Agglomerate formation during coal combustion: A mechanistic model

Agglomerate formation during coal combustion: A mechanistic model

COMBUSTION A N D F L A M E 86: 258-268 (1991) 258 Agglomerate Formation During Coal Combustion: A Mechanistic Model SHIN-WON KANG Department of Mech...

748KB Sizes 3 Downloads 207 Views

COMBUSTION A N D F L A M E 86: 258-268 (1991)

258

Agglomerate Formation During Coal Combustion: A Mechanistic Model SHIN-WON KANG Department of Mechanical Engineering and

ADEL F. SAROFIM and J~,NOS M. BEi~R Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

During the plastic stage of coal pyrolysis, there is competition between centrifugal force, which favors the breakup of coal agglomerates, and adhesive force between coal particles. A theoretical model of agglomeration was developed to investigate the adhesive force between contiguous coal particles in an agglomerate. The adhesive force in the process of agglomeration of coal particles was found to be proportional to the duration of plasticity of the particles. It was also found that rapid heating reduces the tendency of coal particles to form agglomerates during the plastic stage of coal pyrolysis. Therefore, whether particles burn individually or as agglomerates can be influenced by the temperature history of the coal or coal-water fuel (CWF) particles and hence by burner design.

NOMENCLATURE

FE3 A dA/dt (~i

C

k E

Eth FA Fe

Eel Fe2 0010-2180/91/$3.50

contact area growth rate of contact area mass fraction of unreacted coal initial mass fraction of unreacted coal (-- 1 - f a ) volume fraction of unreacted coal mass fraction of coke residue (char) volume fraction of coke residue (char) threshold volume fraction of coke residue (char) [ - (1 - f a ) / 2 ] adhesive force between two coalescing coal particles adhesive force due to coke interconnection adhesive force due to coke interconnection in stage 1 adhesive force due to coke inter-

F~ fa fa kl kil L L Ls /elf rc rm r*

connection in stage 2 adhesive force due to coke interconnection in stage 3 surface tension force due to liquid metaplast mass fraction of ash (mineral matter) volume fraction of ash (mineral matter) rate constant in Eq. 3 rate constant in Eq. 4 mass fraction of liquid metaplast volume fraction of liquid metaplast mass fraction of solid metaplast initially existing in coal effective circumference radius of coal particle rate of physical melting radius of contact area in neck region Copyright © 1991 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 655 Avenue of the Americas, New York, NY 10010

AGGLOMERATE FORMATION DURING COAL COMBUSTION Tm Tp t Normalized A

mean melting temperature of coal particle temperature of droplet/ agglomerate time normalized contact area, given by A /rr 2

Greek Symbols 7 7c 0 #* Pa

pc Ol ae or

surface tension surface tension of liquid metaplast contact angle viscosity viscosity of liquid metaplast density of ash (mineral matter) density of unreacted coal density of liquid metaplast bond stress of coke residue (char) standard deviation of melting temperature of coal

1. INTRODUCTION The formation of agglomerates during the combustion of coal or coal-water fuel (CWF) is of concern because of both the increased burning times of the agglomerates and their potential for forming large ash particles, which can be deposited on surfaces by inertial forces. The agglomerates are produced by either particle collision during dense-phase feeding of pulverized coal or the adhesion of coal particles in a CWF droplet during the evaporation of the interstitial water. Such initial agglomeration is further strengthened by the plasticity of pyrolyzing bituminous coals. The question to be addressed in this paper is whether the particles in an agglomerate produced by either mechanism break apart as a result of thermal stresses or intertial forces during devolatilization or fuse together in the temperature interval during which the coal is plastic. The extent of fusion depends on the duration of the plastic period, which is strongly affected by both the time-temperature history of the coal particles and the coal type. When the duration of the plastic period is

259

long enough for particles to fuse and coalesce, a strongly fused agglomerate will be formed. Due to the strong adhesive force between contiguous coal particles, the agglomerates will be less likely to break up, thus requiring increased residence times for complete burnout and forming oversized ash particles. In contrast, when the duration of the plastic period is so short that coal particles cannot completely fuse and coalesce, a loosely fused agglomerate will be formed, the adhesive force between contiguous coal particles will be weak, and the agglomerates will easily break up, resulting in better combustion and finer fly-ash particle size. Consequently, the plasticity-time history of the coal particles is found to be important for the study of agglomeration. Combustion experiments with coal particles and CWF droplet streams in a laminar flow reactor (LFR) showed the importance of particle rotation induced by the volatile evolution on the breakup of coal agglomerates and the release of ash particles [ 1, 2]. Particle rotation during devolatilization and char combustion generates centrifugal force at the particle surface, which can promote the separation of both weakly adhering char fragments and ash particles. During the plastic stage of coal pyrolysis, there is competition between centrifugal force, which favors the breakup of coal agglomerates, and adhesive force between coal particles. Hence, whether particles burn individually or as agglomerates can be influenced by the temperature history of the coal or CWF particles and by burner design.

2. T H E O R E T I C A L MODEL

A. Plasticity of Bituminous Coal While heating bituminous coal to about 400°C or above, the transient occurrence of plastic behavior of coal particles can be observed. We have adopted the metaplast theory [3, 4] modified by Fong et al. [5], which provides a quantitative, readily usable description of the transient viscosity of the coal during pyrolysis. The objective of the present contribution is to make use of the metaplast theory for predicting the

260

S.-W. KANG ET AL.

adhesive force between agglomerating coal particles. According to the metaplast theory, a liquid

metaplast is generated and depleted by the following pyrolytic reactions:

kl

Coking coal (C) ---*metaplast (L) ~ semicoke ~ coke

primary gas

secondary gas

where t~ and L are the mass fractions of unreacted coal and liquid metaplast, respectively. The rate of change with time of the fractions of the unreacted coal and the liquid metaplast, respectively, can be given as

where C and L are the mass fractions of unreacted coal and liquid metaplast, respectively, rm is the rate of physical melting, and kl and kn are the rate constants. The initial conditions of Eqs. 3 and 4 are

d~

~(0) --ci

--

dt

dL dt

-

O)

-kiC,

and -- R I G - k i l l

-

knlL.

(2) L(0) = 0 ,

It is assumed that the above reactions are first order with respect to C and L. Fong et al. elaborated on this model by taking into account the liquid formed by physical melting. According to Fong et al.'s model, some fraction of the liquid is initially formed by physical melting above a critical temperature. With a further temperature increase, pyrolytic bond breaking generates additional liquid. Simultaneously, the liquid forms a volatile product, which escapes from the coal and leaves a solid coke residue. The reaction scheme and corresponding rate expressions during the plasticity of bituminous coal particles are, according to Fong [6], Coal (t~)

~ physical melting rm

liquid metaplast (L)

=~I~coke (/~) and volatiles (170

d~ dt

dL dt

(5)

--

kl(~ -rm,

-- k t C

+ rm - k n L .

(3)

(4)

(6)

where C i is the initial mass fraction of unreacted coal, given by 1 - m a s s fraction of mineral matter

L For the calculation of the adhesive force that develops between contiguous coal particles during the plastic stage of their pyrolysis, information is needed on the volume fractions of the unreacted coal, C, the liquid metaplast, L, the coke, E, and the mineral matter, fa. The adhesive force is also dependent upon the contact area or "neck" between agglomerating particles, which in turn is dependent on the liquid metaplast volume fraction, L. In the following mathematical treatment, relationships for the temporal variation of the volume fractions C, L, E, and f~ are developed first, followed by those for the contact area between agglomerating particles and eventually the adhesive force.

B. Determination of C, L, E, and fa From Eqs. 3 and 5, we can express the mass fraction of unreacted coal (C) as a function of the reaction rate constant ki and the physical melting

AGGLOMERATE FORMATION DURING COAL COMBUSTION rate rm as

C

=exp(-footkldt) × [foot(-rm)exp (ftkl dt) dt +C il . (7)

Further, from Eqs. 4, 6, and 7, the mass fraction of liquid metaplast (L) is derived as

L = exp (-~oo'kndt) { footeXp( footkndr) ×Irm+Cik~ exp (- fotk~dr) + kl exp

(/o')/o - kldt

exp

(

(8)

\-dt-)

'

where Tp is the temperature of the coal particle, Tm is the mean melting temperature of the coal particle (623 K), is the heating rate of the coal particle, aT is the standard deviation of the melting temperature (30 K), and Ls is the mass fraction of solid metaplast initially existing in the coal. The rate constants ki and kn are obtained from experimental data for a Pittsburgh Seam bituminous coal [5] as follows:

dTp/dt

6.6

× 10 7

where t~ denotes the mass fraction of unreacted coal, given by Eq. 7, and denotes the density of unreacted coal. From Eqs. 7 and 11, the volume fraction of unreacted coal (C) is expressed as

pc

C = pc--Iexp(-footkldt) × [~oo'(-rm)exp(footkldt) dt+(~i]. (12)

2a~

(9)

kI =

(11)

Pc

The rate of physical melting (rm) is given according to Fong et al. [5] by the heating rate of the coal particle, multiplied by a Gaussian distribution of melting points, centered at a mean melting temperature of 623 K with a standard deviation of 30 K, as

~

In the present model, it is assumed that swelling due to expansion of volatile bubbles in the liquid metaplast is not significant, and therefore the radius of the CWF agglomerate remains constant (i.e., assumption of negligible swelling). It is also assumed that volatile bubbles formed in the liquid metaplast escape instantly and leave porous coke residue in the liquid metaplast, and that a coal particle during the agglomeration process consists of unsoftened coal, liquid metaplast, mineral matter, and porous coke residue. Based on the above assumptions, the volume fractions of each component will be derived as follows. The volume fraction of unreacted coal (C) is C -- 1 C ,

(-rm)

×exp (ftk, dt) dt] dt}.

rm =

261

exp(-14,500/Tp) s - l

L -- 1 L , Pl

(13)

where/S denotes the mass fraction of liquid metaplast, given by Eq. 8, and Pl is the density of liquid metaplast. From Eqs. 8 and 13, and volume fraction of liquid metaplast (L) is expressed as L - - - - 1 exp pl

- kn dt kn dt (1'){I (1')

(10)

exp

X [rm+(~ikl exp (- footkldr) +kiexp

and ku --- 1.9 × 101° exp(-21,200/Tp) s -1.

The volume fraction of liquid metaplast (L) is

- tkidt ) (foo

×~oot(-rm)exp (~tkldt) dt] dt} .

(14)

262

S.-W. KANG ET AL.

The volume fraction of mineral matter 0Ca) is fa = 1 • .

(15)

Oa Using the above values for C, L, and fa and the previously stated assumption of negligible swelling, the volume fraction of coke (E) is derived as (16)

E=I-C-L-fa.

C. Development of Contact Area During Particle Agglomeration During the particle agglomeration process, coal particles in the agglomerate fuse and coalesce, and the contact area between the contiguous coal particles increases until the liquid metaplast in the coal is completely depleted. Theoretical calculations of the sintering of a Newtonian viscous fluid, using the approximate flow field of simple uniaxial contraction, were made by Frenkel [7]. He derived a neck growth rate law for the sintering of two spheres. This law was verified by other authors [8-10] to determine the accuracy of time dependency and expressed as A = ~

t,

(17)

where A is the contact area at time t, r the radius of the coalescing sphere, 3' the surface tension of the coalescing sphere, # the apparent viscosity of the coalescing sphere, and t is time. The growth rate of this contact area during the agglomeration process for coal particles, d A / d t , is expressed as d A - 3 ( 72) d t

"

(18)

Using a concentrated suspension model of Frankel and Acrivos [11], the apparent viscosity of liquid, #, is assumed to depend on the viscosity of the solids-free liquid,/**, and on the volume fraction of solids in the liquid, 1 - L, where L is the volume fraction of liquid metaplast discussed in Section 2.B. Their relationship for apparent vis-

cosity is

(9/8)#* P = (1 - L ) -U3 - 1"

(19)

Frankel and Acrivos found that this expression agreed well with experimental data over a wide range of volume fractions of solids (i.e., 0.4 < 1 - L < 1.0). This implies that 0 < L < 0.6, which is compatible with the calculated values of L in the present modeling effort. In the present model, the major emphasis is on the effect of liquid metaplast fraction L on viscosity. An average value of #* is estimated from Nazem's [12] work on carbonaceous mesophase pitch at a temperature of 623 K neglecting the temperature dependence. The surface tension of the liquid metaplast is assumed to be constant, neglecting the small decrease with increasing temperature as reported in the literature for coal liquids [13], y = %.

(20)

From Eqs. 18-20, the growth rate of the contact area between contiguous coal particles during agglomeration, d A / d t , is derived as dA dt

4rc3,c 3#* [(1 - L ) -U3 - 1],

(21)

where re is the coal particle radius. The initial condition of Eq. 21 for the contact area A is A(0) = 0,

(22)

and therefore the contact area A between two contiguous coal particles during agglomeration is written as

4rc% f t A -- 3#* Jo [(1 -- L ) -U3 -- 1] d t .

(23)

D. Adhesive Force During Particle Agglomeration The adhesive force between two coalescing coal particles during the particle agglomeration process is expressed as the sum of the surface tension force due to the liquid metaplast and the adhesive force

AGGLOMERATE FORMATION DURING COAL COMBUSTION

263

i

UNREACTED

COALESCING COAL PARTICLES

STAGE1

1

STAGE2

AGGLOMERATE ~ ~-"~E~.:I~"s-I,l,.~..~i~ U N R E A C T E D

r,c '.

2gW

/

,

_.,.

X;

,

\.

ou,o

META" ST

'-

\

-,/

".t

Fig. 1. Surface tension force at neck region of two coalescing coal particles in an agglomerate.

COKEFORMATION due to coke interconnection. Figure 1 shows two coalescing coal particles in the agglomerate. The surface tension force due to the liquid metaplast in the neck region is proportional to the effective circumference of the neck region (leff), expressed as

leff = 27rr*L,

(24)

where r* is the radius of the neck region, r* is given as r* -- (A/~r) 1/2.

(25)

The surface tension force, F~, is F.y

=

3,c(sin/9)leff,

(26)

where O is the contact angle, taken to be 90 ° as indicated in Fig. 1. Hence, the surface tension

Fig. 2. Agglomeration process of coal particles in an agglomerate.

force due to the liquid metaplast is derived as F~ = 2 ~ L 3 , c .

(27)

Figure 2 shows three stages in the period of plasticity of two coalescing coal particles in an agglomerate. The classification of each of these stages depends upon the solids in suspension in the liquid metaplast--coke and ash; coke, ash, and unreacted coal; unreacted coal and ash--in stages 1, 2, and 3, respectively. According to Taylor [14] and Friel et al. [15], a characteristic mosaic structure of coke is found to develop during the carbonization of vitrinite. The spherical bodies, each of which has a single crystallographic orientation, enlarge until they begin to interfere with one another's growth as the

264

S.-W. KANG ET AL.

mosaic-type structure starts to form. Completion of the mosaic formation coincides with completion of the resolidification of the coal. Taylor also found that when the proportion of the coke residue (char) was increased to about one-half, the spherical bodies began to interfere with each other's growth. Hence, in the present study, the threshold volume fraction of coke residue (Eth), which represents a borderline between stages 2 and 3, is defined as 50% of (1 - f a ) [i.e., Eth = (1 --fa)/2]. In stages 1 and 2, when the volume fraction of coke residue (E) is smaller than the threshold volume fraction of coke-residue (Eth), each mosaictype coke residue grows separately, and therefore there is no adhesive force due to the coke interconnection. However, in stage 3, when E is larger than Eth, the coke residue starts interlocking and the adhesive force due to the coke interconnection begins to be affected. The coke residue (char), which is formed after the initiation of the coke interlock, strengthens the connection between individual coke crystalline structures. Hence, the adhesive force due to the coke interconnection (FE3) in stage 3 is assumed to be proportional to the fraction E - Eth of coke residue (char) that is formed after the initiation of the coke interconnection. Thus, the adhesive force Fe3 in stage 3 is written as FE3 :- a e A

( 1 ~E-Eth L

--~Eth fl '

(28)

where oe denotes the bond stress of the coke residue (char), and the normalizing factor (in the brackets) leads to Fe~ ---, aEA when E --~ Emax : 1 - f a , from Eq. (16). It is also assumed that in stages 1 and 2 F E , : F E 2 : O.

(29)

During the particle agglomeration process, the adhesive force FA between two coalescing coal particles in the agglomerate is expressed as the sum of the surface tension force Fv and the adhesive force due to the coke interconnection (FE) discussed above. Thus, using Eqs. 27-29, the adhesive force is written as FA

=

F v + FE.

(30)

2000[

2000 2

,5°0 I

,

,oo0l

5

0

0

[

too0

50o t.J~ o.oo

5OO

o.o5

,o

O.lO

0.000

0 . 0 0 5 0.0,0

~ o.s

o.5 o.o

1.00,00

0.05

0.0

0.,0

0.000

1.0

0.005

0.010

-~ O.5 0.0

0,00 1.0

0.05

O0 0.000 ,.0

0. I0

0.5 o.o

N o.s 0.0

.

0.0200.00 1 0.015

0.05

010 ~ 0,0200000

[

0.005 O.OlO

0.005

0.010

0.005

0.010

o,o15 N 0,010 0,005

oo,o I

i o.005 I 0.000 i

0.05

z ~ 203°4~i°10 00.00

_/ 0.05

o,ooo

0.10 z

0. !0

i

4~000 30

20 I0 0 0.000

Time (see) (a)

0005 0.010 Time (see) (b)

Fig. 3. Comparisons of C, L, E, normalized A, and adhesive force F~ versus time for different particle heating rates: (a) 104 K/s; Co) 105 K/s.

3. RESULTS AND DISCUSSION A. Adhesive Force During Particle Agglomeration The adhesive force during particle agglomeration for different particle heating rates can be predicted by the mathematical model (Eqs. 3-30). Figure 3 shows predicted volume fractions of unreacted coal C, liquid metaplast L, and coke residue (char) E, the normalized contact area A, and the adhesive force FA as a function of time for two typical particle heating rates of 104 K/s and 105 K/s. The time-temperature histories of the agglomerate, which are obtained for various furnace gas temperatures, agglomerate diameters, and oxygen concentrations by the model of time-temperature history [16] are used as input data to predict the adhesive force in Figs. 4-6. Figures 4 and 5 show

AGGLOMERATE FORMATION DURING COAL COMBUSTION

~2oo/o . ~

~,~ 1000

1.0 O0 0.02 0,04 0.08 0.08

~

~- o.5

0.0 1.0

0.0 0.0 1.0

QO0 0.005 0.010 0015 0.020

0.5 0.0

1,0

~ O0

,

O0 0.02 0.04 0.08 0.08

i

0.015 0.010

0.005

0.005

-

O0 002 0.04 0.05 0.05

o

O0 0.02 0.04 0.06 0.08 Time (see)

(a)

0.I0

1

0.0 O~ 1.0

0.0

1.00,00 0 . 0 0 5 0 . 0 1 0 0.015 0.02

0.05

0.10

00

'

1.00~0 0.005 0.010 0.015 0,02

~- 0.5

0.0 0D 0.020

~

1.oaOO0.005 o.01o o.0a5 o.o2

0.5

0.05

0,10

00

' 0.005 0.010 0.015 0.02

1

0.010 ~

.~ 0.010 0.005

40 O0 0.005 0.010 0.015 0.020

20 10 0

0.05

0.5

o 0.000 z ~ CLO z

20 10

o.1o

,~ 0.015

o 0.000

z

\

0.05

~- 0 5

, , ,/~ 0.0 0.020 30 0.005 0.010 0.015 0.020

0.015 0,010

40 30

,

~. 0.5

0.0 0.020 O 002 0.04 0.06 0.08

0.000

/

1.0C30 0,005 0.010 0.015 0.020

~- 0.5

.= :~ E :~

1o ~o

O0 0.005 0.010 0.015 0.020

C" 0.5

(~0 0.02 0,04 0.08 0.08

1000

1ooo

1.0

~. o.5 0.0

2.o[

2000

"-~ E- 1000

265

0.05

0.10

~" 30 . 20

30 20

~. 10

(I.00 O.00S 0.010 0.015 0.020

0

z ~ 400,00 0.005 0.010 0.015 0.02

I0

0.0

0.05

0~I0

0

0.00 0.005 0.010 0.015 0.02

Time (see)

(b)

Fig. 4. Predictions of C, L, E, normalized A, and adhesive force Fa versus time for different furnace gas temperature (agglomerate diameter = 100 #m, oxygen concentration = 20%). (a) 1100 K; (b) 1750 K.

the effects of furnace gas temperature and agglomerate diameter, respectively, on the adhesive force [1, 2] during particle agglomeration. The particle heating rate during the heat-up stage (i.e., during pyrolysis) increases with increasing furnace gas temperature and with decreasing agglomerate diameter. As shown in Figs. 3-5, the general trends of the curves of C, L, and E for different particle heating rates are very similar, even though the time scales are totally different. The normalized contact area A, given by the contact area divided by r(radius of coal particle) 2, tends to decrease as the particle heating rate increases, mainly due to the decrease in the duration of the coal plasticity that is necessary for particle agglomeration. Hence, the adhesive force, which is proportional to the contact area, tends to decrease as the particle heating rate increases. Figure 6 shows the effect of oxygen concen-

Time (see)

Time (see)

(a)

CO)

Fig. 5. Predictions of C, L, E, normalized A, and adhesive force Fa versus time for different agglomerate diameter (furnace gas temperature = 1400 K, oxygen concentration = 20%). (a) 200 #m; (b) 60/~m.

tration on the adhesive force during particle agglomeration. The particle heating rate during the heat-up stage (i.e., during pyrolysis) is not significantly influenced by the oxygen concentration. Therefore, as shown in Fig. 6, during pyrolysis the curves of C, L, E, the normalized contact area A, and the adhesive force FA are almost the same for both oxygen concentrations of 20% and 100%. Hence, it is concluded that a higher particle heating rate (caused by a higher furnace gas temperature and a smaller agglomerate diameter) reduces the tendency of coal particles to form an agglomerate during the heat-up stage, because it both decreases the strength of the bonding of particles to each other and increases the centrifugal force [1, 2] during devolatilization and char burnout. However, the oxygen concentration does not significantly affect the adhesive force between contiguous coal particles in the agglomerate.

266

S.-W. KANG ET AL.

ooo i

~" 2000 1000 1.0 U

t-~ tO00

0.0 0 0 2

0.04 0.06 0.08

1.0

0.0 0.02

0.04

0.08

0.0 0.0 0.02 0.04 0 . 0 8 1.0

o.o 0.08

1.0

3O a" O

0.08

20

v

~. 0.s

o.5

40 v

...J r. OjO 0.02

0.04 0.08

0 000

0.08

/

I0 .~-~

/ Fcen t r i f

~,I~ 0.05

Time

010

(sec)

(a)

~ 0.5 0.0 0.0 0.02 0.04 0.06 0.08 1.0

8

0.0 l.O 0.0 0.02

0.04

0.06

0.08

eA/.

o.5

N 05 0,0 0.020 0.0 0.02 0.04 0.08 0 . 0 8 o o16 N 0.010 0.005 o 0.000 0.o 0 0 2 0.04 008 008 m 40 ~g 3o "~ 2o ~'~ o

/

0.0 0.020 o.o 0.02 0.04 0 . 0 8

(a)

(b)

008

0 0.00

O.'Ol

0.02

Time

0.03

(sec)

(b)

0.0 0.02 0.04 0.08 0.08 'rime (=ec)

0.04 0.06

.

Comparisons of adhesivc force Fa with centrifugal force Fc,.triffor different furnace gas temperatures. (Agglomerate diameter = I00 ~ m ; oxygen concentration = 2 0 % . ) (a) Fig. 7.

"rime (tec)

0.0 0.02

.

0.08

0.010 0.005 0.000 z ~ 0D 0.02 0.04 0.06 008 00 20 10 0

.

Fig. 6. Predictions of C , L , E , n o r m a l i z e d A , and adhesive force Fa versus time for different o x y g e n concentration (agg l o m e r a t e diameter = 100 # m , furnace gas temperature = 1100 K). (a) 2 0 % 0 2 ; (b) 1 0 0 % 0 2 .

B. Comparison of Centrigual Force with Adhesive Force Competition between the centrifugal force [1, 2], which favors the breakup of the agglomerate, and the adhesive force between contiguous coal particles in the agglomerate during the plastic stage of coal pyrolysis through char burnout is illustrated in Figs. 7a and 7b. The predictions of the centrifugal force and the adhesive force were made for a coal particle with a diameter of 30 pm and a mass of 2.0 × 10 -]1 kg located on the outer edge of an agglomerate with a diameter of 100 #m in Figs 7a and 7b. The details for the calculation are presented elsewhere [16]. Figure 7a shows the comparison of the adhesive force with the centrigual force for the lower heating rate, which is represented by a furnace gas temperature of 1100 K, an oxygen concentration of 20%, and an agglomerate diameter of 100 #m.

If00 K; (b) 1750 K.

The duration of plasticity of the coal particles is long enough for coal particles to fuse and coalesce, and therefore a strongly fused agglomerate is formed and the adhesive force between contiguous coal particles in the agglomerate is strong. It is also found that, due to the lower particle heating rate, the centrifugal force, which is directly influenced by the angular velocity of the agglomerate, is weaker than the adhesive force. In contrast, Fig. 7b shows the comparison of the adhesive force with the centrifugal force for the higher particle heating rate, which is represented by a furnace gas temperature of 1750 K, an oxygen concentration of 20%, and an agglomerate diameter of 100/~m. During coal combustion with a higher heating rate, the duration of the plastic period is so short that coal particles cannot completely fuse and coalesce; therefore a loosely fused agglomerate is formed and the adhesive force between contiguous coal particles is weak. Due to the higher particle heating rate, and thus the faster angular velocity, the strong centrifugal force that can promote the separation of weakly adhering char fragments is generated. Consequently, the ag-

AGGLOMERATE FORMATION DURING COAL COMBUSTION glomerates will easily break up, resulting in better combustion.

267

700 Furnace Tempetalut8 • 1510K O 1740K 1940K £3 2100K

600

4. P R A C T I C A L R A M I F I C A T I O N S

500 v

The model presented above provides a theoretical framework for assessing the conditions under which agglomerates formed by evaporation of CWF droplets or by collision of particles in a pulverized coal flame may fuse to form a particle that persists into the char oxidation stage. Many assumptions were introduced, and there is significant scope for refinement of the model. In particular, the viscosity-time relationship from the data of Fong et al. [5] will have to be developed for a variety of coals. It is of interest, however, to find experimental support for one of the major findings of the study--that agglomerates break up at high heating rates as a consequence of the high centrifugal force promoted by volatile release and the decreased time available for the plastic flow that "welds" particles together. Previous studies at MIT [17] on the injection of a Pittsburgh Seam No. 8 hvA bituminous coal into a pyrolysis furnace heated to various temperatures showed that agglomerates were produced at furnace temperatures below about 1500 K. The results on the char particle size versus volatile loss for several furnace temperatures are shown in Fig. 8. Size-graded 45-53 /zm coal particles were fed in an argon carrier gas through a 1.2 mm I.D. water-cooled stainless steel tube along the axis of a furnace into a plasma preheated argon stream confined by a 50.8 mm I.D. cylindrical graphite muffle tube. The particles were collected at various distances from the feeder in a water-cooled sintered bronze filter after being quenched by water jets at the mouth of the collector. A uniform feed rate of about 2.5 mg/s was achieved by use of a mechanical vibrator and by partial fluidization of the coal particles. The temperatures of the argon stream and the furnace wall were maintained constant, and the reactor times at each experimental temperature were varied by changing the position of the collector. A more detailed description of the laminar flow experiment can be found elsewhere 118, 19]. Agglomerates of 200 ~m diameter and larger

~ 4o0 O

300

~ 200 100 0

I

I

I

I

I

I

10

20

30

40

50

60

WEIGHT LOSS ( % )

d.a.f.

Fig. 8. Particle size changes of bituminous coal during devolatilization.

are observed only at the lower temperatures. For temperatures above 1740 K, no agglomeration was found, in qualitative agreement with the predictions in Fig. 7. Similar experiments with a noncaking coal, a Montana lignite, showed no agglomeration (see Fig. 9). The results for a bituminous coal obtained in a laminar flow furnace show that particle agglomeration can be very significant under the conditions predicted by the model. The model may therefore be used to assess the possibility of agglomerate formation in practical combustors allowing for particle collisions by turbulent motion and heating by internal flue gas recirculation, factors that would be strongly dependent on burner design. 70 60 S0

- 40 ~ 30 Furnace Temperature @ 1510K 0 174OK 1940K

20

[] 2100K

10

0

I

I

i

I

I

I

10

20

30

40

50

60

WEIGHT LOSS ( % )

70

d.a.f.

Fig. 9. Particle size changes of lignite coal during devolatilization.

268 5. C O N C L U D I N G

S.-W. K A N G E T AL. COMMENTS

A mathematical model of the c o m p e t i n g centrifugal and adhesive forces is presented to determine the conditions u n d e r which coal particles that are in touch with each other d u r i n g the plastic stage of their pyrolysis will agglomerate or separate into discrete particles. Results o f computation show that the adhesive force in the process o f a g g l o m e r a t i o n of coal particles is dependent u p o n the duration of plasticity o f the coal particles and that rapid particle heating reduces the tendency of coal particles to form agglomerates during the particle heat-up stage, because it both increases the centrifugal force during devolatilization and decreases the strength of b o n d i n g o f particles to each other. The theoretical model provides a basis for calculating the separation of char fragments and ash particles as functions of coal properties and the thermal history of coal particles. The model also provides a framework for d e t e r m i n i n g the effects o f furnace gas temperature, particle size, and oxygen concentration on agglomeration, but there is r o o m for significant refinement, as factors governing both particle rotation and particle fusion are u n d e r s t o o d better. Practical implications of the present study bear on the problems of the combustion space requirement o f pulverized coal and C W F flames and of deposit formation w h e n the fly-ash particle size is coarse.

We thank Mr. S. G. Kang f o r his assistance and helpful discussion and Ms. B. Caputo f o r typing the manuscript. This research was sponsored by the U.S. Department o f Energy (Pittsburgh Energy Technology Center) under Contract N o . DE-FG22-84PC70268.

REFERENCES 1. Kang, S. W., Sarofim, A. F., and Be6r, J. M., Particle Rotation in Coal Combustion: Statistical, Experimental and Theoretical Studies, Twenty-Second Symposium (International) on Combustion, The Combustion Institute, 1988. 2. Kang, S. W., Sarofim, A. F., and Be6r, J. M., Fundamentals of Coal-Water Fuel Droplet Combustion, Third European Conference on Coal Liquid Mixtures, The

Institution of Chemical Engineers, Sweden, 1987. 3. Fitzgerald, D., Kinetic Study of Coal Carbonization in the Plastic Zone, Fuel 35:178-183 (1956). 4. Chermin, H. A. G., and Van Krevelen, D. W., Chemical Structure and Properties of Coal XVII--Mathematical Model of Coal Pyrolysis, Fuel 36:85-104 (1957). 5. long, W. S., Peters, W. A., and Howard, J. B., Kinetics of Generation and Destruction of Pyridine Extractables in a Rapidly Pyrolyzing Bituminous Coal, Fuel 65:251-254 (1986). 6. Fong, W. S., Plasticity and Agglomeration in Coal Pyrolysis, Sc.D. Thesis, Department of Chemical Engineering, MIT, Cambridge, Mass., February 1986. 7. Frenkel, J., Viscous Flow of Crystalline Bodies under the Action of Surface Tension, J. Phys. (USSR) 9:385-391 (1945). 8. Kingery, W. D., and Berg, M., Study of lnitial Stages of Sintering Solids by Viscous Flow, EvaporationCondensation, and Self-Diffusion, J. Appl. Phys. 26:1205-1212 (1955). 9. Kuczynski, G. C., Study of the Sintering of Glass, J. Appl. Phys. 20:1160-1163 (1949). 10. Huang, D. D., Flow Fields during Coalescence of Viscous Spheres, S.M. Thesis, Department of Materials Science and Engineering, M1T, Cambridge, Mass., 1976. II. Frankel, N. A., and Acrivos, A., On the Viscosity of a Concentrated Suspension of Solid Spheres, Chem. Eng. Sci. 22:847 (1967). 12. Nazem, F. F., Rheology of Carbonaceous Mesophase Pitch, Fuel 59:851-858 (1980). 13. Hwang, S. C., Tsonopoulos, L., Cunningham, J. R., and Wilson, G. W., Density, Viscosity, and Surface Tension of Coal Liquids at High Temperatures and Pressures, Ind. Eng. Chem. Proc. Des. Div. 21:127 (1982). 14. Taylor, G. H., Development of Optical Properties of Coke during Carbonization, Fuel 40:465-471 (1961). 15. Fxiel,J. J., Mehta, S., Mitchell, G. D., and Karpinski, J. M.. Direct Observation of the Mesophase in Coal, Fuel 59:610-616 (1980). 16. Kang, S. W., Combustion and Atomization Studies of Coal-Water Fuel in a Laminar Flow Reactor and in a Pilot-Scale Furnace, Ph.D. Thesis, Department of Mechanical Engineering, MIT, Cambridge, Mass., February 1988. 17. Pohl, J. H., Kobayashi, H., and Sarofim, A. F., The Effects of Temperature and Time on the Swelling of Pulverized Coal Particles, Combustion Institute (Western Section) Technical Meeting, Colorado, Apr. 17-18, 1978. 18. Kobayashi, H., Devolatilization of Pulverized Coal at High Temperatures, Ph.D. Thesis, Department of Mechanical Engineering, MIT, Cambridge, Mass., 1976. 19. Kobayashi, H., Howard, J. B., and Sarofim, A. F., Coal Devolatilization at High Temperatures, Sixteenth Symposium (International) on Combustion, The Combustion Institute, 1976, pp. 411-425.

Received 15 July 1988; revised 15 December 1988