Thin-layer drying kinetics of lignite during hot air forced convection

Accepted Manuscript Title: Thin-layer drying kinetics of lignite during hot air forced convection Author: B.A. Fu M.Q. Chen PII: DOI: Reference:

S0263-8762(15)00275-0 http://dx.doi.org/doi:10.1016/j.cherd.2015.07.019 CHERD 1969

To appear in: Received date: Revised date: Accepted date:

30-1-2015 18-6-2015 19-7-2015

Please cite this article as: Fu, B.A., Chen, M.Q.,Thin-layer drying kinetics of lignite during hot air forced convection, Chemical Engineering Research and Design (2015), http://dx.doi.org/10.1016/j.cherd.2015.07.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights

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Modified Page model showed the perfect prediction for lignite thin layer drying.

3

Effects of hot air temperature and speed on thin layer drying kinetics of lignite.

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Thin layer drying of lignite had two obvious falling rate periods.

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Hot air temperature and speed had great effect on effective moisture diffusivity.

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Activation energy of lignite thin layer in two falling rate periods was determined.

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*

Corresponding author. Tel.:+86 10 51683423 E-mail address: [email protected] (M.Q. Chen). 1

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Thin-layer drying kinetics of lignite during hot air forced convection

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B.A. Fua,b, M.Q. Chena,b*,

9

a

Institute of Thermal Engineering, School of Mechanical, Electronic and Control

Engineering, Beijing Jiaotong University, Beijing 100044, China

11

b

12

Small Scale, Beijing 100044, China

13

Abstract: Kinetics on the lignite thin-layer during hot air forced convective drying

14

was investigated experimentally as a function of drying conditions (hot air

15

temperature and speed). The experiments were conducted at hot air temperatures of

16

100, 110, 120, 130, 140, 150, and 160 °C and hot air speeds of 0.6, 1.4, and 2.0 m/s.

17

The drying process of lignite presented a combination of the short warm-up period,

18

the first falling rate period and the second falling rate period. The Midilli model gave

19

a perfect prediction for the lignite thin layer drying. The effective moisture diffusivity

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of lignite thin layer was from 5.098×10−9 to 1.481×10−8 m2/s for the first falling rate

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Beijing Key Laboratory of Flow and Heat Transfer of Phase Changing in Micro and

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period, and from 7.003×10−9 to 1.907×10−8 m2/s for the second falling rate period. The hot air temperature and speed had significant effect on the effective moisture diffusivity of the lignite sample（P＜0.05). On the hot air speeds of 0.6, 1.4, and 2.0 m/s, the apparent activation energy of lignite thin layer in the first falling rate period

25

was determined as 17.652, 15.495, and 15.175 kJ/mol, whereas it was 16.340, 14.787,

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and 13.672 kJ⁄mol in the second falling rate period.

27

Keywords: Lignite; Thin-layer drying; Kinetics; Effective moisture diffusivity;

28

Forced convection. 2

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1. Introduction Although the star-rising energy such as the petroleum and natural gas may

31

gradually take a place in the energy consumption structure, coal is still an important

32

energy source in the world due to its availability (Li, 2004). With the consumption of

33

coal sources, high-rank coal is in short supply. However, lignite accounts for nearly

34

half of the global coal reserves (Karthikeyan et al., 2009). Lignite resources in China

35

are abundant with about 129 ×1012 tons, accounting for 12.69% of the total coal

36

reserves (Zhu et al., 2015). Generally, lignite is cheap and emerging as an economic

37

fuel of power plants, provided the SO2 emission could be controlled (P.Selvakumaran

38

et al., 2014). However, high moisture content (up to 65%, wet basis) and low energy

39

output of lignite have restricted its wide use (Pusat et al., 2015). The direct

40

combustion of lignite in the boiler can lead to low thermal efficiency (up to 20% of

41

the chemical energy of the coal is wasted during the evaporation of water that

42

contained within the lignite structure (Bergins, 2003)), high greenhouse gas emission,

44 45 46

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43

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30

high operation and maintenance costs (Zheng et al., 2014b). It is estimated that the optimization of the drying process in future lignite power plants may lead to an efficiency increase of 4-6 points (Agraniotis et al., 2012). Besides, reduced moisture content of lignite decreases transportation costs, lowers ash disposal requirements and

47

decreases power plant emissions (C.A.Pickles et al., 2014). Consequently, the

48

development of an efficient lignite drying process is a necessary step towards the

49

implementation of the existing lignite-fuelled power plants (Bergins et al., 2007).

50

Allardice and Evans (Allardice and Evans, 1971) suggested that at least two 3

Page 3 of 36

classes of water exist in Yallourn brown coal at any particular temperature, firstly

52

water which can be removed by evacuation at that temperature and secondly

53

chemisorbed water, which can be removed only by raising temperature to cause

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thermal decomposition of functional groups. Progressively more of this water is

55

released as the temperature is raised. Norinaga et al (Norinaga et al., 1997)

56

investigated the classification of water in brown coal based on the differential

57

scanning calorimetry (DSC) technique over temperature range from 123 to 293 K. On

58

the basis of its congelation characteristics, the water was classified into free water,

59

bound water, and nonfreezable water. Evans (Evans and G., 1973) clarified the water

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in the lignite into bulk water (free water), capillary water, and sorbed water, and

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suggested that the bulk water was removed during the initial period, while the

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capillary water and sorbed water were removed during the falling rate period.

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Tahmasebi et al. (Tahmasebi et al., 2012) examined the effect of temperature,

64

particle size and gas flow rate on drying characteristics of lignite. They revealed that

65 66 67 68

Ac ce p

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drying rate increased with increasing drying temperature, gas flow rate, and decreasing particle size. Vorres et al. (Vorres et al., 1992) obtained the isothermal drying characteristics of Beulah-Zap lignite using the thermogravimetric analysis method and found that the drying process presented two distinguishable periods. The

69

results are in agreement with investigation drying behavior on lignite and

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subbituminous coal conducted by Vorres (Vorres, 1994). According to isothermal

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thermogravimetric analysis experiment on lignite drying at drying temperatures of 50

72

to 170 °C, Liu et al. (Liu et al., 2013) suggested that the falling rate period of lignite 4

Page 4 of 36

was best represented by the first falling rate and second falling rate period, and the

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activation energy was estimated 18.53 and 15.26 kJ/mol for the two periods,

75

respectively. During the drying process, the first falling rate period was supposed to

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be dominated by liquid diffusion while vapor diffusion was the controlling process of

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the second falling rate period (Hassini et al., 2007). Li et al. (Li et al., 2009) found

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that the drying kinetics of an Indonesian low rank coal at the drying temperature of

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100 °C and particle size less than 0.355 mm was best represented by the constant rate

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stage followed by the rate decay stage.

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A number of drying models have been widely used by many researchers

82

(Akpinar, 2006). Based on a thermogravimetric analysis technique, Tahmasebi et al

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(Tahmasebi et al., 2013) deduced that the Midilli model was the best one to describe

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the drying characteristics of Chinese lignite under nitrogen atmosphere. Pusat et al.

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(Pusat et al., 2015) found that the Wang and Singh model was the best one to describe

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the drying behavior of coarse lignite particles in a fixed bed. Tahmasebi et al.

88 89 90

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(Tahmasebi et al., 2014) highlighted that drying characteristics of lignite particles (224-355 m) under nitrogen atmosphere in a quartz fluidized-bed reactor was still well described by the Midilli model. Thin-layer drying is a convenient approach in investigating diffusion and

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convection transient problems which may be used whenever diffusion inside the

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material is much faster than the diffusion across the boundary of the solid (de Lima et

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al., 2012). Yet the validity of the deep-bed drying model is directly dependent on how

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accurately the thin layer drying kinetics behaved (Dissa et al., 2011; Duc et al., 2011; 5

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Hemis et al., 2009). Celma et al. (Celma et al., 2007) examined the thin-layer drying behavior of

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sludge at air temperature of 20 to 80 °C and air velocity of 1 m/s. The effective

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diffusivity coefficient varied from 2.224×10 − 10 to 6.993×10 − 10 m2/s and the

99

activation energy was 15.77 kJ/mol. Olive stone was a valuable source of biomass and

100

suitable for thermal purpose in industrial. The drying kinetics of olive stone thin-layer

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(thickness of 10 mm) at air temperature of 100 to 250 °C and air velocity of 1 m/s

102

were studied by Gómez-de la Cruz et al(Gómez-de la Cruz et al., 2014). The effective

103

diffusivity values ranged from 0.4×10−8 to 1.45×10−8 m2/s and the activation energy

104

was 14.208 kJ/mol. The thin-layer drying behavior of vegetable wastes at a

105

temperature range of 50 to 150 °C and air velocity of 0.6 m/s was determined by

106

Lopez et al (Lopez et al., 2000). The effective diffusion coefficient varied from 6.03

107

×10−9 to 3.15×10−8 m2/s with an activation energy of 19.82 kJ/mol.

109 110 111 112

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However, no literature on drying of lignite thin-layer is found. There were many

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studies primarily focused on the thin-layer drying of agricultural products under low drying temperature. Mortaza Aghbashlo et al. (Aghbashlo et al., 2008) evaluated the influence of hot air velocity on thin-layer drying of berberis fruit and the effective moisture diffusivity and the activation energy of samples were calculated, which

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varied from 3.320×10−10 to 9.000×10−9 m2/s and from 110.83 to 130.61 kJ/mol at

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temperatures of 50 to 70 °C and hot air velocities of 0.5 to 2 m/s, respectively.

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Eduardo (Jacob Lopes et al., 2007) investigated the drying characteristics of the

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cyanobacterium in a convective hot-air dryer at air temperatures of 40, 50, and 60 °C. 6

Page 6 of 36

Doymaz (Doymaz, 2006) revealed the thin-layer drying kinetics of mint leaves at hot

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air temperatures of 35 to 60 °C and found that the effective moisture diffusivity

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increased with increasing temperature. The results are in agreement with drying

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characteristics of carrots thin layer (Doymaz, 2004).

ip t

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Although some work has been conducted on convective drying kinetics of lignite,

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but little information is available to data on the potential impact of the drying

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behavior for lignite thin layers at medium temperatures, especially the drying kinetics

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of lignite thin layer based on two-stage scheme is not found in the literatures. In the

125

present work, thin-layer drying behavior of the lignite during hot air forced

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convective drying was investigated experimentally. The moisture diffusivities of the

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lignite sample in the falling rate periods during thin layer drying were determined

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based on the Fick diffusion law. The effect of hot air temperatures and speeds on the

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thin-layer drying kinetics of lignite based on two-stage scheme was revealed

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according to the Arrenius principle. This research will provide fundamental data for

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understanding the drying kinetics of lignite, and scientific reference for the design and improvement of the boiler. 2. Methods

2.1. Materials

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The pulverized Chinese lignite was obtained from a power plant (Hebei province).

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The sample was sieved by using 425-500  m sieves, and was stored in an air-tight

137

container to prevent the water evaporation. Proximate analyses of the lignite samples

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were performed in the analyzer, detailed measuring method from the references (Varol 7

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et al., 2010). The proximate analysis was listed in Table 1. The ultimate analysis for

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the lignite samples (Liu et al., 2013) were also presented in Table 1. Table 1 Proximate and ultimate analyses of lignite .

141

Proximate analysesa (wt.%)

Ultimate analysesb (wt.%)

sample Var

FCar

Aar

Cdaf

11.11

38.77

14.61

35.51

56.72

142

a

143

a received dried basis, respectively.

144

b

145

respectively.

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c

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2.2. Experimental apparatus and procedure

Hdaf 3.61

Ndaf 0.71

Odaf

(MJ/kg)

Sdaf

cr

lignite

Mar

ip t

HHVc

15.98

9.73

12.61

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Mar, Var, FCar and Aar refer to the moisture, volatile, fixed carbon and ash content on

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Hdaf, Ndaf, Odaf and Sdaf refer to the element content on a dry ash free basis,

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HHV refers to the higher heating value on a received dried basis.

The experiments were carried out in a laboratory convective dryer shown in Fig.1.

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The system consisted of a tunnel, a frequency fan, a heater, a drying chamber, a

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dehumidification unit and a set of data acquisition. The air induced from the frequency conversion fan was heated by the 3000W heater. Then the hot air was dehumidified through the dehumidification unit containing calcium oxide drying agent and circulated about 15 minutes. About 40 g of the prepared lignite sample was

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uniformly spread as a thin layer on a square steel tray (80 mm×80 mm×10 mm),

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which was over a digital balance was placed in the drying chamber. The bottom and

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other sides of the steel tray were approximately insulated because they were covered

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by a layer of foamed ceramics. The samples had initial moisture content of 0.03-0.04 8

Page 8 of 36

kg/kg (d.b.), and the thickness of the thin layer was about 10 mm. The thin layer was

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dried by the convective heat exchange of the dehumidified hot air, which was back to

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the dehumidification unit for dehumidification. Drying experiment was finished when

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the weight change rate was less than 0.002% in 10 minutes. The rectangular tunnel

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which was made of stainless steel was 100 cm in length, 14 cm in width, and 9 cm in

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height. The tunnel was insulated by covering a layer of rock wool to minimize the

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energy loss. The air speed was adjusted by regulating the output power of the fan

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(XINXING; 150FLJ, China). The air speed over the thin layer was measured by

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digital anemometer (TECMAN; TM826, China). The drying temperature was

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regulated by a temperature controller (YUYAO; XMTD-808P, China).

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A temperature sensor (PT100) was used to measure the air temperature. A data

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acquisition card (ADVANTECH; ADAM4017, China) was applied for collecting the

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temperature. During the drying process, mass of thin layer was recorded at an interval

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of 90 s by the digital balance (OHAUS; CP413, China) with an accuracy of 0.0001 g.

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Fig. 1. Convective dryer setup. 9

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glass, 9. tray, 10. digital balance, 11. speed regulation, 12. data acquisition, 13. dehumidification unit, 14. air

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The experimental conditions were selected as drying temperatures of 100, 110,

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120, 130, 140, 150, and 160 °C, hot air speeds of 0.6, 1.4, and 2.0 m/s. To ensure

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reproducibility, the every run experiment was repeated three times. The results

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demonstrated that a good reproducibility was maintained for each run because the

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relative deviation was generally within ±1.5%. The repetitive experiment at 100 °C,

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and 0.6 m/s was shown in Fig.2.

(1. frequency conversion fan, 2. steam generator, 3. heater, 4. tray, 5. balance, 6. radiation heater, 7. CCD, 8. silica

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chamber, 15. steel baffle, 16. pressure sensor, 17. temperature sensor.)

1.0

1 2 3

0.8

M

MR

0.6 0.4

0.0

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4000 6000 t (s)

8000

Fig.2. Repetitive experiment at 100 °C, and 0.6 m/s

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2000

te

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0

d

0.2

The uncertainties of the measurement in the experiment are dependent on the

experimental conditions and the measurement instruments. The uncertainties of the measured parameters were estimated by using the method in reference (Luo et al., 2014; Yang et al., 2005), and listed as follows. Hot air temperature:

2

 T   T    system    display   T   T  2

2

2

 0.35 / 3   0.1 / 2 3        0.20%  100   100  Hot air speed:



V 0.018   3.00% V 0.6

10

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Mass of lignite:

189



m 0.001/ 2 3   0.0008% m 38

2.3. Drying models of thin layer Several common models are widely used to describe the relation between

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moisture ratio and drying time in the thin layer drying, as shown in Table 2 (Doymaz,

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2006).

cr

The moisture ratio (MR) can be expressed as:

MR 

Mt  Me M0  Me

(1)

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us

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where Mt, M0 and Me are the moisture content at any time, initial moisture content(%,

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d.b.) and equilibrium moisture content(%, d.b.), respectively. The values of Me are

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relatively small compared to Mt or M0, thus, the moisture ratio is simplified as

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(I.Doymaz, 2004):

200 201 202 203

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d te

MR 

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199

M

195

Mt M0

(2)

2.4. Effective moisture diffusivity With the assumptions of moisture migration being by diffusion, negligible

shrinkage, constant diffusion coefficient and temperature, the solution of Fick’s second law in slab geometry, was as follows (Goyal et al., 2006): 8 MR  2 





n 1

1

 2n  1

2

  2n  12  2 D t  eff  exp   2   L  

(3)

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where MR stands for sample moisture ratio, L the thickness (m) of the thin-layer (hot

206

air near only one side of the sample), Deff the effective moisture diffusivity (m2/s), t

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the drying time (s). The moisture migration properties are lumped into the effective 11

Page 11 of 36

208

moisture diffusivity, which are a function of the sample properties, the moisture

209

content and hot air temperature and speed.

first term of the series, as follows:

  2Deff t  8 MR  2 exp    2   L   

212

Then, Eq. (4) can be written in logarithmic form:

(4)

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ip t

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For long drying periods (setting n=1), the equation (3) can be simplified to the

cr

210

214

 2 Deff 8 l n MR  l n 2  t  L2

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The effective moisture diffusivity under each drying condition can be determined

an

by plotting lnMR vs. t.

217

2.5. Apparent activation energy

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d

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Apparent activation energy was estimated by using Arrhenius equation (A.O.Dissa et al., 2008) :

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 E  Deff  D0 exp  a   RT 

(6)

where D0 is the diffusion factor (m2/s), Ea the apparent activation energy (kJ/mol), T the hot air temperature (K), R the gas constant (kJ/mol·K). Taking natural logarithms, Eq. (6) can be linearized as: ln Deff  ln D0 

224

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M

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(5)

Ea RT

(7)

By plotting lnDeff vs. 1/T, Ea and D0 can be subsequently determined.

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3. Results and discussion

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3.1. Drying curves 12

Page 12 of 36

Drying curves (moisture ratio versus time) and drying rate curves (drying rate

229

versus moisture ratio) were shown in Fig. 3(a)-(c). The experimental conditions were

230

selected as hot air speeds of 0.6 m/s, 1.4 m/s, and 2.0 m/s and drying temperatures of

231

100 °C, 110°C, 120 °C, 130 °C, 140 °C, 150 °C and 160 °C. 1.0



0.8

0.0006 -1

dMR/dt (s )

0.7

MR

0.6 0.5 0.4 0.3

0.0005 0.0004 0.0003 0.0002

100C 120C 140C 160C

0.2 0.0001

0.1 0.0 2000

4000 t (s)

232

6000

an

0.0000

0

0.0

8000





0.0007

110C 130C 150C

a

cr

100C 120C 140C 160C

us

0.9

ip t

228

0.2

0.4

0.6

110C 130C 150C

0.8

1.0

MR

(a) 0.6 m/s. 1.0 100C 120C 140C 160C

0.8

110 C 130 C 150 C

M

233

0.0008

100 C 120 C 140 C 160 C

110 C 130 C 150 C

0.2

0.4

0.0006 -1

dMR/dt (s )

d

0.4 0.2 0.0

234 235

2000

4000

6000

0.0002

0.0000 0.0

t (s)

0.0008

0.6

MR

100C 120C 140C 160C

0.0010

110C 130C 150C

-1

0.8

0.4

1.0

110C 130C 150C

0.0006 0.0004 0.0002

0.2

0.0000

0.0 0

2000

4000

6000

0.0

8000

0.2

0.4

0.6

0.8

1.0

MR

t (s)

236

0.8

(b) 1.4 m/s.

dMR/dt (s )

100C 120C 140C 160C

0.6

MR

1.0

(c) 2.0 m/s.

237

Fig. 3.Variation of moisture ratio and drying rate with drying conditions.

238 239

0.0004

8000

Ac ce p

0

te

MR

0.6

a

Ⅰ:warm up period;Ⅱ: the first falling rate period; Ⅲ: the second falling rate period. 13

Page 13 of 36

As can be observed in Fig. 3, the total drying time reduced significantly as drying

241

temperature increased. At the hot air speed of 0.6m/s, the drying time was about 2

242

hours at 100 °C, whereas it was only 1.25 hours at 120 °C, 1.05 hours at 140 °C, and

243

0.9 hour at 160 °C. The drying rate of the thin layer increased with increasing the

244

drying temperature because of the reinforcing of moisture migration, which resulted

245

from the enhancement of driving force on heat transfer in the samples. Meanwhile,

246

during the thermal drying, coal successively experienced the removal of internal water,

247

which can destroy and cause the pore structure to collapse (Jiefeng Zhu, 2014). The

248

pore volume and surface area increased with the rising of temperature (Salmas et al.,

249

2001), which could lead to water removal more easily.

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The drying of the thin layer presented three distinct periods, an initial period

251

(warm-up period), two falling rate periods so called the first falling rate period and the

252

second falling rate period. The initial period was the beginning of drying, during

253

which drying rate depended on the external process parameters. The slope of the

255 256 257

te

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254

d

250

drying rate curve increased in a short time and the drying rate reached its maximum value rapidly. In this period, bulk water evaporated from the surface of the sample and since heat transfer promoted the evaporation, the radius of the liquid/vapor interface over the exterior surface decreased continuously. This period sustained for a very

258

short time, approximately 180-360 sec depending on the drying temperature and hot

259

wind speed. No constant drying rate period was observed, only the falling rate period

260

was detected after initial stage, which indicated that the internal moisture diffusion

261

process progressively became the most important controlling factor (Belhamri, 2003). 14

Page 14 of 36

The maximum drying rate point was taken as a turning point of the initial period and

263

the falling rate period. The turning point was usually used to demarcate the warm up

264

period and the first falling rate period. At the turning point, there is no moisture at the

265

surface since the ability of the capillaries to supply the bulk water was diminished.

266

The drying front had entered the pores. The first falling rate period, just beyond the

267

turning point, during which the capillary water in the pore channel evaporated by

268

molecular diffusion through the unoccupied capillaries. During this period, the rate of

269

evaporation of surface of outside decreased rapidly due to the increasing resistance of

270

internal moisture migration and the decreasing moisture content, the drying rate

271

clearly decreased. During the transition of the first falling rate period to second falling

272

rate period, there was possibly a change from capillary water to sorbed water, which

273

was even less than capillary water. The first falling rate period and the second falling

274

rate period can be differed by the slope of the drying rates profiles. The critical

275

moisture ratio, MRcr, is usually regarding to the transition point from the first and the

277 278 279

cr

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d

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Ac ce p

276

ip t

262

second falling rate periods. Moreover, the sorbed water was strongly bounded to the solid particles and less active than any other water (Choudhury et al., 2011; Lasagabaster et al., 2006), which increased the resistance to moisture movement and evaporation, therefore the drying rates in the second falling rate period decreased

280

slowly than the first falling rate period. The drying rate of the thin layer increased

281

with increasing the drying temperature because of the reinforcing of moisture

282

migration, which resulted from the enhancement of driving force on heat transfer in

283

the samples. For example, when the drying air temperature rose from 100°C up to 160 15

Page 15 of 36

284

°C, the maximum drying rates increased by about 111%, 108%, and 84% at hot air

285

speeds of 0.6, 1.4, and 2.0 m/s, respectively, indicating that effect of temperature on

286

drying rate began to reduce with increasing the hot air speed.

1.0

0.0008 2.0m/s 1.4m/s 0.6m/s

0.6m/s 1.4m/s 2.0m/s

0.0007

us

0.8

0.0006 0.0005

-1

dMR/dt (s )

0.6

MR

cr

drying temperature of 130 °C.

0.4

0.0004 0.0003

an

288

ip t

Fig. 4 illustrated the influence of the hot air speed on drying characteristics at the

287

0.0002

0.2

0.0001

0.0000 0.0

0.0 0

290

2000

3000

4000

t (s)

5000

M

289

1000

0.2

0.4

0.6

0.8

1.0

MR

Fig. 4. Variation of drying curves and drying rates curves with air speeds at 130 °C. Increments in hot air speed would give rise to an increase of the drying rate and a

292

decrease of the drying time, which resulted from the enforcement of heat transfer

293

between air and thin layer. At 130 °C，the drying time decreased about 1512 s and the

295 296 297

te

Ac ce p

294

d

291

drying rate increased by about 47% as air speed increased from 0.6 to 2.0 m/s . A higher hot air speed resulted in a lower moisture content corresponding to the drying rate maximum point. Because, increment in hot air speed would lead to an increase of global heat and mass transfer coefficients, as the boundary layer got progressive

298

thinning, which enhanced the evaporation of water from lignite and migration of

299

water near the surface.

300

3.2. Evaluation of the drying models

301

In order to determine the moisture content as a function of drying time, nine 16

Page 16 of 36

302

shared drying models in Table 2 were fitted for the thin layer drying behavior. Table 2 Thin layer drying models.

303 Models

Model equations

Model

References

1

(Lewis, 1921)

(Overhults et al., 1973)

MR = a exp( -kt )

2

Page

MR = exp( -kt n )

3

Modified Page

MR = exp[ -( kt )n ]

MR = 1  at  bt 2

Wang and Singh

Approach of Diffusion

M

MR = a exp( -k0t )  c exp( -k1t )

Two term

MR = a exp( -kt )  (1  a) exp( -kbt )

d

M R = exp( -kt n )  bt

(Özdemir and Onur Devres, 1999)

5

(Zhu and Shen, 2014)

6

(Wang et al., 2007)

7

(Toğrul and Pehlivan, 2002)

8

(Yaldiz et al., 2001)

9

(Midilli et al., 2002)

te

Midilli et al.

4

an

MR = a exp( -kt )  c

Logarithmic

(Page, 1949)

us

Henderson and Pabis

cr

MR  exp( -kt )

Lewis

ip t

number

The statistical analysis values were presented in Table 3. As can be seen in Table

305

3, in comparison with other models, the Page, Modified Page and Midilli models gave

306 307 308 309

Ac ce p

304

good agreement between experimental and predicted moisture ratio. The average 2 values of R2, RMSE and χ for the Page model were 0.998, 7.551×10-3 and 1.092×

10-4, while they were 0.998, 7.551×10-3 and 1.005×10-4 for the Modified Page model, 0.999, 2.321×10-3 and 7.100×10-5 for the Midilli model.

310

Table 3 Statistical results obtained from various thin-layer drying models.

311

(a) u=0.6 m/s. T (°C) 100

Models number

Models parameters

R2

RMSE

χ2

1

k=4.283E-4

0.981

0.201

1.425E-4

2

k=4.491E-4,a=1.048

0.983

0.182

1.332E-3

3

k=1.463E-4,n=1.131

0.999

8.6E-4

6.101E-6

17

Page 17 of 36

8.6E-4

6.002E-6

5

k=3.632E-4,a=1.072,c=-0.065

0.987

0.137

9.512E-4

6

a=-2.4E-4,b=1.29E-8

0.924

0.800

5.555E-3

7

a=0.521,c=0.525,k0=4.480E-4,k1=4.480E-4

0.983

0.182

1.280E-3

8

k=6.670E-4,a=-35.533,b=0.991

0.987

0.132

9.290E-4

9

k=2.800E-4,n=1.042,b=-5.130E-6

0.999

8.3E-4

5.811E-4

1

k=4.833E-4

0.993

0.063

4.936E-4

2

k=5.131E-4,a=1.062

0.996

0.031

2.525E-4

3

k=1.272E-4,n=1.172

0.999

0.003

2.823E-5

4

k=4.681E-4,n=1.171

0.999

0.003

2.722E-5

5

k=4.823E-4,a=1.070,c=-0.023

0.998

0.011

9.611E-5

6

a=-2.800E-4,b=1.890E-8

7

a=0.232,c=0.842,k0=5.140E-4,k1=5.140E-4

8

k=7.846E-4,a=-36.238,b=0.987

9

k=1.4332E-4,n=1.153,b=-9.060E-7

1

k=6.328E-54

2

k=6.822E-4,a=1.092

3

k=8.272E-5,n=1.261

4

k=5.936E-4,n=1.284

5

k=5.745E-4,a=1.124,c=-0.060

6

a=-3.600E-4,b=3.000E-8

0.950

0.385

4.090E-4

7

a=0.548,c=0.548,k0=6.800E-4,k1=6.800E-4

0.983

0.120

1.310E-4

8

k=1.100E-3,a=67.77,b=1.012

0.053

5.738E-4

9

d

0.993

k=1.280E-4,n=1.201,b=-5.160E-8

0.999

4.264E-4

4.585E-6

1

k=6.918E-4

0.976

0.151

2.108E-3

2

k=7.533E-4,a=1.101

0.984

0.102

1.404E-3

3

k=7.012E-5,n=1.301

0.997

0.017

2.540E-4

4

k=6.533E-4,n=1.323

0.997

0.017

2.442E-4

130

5

k=6.034E-4,a=1.130,c=-0.075

0.996

0.025

3.715E-4

6

a=-4.400E-4,b=4.550E-8

0.983

0.108

1.540E-4

7

a=0.551,c=0.551,k0=7.500E-4,k1=7.500E-4

0.983

0.101

1.490E-3

8

k=1.250E-3,a=-58.421,b=0.992

0.995

0.029

4.192E-4

9

k=1.093E-4,n=1.242,b=-6.686E-6

0.999

4.235E-4

6.138E-6

1

k=7.352E-4

0.987

0.08

1.118E-4

2

k=7.823E-4,a=1.082

0.991

0.051

6.812E-4

3

k=1.282E-4,n=1.231

0.998

0.009

1.230E-4

4

k=6.911E-4,n=1.245

0.998

0.009

1.230E-4

5

k=6.891E-4,a=1.093,c=-0.041

0.997

0.015

2.036E-4

6

a=-4.400E-4,b=4.500E-8

0.957

0.259

3.450E-3

140

7

a=0.682,c=0.397,k0=7.790E-4,k1=7.790E-4

0.991

0.051

7.000E-4

8

k=1.250E-3,a=-108.848,b=0.990

0.998

0.009

1.269E-4

150

9

k=1.589E-4,n=1.200,b=-3.230E-6

0.999

9.846E-4

1.331E-5

1

k=8.436E-4

0.986

0.072

1.138E-3

cr

ip t

0.999

an M

0.586

4.930E-3

0.996

0.030

2.572E-4

0.999

0.004

3.087E-5

0.999

7.0E-4

5.892E-6

0.978

0.170

1.814E-3

0.984

0.123

1.319E-3

0.998

0.013

1.530E-4

0.998

0.013

1.420E-4

0.993

0.051

5.401E-4

us

0.932

Ac ce p

120

k=4.114E-4,n=1.163

te

110

4

18

Page 18 of 36

k=9.112E-4,a=1.092

0.992

0.041

6.632E-4

3

k=1.162E-4,n=1.271

0.999

0.001

1.912E-5

4

k=8.136E-4,n=1.272

0.999

0.001

1.912E-5

5

k=8.372E-4,a=1.102,c=-0.032

0.995

0.023

3.811E-4

6

a=-5.200E-4,b=6.490E-8

0.963

0.191

3.070E-3

7

a=0.533,c=0.558,k0=9.120E-4,k1=9.120E-4

0.992

0.041

6.790E-4

0.999 0.999

0.001

1.990E-5

8.147E-4

1.336E-5

1

k=8.952E-4

0.974

0.125

2.411E-3

2

k=9.833E-4,a=1.112

0.983

0.080

1.627E-3

3

k=6.728E-5,n=1.361

0.998

0.009

1.813E-4

4

k=8.421E-4,n=1.372

5

k=7.913E-4,a=1.141,c=-0.076

0.998

6

a=-5.900E-4,b=8.360E-8

7

a=0.554,c=0.554,k0=9.750E-4,k1=9.750E-4

8

k=4.607E-4,a=36.843,b=0.982

9

k=9.148E-5,n=1.308,b=-6.250E-6

ip t

k=1.510E-3,a=-67.792,b=0.994 k=1.230E-4,n=1.263,b=-9.130E-7

cr

8 9

0.009

1.727E-4

0.994

0.025

5.111E-4

0.990

0.047

9.370E-4

0.982

0.080

1.680E-3

0.993

0.031

6.328E-4

0.999

9.488E-4

1.936E-5

R2

RMSE

χ2

0.974

0.125

2.411E-3

us

an

160

2

(b) u=1.4 m/s. Models number 1

k=8.952E-4 k=9.833E-4,a=1.112

0.983

0.080

1.627E-3

k=6.728E-5,n=1.361

0.998

0.009

1.813E-4

4

k=8.421E-4,n=1.372

0.998

0.009

1.727E-4

5

k=7.913E-4,a=1.141,c=-0.076

0.994

0.025

5.111E-4

6

a=-1.070E-3,b=2.770E-7

0.991

0.022

8.145E-4

7

a=0.537,c=0.537,k0=1.702E-3,k1=1.702E-3

0.987

0.031

1.240E-3

8

k=2.800E-3,a=-55.112,b=0.993

0.997

0.007

2.789E-4

9

k=3.544E-4,n=1.221,b=-8.470E-6

0.998

0.004

1.727E-4

1

k=4.833E-4

0.993

0.063

4.936E-4

d

2 3

Ac ce p

100

Models parameters

te

T (°C)

M

312

110

120

2

k=5.131E-4,a=1.061

0.996

0.031

2.525E-4

3

k=1.272E-4,n=1.172

0.999

0.003

2.823E-5

4

k=4.681E-4,n=1.171

0.999

0.003

2.722E-5

5

k=4.823E-4,a=1.072,c=-0.023

0.998

0.011

9.611E-5

6

a=-3.400E-4,b=2.830E-8

0.958

0.272

3.030E-3

7

a=0.613,c=0.428,k0=5.400E-4,k1=5.400E-4

0.999

0.007

7.446E-5

8

k=1.550E-3,a=-0.162,b=0.373

0.999

0.003

3.044E-5

9

k=3.024E-4,n=1.070,b=-4.390E-7

0.999

0.002

2.460E-5

1

k=6.328E-54

0.978

0.170

1.814E-3

2

k=6.822E-4,a=1.087

0.984

0.123

1.319E-3

3

k=8.272E-5,n=1.261

0.998

0.013

1.530E-4

4

k=5.936E-4,n=1.284

0.998

0.013

1.420E-4

5

k=5.745E-4,a=1.122,c=-0.058

0.993

0.051

5.401E-4

19

Page 19 of 36

0.990

0.042

8.238E-4

7

a=0.524,c=0.524,k0=7.840E-4,k1=7.840E-4

0.994

0.023

4.673E-4

k=1.190E-3,a=-68.022,b=0.985

0.999

0.004

7.334E-5

k=3.199E-4,n=1.110,b=-4.930E-6

0.999

0.002

4.719E-5

1

k=6.918E-4

0.976

0.151

2.108E-3

2

k=7.533E-4,a=1.102

0.984

0.102

1.404E-3

3

k=7.012E-5,n=1.301

0.997

0.017

2.540E-4

4

k=6.533E-4,n=1.323

0.997

0.017

2.442E-4

5

k=6.034E-4,a=1.132,c=-0.075

0.996

0.025

3.715E-4

6

a=-5.880E-4,b=8.630E-8

0.994

0.023

5.096E-4

7

a=0.536,c=0.536,k0=8.970E-4,k1=8.970E-4

0.990

0.040

9.031E-4

8

k=1.450E-3,a=-113.574,b=0.992

0.999

9

k=1.997E-4,n=1.192,b=-5.29E-6

1

k=7.352E-4

2

k=7.823E-4,a=1.082

3

k=1.282E-4,n=1.277

4

k=6.911E-4,n=1.245

5

k=6.891E-4,a=1.093,c=-0.041

6

a=-6.210E-4,b=9.450E-8

7

150

160

cr

ip t

8 9

1.010E-4

0.002

4.926E-5

0.987

0.08

1.118E-4

0.991

0.051

6.812E-4

0.998

0.009

1.230E-4

0.998

0.009

1.230E-4

0.997

0.015

2.036E-4

0.993

0.028

6.056E-4

a=0.723,c=0.366,k0=9.800E-4,k1=9.810E-4

0.986

0.057

1.300E-4

8

k=1.650E-3,a=-146.318,b=0.992

0.999

0.006

1.382E-4

9

k=1.200E-4,n=1.277,b=-3.610E-6

0.999

0.003

7.660E-5

1

k=8.436E-4

0.986

0.072

1.138E-3

2

k=9.112E-4,a=1.092

0.992

0.041

6.632E-4

3

k=1.162E-4,n=1.271

0.999

0.001

1.912E-5

4

k=8.136E-4,n=1.272

0.999

0.001

1.912E-5

5

k=8.372E-4,a=1.104,c=-0.032

0.995

0.023

3.811E-4

6

a=-6.680E-4,c=1.070E-7

0.931

0.262

5.240E-3

d

M

an

us

0.005

0.999

Ac ce p

140

a=-5.280E-4,b=7.700E-8

te

130

6

7

a=0.523,c=0.542,k0=1.240E-3,k1=1.240E-3

0.994

0.020

4.257E-4

8

k=1.960E-3,a=-73.582,b=0.993

0.999

0.001

2.901E-5

9

k=3.017E-4,n=1.194,b=-8.330E-7

0.999

0.002

3.250E-5

1

k=8.952E-4

0.974

0.125

2.411E-3

2

k=9.833E-4,a=1.112

0.983

0.080

1.627E-3

3

k=6.728E-5,n=1.361

0.998

0.009

1.813E-4

4

k=8.421E-4,n=1.372

0.998

0.009

1.727E-4

5

k=7.913E-4,a=1.141,c=-0.076

0.994

0.025

5.111E-4

6

a=-1.070E-3,b=2.770E-7

0.991

0.022

8.145E-4

7

a=0.537,c=0.537,k0=1.702E-3,k1=1.702E-3

0.987

0.031

1.240E-3

8

k=2.800E-3,a=-55.112,b=0.993

0.997

0.007

2.789E-4

9

k=3.544E-4,n=1.221,b=-8.470E-6

0.998

0.004

1.727E-4

R2

RMSE

χ2

(c) u=2.0 m/s.

313 T (°C)

Models number

Models parameters

20

Page 20 of 36

0.201

1.425E-4

2

k=4.491E-4,a=1.052

0.983

0.182

1.332E-3

3

k=1.463E-4,n=1.131

0.999

8.6E-4

6.101E-6

4

k=4.114E-4,n=1.163

0.999

8.6E-4

6.002E-6

5

k=3.632E-4,a=1.071,c=-0.065

0.987

0.137

9.512E-4

6

a=-4.578E-4,b=5.278E-8

0.994

0.029

4.943E-4

0.990 0.999

130

140

0.050

8.828E-4

0.006

1.108E-4

9

k=8.324E-5,n=1.271,b=-4.382E-9

0.999

0.006

1.075E-4

1

k=4.833E-4

0.993

0.063

4.936E-4

2

k=5.131E-4,a=1.061

0.996

0.031

2.525E-4

3

k=1.272E-4,n=1.172

4

k=4.681E-4,n=1.171

0.999

5

k=4.823E-4,a=1.07,c=-0.023

6

a=-5.875E-4,b=8.414E-8

ip t

a=0.547,c=0.547,k0=6.976E-4,k1=6.976E-4 k=1.160E-3,a=-54.870,b=0.987

cr

7 8

2.823E-5

0.003

2.722E-5

0.998

0.011

9.611E-5

0.980

0.088

1.700E-3

0.992

0.032

6.341E-5

0.999

0.004

7.929E-5

0.999

0.003

6.820E-5

0.978

0.170

1.814E-3

0.984

0.123

1.319E-3

0.998

0.013

1.530E-4

0.998

0.013

1.420E-4

us

0.003

0.999

a=0.538,c=0.538,k0=9.447E-4,k1=9.445E-4 k=1.790E-3,a=-1.940,b=0.751

9

k=1.425E-4,n=1.254,b=2.203E-6

1

k=6.328E-54

2

k=6.822E-4,a=1.092

3

k=8.272E-5,n=1.261

4

k=5.936E-4,n=1.284

5

k=5.745E-4,a=1.123,c=-0.060

0.993

0.051

5.401E-4

6

a=-6.337E-4,b=9.933E-8

0.972

0.101

2.150E-3

M

an

7 8

7

a=-14.275,c=15.305,k0=7.287E-4,k1=7.423E-4

0.997

0.011

2.540E-4

8

k=3.170E-3,a=-0.214,b=0.344

0.998

0.007

1.448E-5

9

k=3.330E-4,n=1.148,b=3.065E-6

0.998

0.006

1.326E-5

1

k=6.918E-4

0.976

0.151

2.108E-3

Ac ce p

120

0.981

d

110

k=4.283E-4

te

100

1

2

k=7.533E-4,a=1.098

0.984

0.102

1.404E-3

3

k=7.012E-5,n=1.301

0.997

0.017

2.540E-4

4

k=6.533E-4,n=1.323

0.997

0.017

2.442E-4

5

k=6.034E-4,a=1.132,c=-0.075

0.996

0.025

3.715E-4

6

a=-7.074E-4,b=1.223E-7

0.986

0.053

1.270E-3

7

a=-16.672,c=17.661,k0=1.960E-3,k1=1.870E-3

0.999

0.004

9.031E-4

8

k=1.910E-3,a=-50.551,b=0.985

0.999

0.004

9.577E-4

9

k=1.308E-4,n=1.296,b=1.297E-6

0.999

0.004

1.013E-5

1

k=7.352E-4

0.987

0.08

1.118E-4

2

k=7.823E-4,a=1.084

0.991

0.051

6.812E-4

3

k=1.282E-4,n=1.277

0.998

0.009

1.230E-4

4

k=6.911E-4,n=1.245

0.998

0.009

1.230E-4

5

k=6.891E-4,a=1.086,c=-0.041

0.997

0.015

2.036E-4

6

a=-7.384E-4,b=1.372E-7

0.994

0.018

5.175E-4

7

a=0.607,c=0.471,k0=1.110E-3,k1=1.110E-3

0.990

0.030

8.958E-4

21

Page 21 of 36

6.032E-5

9

k=1.831E-4,n=1.245,b=-1.323E-6

0.999

0.002

6.355E-5

1

k=8.436E-4

0.986

0.072

1.138E-3

2

k=9.112E-4,a=1.093

0.992

0.041

6.632E-4

3

k=1.162E-4,n=1.271

0.999

0.001

1.912E-5

4

k=8.136E-4,n=1.272

0.999

0.001

1.912E-5

5

k=8.372E-4,a=1.102,c=-0.0315

0.995

0.023

3.811E-4

6

a=-8.560E-4,c=1.838E-7

0.999

0.002

8.815E-5

7

a=0.545,c=0.546,k0=1.280E-3,k1=1.280E-3

0.977

0.052

2.290E-4

8

k=1.960E-3,a=-73.583,b=0.99

0.999

0.001

2.901E-5

9

k=1.976E-4,n=1.245,b=-2.452E-7

0.999

0.002

6.838E-5

1

k=8.952E-4

0.974

2

k=9.833E-4,a=1.113

3

k=6.728E-5,n=1.361

4

k=8.421E-4,n=1.372

5

k=7.913E-4,a=1.143,c=-0.076

6

a=-6.765E-3,b=1.014E-7

7

cr

ip t

0.002

2.411E-3

0.080

1.627E-3

0.998

0.009

1.813E-4

0.998

0.009

1.727E-4

0.994

0.025

5.111E-4

0.750

0.904

1.586E-2

a=0.541,c=0.541,k0=1.590E-3,k1=1.590E-3

0.987

0.043

7.837E-4

8

k=2.720E-3,a=-57.284,b=0.987

0.997

0.009

1.558E-4

9

k=1.664E-4,n=1.326,b=1.869E-6

0.998

0.005

1.047E-4

us

0.125

0.983

d

3.3. Kinetic analysis

In order to accurately identify the drying behavior of lignite thin layer in whole

316

falling rate stage, the drying kinetics of the first falling rate period and the second

317

318

319

te

315

Ac ce p

314

0.999

an

160

k=1.840E-3,a=-67.543,b=0.990

M

150

8

falling rate period were distinguished. Fig. 5 presented the linear fitting by plotting

lnMR∼ t from Eq. (5) for the thin layer in the first falling rate period and the second

falling rate period at hot air temperature of 160 °C, hot air speed of 0.6 m/s.

22

Page 22 of 36

-1.6

0.0 experiment value linear fitting lnMR=-0.00111t+0.0198 2 R =0.993

-0.2 -0.4

-2.0 -2.2 -2.4

-1.0

-2.6 -2.8

-1.2

-3.0

-1.4

-3.2 -3.4

-1.6

-3.6 250

500

750 1000 1250 1500 1750

1750

2000

2250 t (s)

2500

2750

cr

t (s)

320 321

ip t

-0.8

lnMR

lnMR

-0.6

experiment value linear fitting lnMR=-0.00147t+1.24 2 R =0.991

-1.8

(a) 1st falling rate period.

(b) 2nd falling rate period.

Fig. 5. Linear fitting between lnMR versus t at 160 °C and 0.6 m/s.

us

322

The values of effective moisture diffusivity of the first falling rate period and the

324

second falling rate period was 1.126×10-8 m2/s and 1.496×10-8 m2/s, respectively.

325

The method might also be applied to other drying temperatures and hot air speeds.

326

The results were presented in Table 4.

M

d

Table 4 Effective moisture diffusivity of lignite thin layer under different drying conditions.

328 u

T

(m/s)

(°C)

te

327

an

323

2nd falling rate

1st falling rate R2

Deff (m2/s)

R2

100

5.098E-09

0.994

7.003E-09

0.989

110

5.610E-09

0.999

8.063E-09

0.986

120

6.928E-09

0.996

9.638E-09

0.991

130

8.238E-09

0.993

1.106E-08

0.995

140

8.533E-09

0.997

1.227E-08

0.987

150

9.660E-09

0.995

1.248E-08

0.996

160

1.126E-08

0.989

1.496E-08

0.991

Ac ce p

Deff (m2/s)

0.6

23

Page 23 of 36

100

4.343E-09

0.997

9.060E-09

0.984

110

7.585E-09

0.999

1.096E-08

0.970

120

8.888E-09

0.997

1.238E-08

0.965

130

9.320E-09

0.998

1.430E-08

0.983

140

1.045E-08

0.993

1.613E-08

0.985

150

1.248E-08

0.992

1.684E-08

160

1.329E-08

0.993

1.724E-08

ip t

100

7.303E-09

0.9928

9.920E-09

0.992

110

8.793E-09

0.998

1.207E-08

0.999

120

9.953E-09

0.995

1.355E-8

0.985

130

1.106E-08

0.977

1.430E-08

0.994

140

1.187E-08

0.991

1.552E-08

0.976

150

1.349E-08

0.987

1.745E-08

0.973

160

1.481E-08

0.992

1.907E-08

0.992

1.4

0.995

cr

us

an

M

2.0

0.990

The effective moisture diffusivity of both periods increased with the increase of

330

drying temperature and hot air speed.The effective moisture diffusivity of lignite thin

331

layer during the first falling rate period ranged from 5.098×10-9 to 1.481×10-8 m2/s.

333 334 335

te

Ac ce p

332

d

329

Whereas in the second falling rate period, the effective moisture diffusivity was greater than in the first period and it ranged from 7.033×10-9 to 1.907×10-8 m2/s， which meant that temperature in lignite thin layer increased rapidly during the second falling rate period, leading the increment of the water molecule in sample (Y.

336

Finkelsteina, 2014). The pore structure in the sample would collapse after the first

337

falling rate period (Jiefeng Zhu, 2014), therefore the moisture diffusion resistance

338

decreases due to the enlargement of the pore volume and surface area (Salmas et al.,

339

2001) and the increment of the permeability (Ling HE, 2014). Similar results of 24

Page 24 of 36

effective moisture diffusivity of two falling rate periods were reported by Velic (D.

341

Velić et al., 2004). Zheng et al. (Zheng et al., 2014a) found that the effective moisture

342

diffusivities of single lignite particle (10-25 mm) under nitrogen atmosphere in a

343

horizontal fixedbed dryer were from 4.46×10−6 to 4.69×10−5 m2/s at high drying

344

temperatures of 600 to 900 °C, and a flow rate of 60 L/h. Tahmasebi et al. (Tahmasebi

345

et al., 2013) estimated the effective moisture diffusivities of lignite powder under

346

nitrogen atmosphere using the thermogravimetric analysis method, which were from

347

1.35×10-10 to 4.14×10-10 m2/s at the drying temperatures of 100 to 250 °C.

an

us

cr

ip t

340

The effects of hot air temperatures and speeds on the effective moisture

349

diffusivity were analyzed by applying the two-way analysis method of variance

350

(Kashaninejad et al., 2007; Moore and McCabe, 1989) and the results were shown in

351

Table 5.

d

M

348

te

Table 5 Analyses of variance for the thin layer drying behavior of the lignitea.

352

SS

Df

MS

F

P

F crit

Air speed

1.207E-16

2

2.011E-17

59.400

3.160E-08

2.996

Temperature

3.440E-17

6

1.720E-17

50.770

1.390E-06

3.885

Error

4.064E-18

12

3.387E-19

Total

1.592E-16

20

Air speed

5.623E-17

2

2.811E-17

87.730

5.047E-08

2.996

Temperature

1.597E-16

6

2.661E-17

92.700

3.303E-09

3.885

Error

3.640E-18

12

5.330E-18

Total

2.200E-16

20

Ac ce p

Source of Variation

st

1 falling rate period

2rdfalling rate period

353

a

354

mean square (sum of squares/degrees of freedom), F is the value of F-test, Fcri is the

355

critical value of F, P is probability.

356

Df is the abbreviation of degrees of freedom, SS is the sum of squares, MS is the

F is given by 25

Page 25 of 36

357

F  MSV/ MSE

(8)

358

where MSV is the mean square of variations (air speed or drying temperature), MSE

359

the mean square error. P value of the F test is the probability that a random variable having the F

361

distribution is greater than or equal to the calculated value of the F statistic. Based on

362

the two-way ANOVA, if the P value corresponding to certain factor is less than 0.05,

363

it means that the factor is statistically significant. The higher F means that the

364

difference caused by the significant factor is larger.

an

us

cr

ip t

360

From Table 5, the effects of the hot air temperature and hot air speed on the

366

effective moisture diffusivity were significant for both the first falling rate period and

367

the second falling rate period (P<0.05). Due to the smaller value of F for the air

368

temperature during the first falling rate period, the influence of the air temperature on

369

the effective moisture diffusivity was less than that of the hot air speed. However, the

370

hot air temperature effect was larger than that of the hot air speed for the second

372 373 374

d

te

Ac ce p

371

M

365

falling rate period. During the first falling rate period, the evaporation rate changed slightly at the range of 100℃ to 160℃, due to the small amount of capillary water and small bond energy between water and pore. However, the increment of hot air speed increased the water migration and leading to thin the mass transfer layer of the

375

sample, which further increased the moisture migration rate. During the second falling

376

rate period, mass transfer layer was thin due to the less amount of the sorbed releasing

377

from the sample, the increment of hot air speed slightly thinned the flow boundary of

378

the sample. The evaporation energy for the sorbed water can be divided into the latent 26

Page 26 of 36

379

energy and the breaking bond energy. Higher temperature can break the strong bond

380

easily, indicating that higher temperature caused the removal of the larger amount of

381

sorbed water. Based on Eq.(7), Fig. 6 presented the linear fitting by plotting lnDeff versus 1/T

383

for the thin layer in the first falling rate period and the second falling rate period at hot

384

air speed of 0.6 m/s. -18.2

-18.0

lnDeff=-13.49-1965.31(1/T)

lnDeff=-13.41-2123.17(1/T)

2

-18.2

2

R =0.980

lnDeff

-18.6 -18.8

R =0.975

an

-18.4

lnDeff

us

cr

ip t

382

-18.4

-18.6

M

-19.0

-18.8

-19.2 -3 2.3x10

385 386

2.4x10

-3

-3

2.5x10 -1 1/T (K )

2.6x10

-3

2.7x10

2.3x10

d

(a) 1st falling rate period.

-3

-3

2.4x10

-3

-3

2.5x10 -1 1/T (K )

2.6x10

-3

2.7x10

-3

(b) 2nd falling rate period.

Fig. 6. Linear fitting between lnDeff versus 1/T at hot air speed of 0.6 m/s.

388

For the first and second falling rate period, the values of apparent activation

390 391 392 393

Ac ce p

389

te

387

energy Ea were determined as 17.652 kJ/mol and 16.340 kJ/mol, respectively, and the values of diffusion factor D0 were 1.501×10-6 m2/s and 1.390×10-6 m2/s, respectively. The method might also be applied to other air speeds. The results were presented in Table 6.

Table 6 Values of apparent activation energy Ea and diffusion factor D0 at different hot air speeds.

394 1st falling rate

u

2nd falling rate

(m/s)

Ea (kJ/mol)

D0 (m2/s)

R2

Ea (kJ/mol)

D0 (m2/s)

R2

0.6

17.652

1.501E-06

0.980

16.340

1.390E-06

0.975

1.4

15.495

9.824E-07

0.972

14.787

1.129E-06

0.952

2.0

15.175

1.008E-06

0.990

13.672

8.432E-07

0.979

27

Page 27 of 36

Table 6 illustrated that an increment of the hot air speed decreased the apparent

396

activation energy. Under the certain hot air speed, the apparent activation energy of

397

the first falling rate period was higher than that of the second falling rate period,

398

indicating that the removal of the bonded water in the sample during the second

399

falling rate period was more easily. During the second falling rate period, the pore

400

collapse caused the permeability increased, leading to the decreasing of the diffusion

401

resistance. The apparent activation energy varied from 13.672 to 17.652 kJ/mol in the

402

experimental hot air speeds. Similar results of the apparent activation energy of two

403

falling rate periods have been reported by Liu et al (Liu et al., 2013).

404

4. Conclusions

M

an

us

cr

ip t

395

During the drying of the lignite thin layer, three periods can be detected, an initial

406

warm-up period, the first falling rate period and the second falling rate period. The

407

average value of R2 for the Midilli model was 0.999, which was higher than that the

408

Page model and the Modified Page model with 0.998. The drying air temperature

410 411 412

te

Ac ce p

409

d

405

varied from 100 to 160 °C, the mean drying rate values increased by about 40% to 85%. The mean drying rate increased by about 35%-40% in the speed range from 0.6 m/s to 2.0 m/s. The increment of hot air temperature and speed would give rise to an increment of the effective moisture diffusivity. The increment of hot air speed would

413

give rise to an slight decreasing of the apparent activation energy. The influence of the

414

air temperature on the effective moisture diffusivity was less than that of the air speed

415

effect in the first falling rate period, while in the second falling rate period, the air

416

temperature effect was larger than the air speed effect. 28

Page 28 of 36

χ2 reduced Chi-Sqr

Nomenclature D0

diffusion factor (m2/s)

R gas constant (kJ/mol·K)

Deff effective moisture diffusivity (m2/s)

t

Ea apparent activation energy (kJ/mol)

T

temperature (°C)

F

the value of F-test

u

air speed (m/s)

L

thickness (m)

Superscripts and subscripts

ip t

cr

us

0

initial

P probability

e

equilibrium

an

MR moisture ratio

R2 coefficient of determination

Acknowledgments

eff

effective

M

RMSE residual sum of squares 417

time (s)

This work was supported by the National Natural Science Foundation of China

419

under No 51376017 and the Fundamental Research Funds of China for the Central

420

Universities under No. 2015YJS142.

422 423 424

te

Ac ce p

421

d

418

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