Chemical Reaction EngineeringâPlenary Lectures - American

4 Fluidized-Bed Coal Combustion: Controlling Parameters A D E L F. SAROFIM

Downloaded by CORNELL UNIV on December 2, 2012 | http://pubs.acs.org Publication Date: July 28, 1983 | doi: 10.1021/bk-1983-0226.ch004

Massachusetts Institute of Technology, Department of Chemical Engineering, Cambridge, MA 02139

The factors controlling the performance of atmospheric-pressure fluidized-bed combustors (AFBC's) are illustrated by order-of-magnitude calculations of the design and operating variables for a hypothetical 100 MW boiler. Bed height, bed cross-sectional area, immersed heat-transfer surface area, sorbent feed size and rate, bed temperature, fluidizing velocity and coal feed size are selected by consideration of the fluids mechanics, heat transfer, and kinetics of the governing gas-solid reactions. The fluid mechanics and heat transfer in AFBC's are shown to be differ distinctly from those in more traditional fluidized bed reactors. t

F l u i d i z e d bed combustion provides one option f o r u t i l i z i n g some of our l a r g e c o a l reserves f o r purposes of energy generation. I t s advantages over a l t e r n a t i v e methods o f d i r e c t c o a l u t i l i z a t i o n , e.g., suspension f i r i n g of p u l v e r i z e d c o a l and the burning of lump c o a l on s t o k e r s , i s that i t i s able to handle coals o f w i d e l y v a r y i n g composition, i n c l u d i n g low-grade coals w i t h high ash content, and i t provides a c a p a b i l i t y of in-bed s u l f u r capture. The development of the technology of AFBC's has been pursued v i g o r o u s l y s i n c e the e a r l y s i x t i e s . Small ( C0 2

2

H S) 2

2

2

2

2

2

2


to s u l f u r capture, CaC0 CaO + CaS0 S0 + CaS0

3

3

2

3

+ CaO S0 •> + 1/2 1/2 0 + 1/2 2

2

+ C0 CaS0 0 + CaS0 -> S 0 0 -> CaS0 2

3

2

4

3

2

4

and to n i t r i c oxide formation

and d e s t r u c t i o n ,

2NH + 3/2 0 -> 2N0 + 3/2 H 0 NH + NO + 1/4 0 -> N + 3/2 H 0 NO + C •> 1/2 N + CO 3

2

2

3

2

2

2

2

N 0

+

C 0

1 / 2

N

+

C

^îïî 2 °2 NO + CaS0 + CaS0 + 1/2 3

4

N

2

From t h i s p a r t i a l l i s t i n g one can f i n d r e a c t i o n s belonging to many of the important c l a s s e s of homogeneous and heterogeneous reactions . The performance of a f l u i d i z e d bed combustor i s s t r o n g l y i n f l u e n c e d by the f l u i d mechanics and heat t r a n s f e r i n the bed, c o n s i d e r a t i o n of which must be part of any attempt to r e a l i s t i c a l l y model bed performance. The f l u i d mechanics and heat t r a n s f e r i n an AFBC must, however, be d i s t i n g u i s h e d from those i n f l u i d i z e d c a t a l y t i c r e a c t o r s such as f l u i d i z e d c a t a l y t i c crackers (FCCs) because the p a r t i c l e s i z e i n an AFBC, t y p i c a l l y about 1 mm i n diameter, i s more than an order of magnitude l a r g e r than that u t i l i z e d i n FCC s, t y p i c a l l y about 50 jJm. The consequences of t h i s d i f f e r e n c e i n p a r t i c l e s i z e i s i l l u s t r a t e d i n Table 1. P a r t i c l e Reynolds number i n an FCC i s much s m a l l e r than u n i t y so that viscous forces dominate whereas f o r an AFBC the p a r t i c l e Reynolds number i s of order u n i t y and the e f f e c t of i n e r t i a l forces become n o t i c e a b l e . Minimum v e l o c i t y of f l u i d i z a t i o n ( f ) i n an FCC i s so low that the b u b b l e - r i s e v e l o c i t y exceeds the gas v e l o c i t y i n the dense phase (u f/c £) over a bed's depth; the FCC s operate i n the s o - c a l l e d f a s t bubble regime to be e l a b o r a t ed on l a t e r . By contrast- the b u b b l e - r i s e v e l o c i t y i n an AFBC may be slower or f a s t e r than the gas-phase v e l o c i t y i n the emulsion f

u

m

m

m

T

In Chemical Reaction Engineering—Plenary Lectures; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

Fluidized-Bed Coal Combustion

SAROFiM

67

Table I . D i f f e r e n c e s i n F l u i d i z a t i o n and Heat Transfer o f AFBC's and F l u i d i z e d C a t a l y t i c Reactors (e.g. FCC s) T

FCC

AFBC

Ρ


T

particle(s) heating

phase, l e a d i n g t o operation i n e i t h e r the slow or f a s t bubble regime. F i n a l l y the c h a r a c t e r i s t i c h e a t i n g time of p a r t i c l e s i n an FCC i s s m a l l r e l a t i v e t o the residence time o f s o l i d s near a tube surface and the heat t r a n s f e r r a t e i s then c o n t r o l l e d by the p e n e t r a t i o n o f a thermal waves i n t o the s o l i d s as f i r s t proposed by M i c k l e y and Fairbanks ( 6 ) . For an AFBC, the c h a r a c t e r i s t i c h e a t i n g times are long compared t o the p a r t i c l e residence time a t the w a l l and the p a r t i c l e s can be t r e a t e d as being a t the b u l k temperature f o r purposes o f heat t r a n s f e r c a l c u l a t i o n s (7). The paper w i l l consider the parameters c o n t r o l l i n g the design and operation of an AFBC, shown s c h e m a t i c a l l y i n Figure 1 . The questions to be addressed are what are the f a c t o r s t h a t guide the s e l e c t i o n of bed h e i g h t , freeboard h e i g h t , c o a l feed l o c a t i o n , immersed h e a t - t r a n s f e r s u r f a c e s , sorbent s i z e and feed r a t e , c o a l feed s i z e , bed temperature and f l u i d i z i n g v e l o c i t y . In order t o help focus the d i s c u s s i o n , order-of-magnitude c a l c u l a t i o n s w i l l be performed f o r the conceptual design of a b o i l e r designed t o produce 1 0 0 MW of steam a t 644 K, f i r e d w i t h a c o a l of elemental composition C H Q ^ S O Q N Q . 0 3 OQ ( 2°)Q.07» 8 value of 2 9 , 1 0 0 kJ/kg* and ten percent ash by weight. The b o i l e r w i l l be operated w i t h 2 0 percent excess a i r . Q

2

H

A

N

E

A

T

I

N

Pressure Drop Across Bed (Bed Height S e l e c t i o n ) The bed height i s determined by c o n s i d e r a t i o n of the work r e q u i r e d t o overcome the pressure drop across the bed and d i s t r i b utor p l a t e . The pressure drop across the bed i s simply the weight of the bed. ΔΡ = P g ( l - e ) h s

(1)

where ε and h are the v o i d f r a c t i o n and height of the unexpanded bed, and p i s the d e n s i t y o f the bed s o l i d s . The a d d i t i o n a l pressure drop across the d i s t r i b u t o r p l a t e w i l l here be taken t o be one t h i r d that across the bed. The fan work, and a i r flow r a t e g



CHEMICAL

SPENT SORBENT

REACTION

ENGINEERING

COAL

Figure 1. Schematic o f atmospheric pressure f l u i d i z e d bed combustor.


4.

SAROFiM


69

i s the product o f the v o l u m e t r i c a i r flow r a t e and the pressure drop, may be expressed as an e q u i v a l e n t amount of f u e l Διη„, given the v o l u m e t r i c a i r requirement v per mass o f f u e l . The f r a c t i o n of the f u e l flow rate m needed t o supply the energy t o d r i v e the fans i s r e a d i l y shown to be a

F

~ζΓ

3 (-AH )n n c

e

v>

f

where -ΔΗ^ i s the heat o f combustion, the fan e f f i c i e n c y , and r) the e f f i c i e n c y o f conversion of thermal t o e l e c t r i c a l energy. For r e a l i s t i c values o f the c o e f f i c i e n t s : p = 2400 Kg/m ,e= 0.5, t ) = 0.3, n = 0.6, v = 24.5 m /Kg c o a l , s e

3

o


3

e

f

a

-:— = 0.028 h *F

(3)

where the bed height h i s i n meters. The unexpanded bed height needs to be kept low i n order to minimize pumping energy l o s s e s , and a value of about 0.7 m i s o f t e n s e l e c t e d to keep the energy l o s s f o r fan power t o 2 percent o f the f u e l ' s h e a t i n g value. A consequence of t h i s c o n s t r a i n t on maximum bed height i s that f l u i d i z e d bed c r o s s - s e c t i o n a l area i s p r o p o r t i o n a l to the c a p a c i t y of a b o i l e r , r e s u l t i n g i n bed widths much l a r g e r than bed depth f o r l a r g e r u n i t s ; t h i s can pose problems o f ensuring uniform f u e l d i s t r i b u t i o n over the bed, as w i l l be discussed l a t e r . Inasmuch as the fan power l o s s i s p r o p o r t i o n a l t o the v o l u m e t r i c a i r requirement v ^ per u n i t mass of f u e l (Eq. 2 ) , the bed height cor responding t o a given Δπι-ρ/τη-ρ i s p r o p o r t i o n a l to pressure so that p r e s s u r i z e d FBC's may be operated w i t h deep beds and much s m a l l e r c r o s s - s e c t i o n a l areas than AFBC's. S u l f u r Capture

( S e l e c t i o n o f Bed Temperature and P a r t i c l e S i z e )

The s u l f u r sorbent that has r e c e i v e d the most a t t e n t i o n i s limestone because o f i t s widespread a v a i l a b i l i t y and low cost. Unfortunately the conversion o f limestone to calcium s u l f a t e r e s u l t s i n a v o l u m e t r i c i n c r e a s e , and i t can be r e a d i l y shown ( B

_ L . o 0.125 m

T'b

0

J

(

5

m

Ο

^Ο

ο

ο

0

Figure Τ· Energy balance on a h y p o t h e t i c a l 100 MW^ b o i l e r and t h e in-bed heat t r a n s f e r area r e q u i r e d t o m a i n t a i n the bed temperature at 1116 K, e.g., 6 rows o f 50 mm O.D. tube w i t h a h o r i z o n t a l p i t c h of 150 mm and a v e r t i c a l p i t c h o f 125 mm.


C H E M I C A L REACTION ENGINEERING

82

w i t h the s o l i d s withdrawn from the bed [K(R) = Ί?ι = 0 ] , and f o r a d i f f u s i o n l i m i t e d carbon burning to C O 2 (R = -6ShPC^yQ /p R, where V i s the oxygen d i f f u s i v i t y , C the t o t a l molar gas c o n c e n t r a t i o n , p the carbon d e n s i t y , and y the oxygen mole f r a c t i o n ) , Eq. 10 can be solved f o r the p a r t i c l e s i z e d i s t r i b u t i o n ρ(R) and the carbon l o a d i n g . The s o l u t i o n s are c

T

c

0

\

ψο

2

γ

and P


W

c

F

c

R

o l

2

-*Γ-

= ÔShPC^

where t ^ i s the burning

2 ( 1 2 )

- f Vb

time of p a r t i c l e s of

i n i t i a l radius

R-^.

The carbon l o a d i n g i s found to be p r o p o r t i o n a l to coal feed rate and p a r t i c l e burning time. I t i s a v a r i a b l e of major impor tance because i t determines the carbon l o s s from the bed and a l s o has an important impact on the emissions of n i t r o g e n oxides. Estimates of the carbon l o a d i n g can be obtained by e v a l u a t i n g t ^ from the r e l a t i o n f o r a s h r i n k i n g sphere model of a d i f f u s i o n l i m i t e d o x i d a t i o n of carbon. I t i s r e a d i l y shown t h a t , f o r p a r t i c l e s of density p and i n i t i a l diameter c

U

b

48ShPC

( 1 3 ) p

where Sh i s the Sherwood Number, V the oxygen d i f f u s i v i t y , and C the oxygen concentration i n the emulsion phase. Although some controversy e x i s t s on the c o r r e l a t i o n of Sherwood Number a p p l i c a b l e to f l u i d i z e d beds, w e l l - d e f i n e d combus t i o n experiments support the use of the Ranz and M a r s h a l l (35) or F r o s s l i n g (36) c o r r e l a t i o n w i t h an approximate c o r r e c t i o n of e f to allow f o r the o b s t r u c t i o n to d i f f u s i o n by the i n e r t p a r t i c l e s surrounding the burning char p a r t i c l e s (37). Thus p

m

Sh * ε[2 +0.6

Re

1 / 2

Sc

1 / 3

]

(14)

The oxygen concentration C w i l l depend upon the excess a i r , expressed as a f r a c t i o n of the s t o i c h i o m e t r i c a i r , and the f l u i d mechanics. Assuming that n e g l i g i b l e amounts of oxygen by-pass the bed i n bubbles, the oxygen concentration C i n the bed can be r e l a t e d to the i n l e t oxygen concentration C and excess a i r by p

p

Q


4.

SAROFiM


83

f o r a w e l l - s t i r r e d emulsion gas, and

C

p

=

( 1 6 )

(l+e)£n(l+l/e)

f o r p l u g flow. With char p a r t i c l e s 1mm i n diameter, an excess a i r e of 0.2, a bed temperature o f 1116 K, and e f of 0.5, the burning times are 185 seconds f o r a w e l l - s t i r r e d gas, and 67 seconds f o r plug flow, The lower times are more p e r t i n e n t t o AFBC s i n which the gas i s approximately i n p l u g flow. The carbon l o a d i n g i n the bed i s then determined by s u b s t i t u t i n g the c o a l feed r a t e (3.83 Kg/s f o r 111 MW thermal i n p u t ) and burning time i n t o Eq. 12. A carbon l o a d i n g o f 103 Kg i s obtained f o r the case o f p l u g f l o w i n the gase phase. The f r a c t i o n o f the t o t a l bed weight which i s i n the form o f carbon i s s m a l l . S u b s t i t u t i n g i n t o m


T

W

W =

W

T

9 Ahp (l- ) s

(17) K ± / J

£

ο the p r e v i o u s l y determined values of h = 0.7 m, A = 87 m and the density of limestone ( p = 2400 Kg/m^), we f i n d that the carbon accounts f o r only 0.14 percent o f the t o t a l bed weight. With carbon l o a d i n g determined, one i s i n a p o s i t i o n t o evaluate the carbon l o s s from the bed. The three p r i n c i p a l sources are carbon withdrawn from the bed w i t h spent s o l i d s , e l u t r i a t i o n o f carbon that has burned down t o an e l u t r i a b l e s i z e range, and the e l u t r i a t i o n o f f i n e s produced by a t t r i t i o n . The f r a c t i o n m /m-p o f the carbon feed l o s s w i t h spent solids i s determined by the rate m o f spent s o l i d w i t h d r a w a l , and the f r a c t i o n (W /W ) of the bed s o l i d s i n the form o f carbon: s

c

s

g

C

T

m m W c,s _ s ^

^

( 1 8 )

Τ The f r a c t i o n m /m l o s t by e l u t r i a t i o n i s determined by the e l u t r i a t i o n r a t e constant K ( R ) , the p a r t i c l e s i z e d i s t r i b u t i o n p(R) of carbon i n the bed, and the carbon l o a d i n g W (Eq. 10). A f i r s t approximation f o r t h i s l o s s may be obtained by assuming that that p a r t i c l e s of feed diameter d^ s h r i n k t o an e l u t r i a b l e s i z e d approximately 300 ym from Figure 4, and are then blown out of the bed. For t h i s simple model c e

F

c

9

Z

m

F

= (~) * (0.3Γ * 2.7 χ 10 i

(19)

d

Another source o f e l u t r i a t e d carbon are the f i n e s produced by the a t t r i t i o n of the carbon surface by a b r a s i o n . This mechanism f o r a t t r i t i o n has been s t u d i e d by M a s s i m i l l a and coworkers (38-41).


C H E M I C A L REACTION

84

ENGINEERING

They f i n d that the r a t e of a t t r i t i o n i s p r o p o r t i o n a l to the energy d i s s i p a t i o n r a t e i n the bed, which i s p r o p o r t i o n a l to u - u ^ f , and that i t i s much higher during o x i d a t i o n than p y r o l y s i s . They p o s t u l a t e that a s p e r i t i e s are produced on the surface of the char during combustion and that these are abraded by c o l l i s i o n s w i t h the bed s o l i d s . The r a t e of the carbon surface r e g r e s s i o n due to a t t r i t i o n i s approximately given by Q

R

(20)

where k i s about 3.5x10"^. The r a t e of feed carbon l o s s due to the e l u t r i a t i o n of a t t r i t e d carbon i s then given by Downloaded by CORNELL UNIV on December 2, 2012 | http://pubs.acs.org Publication Date: July 28, 1983 | doi: 10.1021/bk-1983-0226.ch004

a

d /2 ±

3p(R)Wk ( u - u c a ο mf) n

_

3k (u -u -) a ο mf .

(21)

For the c o n d i t i o n s we have s e l e c t e d , m /m.p equals 1.1x10 The above c a l c u l a t i o n s show a carbon l o s s of about 4 percent of the c o a l feed, p r i m a r i l y as f i n e s produced by carbon a t t r i t i o n or by the shrinkage of the c o a l feed. As c o a l p a r t i c l e feed s i z e increases the a t t r i t t e d carbon increases (note t ^ i n Eq. 21 i s p r o p o r t i o n a l to d^) but the e l u t r i a t e d carbon (Eq. 19) decreases. Carbon l o s s e s can t h e r e f o r e be minimized by the j u d i c i o u s choice of c o a l feed s i z e . The s i m p l i f i e d model presented above y i e l d s the f o l l o w i n g expression f o r the optimum s i z e : c

a

1/4 3

d

( i>opt

48ShPCp(d*) ρ k (u -u ,) c a ο mf

(22)

For the t e s t case, being considered, the optimum c o a l feed s i z e given by Eq. 22 i s 1.6mm. C l e a r l y , the optimum depends upon o p e r a t i n g c o n d i t i o n s , and a l s o on the model assumptions. The f i n e s e l u t r i a t e d from the bed are u s u a l l y captured i n a cyclone and r e c y c l e d to the bed, so that high combustion e f f i c i e n c i e s are achievable w i t h AFBC's. B e t t e r understanding of the residence time of f i n e s i n a bed i s needed i n order to deter mine the r e c y c l e r a t e . The above s i m p l i f i e d a n a l y s i s was intended to provide a f e e l f o r the r e l a t i v e importance of the processes that govern carbon l o a d i n g , and t h e r e f o r e carbon combustion e f f i c i e n c y . More com p l e t e treatments of AFBC s are a v a i l a b l e which consider the d e t a i l e d population balance equations f o r the char p a r t i c l e s coupled w i t h an oxygen balance (41-50). These treatments have given r e s u l t s which p a r a l l e l observations on o p e r a t i n g AFBC*s but 1


4.

85


SAROFiM

are q u a l i f i e d by u n c e r t a i n t i e s i n the flow models and mass t r a n s f e r models which are used t o c a l c u l a t e the t r a n s f e r o f oxygen t o the dense phase and by d i f f e r e n c e s i n assumptions concerning the comb u s t i o n of the char. The refinements that can be made t o the model f o r c o a l char o x i d a t i o n are seemingly endless (51), A few o f these w i l l be discussed b r i e f l y . Dominant Oxidant. Carbon g a s i f i c a t i o n i n f l u i d i z e d bed combustors can occur by both the C O 2 / C and the O 2 / C r e a c t i o n s :


C0

(1

2

+ C= - |)

0

(23)

2C0

2

+ C = xCO

+

(1 - x ) C 0

2

(24)

Avedasian and Davidson (37) i n t h e i r p i o n e e r i n g work on the modelling of char o x i d a t i o n i n f l u i d i z e d beds assumed a t w o - f i l m model f o r char o x i d a t i o n , i n which C O 2 reacts w i t h carbon a t the surface t o form CO w i t h the CO b e i n g o x i d i z e d i n a d i f f u s i o n flame enveloping the p a r t i c l e . L a t e r s t u d i e s (52) showed that the C O 2 / C r e a c t i o n was too slow a t f l u i d i z e d bed temperatures t o c o n t r i b u t e s i g n i f i c a n t l y t o the carbon g a s i f i c a t i o n r a t e . The primary product o f the C / O 2 r e a c t i o n i s b e l i e v e d to be CO, based on molecu l a r beam s t u d i e s on graphite (53). CO i s then converted t o C O 2 as i t d i f f u s e s from the p a r t i c l e surface. A g e n e r a l i z e d treatment of the carbon o x i d a t i o n r e a c t i o n s a l l o w i n g f o r the two g a s i f i c a t i o n r e a c t i o n s , Eqs. 23 and 24, and the carbon monoxide o x i d a t i o n i n the boundary l a y e r has been presented by Amundson and coworkers (54-58). E x t e r n a l D i f f u s i o n vs. Chemical K i n e t i c s . As expected, the rate of carbon o x i d a t i o n i s determined by the combination o f e x t e r n a l d i f f u s i o n and the k i n e t i c s o f the carbon o x i d a t i o n . E a r l y c a l c u l a t i o n s by Borghi e t a l (59) determined the c o n t r i b u t i o n s of k i n e t i c s and e x t e r n a l d i f f u s i o n as a f u n c t i o n of bed temperature, p a r t i c l e s i z e , and oxygen concentrations. These show that f o r p a r t i c l e s o f 1 mm diameter 1116 K, c o n d i t i o n s t y p i c a l o f commercial p r a c t i c e , the d i f f u s i o n and k i n e t i c r e s i s t a n c e s are of equal importance. Experimental support f o r these p r e d i c t i o n s i s provided by Ross and Davidson (60, 61). Reaction Order. Studies o f the r e a c t i o n o f oxygen w i t h carbon a t temperatures o f i n t e r e s t f o r AFBC's suggest that i t i s near zero order i n oxygen (62). Most models have been based on an assumed f i r s t order r e a c t i o n but they can be r e a d i l y m o d i f i e d t o accommodate the more r e a l i s t i c lower r e a c t i o n order (63, 64). The c o r r e c t i o n f o r order o f r e a c t i o n w i l l be most important f o r the p r e d i c t i o n of the combustion of r e c y c l e d f i n e s which are i n the s i z e range i n which chemical k i n e t i c s dominate and f o r p r e d i c t i n g the performance o f p r e s s u r i z e d f l u i d i z e d beds.



86

C H E M I C A L R E A C T I O N ENGINEERING

Pore S t r u c t u r e . The chars produced from coals are h i g h l y porous, w i t h i n t e r n a l surface areas of 100 to 1000 m^/g, and pore r a d i i ranging from nanometer to micron i n s i z e . Models of i n c r e a s i n g s o p h i s t i c a t i o n have been developed to describe the r e a c t i o n i n porous chars (65-71) which a l l o w f o r d i f f u s i o n and chemical r e a c t i o n , pore s i z e d i s t r i b u t i o n , and v a r i a t i o n i n pore s i z e w i t h i n c r e a s i n g extent of r e a c t i o n . The added refinements are not needed f o r purposes of c a l c u l a t i n g char burnout times f o r most of the carbon i n AFBC's, since the e x t e r n a l r e s i s t a n c e c o n s t i t u t e s a s i g n i f i c a n t f r a c t i o n of the t o t a l r e s i s t a n c e . Use of such models are, however, d e s i r a b l e when examining d e t a i l s of secondary r e a c t i o n s such as those that i n f l u e n c e p o l l u t a n t forma t i o n which occur w i t h i n the pores, or i n e v a l u a t i n g the e f f e c t of pore s t r u c t u r e on a t t r i t i o n and fragmentation r a t e s . P a r t i c l e Temperature Overshoot. The temperature of the burn ing char p a r t i c l e s w i l l run h o t t e r than that of the bed by amounts that depend upon p a r t i c l e s i z e , r e a c t i v i t y , bed temperature. I t i s determined i n p a r t by the heat r e l e a s e d at the p a r t i c l e surface due to r e a c t i o n and i n part to the a d d i t i o n a l heat released by carbon monoxide o x i d a t i o n near the p a r t i c l e surface (54-58). Measurements f o r 1.8 to 3.2 m i l l i m e t e r s i z e coke p a r t i c l e s burning i n a f l u i d i z e d band of sand at 1173 Κ increased from the bed temp erature at low oxygen concentrations to values 150 to 200 Κ above the bed temperature f o r oxygen concentrations approaching that of a i r (72). E s t i m a t i o n of t h i s temperature r i s e i s important f o r purposes of e v a l u a t i n g the NO/C r e a c t i o n and a l s o f o r p r e d i c t i o n of the burnout times of f i n e s . Carbon Monoxide Oxidation. A n a l y s i s of the carbon monoxide o x i d a t i o n i n the boundary l a y e r of a char p a r t i c l e shows the pos s i b i l i t y f o r the existence of m u l t i p l e steady s t a t e s (54-58). The importance of these at AFBC c o n d i t i o n s i s u n c e r t a i n . From the theory one can a l s o c a l c u l a t e that CO w i l l burn near the surface of a p a r t i c l e f o r l a r g e p a r t i c l e s but w i l l react outside the boundary l a y e r f o r s m a l l p a r t i c l e s , i n q u a l i t a t i v e agreement w i t h experimental observations. Q u a n t i t a t i v e agreement w i t h theory would not be expected, s i n c e the t h e o r e t i c a l c a l c u l a t i o n s , are based on the use of g l o b a l k i n e t i c s f o r CO o x i d a t i o n . Hydroxyl r a d i c a l s are the p r i n c i p a l oxidant f o r carbon monoxide and i t can be shown (73) that t h e i r concentration i s lowered by r a d i c a l r e combination on surfaces w i t h i n a f l u i d i z e d bed. I t i s therefore expected that the CO o x i d a t i o n rates i n the dense phase of f l u i d i z e d beds w i l l be suppressed to l e v e l s considerably below those i n the bubble phase. This expectation i s supported by s t u d i e s of combustion of propane i n f l u i d i z e d beds, where i t was observed that i g n i t i o n and combustion took place p r i m a r i l y i n the bubble phase (74). More a t t e n t i o n needs to be given to the e f f e c t of bed s o l i d s on gas phase r e a c t i o n s occuring i n f l u i d i z e d r e a c t o r s .


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A s h - D i f f u s i o n C o n t r o l . A U.S. c o a l contains on the average about 10 percent by weight of m i n e r a l c o n s t i t u e n t s . These y i e l d an ash during combustion which tends t o accumulate on the surface of the receding char. Since AFBC s operate below the f u s i o n temperature of ash, the ash e i t h e r f l a k e s o f f as the carbon surface recedes or forms a h i g h l y porous, l o o s e l y - s i n t e r e d , f r i a b l e cage about the char. In p r i n c i p l e , the ash l a y e r should r e t a r d the r a t e of char combustion (34) but the experimental evidence t o date suggests that i t s e f f e c t i s s m a l l i n determining o v e r - a l l burning r a t e s . I t may, however, i n f l u e n c e the l a t t e r stages of combustion and the achievement of h i g h carbon burnout.


T

P a r t i c l e Fragmentation. An added complication i n the modell i n g of c o a l combustion i s provided by the d e v o l a t i l i z a t i o n step, which determines the y i e l d of the char, i t s p o r o s i t y , p a r t i c l e s i z e , and p a r t i c l e number. M a s s i m i l l a and coworkers (41) have measured the c o a l fragments produced during p y r o l y s i s . I n d i r e c t evidence f o r fragmentation of various chars during combustion was a l s o provided by Campbell and Davidson (75) who a t t r i b u t e d the d e v i a t i o n of the p a r t i c l e s i z e d i s t r i b u t i o n during the combustion of char p a r t i c l e s of uniform i n i t i a l s i z e from the p r e d i c t e d s i z e d i s t r i b u t i o n given by Eq. 11 as b e i n g due t o fragmentation. Although a complete model f o r s i n g l e p a r t i c l e burning requires d e t a i l e d i n f o r m a t i o n on p h y s i c a l parameters, such as pore s t r u c t u r e and chemical parameters, such as i n t r i n s i c r e a c t i v i t i e s o f char/ oxygen, the near dominance o f the e x t e r n a l d i f f u s i o n r e s u l t s i n good agreement being obtained between the p r e d i c t i o n s o f burning times obtained using r e l a t i v e l y simple models and experimental r e s u l t s . The d e t a i l e d models w i l l prove u s e f u l i n r e s o l v i n g i s s u e s that cannot be addressed by simpler models, such as the importance of h i g h i n t e r n a l CO concentrations on the augmentation of the reduction of NO by char, on the e f f e c t o f e v o l v i n g pore s t r u c t u r e on a t t r i t i o n and fragmentation, and on where CO combustion occurs. V o l a t i l e E v o l u t i o n (Coal Feed L o c a t i o n ) Most models o f f l u i d i z e d - b e d combustors have been developed for chars on cokes w i t h n e g l i g i b l e v o l a t i l e content o r , i f address i n g c o a l s , have t r e a t e d the v o l a t i l e e v o l u t i o n as being e i t h e r instantaneous o r uniformly d i s t r i b u t e d throughout the f l u i d i z e d bed. The c o a l d e v o l a t i l i z a t i o n step i s , however^ of major importance t o the operation o f AFBC s s i n c e the c o a l must be d i s t r i b u t e d throughout a bed i n a manner that ensures t h a t the v o l a t i l e s w i l l have access t o s u f f i c i e n t a i r f o r t h e i r complete oxidation. I f the v o l a t i l e r e l e a s e r a t e i s slow r e l a t i v e t o the rate of s o l i d c i r c u l a t i o n , the assumption of uniform v o l a t i l e r e l e a s e would be j u s t i f i e d . Estimates of the v o l a t i l e r e l e a s e r a t e may be obtained from the e x t e n s i v e l i t e r a t u r e on c o a l p y r o l y s i s (76). T




88

Using the data of Howard and coworkers (77) Borghi et a l (59) have modeled the v o l a t i l e r e l e a s e rate f o r AFBC c o n d i t i o n s . Their pred i c t i o n f o r both the duration of a v o l a t i l e flame and the subsequent char burnout times have been confirmed by the experimental measurements of Andrei (78). Sample r e s u l t s are shown i n Figure 8, which presents the c a l c u l a t e d ( s o l i d l i n e ) and measured (data p o i n t s ) weight l o s s of 3 m i l l i m e t e r p a r t i c l e s burned i n 5 percent oxygen stream i n a f l u i d i z e d bed maintained a t 1173 K. The i n i t i a l steep drop i n weight i s due to v o l a t i l e e v o l u t i o n , and i t i s followed by the slower char burnout stage. T h i r t y percent of the weight of coal i s l o s t i n a p e r i o d of a l i t t l e under 4 seconds for the 3 mm p a r t i c l e . For 1 mm p a r t i c l e s the time f o r d e v o l a t i l i z a t i o n i s under 1 second. These times can be compared w i t h the estimates of the s o l i d c i r c u l a t i o n time of 3 to 6 seconds obtained above. The v o l a t i l e r e l e a s e time i s therefore comparable to the s o l i d c i r c u l a t i o n time and n e i t h e r the model of instantaneous or distributed v o l a t i l e release i s v a l i d . Park et a l (42) recognized the importance of modeling the v o l a t i l e release i n AFBC s and developed a plume model based on the instantaneous r e l e a s e of v o l a t i l e s and l a t e r a l d i f f u s i o n using a d i f f u s i v i t y based on t r a c e r d i s p e r s i o n . Their model succeeded i n showing the major importance of l a t e r a l d i f f u s i o n w i t h i n AFBC*s i n determining feed p o i n t l o c a t i o n . Stubingdon and Davidson (79) however showed that the combustion of hydrocarbons, which are a v a l i d surrogate f o r c o a l v o l a t i l e s , i s governed by molecular d i f f u s i o n which i s considerably lower than the r a d i a l d i f f u s i o n obtained from t r a c e r s t u d i e s . (The t r a c e r s t u d i e s apparently provide a measure of the meandering of a laminar stream without mixing at the molecular l e v e l needed f o r r e a c t i o n ) . The mechanism for r a d i a l d i s p e r s i o n i s due to s o l i d and not gas d i f f u s i o n . A s l i g h t v a r i a n t on the plume model of Park et a l (42) i s shown i n F i g . 9. Coal p a r t i c l e s i n j e c t e d a t the bottom of the bed are convected upward and d i f f u s e r a d i a l l y as a consequence of bubble motion. V o l a t i l e s w i l l be r e l e a s e d at a decaying r a t e f o r s e v e r a l seconds, depending upon p a r t i c l e s i z e and bed temperature. The radius r of the c r o s s - s e c t i o n over which the v o l a t i l e s are r e leased i s determined by the s o l i d d i f f u s i v i t y P . To a f i r s t approximation 1

g

r = ifuZt

(25)

The c o r r e l a t i o n proposed by K u n i i and L e v e n s p i e l (34) w i l l be here used to obtain an estimate f o r f} 3

(26)

The mechanism of s o l i d d i s p e r s i o n i s complex and p o o r l y understood so that Eq. 26 represents only a f i r s t approximation. For



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Figure 8. Time-resolved values o f the f r a c t i o n a l weight r e t e n t i o n o f c o a l p a r t i c l e s i n i t i a l l y 3 mm i n diameter burned i n a f l u i d i z e d bed at 1173 Κ and an oxygen c o n c e n t r a t i o n o f 5 percent. S o l i d l i n e c a l c u l a t e d from t h e o r y , data p o i n t s experimental.

F i g u r e 9· Schematic e l e v a t i o n and p l a n views o f v o l a t i l e plume formed by c o a l i n j e c t e d at base o f bed.



90

a v o i d volume δ of 0,3, a mean bubble diameter of 0.5, the value of Vs = 0.03 m^/s. The time f o r the bubble to r i s e to the surface we have p r e v i o u s l y shown to be of the order of 1.5 to 3 second. Consequently r - 0.4 to 0.6 m. The spacing Β of c o a l feed p o i n t s (Figure 9) should be such that the a i r f l o w i n g i n the c r o s s - s e c t i o n ïïr^ of the v o l a t i l e plume should be s u f f i c i e n t to o x i d i z e the v o l a t i l e s . The f r a c t i o n f of the s t o i c h i o m e t r i c a i r requirement needed to consume the v o l a t i l e s w i l l depend upon the v o l a t i l e y i e l d and composition (76, 79 80). A t y p i c a l value f o r f i s about 0.4. A f r a c t i o n f of about 0.1 of the s t o i c h i o m e t r i c a i r i s used to t r a n s p o r t the c o a l . The oxygen requirements of the v o l a t i l e s i s then s a t i s f i e d when v


y

v

a

2 f -f Trr _ y a 2~ 1+e π

(27)

B

For the values s e l e c t e d above Β i s 1.4 to 2.1 m. This estimate agrees w i t h current commercial p r a c t i c e of spacing feed p o i n t s at i n t e r v a l s of 1 to 3 m. For our t e s t case, t h i s corresponds to one c o a l feed p o i n t f o r every 1.8 to 4 MW, or approximately 25 to 55 feed p o i n t s . The requirement f o r a l a r g e number of feedpoints i s one of the shortcomings of AFBC s. Methods of overcoming the problem of m u l t i p l e feed p o i n t s i n c l u d e the use of a spreaders t o k e r to d i s t r i b u t e the c o a l evenly over the surface of the bed or the promotion of l a t e r a l mixing by r e c i r c u l a t i n g bed s o l i d s . 1

Emissions of Nitrogen Oxides (Staging of A i r A d d i t i o n ) 1

One of the advantages of AFBC s i s that t h e i r emissions of n i t r o g e n oxides can be c o n s i d e r a b l y lower than corresponding values from p u l v e r i z e d c o a l f i r e d b o i l e r s . The n i t r o g e n oxides are produced p r i m a r i l y by the o x i d a t i o n of n i t r o g e n o r g a n i c a l l y bound i n the c o a l (82, 83). Rapid conversion of the f u e l bound n i t r o g e n occurs near the d i s t r i b u t o r place w i t h peak l e v e l s of 1000 ppm NO and higher being observed. The NO concentration then decays as a consequence of both heterogeneous and homogeneous reactions. AFBC's operate i n the temperature regime i n which ammonia reacts s e l e c t i v e l y w i t h NO i n the presence of oxygen (84): NH

3

+ NO + 1/4 °

= 2

N

+ 2

3 / 2

H

2°

28>

( *

Ammonia i s evolved w i t h the c o a l v o l a t i l e s and may be t h e r e f o r e p a r t i a l l y r e s p o n s i b l e f o r the reduction of NO that occurs i n AFBC's. Because of the i n h i b i t i o n of f r e e r a d i c a l r e a c t i o n s w i t h i n the bed t h i s r e a c t i o n i s expected to be most important i n bub b l e s and i n the s o l i d disengaging height above the bed. This importance of the NII3/NO r e a c t i o n and i t s p a r t i a l suppression by bed s o l i d s has been demonstrated by the i n j e c t i o n of N H 3 i n t o


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d i f f e r e n t p o s i t i o n s w i t h i n a f l u i d i z e d bed combustor (85). These experiments showed that the NO r e d u c t i o n was most e f f e c t i v e when the ammonia was i n j e c t e d d i r e c t l y above the bed. Several heterogeneous r e a c t i o n s c o n t r i b u t e t o the r e d u c t i o n of NO i n AFBC's. Carbon w i l l reduce NO d i r e c t l y : (1 - γ)NO + C = 1/2 N

2

+ xCO + ( l - x ) C 0

(29)

2

The r a t e o f the r e a c t i o n (86-90) i s about two orders of magnitude slower than the O2/C r e a c t i o n , c o n s i s t e n t w i t h the greater strength o f the NO bond than that i n 0 . The C0/C0 r a t i o i n the products of the r e a c t i o n increases w i t h i n c r e a s i n g temperature (86, 87). At low temperatures (850 Κ ) , a s t a b l e chemisorbed oxygen compled (86) forms and i n h i b i t s the r e a c t i o n . At AFBC temperatures, however, i t has been observed that the r e a c t i o n i s a c c e l e r a t e d i n the presence o f oxygen (91). This l a t t e r r e s u l t may be a consequence o f the increase i n the CO concentration w i t h i n a char p a r t i c l e as the 0 concentration i s r a i s e d . Because the O2/C r e a c t i o n i s so much f a s t e r than the NO/C o r the carbon c a t a l y z e d CO/NO r e a c t i o n (86, 91), the s i t u a t i o n e x i s t s i n which the e f f e c t i v e n e s s f a c t o r f o r the O2/C r e a c t i o n i s s m a l l and l i t t l e O 2 p e n e t r a t i o n i n t o char occurs a t a time when the e f f e c t i v e n e s s f a c t o r f o r the NO reduction r e a c t i o n s are near u n i t y . A d d i t i o n a l NO reduction r e a c t i o n s that may occur are the CO/NO r e a c t i o n c a t a l y z e d by bed s o l i d s (90 - 92) and the reduction of NO by s u l f i t e - c o n t a i n i n g , p a r t i a l l y s u l f a t e d limestone (93).


2

2

2

CaS0 + NO = CaS0 + 1/2 N 3

4

(30)

£

T

A complete modeling of NO formation i n AFBC s i s a formidable task, depending upon the knowledge of the (1) d e v o l a t i l i z a t i o n chemistry and k i n e t i c s of f u e l n i t r o g e n which determines the d i s t r i b u t i o n of n i t r o g e n between char n i t r o g e n , ammonia, and other s p e c i e s , ( i i ) the k i n e t i c s o f formation o f NO by the o x i d a t i o n of the products o f d e v o l a t i l i z a t i o n , ( i i i ) the k i n e t i c s of reduction of NO by NH , C, CO, and CaS0 . In order t o solve f o r the NO concentration one needs t o a l s o determine the concentration of C, CO, and CaSO^ i n the bed and f o r the temperature overshoot by the carbon. Because o f the many chemical r e a c t i o n s i n v o l v e d , and the a d d i t i o n a l complexity introduced by the f l u i d mechanics, models of NO formation i n beds are only p a r t i a l . Several have been developed which adequately c o r r e l a t e a v a i l a b l e experimental data (94-98) but t h e i r p r e d i c t i v e c a p a b i l i t y i s yet to be proven. The understanding o f the dominant mechanism f o r NO formation and r e d u c t i o n can, however, guide the s e l e c t i o n of appropriate c o n t r o l s t r a t e g y . For example, the NO reduction by char can be a c c e l e r ated by i n c r e a s i n g the carbon l o a d i n g i n the bed by s t a g i n g the a i r a d d i t i o n (99-100). But s t a g i n g the oxygen w i l l increase the carbon l o a d i n g and correspondingly the formation o f carbon f i n e s , so that the reduction i n NO may be a t the expense of an increase i n carbon l o s s o r an increase i n r e c y c l e of t i n e s . 3

3



92

ENGINEERING

Freeboard Reactions (Determination of Freeboard Height) A height of three to four meters above the bed i s r e q u i r e d to a l l o w s o l i d s e n t r a i n e d by the bubble wakes i n t o the freeboard to r e t u r n to the bed s u r f a c e . The i n i t i a l v e l o c i t y of the s o l i d s that splash i n t o the freeboard i s 4 to 8 times the bubble r i s e v e l o c i t y (100) and the freeboard height i s determined by the k i n e t i c energy of the l a r g e r p a r t i c l e s f o r which drag forces are r e l a t i v e l y unimportant. For a bubble r i s e v e l o c i t y of 3.2 m/s (estimated from u - u f + 0.7l/gd^ (29) and a bubble diameter of 0.5 m), the maximum h e i g h t obtained by a p a r t i c l e w i t h an i n i t i a l v e l o c i t y s i x times the bubble r i s e v e l o c i t y i s 4.3 m, a t y p i c a l h e i g h t s e l e c t e d f o r the freeboard. The s o l i d concentration i n the freeboard i s s u f f i c i e n t l y h i g h to c o n t r i b u t e s i g n i f i c a n t l y to the r e a c t i o n s occuring i n AFBC's. Reactions of p a r t i c u l a r importance are those between NO and char, the burnout of carbon monoxide, and the combustion of the r e c y c l e d f i n e s . Space i s not a v a i l a b l e to cover the s u b j e c t adequately and the reader i s r e f e r r e d to s e l e c t e d l i t e r a t u r e on the subject (101-104). I t i s of i n t e r e s t to n o t e , however, that the e l u t r i a t i o n r a t e of l a r g e r p a r t i c l e s has been found to be g r e a t l y augmented by the concentration of f i n e s (103) i n a bed, so that the r e c y c l e of f i n e s may i n f l u e n c e bed behavior i n an unobvious manner.


0

m

Impact of Immersed Tubes on Flow Regimes In the above attempt to provide an order-of-magnitude e s t i mate of the f a c t o r s c o n t r o l l i n g the design and operation of AFBC s gross approximations were made, p a r t i c u l a r l y i n e s t i m a t i n g some of the flow and mixing parameters. A number of the c o r r e l a t i o n s used were derived from the l i t e r a t u r e on b u b b l i n g beds of f i n e p a r t i c l e s . I t must be emphasized that the flow regimes i n beds of coarse p a r t i c l e s d i f f e r from those i n beds of f i n e p a r t i c l e s (105, 106) and that t h i s must be taken i n t o c o n s i d e r a t i o n i n the s e l e c t i o n of the most r e l e v a n t models. The e a r l y s t u d i e s of flow i n coarse p a r t i c l e systems was f o r beds without immersed tubes (107, 108). More recent s t u d i e s have shown that the f l u i d mechanics and gas and s o l i d mixing can be considerably i n f l u e n c e d by the presence of tubes i n the bed (109114). The e f f e c t of tubes i n the bed i s t o decrease the pressure f l u c t u a t i o n s , presumably due to a r e d u c t i o n i n the s i z e of the bubbles. The net consequence of t h i s would be to i n c r e a s e the importance of the slow or c l o u d l e s s bubble regime (see Figure 4 ) . The data of F i t z g e r a l d , L e v e n s p i e l and co-workers (109) show that the impact of tubes i s to reduce the d i s p e r s i o n of gas due to the meandering of a t r a c e r gas plume but to increase the d i f f u s i o n due to t u r b u l e n t mixing. This augmentation of mixing by the tubes should be taken i n t o account i n the modeling of v o l a t i l e combustion. T


4.

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93


Although general treatments o f the flow i n f l u i d i z e d beds o f coarse p a r t i c l e s , i n view of the d i f f i c u l t y o f the problem, w i l l only evolve s l o w l y , there have been some promising developments. These i n c l u d e the success achieved i n c o r r e l a t i n g heat t r a n s f e r data (7_, 113, 114) and the development o f s c a l i n g parameters t h a t permit the use o f c o l d flow models t o study many of the c h a r a c t e r i s t i c s o f AFBC s (114,115), 1

Concluding Comments The above c o n s i d e r a t i o n o f the f a c t o r s that govern the design and operation o f the f i r s t generation of AFBC s provide an a p p r e c i a t i o n f o r the parameters t h a t c o n s t r a i n t h e i r perform ance. There i s c l e a r l y opportunity f o r improvement, p a r t i c u l a r l y w i t h respect t o reducing the amounts o f sorbent used f o r s u l f u r capture, reducing the number of c o a l feed p o i n t s , reducing the l o s s o f carbon f i n e s , and changing heat l o a d without v a r y i n g bed temperature. A number o f f l u i d i z e d bed combustors o f advanced design have been developed o r are under i n v e s t i g a t i o n . These i n c l u d e f a s t f l u i d i z e d beds, p r e s s u r i z e d beds, m u l t i - s t a g e beds, c i r c u l a t i n g beds, and r o t a t i n g beds. The f a s t - f l u i d i z e d r e c i r c u l a t i n g bed i s f u r t h e s t developed of those advanced concepts, and has already been commercialized. From a fundamental standpoint, the order o f magnitude e s t i mates of many o f the parameters i n the bed was intended t o i n d i c a t e which processes were important. There i s c l e a r l y a need f o r a b e t t e r understanding o f the processes that govern ( i ) par t i c l e c i r c u l a t i o n and e l u t r i a t i o n i n l a r g e p a r t i c l e systems, ( i i ) g r a i n growth f o r purposes o f improving stone u t i l i z a t i o n , ( i i i ) the generation and burnout o f f i n e carbon p a r t i c l e s . An attempt was made i n the p r e s e n t a t i o n t o show the complex i n t e r a c t i o n between the d i f f e r e n t processes occuring i n the bed. For example, sorbent u t i l i z a t i o n may a f f e c t N 0 through the formation o f CaSO^ and bed pressure drop through the dependence of s o l i d d e n s i t y on extent of s u l f a t i o n ; carbon burning times deter mine the carbon l o a d i n g i n the bed which i n turn governs both the amount of f i n e char p a r t i c l e generation and the r e d u c t i o n of NO; the carbon f i n e s i n f l u e n c e the e l u t r i a t i o n r a t e s of coarser p a r t i c l e s ; the carbon monoxide i n f l u e n c e s the carbon p a r t i c l e temperature overshoot and a l s o p a r t i c i p a t e s i n the surface c a t a l y z e d r e d u c t i o n o f NO. Such i n t e r a c t i o n s add t o the challenges of modeling t h i s c l a s s o f chemical r e a c t o r s .


1

X

Legend of Symbols ο A

0

Β C

bed c r o s s e c t i o n a l area, m spacing between c o a l feed p o i n t s , ra

Q

Cp

i n l e t oxygen c o n c e n t r a t i o n , mole/m

3

average oxygen concentration i n emulsion phase, mole/m

3

Continued on next page


94

C H E M I C A L R E A C T I O N ENGINEERING

Legend o f Symbols—Continued


3

C

t o t a l gas-phase molal c o n c e n t r a t i o n mole/m

d^

bubble diameter, m

d^

i n i t i a l diameter of char p a r t i c l e , m

dp

bed p a r t i c l e diameter, m

d*

diameter of p a r t i c l e s w i t h t e r m i n a l v e l o c i t y lower than fluidizing velocity, m ο gas-phase d i f f u s i v i t y , m /s 2 d i f f u s i o n c o e f f i c i e n t s f o r s o l i d s i n emulsion phase, m /s

V V

s

e

excess a i r , f r a c t i o n of s t o i c h i o m e t r i c

f

f r a c t i o n of s t o i c h i o m e t r i c coal feed

f

oxygen requirement to completely combust the v o l a t i l e s , f r a c t i o n o f s t o i c h i o m e t r i c a i r requirement

F

q

F^

a i r requirement

a i r used as c a r r i e r gas f o r

c o a l feed r a t e , Kg/s s o l i d s withdrawal r a t e , Kg/s 2

g

grativational acceleration,

m/s

h

height of bed, m

h

convective heat t r a n s f e r c o e f f i c i e n t i n Equation 8, W/(m )(°C)

2

2 h^

r a d i a t i v e heat t r a n s f e r coefficient,W/(m )(°C)

-ΔΗ^ k K(R)

heat of combustion, J/Kg c o e f f i c i e n t of a t t r i t i o n defined by Equation 20, dimension less e l u t r i a t i o n constant f o r p a r t i c l e s of s i z e R, s

Κ

r a t e constant f o r the S0 /Ca0 r e a c t i o n ,

s

2 o

9

cm/s

m

f r a c t i o n of calcium converted t o the s u l f a t e

m^

value of m approached a s y m p t o t i c a l l y a t l o n g times

m

rate of carbon l o s s from the bed, Kg/s. S u b s c r i p t s s, e, and a r e f e r t o l o s s w i t h s o l i d s w i t h d r a w a l , by e l u t r i a t i o n , and by a t t r i t i o n r e s p e c t i v e l y


4.

SAROFiM


95

Legend o f Symbols—Continued m

c o a l feed r a t e , Kg/s

Γ

Δτη

c o a l feed r a t e needed t o supply power f o r a i r fans, Kg/s

Γ

m

r a t e of s o l i d s withdrawal from bed, Kg/s

p(R)

f r a c t i o n o f mass of c o a l i n s i z e range R t o R + dR, m ^~

g


ρ (R) p(R) f o r c o a l feed stream, m ^ 2 ΔΡ

pressure drop across bed, N/m

r

radius of v o l a t i l e plume, m

R

p a r t i c l e radius, m

R^

p a r t i c l e r a d i u s o f monodisperse feed, m

Re

Reynolds number based on v e l o c i t y

R

r a t e of change of p a r t i c l e r a d i u s , m/s

Sc

Schmidt number

Sh t t Τ

Sherwood number residence time, s p a r t i c l e burnout time, s absolute temperature, °K. S u b s c r i p t s b, w r e f e r t o bed and tube w a l l temperature, r e s p e c t i v e l y

u^

bubble r i s e v e l o c i t y , m/s

b

u U

£

u m

f

/

£ m

f

i n

emulsion phase

minimum f l u i d i z i n g v e l o c i t y , m/s

mr

u

Q

f l u i d i z i n g v e l o c i t y , m/s

t

p a r t i c l e t e r m i n a l v e l o c i t y , m/s 3

ν

a

W

v o l u m e t r i c a i r supply per u n i t mass o f c o a l , m /Kg carbon mass i n the bed. Kg

c W

t o t a l mass o f the bed, Kg

^2

mole f r a c t i o n of oxygen

α

r a t i o of wake to bubble volume

δ

f r a c t i o n of bed volume occupied by bubbles


96

CHEMICAL

REACTION

ENGINEERING

Legend o f Symbols—Continued ε e

bed v o i d f r a c t i o n

mf

n

e

n

f

v o i

d f r a c t i o n a t minimum f l u i d i z i n g v e l o c i t y

f r a c t i o n a l e f f i c i e n c y o f conversion of thermal t o e l e c t r i c a l energy fan e f f i c i e n c y 3

ρ

carbon d e n s i t y , Kg/m 3

C

ρ


σ

bed s o l i d d e n s i t y , Kg/m s

τ

2 4 Stefan-Boltzmann constant, W/(m )(°K ) c h a r a c t e r i s t i c h e a t i n g time o f p a r t i c l e s , s

Acknowledgments The above overview has drawn on background developed as p a r t of an i n t e r d i s c i p l i n a r y program on f l u i d i z e d bed combustion a t MIT funded by DOE, w i t h p a r t i a l support from Stone and Webster E n g i n e e r i n g Corp, The authors i s indebted t o h i s students and c o l leagues f o r h i s education on many aspects o f the problem especially to Janos M. Beer, C h r i s t o s Georgakis, and Leon R. Glicksman whose views are r e f l e c t e d , a l b e i t through a g l a s s d a r k l y , i n the paper. Literature Cited 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11. 12. 13.

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1983


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