Research on the Testing Method for the Rheological Properties of Large-Particle Gangue Filling Slurry

Abstract

Coal mine gangue cementation filling technology has increasingly become an effective and major means of dealing with “coal mining under buildings, railways, and bodies of water” and other complex hard-to-mine coal seams; but also, an important part of a large number of treatments of coal gangue stockpiled on the ground is to realize the green mining of coal mines. Coal mine cement filling often contains gangue particles with particle sizes larger than 15 mm; however, the viscometer and rheometer currently used at home and abroad are unable to accurately measure the rheological parameters of the slurry containing large-particle-sized gangue. In order to accurately measure the rheological parameters of slurry containing large-sized gangue particles combined with the site filling materials, the torque values obtained on the mixing blades at different speeds were generated by the combined action of the slurry between the blade side edge and the mixing drum wall, as well as the slurry between the blade lower edge and the mixing drum bottom. A new type of gangue slurry rheometer was developed. The new type of gangue slurry rheometer mainly included components such as the power system, sensing system, mechanical system, and other auxiliary units. Finally, using Fluent software ANSYS2023 to numerically simulate the fluidity of the slurry under the same conditions, the results obtained after the calculation and the test results showed that the error was within a reasonable range, indicating the correctness of the test principles of the new gangue slurry rheometer and the effectiveness of the instrument. This research offers new insights for accurately measuring the rheological parameters of particles with large sizes.

1. Introduction

The development and utilization of mineral resources have greatly promoted the rapid development of human economy, society, and the progress of social civilization, and will continue to be a source of human development in the future [1,2,3,4]. With the continuous development of mineral resources, the number, scale, and depth of mining operations continue to increase [5,6,7,8,9].

Long-term large-scale and continuous mining has led to the depletion of mineral resources with good storage conditions [10]. The recovery and utilization of complex and difficult to mine coal seams, “coal mining under buildings, railways, and bodies of water”, roadway coal pillars, and corner coal, as well as the re-mining of residual coal under other conditions, have gradually entered people’s vision [11]. On the other hand, as the largest industrial solid waste currently stored in China, the massive storage and discharge of coal gangue not only occupies a large amount of land, but its unique physical and chemical properties can also pollute soil and water bodies. At the same time, the spontaneous combustion of gangue mountains can produce a large amount of toxic and harmful gases, pollute the atmosphere, and have a great impact on the ecosystem around the mine [12,13,14]. However, the single utilization method of gangue, its low product added value, and small disposal and utilization capacity and scale cannot meet China’s practical requirements for ecological environmental protection, pollution reduction, and carbon reduction under the “dual carbon” goal. There is an urgent need for effective integrated and systematic action plans to solve these fundamental problems. From the perspective of coal resource recovery and environmental protection, using gangue filling coal mining technology to solve the above special coal mining problems is an effective method [15].

Compared with traditional low-concentration water sand filling, high-concentration cemented filling coal mining technology (such as paste and paste-like filling) has the advantages of a high slurry concentration [16,17,18,19,20], no need for dehydration (or only a small amount of dehydration), the good integrity of the filling body, high strength [21], a significant roof control effect, and a good underground working environment. It has gradually been applied in coal mine goaf treatment in the past decade [22,23,24]. Currently, research on high-concentration cemented filling coal mining technology in coal mines mainly focuses on the development and application of filling coal mining technology and filling systems, as well as the mechanical properties of filling materials and their interaction mechanisms with the surrounding rocks [25,26,27,28,29,30,31]. There is relatively little research on the flow performance and pipeline transportation characteristics of gangue filling slurry [32].

Unlike the tailing filling aggregates used in metal mines, the gangue particles used in coal mine cemented filling have larger particle sizes, some of which can reach 15 mm or even larger. Traditional methods such as NXS-11A rotational viscometer and RheolabQC rheometer cannot accurately measure gangue, as due to their small measurement space, large-sized gangue particles cannot be placed inside. On the other hand, when measuring high concentration slurries containing large-sized gangue particles, the mixing element is prone to slipping due to slip effects, making it difficult to accurately test the rheological parameters of this type of slurry. Based on the above reasons, the author has developed a new type of gangue slurry rheometer suitable for measuring large-sized gangue particles from the perspective of the testing process and the principle of the viscometer for slurry. The improvement in the testing accuracy lays the foundation for the smooth pipeline transportation of coal mine gangue filling slurry.

2. Structure and Working Principle of a New Type of Gangue Slurry Rheometer

2.1. Structure of a New Type of Gangue Slurry Rheometer

In order to adapt to the smooth flow of large-sized gangue particles in the mixing drum, generate accurate shear torque, and improve the automation level and data processing accuracy of slurry testing, a new type of gangue slurry rheometer has been developed. Its structural schematic diagram is shown in Figure 1.

After assembling the various components, the new type of gangue slurry rheometer obtained is shown in Figure 2.

2.2. Working Principle of a New Type of Gangue Slurry Rheometer

The new type of gangue slurry rheometer adopts a cross-blade type of mixing element. When the rheometer works, the mixing drum is fixed, and the blades are vertically placed into the slurry along the center of the mixing drum. The rotating blades drive the slurry in the drum to make a circular motion, and the slurry is layered due to the combined action of shear stress and friction force [33,34,35]. During this process, the slurry obstructs the stirring blades and generates torque. The received electrical signal is converted into the corresponding torque value by the torque sensor on the stirring rod, and different torque values can be obtained at different speeds. A functional relationship is established between the obtained different torque values and rotational speeds, and finally, the yield stress and viscosity of the tested slurry are calculated. The mixing system and its related dimensions are shown in Figure 3.

When the rheometer is working, the shear deformation rate of the slurry at any point between the stirring blade and the stirring drum wall can be expressed as

$$\dot{\gamma }={\displaystyle \frac{\mathrm{d}\gamma }{\mathrm{dt}}}=r{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{dr}}}$$

(1)

In Formula (1), $\dot{\gamma }$ is shear rate; r is the distance between any point of the slurry between the blade and the mixing drum wall and the mixing center, m; d_ω is the rotational angular velocity of the slurry at any point between the blade and the mixing drum wall; and d_r is the width of the slurry at any point between the blade and the mixing drum wall, m.

Numerous experiments and studies have shown that as a high concentration fluid, the rheological properties of gangue filling slurry can be expressed using the Bingham model [12]. Therefore, the relationship between shear stress and shear rate can be expressed as:

$$\tau ={\tau }_0+\eta \dot{\gamma }$$

(2)

In this formula, τ is shear stress, Pa; τ₀ is the yield stress; and η is viscosity.

Substituting Equation (1) into Equation (2) yields the following:

$$\tau ={\tau }_0+\eta r{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{dr}}}$$

(3)

At this point, the micro torque generated by the slurry at any point between the mixing blade and the inner wall of the mixing drum can be expressed as:

$$M_1=2\pi rh\tau r=2\pi r^{2}h({\tau }_0+\eta r{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{dr}}})$$

(4)

Integral to the above equation:

$${\displaystyle {\int }_0^{\mathsf{\Omega }}d\omega }={\displaystyle {\int }_{R_1}^{R_2}\left(\frac{M_1}{2\pi h\eta r^3}-\frac{{\tau }_0}{\eta r}\right)dr}$$

(5)

$$\mathsf{\Omega }={\displaystyle \frac{M_1\left(R_2^2-R_1^2\right)}{4\pi h\eta R_1^2{R}_2^2}}-{\displaystyle \frac{{\tau }_0}{\eta }}\ln {\displaystyle \frac{R_2}{R_1}}$$

(6)

From Equation (6), it can be concluded that:

$$M_1={\displaystyle \frac{4\pi h{R}_1^2{R}_2^2}{R_2^2-R_1^2}}\eta \mathsf{\Omega }+{\displaystyle \frac{4\pi h{R}_1^2{R}_2^2}{R_2^2-R_1^2}}\ln {\displaystyle \frac{R_2}{R_1}}{\tau }_0$$

(7)

Two parameters are defined:

$$\left\{\begin{array}{l}{k}_1={\displaystyle \frac{4\pi h{R}_1^2{R}_2^2}{R_2^2-R_1^2}}\\ k_2={\displaystyle \frac{4\pi h{R}_1^2{R}_2^2}{R_2^2-R_1^2}}\ln {\displaystyle \frac{R_2}{R_1}}\end{array}\right.$$

(8)

According to Equation (8):

$$M_1=k_1\eta \mathsf{\Omega }+k_2{\tau }_0$$

(9)

From the above equation, it can be seen that the two parameters k₁ and k₂ are only related to the size of the rheometer stirring blades and stirring drum. For a given testing instrument, these two parameters are constant values.

When measuring the rheological parameters of fine-grained mixture slurry using a coaxial cylindrical viscometer, the concave and convex settings at the upper and lower ends of the measuring inner cylinder allow a small amount of the measured slurry to overflow, while the convex setting at the lower end seals some air in the space when the measured slurry is placed in the measuring inner cylinder, forming an air cushion. At this time, both the upper and lower ends have no shear effect on the measured slurry, thereby reducing and eliminating the hindering effect of the slurry at the upper and lower ends on the measuring inner cylinder, so that the measured torque value is entirely generated by the slurry in the side slit [36].

However, for measuring the new type of gangue slurry rheometer containing the large-particle-sized gangue filling slurry, the stirring element is a rotatable blade. When it is vertically placed into the measured slurry, the influence of the end of the slurry on the torque value obtained by the blade cannot be eliminated. To achieve this, the first step is to design the blade to be immersed in the measured slurry, with its upper edge tangent to the slurry level, in order to minimize and eliminate the effect of the upper end of the stirring blade. At this point, we only need to consider and calculate the torque generated by the slurry between the lower edge of the blade and the bottom of the slurry storage cylinder on the stirring blade.

The flow behavior of the slurry at the lower end is also caused by the rotation of the mixing blade. The distance between any point on the lower edge of the mixing blade and the mixing center is r, and there is also a velocity gradient due to the frictional force. The movement speed of the slurry decreases layer-by-layer from top-to-bottom until the bottom of the mixing drum reaches 0. Therefore, it can be regarded as a flow model between flat plates, as shown in Figure 4.

Assuming that the distance between the lower part of the mixing blade and the mixing center is r and the width is d_r, a section of slurry moves uniformly in a circular motion around the mixing center at a certain speed, and the bottom of the mixing drum is considered as a stationary plate. The shear rate of the end slurry is expressed as:

$$\dot{\gamma }={\displaystyle \frac{\mathsf{\Omega }r}{\mathrm{L}}}$$

(10)

The corresponding shear stress is:

$$\tau ={\tau }_0+\eta {\displaystyle \frac{\mathsf{\Omega }r}{L}}$$

(11)

The micro torque generated by the slurry at this point is:

$$d{M}_2=\left({\tau }_0+\eta {\displaystyle \frac{\mathsf{\Omega }r}{L}}\right)2\pi r^{2}dr$$

(12)

The integral to Equation (12) is:

$${\displaystyle {\int }_0^{M}d{M}_2}={\displaystyle {\int }_0^{R_1}\left({\tau }_0+\eta \frac{\mathsf{\Omega }r}{L}\right)2\pi r^{2}dr}$$

(13)

The additional torque of the end slurry is:

$$M_2={\displaystyle \frac{\pi R_1^4}{2L}}\eta \mathsf{\Omega }+{\displaystyle \frac{2\pi R_1^3}{3}}{\tau }_0$$

(14)

Two parameters are defined equally:

$$\left\{\begin{array}{l}{k}_3={\displaystyle \frac{\pi R_1^4}{2L}}\\ k_4={\displaystyle \frac{2\pi R_1^3}{3}}\end{array}\right.$$

(15)

$$M_2=k_3\eta \mathsf{\Omega }+k_4{\tau }_0$$

(16)

As can be seen from the above equation, K₁ and k₂ are still two parameters that are only related to the size of the rheometer stirring blades and stirring drum, and are also constant values for a given testing instrument.

Therefore, the shear torque obtained when testing the rheological parameters of the new gangue slurry rheometer should be:

$$M=M_1+M_2=\left(k_1+k_3\right)\eta \mathsf{\Omega }+\left(k_2+k_4\right){\tau }_0$$

(17)

By adjusting the rotational speed of the stirring blades to obtain their corresponding different torque values, multiple sets of recorded data are analyzed through regression to obtain a linear function. The ratio of the intercept of the curve on the shear torque axis to (k₂ + k₄) is the yield stress of the tested slurry, and the ratio of the curve slope to (k₁ + k₃) is the viscosity of the tested slurry:

$$\left\{\begin{array}{l}{\tau }_0={\displaystyle \frac{M_0}{k_2+k_4}}\\ \eta ={\displaystyle \frac{\mathrm{k}}{k_1+k_3}}\end{array}\right.$$

(18)

In the formula, M₀ is the intercept of the curve on the torque axis, and N·m;k is the slope of the curve.

According to the size of the mixing system, it can be calculated that:

$$\left\{\begin{array}{l}{k}_1+k_3=0.000189477\\ k_2+k_4=0.000181156\end{array}\right.$$

3. New Type of Gangue Slurry Rheometer for Testing Rheological Parameters of Slurry

3.1. Preparation of Gangue Filling Slurry

This article selected the actual filling gangue used in the Linxi mine of Kailuan Mining, with a maximum particle size of 15 mm, and the nearby power plant produced fly ash, local PO42.5 ordinary Portland cement, and urban tap water. The specific content is shown in

Table 1. Test ratio of gangue slurry.

Content	Cement	Fly Ash	Gangue	Water
76%	76 g	228 g	456 g	240 g

.

First, all the dry ingredients were poured into a large beaker according to the ratio, mixed well with a spatula, then stirred with water, and finally poured into the test mixing cylinder for testing.

3.2. Test Data Analysis of Gangue Slurry at Different Rotational Speeds

The torques of the gangue slurry at different speeds obtained through testing are shown in

Table 2. Test results of slurry with a concentration of 76%.

n (r/min)	200	250	300	350	400
M (N·m)	0.0255	0.0262	0.0289	0.0299	0.033
$\mathsf{\Omega }$ (rad/s)	20.935	26.173	31.409	36.628	41.888

.

Figure 5 shows the expression of the curve obtained by fitting the torque values obtained at different rotational angular speeds of the blade, thus obtaining the slope of the curve and its intercept on the torque axis. The yield stress and viscosity values of the tested slurry can be obtained from Formula (18), as follows:

$$\left\{\begin{array}{l}{\tau }_0={\displaystyle \frac{0.01748}{0.000181156}}=96.49\left(Pa\right)\\ \eta ={\displaystyle \frac{0.000357188}{0.000189477}}=1.89\left(Pa·s\right)\end{array}\right.$$

4. Numerical Simulation of the Testing Process of a New Type of Gangue Slurry Rheometer

Using Fluent numerical simulation software ANSYS2023, a three-dimensional model of the mixing system for the gangue slurry is established to simulate the velocity and pressure distribution of the cross-shaped mixing blades at different gangue slurry speeds, and the corresponding measured torques are obtained.

4.1. Model Establishment and Grid Division

The mixing element of the new type of gangue slurry rheometer consists of two rectangular thin sheets of identical size that pass through the axis and are perpendicular to each other, as shown in Figure 6. The blade size is 40 mm long, 30 mm high, and 2 mm thick, and the transmission connecting rod is 60 mm long. The mixing drum is a standard cylinder with a diameter and height of 100 mm. The three-dimensional model of the mixing blades and drum is shown in Figure 7.

A three-dimensional model of the mixing blade and mixing drum are established, and sliding mesh technology is used to divide the model calculation domain into two nested concentric cylinders. The data continuously transitioned and interacted through the Match Interface between the two cylinders.

In order to describe the flow behavior of the slurry at the blade rotation in detail, using a tetrahedral mesh partitioning model, as shown in Figure 8, the mesh refinement at the blade is set to 0.02 mm, and the rest is set to 0.08 mm. Therefore, a total of 275,584 tetrahedral mesh elements are partitioned.

4.2. Parameter Setting of Slurry Model

The numerical simulation of the flow behavior of gangue slurry requires the physical parameters of the measured slurry, including density, viscosity, and yield stress, as shown in

Table 3. Physical parameters of slurry.

Physical Parameters
Density	1800	${\mathrm{kg}/\mathrm{m}}^3$
Viscosity	1.89	$\mathrm{Pa}\cdot \mathrm{s}$
Yield stress	96.49	$\mathrm{Pa}$

.

The constitutive equation of the Herschel–Bulkley model is used to define the gangue slurry. During initialization, the upper edge of the blade is set to coincide with the slurry level, and the lower edge of the blade is 2.5 cm away from the bottom of the mixing drum. When the blade speeds are 200 r/min, 250 r/min, 300 r/min, 350 r/min, and 400 r/min, the flow behavior of the slurry at a cross-section 1.5 cm below the slurry level, where the lower edge of the mixing blade is located, is observed, and the torque obtained by the mixing blade is detected.

4.3. Observation of Velocity Distribution of Cross-Sectional Slurry at Different Rotational Speeds

Figure 9 shows the velocity distribution cloud map of the slurry observed at different speeds. It can be seen from the figure that the flow velocity of the slurry at the edge of the stirring blade is the fastest on the observed section, gradually decreases as it moves away from the blade edge, and reaches zero at a certain distance from the blade edge. This is because the slurry is subjected to the thrust generated by the rotation of the blades, causing the slurry near the edge of the blades to have the same rotational speed as the stirring blades. However, due to the frictional resistance inside the slurry, the speed gradually decreases to zero as it moves away from the blades, showing a gradient change pattern. As the rotational speed of the blade increases, the velocity of the slurry near the edge of the blade also increases. At the same time, the range of the maximum velocity gradually increases and extends away from the edge of the blade. Therefore, the area of minimum velocity gradually decreases.

4.4. Pressure Distribution of Observed Cross-Sections at Different Rotational Speeds

Figure 10 shows the pressure distribution cloud map of the observed cross-section of slurry at different speeds, which reflects the force situation of the slurry during the mixing process on the observed cross-section. From the figure, it can be seen that the stirring blades rotate counterclockwise, and the slurry located in front of the blade movement on the observation section is subjected to compressive stress, as shown in the red area in the figure. The slurry located behind the blade movement is subjected to tensile stress, as shown in the blue area in the figure. The maximum stress occurs a little further in from the edge of the mixing blades. As the blade speed increases, the range and magnitude of the compressive stress on the front of the blade movement gradually increase, and stress minima occur at the blade crossings immediately adjacent to the blades. At the same time, the range and magnitude of tensile stress on the back of the blade movement also gradually increase and eventually become integrated, closely adhering to the back of the blade movement direction. The difference between the two stresses gradually increases with the rotational speed and eventually forms a clear boundary.

4.5. Torque of Stirring Blades at Different Speeds

During the testing process of the new type of gangue slurry rheometer using numerical simulation, the torque obtained by the stirring blades over time at different speeds can be obtained through a monitor, as shown in Figure 11. The torque on the stirring blades gradually increases within a short time range and eventually stabilizes before no further changes occur.

The torque values on the stirring blades at different speeds are shown in

Table 4. Simulated torque values on the blade at different speeds.

No.	Blade Speed (rpm/min)	Blade Angular Velocity (rad/s)	Blade Torque (N·m)
1	200	20.9333	0.02531
2	250	26.1666	0.02721
3	300	31.4	0.02912
4	350	36.6333	0.03102
5	400	41.8667	0.03292

.

After conducting a regression analysis on the blade angular velocity and torque in the table above, the linear functions of the two were obtained, as shown in Figure 12.

The yield stress and viscosity of the simulated slurry can be obtained from Figure 12 and Formula (18), as follows:

$$\left\{\begin{array}{l}{\tau }_0={\displaystyle \frac{0.01783}{0.000181156}}=98.42\left(Pa\right)\\ \eta ={\displaystyle \frac{0.000364012}{0.000189477}}=1.92\left(Pa·s\right)\end{array}\right.$$

From

Table 5. Comparison of rheological parameters between setup (test) and simulated values.

Physical Parameters	Set (Test) Value	Simulated Value	Relative Error
Viscosity (Pa·s)	1.89	1.92	1.59%
Yield stress (Pa)	96.49	98.42	2%

, it can be seen that the yield stress and viscosity of the slurry obtained from numerical simulation are 98.42 Pa and 1.92 Pa·s, respectively, while the measured yield stress and viscosity of the slurry under the same conditions are 96.49 Pa and 1.89 Pa·s, respectively; the differences are 1.93 and 0.03, respectively, with errors of 2% and 1.59%, respectively. It can be seen that the errors are within a reasonable range, indicating the effectiveness of the testing principle of the new gangue slurry rheometer.

5. Conclusions

This paper analyzes the issue of being unable to obtain accurate rheological parameter test values in current coal mine gangue filling slurry due to the presence of large-sized particles. The specific research findings are as follows:

(1)

Due to the current inability to accurately measure the rheological parameters of slurry containing large-sized gangue particles, a new type of gangue slurry rheometer has been developed. The working principle of the newly developed gangue slurry rheometer is to obtain the torque of the stirring blades at different speeds and calculate the rheological parameters of the slurry. The torque is generated by the combined action of the slurry between the blade side edge and the cylinder wall, and the slurry between the blade lower edge and the cylinder bottom.

(2)

Testing is conducted on a slurry containing a 76% concentration of large-sized gangue material, and the torque on the stirring blades is obtained at a speed of 200–400 r/min. As the speed increases, the torque values obtained on the blades gradually increase. The yield stress and viscosity are calculated to be 96.49 and 1.89, respectively.

(3)

Fluent is used to simulate the flow behavior of gangue slurry under the same conditions, and it is found that the maximum velocity of the slurry appears at the edge of the mixing blade and decreases towards the direction away from the blade edge, forming a velocity gradient. The front of the blade’s direction displays compressive stress, while the rear displays tensile stress. As the rotational speed increases, the difference between the two stresses gradually increases and a clear boundary appears. Based on the torque values obtained on the blades at different speeds, through regression analysis and calculation, the yield stress and viscosity of the slurry are found to be 98.42 and 1.92, respectively, with errors of 2% and 1.59%, respectively. This demonstrates the effectiveness of the new gangue slurry rheometer test.

(4)

This study provides a basis for the accurate measurement of the rheological parameters of large particle sizes, ensuring the smooth transportation of high-concentration gangue slurry in pipelines and providing a reference for the design of filling processes and filling systems.