward-moving plate in the foundation model to apply a load on the particles, the accumulated particles in the foundation model can be compacted to achieve the desired void fraction for the study. The filling of the broken rock particles is stopped after the particles stop moving to maintain a stationary and stable state. The cohesion between the particles needs to be considered in the simulation stage, so the Hertz–Mindlin contact model is modified to the Hertz–Mindlin contact model with JKR Cohesion. A circular plane with a diameter of 20 mm was set at the model’s entrance for the generation of suspended particles. The particle generation rate was determined based on the liquid flow rate and the concentration of particles in the liquid. A custom wall boundary condition DLL file was compiled and loaded, which allowed suspended particles to escape from the wall boundary. The time step needed to be set to 5% to 10% of the Rayleigh time step, which is the time for shear wave propagation in the particles. The smaller the time step, the more accurate the calculation results.

2.5. Fluid Domain Settings

The fluid cells are divided by triangular mesh, and the specific mesh division of the model is shown in Figure 7. The mesh number of the model with size 300 mm × 200 mm × 150 mm is 158,384, the minimum volume is 6.6 × 10⁻⁹ m³, and the maximum volume is 1.4 × 10⁻⁷ m³. The number of meshes is 18,465 for the 100 mm × 100 mm × 100 mm model and 20,355 for the 500 mm × 100 mm × 100 mm model. The model inlet is set as a velocity inlet. The outlet is set to a pressure outlet, and the pressure is set to 0. The size of the outlet and inlet is a circle with a diameter of 20 mm. The time step is set to an integer multiple of the DEM time step. According to the geological specification of the No. 15 coal seam of the Lingzhida coal mine, the concentration of gas in the mining area is low, the possibility of spontaneous combustion is low, and the temperature inside the mining area is stable, so the temperature change can be disregarded. The degree of influence of water temperature on the behavior of suspended particles inside the mining area is small. Therefore, the simulated temperature is set to 20 °C. Convective flow in water exists in the extraction area. In this simulation, the effect of this part on the results was not considered. This simulation mainly considers the effect of particle size on the deposition behavior of suspended particles. The source of water flow dynamics inside the goaf is the difference in elevation between the bottom plate and the head difference between the inlet and outlet. The movement of water flow in the region is relatively stable with slow water velocity [57]. Convection in the water affects the results to a lesser extent. Therefore, according to the actual situation of water movement inside the goaf, three water velocities were set, which were 0.02 m/s, 0.04 m/s, and 0.06 m/s.

This paper uses four pore size conditions of broken rock mass, three inlet flow conditions, and three different model sizes. A total of 16 simulation tests were conducted to compare the deposition variation in suspended solids under different conditions. The specific groups are shown in

Table 1. Simulation groups.

Cases	Rock Particle Diameter (mm)	Model Size (mm)	Number of Rock Particles	Void Ratio	Average Pore Diameter (mm)	Inlet Velocity (m/s)
1	4	100 × 100 × 100	22,053	0.26	0.47	0.02
2	4	300 × 200 × 150	198,702	0.26	0.47	0.02
3	8	100 × 100 × 100	2601	0.3	1.14	0.02
4	8	300 × 200 × 150	23,530	0.3	1.14	0.02
5	8	300 × 200 × 150	23,530	0.3	1.14	0.04
6	8	300 × 200 × 150	23,530	0.3	1.14	0.06
7	8	500 × 100 × 100	13,034	0.3	1.14	0.02
8	16	100 × 100 × 100	299	0.36	3.00	0.02
9	16	100 × 100 × 100	299	0.36	3.00	0.04
10	16	300 × 200 × 150	2701	0.36	3.00	0.02
11	16	300 × 200 × 150	2701	0.36	3.00	0.04
12	16	500 × 100 × 100	1513	0.36	3.00	0.02
13	24	100 × 100 × 100	83	0.4	5.33	0.02
14	24	300 × 200 × 150	741	0.4	5.33	0.02
15	24	300 × 200 × 150	741	0.4	5.33	0.04
16	24	300 × 200 × 150	741	0.4	5.33	0.06

.

2.6. Material Parameters

The DEM calculates the forces acting on each particle, such as normal force, tangential force, and rolling friction, to update information such as the position and velocity of the particle. Calculating the forces requires determining parameters such as shear modulus, Poisson’s ratio, and friction coefficient of the particles. The broken rock mass inside the goaf consists of residual coal and collapsed rock [56]. Among the various suspended substances in coal mine wastewater, coal dust accounts for the most significant percentage [59]. Therefore, this paper selected coal rock as the broken rock material and coal dust as the suspended material. Existing research results can determine parameters such as shear modulus, Poisson’s ratio, and friction coefficient of coal rock and pulverized coal materials [27,36,50,57,60,61]. The fluid in the fluid domain is set to water, and the specific parameters are shown in

Table 2. Material parameters.

Materials	Parameter Types (Units)	Values
Coal rock	Particle density (kg/m3)	1.44 × 103
	Poisson’s ratio	0.3
	Shear modulus (Pa)	1.0 × 109
	Coefficient of restitution	0.5
	Coefficient of static friction	0.6
	Coefficient of rolling friction	0.05
Pulverized	Particle density (kg/m3)	0.9 × 103
	Poisson’s ratio	0.3
	Shear modulus (Pa)	1.0 × 108
	Coefficient of restitution	0.5
	Coefficient of static friction	0.5
	Coefficient of rolling friction	0.05
Water	Density (kg/m3)	998.2
	Viscosity (kg/(m−s))	1.003 × 10−3

.

3. Model Validation

Before numerical calculations, the model’s accuracy and reliability must be tested. In the preliminary stage of the study, to analyze the variation in the number of suspended solids deposited, an indoor model test was conducted to measure the number of suspended solids deposited inside the glass beads. The test results include the deposition number and distribution range of suspended solids. Based on the model test results, a set of numerical calculations is added in this paper to verify the accuracy of the simulation model by comparing the calculated values with the test values under the same conditions.

3.1. Indoor Test Setup

The anthracite coal dust (average diameter 0.045 mm) sieved by a 325 mesh sieve was selected as the suspended material for the indoor experiment. Meanwhile, in order to be able to observe the deposition distribution of suspended solids inside the filler particles, glass beads with a diameter of 1.5 mm were selected as the filled particle material for the experiment.

The model’s size is 300 mm × 200 mm × 150 mm, and the model is equipped with a circular inlet and outlet with a diameter of 20 mm and an inlet and outlet depth of 50 mm. The inlet flow rate is 300 mL/min, corresponding to 0.02 m/s. The peristaltic pump does not come into contact with the liquid or the particles inside the liquid during operation to reduce the error in the number of particles caused by external factors. The experiment ended after 60 s of operation. Water samples were taken every 50 mm in the liquid flow direction at 50 mm depth of the model box to measure the liquid turbidity. A total of three water samples were taken from each plane. In order to observe the distribution of coal dust deposition inside the glass beads, the liquid inside the box was slowly discharged at a rate of 100 mL/min using a peristaltic pump, and the glass beads were finally dug out in layers. The experimental steps are shown in Figure 8.

In this paper, the number of particles at different locations is used as an indicator to analyze the deposition of suspended solids. Assuming that each pulverized coal particle in the model test is the same size, the number of particles in a specific volume can be obtained by measuring the concentration of suspended solids at different locations inside the model. The concentration of suspended solids is a standard indicator for measuring the number of suspended solids in wastewater [15]. However, the process of measuring the concentration of suspended solids is tedious, so liquid turbidity is used instead of the concentration of suspended solids to improve efficiency. The feasibility of using turbidity instead of suspended solids concentration has been demonstrated empirically [62], and the turbidity and the concentration of suspended solids are mostly quadratic polynomial curve relationships. This paper measured the anthracite coal dust used, and the fitted curves are shown in Figure 9.

3.2. Simulation Setup

The model size and particle material of the simulation model are consistent with the indoor model. Among them, the parameters of glass beads can be found in existing research results [63], and the parameters of glass beads and coal dust are shown in

Table 3. Parameters of the particles.

Parameter Types (Units)	Glass Bead	Pulverized
Particle density (kg/m3)	2.53 × 103	0.9 × 103
Poisson’s ratio	0.25	0.3
Shear modulus (Pa)	1.2 × 104	1.0 × 108
Coefficient of restitution	0.75	0.5
Coefficient of static friction	0.45	0.5
Coefficient of rolling friction	0.1	0.05

. The generation rate of particles was 5 × 10⁻⁷ kg/s, without limiting the total number of particles. Only the type of wall boundary condition at the outlet was set to allow the suspended particles to escape. In the numerical simulation model, a monitoring plane is set at intervals in the forward direction of the water flow. The plane monitors the number of particles passing at each moment. The accuracy of the simulation model is verified by comparing the experimental values of the number of particles at different locations with the calculated values.

3.3. Results Validation

Figure 10 shows the deposition distribution of suspended solids at depths of 10 mm, 50 mm, and 100 mm in the box, with the observation viewpoint directly above the model. The black area is the leading distribution area of the suspended solids, while other areas also have suspended particles.

However, the small number of particles makes it difficult to show them in the figure. If S is used to indicate the area of the main distribution area of suspended solids, then S₅₀ > S₁₀ > S₁₀₀. It can be observed that the color is darker in the distribution range at a depth of 50 mm and the number of suspended sediment is higher at this depth, as shown in Figure 10b. Notably, the liquid inlet is located in a plane of 50 mm, indicating that the hydraulic conditions are an essential factor affecting the migration behavior of the suspended solids.

Figure 11 shows the top and front views of the suspended particle distribution obtained from numerical simulations under identical conditions. No glass bead particles are shown in the model, only suspended particles. Due to the excessive number of suspended particles, the particle distribution can be viewed more intuitively in the post-processing stage by ignoring some suspended particles and adjusting the particle display size with the particle velocity as the standard. As shown in Figure 11a,b, the particle advance direction is in the Y direction, the particles are more aggregated at the inlet, and the model differs significantly in the range of 0~150 mm in the Y direction from the particle deposition in the range of 150~300 mm. The average migration distance of particles in the same depth range as the inlet is large, and the distribution range is broader while showing a decreasing trend in the surrounding area, which is very similar to the distribution law obtained from the experiment.

Figure 12 shows the experimental and calculated values of the number of particles within each 50 mm in the Y direction. The bar graph shows the proportion of particles in different locations to the total number, and the line graph shows the relative error between the calculated and experimental values. As shown in Figure 12, the number of particles at the inlet is the largest, and the percentage of both experimental and calculated values is greater than 30%. The proportion of the experimental value of the number of particles in the range of 0 mm to 150 mm in the Y direction is 76.5%, and the calculated value is 78%.

In the range of 150~300 mm, the percentage of particles in each area did not exceed 10%.

Comparative results show that except for the relative error between the experimental and calculated values at 200~250 mm, the relative error in the rest of the area does not exceed 20%. The lowest error is 5.1% at 50~100 mm, which is within the acceptable range and indicates that the model parameters are set reasonably.

4. Results and Discussion

4.1. Microscopic Deposition Behavior of Suspended Solids

Due to the complex shape of pores within the broken rock mass, the average pore size D_pore represents the pore size within the broken rock mass. As mentioned earlier, many studies have been conducted on particle movement behavior at different pore sizes. The ratio of fine particle size to large particle pore size is the PPTR, and studies have found significant differences in the movement behavior of particles before and after the critical value of the PPTR [21,22]. However, these studies are not fully applicable to the deposition pattern of suspended solids inside the goaf due to the large particle size and the different properties of the coal rock masses in the goaf. Different rock mass characteristics and rock block sizes will lead to different critical values. It is still necessary to analyze the deposition behavior of suspended solids within the broken rock mass according to the actual situation.

According to the local magnification of the broken rock mass (Figure 13), it can be seen that under the condition that the pore size of the broken rock mass is 0.47 mm and the particle size is 4 mm, part of the particles is intercepted in the contact part of the rock particles during the migration process of the suspended particles. Some of the suspended particles in the collision come into contact with coal rock particles to produce adhesion, and suspended particles adsorb to the surface of coal rock particles. At this time, the PPTR is 0.11, and the probability of interception and adsorption is comparable. However, the suspended solids are only intercepted at the smallest pore space in the contact part of the rock particles, and bridging blockage of the pore space does not occur. From the macroscopic point of view, it can be seen that the number of particles inside the broken rock mass is the largest at this time, and the particles are more aggregated. When the pore size of the broken rock mass is 1.14 mm, the particle size is 8 mm, and the PPTR is 0.04, the broken rock mass still produces interception and adsorption of suspended solids, but the probability of interception is smaller than that of adsorption. The number of particles penetrating the broken rock mass is increasing. When the pore size of the broken rock mass is 3 mm, the particle size is 16 mm, and the PPTR is 0.02, only the adsorption of the suspended solids exists on the surface of the rock mass particles, and the interception rarely occurs. Most of the suspended solids directly penetrate the broken rock mass. At this time, the number of particles inside the broken rock mass is the least.

Numerical results show that the simulation results of the model used in this study for the motion behavior of suspended solids under different pore size conditions agree with the theoretical model [47,48]. When the pore size of the broken rock mass is 3 mm and the particle size is 16 mm, the deposition of micron-sized suspended solids inside the broken rock mass is mainly produced by adsorption. The pore size of the rock particles under these conditions can no longer intercept the suspended matter. However, the data show [51,64] that the particle size range of the broken rock mass in the goaf is 0.001–12 m, and most of the rock masses are between 150 mm and 350 mm in size. It can be seen from the data that the particle size of most of the broken rock masses in the goaf is much larger than 16 mm, and the pore size is much larger than the critical value. These data indicate that adsorption is the primary deposition behavior of micron-sized suspended solids within the goaf’s broken rock mass. Interception also occurs but with much less probability than adsorption.

4.2. Deposition Process of Suspended Materials in the Broken Rock Mass

Figure 14 shows the deposition process of suspended particles in the accumulation formed by coal rock, setting the ratio of the displayed size of suspended particles to the actual size to 65:1 and the transparency of coal rock particles to 0.05. To better match the suspended particles’ movement within the broken mass, suspended particles are not constrained by the boundary. They can escape from the model boundary, so the statistics do not include particles outside the model range. Figure 14 shows the calculation results under the condition that the particle size of coal rock is 16 mm, the flow velocity at the inlet is 0.02 m/s, and the model size is 300 mm × 200 mm × 150 mm.

In Figure 14a, the suspended particles’ color indicates the particles’ residence time. After the particle injection is started, the suspended particles are subjected to fluid action to migrate in the pore channels inside the coal rock particle pile. The red particles are the first to enter the model interior and stay inside the coal rock particle pile for the longest time. When comparing Figure 14a,b, it can be found that the position of some of the red particles did not change, which indicates that these particles were deposited inside the coal rock particle pile.

As shown in Figure 14b,d, the aggregation of suspended particles in the range of 0~100 mm in the Y direction at the inlet of the model is evident at the beginning, and the particles in the range of 150~300 mm are distributed in a way that is more scattered. The number of particles distributed inside the coal rock particle pile decreases continuously in the Y-direction, and the number of particles around the inlet is the largest. With increased time, the deposition of suspended particles in the range of 150~300 mm keeps increasing, and the suspended particles begin to appear to aggregate at the pore channels. The above phenomenon indicates that the longer the time, the more suspended solids are deposited during the migration process and the longer the average migration distance in the suspended solids.

The number of suspended particles in the range of 15 mm was counted at different locations at four moments, t = 1 s, t = 5 s, t = 10 s, and t = 20 s. The number of particles (NP) and the percentage of the number of particles to the total number (NPT) were plotted. In Figure 15a, it can be seen that the number of particles at different locations increases with time in a non-linear trend. The number of particles varied the most in the range of 50 mm to 100 mm. According to the variation in the number of suspended solids at different locations, it can be seen that there exists a significant deposition region for the suspended solids. Under the condition that the particle size of coal rock is 16 mm and the flow rate of water at the inlet is 0.02 m/s, 50~100 mm is the main deposition area of suspended particles. In this range, the increase in the number of particles is the largest. The NPT before the range of 50~100 mm shows a decreasing trend with time, and the NPT after the range of 50~100 mm shows an increasing trend.

4.3. Deposition of Suspended Solids under Different Pore Size Conditions

Figure 16 shows the proportion of suspended particles in the model range at different moments to the total number of suspended particles generated and the distribution of particles at t = 1 s and t = 5 s for 4 different pore size conditions (0.47 mm, 1.14 mm, 3 mm, and 5.33 mm).

As shown in Figure 16, after 1 s of migration of the generated suspension, a part of the particles remained inside the broken rock mass. In contrast, the others migrated outside the model range from the X direction to the Z direction. The proportions of the number of particles remaining within the model range to the total generated particles are 90.6%, 71.2%, 39.2%, and 24.8% for the 4 pore size conditions (0.47 mm, 1.14 mm, 3.00 mm, and 5.33 mm). It can be seen that the percentage of particles shows a decreasing trend with the increase in pore size.

After the suspended particles migrated for 1 s under the condition of 0.47 mm pore size of coal rock, most of the suspended particles gathered at the inlet. Only a tiny number entered the inside of the broken rock mass. Comparing the distribution under different pore size conditions with the increase in pore size shows that the particle distribution range becomes more extensive in the X, Y, and Z directions. In the Y direction, 75% of the suspensions in the 0.47 mm condition are distributed in the range of 0~19 mm. This range can be regarded as a significant distribution range of the particles. The other 3 pore size conditions (1.14 mm, 3.00 mm, and 5.33 mm) are 0~55 mm, 0~76 mm, and 0~101 mm. The above phenomenon indicates that the average migration distance of suspended particles inside the 0.47 mm pore-size broken rock mass is the shortest. Moreover, as the pore size of coal rock increases, the average migration distance of suspended particles is farther.

Visualizing the suspended solids’ microscopic movement process helps to analyze the deposition pattern of the suspended solids within the broken rock mass. Numerical results show that the simulation results of the deposition pattern of suspended solids match the experimental results [65], and the deposition of suspended solids within the broken rock under different pore size conditions varies greatly. From the microscopic point of view, the pore channels of coal rocks with small pore sizes are narrow, and their complexity is greater than that of coal rocks with large pore sizes. This phenomenon leads to more particles being intercepted inside the pore channels or adsorbed on the coal rocks’ surfaces. At this time, the interception of suspended solids by the broken rock mass has an equal probability of occurring with adsorption, and the deposition of suspended particles is significant. In contrast, the probability of interception within the broken rock with a larger pore size is low, reducing the number of total suspended solids deposition within the broken rock mass. At this time, deposition is mainly generated by adsorption.

After the collapse of the rocks in the upper part of the goaf, the rock grain size and pore size distribution in different areas within the goaf differ due to the difference in the internal structure of the goaf and the different compaction of the broken rock masses. At the same time, the broken rock masses in the same area have some similarities. Suppose the particle size distribution and average pore size of the broken rock masses in different areas can be obtained. In that case, the deposition behavior of suspended materials inside different areas of the goaf can be deduced based on the average pore size. Eventually, the suspended matter’s migration pattern within the mining area can be deduced. The most challenging problem in the current air-mining zone simulation is determining the size of the fractured rock mass. Pappas and Mark [64] took photographs of the collapse zone in the field and analyzed the grain size gradation of the fractured rock masses. However, the photographs were taken only for a part of the collapse zone, and there are still some limitations in obtaining the grain size gradation results. Therefore, the particle size distribution of fractured rock in different areas of the mining area still needs further study.

4.4. Factors Affecting the Number of Suspended Solids Deposited

The pore size affects the deposition behavior of suspended solids in the broken rock mass, affecting the number of suspended solids deposited. The more suspended solids are deposited, the better the purification effect of the broken rock mass on the coal mine wastewater. The purification of coal mine wastewater in underground reservoirs is a long and complex process, and many factors affect coal mine wastewater’s purification effect. This paper considers two of these factors: distance and percolation rate. The effects of these two factors are discussed below based on the test results.

4.4.1. Distance

Using a model with dimensions of 500 mm × 100 mm × 100 mm, five monitoring planes (0.1 m, 0.2 m, 0.3 m, 0.4 m, and 0.5 m) were set in the Y direction of the model, and the number of suspended solids passing through each plane was counted. These suspensions are not trapped by the broken rock mass and are called fugitive particles. The number of fugitive particles can be used to analyze the effect of distance on the number of suspension depositions. The simulation was run for 20 s, and the results are shown in Figure 17.

The number of escaped suspended solids was observed to vary by distance for coal rock particle size 8 mm and 16 mm conditions. The least number of escaped particles was found at 0.5 m. When the number of escaped particles at 0.1 m reached 12.8% (8 mm) and 29.9% (16 mm) of the total particles, the number at 0.5 m remained 0%. The growth rate of the number of escaped particles at longer distances is much lower than that at closer distances, and increasing the distance can significantly improve the deposition of suspended solids. The low number of fugitive particles represents the high number of suspended solids trapped, which means that the broken rock mass is highly efficient in purifying the suspended solids. Therefore, the purification efficiency of suspended solids can be effectively increased by increasing the distance between the inlet and outlet of the groundwater reservoir.

4.4.2. Seepage Velocity

In the numerical simulation, the water flow enters the models’ interior in the Y direction. The initial velocity of particles is mainly in the Y direction due to the drag effect of water flow on particles. Figure 18 shows the average velocity of the suspended particles inside the model in the Y direction from 0 to 5 s. Figure 18 shows the calculated results under two different particle sizes of coal rock particles (8 mm, 24 mm) and three different inlet velocities (0.02 m/s, 0.04 m/s, and 0.06 m/s).

As shown in Figure 18, a more significant inlet flow velocity increases the percolation velocity of the water inside the model. The velocity variation trends are relatively similar for several conditions, and the average velocity of particles shows a decreasing trend in the range of 0 to 5 s. Under the condition of a coal rock particle size 8 mm, the average velocity of particles at 0~1 s is relatively larger. This phenomenon indicates that the particle motion state is unstable within 0~1 s when the particles enter the pile, and the velocity difference between different particles is significant. Moreover, under the condition that the particle size of coal rock is 24 mm, this unstable motion state occurs in the range of 0~2 s, as shown in Figure 18b. According to the assumption of fluid continuity, the inflow and outflow of fluid flowing through the channel should be equal at any moment. Considering the slight compressibility of water, the narrow pore channel and smaller flow area in the broken rock mass will inevitably lead to an increase in flow velocity to meet the requirement of fluid volume conservation in and out. Due to the complexity of the pore channels in the broken rock mass, the seepage velocity inside the rock mass varies greatly, so the velocity varies widely between different particles.

Figure 19 shows the velocity distribution of suspended particles in the broken coal mass at t = 5 s under the abovementioned six conditions. It can be seen that the more significant percolation velocity brings more kinetic energy to the particles. The average velocity of the particles is maximum at the inlet velocity of 0.06 m/s and minimum at the inlet velocity of 0.02 m/s, which is reflected in both particle size conditions. The increase in flow velocity leads to an increase in the drag force of the fluid on the suspended particles, which is the leading force in the migration of suspended particles. Therefore, the greater the percolation velocity during particle migration, the greater the velocity of the particles. With the increase in particle velocity, the distribution range of suspended particles in the broken rock mass is more extensive, but the number in the coal rock medium decreases. As shown in Figure 20, the number of suspended solids deposited within the broken rock mass decreases as the percolation velocity increases.

The force of water flow on the particles makes the particles gain kinetic energy, and the increase in kinetic energy makes the particles able to migrate farther. Under the greater seepage velocity, the force on the deposited suspended particles increases, and they may break away from the deposited surface and migrate again. This secondary migration phenomenon will also reduce the deposition of suspended particles. In conclusion, the greater significant seepage velocity will make the suspended particles migrate farther, and the deposition of suspended particles in the broken rock mass will be reduced, obstructing the purification of the broken rock mass.

5. Conclusions

This paper studies the microscopic deposition behavior of micron-sized suspended solids in the broken rock mass. The deposition pattern of suspended solids in a broken rock mass with different pore sizes is explained using a numerical simulation method. The research results can provide a reference for studying wastewater purification mechanisms in goafs. The main conclusions drawn are as follows.

(1)

The deposition behavior of micron-sized suspended solids varies widely under three broken rock mass pore sizes (0.47 mm, 1.14 mm, and 3 mm). When pore size exceeds 3 mm, adsorption mainly influences suspended solids. The pore size of most broken rock masses in the goaf is much larger than the tested pore size, indicating that adsorption is the dominant deposition behavior of micron-sized suspended solids within the broken rock mass in the groundwater reservoir. Subsequent research should focus on methods and materials that can improve the adsorption capacity of coal rock masses. By improving the adsorption capacity of the coal rock mass, we can improve the purification effect of coal mine wastewater in goafs and increase the service life of the purification space in goafs.

(2)

As the pore size of coal rock decreases, the average migration distance of the suspended solids inside the broken rock mass becomes shorter. At the same time, the suspended solids are deposited in the broken rock mass with a small pore size with a large number. The smaller the pore size, the better the purification effect of the broken rock mass on the suspended solids. The pore size can be expressed using the void ratio and coal rock particle size, so the relationship between the microscopic movement behavior of the broken rock mass and the suspended solids can also be expressed using these two parameters.

(3)

The more extensive the broken rock mass range, the greater the number of suspended solids trapped. The purification efficiency of suspended solids can be effectively increased by increasing the range of broken rock mass. Moreover, the more significant particle velocity makes the migration distance of the suspended solids within the broken rock mass longer and the number of suspended solids deposited less, which adversely affects the purification effect of the broken rock mass. At the stage of siting the purification space in the goaf, the flow distance of coal mine wastewater in the mining area should be maximized, while a flat terrain area should be selected to avoid excessive water flow velocity.