Method for evaluating packing condition of particles in coal water slurry

Powder Technology 281 (2015) 121–128

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Method for evaluating packing condition of particles in coal water slurry Yanan Tu ⁎, Zhiqiang Xu, Weidong Wang School of Chemical and Environmental Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China

a r t i c l e

i n f o

Article history: Received 23 December 2014 Received in revised form 29 April 2015 Accepted 1 May 2015 Available online 10 May 2015 Keywords: Packing density Model Coal water slurry Particle size distribution

a b s t r a c t In the coal water slurry (CWS) industry, it is essential to achieve high packing density of product particles in order to obtain a high concentration without affecting the flowability. In this study, a method based on an index E is proposed for evaluating the packing density of particles in CWS with given particle size distribution (PSD) and tested on bituminous and lignite coal. These two types of coal were ground and mixed in different proportions to obtain different packing densities. The experimental results show that the CWS concentration increased with E, implying the good applicability of the proposed method. By calculating E for different PSDs, it was found that the packing got closest when the parameters in Rosin–Rammler equation and Alfred equation were 0.75–0.85 and ~ 0.5, respectively. In addition, the packing density for unimodal PSD is generally lower than that for multimodal PSD. In contrast, the average sizes of the mixed samples did not affect the packing status in CWS and the product concentration consistently. With some adjustments, the proposed method can also be used to evaluate the tapped packing density of dry coal powders, with some applicability. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The packing density is a parameter that is commonly used to describe the packing condition of particles. It is an important index that is used to characterize many powder products or suspensions such as pharmaceuticals, composite materials, coal water slurry (CWS), and concrete. CWS is a kind of slurry fuel mixed with coal powder, water and small quantities of dispersant, and has been studied for decades since the Oil Crisis in 1970s as a replacement for fuel oil in boilers for power generation and industrial heating [1]. In China, the development of CWS has become one of the research focuses of clean coal technology. In the CWS industry, high packing density always leads to high concentration (high calorific value) at required flowability without other highenergy consumption processes, such as thermal upgrading [2,3]. In the last few decades, several models have been developed to predict the packing density of materials under given conditions (size distribution, density, sphericity, etc.). Furnas [4] and Westman et al. [5,6] conducted the earliest studies on systematically describing the packing conditions of mixed particles with different sizes; they mainly focused on the packing behavior of discrete-sized particles with large size differences. However, in practice, it is more important to describe the packing condition of nonspherical particles with continuous size distribution. Andreasen [7] was the first to study the packing behavior of continuous

⁎ Corresponding author at: Yifu 225, China University of Mining & Technology (Beijing), D11, Xueyuan Road, Haidian District, Beijing 100083, China. Tel.: + 86 10 62339169; fax: +86 10 62339899. E-mail address: [email protected] (Y. Tu).

http://dx.doi.org/10.1016/j.powtec.2015.05.001 0032-5910/© 2015 Elsevier B.V. All rights reserved.

size distribution powders; he used the Gaudin–Schuhmann (G–S) equation to describe the real particle size distribution (PSD):
F ðdÞ ¼ 100 

β

d

Dmax

;%

ð1Þ

where d is the particle size, F(d) is the cumulative mass content of particles finer than d; Dmax, the size of the largest particle; β, the characteristic parameters. And he found that the packing system tended to show relatively higher packing density when β was 0.3–0.5. Funk and Dinger [8] introduced the minimum particle size to G–S equation: F ðdÞ ¼

β d β −Dmin

β β Dmax −Dmin

 100; %

ð2Þ

where Dmin is the size of the smallest particle. This modified equation was called Alfred equation. Through a computer simulation, they found that the system had the closet packing when β was 0.37. Suzuki et al. [9–11] derived a theoretical equation for the relationship between the average coordination number and the void fraction, and they obtained a result different from that in Andreasen's study, indicating that β should be 0.5–0.8 if dense packing is required. In the concrete industry, the Fuller curve [12] is a well-known method for evaluating the packing condition of concrete's PSD. However, the packing density could not be directly obtained using Fuller's method. Stovall derived the “linear packing density model”, the most frequently used model for predicting the dry particle packing density, using two parameters representing the loose effect and wall effect [13]. Yu et al. [14–18] expanded the model to evaluate the packing of

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Based on Zhang's achievement, an improved approach for evaluating the packing condition of particles in CWS is proposed in this study. The following discussion indicates that our method is much simpler than abovementioned models. 2. Model description 2.1. Simplification Because of the surface forces as the Van der Waals force, electrostatic repulsion, and mechanical barrier force of hydration shell [2,33], particles in CWS behave quite differently from dry coal powders, mainly in the following respects:

Fig. 1. Imaginary pretreatment.

nonspherical particles by using the concept of equivalent packing diameter. De Larrard [19] improved Stovall's model and derived the “compressible packing model” with a new parameter to represent the difference between the theoretical and actual packing. Kwan et al. [20] improved Stovall's and Yu's models by adding a new parameter representing the “wedging effect” and derived a three-parameter model. Chan [21] tested these three models and found that the threeparameter model was more accurate. However, these abovementioned parameters are commonly different for various materials, making it difficult to apply these models. Since 1960s, various computer simulation algorithms have been proposed to simulate the particles packing [22–28]. These methods provided a clear insight to the particle interaction behavior and could help in studying the packing phenomenon. However, they required advanced hardware, complex designs, incurred long calculation times and high costs. Fewer studies have focused on particle packing in slurry than in dry powders. Funk employed his studies on packing density of dry powders [29,30] to CWS preparation and got the US patent [31]. Zhang [2,32] derived a so-called “compartment packing method” for CWS preparation, and obtained the same result with Funk's studies [8] through mathematical analysis. In addition, Zhang pointed out that the difference between Funk's [8] and Suzuki's studies [9–11] was caused by the size difference between their study subjects. Zhang also studied the packing density of PSD governed by Rosin–Rammler (R–R) equation: 
α  d F ðdÞ ¼ 100−100 EXP − ;% dx

ð3Þ

where α is the characteristic parameters whose value affects the shape of the PSD curve, and dx is the characteristic size whose value affects the apparent size of the packing system and equals the size value when F(d) = 63.21%. He indicated that the packing got closest when α was 0.7–0.8.

(1) Under stable conditions, particles could not touch each other directly owing to the water among particles. Therefore, the particles are movable in a specific path depending on the packing condition, concentration and compressibility of the water layer. (2) The particles' spatial distribution is more uniform than in dry powders because of the shearing process. (3) The entire system is flowable and deformable. As a result, the packing density does not change when the CWS is evenly divided into parts unless some components are removed from the system.

Therefore, packing in slurry could be simplified as follows: the three abovementioned effects in dry powders packing could be unified by a loose effect that, in turn, could be simplified as the voidage expansion of the self-packing of coarse particles. 2.2. Modeling Based on the above-described analysis, the following assumptions were made in our model to simplify the calculation for packing condition: (1) Particles are nonporous and spatially uniformly distributed. (2) The entire system could be divided into a limit number of microclusters, each of which has the same packing mode and PSD as the system. (3) Microclusters could be deformed, reorganized and repacked artificially without changing the packing density. The water among the particles is removed imaginarily, and the packing system is compressed without changing the particles' relative position, as shown in Fig. 1. First, the particles are divided into n narrow grades by particle sizes. Dmax is the size of the largest particle in the system; S, the size ratio of neighboring size grades (coarse to fine); Vi, the volumetric fraction of the ith grade (%); εi, the self-packing voidage of the ith grade; di, the ceiling size of the ith grade (μm). Therefore, n

dn = Dmax, d1 = Dmax/Sn − 1, di = Dmax/Sn − i and ∑ V i ¼ 100%. i

Fig. 2. Model simplifying process.

Y. Tu et al. / Powder Technology 281 (2015) 121–128

To ensure the fine particles could completely fill the void of coarse particles, the size ratio should not be less than 5 [34]. This size ratio is denoted as S⁎. However, for two neighboring grades, the ceiling size of the fine grade equals the floor size of the coarse grade even when the size ratio (S) is larger than 5. Besides, S should be small enough in order to decrease the size difference in one grade. Therefore, in this method, the particles in fine size grade needs be filled into much coarser grade rather than its neighboring coarse grade, meaning a certain number of grades should be skipped in order to ensure the size ratio (S⁎) is still larger than 5. This number is denoted as m. Therefore, ffiffiffiffiffi p m S ¼ S . Then the ith grade particles could be considered to fill the (i + m)th grade's void exclusively. Based on the abovementioned assumptions, the packing mode could be represented by one microcluster, and be deformed and reorganized to several sub-microclusters, as shown in Fig. 2. The size ratios of neighboring grades in the two sub-microclusters all exceed 5. Obviously the packing density is not changed during this artificially simplification process. For ease of calculations, n should be an integer multiple of m. The calculating procedure is described below: If the void of the (i + m)th grade (denoted as V ⁎i + m,%) could contain all particles in the ith grade, V iþm ≥Vt i

ð4Þ

where Vti (%) is the space volumetric fraction that the ith grade occupies n

(note that ∑ Vt i N100%). The required voidage of the (i + m)th grade i¼1

(denoted as εi + m⁎) is then given as εiþm ¼

Vt i : Vt i þ V iþm

ð5Þ

123

Table 2 Grinding methods. Samples Shanxi Coal

Inner Mongolia Coal

CS FS UFS

Ball-milled for 45 min, then sieved Ball-milled for 4 h Ball-milled for 4 h, then planetary-milled for 4 h

Ball-milled for 20 min, then sieved Ball-milled for 3 h Ball-milled for 3 h, then planetary-milled for 4 h

Then the packing density of the microcluster (denoted as E) is n X

E¼

Vi

i¼1

V

 100 ¼

100 ;% n X Vi 1−εi i¼n−mþ1

and the packing density of CWS (denoted as ECWS) is n X

ECWS ¼ σ

i¼1

V

Vi  100 ¼ σ

100 ;% n X Vi 1−ε i i¼n−mþ1

ð6Þ

and the space that the (i + m)th grade occupies is Vt iþm ¼

V iþm : 1−εiþm

ð7Þ

By using the same technique repeatedly, the (i + 2 m)th grade should contain the whole space that the (i + m)th grade occupies and is given by Eq. (7). Finally, all particles with size less than dn − m completely fill the top m grades, varying from the (n − m + 1)th to the nth grades. Therefore, the total space occupied by the microcluster (denoted as V, %) is V¼

n X

Vi : 1−ε i i¼n−mþ1

ð8Þ

Table 1 Proximate analysis of dried samples.

Shanxi Coal Inner Mongolia Coal

Ash (%)

Volatile (%)

Fixed carbon (%)

10.77 19.33

33.11 39.45

56.12 41.22

ð10Þ

where σ is the parameter representing the increase in system volume when the existence of water is considered. Obviously, σ is determined by the CWS concentration and porosity of coal particles. However, it is difficult to determine σ before the CWS is prepared and determined owing to the various types of coal, product requirements, and preparation methods. Therefore, E is more valuable and usable in practice. In this method, εi should be different for each grade. Yu et al. proposed an equation to calculate its value for 11 alumina powders with fine size

Obviously, if εi + m ≥ ε⁎i + m, the ith grade occupies the void of the (i + m)th grade without affecting its self-packing mode. However, if ε i + m b ε⁎i + m, the void of the (i + m)th grade is not sufficient to contain the whole space that the ith grade occupies, indicating that the voidage of the (i + m)th grade (denoted as εiþm) need to be increased to ε⁎i + m. Therefore,    εiþm ¼ max εiþm ; εiþm

ð9Þ

Fig. 3. PSD of grinded samples (a, Shanxi Coal; b, Inner Mongolia Coal).

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Table 3 Parameters in Eq. (3) for the PSDs of ground samples. Samples

CS FS UFS

Table 5 Narrow grades partition. Inner Mongolia Coal

Ceiling size of narrow grades (μm)

α

Shanxi Coal dx (μm)

α

dx (μm)

1.20 1.22 1.23

90.30 15.53 6.32

1.05 0.88 0.82

76.30 42.67 28.34

300 70 16 3.8 0.9

[18]; however, this method cannot be introduced directly into our model owning to the difference between the dry powders and the solid–liquid dispersion. Considering the pretreatment shown in Fig. 1 and Section 2.1, the influence of size on packing density could be ignored in CWS, and the particles in each grade could be imaginarily treated as the random contact packing of isodiametric spheres, the voidage of which is commonly 0.36–0.44 with an average of 0.4 [35]. Therefore, εi is set as 0.4 initially and fixedly if not specified. In the case of closest packing, εi + m = ε⁎i + m. Therefore, V ⁎i + m = Vti. For the packing system with the PSD governed by Eq. (1), h

i 1 1 ¼ F ðdi Þ−F S−1 di Vt i ¼ ½ F ðdi Þ−F ðdi−1 Þ 1−ε 1−ε ð Þδ ð i i Þδ "
β
β # di di 1 ¼ 100 ;% − Dmax SDmax ð1−εi Þδ

ð11Þ

and h 

i  εiþm εiþm V iþm ¼ ½ F ðdiþm Þ−F ðdiþm−1 Þ ¼ F Sm di −F S m−1 di ð 1−ε Þδ ð1−εiþm Þδ iþm 2 3 !β
m β S di S m−1 di 5 εiþm − ¼ 1004 ;% Dmax Dmax ð1−εiþm Þδ

ð12Þ where δ is the relative density of coal. The voidage of each narrow grade is assumed to be the same ε. Let Eq. (11) = Eq. (12). Therefore, Smβ ¼

1 : ε

ð13Þ

Take logarithm to the both sides of Eq. (13), then β¼−

lnε : m ln S

ð14Þ

For the packing system with the PSD governed by Eq. (2), the same result as Eq. (14) can be derived through the above method. When m = 2, the same result as Zhang's study is obtained. However, this method is not applicable to a narrow PSD because the size ratio of the largest to the smallest particle should be sufficiently large, in case of calculation failure.

250 58 14 3.1 0.7

208 49 11 2.6 0.6

174 40 9.4 2.2 0.5

145 34 7.8 1.8 0.42

121 28 6.5 1.5 0.35

4. Results and discussion 4.1. Packing evaluation To lessen the size variation of particles of the same grade, m should be set to a relatively higher value, which is 10 in this study. Table 5 shows the narrow grades of mixed samples with n = 40, m = 10, S = 61/10 ≈ 1.2, Dmin = 0 μm and Dmax = 300 μm. Table 6 shows E at different sample proportions and the PSD characteristics of mixed samples fitted by Eq. (3). Obviously, Shanxi Coal has relatively higher E but also larger fitting inaccuracy than Inner Mongolia Coal.

Table 6 Evaluation for packing of mixed samples. Coal

Shanxi Coal

Table 4 Average size at grinding time. Grinding time (min) Average size (μm)

20 81.30

45 36.80

80 23.82

120 19.14

180 14.62

84 19 4.5 1.1 0.24

mill and a planetary mill for various durations and sieved to ≤0.3 mm to obtain coarse samples (CS), fine samples (FS) and ultrafine samples (UFS) for CWS preparation. Table 2 shows the treatment methods used in the experiments. Fig. 3 shows the samples' PSDs as tested on an Omic LS-C(1) laser size analyzer. The raw data were fitted using Eq. (3). Table 3 lists the α and dx values in Eq. (3) for different ground samples. For each type of coal, the samples were mixed with different weight proportions to obtain different packing densities. Then, CWS was prepared with the mixed samples, water and a compound additive using stirrer. The main component of the additive is sodium poly [(naphthalene formaldehyde) sulfonate]. The viscosity and concentration of the prepared CWS were determined using a NXS-11(B) viscometer and a Sartorius MA35 moisture meter, respectively. For checking the acceptability of the method for dry powders, Shanxi Coal was grinded for 20, 45, 80, 120, and 180 min and sieved to ≤0.3 mm. Table 4 shows the average size determined using the Omic LS-C(1) laser size analyzer. These ground samples were collected and tapped 3000 times on a tapping apparatus to determine the tapping density.

Proportion of CS:FS:UFS

E (%)

7:1:2 7:0:3 7:2:1 6:1:3 6:3:1 7:3:0 6:4:0 4:0:6 5:0:5 0:7:3 1:7:2 5:2:3 4:5:1 7:1:2 6:4:0 8:2:0

90.95 90.68 90.16 89.28 88.58 87.18 86.24 90.30 90.07 89.54 89.39 89.35 88.69 88.12 87.20 85.67

Characteristics of PSD α

Average size (μm)

Sum of variance

0.78 0.74 0.84 0.70 0.79 0.89 0.84 0.83 0.85 0.85 0.86 0.88 0.90 0.94 0.96 1.01

60.18 59.30 61.05 52.61 54.35 61.92 55.23 48.24 52.14 41.55 45.44 54.68 54.59 61.20 61.12 66.37

91.35 145.67 54.65 119.49 56.41 37.87 50.29 12.53 13.00 8.99 8.14 11.81 9.33 14.66 11.18 13.39

3. Experimental Samples of bituminous and lignite coal that were respectively obtained from Shanxi and Inner Mongolia in China were used to prepare the CWS. Table 1 shows the samples properties. Both types of coal were first crushed to b6 mm, and then dried at a temperature of 18–25 °C and humidity of 40–60% for 2 days to remove the outer moisture. The air-dried coals were then ground on a ball

100 23 5.4 1.3 0.29

Inner Mongolia Coal

Y. Tu et al. / Powder Technology 281 (2015) 121–128

125

Fig. 6. Water classification in CWS.

the prepared CWS. All points shown in Fig. 4 were fitted using the rheological equation

νa ¼

 1 τy þ Kη q ; η

ð15Þ

where va is the apparent viscosity, mPa·s; η, the shearing rate, s−1; τy, yield stress, mPa; K and q, the model parameter. Most of the prepared CWS showed pseudoplastic or Bingham properties, except Shanxi Coal at proportions of 6:1:3 and 6:3:1 with dilatant property. The dilatant property might cause high energy consumption in high shearing use and is usually unacceptable in practice.

Fig. 4. Flow curve of prepared CWS (a, Shanxi Coal; b, Inner Mongolia Coal; the values following the legend are the proportion of mixed samples and the concentration of prepared CWS, respectively).

4.2. CWS rheology CWS is a kind of non-Newtonian fluid, the viscosity of which changes under different shearing rates [1–3,33]. Fig. 4 shows some flow curves of

Fig. 5. RC at different E.

Fig. 7. Influence of average size (a, on E; b, on RC).

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Y. Tu et al. / Powder Technology 281 (2015) 121–128

Fig. 8. Average size vs. adjusted E and tapped packing density.

4.3. Influence of E on CWS concentration According to the requirement for industrial combusting CWS, an index called “reachable concentration” (RC) is introduced to represent the concentration limits at a viscosity of 1200 mPa·s and shearing rate of 100 s−1. The RC values were obtained by the linear fitting of measured values. Fig. 5 shows that RC increases with E; the increase is ~2% for Shanxi Coal and ~3% for Inner Mongolia Coal. Fig. 6 shows that the water in CWS could be classified as water layer water, packing water, and free water when the water in the pores is ignored. Water molecules in the water layer isolate particles by electrostatic force and steric force, and they are commonly irreplaceable by other particles unless a severe collision occurs among particles. The free water ensures the flowability of the CWS. The viscosity increases significantly if the free water reduces. Packing water, behaving like “particles”, fills up the voids among hydrated particles. The CWS viscosity does not change remarkably if the particles replace the packing water [36]. Furthermore, the viscosity even decreases if fine particles supplant packing water to free water. Therefore, increasing the packing density could lead to an increase in RC. Considering Fig. 5, E could well represent the packing condition of particles in CWS. However, overpacking should be prevented to maintain sufficient space for hydration shell water and free water and ensure stability and flowability. Overpacking might occur in the Shanxi Coal samples at the proportion of 7:1:2, along with another explanation for calculation errors.

Fig. 10. Influence of α (a, α vs. E; b, α vs. RC).

Another kind of water existing in the pores of coal particles is not shown in Fig. 6 because these do not affect the packing conditions. Water in particle pores dose not directly influence the flowability of CWS. However, RC will decrease with an increase in the sample's porosity because water will fill up pores preferentially instead of dispersing particles. As lignite coal commonly has higher porosity than bituminous coal, the RC of Inner Mongolia Coal is ~ 12% lower than that of Shanxi Coal.

4.4. Influence of size on E and RC As the size effect was ignored when calculating E, the average size affects E erratically, as shown in Fig. 7(a). However, consistent influence of the size on RC is not found either when the average size is 40–70 μm,

Fig. 9. Adjusted E vs. RC.

Fig. 11. E at PSD governed by Eq. (3).

Y. Tu et al. / Powder Technology 281 (2015) 121–128 Table 7 Parameters set for Eq. (3). α

dx (μm)

0.5 2.6 0.6 5.5 0.7 10.0 0.8 15.0 Dmax = 300 μm

α

dx (μm)

α

dx (μm)

α

dx (μm)

0.9 1.0 1.1 1.2

20.0 26.0 33.0 37.0

1.3 1.4 1.5 1.6

43.0 49.0 55.0 60.0

1.7 1.8 1.9 2.0

65.0 70.0 75.0 80.0

the ground samples of Inner Mongolia Coal have less size difference, thus lowering the fitting inaccuracy for the mixed samples. As a result, the mixed samples of Inner Mongolia Coal could be well evaluated by α, as shown in Fig. 10(b). 4.6. Influence of unimodal PSD characteristics

as shown in Fig. 7(b), indicating the rationality of ignoring the size effect when calculating the packing of CWS. In contrast, the packing density of dry powders commonly decreases with the size when the particles size is less than 500 μm [37–39]. If E is used for evaluating the packing condition of dry powders, different values of εi must be set owing to the size effect. It is difficult or even unrealistic to obtain an accurate εi for coal powders for each grade through experiments or theoretical analysis owing to the inaccuracy of sieving coal with size lower than 0.3 mm, limits of current technical capabilities, and uncertainty of interaction among fine particles. Therefore, the data reported in Ref. [37–39] is used and fitted to temporarily represent the εi value of coal particles using the following equation: εi ¼ 0:7663−0:067 ln di

127

ð16Þ

where di is the average size of the ith grade. Eq. (16) is only a statistical method obtained by previous data and lacks accuracy. However, adjusted by Eq. (16), E presents some applicability for directly calculating the tapped packing density of dry powders after the adjusting, as shown in Fig. 8. In contrast, E with fixed εi could not represent the packing conditions of dry powders, causing huge errors. The same adjustment is also used to check the applicability for evaluating the packing conditions of CWS. As shown in Fig. 9, adjusted by Eq. (16), E could not represent the packing condition of particles in CWS, indicating the packing difference between the dry powders and the solid–liquid dispersion. 4.5. Influence of α on E and RC Fig. 10 shows E and RC for different α values in Table 6, indicating that the packing generally becomes the closest when α is 0.75–0.85; nonetheless, it contains several errors. These error points are attributed to Shanxi Coal samples, whose inaccuracy is larger than that of Inner Mongolia Coal, during fitting using Eq. (3), as shown in Table 6. Eq. (3) is actually formulated for unimodal PSDs. As the mixed samples of Shanxi Coal are multimodal, the errors shown in Fig. 10(a), possibly caused by the inaccuracy in fitting the PSD using Eq. (3), might hamper the packing evaluation singly by α, as shown in Fig. 10(b). In contrast,

Fig. 11 shows the ideal E of unimodal PSDs governed by Eq. (3), whose PSD characteristics are listed in Table 7 (note that dx varies to maintain F(d = Dmax) ≥ 99%), indicating that the packing is closest when α is 0.75–0.85, which is consistent with Zhang's study [2,32]. In addition, the packing density of unimodal PSD (shown in Fig. 11) is generally lower than that of multimodal PSD (shown in Fig. 10(a)). The packing condition of PSDs governed by Eq. (2) is also evaluated at dmin = 0.2 μm, dmax = 300 μm, and εi = 0.4. E is calculated when β is 0.1–1.0, as a comparison with previous studies. The result is shown in Fig. 12, indicating that the packing is closest when β is ~0.5. In fact, the β at closest packing could be calculated by Eqs. (14): when m = 10, S = 1.2 and ε = εi = 0.4, β = − ln 0.4/(10 × ln 1.2) ≈ 0.51. This value is consistent with Andreasen's study [7], but higher than Dinger and Funk's study [8]. According to Eq. (14) and Zhang's study [2,32], the difference is actually caused by the selection of self-packing voidage. When ε = 0.52, the same result is obtained as Ref. [8]. Compared with Fig. 11, Fig. 12 shows that PSD governed by Eq. (2) could have relatively higher packing density than that obtained by Eq. (3). 5. Conclusions In this study, a method for evaluating the packing density of particles in CWS was derived and discussed systematically. This method has only one unknown parameter and was proved to be well-applicable to assist CWS preparation. The reachable concentration of both types of coal tested in this study tended to increase with E. In contrast, the average sizes of mixed samples did not affect the CWS concentration and packing condition consistently owing to the difference between the dry powders and the solid–liquid dispersion. With some adjustments, this method was used to evaluate the tapped packing density for dry coal powders, and it showed some applicability. For the PSD governed by Eq. (3), E tends to increase when α is 0.75–0.85. For the PSD governed by Eq. (2), E has its highest value when β is ~0.5, and is generally higher than the PSD governed by Eq. (3). In addition, the packing density of unimodal PSD is generally lower than that of multimodal PSD. However, evaluating the packing condition singly using equation parameters might be failed owing to the inaccuracy of fitting multimodal PSD with given distribution models that were developed for unimodal distributions. This method has been successfully applied for designing CWS experiments in our lab. Owing to some limitations, the real packing of particles in CWS was simplified to a nonporous sphere packing mode. The influence of the shape, surface property, interaction, and pore structure was not discussed in this study. These will be discussed in our future study. Acknowledgments The authors gratefully acknowledge the financial support provided by the China National Nature Science Foundation (No. 51274208 and No. 51204190) and China National Project 973 (No. 2012CB214900). The advice and instructions provided by Prof. R.Z. Zhang are greatly appreciated. References

Fig. 12. E at PSD governed by Eq. (2).

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