Thin-layer drying characteristics and modeling of Ximeng lignite under microwave irradiation

Fuel Processing Technology 130 (2015) 62–70

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Thin-layer drying characteristics and modeling of Ximeng lignite under microwave irradiation Jie-Feng Zhu, Jian-Zhong Liu ⁎, Jun-Hong Wu, Jun Cheng, Jun-Hu Zhou, Ke-Fa Cen State Key Lab of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China

a r t i c l e

i n f o

Article history: Received 5 May 2014 Received in revised form 25 September 2014 Accepted 25 September 2014 Available online xxxx Keywords: Lignite Microwave drying Drying kinetic Thin-layer drying Moisture reabsorption

a b s t r a c t The thin-layer drying characteristics of Ximeng lignite (XL) were investigated under microwave irradiation, and mathematical modeling using thin-layer drying models from literature was performed. The effects of coal particle size and microwave power level on drying characteristics were studied. The drying rate increased and drying time decreased with increasing particle size or microwave power level. The drying rate and drying rate to moisture ratio curves, which contained a constant rate period at lower microwave output powers, exhibited fast heating and falling rate periods at different coal-particle sizes and microwave output power levels. Among the 14 thin-layer drying models proposed, the Midilli–Kucuk model provided a better fit for all applied drying conditions and could be used to estimate moisture in XL at any time during the microwave-drying process after running a multiple regression analysis. The drying rate constants and apparent diffusion coefficients (determined from the Midilli–Kucuk model and Fick's second law, respectively) increased with increasing particle size or microwave power level. The activation energy estimated from a modified Arrhenius equation was Ea = 77.0485 W/g. The equilibrium moisture of XL decreased with increasing microwave output power or decreasing particle size. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Presently, global energy consumption heavily relies on fossil fuel, which accounts for 87% of energy consumption. Oil dominates the fossil fuels; however, coal is the fastest-growing fossil fuel. In 2012, coal accounted for 29.9% of global energy consumption and China accounted for 50.2% of global coal consumption [1]. Because of increasing coal consumption, high-rank coal, such as anthracite and bituminous, is in short supply. Therefore, there is increased interest in utilizing low-rank coal, such as lignite. China has abundant lignite resources, with about 129 billion tons of proven lignite reserves, which account for about 12.69% of total coal reserves [2]. Because of lignite's high moisture and low fixed carbon content, its calorific value is low. Lignite weathers easily and suffers from spontaneous combustion owing to its high volatile content; hence, it is not suitable for long-distance transport and storage [3]. Most lignite is used as fuel in nearby power plants or as raw material in the chemical industry. The use of lignite in practical applications has several disadvantages, including low energy efficiency, environmental pollution, and high costs. In order to utilize lignite resources cleanly, efficiently, and at a reduced cost, it is important to dehydrate and modify lignite prior to its deep processing and further utilization [4,5]. Although many kinds ⁎ Corresponding author. Tel.: +86 571 87952443 5302; fax: +86 571 87952884. E-mail address: [email protected] (J.-Z. Liu).

http://dx.doi.org/10.1016/j.fuproc.2014.09.033 0378-3820/© 2014 Elsevier B.V. All rights reserved.

of drying methods have been developed because of lignite's high moisture, successful reduction of energy consumption and drying costs, among other goals, remains to be achieved. The dehydration process of lignite can be classified into two categories: evaporation drying and non-evaporation drying [6]. During evaporation drying, heat equal to the latent heat of water evaporation is added to the coal sample either directly or indirectly; moisture within the coal is then gasified and removed. Evaporation drying methods include the coal mill dryer [7,8], flue gas drum dryer or fluid bed dryer [9], steam-fluidized bed dryer [10], microwave drying [11,12], solar drying [13], and so forth. During non-evaporation drying, moisture is removed from the coal sample in liquid form. Therefore, the latent heat of water evaporation is saved and the emission of greenhouse gases is reduced; however, non-evaporation drying is usually done using high temperatures and high pressure. Methods of non-evaporation drying include mechanical thermal expression [14,15] and hydrothermal dewatering [16,17]. During the microwave-drying process, the polar molecules of the coal sample under microwave irradiation cause dipoles or ions to align within the applied high-frequency alternating electric field. As the applied alternating electric field oscillates, the aligned dipoles or ions attempt to realign themselves. This causes energy loss in the form of heat through molecular friction or dielectric loss, which raises the temperature of the coal sample and dries the material [18]. Because of microwave heating’s unique features (such as selective heating, volumetric heating, and instantaneous heating), it offers a

J.-F. Zhu et al. / Fuel Processing Technology 130 (2015) 62–70

number of advantages compared with conventional heating: (i) rapid heating; (ii) energy transfer instead of heat transfer; (iii) uniform heating; (iv) enhanced moisture loss; (v) quick starting and stopping; (vi) greater safety and automation; and (vii) superior dried-product quality [19]. Due to these unique features, microwaves have been widely used to heat or dry materials in various technological and scientific fields, such as the food industry, light industry, chemical industry, and agricultural industry[20,21]. Furthermore, microwaves have been used in mineral processing to improve grindability, to decompose or dehydrate minerals, and so on [22,23]. These unique features also make microwave heating an effective method of dehydrating and modifying lignite. Investigating the use of microwaves in Inner Mongolia lignite dehydration is important because proven lignite reserves in Inner Mongolia account for 77.55% of the total lignite reserves in China; thus, an investigation of Inner Mongolia lignite dehydration will allow for better utilization of China's lignite resources. In order to systematically investigate the microwave-drying characteristics of Ximeng lignite (XL) and to analyze moisture migration during the drying process, this paper investigates the thin-layer drying and reabsorption characteristics of XL at different coal particle sizes and microwave power levels. The goal is to provide references for processing and utilizing XL. 2. Experimental 2.1. Material This study used lignite from the Ximeng region in Inner Mongolia, which is the largest producer of lignite in China. Naturally dried XL was ground in a bowl mill and sieved to four different coal particlesize fractions (less than 154, 154 to 600, 600 to 1000, and 1000 to 1700 μm). The sieved coal powder was sealed and stored. To determine the initial moisture of coal samples at different particle sizes, three 2 g XL at each particle size were dried in an oven at 105 °C for 2 h. Results from each of the three samples were averaged together to reach the data shown in Fig. 1. Proximate and ultimate analyses of the raw coal sample (less than 154 μm) can be found in Table 1. The ash content and composition of coal sample with different particle sizes are shown in Table 2. 2.2. Methods 2.2.1. Microwave-drying experiments Microwave-drying experiments were performed in an atmosphericpressure microwave reaction workstation (MAS-II; Sineo Microwave Chemistry Technology Ltd., Shanghai, China) with a microwave frequency of 2450 MHz (a wavelength of 12.24 cm). The microwave workstation is capable of operating at eight different microwave output

63

Table 1 Proximate and ultimate analyses of XL. Qnet,ad

Ultimate analysis (%)

Mad

Aad

Vad

FCad

(J/g)

Cad

Had

Nad

St,ad

Oad

32.39

15.84

24.75

27.02

17355

41.52

2.99

0.62

0.6

6.04

Proximate analysis (%)

Mad, Aad, Vad and FCad refer to the moisture, ash, volatile and fixed carbon content on an air dried basis, respectively; Qnet,ad refers to the net calorific value on an air dried basis.

power levels: 300, 400, 500, 600, 700, 800, 900, and 1000 W. The workstation is equipped with a non-contact infrared thermometer and, using frequency conversion, the power level is automatically adjusted for temperature. The processing time is adjusted and displayed with the aid of a digital-control facility located on the microwave workstation. During microwave-drying experiments, each sample was put in a glass Petri dish (diameter of 71 mm, height of 15 mm) and placed in the center of the workstation. Moisture loss was measured in 1-min intervals by taking out the glass Petri dish from the workstation and weighing it on a digital balance (Sartorius BS 224S, with a precision of 0.1 mg). The total microwave applied time was 10 min. To obtain the temperature history of the drying process, sample temperatures were measured with a hand-held infrared thermometer (GM700, Benetech, Shenzhen, China, with a precision of ± 1.5% °C within the range of b700 °C) between the time the microwave was shut down and the time the sample was removed to be weighed. Each experiment was replicated at least three times and average measurement values were used for statistical analyses. The reproducibility of the drying experiments and temperature-measurement experiments were within the range of ±3.25% and ±13.02%, respectively. All weighing processes (including temperature measurement) were completed in less than 12 s during the drying process. To investigate the effect of coal particle size on the drying characteristics of XL, four different coal particle-size fractions (i.e., less than 154, 154 to 600, 600 to 1000, and 1000 to 1700 μm) were periodically irradiated at a constant microwave power level of 500 W using 5 g XL. In order to investigate the effect of microwave output power on the drying characteristics of XL, three different power levels, namely, 300, 500, and 700 W, were used for drying 5 g XL with particle sizes of 154 to 600 μm. 2.2.2. Moisture reabsorption of dried coal sample The effects of coal particle size and microwave power level on the moisture reabsorption performance of coal sample were investigated. A 2 g processed XL was placed into an atmosphere with constant temperature and humidity (temperature of 30 °C, relative humidity of 70%), and the moisture reabsorption of coal sample was studied. The samples" mass changes were recorded for 130 h.

Initial moisture (wt%, ad)

2.3. Mathematical modeling In order to determine the moisture ratio as a function of drying time, the moisture data obtained from the drying experiments were curve fitted to find the most suitable model among 14 different expressions proposed by earlier authors (Table 3).

40

30

20 Table 2 The ash content and composition of coal sample with different particle sizes.

10

0 < 154

154-600

600-1000

1000-1700

Particle size (µm) Fig. 1. Initial moisture of coal samples with different particle sizes.

Particle-size fraction (μm)

Aad (%)

Ash composition (%) SiO2

Al2O3

Fe2O3

CaO

MgO

K2O

Na2O

b154 154–600 600–1000 1000–1700

15.84 12.72 9.23 8.55

62.08 54.63 46.65 45.35

13.67 14.09 14.86 15.48

5.09 6.52 6.26 4.80

3.09 5.42 6.96 9.03

7.19 6.85 7.64 6.40

0.92 1.05 1.12 1.26

1.49 2.33 3.01 3.12

64

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Table 3 Mathematical thin-layer drying models used. Model

MR

Ref.

Newton Henderson and Pabis Logarithmic Wang and Singh Diffusion approach Verma Midilli–Kucuk Page Modified page Two-term Two-term exponential Modified Henderson and Pabis Simplified Fick's diffusion Modified page equation-II

exp(−kt) a exp(−kt) a exp(−kt) + c 1 + at + bt2 a exp(−kt) + (1 − a) exp(−kbt) a exp(−kt) + (1 − a) exp(−gt) a exp(−ktn) + bt exp(−ktn) exp(−(kt)n) a exp(−k0t) + b exp(−k1t) a exp(−kt) + (1 − a) exp(−kat) a exp(−kt) + b exp(−gt) + c exp(−ht) a exp(−c(t / L2)) a exp(−k(t / L2)n)

[27–29] [30,31] [32] [33] [34] [35] [36] [37,38] [39,40] [41,42] [43] [44] [45] [45]

In all experiments, the moisture value (M), drying rate (DR), and moisture ratio (MR) of coal samples were calculated using the following equations: M¼

W t −W d:s W d:s

ð1Þ

DR ¼

M t −Mtþdt dt

ð2Þ

MR ¼

Mt −M e M 0 −M e

ð3Þ

where M is the moisture (g/(g db)), Wt is XL"s mass at t (g), t is the drying time (min), Wd.s is the dry coal mass (g), DR is the drying rate (g/(g db min)), Mt and Mt + dt are the moisture at t and t + dt (g/(g db)), respectively, MR is the moisture ratio, M0 is the initial moisture (g/(g db)), and Me is the equilibrium moisture (g/(g db)), which was assumed to be zero for microwave drying [24–26]. Therefore, the moisture ratio can be expressed as MR = Mt/M0. 3. Results and discussion 3.1. Effect of coal particle size As shown in Fig. 2a, because the initial moisture was different for different-sized coal particles and increased with increasing particle size (see Fig. 1), XL"s residual mass decreased with increasing particle size. Fig. 2b and d shows that, within 5 min, moisture was quickly removed from all particle-size fractions and that the moisture that was removed within 3 min accounted for 80.82%, 82.84%, 82.79%, and 86.49% of the total removed moisture for particle-size fractions of less than 154, 154 to 600, 600 to 1000, and 1000 to 1700 μm, respectively, which shows that microwave drying is fast and saves time over conventional methods. The moisture of various particle-size fractions tend to be the same after 5 min and is close to zero at the end of the drying process. This is connected with the temperature variations that occur within coal samples of different particle sizes during the microwave-drying process. As Fig. 3 shows, XL's temperatures changed similarly after 5 min and there was little difference in the final temperatures recorded (which were between 150 and 170 °C). In fact, because the dielectric coefficient of water is much larger than that of dry coal and therefore water can absorb much more microwave energy [46], the dominant parameter that effected XL's temperature was the moisture. At the initial stage of the drying process (before 5 min), the moisture increased with increasing coal particle size, and therefore XL's temperature also increased with

increasing coal particle size. However, as most of the water in the coal sample was removed at the final stage of the drying process, XL's temperature depended on the ash content that had higher dielectric coefficient compared to organic materials in coal. According to Table 2, the dominant ash composition of coal sample with different particle sizes was SiO2. Because SiO2 has low dielectric constant, it did little effect on the temperature variation of coal samples during microwave drying process. With decreasing coal particle size, the content of metal oxide (including Al2O3, Fe2O3, MgO, K2O and Na2O) that has relative high dielectric constant indistinctively changed and the ash content of coal sample significantly increased, therefore the final temperature of coal samples increased with decreasing coal particle size. Drying rates increased and drying times decreased as the coal particle size increased (see Fig. 2a, b, and c). This is completely different from conventional drying methods, where the drying rate increases with decreasing coal particle size [47], because the drying mechanism that happened in each method is different. In conventional drying methods, heat carried by the drying medium is transferred progressively from the particle surface to the inner particle. Therefore, the smaller the particle size, the larger the specific external surface area; this enables the coal particle to have more contact with the drying medium, thus making the heating process easier. As the coal particle size decreases, the diffusion path (by which the particle's internal moisture diffuses from the inner particle to the particle's surface) is shortened, thus decreasing diffusion resistance [47]. Hence, in conventional drying methods, the drying rate increases with decreasing particle size. However, microwave drying has unique features (i.e., selective, volumetric, and instantaneous heating) that make it different from conventional drying methods. When polar molecules (especially water) contained within the coal are irradiated under a high-frequency alternating electric field, heat is generated through molecular friction and dielectric loss. During the microwave-drying process, the microwave output power could not be absolutely absorbed by XL placed in the workstation and the amount of absorbed microwave power was dependent on the dielectric property of XL. As the dielectric coefficient of water is much larger than that of dry coal [46], the content and existing state of water contained within the coal were the most important parameters affecting the dielectric property of coal. In general, the dielectric coefficient of coal sample increases with increasing moisture, which is good for absorbing microwave power. As mentioned above, initial moisture increased with increasing particle size; therefore, coal samples with a larger particle size could absorb more microwave power. Furthermore, power absorption per unit surface area for microwave drying decreased with increasing surface area (i.e., decreased particle size), and the focusing effect that happened in larger particle sizes made the heating rate inside those particles faster than that near the particles' surface [48]. Thus, the internal moisture of large coal particles evaporated faster and generated higher-pressure jet flows (leading to faster internal moisture transport and enhanced moisture loss) than did the internal moisture of small coal particles [12]. All curves shown in Fig. 2c and d exhibited two drying periods: a fast heating period (0–1 min) and a falling rate period (1–10 min) in which internal moisture diffusion is controlled throughout the particle. For each particle size (less than 154, 154 to 600, 600 to 1000, and 1000 to 1700 μm), the largest drying rates appeared at 1 min and were 11.96, 16.10, 18.26, and 19.93 g/(g db min), respectively. Neither the drying rate vs. the drying time nor the drying rate vs. the moisture ratio curves exhibited a constant rate period, which is consistent with the results of high ash content coal presented in a previous study conducted by Tahmasebi and colleagues [12]. According to Fig. 3, the temperatures of various-sized coal samples reached or exceeded 90 °C after 1 min of microwave irradiation (corresponding to the fast heating period) and then kept rising (corresponding to the falling rate period). A period of constant

J.-F. Zhu et al. / Fuel Processing Technology 130 (2015) 62–70

<154 154-600 600-1000 1000-1700

4.8

Weight (g)

4.6 4.4 4.2 4.0 3.8

(b)45 35 30 25 20 15 10 5

3.6 3.4

0 0

1

2

3

4

5

6

7

8

9

0

10

Time (min)

18 16 14 12 10 8 6 4 2 0 1

2

3

4

5

2

3

4

5

6

6

7

8

9

10

Time (min)

(d) 20 Drying rate (g/g db min )

<154 154-600 600-1000 1000-1700

0

1

7

8

9

10

Time (min)

(c) 20 Drying rate (g/g db min )

<154 154-600 600-1000 1000-1700

40

Moisture (%)

(a) 5.0

65

-154 154-600 600-1000 1000-1700

18 16 14 12 10 8 6 4 2 0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Moisture ratio

Fig. 2. Drying curves of XL at various particle sizes. (a) Weight loss vs. time; (b) moisture vs. time; (c) drying rate vs. time; and (d) drying rate vs. moisture ratio.

temperature could not be found because the energy offered by any given microwave output power was much larger than that needed to evaporate the moisture within XL. As a result, moisture could rapidly be heated to near boiling and thus quickly removed from XL. However, the heating rate during the falling rate period was clearly smaller than that during the fast heating period. Since a large amount of water (mostly surface water) was already removed from XL during the fast heating period (see Fig. 2d), the vapor pressure and pressuredriven jet flow generated during the falling rate period were smaller than those generated during the fast heating period. Meanwhile, the capillary adsorption force and flow resistance, which should be overcome when inherent moisture is removed, were larger during the falling rate period than at the fast heating period. Therefore, the drying rate curves in this paper don't exhibit a constant rate period. 3.2. Effect of microwave power level Fig. 4a and b shows that drying time was reduced and the moisture of dry coal was smaller with increasing microwave power levels.

165

Temperature (oC)

150 135 120

<154

105

154-600

90

600-1000

75

1000-1700

60 45 30 0

1

2

3

4

5

6

7

8

9

10

Time (min) Fig. 3. Temperature variations of different particle-size fractions during microwave drying.

The moisture of dry coal samples irradiated at 300, 500, and 700 W for 10 min decreased to 1.36%, 0.46%, and − 0.18%, respectively. This drop in moisture is connected with the temperature variations of coal samples at different microwave power levels during the microwave-drying process. According to Fig. 5, the heating rate and final temperature of XL increased with increasing microwave power level. When XL was irradiated at 700 W for 10 min, the final temperature of XL could reach 206.8 °C. Depending on the microwave power level used, not only could the moisture within XL be completely removed, but also the organic matrix (such as oxygen-containing functional groups and methylene) within the coal could begin to thermally decompose [49], decreasing XL's mass. The moisture of all samples shown in Fig. 4b, c, and d was quickly removed within 5 min and the removed moisture within 3 min accounted for 73.19%, 82.84%, and 86.10% of the total removed moisture of coal samples irradiated at 300, 500, and 700 W, respectively. The microwave power level had important effects on the diffusion rate of internal moisture within XL, and the maximum drying rate of all samples increased with increasing power level. When XL was irradiated at 300 W, the escaping velocity of the moisture within XL was relatively slow because the given energy was relatively less. As a result, the drying curves exhibited three drying periods: a fast heating period (0–1 min) followed by a constant rate period (1–2 min) and a falling rate period (2–10 min), which was consistent with XL's temperature variation trends. As the moisture removed during the fast heating period was reduced, the maximum drying rate appeared at 2 min (the constant rate period) and was 12.32 g/(g db min). Meanwhile, the drying rate during the falling rate period decreased slower and was higher than that at high microwave power levels. The drying curves of coal samples irradiated at 500 and 700 W exhibited a fast heating period (0–1 min) and a falling rate period (1–10 min), which is the dominant drying-process period; maximum drying rates appeared at 1 min and were 16.10 and 18.84 g/ (g db min), respectively.

66

J.-F. Zhu et al. / Fuel Processing Technology 130 (2015) 62–70

(a) 5.0

300 W 500 W 700 W

4.8

4.4 4.2 4.0

30

3.8

25 20 15 10 5

3.6

0 0

1

2

3

4

5

6

Time (min)

7

8

9

0

10

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

Time (min)

7

8

9

10

Drying rate (g/g db min )

300 W 500 W 700 W

18 16 14 12 10 8 6 4 2 0

10

Time (min)

(d) 20

(c) 20 Drying rate (g/g db min )

300 W 500 W 700 W

35

Moisture (%)

Weight (g)

4.6

(b) 40

300 W 500 W 700 W

18 16 14 12 10 8 6 4 2 0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Moisture ratio

Fig. 4. Drying curves of XL at various microwave power levels. (a) Weight loss vs. time; (b) moisture vs. time; (c) drying rate vs. time; and (d) drying rate vs. moisture ratio.

were eventually included in the final model. The acceptable model, with its constants and coefficients, follows:

To describe the microwave-drying kinetics of XL, the drying data gathered with different coal particle sizes and microwave power levels are demonstrated as moisture ratio (MR) vs. drying time curves, shown in Figs. 6 and 7, respectively. These were fitted with each of the 14 thinlayer drying models listed in Table 3. Among these models, the Midilli– Kucuk model was found to be the most suitable for all experimental data and provided higher values for the coefficient of determination (R2) and F-value while reducing the chi-square (χ2) and root mean square error (RMSE) compared with statistical values obtained for the other models. The estimated parameters and statistical analysis of this model for all drying conditions applied in this paper are shown in Table 4. To account for the drying variables' effect on the Midilli–Kucuk model's drying constant k (min−1) and dimensionless coefficients a, b, and n, the values of these parameters were regressed against those of the microwave power level (P, W) and coal particle size (D, mm) by multiple regression analysis. Multiple combinations of these parameters


n MR ¼ a exp −kt þ bt

ð4Þ

where:   −5 P þ 0:00124D a ¼ 1:01071− 2:2434  10   −8 2 2 2 þ 1:1184  10 P −0:00178D R ¼ 0:84461   −7 2 P k ¼ −0:18038 þ 0:00183P þ 0:14023D− 9:76441  10 2

2

−0:04135D R ¼ 0:99652 −5

b ¼ 0:00888−1:02573  10 2

  −9 2 P P−0:0043D− 2:99271  10

2

þ0:00271D R ¼ 0:99676

200

1.0

180

0.9

160

0.8

600-1000, Experimental

0.7

1000-1700, Experimental

Moisture ratio

Temperature (oC)

3.3. Modeling of drying curves

140 120 100

300 W

80

500 W 700 W

60

<154, Experimental 154-600, Experimental

<154, Fitted

0.6

154-600, Fitted

0.5

600-1000, Fitted

0.4

1000-1700, Fitted

0.3 0.2

40

0.1 0.0

20 0

1

2

3

4

5

6

7

8

9

10

Time (min) Fig. 5. Temperature variations of different microwave power levels during microwave drying.

0

1

2

3

4

5

6

7

8

9

10

Time (min) Fig. 6. Variations of experimental and predicted moisture ratios using the Midilli–Kucuk drying model with different particle sizes.

J.-F. Zhu et al. / Fuel Processing Technology 130 (2015) 62–70

1.0

300 W, Experimental

0.9

500 W, Experimental

0.9

0.8

700 W, Experimental

0.8

0.7

300 W, Fitted

0.6

500 W, Fitted

MR (experimental)

Moisture ratio

1.0

700 W, Fitted

0.5 0.4 0.3 0.2 0.1 0.0 0

1

2

3

4

5

6

7

8

9

67

0.7 0.6

300 W

0.5

500 W 700 W

0.4

<154

0.3

154-600

0.2

600-1000

0.1

1000-1700

0.0 0.0

10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

MR (predicted)

Time (min) Fig. 7. Variations of experimental and predicted moisture ratios using the Midilli–Kucuk drying model with different power levels.

Fig. 8. Predicted MR by Midilli–Kucuk model vs. experimental MR at different particle sizes and microwave power levels.

  −6 2 n ¼ 2:22117−0:00373P−0:19186D þ 3:03177  10 P

Eq. (5) could be further simplified to a straight-line equation, such as Eq. (6)[54–56]:

2

2

þ0:10714D R ¼ 0:99948:

!  π 2  Deff 8 − t π2 4R2

 ln ðMRÞ ¼ ln

These expressions can be used to estimate the moisture in XL at any time during the microwave-drying process. In order to validate the established model, the experimental moisture ratio values at different particle sizes and microwave power levels were compared with the predicted values; results are illustrated in Fig. 8. The values distributed around the 45° oblique line, indicating that the Midilli–Kucuk model was suitable for describing the microwave-drying kinetics of XL. 3.4. Estimation of apparent diffusion coefficient and activation energy During the drying process, the moisture within the materials was transferred from the internal structure to the external environment using diffusion, which was controlled by on-way resistance; therefore, the apparent diffusion coefficient could be calculated with Fick's second law [50]. As the diffusion coefficient indicated the mass transport rate during the drying process [51], it could be used to describe how well moisture was removed per unit of time under specific conditions. To calculate the apparent diffusion coefficient of coal particles, some assumptions were made, including: (i) coal particles are spherical; (ii) moisture is initially uniformly distributed within the coal particles; (iii) mass transfer is symmetric to the center; (iv) mass transfer is controlled by a diffusion mechanism; (v) moisture diffusion during the drying process is one-dimensional and isothermal; (vi) resistance to mass transfer at the surface is negligible compared with the sample's internal resistance; and (vii) the diffusion coefficient is constant and shrinkage of the coal particles is negligible [52]. These assumptions led to an analytically derived equation [52,53]: t¼

4R2 ln π2 Deff



 8 : π2 MR

ð5Þ

ð6Þ

where t is the drying time (min), R is the radius of the coal particle (m), and Deff is the effective diffusion coefficient (m2/s). Then the apparent diffusion coefficient Deff could be calculated by plotting experimental drying data in terms of ln (MR) versus drying time. According to Figs. 9 and 10, the apparent diffusion coefficient and drying rate constants increased with increasing particle size or microwave power levels. The increasing extent of the apparent diffusion coefficient at different particle sizes was almost 1000 times—surely very significant—increasing from 8.4478 × 10−11 m2/s at less than 154 μm to 7.9329 × 10−8 m2/s at 1000–1700 μm. The diffusion coefficient increased in this way because the energy absorbed by moisture within the coal particles increased with increased coal particle size or microwave power level, which caused XL's drying rate to increase. A multiple regression analysis was undertaken to develop a combined mass transfer model for relating the apparent diffusion coefficients in the coal sample to the coal mean particle size (D, mm) and microwave power level (P, W). To account for the effect of drying variables on the apparent diffusion coefficient, the results from that analysis are given by the following equation with R2 = 0.99816, RMSE = 2.97582 × 10−9, RSS = 8.85553 × 10−18, and χ2 = 8.85553 × 10−18: −8

Deff ¼ −1:41068  10 −8

 10

−11

þ 3:86491  10

D−2:925  10

−14 2

P þ 1:91926 −8

P þ 3:06778  10

2

D :

ð7Þ

This equation can be used to estimate the apparent diffusion coefficient of moisture at any microwave power level and coal mean particle size during the process of microwave drying XL. Because the microwave-drying process is not an isothermal process, a modified Arrhenius equation was used in this study to explain the

Table 4 Results of statistical analysis of Midilli–Kucuk model. Experimental parameter

5 g/500 W

5 g/154–600 μm

Estimated parameter

b154 μm 154–600 μm 600–1000 μm 1000–1700 μm 300 W 500 W 700 W

a

k

b

n

1.0030 1.0013 1.0029 1.0005 1.0052 1.0013 1.0007

0.4927 0.5425 0.5710 0.6089 0.3198 0.5425 0.6631

0.0029 0.0018 0.0014 0.0021 0.0045 0.0018 −0.0008

1.1040 1.0722 1.0273 1.0520 1.3284 1.0722 1.0498

R2, RMSE and χ2 are the coefficient of determination, root mean square error and the chi-square, respectively.

R2

RMSE

χ2

F-value

0.9989 0.9996 0.9982 0.9994 0.9990 0.9996 0.9992

0.0127 0.0076 0.0157 0.0095 0.0127 0.0076 0.0107

0.0002 0.0001 0.0002 0.0001 0.0002 0.0001 0.0001

2458.57 6421.59 1492.64 3960.80 2920.54 6421.59 2971.88

68

J.-F. Zhu et al. / Fuel Processing Technology 130 (2015) 62–70

80

-0.4

0.60

70

-0.5

60

-0.6

50

-0.7

0.56

40

0.54

30

ln (k)

k (min-1)

0.58

Deff×10-9(m2/s)

0.62

-0.8 -0.9

ln(k)=0.14751-77.04846×(m/P) R2=0.99927

-1.0

20 0.52

-1.1

10

-1.2

0.50

0

0.00

0.25

0.50

0.75

1.00

0.008

0.010

0.012

0.014

0.016

m/P (g/W)

1.25

Mean particle size (mm) Fig. 11. Fitting figure of ln (k) ~ m/P at different microwave power levels. Fig. 9. Changes in drying rate constants and apparent diffusion coefficients of XL at different particle sizes.

relationship between the drying rate constant and the ratio of the microwave power level to XL's mass in order to calculate activation energy [52,57]:   −Ea  m P

ð8Þ

where k is the drying rate constant obtained from the Midilli–Kucuk model (min−1), k0 is the pre-exponential constant (min−1), Ea is the activation energy (W/g), P is the microwave power (W), and m is XL's mass (g). The values of ln (k) vs. m/P of the coal sample for particlesize fractions of 154 to 600 μm, shown in Fig. 11, were accurately fitted to Eq. (8) with R2 = 0.99927 and χ2 = 2.0578 × 10−4. Then k0 and Ea values were estimated as 1.1589 min−1 and 77.0485 W/g. 3.5. Moisture reabsorption of dried coal sample According to Figs. 12 and 13, the moisture rapidly increased within the initial 10 h and reached to a certain equilibrium level thereafter. The coal's equilibrium moisture (EM) decreased with increasing microwave power level and with decreasing particle size, which meant that increasing microwave power level and smaller particle size could restrain the moisture reabsorption performance of the dried coal sample. Dewatered coal sample's moisture reabsorption characteristics are affected by many factors such as coal particle size, pore structure, test temperature, oxygen and moisture in both the coal and ambient atmosphere, and so forth [58,59]. Meso- and macropores are the dominant porous structures of low-rank coal, the surface area of which is mainly 0.70

7.0

0.65

6.5

0.60

5.5

0.50 5.0 0.45 4.5

0.40

Deff×10-9(m2/s)

18

0.55

k (min-1)

20

6.0

4.0

0.35

16

Moisture (%)

k ¼ k0 exp

controlled by mesopores [60]. When the coal sample was dried at lower temperatures, the macropores collapsed because of shrinkage forces caused by the removal of moisture adsorbed on the coal surface. As a result, both the number of mesopores and the surface area increased [11,49]. However, when XL was dried at high temperatures, stronger shrinkage forces made the mesopores collapse and the crosslinking reactions that occurred in the coal matrix may have blocked mesopores, resulting in a decreased surface area [61]. When XL was dried at different microwave power levels, the main factors affecting its moisture reabsorption characteristics were changes in the coal's pore structure and hydrophilicity due to oxygen-containing functional groups on the coal particle's surface [61]. Increasing microwave power levels, combined with the temperature variations associated with different microwave power levels (Fig. 5), observably increase the heating rate and raise the final temperature of XL. As a result, oxygen-containing functional groups decomposed under microwave irradiation and the amount of oxygen-containing functional groups decreased with increasing microwave power level [62,63]. Because of the removal of oxygen-containing functional groups, the coal sample's hydrophobicity and loss of the colloid structure increased, which decreased its moisture-holding capacity. The volumetric heating and focusing effect within large-sized coal particles, combined with the temperature variations of coal samples of different particle sizes (Fig. 3), increase the heating and drying rates during the initial period. Therefore, a coal sample with a large particle size experienced more significant pore-structure collapse and macropore disintegration (caused by shrinkage forces resulting from the removal of moisture adsorbed on the surface) than did samples with smaller particle sizes. The number of micro- and mesopores in samples with large particle sizes also increased, due to the removal of moisture from the micropore and small capillaries, resulting in increased surface areas [11,61]. As a result, the coal's EM increased with increasing particle size.

14 12

<154

10

154-600

3.5

4

0.25

3.0

2

400

500

600

700

Microwave power (W)

1000-1700

6

0.30 300

600-1000

8

0 0

15

30

45

60

75

90

105

120

Time (h) Fig. 10. Changes in drying rate constants and apparent diffusion coefficients of XL at different microwave power levels.

Fig. 12. Trend of coal samples at different particle sizes.

J.-F. Zhu et al. / Fuel Processing Technology 130 (2015) 62–70

20 18

Moisture (%)

16 14 12

300 W

10

500 W

8

700 W

6 4 2 0 0

15

30

45

60

75

90

105

120

Time (h) Fig. 13. Trend of coal samples at different microwave power levels.

Considering the results of these moisture reabsorption experiments, further study will focus on the effects on the slurrying ability, rheological behavior, and stability of coal water slurry (CWS) prepared by XL at less than 154 μm under microwave irradiation and changes in the physical and chemical structures will also be investigated. 4. Conclusions Within 3 min, the overwhelming majority of moisture in XL was quickly removed for all applied drying conditions, which shows that microwave drying is fast and saves time over conventional methods. The drying curves of coal samples, which contained a constant rate period at lower microwave output powers, exhibited fast heating and falling rate periods at different coal-particle sizes and microwave output power levels. Among the 14 thin-layer drying models proposed, the Midilli–Kucuk model provided a better fit for all applied drying conditions after running a multiple regression analysis. The drying rates, drying rate constants and apparent diffusion coefficients increased with increasing particle size or microwave power level. To estimate the activation energy of the coal sample for particle-size fractions of 154 to 600 μm, a modified Arrhenius equation was used and the result was Ea = 77.0485 W/g. The equilibrium moisture of XL decreased with increasing microwave output power or decreasing particle size. Considering the results of these moisture reabsorption experiments, further study will focus on the effects on the slurrying ability, rheological behavior, and stability of CWS prepared by XL at less than 154 μm under microwave irradiation and changes in the physical and chemical structures will also be investigated. Acknowledgment The authors wish to acknowledge the financial support provided by the National Basic Research Program of China (Grant No. 2010CB227001). References [1] BP, BP Statistical Review of World Energy, BP, 2013. [2] X.H. Fu, L. Lu, Y.Y. Ge, J.J. Tian, P.P. Luo, China lignite resources and physical features (in Chin.), Coal Science and Technology 40 (2012) 104–108. [3] D.F. Umar, B. Daulay, H. Usui, T. Deguchi, S. Sugita, Characterization of upgraded brown coal (UBC), Coal Preparation 25 (2005) 31–45. [4] M. Agraniotis, S. Karellas, I. Violidakis, A. Doukelis, P. Grammelis, E. Kakaras, Investigation of pre-drying lignite in an existing Greek power plant, Thermal Science 16 (2012) 283–296. [5] K. Atsonios, I. Violidakis, M. Agraniotis, M. Agraniotis, P. Grammelis, N. Nikolopoulos, E. Kakaras, Thermodynamic analysis and comparison of retrofitting pre-drying concepts at existing lignite power plants, Applied Thermal Engineering (2013) 1–9. [6] C.Z. Li, Advances in the Science of Victorian Brown Coal, Elsevier, 2004. [7] M.J. McIntosh, Mathematical model of drying in a brown coal mill system. 1. Formulation of model, Fuel 55 (1976) 47–52.

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