6 Modeling and Simulation of Dynamic and SteadyState Characteristics of Shallow Fluidized Bed Combustors L. T. F A N and C. C. CHANG Downloaded by CORNELL UNIV on October 15, 2016 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch006
Department of Chemical Engineering, Kansas State University, Manhattan, KS 66506
The dynamic and steady-state c h a r a c t e r i s t i c s of a shallow fluidized bed combustor have been simulated by using a dynamic model in which the lateral s o l i d s and gas d i s p e r s i o n a r e taken i n t o account. The model is based on the two phase theory of fluidizat i o n and takes i n t o c o n s i d e r a t i o n the e f f e c t s of the c o a l p a r t i c l e s i z e d i s t r i b u t i o n , r e s i s t a n c e due to d i f f u s i o n , and r e a c t i o n . The r e s u l t s of the s i m u l a t i o n i n d i c a t e that c o n c e n t r a t i o n gradients e x i s t in the bed; on the other hand, the temperature in the bed is q u i t e uniform a t any i n s t a n t in all the cases s t u d i e d . The r e s u l t s of the simulat i o n a l s o i n d i c a t e that there e x i s t a critical bubble s i z e and carbon feed r a t e above which "concentration runaway" occurs, and the bed can never reach the steady s t a t e .
F l u i d i z e d bed combustion is b e l i e v e d to be one of the most promising methods f o r d i r e c t burning of c o a l in an environmentally acceptable and economically competitive manner. Many mathematical models have been proposed to p r e d i c t the performance of fluidized bed combustors (see, e.g., l_-7). A review of the models has been presented by C a r r e t t o (8). Most of these models are steady-state ones, and, furthermore, assume that c o n c e n t r a t i o n and temperature v a r i a t i o n s do not e x i s t in the l a t e r a l d i r e c t i o n of the bed. However, it has been shown that there could be s i g n i f i c a n t v a r i a t i o n in the carbon c o n c e n t r a t i o n across a l a r g e fluidized bed r e a c t o r (9). Fan et a l . (10) have proposed an isothermal dynamic model f o r estimating the l a t e r a l carbon c o n c e n t r a t i o n d i s t r i b u t i o n in a shallow fluidized bed combustor. Simulation based on the model has i n d i c a t e d that an a p p r e c i a b l e carbon c o n c e n t r a t i o n gradient can e x i s t in the l a t e r a l d i r e c t i o n in the bed. The o b j e c t i v e of this work is to improve the model by e l i m i n a t i n g the assumption of isothermal c o n d i t i o n in the bed. 0097-6156/81/0168-0095$05.25/0 © 1981 American Chemical Society Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
CHEMICAL REACTORS
96
In the present work, the t r a n s i e n t and s t e a d y - s t a t e c h a r a c t e r i s t i c s of a fluidized bed combustor a r e s t u d i e d by s o l v i n g numeri c a l l y a dynamic model in which l a t e r a l s o l i d s and gas d i s p e r s i o n , l a t e r a l temperature d i s t r i b u t i o n and wide s i z e d i s t r i b u t i o n of c o a l feed are taken i n t o account. The i n f l u e n c e s of bubble s i z e , excess a i r r a t e , s p e c i f i c area of heat exchangers and c o a l feed r a t e on the performance of the fluidized combustor a r e examined by means of s i m u l a t i o n with the model.
Downloaded by CORNELL UNIV on October 15, 2016 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch006
Mathematical Formulation Let us consider a shallow fluidized bed combustor with mul t i p l e c o a l feeders which are used to reduce the l a t e r a l concentra t i o n gradient of c o a l (11). For s i m p l i c i t y , l e t us assume that the bed can be d i v i d e d i n t o Ν s i m i l a r c y l i n d e r s of radius R^, each with a s i n g l e feed point in the center. The assumption allows us to use the symmetrical p r o p e r t i e s of a c y l i n d r i c a l coordinate sys tem and thus g r e a t l y reduce the d i f f i c u l t y of computation. The model proposed is based on the two phase theory of fluidization. Both d i f f u s i o n and r e a c t i o n r e s i s t a n c e s in combustion a r e c o n s i d ered, and 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 of c o a l is taken i n t o account a l s o . The assumptions of the model are: (a) The bed con s i s t s of two phases, namely, the bubble and emulsion phases. The voidage of emulsion phase remains constant and is equal to that at incipient fluidization, and the flow of gas through the bed in excess of minimum fluidization passes through the bed in the form of bubbles (12). (b) The emulsion phase is w e l l mixed in the a x i a l d i r e c t i o n , and the s o l i d s mixing can be described by the d i f f u s i o n equation in the l a t e r a l d i r e c t i o n ( 9 ) . The bed can be c h a r a c t e r ized by an e f f e c t i v e bubble s i z e , and the bubble flow is of the plug type (10). (c) No e l u t r i a t i o n o c c u r s . (d) The convective transport o f c o a l p a r t i c l e s in the l a t e r a l d i r e c t i o n can be ne glected, (e) Ash is c o n t i n u o u s l y withdrawn from the bed a t the same r a t e as that in the feed. ( f ) The only combustion r e a c t i o n is C + 0 (g) The s o l i d s and gas are a t the same temperature. (h) The s i z e d i s t r i b u t i o n of c o a l p a r t i c l e s in the bed is the same as that in the feed; the s i z e s of c o a l p a r t i c l e s are widely d i s t r i b u t e d (_1) . These assumptions g i v e r i s e to the f o l l o w i n g equations: M a t e r i a l balances in the emulsion phase 3[CP (R)] b
)
3[CP, (R)S(R)]
3CP (R) S(R)
Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
(1)
6.
F A N A N D CHANG
Shallow
Fluidized
Bed
97
Combustors
^ C P - d R
ae a
e
ε
E
mf
,.
u, =
rc
5Ë
3t
(1 - 6 J L
(
ao
+-—
)
- C ae
>
(2)
ac a e
f rD
r 5r ^
ae
)
3r '
D δ
L
κ 1 1 - 6, L
i U
D
Downloaded by CORNELL UNIV on October 15, 2016 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch006
- Γ "
Τ
"
be
L
ab
v
ae
J
(3)
CP (R)dR h
B
0
M a t e r i a l balance in the bubble phase 3C
3C C
U
Τ Γ
" " b I T
"
*be
Energy balance
p C |f = - I - (rk |^) + V s S g m pm 3t r 3r e 3r' L K
v
+ {(1 - δ. ) Ζ"** B
v
(Τ go
- Τ) + Ψ_(1-6, )C (Τ -T) F b' p s so v
v
^ f ^ - CP. (R) dR}(-AH)
0
- ha(T - Τ ) + î>(t) w
(5)
where
pC
m pm
=pC
The appropriate t = (
C
δ +pC
g Pg g
initial
ab » C ae
C
ab
ac 3r
ac 3r
-
s ps
and boundary c o n d i t i o n s are ao* at ζ =
C
(1-6) g
Τ = Τ
(6)
p
ΪΓ + ΪΓ g
s
The heat source f u n c t i o n ,
