Abstract
This article proposes using abrasion equilibrium equations for refining coarse-grained coal slurry hydrodynamic conveying, combining experimental data and theoretical analysis. It presents a particle refinement solution model and a viscosity prediction formula for mixed coarse and fine coal samples. Experimental data indicate that prolonged conveying time decreases coarse particle content and increases fine particles (< 0.074 mm), with a tendency for slurry viscosity to rise, though the rate of increase slows. Comparing predicted and measured particle refinement values showed a maximum deviation of 10% for 30 and 50-minute conveying times. Using the Herschel-Bulkley fluid model for viscosity prediction post-grading, verified with experimental data, the minimum viscosity value is observed at a 58% slurry concentration with varying coarse and fine coal ratios. The deviation between predicted and measured viscosity values is 5.23%, providing a formula for the viscosity reduction effect of blending.
Keywords: Hydrodynamic conveying, Grade refinement, Viscosity, Grinding balance equation, Crushing rate function
Subject terms: Mineralogy, Fluid dynamics
Introduction
Coal slurry pipeline conveying is a new type of coal transportation method, in which coal lumps are crushed into coarse particles with a particle size of less than 1.5 mm, mixed with water to form a solid-liquid two-phase flow of coarse particles, and transported over long distances through pipelines, which has many advantages, such as energy saving, economy, practicality, and environmental protection1–3. Therefore, an in-depth study of the rheological properties of coal slurries is essential for improving transport efficiency and ensuring safety.
In this field, Fan4 used coal slurry in the same slurry system preparation conditions, the gangue company produced additives, lignosulfonate and nano-system additives were tested, the same concentration, the addition of additives compared to the original sample are reduced viscosity of the slurry, gangue company provided additives compared to other can be decreased by 700、200mpa·s; Song5found that if a certain amount of ultrafine particles (< 10 μm) are added to the solid particles, although the viscosity of the slurry increases, the consistency of the formed slurry also increases; Liu6 investigated the rheological properties of high-concentration tailing sand slurries and showed that particle size distribution’s effect on the slurry’s viscosity was particularly significant under the multifactorial coupling conditions of mass concentration, temperature and particle size distribution. It was found that the yield stress and viscosity showed a significant trend with the change of particle size, and the effect of particle size distribution was more pronounced, especially at high mass concentration, which was quantitatively described by an exponential function.
However, since coal with less hardness is easily broken and refined during hydraulic transportation7–11, some factors such as the effect of pumps on particles, wear at the bottom of the pipeline, the impact of instruments and pipe valves on particles, and inter-particle collisions may lead to this phenomenon12,13,14,15.After refinement, changes in the specific gravity of different particle sizes can lead to changes in viscosity, affecting the conveying efficiency. Therefore, it is crucial to research the particle size gradation of particles in the pipeline hydraulic coal conveying process. Zhao’s team16,17investigated the erosion behaviour of coarse particles in pipeline transport through numerical simulation and found that the effect of particle wear on particle size gradation has not been widely explored. Xiao’s18 team also pointed out that although there have been studies on pipeline wear and machine wear, there is still a lack of information on particle wear during transport and its specific effect on grain size gradation. These literatures provide references for further research.
The phenomenon of particle industrial refinement has been observed in experiments many times, Chen Zuobing19explored the effect of different particle size grades of slag on the grinding efficiency and used a vertical roller mill for industrial slag processing, and the experimental data showed that for the optimized particle size gradation, the grinding rate was increased significantly; Li Guofeng20investigated the effect of the milling process parameters on the particle size characteristics of the product, and used a laser particle size meter to measure the particle size distribution of the milled The particle size distribution of the product after grinding was measured using a laser particle size meter, and the R-R particle size characteristic equation was also used for particle size analysis, which suggested that the grinding rate was relatively uniform when the media ratio was 2:3 and the material ball ratio was 0.6. However, the grading refinement laws are poorly studied, despite individual prior foundations8,23,30. Chen21found that very fine particle size (<53 μm) leads to a significant increase in the dynamic viscosity of the slurry. In this case, particle size distribution plays a role, for which particle size distribution (e.g., bimodal PSD) is optimized based on the type of coal to keep the dynamic viscosity of the slurry as low as possible; Zhao Bingchao22investigated the effect of particle grade pairing on rheological parameters for the rheological properties of gangue slurries with different particle sizes and different concentration of static time; these scholars found that particles with different sizes can be optimized for the rheological parameters by appropriate These scholars found that different particle size particles through the appropriate combination can optimize the rheological parameters, the research in this area has a certain preliminary basis, but not in-depth, need further research31,32,34,36.
A prediction model of pipe particle refinement was established, and the Herschel-Bulkley fluid model was used to derive a mixing viscosity calculation method after considering a shift in its relative flow viscosity following a change in gradation.
Experimental set-up and material preparation
Experimental piping and equipment
In the experiment, the coarse-grained coal slurry conveying pipeline used, as shown in Fig. 1, the length of the pipeline is about 20 m, and the inner diameter of the main pipe is 0.15 m. A slurry pump with a flow rate range of 4.5–2340.0 m3/h and a head of 6.0–130.0 m was selected with a 400 kW motor for the coal slurry pipeline conveying. For the coal slurry flow rate, flow meter 4 was used to measure the flow rate, and the pressure loss was measured by the mercury differential pressure meter 7. The observation of transparent acrylic pipe Sect. 8 helped to understand the flow of coal slurry. In addition, a heat exchanger 5 was installed in the pipeline to maintain the temperature of the coal slurry constant.
Fig. 1.
Coal 94 slurry transportation test pipeline
In the experiments, a PE-180 crusher was used for the initial crushing of coal particles, and a HLMX mill was used for the fine-grinding process. To obtain the viscosity values of the coal slurry, the viscosity of the slurry was measured using a Brookfield RS T-CC rheometer. For the coal slurry particle size, it was analyzed by Mastersizer 2000 type instrument and the sieving operation was carried out by a standard sieve. Coal powder mass can be given by YP20K-1 type electronic balance.
Experimental material characteristics
The coking coal concentrate from a mine was first crushed to < 30 mm by a crusher and then ground by a mill, and finally, the ultrafine coal powder was obtained. The specific gravity of coal particles was 1.36, and the ash content was 2.25%. A particle size analyzer combined with the sieving method was used to analyze the particle composition, considering the sieve hole size of the standard sieve, combined with the specific gravity of the particles in the field and the reduction of the amount of sieving work surface, the particle gradation is shown in Table 1.
Table 1.
Particle size gradation.
| Particle size interval(mm) | Gradation I Mass Percentage in Grain Size Interval % | Grading II Mass Percentage in Grain Size Interval % |
|---|---|---|
| 10.000-29.4000 | 0 | 10.10 |
| 5.000-10.000 | 18.55 | 13.50 |
| 2.000-5.000 | 25.05 | 20.00 |
| 0.500-2.000 | 21.40 | 21.40 |
| 0.074-0.500 | 25.00 | 15.00 |
| <0.074 | 10.00 | 20.00 |
In the experiments, the slurry volume concentration was around 11.0-12.0%. Two particle grades were used, the maximum particle size was 10.0 mm for grade I and 29.4 mm for grade II.
Experiments
In this study, raw coal samples were first crushed and ground to ensure that their particle size was suitable for subsequent experiments. Subsequently, the specific gravity and water content of the coal particles were determined by the specific gravity bottle method and the weight loss by drying method, respectively. Based on these measurements, the mass of coal and water required for the preparation of coal slurry was calculated using a specific slurry formulation. Next, the coal and water were accurately weighed according to the calculations and mixed well to prepare the coal slurry. The prepared coal slurry was injected into the experimental annulus and allowed to flow steadily in the line. After the flow of the slurry was stabilised, samples of the slurry were extracted through the sampling valve at critical time points of 30, 40, 50 and 60 min, and quickly transferred to beakers, sealed with cling film to prevent evaporation of water and contamination, and finally used for subsequent analytical tests.
The taken slurry samples (Grade I and Grade II) were stirred fully with an electric stirrer to fully suspend the particles at the bottom, and the viscosity of the taken slurry was measured with a Brookfield RS T-CC rheometer. After the viscosity of the slurry was measured for all periods, the samples were put into a blower drying oven for drying the samples, and when the water was evaporated, the dried samples were sieved, and then the samples were subjected to particle size determination with a Mastersizer After evaporation of water, the dried samples were sieved and the particle size was determined using a Mastersizer 2000 laser particle sizer.
Results and discussions
Analysis of experimental data
In the experiment, the average velocity of the coal slurry was about 2.5 m/s, and the particulate matter was partially suspended and partially slip-jumped during pipeline transportation. The experiment measured 10 sets of viscosity data and 55 sets of particle size distribution data.
The data on the mass percentage of particles of each grain level at different conveying times are shown in Fig. 2.
Fig. 2.
Trend of each particle size percentage variation of pulp with conveying time.
According to Fig. 2(a), it can be observed that the mass percentage content of each particle grade varies with the conveying time. 5.0–10.0 mm, 2.0–5.0 mm and 0.5–2.0 mm particle grades show a decreasing trend in mass percentage, with a rapid decrease in the mass percentage of 5.0–10.0 mm grades, while the mass percentage of 0.074–0.5 mm and < 0.074 mm grades show an increase in mass percentage, with a significant increasing trend in the < 0.074 mm grade. Percentages, on the other hand, showed an increase, with a significant increasing trend in the < 0.074 mm grain size. Figure 2(b) shows that as conveying proceeds, the mass percentage of the largest particle size class 10.0–29.4 mm decreases significantly, and 5.0–10.0 mm and 2.0–5.0 mm also show a decreasing trend. While the proportion of < 0.074 mm fine particles increased significantly, the content of 0.074–0.5 mm particle size class also showed an increasing trend.
According to the trend of conveying time and coal slurry viscosity shown in Fig. 3, the viscosity tends to increase with the extension of time, but the increase gradually slows down. Previous studies have shown that the coal slurry viscosity is mainly related to the volume concentration of fine particles and the limiting concentration23.
Fig. 3.
The trend of viscosity changes of coal slurry at different transportation times.
The above analyses show that in the process of coal slurry conveying, due to the joint collision and friction effects of pumps, various instruments, pipe elbows, and the bottom of the pipeline, it leads to the reduction of the content of coarse particles, At the same time, the abraded coarse particles will be added in the form of fine particles, which will lead to an increase in the content of the fine particle level.
Theoretical analysis of coal slurry particle refinement
The particle refinement process in the pipeline transport of coarse-grained coal slurry is complex, involving slurry pumping, particle-pipe friction and collision, interparticle collision, and particle interaction with various gauges, pipe valves, and bends, Therefore no theory or model has yet been developed to describe coarse coal particle refinement. The results of the authors’ previous research also indicate that the analogy method can be used to analogize the coarse particle coal slurry pipeline hydrodynamic conveying process to a special ball mill grinding process, based on the grinding theory, to study the pipeline coal particle refinement8. Most of the research of domestic and foreign scholars on this theory focuses on the grinding mechanism of iron ore concentrate and lead-zinc ore and the method of determining relevant parameters–26.
According to the grinding theory, the following grinding equilibrium equation exists27:
 |
1 |
Where: fi(t) is the mass percentage of the particles of the ith particle size class at time t; bij is the fragmentation distribution function, which is the mass percentage of the particles that go from the ith size class to the jth size class after fragmentation; and Si fragmentation rate function (selection function), which indicates the probability that the particles are fragmented per unit of time.
Equation (1) can be expressed in matrix form:
 |
2 |
Where I is the unit matrix; and B is the broken matrix.
According to the relevant studies, the form of Bcan be28:
 |
3 |
Then the matrix A in Eq. (2) takes the form:
 |
4 |
Combined with Eq. (2), the solution can be obtained in the form of:
 |
5 |
Where i is the number of particle sizes other than the finest (i.e. <0.074 mm), it is considered here that particle sizes < 0.074 mm cannot be re-worn and refined during conveying. The smaller the value of i, the larger the average particle size d0 of that particle size class.
From Eq. (5) above, it can be seen that if the initial particle gradation fi(0) and the crushing rate function Si are known, the particle gradation f(t) at time t can be predicted.
Experimental data analysis and model validation of coal slurry particle refinement
In coal slurry conveying, if Eq. (5) above is to be used to predict the particle gradation at different moments, and generally the initial particle gradation fi(0) is known, the solution of the fragmentation rate function Si is especially critical. Currently, relevant studies have shown that the crushing rate function Siis related to the nature of particles and operating conditions27,29. Here, to verify Eq. (5), using the two kinds of grades in Table 1 (grades I and II) slurry conveying 40 min and 60 min when the grades data, combined with the inverse calculation of the value of Si in the Eq. (5), each kind of slurry obtained by averaging the two groups of Si, to obtain the value of Si at the grades, the data fitting results found that the crushing rate function Si and the average particle size of each particle level has a close relationship, with each particle level particle size increases, the crushing rate function shows an increasing trend, compared with other function types, the power function has a smaller relative deviation, the crushing rate function Si can be approximated as a power function of the average particle size d0 of each particle level, as shown in Fig. 4.
Fig. 4.
The relationship between the Si value of coal slurry and the average particle size d0 of each particle grade.
The particle gradation of the two coal slurries was predicted using Eq. (5) when they were transported for 30 min and 50 min, respectively. The results are shown in Fig. 5, and the maximum deviation between the predicted value of the formula and the actual measured value is not more than 10%.
Fig. 5.
Comparison between predicted and measured values of coal slurry gradation changes.
Study of the rheological properties of different graded particle mixtures
The volume concentration of the coal slurry is around 11.0-12.0% and the fluid behaves as a Newtonian body10,30. The results of the above analysis show that there is a particle refinement phenomenon during its transport and the rheological parameters such as the viscosity of the refined coal slurry change. However, its degree of refinement stops with the increase of time. In addition to this phenomenon, artificially matching different coarse and fine particle sizes and changing the composition of slurry gradation can achieve the effect of optimizing the viscosity and thus reducing the resistance.
Here, two groups of coal samples of coarse grading (B) and fine grading (H) were used to be mixed according to different ratios, and six groups of mixing were obtained for analytical study, and the particle size distribution of each group is shown in Table 2. as Fig. 631.
Table 2.
Basic experimental parameters
| Mixing ratio | Average particle size (mm) | Particle content below 0.0445 mm particle size (%) | Yield stress (pa) | Relative viscosity |
| 100%H（fine 100%） | 0.03 | 97.70 | 19.90 | 101.52 |
| 20%B+80%H（coarse: fine 2:8） | 0.08 | 79.20 | 12.70 | 58.31 |
| 40%B+60%H（coarse: fine 4:6） | 0.13 | 60.60 | 8.50 | 43.02 |
| 60%B+40%H（coarse: fine 6:4） | 0.18 | 42.00 | 4.60 | 38.49 |
| 80%B+20%H（coarse: fine 8:2） | 0.23 | 23.00 | 4.10 | 52.84 |
| 100%B(coarse 100%) | 0.28 | 4.00 | 6.30 | 55.21 |
Fig. 6.
Grain Size Profile.
The concentration of each group of the slurry was 58% and the results of the rheological tests are shown in Fig. 7. The rheological behaviour of the coal slurry consisting of shear rate and shear stress agrees well with the Herschel-Bulkley fluid model of the form:
 |
6 |
Fig. 7.
Relationship between shear rate and shear stress curve.
Among them: 
indicates the shear stress, 
indicates the yield stress, K indicates the coefficient of consistency, 
indicates the shear rate, and n indicates the rheological index.
Assuming that the mass proportion of fine particles of coal dust in the mixture is a, the apparent viscosity of this fraction of particles is then:
 |
7 |
 |
8 |
indicates the apparent viscosity of fine-grained samples, 
indicates the shear stress at the same strain rate for a slurry containing only a coarse-grained sample, and indicates the strain rate of the mixture. 
indicates the apparent viscosity of the coarse-grained sample.
Considering the effect of mixing particle size ratio on flow properties, the shear stress and strain rate of the whole slurry can be further expressed as a weighted average of 
and
.
 |
9 |
 |
10 |
Substituting into the defining equation for apparent viscosity reduces to:
 |
11 |
Among them, 
indicates the apparent viscosity of the mixture, 
and denotes the apparent viscosity of coarse and fine particle samples, respectively, n denotes the rheological index in the Herschel-Bulkley model, A expresses a coefficient (math.), and the formula is as follows:
 |
12 |
A represents the proportion of fine particle samples of coal dust, i.e. the content of fine particle samples of coal dust.
For Eq. (6) the rheological index n was fitted using 100% B (coarse) and the fitted data are shown in Table 3.
Table 3.
Rheological parameters of the Herschel-Bulkley model.
| Yield stress /τ0 | Rheology index /n | Consistency factor /K | Goodness of fit /R2 |
|---|---|---|---|
| 6.30 | 0.90 | 0.10 | 0.93 |
| 6.30 | 0.95 | 0.07 | 0.96 |
| 6.30 | 1.01 | 0.04 | 0.99 |
| 6.30 | 1.21 | 0.01 | 0.92 |
From Table 4, it can be seen that the maximum deviation between the predicted and measured values using Eq. (11) does not exceed 5.23%. Therefore, the model can be used to study the flow of coal slurry with a concentration of 58%. The model for other concentrations of coal slurry flow characteristics will be further explored subsequently.
Table 4.
Prediction of mixed viscosity.
| Proportions (coarse: fine) | μ(count) | μ(surveying) | Relative error (%) |
|---|---|---|---|
| 10:0 | 0.0490 | ||
| 8:2 | 0.0415 | 0.0437 | 5.23 |
| 6:4 | 0.0507 | 0.0531 | 4.80 |
| 4:6 | 0.0677 | 0.0712 | 5.10 |
| 2:8 | 0.1093 | 0.1131 | 3.52 |
By mixing different ratios of coarse and fine coal samples, it was found that the relative viscosity of the coal slurry decreased with the gradual addition of fine coal samples and was minimal when the mixing ratio reached 60B/40H (i.e., 60% coarser and 40% finer). With further addition of fines, the viscosity of the coal slurry started to increase. Therefore, the optimum coarseness/fines ratio for both coarse and fine coal samples was found to be 60B/40H.
Concerning the optimum ratio of coarse and fine particles in the slurry, studies have concluded that there exists an optimum ratio of coarse and fine particles in the slurry with the lowest concentration32,33,34,35. According to the results of theoretical studies on the viscosity-reducing effect of blending coarse and fine particles, the optimum ratio of coarse particles x33,35:
 |
13 |
Among them: 
indicates total solids concentration before mixing, 
indicates the limiting concentration of fine particles.
Here is taken as 58%, According to the results of the authors’ previous studies, the approximation for coal slurry with an average particle size of less than 0.03 mm without chemical additives is 64%36. From this calculation based on Eq. (13), we can get x = 58%, which is consistent with the experimental situation of 60% of coarse particles at the lowest viscosity as shown in Fig. 8; Table 2.. Table 2. also shows that when the combination of coarse and fine particles is used, there should be a large difference between the particle sizes of coarse and fine particles, and a good viscosity reduction effect can be achieved when the difference is one order of magnitude.
Fig. 8.
Relationship between relative viscosity and the ratio of coarse to fine particle content.
Based on this paper’s study of the effect of particle size gradation on slurry viscosity, our future research direction will focus on the finer optimisation of particle size distribution to further reduce slurry viscosity while ensuring efficient conveying. Improving the flow properties of slurries by controlling the particle size gradation is particularly important for high-consistency slurry conveying applications.
Conclusion
1)Through the experimental research method to study the different conveying periods of two kinds of coal slurry particle distribution rule of change, the experiment shows that with the increase of conveying time, the mass percentage of coarse-grained coal declined, the abraded part of the coarse particles in the form of fine particles supplemented to the fine particles in the granularity of fine particles, resulting in the rise in the content of fine particles of granularity, but the growth of the magnitude of the gradual slowing down.
2)Through the theoretical analysis method, it is proposed to use the grinding balance equation to describe the particle refinement problem of slurry conveying of coarse coal particles, and the solution model of particle refinement is given; the measured values of particle gradation at 30 min and 50 min of conveying are compared with the predicted values of the model and it is found that the maximal deviation is not more than 10%, and the result of the data fitting is found that the function of the crushing rate, Si, is a power function of the average size of d0 for all the particle grades, and the ratio of the finer particles is increased with the increase in the crushing time and the viscosity of the slurry is also increased.
3)Through the Herschel-Bulkley fluid model combined with the viscosity parameter, the viscosity prediction formula was derived, using the research data of relevant scholars to verify that, from different coarse and fine ratios of coal particles with the pulping, the concentration of a certain (58%), there is a minimum value of the viscosity of the coal slurry, the model predicted value and the maximum deviation from the measured value of 5.23%, and at the same time, the minimum value of the viscosity corresponding to the content of the coarse particles using the blended The theoretical formula of viscosity reduction effect can be solved.
Author contributions
Jian wrote the main manuscript text. Zhao conducted the data collection. Cai and He made formatting changes to the paper.
Data availability
The experimental data can be made public.The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Declarations
Conflict of interest
The authors declare no conflicts of interest.
Footnotes
Publisher’s note
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References
- 1.Zhao Li-an. Introduction to Clean Coal Technology[M].Shengyang (Northeastern University, 2011). [Google Scholar]
- 2.Yu, X. Chen Yi-bin. Application status and prospect of pipeline coal transport[J]. Coal Eng.52 (05), 1–4 (2020). [Google Scholar]
- 3.Zhang, X. et al. Correlation and stage change of key groups and thermal effects of spontaneous coal combustion due to long-term ultraviolet illumination[J]. Energy. 293, 130775 (2024). [Google Scholar]
- 4.Fan, F. S. & Ma, Y. L. Hei Dai Gou Coal Processing Plant High Concentration Coal Mud Slurry Preparation. Clean. Coal Technol.30 (S1), 625–629 (2024). [Google Scholar]
- 5.Song, F. L. et al. Characteristics of ultrafine particles and their effect on pulp formation properties. Coal Technol.43 (09), 272–277 (2024). [Google Scholar]
- 6.Liu, Z. S. & Guo, L. J. Study on the rheological properties of high concentration whole tail sand slurry under multi-factor coupling conditions. China Min. Magazine. 29 (10), 116–121 (2020). [Google Scholar]
- 7.BOYLU, F. & DINER, H. Effect of coal particle size distribution, volume fraction and rank on the rheology of coal-water slurries[J]. Fuel Process. Technol.85 (4), 241–250 (2004). [Google Scholar]
- 8.Zhao, L. A., Wang, T. & Cai, R. Prediction of coal slurry pipeline transportation grading reduction and its influence on pipe transportation parameters[J]. Braz. J. Chem. Eng.36 (2), 845–853 (2019). [Google Scholar]
- 9.Zhao, L. A., Cai, R. & Wang, T. L. Influence of coal slurry particle composition on pipeline hydraulic transportation behaviour [J]. IOP Conference Series Earth and Environmental Science, 113(1):012163. (2018).
- 10.Zhao Li-an. Test analysis of particle size distribution degradation for coal slurry conveying by pipelines[J]. Hydro-Science Eng., (6):109–115. (2016).
- 11.MOSA E S et al. A study on the effect of slurry temperature, slurry pH and particle degradation on rheology and pressure drop of coal-water slurries[J]. J. Eng. Sci. Assiut Univ.35 (05), 1297–1311 (2007).
- 12.Wang, J. et al. Effects of particle diameter on performance of slurry erosion wear[J]. J. Drain. Irrig. Mach. Eng.32 (10), 840–844 (2014). [Google Scholar]
- 13.Wu, B. et al. Numerical simulation about erosion characteristics of the solid particle in a slurry pump[J]. J. Cent. South. Univ. (Science Technology). 43 (01), 124–129 (2012). [Google Scholar]
- 14.Wu, X. S. H., Wang, Y. P. & Tang, D. R. Analysis of the effect of solid particle concentration on wear of horizontal pipelines[J]. Education Modernization, 6(34):200–201.
- 15.Chen YF, Investigation on the Particle Motion and Distribution Characteristics in Rotational Flow Field[D].Nanjing: Southeast University, 2016 (2019).
- 16.Zhao, R. J. et al. Effect of sparse solid particles concentration on the performance and erosion of centrifugal pump.[J]Chinese. J. Hydrodynamics, 2021(5):640–647 .
- 17.Zhao, R. J. et al. Numerical simulation of coarse particle erosion characteristics of solid-liquid two-phase flow in 90°elbow. [J]Journal Huazhong Univ. Sci. Technology(Natural Sci. Ed. ),2021(10)47–66 .
- 18.Xiao, Q. K. et al. Numerical simulation study of slurry pipeline erosion and wear based on DDPM-RSM.[J]Journal of Chinese Society for Corrosion and Protection,2024,44(6)1–16 .
- 19.Chen, Z. B. et al. Experimental Research on Grinding kinetics of Slag[J]. J. Wuhan Univ. Technol. 2021, 43(05):16–20 .
- 20.Li, G. F. et al. Effect of grinding process parameters of stirring Mill on particle size characteristics of. Products[J] Metal Mine, 2022(07):212–218
- 21.Chen, R. et al. Preparation and rheology of biochar, lignite char, and coal slurry fuels[J]. Fuel,2011,90(4).
- 22.Zhao, B. C. et al. Influence of particle gradation and timeliness on rheological properties of filling slurry[J]. Saf. Coal Mines 2023, 54(10):117–127 .
- 23.Li-an, Z. H. A. O. & Tieli, W. A. N. G. Study on grading degradation of coarse coal slurry pipeline transportation and its influence[J]. Hydro-Science Eng., (03):115–121. (2022).
- 24.YANG, J. L. et al. Rev. Grind. Kinetics Res. [J] Multipurp. Utilization Mineral. Resour., 2017(4):4–10 .
- 25.Kui, H. E. et al. Grinding kinetics of Vanadic Titanomagnetite from Panzhihua[J]. Min. Metall. Eng.36 (06), 35–38 (2016). [Google Scholar]
- 26.HENDERSON, C. B. Optimum particle-size distribution of coal for coal-water slurries,[J] Prepr. Pap - Am. Chem. Soc. Div. Fuel Chem.36 (3), 2–28 (1983). [Google Scholar]
- 27.Huang Lilong, Z. H. A. N. G. et al. Modeling and Simulation of batch grinding with Vertical stirred Mill based on MATLAB/Simulink[J]. Min. Metall. Eng.36 (03), 26–30 (2016). [Google Scholar]
- 28.BERTHIAUX, H. & VARINOT, C. Approximate calculation of breakage parameters from batch grinding tests[J]. Chem. Eng. Sci.51 (19), 4509–4516 (2017). [Google Scholar]
- 29.Pengcheng, T. I. A. N., Zehong, W. A. N. G. & Yong, M. A. O. Research status and application of grinding kinetics[J]. China Min. Magazine. 31 (07), 112–121 (2022). [Google Scholar]
- 30.Dr. B. K. Sah. Optimize the amount of additives to minimize the relative viscosity of coal-water slurry[J]. J. Appl. Chem., 2014 (ICAET-2014) 58–62 .
- 31.Yan, M. A., Jiaqi, C. H. E. N. & Zhuming, M. E. N. Optimization of coal pipeline transportation parameters[J]. Coal Eng. 2017, 49(05):107–111 .
- 32.Dong, W. A. N. G., Zhenliang, X. U. & Meihua, L. I. U. Feasibility of size of particles and the composition of sediment in high-concentration slurry pipeline transportation[J]. J. Hunan Univ. Sci. Technology(Natural Sci. Edition), (02):45–47. (2005).
- 33.Chen Hao. Mechanism Study on Flow of CWM(Coal Water Mixture)Based on the Discontinuous Gradation[D] (General Administration of Coal Science and Research, 2016). [Google Scholar]
- 34.WANG Jian-jun, C. H. A. N. G. & Xuan Application of discontinuous gradation technology in high concentration coal water slurry preparation[J]. Coal Engineering, 54(02):89–92.
- 35.Fei Xiang-jun. Hydraulics for slurry and granular material handling[M].Beijing: Tsinghua University Press, 1994:340–344. (2022).
- 36.Li-an, Z. H. A. O., Tieli, W. A. N. G. & Kaipeng, G. U. O. Study on Rheological Parameters and Hydraulic Gradient of High Concentration Coal Water Slurry[J]. Coal Convers.43 (05), 88–96 (2020). [Google Scholar]
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Data Availability Statement
The experimental data can be made public.The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.