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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).
METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—351
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.
352—VOLUME 1E, DECEMBER 2014 METALLURGICAL AND MATERIALS TRANSACTIONS E
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.
METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—353
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
354—VOLUME 1E, DECEMBER 2014 METALLURGICAL AND MATERIALS TRANSACTIONS E
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.
METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—355
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.
356—VOLUME 1E, DECEMBER 2014 METALLURGICAL AND MATERIALS TRANSACTIONS E
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.
METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—357
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.
358—VOLUME 1E, DECEMBER 2014 METALLURGICAL AND MATERIALS TRANSACTIONS E
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)
METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—359
(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.
360—VOLUME 1E, DECEMBER 2014 METALLURGICAL AND MATERIALS TRANSACTIONS E
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.
METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—361
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.
362—VOLUME 1E, DECEMBER 2014 METALLURGICAL AND MATERIALS TRANSACTIONS E
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
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METALLURGICAL AND MATERIALS TRANSACTIONS E VOLUME 1E, DECEMBER 2014—363