size dependence of the drying characteristics of single lignite

Size Dependence of the Drying Characteristics of Single LigniteParticles in Superheated Steam

TSUYOSHI KIRIYAMA, HIDEAKI SASAKI, AKIRA HASHIMOTO, SHOZO KANEKO,and MASAFUMI MAEDA

Loy Yang lignite particles 10, 5, and 2.5 mm in diameter were dried with superheated steam attemperatures ranging from 383 K to 443 K (110 �C to 170 �C) under atmospheric pressure. Thedrying rates were obtained by measuring their weights with an electronic balance, while tem-peratures of the particles were monitored. The following typical drying characteristics wereobserved: (i) Temperature of lignite rose to 373 K (100 �C) accompanied by condensation ofsteam on the surface. (ii) A constant drying rate period was then observed, while temperature ofthe overall particle was maintained at 373 K (100 �C). (iii) A decreasing drying rate periodbegan accompanied by a rise in surface temperature, and eventually the overall particle reachedthe temperature of the superheated steam. Based on these results, the evaporation rate of waterwas expressed as a function of particle diameter. A numerical model for simulating the dryingprocess of lignite, which was developed for a large particle in a previous study, was modified tomake it applicable to small particles. The model is applicable for simulations of dryingbehaviors of lignite with size distribution in various dryers when an appropriate heat transfercoefficient is given.

DOI: 10.1007/s40553-014-0037-2� ASM International (ASM) and The Minerals, Metals, & Materials Society (TMS) 2014

I. INTRODUCTION

LIGNITE, or brown coal, is the lowest rank of coal,and accounts for 23 pct of the proven recoverablereserves of all coal.[1] Because of its high moisturecontent, which makes the cost of transporting the rawlignite high, it is mainly used as a fuel in thermal powerstations located near source mines. In addition, driedlignite is difficult to transport and store because it has apropensity to combust spontaneously.

Since water vaporization causes heat loss in lignite-firedpower stations, a drying system is necessary to improvethermal efficiency and reduce CO2 emissions. Drying withsuperheated steam is promising because it can preventspontaneous combustion of lignite, and thermal efficiencycan be improved with self-heat recuperation systems. Asteam fluidized bed dryer (SFBD) on a commercial scalehas been developed recently in Germany,[2] and a pilotdryer using pressurized steam also has been constructed.[3]

While the drying characteristics of lignite in an airfluidized bed dryer have been studied,[4-7] availableinformation on steam fluidized bed drying is limiteddespite continuing dryer research and development.Additionally, the behavior of single lignite particles,which is fundamental to comprehending the dryingprocesses, has been reported only for particles 10 mm or

larger,[8,9] although sizes are assumed to be less than10 mm in an actual process.To develop a greater understanding of steam fluidized

bed drying, the authors previously examined steamdrying of 30 mm single lignite particles,[10] and a single-particle model based on the experimental results wasdeveloped in order to simulate the drying of a coarseparticle. The purpose of the present study was toexamine the drying of smaller lignite particles insuperheated steam using particles 10, 5, and 2.5 mm indiameter. The size dependence of their drying charac-teristics was determined, and the numerical model wasimproved to adapt it to a wider range of sizes.

II. EXPERIMENTAL METHOD

A. Sample Preparation

Loy Yang lignite from Victoria, Australia, with amoisture content of about 62 mass pct was cut intospherical samples with specialized tools. Initial diame-ters of the samples, D, were 10, 5, and 2.5 mm, and theiraverage weights were 0.59, 0.073, and 0.009 g, respec-tively. Figure 1 shows the samples and their settingschemes. A glass rod 0.5 mm in diameter was used tosuspend the samples with D = 10 and 5 mm under anelectronic balance (Figures 1(a) and (b)), and a K-typethermocouple was used to measure the temperature atthe sample center, Tcenter. The thermocouple was com-posed of insulated chromel and alumel wires 0.08 mm indiameter, and was set in 0.2-mm-diameter drilled holes.For samples with D = 10 mm, another thermocouplewas used to measure the temperature at the midpoint

TSUYOSHI KIRIYAMA, Cooperative Research Fellow,HIDEAKI SASAKI, Research Associate, AKIRA HASHIMOTO,SHOZO KANEKO, and MASAFUMI MAEDA, Professors, are withthe Institute of Industrial Science, The University of Tokyo, 4-6-1Komaba, Meguro-ku, Tokyo, 153-8505 Japan. Contact e-mail:[email protected]

Manuscript submitted January 12, 2014.Article published online November 5, 2014

METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—349

between the center and the surface, Tmidpoint. For the10 mm samples, a minuscule quantity of silicon resinwas used to fix the positions of the thermocouples. Toaccurately observe the changes in weight of 2.5 mmsamples, 4 particles were dried in a test as shown inFigure 1(c). They were supported by a branched glassrod (0.6 mm in diameter) which had curved pipes(0.7 mm in outer diameter) on each end. Insulated0.1-mm-diameter chromel wire was set in a drilled holeof each sample 0.1 mm in diameter and 1.0 mm indepth, and the other end of the wire was inserted in thepipe attached to the glass rod.

B. Apparatus

A schematic configuration of the experimental systemis shown in Figure 2, where the sample was placed in atest section of 133 mm in diameter and 152-mm high.Temperature in the test section was controlled byelectric heaters. Weight of the sample, W, was measuredby an electronic balance having a resolution of 0.1 mg(HR-200, A & D Company). The sample could beisolated from the atmosphere in the test section byraising the starting pipe until the drying test was started.

Pure water was degassed and pumped up to anevaporator and a superheater. The superheated steamwas sent into the top of the test section, to which a baffleplate was attached, and exhausted from the bottomusing a fan. At the top of the test section, another smallfan exhausted the leakage of superheated steam from anorifice, through which the glass rod suspending thesample had been passed. The glass rod was heated by ahalogen lamp to prevent condensation of the steam onit. Air was supplied to an acryl pipe attached under thebalance along the suspension wire at a rate of 1.0

(dm3 min�1) (ANR, 293 K (20 �C), 101,325 Pa) tostabilize temperature and flow.Temperatures inside samples (Tcenter and Tmidpoint)

were measured with the K-type thermocouples men-tioned above. Surface temperature, Tsurface, was mea-sured by a thermograph (R-300, NEC/Avio) havinginfrared bolometers capable of detecting wavelengthfrom 8 to 12 lm. An optical path for the thermographwas located on the side of the test section, and apolymethylpentene film 10-lm thick was set there as awindow. The inside wall of the test section and theoptical path were painted with a black body sprayhaving an emissivity of 0.94 (THI-1B, Tasco Japan).Because lignite is maintained at 373 K (100 �C) duringthe early period of a drying process and then reaches thesame temperature as surrounding superheated steam,the thermograph was calibrated on the basis of thesetwo temperatures. The sample was observed with avideo camera (HDR-CX170, Sony) through a glasswindow.The area indicated by the dotted line in Figure 2 was

enclosed with polyvinyl chloride sheets to prevent anyfluctuations caused by air. The relative humidity in theenclosure was maintained at over 45 pct to eliminate theeffect of static electricity.

C. Procedure

Considering the spontaneous combustion tempera-tures of Loy Yang lignite [433 K to 443 K (160 �C to170 �C)],[11] the samples were dried by superheatedsteam at 383 K, 403 K, 423 K, and 443 K (110 �C,130 �C, 150 �C, and 170 �C, hereafter referred to as testtemperature, Ta). Before setting the sample, a testsection was heated to Ta under a flow of nitrogen, then

TC forthe centerTC abovethe particle

TCfor themidpoint

Glass rod

Sample

(a)

Siliconresin

D= 10 mm

TC forthe centerTC abovethe particle

Sample

Glass rod

(b)

D= 5 mm

Sample

Glass rod

Glassrod

Glasspipe

Chromelwire

(c)

D= 2.5 mm

10 mm5 mm

5 mm

Fig. 1—Samples and their setting schemes. (a) 10, (b) 5, and (c) 2.5 mm in diameter. TC: Thermocouple.

350—VOLUME 1E, DECEMBER 2014 METALLURGICAL AND MATERIALS TRANSACTIONS E

the fluid was replaced with superheated steam. The testsection was presumed to be filled with superheatedsteam under atmospheric pressure. The feed rate ofwater to the evaporator was 8 cm3/min. Calculated fromcross-sectional area, the average velocity of superheatedsteam was about 0.02 m/s in the test section. TheReynolds numbers in this condition were about 6, 3, and2 for D = 10, 5, and 2.5 mm, respectively, whichenabled accurate weighing of the sample in a laminarflow. After the test section was stabilized, the startingpipe was lifted to separate its internal space from the testsection. The inside of the pipe was then purged withnitrogen, and the sample was hung under the electronicbalance. From the time the pipe was lowered again, the

sample was exposed to superheated steam and measure-ments were started. For samples with D = 10 and5 mm, the start of drying was also monitored by athermocouple placed above them (Figures 1(a) and (b)).W and T were recorded every 1 second. Drying wasjudged to have been completed when the change in Wbecame less than 0.1 mg min�1. Subsequently, the fluidwas switched to nitrogen in order to evaporate residualwater in the sample. W after the nitrogen drying wasregarded as the weight of coal contained in the lignite(dry coal), Wc. The weight of water in the lignite, Ww,was determined by subtracting Wc from the weight ofthe sample, W. The drying tests were conducted threetimes at each Ta.

III. EXPERIMENTAL RESULTSAND DISCUSSION

A. Changes in Temperature and Weight During Drying

Figure 3 shows time variations of temperatures(Tsurface, Tmidpoint , and Tcenter) and the weight of samples(W) during three drying tests under identical conditions(D = 10 mm and Ta = 373 K (170 �C)). Results fromthe three tests were similar, confirming reproducibilityof the measurements. Experiments under other condi-tions also provided reproducible results, and thusrepresentative data are shown hereafter.Figure 4 shows results with samples of (a) 10, (b) 5,

and (c) 2.5 mm at various temperatures. The appearanceof the samples dried at Ta = 443 K (170 �C) is shown inFigure 5, where moisture content, X, is indicated. The

MFC

Purewater

D P

Gas heater

Evaporator

Electronicbalance

Starting pipe

F

TC

Superheater

N2

Test section

PC

LoggerMFC

AirF

Acryl pipe

Enclosure of polyvinyl chloride sheets

Heater

TGBP

Film

Exhaustchamber

Halogen lamp

Fig. 2—Schematic configuration of experimental system. MFC: Mass flow controller, D: degasser, P: feed pump, BP: baffle plate, TC: thermo-couples, TG: thermograph, F: exhaust fan.

300280

320340

420440460

0.40.50.6

0.30.2Te

mpe

ratu

re, T

/K

Wei

ght, W

/g

0.10

Time, t/min0 10 20 40

Tsurface Tcenter

Tmidpoint

Test 1Test 2Test 3

W

400

360380

0.70.80.9

30 50

Fig. 3—Temperatures and weights of the samples 10 mm in diameterat a test temperature of 443 K (170 �C).


moisture content was defined as the weight of waterdivided by that of dry coal (X ¼Ww=Wc), and its initialvalue (Xini) is shown in Table I (size dependence of X isdiscussed later in Section III–B.).

Initially, drop-wise condensation of steam occurredon the surface (Figure 5). Figure 6 shows magnifiedviews of Figure 4 at the initial stage, where W tempo-rarily increased. Meanwhile, the surface and inside ofthe samples reached 373 K (100 �C) in that order, asshown in Figures 6(a) and (b). Presumably, tempera-tures of lignite were increased in this stage mainly by theheat of condensation of the superheated steam. As

shown in our previous study,[10] the condensed water onthe surface was removed by external force as a dropletunder certain conditions. In this study, the falling of awater droplet was caught by video camera atTa = 383 K (110 �C) after a lapse of 0.5 to 1.0 minutesin the drying of 10 mm particles. This loss of moisturecorresponds to the sudden drop inW in Figure 6(a), andlooks significantly different from that in the previousstudy of 30 mm particles, where falling droplets wereobserved more than 10 times.[10] Because the overalllignite particle was heated to 373 K (100 �C) by thecondensation of steam in this period, more watercondensed on larger particles, resulting in dropletsfalling at higher frequency. Additionally, the dropletfell only at Ta = 383 K (110 �C) in Figure 6(a), sug-gesting an influence from Ta; also shown is that theinitial increases in W are greater for lower Ta. Thetemperature dependency is explained by convective andradiant heat transfer, which is larger at higher Ta,resulting in a smaller amount of condensed water on thelignite particles.Measurements of the samples with D = 5 mm con-

firmed that Tcenter rose more slowly than Tsurface, andreached 373 K (100 �C) (Figure 6(b)). When D = 2.5 mm,Tsurface immediately became constant, which wasbelieved to be at 373 K (100 �C) (Figure 6(c)). Nofalling droplets were observed for the samples withD = 5 and 2.5 mm.During the initial period shown in Figure 6, time

variations of the temperatures were independent of Ta.The results indicate that the internal temperature of thelignite particles was increased by heat conduction fromits surface maintained at 373 K (100 �C).After Tcenter reached 373 K (100 �C), typical drying

characteristics in superheated steam[12] were observed.The temperatures of lignite were maintained at 373 K(100 �C) for a period (Figure 4), where W decreasedconstantly. Then, Tsurface; Tmidpoint; and Tcenter beganrising from 373 K (100 �C) in that order, and reachedTa: The formation and widening of cracks on the surfaceare shown in Figure 5, where more cracks can beobserved on larger particles. Although not shown here,the cracks were fewer at lower Ta as was the case forsamples of 30 mm.[10] The generated cracks were thenclosed as the drying proceeded due to shrinkage of thesample. The time to complete drying, tcomp, is shown inTable I.

B. Moisture Content and Drying Rate

Figure 7 shows average water percentages by weight,Ww=ðWc þWwÞ � 100, in the lignite before and afterdrying with superheated steam. Initial water was 63and 62 mass pct (moisture content: 1.71 and 1.63,respectively) in the samples of 10 and 5 mm. Waterpercentage in the 2.5 mm samples was 60 mass pct(moisture content: 1.47), indicating a slight dryingbefore measurements. All samples were placed innitrogen of about 373 K (100 �C) for about 10 secondsbefore the exposure to superheated steam, and smallersamples are more likely to be affected by drying duringthis period.

420

440

460

0.4

0.5

0.6

0.3

0.2

Tem

pera

ture

, T/K

Wei

ght, W

/g

Time, t/min

Tsurface

Tcenter

Tmidpoint

W

400

360

380

0.7443 K423 K403 K383 K

0 60 120 300180 240

10 mm

0.04

0.06

0.02Tem

pera

ture

, T/K

Wei

ght, W

/g

0

Time, t/min0 20 40 100

TsurfaceTcenter

0.08

0.1

60 80

W

443 K423 K403 K383 K

5 mm

420

440

460

400

360

380

0.02

0.03

0.01Tem

pera

ture

, T/K

Wei

ght, W

/g

0

Time, t/min0 0401

0.04

0.05

20 30

Tsurface

W

443 K423 K403 K383 K

2.5 mm

420

440

460

400

360

380

(a)

(b)

(c)

Fig. 4—Temperatures and weights of the samples (a) 10 mm, (b)5 mm, and (c) 2.5 mm in diameter during entire drying process.


Figure 8 shows moisture contents, X, and dryingrates, �dX/dt at Ta = 443 K (170 �C). The dryingrates were smoothed by calculating the moving averagesof 20 seconds. Both constant drying rate period (CDRP)and decreasing drying rate period (DDRP) wereobserved in all tests. The CDRP coincided with a periodwhen the overall sample was 373 K (100 �C), suggestingthat a constant heat was transferred onto the surfaceand consumed only by the water evaporation. It alsoindicated the transfer of free water from the inner part

to the surface. The temperature is assumed to rise from373 K (100 �C) when the free water is depleted there,after which the drying rate decreases until drying isapparently completed.Similar drying characteristicswere observedunder other

experimental conditions. In the following discussion onexperimental results, CDRP is defined for simplicity as aperiod, whereX is between 1.4 and 1.0. The drying rates inCDRP were calculated from the time required to decreaseX from 1.4 to 1.0 and are tabulated in Table I.

10 mm X=0.8

X=0.4 Final (X=0.02)

Condensation

(a) 10 mm (Test 1)

5 mmX=0.8

X=0.4 Final (X=0.03)

Condensation

(b)

(c)

5 mm (Test 1)

2.5 mm

X=0.8

X=0.4 Final (X=0.01)

Condensation

2.5 mm (Test 1)

Fig. 5—Changes in appearance of the samples during drying process at 443 K (170 �C). (a) D = 10 mm (b) D = 5 mm (c) D = 2.5 mm.


C. Size Dependence of Evaporating Rates

Anevaporation rate ofwater from lignite, v (g m�2 s�1),is defined as the decreasing rate of W divided by theapparent surface area of the sample, pD2. The shrinkage ofthe sample was neglected in the calculation. Figure 9(a)shows the average rates during CDRP, vCDRP, calculatedfrom�dX/dt in Table I. The vCDRP shows linear relation-shipwithTa for each particle size; additionally, their slopesshow a rough linear relationshipwith the reciprocal ofD asshown in Figure 10. vCDRP is approximately expressed asEq. [1]

vCDRP ¼ ð3:56=Dþ 831Þ � ðTa � 373Þ=105 ½1�

Average evaporation rates throughout the dryingprocess, vave, were calculated from time required tocomplete the drying and total weight of the evaporatedwater (Table I). As shown in Figure 9(b), vave alsoshowed linearity with Ta. Assuming a linear relationshipbetween the slopes and D�1 shown in Figure 10, vave isapproximately expressed as Eq. [2]

vave ¼ ð2:37=Dþ 358Þ � ðTa � 373Þ=105 ½2�

Using Eq. [2], the time to complete drying, tcomp

(seconds), can be predicted for a given particle size andtemperature. The mass balance is expressed by Eq. [3]

pD2vavetcomp ¼pD3

6� uc;iniqcðXini � XeqÞ; ½3�

where uc;ini is the initial volume fraction of dry coal inlignite, and is about 0.3 for Loy Yang lignite. qc is thedensity of dry coal, and about 1434 (kg m�3). Xini and

Xeq are moisture content before and after dry-ing. Assuming Xini � Xeq is constant at 1.6, tcomp isexpressed by Eq. [4]

tcomp ¼ 1:15D=vave � 105 ½4�

IV. NUMERICAL MODELING

A. Physical Model

A numerical model for drying lignite has beendeveloped based on the physical model illustrated inFigure 11. A lignite particle was assumed to initiallyconsist of dry coal, free water, and bound water(Figure 11(a)). ‘‘Free water’’ is defined as water thatevaporates at 373 K (100 �C) under atmospheric pres-sure, and accounts for moisture content from the initialvalue (about 1.6) to 0.56.[13,14] The remainder is definedas ‘‘bound water’’ that evaporates above 373 K(100 �C). Volume fractions of coal, water, and steam(uc, uw, us) are 0.3, 0.7, and 0, respectively, in the initialstate. When free water evaporates during the dryingprocess, its space becomes occupied by steam as shownin Figure 11(b): meanwhile, free water is suppliedfrom the inside to the surface, resulting in CDRP.After free water on the surface has evaporated com-pletely, the temperature rises from 373 K (100 �C), andDDRP begins with the evaporation of bound water(Figure 11(c)).Figure 12 shows a simulation model. If a lignite

particle is assumed to be isotropic, a one-dimensionalmodel can be used. A particle is divided into 51concentric spherical shells with an initial thickness of

Table I. Overview of Drying Tests

ParticleSize,D (mm)

TestTemperature,

Ta (K)Initial MoistureContent, Xini

�dX/dt 9 104 (s�1)(CDRP)

Time for CompleteDrying, tcomp (min)

EquilibriumMoisture

Content, Xeq

Time Required toAchieve the TargetMoisture Content,X = 0.18, t (min)

Experiment Simulation

30[10] 443 1.62 3.1 180 0.03 104 103423 1.68 2.2 270 0.04 148 142403 1.63 1.2 450 0.06 247 229383 1.58 0.4 1260 0.12 765 689

10 443 1.75 12.9 50 0.02 26 27423 1.74 8.9 67 0.04 38 38403 1.66 4.8 110 0.06 67 63383 1.68 1.6 300 0.13 210 172

5 443 1.61 31.2 17 0.03 10 10423 1.66 22.4 21 0.04 14 14403 1.63 13.3 37 0.04 23 23383 1.61 4.3 95 0.14 79 71

2.5 443 1.44 84.6 5 0.02 3 3423 1.48 58.5 7 0.02 5 5403 1.46 36.1 11 0.04 8 7383 1.51 11.7 35 0.13 27 23


the initial radius (Rini = D/2 = 5, 2.5 and 1.25 mm)divided by 50, except for surface and center layers,which have the initial thickness of Rini divided by 100.The 51 layers are numbered from surface (1st) to center(51st), and outer radius of the n-th layer is representedby rn.

Weight and temperature in each layer are assumed tobe homogeneous, and the temperature of n-th layer, Tn,is represented by the midpoint in the radial direction for2 � n � 50. For the 1st and 51st layers, temperatures are

represented by the surface and center of the parti-cle, respectively. Distance from the representative pointof n-th layer to the next layer is defined as dn.Parameters used in this simulation are listed in

Table II. Transfer and consumption of heat, evapora-tion and transfer of water, shrinkage of lignite, andbehavior of water condensed on the surface are consid-ered as explained in the following sections. The modeldeveloped in a previous study[10] was modified in somerespects, and drying of lignite 30 mm in diameter wasthen recalculated using the new model and comparedwith the previous simulation.

B. Heat Transfer to the Surface

Initial temperatures of lignite are determined to be303 K and 318 K (30 �C and 45 �C) for the particle sizesof 10 and 5 mm, respectively, from Figure 6. Initialtemperature of lignite particles 2.5 mm, which isbelieved to be higher than that of the samples 5 mm,is assumed to be 333 K (60 �C). When the temperatureof the 1st layer, T1, is below 373 K (100 �C), heat flux tothe surface, DQ1, is believed to be accomplished mainlyby the condensation of steam. Assuming the condensedwater on the surface is 373 K (100 �C), the heat flux isexpressed by Eq. [5]

DQ1 ¼ hcond � 4pr21ð373� T1Þ � Dt; forT1<373; ½5�

where hcond is the condensing heat transfer coeffi-cient and r1 equals the radius of the particle, Rini. hcondwas assumed from experimental results to be5000 W m�2 K�1. Time step, Dt, is 0.001 second in thiscalculation.After T1 reaches 373 K (100 �C), the temperature is

maintained until the water on the surface dries up.Therefore, DQ1 equals heat flux to the inner layer, DQ2,which is defined in Section IV–C.

DQ1 ¼ DQ2; forT1 ¼ 373 andMsurf>0; ½6�

where Msurf is the weight of water on the surfaceintroduced in Section IV–E.

70

4000

Test temperature, Ta/K380 420 440 460

203040

30 mm10 mm5 mm

2.5 mm

10

5060

Initial water

Residual water

Wat

er p

erce

ntag

e,W

w/(W

w+W

c)

100(

mas

s%)

Fig. 7—Initial and residual water percentages.

300

280

320

340

360

380

400

0.61

0.63

0.65

0.59

0.57

Tem

pera

ture

, T/K

Wei

ght, W

/g

0.55

0.53

Time, t/min0 1 2 3

Tsurface

Tcenter

Tmidpoint

W

10 mm

443 K423 K403 K383 K

300

280

320

340

360

380

400

0.076

0.078

0.080

0.074

0.072

Tem

pera

ture

, T/K

Wei

ght, W

/g0.070

0.068

Time, t/min0 0.5 1

Tsurface

Tcenter

W

5 mm

443 K423 K403 K383 K

300

280

320

340

360

380

400

0.039

0.040

0.041

0.038

0.037

Tem

pera

ture

, T/K

Wei

ght, W

/g

0.036

0.035

Time, t/min0 1

W

443 K423 K403 K383 K

2.5 mmTsurface

0.5

(a)

(b)

(c)

Fig. 6—Temperatures and weights of the samples (a) 10 mm, (b)5 mm, and (c) 2.5 mm in diameter during the initial period.


After water on the surface evaporates, DQ1 is assumedto be accomplished by convection and radiation.Although the previous calculation used general formulasfor heat transfer by natural convection,[10] this study

uses the heat transfer coefficient, ha, derived fromexperimental results. Because DQ1 is believed to be usedonly for evaporation of water during CDRP, the linearrelationships in Figure 9(a) are regarded as an indica-tion of a proportional relationship between DQ1 andTa � T1. Equation [7] was derived from Eq. [1] and usedin this model.

ha ¼ vCDRPL=ðTa � 373Þ ¼ 0:0401=r1 þ 18:7; ½7�

where L is the latent heat of free water at 373 K(100 �C). DQ1 is expressed by Eq. [8]

DQ1 ¼ ha � 4pr21ðTa � T1Þ � Dt; for T1 � 373 and Msurf ¼ 0

½8�

C. Heat Transfer Inside the Lignite Particle

Heat input to the n-th layer from the outer layer byconduction, DQn, is expressed by Eq. [9]

DQn ¼ kn�1;n=ðdn�1 þ dnÞ � 4pr2nðTn�1 � TnÞ � Dt;for 2 � n � 51;

½9�

where kn�1;n is thermal conductivity between adjacentlayers. kn�1;n is expressed by Eq. [10]

10

4Moi

stur

e co

nten

t, X

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

0

Time, t/min0 10 20

-dX/dt

16

20

X

30 40 50

10 mm

CDRP DDRP

0.0

0.4

1.6

2.0

1.0

1.8

1.41.2

0.80.6

0.2 2

86

18

1412

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

0.0

0.4

1.6

2.0

20

10

Moi

stur

e co

nten

t, X

0

Time, t/min0 5 10

-dX/dt1.0

30

40

X

20

1.8

1.41.2

0.80.6

0.2

50

15

5 mm

CDRP DDRP

0.0

0.4

1.6

60

40

Moi

stur

e co

nten

t, X

0

Time, t/min0 1 2

-dX/dt

1.080

100

X

1.8

1.41.2

0.80.6

0.2

120

653 4

2.5 mm

20

CDRP DDRP

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

(a)

(b)

(c)

Fig. 8—Moisture contents and drying rates of the samples (a)10 mm, (b) 5 mm, and (c) 2.5 mm in diameter at 443 K (170 �C).

380

0.4

0

Eva

pora

tion

rate

, vC

DR

P/ (g

m−2

s−1 )

Test temperature, Ta/K360 420 460

1.01.2

1.8

400

0.80.6

30 mm10 mm5 mm

2.5 mmEq. [1]

0.2

1.41.6 (a) CDRP

440

380

0.4

0E

vapo

ratio

n ra

te, v

ave/(

g m

−2s−

1 )

Test temperature, Ta/K360 420 460

1.01.2

1.8

400

0.80.6

30 mm10 mm5 mm

2.5 mmEq. [2]

0.2

1.41.6 (b) Entire drying process

440

Fig. 9—Evaporation rates during (a) the constant drying rate periodand (b) entire drying process.


kn�1;n ¼ ðdn�1 þ dnÞ=dn�1kn�1

þ dnkn

� �; for 2 � n � 51

½10�

kn ¼ uwkw þ uckc þ usks ½11�

uw þ uc þ us ¼ 1; ½12�

where kn is thermal conductivity of the layer calculatedusing Eq. [11] from thermal conductivity and volume

fraction of water, coal, and steam (Table II). There is noheat transfer from the center layer (n ¼ 51).

D. Heat Consumption

Difference between heat input and output of the n-thlayer, DQn � DQnþ1, is consumed by rising temperatureor evaporation of water depending on conditions. Theheat consumption is expressed by Eq. [13]

DQn � DQnþ1 ¼ CcMc;n þ CwðMw;n � DMevap;nÞ� �

DTn

þ DMevap;nDHevap

½13�

where Cc and Cw are the specific heat of coal and water,Mc;n and Mw;n are the weight of coal and water in thelayer, DTn is the temperature increase, DMevap;n is theweight of water evaporated from the layer, and DHevap isthe enthalpy change of the water evaporation. Thermalcapacity of steam is neglected.When Tn is below 373 K (100 �C), the heat is

consumed only to increase the temperature, andEq. [13] is substituted by Eq. [14]

DQn � DQnþ1 ¼ ðCcMc;n þ CwMw;nÞDTn ½14�

After Tn reaches 373 K (100 �C), the heat is used onlyfor evaporating free water. Because DTn is zero during

Free water

(a) Initial

(b) CDRP

Surface Center

Coal + Bound water

(c) DDRP

Steam

Bound water evaporating

Superheatedsteam

Evaporationof free water

Evaporation of free water and bound water

Drying process

Transfer of free water

Transfer of free water

Fig. 11—Schematic illustration of drying process. (a) Initial state, (b) constant drying rate period, and (c) Decreasing drying rate period.

100

0.005

0Slop

e of

eva

pora

tion

rate

,(Δv/

ΔTa)/

(g m

−2s−

1K

−1)

Inverse of particle diameter, D−1/m−10 400 500

0.015

0.025

200

0.010

CDRPEntire drying process

0.020

300

Fig. 10—Relationship between slope of evaporation rate in Fig. 9and inverse of particle diameter.


this period, Eq. [13] is substituted by Eq. [15], where L isthe latent heat of free water at 373 K (100 �C).

DQn � DQnþ1 ¼ DMevap;nL ½15�

When the moisture content in the layer, Xn, becomes0.56, free water is regarded as having evaporatedcompletely.[10,13,14] Thereafter, the heat is used for bothevaporating bound water and increasing temperature.The Newton method is used to simulate drying duringthis period, assuming the relationship between T and Xfollows the equilibrium moisture content curve inFigure 13, which was assumed in the previous study.[10]

When bound water evaporates above 373 K (100 �C),DHevap is assumed to be larger than that for free water.In the previous study,[10] DHevap was expressed as afunction of the evaporating temperature based onthermodynamic information on bound water in lig-nite.[15] This study used the same equation shown byEq. [16]

DHevap ¼ 2:932� 106 � 6:76� 105 � expð�0:077ðT� 373ÞÞ½16�

Figure 14 shows the relationship between DHevap andX.

E. Condensation, Exudation, and Water Droplets Fallingon the Surface

In the same manner as the previous study,[10] thetemperature dependence of water density was consid-ered because expansion of water in the lignite wassignificant during the condensation period (Table II).The expanded water was assumed to exude on thesurface and to form droplets with condensed steam.

Therefore, the weight of the water on the surface, Msurf,is defined as Eq. [17]

DMsurf ¼ ðDQ1 � ha � 4pr21ðTa � 373Þ � DtÞ=Lþ DMex;

forT1 � 373

½17�

where DMex is the weight of the exuded water. Msurf is 0in the initial state.Sizes of the falling droplets and their frequency

depended on Rini in experiments. For convenience, thisstudy used the model shown in Figure 14 to formulatethe relationship between the size of a droplet and Rini.Water was assumed to form a thin layer on the surfaceof lignite and to have a hemispheric droplet hangingfrom its bottom. Angle h in Figure 14 gives the relationof sinh¼rwd=Rini, where rwd is the radius of the droplet.The droplet was assumed to be bound under the ligniteby surface tension, of which the vertical component isapproximately expressed by 2prwdc� cosh. If the grav-itational force acting on the droplet is expressed as4pr3wd=3� g�A, the bonding force between lignite andwater droplet equals the gravitational force when

r2wdcos h

¼ 3c2gA

½18�

The relation of cos h¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�ðrwd=RiniÞ2

qgives Eq. [19]

rwd ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðE=RiniÞ4 þ 4E2

q� ðE=RiniÞ2

2

0@

1A

1=2

½19�

where E ¼ 3c=2gA.In measurements of the samples with D = 10 mm,

the weight of a falling droplet observed at 383 K

Surface(1st layer)2nd layer 3rd layer

T2

T3

T1

d1 d2

d3

n-th layer Tndn

Water + Dry coal(Initial)

Superheated steam

∆Q1

rn

r1

Center(51st layer ) T51d51

∆Qn

Fig. 12—Simulation model.


Table

II.

InputParametersforSim

ulation

Parameter

Correlation/V

alue(T:Tem

perature

(K))

Source

Properties

oflignite(raw

coal)

uc,ini

Initialvolumefractionofcoal

0.30

10

uw,ini

Initialvolumefractionofwater

0.70

10

us,ini

Initialvolumefractionofsteam

010

Tn,ini

Initialtemperature

303K,303K,318K,and333K,forD

=30,10,5and2.5

mm

Thisstudy

Properties

ofcoal(dry

coal)

q cDensity

1434(kgm�3)

10

Cc

Specific

heat

1.28

9103(J

kg�1K�1)

10

kc

Thermalconductivity

0.20(W

m�1K�1)

10

Properties

ofwater(free

waterandboundwater)

q wDensity

5.12

910�6T

3�

8.18

910�3T

2+

3.24T+

621(kgm�3)

21

Cw

Specific

heat

1.85

910�5T

3�

8.35

910�3T

2�

2.75

910�1T+

4519(J

kg�1K�1)

21

kw

Thermalconductivity

�8.71

910�6T

2+

6.76

910�3T�

0.635(W

m�1K�1),forT

£373

22

�5.29

910�6T2+

4.33

910�3T�

0.202(W

m�1K�1),forT

>373

22

Properties

ofsteam

ks

Thermalconductivity

1.16

910�7T

2�

1.18

910�5T+

0.0130(W

m�1K�1)

22

Parametersforheatinput

hcond

Heattransfer

coefficientbycondensation

5000(W

m�2K�1)

Thisstudy

ha

Heattransfer

coefficientin

test

section

0.0401/r1+

18.7

(Wm�2K�1)

Thisstudy

Ta

Testtemperature

443K,423K,403K,and383K

Thisstudy

Assumptionsofdryingprocess

LLatentheatoffree

water

2.256

9106(J

kg�1)

21

DH

evap

Enthalpychangeofboundwaterevaporation

2.932

9106�

6.76

9105exp(�

0.077(T�

373))(J

kg�1)

10

Xeq

Equilibrium

moisture

content

7.06

910�1/(T–372)+

6.23

910�3,for373

£T

£383

10

�7.43

910�7T

3+

9.58

910�4T

2�

4.12

910�1T+

59.1,forT

>383

r wd

Maxim

um

radiusofawaterdropletonthesurface

(((E

/Rini)4+

4E2)1/2�(E/R

ini)2)/2)1/2,E=

1.05

910�5m

2Thisstudy

dsurf

Maxim

um

thicknessofwaterfilm

onthesurface

4.1

910�5m

Thisstudy

KApparenttransfer

coefficientoffree

water

3.0

910�9(m

2s�

1)

10

1-l/lini

Linearshrinkage

�0.269(V

w/V

w,ini)3+

0.655(V

w/V

w,ini)2�0.547

9(V

w/V

w,ini)+

0.162

10

Sim

ulationconditions

Dt

Tim

estep

0.001s

Thisstudy(SectionIV

–B)


(110 �C) was 0.05 g (Figure 6). On the assumption thatthe droplet is hemispheric, rwd is calculated to be2.9 9 10�3 m, and thus E in Eq. [19] is 1.05 910�5 m2. Using this value, rwd for D = 30 mm iscalculated to be 3.2 9 10�3 m by Eq. [19]. Weight ofthe hemispheric droplet with this radius is 0.07 g, whichgives an acceptable fit with the weight of dropletobserved in the previous study.[10] Consequently,Eq. [19] with E = 1.05 9 10�5 m2 was adopted insimulation, and the relationship between Rini and rwdis shown in Figure 14. On the other hand, the thicknessof water film formed on the surface was estimated fromsimulation results in the previous study,[10] where awater droplet of 0.08 g fell from a 30 mm particle whenthe weight of surface water became 0.19 g. Assuming theremaining 0.11 g of water was forming a layer, itsthickness, dsurf, was 4.1 9 10�5 m. A falling droplet isassumed to occur if the weight of surface water, Msurf,exceeds the sum of a hemispheric water droplet with

radius of rwd and water film with a thickness of4.1 9 10�5 m.

F. Transfer of Free Water

Free water in lignite is thought to be transferred bycapillary pressure gradient, diffusion, or vapor pressuregradient.[16,17] Because of the difficulty in formulatingthese factors, previous study[10] assumed that the trans-fer can be approximately expressed by the moisturecontent as in Eq. [20]

DMtrans;n ¼ �Kqc �4pr2nþ1

dn þ dnþ1ðXn � Xnþ1Þ � Dt;

for n � 50 and Xnþ1>0:56;

½20�

where DMtrans;n is water transfer from (n+1)th layer ton-th layer, and K is the apparent transfer coefficient, and

02000

Enth

alpy

cha

nge

of v

apor

izat

ion,

ΔHev

ap/(k

J kg

−1)

Moisture content, X0.6 0.8 1.00.2

2200

2400

2600

2800

3000

400

Tem

pera

ture

,T/K

420

440

460 3200

ΔHevap

T

0.4360

380

Bound water Free water

L

Drying process

Fig. 13—Relationships between moisture content, enthalpy changeof water vaporization and evaporating temperature under atmo-spheric pressure.

Approximate curveExperimental results

5

0.50

Radi

us o

f a w

ater

dro

plet

, rw

d/mm

Radius of a lignite particle, Rini/mm2.5 15 17.5 20

1.52.0

3.03.54.0

10

1.0

2.5

7.5 12.5

Rini θ

rwd

dsurf

θ

Fig. 14—Simple model for a water droplet and film attached to the surface of a lignite particle and relationship between the radius of a ligniteparticle and that of a water droplet.

300280

320340

420440460

2.02.53.0

1.51.00.50.0

Time, t/h0 1 2 3

-dX/dt

400

360380

3.54.04.5

Tem

pera

ture

, T/K

X

Tsurface

TcenterTmidpoint

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

1.5

Moi

stur

e co

nten

t, X

1.8

1.2

0.9

0.6

0.3

0.0

Fig. 15—Simulated moisture content, drying rate, and temperaturesof the samples 30 mm in diameter at a test temperature of 443 K(170 �C) compared to those in a previous study.[10] Black solid linesrepresent simulation results in this study. Gray solid lines and da-shed lines represent simulation and experimental results, respectively,in a previous study.


was assumed to be 3 9 10�9 (m2 s�1) which fittedexperimental results in the previous study.[10] This studyadopts Eq. [20] and the same value for K in modeling.

G. Shrinkage

When water in lignite evaporates, its space is thenoccupied by steam (Section IV–A) in this model. Tosimulate the volume change of lignite during the drying,the volume of steam is assumed to decrease. Linearshrinkage of lignite, 1� l=lini, caused by drying has been

examined in previous study, and expressed as a functionof water volume fraction[10]

1� l=lini ¼ � 0:269� Vw

Vw;ini

� �3

þ0:655� Vw

Vw;ini

� �2

� 0:547� Vw

Vw;ini

� �þ 0:162: ½21�

280

330

430

480

10

5

0

Time, t/min0 10 20

-dX/dt

380

15

20

Tem

pera

ture

, T/K

X

Tsurface

TcenterTmidpoint

30 40 50

10 mm

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

1.5M

oist

ure

cont

ent, X

2.0

1.0

0.5

0.0

0

10

30

40

Time, t/min0 5 10

-dX/dt 20X

Tsurface

Tcenter

15 20

5 mm

Tem

pera

ture

, T/K

280

330

430

480

380

50

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

1.5

Moi

stur

e co

nten

t, X

2.0

1.0

0.5

0.0

0

20

60

80

Time, t/min0 1 2

-dX/dt 40X

Tsurface

3 6

2.5 mm

Tem

pera

ture

, T/K 420

460

380

120

100440

400

360340320300280

4 5 Dry

ing

rate

, (-dX/

dt)

104 /s

−1

1.5

Moi

stur

e co

nten

t, X

1.8

1.2

0.9

0.6

0.3

0.0

(a)

(b)

(c)

Fig. 16—Simulated moisture contents, drying rates, and temperaturesof the samples (a) 10 mm, (b) 5 mm, and (c) 2.5 mm in diameter at atest temperature of 443 K (170 �C). Black solid lines and gray dashedlines represent results of simulation and experiments, respectively.

300

280

320

340

360

380

400

0.61

0.63

0.65

0.59

0.57

Tem

pera

ture

, T/K

Wei

ght, W

/g

0.55

0.53

Time, t/min0 1 2 3

Tcenter

Tmidpoint 443 K403 K Simulation

W

10 mm

423 K383 K

383 K

403 K 423 K443 K

Tsurface

300

280

320

340

360

380

400

0.076

0.078

0.080

0.074

0.072

Tem

pera

ture

, T/K

Wei

ght, W

/g

0.070

0.068

Time, t/min0 0.5 1

Tsurface

TcenterW

5 mm

443 K 403 K Simulation

423 K 383 K

383 K 403 K

423 K 443 K

300

280

320

340

360

380

400

0.039

0.040

0.041

0.038

0.037

Tem

pera

ture

, T/K

Wei

ght, W

/g

0.036

0.035

Time, t/min0 1

W

2.5 mmTsurface

0.5

383 K

403 K

423 K443 K

443 KSimulation

423 K 403 K 383 K

(a)

(b)

(c)

Fig. 17—Simulated temperatures and weights compared to experi-mental results during the initial period. (a) 10 mm, (b) 5 mm, and (c)2.5 mm.


In the simulation of drying behaviors, thickness ofeach layer was defined as the product of initial thicknessand the linear shrinkage, from which dn and rn were also

derived in every time step. Volume loss is counted as thechange in the volume of steam at each layer.

V. SIMULATION RESULTS AND DISCUSSION

In Figure 15, simulation results for a lignite particlewith D = 30 mm dried at 443 K (170 �C) are com-pared with the previous model.[10] Although the mod-ification of heat input (Section IV–B) caused minordeviations of the simulated drying rates and tempera-tures, the moisture contents coincided well, suggestinga practical applicability of a new model to coarselignite particles.Figure 16 shows simulation results compared to

experimental results at 443 K (170 �C) for the sampleswith D = 10, 5, and 2.5 mm, respectively. The exper-imental drying rates were smoothed by calculating theirmoving averages of 20 seconds. Simulated moisturecontents, drying rates, and Tsurface agree well with theexperimental results. Temperatures of inner parts(Tmidpoint and Tcenter), however, started rising from373 K (100 �C) earlier in the experiments than in thesimulated results. One possible reason for these devia-tions is measurement errors caused by conductive heattransfer along thermocouples from outside a sample, asreported in other studies.[8,18] Another reason is thoughtto be the diffusion of bound water in lignite, which is notconsidered in this model.Figure 17 shows temperatures and weights of lignite

during the initial period of drying. A falling droplet wasobserved in the simulation for a sample 10 mm in diameterat 383 K (110 �C), similar to the experiment. Figure 18shows the drying characteristic curves from experimentaland simulation results to be in good agreement.For confirmation of the availability of the simulation

model, time required to achieve the target moisturecontent was calculated. This target value is set at15 mass pct,[19,20] which corresponds to X = 0.18. Asshown in Table I, differences between the calculationand experiments are larger at lower drying temperature.This is because the evaporation of water becomes slighttoward the end of drying especially at low temperatures,and the results seem acceptable.

VI. CONCLUSIONS

The drying of 10, 5, and 2.5-mm-diameter ligniteparticles was observed in superheated steam at temper-atures ranging from 383 K to 443 K (110 �C to 170 �C)under atmospheric pressure. Weights and temperaturesof the samples were measured during the drying, and theresults showed typical drying characteristics includingCDRP and DDRP. Dependence of the drying rate onparticle size was determined, and the heat transfer fromsuperheated steam to lignite surface was evaluated as afunction of this size. Generation of cracks during dryingalso depended on the temperature and particle size.

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

Moisture content, X0.0 0.5 1.0 1.5

443 K

423 K

403 K

383 K

2.0

81012

6420

141618

10 mmD

ryin

g ra

te, (

-dX/

dt)

104 /s

−1

202530

151050

Moisture content, X0.0

3540

0.5 1.0 1.5

443 K

423 K 403 K

383 K

2.0

5 mm

Dry

ing

rate

, (-dX/

dt)

104 /s

−1

60

80

40

20

0

Moisture content, X0.0

100

120

0.5 1.0 1.5

443 K 423 K403 K

383 K

2.0

2.5 mm

(a)

(b)

(c)

Fig. 18—Drying characteristic curves of samples (a) mm 10, (b)5 mm, and (c) 2.5 mm in diameter (experimental and simulation re-sults). Black solid lines and gray dashed lines represent results ofsimulation and experiments, respectively.


A numerical model previously developed for thedrying of a coarse lignite particle has been modifiedmaking it applicable to smaller particles based on thepresented results. The model can predict the behavior oflignite particles ranging from a few millimeters to severalcentimeters in size and dried at temperatures from383 K to 443 K (110 �C to 170 �C), making it applicablefor simulations of drying behaviors of lignite of a varietysize distribution in various dryers when an appropriateheat transfer coefficient is given.

ACKNOWLEDGMENTS

The authors acknowledge financial support from theJapan Coal Energy Center. Lignite for samples wassupplied by Mitsubishi Heavy Industries, LTD.

LIST OF SYMBOLS

C Specific heat at constant pressure, J kg�1 K�1

D Initial diameter of the sample, md Distance from the representative point of the

layer to the next layer, mdsurf Critical thickness of surface-water film, mDH Enthalpy change, J kg�1

h Heat transfer coefficient, W m2 K�1

K Apparent transfer coefficient, m2 s�1

k Thermal conductivity, W m�1 K�1

L Latent heat of water vaporization underatmospheric pressure, J kg�1

l Length, mM Weight of coal or water (in simulation), kgDQ Heat transfer, JR Radius of the sample, mr Outer radius of the layer, mrwd Critical radius of a water droplet attached to

the surface of lignite, mT Temperature, Kt Time, seconds or minutes or hours (shown in

each Figure)tcomp Time to complete superheated steam drying, sDt Time step, secondsV Volume, m3

W Weight (in experiments), gX Moisture content, dimensionless (kg-H2O/kg-

dry coal)Xeq Equilibrium moisture content, dimensionless

(kg-H2O/kg-dry coal)

GREEK SYMBOLS

q Density, kg m�3

u Volume fraction, dimensionless

SUBSCRIPTS

a Ambient (superheated steam)ave Average throughout the drying processc Coal (dry coal)center Center of a lignite particleCDRP Constant drying rate periodcond Condensationevap Evaporation of waterex Exuded waterini Initialmidpoint Midpoint between the center and the surface

of a lignite particlen Number assigned to the layers Steamsurf Water on the surfacesurface Surface of a lignite particletrans Transfer of waterw Water

REFERENCES1. A.W. Clarke and J.A. Trinnaman: 2010 Survey of Energy

Resources, World Energy Council, UK, 2010.2. S.V. Jangam, M. Karthikeyan, and A.S. Mujumdar: Dry. Tech-

nol., 2011, vol. 29, pp. 395–407.3. O. Hoehne, S. Lechner, M. Schreber, and H.J. Krautz: Dry.

Technol., 2010, vol. 28, pp. 5–18.4. D. Stokie, M.W. Woo, and S. Battacharya: Energy Fuels, 2013,

vol. 27, pp. 6598–6606.5. A. Tahmasebi, J. Yu, Y. Han, H. Zhao, and S. Battacharya: Asia-

Pac. J. Chem. Eng., 2013, vol. 8, pp. 793–803.6. D. Jeon, T. Kang, H. Kim, S. Lee, and S. Kim: Science China,

2011, vol. 7, pp. 1680–83.7. H.S. Kim, Y. Matsushita, M. Oomori, T. Harada, J. Miyawaki,

S.H. Yoon, and I. Mochida: Fuel, 2013, vol. 105, pp. 415–24.8. K. Zhang and C. You: Energy Fuels, 2010, vol. 24, pp. 6428

36.9. A.Y. Looi, K. Golonka, and M. Rhodes: Chem. Eng. J., 2002,

vol. 87, pp. 329–38.10. T. Kiriyama, H. Sasaki, A. Hashimoto, S. Kaneko, and M.

Maeda: Mater. Trans. JIM, 2013, vol. 54, pp. 1725–34.11. Y. Fei, A.A. Aziz, S. Nasir, W.R. Jackson, M. Marshall, J.

Hulston, and A.L. Chaffee: Fuel, 2009, vol. 88, pp. 1650–55.12. R. Toei, M. Okazaki, M. Kimura, and K. Kubota: Chem. Eng.

Jpn, 1966, vol. 30, pp. 949–50.13. D.J. Allardice, L.M. Clemow, G. Favas, W.R. Jackson, M.

Marshall, and R. Sakurovs: Fuel, 2003, vol. 82, pp. 661–67.14. Y. Fei, A.L. Chafee, M. Marshall, and W.R. Jackson: Fuel, 2005,

vol. 84, pp. 1557–62.15. D.J. Allardice and D.G. Evans: Fuel, 1971, vol. 50, pp. 201–10.16. R.B. Bird, W.E. Stewart, and E.N. Lightfoot: Transport Phe-

nomena, 2nd ed., John Wiley & Sons, New York, 2006, pp. 764–804.

17. L.A. Richards: J. Appl. Phys., 1931, vol. 1, pp. 318–33.18. T. Inoue, H. Iyota, N. Nishimura, and T. Nomura: Trans. Jpn.

Soc. Mech. Eng. B, 2007, vol. 73, pp. 1068–76.19. J. Ewers, H.J. Klutz, W. Renzenbrink, and G. Scheffknecht: VGB

PowerTech, 2003, vol. 11, pp. 60–65.20. H.J. Klutz, C. Moser, and D. Block: VGB PowerTech, 2006,

vol. 11, pp. 2–6.21. W. Wagner and A. Pruß: J. Phys. Chem. Ref. Data, 2002, vol. 31,

pp. 387–535.22. JSME Data Book: Thermophysical Properties of Fluids, The Japan

Society of Mechanical Engineers, Tokyo, 1983.


size dependence of the drying characteristics of single lignite

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