Transient Simulation of Moving-Bed Coal Gasifiers - American

30 Transient Simulation of Moving-Bed Coal Gasifiers 1

WEN-CHING Y U and MORTON M . D E N N

2

University of Delaware, Newark, D E 19711 JAMES WEI Downloaded by CORNELL UNIV on October 9, 2016 | http://pubs.acs.org Publication Date: September 16, 1982 | doi: 10.1021/bk-1982-0196.ch030

Massachusetts Institute of Technology, Cambridge, M A 02139

A model for transient simulation of radial and axial composition and temperature profiles in pressurized dry ash and slagging moving bed gasi fiers is described. The model is based on mass and energy balances, thermodynamics, and kinetic and transport rate processes. Particle and gas temperatures are taken to be equal. Computation is done using orthogonal collocation in the radial variable and exponential collocation in time, with numerical integration in the axial direction. The transient response to feed rate changes is found to be approximately first order, but dependent on the direction of the change. Strategies for changes in operating level have been studied. The proposed use o f c o a l g a s i f i c a t i o n r e a c t o r s i n e l e c t r i c power systems w i l l r e q u i r e that the g a s i f 1 e r respond t o both l a r g e and small t r a n s i e n t s , i n c l u d i n g turndown t o , and s t a r t u p from, a hot banked s t a t e . We describe here a model f o r t r a n s i e n t s i m u l a t i o n o f r a d i a l and a x i a l composition and temperature p r o f i l e s i n a p r e s s u r i z e d moving bed g a s i f i e r l i k e the dry ash L u r g i r e a c t o r o r the BGC/Lurgi s l a g g e r . The countercurrent system i s shown s c h e m a t i c a l l y i n Figure 1. The model i s based on fundamental thermodynamic, k i n e t i c , and t r a n s p o r t p r o p e r t i e s , and hence i t can be used t o determine e f f i c i e n t operating and c o n t r o l p o l i c i e s f o r load f o l l o w i n g , s t a r t u p and shutdown, and changes i n feed p h y s i c a l and chemical p r o p e r t i e s .

1 2

Current address: Ε. I. DuPont de Nemours & Co., Inc., Seaford, D E 19973 Current address: University of California, Berkeley, CA 94720

0097-6156/82/0196-0359$06.00/0 © 1982 American Chemical Society Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

360

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

product gas

Downloaded by CORNELL UNIV on October 9, 2016 | http://pubs.acs.org Publication Date: September 16, 1982 | doi: 10.1021/bk-1982-0196.ch030

coal

Drying

Zone

(moisture d r i v e n

off)

Endothermic

Devolatilization

(

coal gas, tar

oil d r i v e n off

Thermally

ο ο NI C ο

/

Neutral

Gasification •

Zone and\

Zone

( l i t t l e or no o x y g e n ) Endothermic

u C o m b u s t i o n Zone (oxygen r i c h gas) Exothermic

ash

steam

+ unreacted carbon Figure 1.

a i r or oxygen

Schematic of a counter-current moving bed coal gasifier.

Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

Υ ϋ ET A L .

Moving-Bed Coal Gasifiers

361

The model development has been d e s c r i b e d i n d e t a i l elsewhere QL» .?)· S o l i d and gas are assumed t o be a t the same temperature, and the f o l l o w i n g chemical r e a c t i o n s a r e assumed t o occur:

AC + 0

+ 2 (λ - 1)C0 +

2

2

(1)

C + H 0

Î

CO + H

C + C0

2

î

2C0

(3)

C + 2H

2

t

CH

(4)

t

C0 + H

2


(2 - X ) C 0

CO + H 0 2

(2)

2

4

2

2

(at equilibrium)

(5)

R a d i a l d i s p e r s i o n o f mass and heat i s i n c l u d e d . A x i a l d i s p e r s i o n o f mass i s always n e g l i g i b l e , but a x i a l heat d i s p e r s i o n must be i n c l u d e d a t low throughputs. The mass balance f o r each gaseous s p e c i e s i s o f the form

i from one through s i x r e p r e s e n t s steam, oxygen, hydrogen, carbon monoxide, carbon d i o x i d e , and methane, r e s p e c t i v e l y ; j from one through four represents r e a c t i o n s one through f o u r , r e s p e c t i v e l y . The mass balance f o r f i x e d carbon i s w r i t t e n i n terms o f f r a c t i o n o f unreacted f i x e d carbon,

F

Ρ- + Σ α,, R = (1 - ε) & c 3Ϊ ' 7 j *J " " 3t j=l T

u

4

V

i

w

(7)

F£ i s the molar feed f l u x o f f i x e d carbon, and s u b s c r i p t 7 r e f e r s t o f i x e d carbon. F i n a l l y , the energy balance leads to the f o l l o w i n g equation f o r the temperature d i s t r i b u t i o n , w i t h p a r t i c l e and gas temperatures taken t o be e q u a l :

dz Tec [ερ gcv g + (1 - ε)p c g Vg

3T ]

S VS

dt


(8)

362

CHEMICAL REACTION ENGINEERING

Boundary c o n d i t i o n s a r e as f o l l o w s : 3C « 0 a t r=0 and r ; i-1,2,

6

o

C i

C. a t ζ = 0 ; 1-1,2, io

6

w = 1 at ζ = L

k

a f


9Z

« (Η g

(9a)

(9b) (9c)

- Η ) (T-T, ) a t z=0 S

(10a)

D

k

a

f3z

= 0 a t z=L

(10b)

k

r

Ρ Br

- 0 a t r=0

(10c)

k

r

f3r

= -h (T-T ) a t r=r w o

(lOd)

r i s the r a d i u s o f the i n n e r w a l l . Equations (10a) and (10b) are not r i g o r o u s l y c o r r e c t when there i s r a d i a l d i s p e r s i o n , but they d i f f e r n e g l i g i b l y from the one-term approximation t o the exact boundary c o n d i t i o n s developed by Young and F i n l a y s o n (3)· A x i a l d i s p e r s i o n of heat i s important only a t throughputs l e s s than t e n percent o f f u l l l o a d ; the appropriate equations a t h i g h e r through puts are obtained by s e t t i n g k to zero i n Equations (8) and (10). a

The w a l l c o o l i n g has a major e f f e c t when there are l a r g e changes i n r e a c t o r throughput. When t u r n i n g down a g a s i f i e r , the temperature o f the bed w i l l be lowered due t o heat l o s s t o the environment, and the thermal boun dary l a y e r w i l l penetrate inwards t o the c e n t r a l core. The i n c r e a s e d r e s i d e n c e time p r o v i d e s time f o r excess steam to react w i t h carbon. These e f f e c t s c o n t r i b u t e to lowering the maximum temperature i n a d r y ash g a s i f i e r l i k e the L u r g i , and the combustion zone moves upwards. 01) Orthogonal c o l l o c a t i o n on two f i n i t e elements i s used i n the r a d i a l d i r e c t i o n , as i n the s t e a d y - s t a t e model ( 1 ) , w i t h J a c o b i and s h i f t e d Legendre polynomials as the approx imating f u n c t i o n s on the i n n e r and outer elements, r e s p e c tively. E x p o n e n t i a l c o l l o c a t i o n i s used i n the i n f i n i t e time domain (4, 5). The approximating f u n c t i o n s i n time have the form


30.

Y U ET A L .


-t y ( z , r , t ) = y ( z , r , ~ ) + e*

N+l Σ i-1 d. ( z , r ) t i-1 " i

363

(11)

The c o l l o c a t i o n p o i n t s a r e the r o o t s o f (12) where Ι Λ i s the Laguerre

polynomial (13)


L

n

=

e

t

t

"

P

" 4

{

e

"'

t

P

^ >

T h i s approximating scheme r e q u i r e s that the process be s t a b l e and approach a new steady s t a t e . The i n i t i a l and f i n a l steady s t a t e p r o f i l e s a r e r e q u i r e d , and these a r e obtained from the steady s t a t e model. The approximating scheme converts the system o f p a r t i a l d i f f e r e n t i a l equations t o a s e t o f o r d i n a r y d i f f e r e n t i a l equations i n the a x i a l s p a t i a l c o o r d i n a t e . The d e t a i l e d equations a r e contained i n Yu e t a l . ( 2 ) . The advantage o f r e d u c t i o n i n t h i s manner i s that the t r a n s i e n t l o c a t i o n o f the combustion zone does not have t o be known a p r i o r i , but can be found i n the course o f the i n t e g r a t i o n s . Gear i n t e g r a t i o n , which i s designed f o r s t i f f systems, i s used t o s o l v e the two p o i n t boundary value problem i n the a x i a l d i r e c t i o n . There a r e three parameters i n e x p o n e n t i a l c o l l o c a t i o n : ρ; N; and a c h a r a c t e r i s t i c time, A t . D i f f e r e n t values o f ρ have been used, and no d i f f e r e n c e has been observed; ρ = 0 was used i n the s i m u l a t i o n s that f o l l o w . The number o f c o l l o c a t i o n p o i n t s (N + 1) i s e q u i v a l e n t t o the r e c i p r o c a l of the step s i z e i n f i n i t e d i f f e r e n c e methods; the more p o i n t s used, the greater i s the accuracy, but the more time consuming the s o l u t i o n . The s e n s i t i v i t y o f the s o l u t i o n t o Ν and At i s shown i n F i g u r e 2, which shows the movement o f the combus t i o n zone i n an a d i a b a t i c d r y ash g a s i f i e r when the throughput i s reduced t o 80% o f f u l l l o a d a t constant feed r a t i o s . Four c o l l o c a t i o n p o i n t s appear t o give reasonable accuracy, and were used i n the s i m u l a t i o n s that f o l l o w , with two c o l l o c a t i o n p o i n t s i n the r a d i a l d i r e c t i o n . The boundary c o n d i t i o n on f i x e d carbon (w • 1) a t ζ • L was s a t i s f i e d t o w i t h i n 0.003; t h i s e r r o r corresponds t o an average u n c e r t a i n t y o f 0.02 i n the normalized l o c a t i o n z/L o f the maximum temperature. The base case f o r a l l c a l c u l a t i o n s shown here i s a 3.7 m diameter d r y ash air-blown L u r g i r e a c t o r w i t h a 3.0 m




364


30.

YU ET AL.

high r e a c t i o n zone, g a s i f y i n g I l l i n o i s No. 6 c o a l a t 25 atm w i t h a steam-to-oxygen r a t i o o f 6.7, a f i x e d carbon-to-oxygen 2 r a t i o o f 2.80, and an oxygen f l u x o f 0.155 kg/m sec ( 6 ) . The t r a n s i e n t s r e s u l t i n g from t u r n i n g the feed f l u x e s down p r o p o r t i o n a l l y from f u l l load t o 80, 50, and 30% throughput were s t u d i e d without c o n s i d e r i n g a x i a l thermal d i s p e r s i o n . Temperature and f i x e d carbon p r o f i l e s i n the c e n t r a l core ( r / r • 0.49) and the boundary l a y e r ( r / r - 0.93) a r e shown i n F i g u r e s 3 and 4, r e s p e c t i v e l y , f o r turndown t o 30%. The f i n a l steady s t a t e i s reached i n about 40 hours. The f r a c t i o n a l approach t o the new steady s t a t e i n the c e n t r a l core i s p l o t t e d on semi-logarithmic coordinates i n F i g u r e 5. A s t r a i g h t l i n e on such a p l o t i n d i c a t e s a f i r s t - o r d e r r e s ponse. T h i s i s a p a r t i c u l a r l y s e n s i t i v e way t o p l o t the r e s u l t s , s i n c e d i f f e r e n c e s o f comparable q u a n t i t i e s a r e being taken. The r e l a t i v e e r r o r i s l a r g e s t f o r turndown to 80%. Within the accuracy used t o s a t i s f y the boundary c o n d i t i o n at ζ = L, the three curves cannot be d i s t i n g u i s h e d from the r e s u l t f o r turndown t o 50%. The apparent f i r s t - o r d e r time Q


365


Q

constant (time t o reach a v a l u e o f e ^) ranges from a p p r o x i mately s i x t o nine hours, depending on the amount o f turndown. The pseudo-steady-state a n a l y s i s f o r s m a l l t r a n s i e n t s used by Yoon e t a l . (7)» which i s based on the speed o f the thermal wave, a l s o gives an apparent f i r s t - o r d e r response, but the computed time constant i s two t o three hours. I t has been shown (1) that the carbon-to-oxygen r a t i o must be i n c r e a s e d when the r e a c t o r i s turned down i n order to keep the combustion zone from moving up i n the bed. The movement o f the combustion zone w i t h time i s shown i n Figure 6 f o r a number o f feed r a t i o programs w i t h turndown to 50% throughput. A sudden i n c r e a s e o f the f i x e d carbonto-oxygen r a t i o t o the new steady-state value w i l l lower the combustion zone a l i t t l e i n i t i a l l y , and then r a i s e i t t o the f i n a l steady s t a t e . Compared w i t h other programs, a sudden i n c r e a s e o f the feed f l u x r a t i o o f 0/0^ i s an e f f e c t i v e way to turn down a g a s i f i e r . The f r a c t i o n a l approach t o steady s t a t e f o l l o w i n g an i n c r e a s e i n the throughput from 30, 50, and 80% t o f u l l load i s shown i n F i g u r e 7. There i s a s i n g l e time constant o f about three hours. The t r a n s i e n t time f o r s t a r t u p i s s h o r t e r than f o r turndown because a sudden i n c r e a s e o f the f l u x i n c r e a s e s the flame v e l o c i t y .



366


2400

H 1500

1250

4

1000 ο

0

Figure 3.

Η

750

Η

500

2 4 6 8 10 AXIAL DISTANCE ABOVE GRATE, ft

Temperature profiles at r/r = 0.49 for turndown from full to 30% load. Key: 1,0 h; 2,9.4 h; 3,33.1 h; and 4,77.6 h. 0


30.

YU ET AL.



m 2400°

'

2000

^ 1600 Lu or

Si 1200 ω CL

ω 800

400

Ο Ο Figure 4.

2 4 6 8 10 AXIAL DISTANCE ABOVE GRATE, ft

Temperature profiles at r/r = 0.93 for turndown from full to 30% load. Key: 1,0 h; 2,9.4 h; 3,33.1 h; and 4,77.6 h. 0




368

TIME, hr Figure 5. Fractional approach to the new steady-state in central core (r/r = 0.49) for turndown from full to various partial loads. Key: O, turndown to 80%; • , turndown to 50%; and Δ , turndown to 30%. 0


Y U ET A L .

369



30.

X

10

20

X

30 TIME, hr

40

50

60

Figure 6. Movement of the combustion zone with time for a number of feed ratio programs with turndown to 50% load.



Figure 7. Fractional approach to the new steady-state at r/r = 0.49 for turning up the gasifier to full load from various initial loads. Key to initial output: O, 80%; Q 50%; and Δ, 30%. 0


30.

YU

ET

371


AL.


When the throughput i s turned down to below 10% o f f u l l l o a d , a x i a l d i s p e r s i o n i s important and i s i n c l u d e d i n the energy equation. F i g u r e 8 shows the t r a n s i t i o n to a 1% throughput, s i m u l a t i n g the approach to a banked c o n d i t i o n , w i t h the f i x e d carbon-to-oxygen feed r a t i o changed to 3.5 a t time zero. The time constants w i t h a x i a l d i s p e r s i o n are s i m i l a r to the other turndown c a l c u l a t i o n s . In the s l a g g i n g g a s i f i e r , the low steam-to-oxygen feed r a t i o and the h i g h temperature burner gas keep the combustion zone low, and t u r n i n g down the throughput does not change the l o c a t i o n of the combustion zone. The major change occurs i n the boundary l a y e r , where the g r e a t e r r e l a t i v e importance of heat l o s s t o the w a l l decreases the c o n v e r s i o n and hence the thermal e f f i c i e n c y . U n l i k e the dry ash g a s i f i e r , the t r a n s i e n t time i s not c o n t r o l l e d by movement of the thermal wave, and the t r a n s i e n t time i s c o n s i d e r a b l y f a s t e r . The computed time t o reach a new steady s t a t e f o l l o w i n g turndown to 30% throughput i s f i v e hours, and i t i s one-half hour f o l l o w i n g turnup from 30% t o f u l l l o a d . The major t r a n s i e n t i s the heat t r a n s f e r between the bed and the water j a c k e t . At the h i g h e r flow r a t e , the thermal boundary l a y e r i s t h i n n e r and the c o n v e c t i o n term i s more important, and hence r e t a r d s the t r a n s i e n t .

0

Figure 8.

2 4 6 8 AXIAL DISTANCE ABOVE GRATE, ft

10

Temperature profiles for turndown to 10% (F.C./O = 3.5) from full load (F.C./Ot = 2.8); 1,0 h; 2,9.4 h; 3,33.1 h; and 4, 77.6 h. t


CHEMICAL REACTION ENGINEERING Symbols

molar c o n c e n t r a t i o n

o f species i

heat c a p a c i t y of gas (g), s o l i d (s) s p a t i a l c o e f f i c i e n t o f approximating f u n c t i o n diffusivity molar feed f l u x o f f i x e d carbon w a l l heat t r a n s f e r c o e f f i c i e n t Downloaded by CORNELL UNIV on October 9, 2016 | http://pubs.acs.org Publication Date: September 16, 1982 | doi: 10.1021/bk-1982-0196.ch030

convective heat c a p a c i t y f l u x o f gas(g),

solid(s)

enthalpy o f r e a c t i o n j a x i a l ( a ) , r a d i a l ( r ) e f f e c t i v e thermal c o n d u c t i v i t y height o f r e a c t i o n zone Laguerre polynomial radial

coordinate

reactor inner

radius

apparent r a t e of r e a c t i o n j time c h a r a c t e r i s t i c time i n e x p o n e n t i a l

collocation

temperature blasrt (b), w a l l (w) temperature gas s u p e r f i c i a l v e l o c i t y f r a c t i o n o f unreacted f i x e d carbon axial

coordinate

s t o i c h i o m e t r i c c o e f f i c i e n t of s p e c i e s i i n r e a c t i o n j v o i d f r a c t i o n o f bed s e l e c t i v i t y parameter f o r o x i d a t i o n r e a c t i o n density of s o l i d

( s ) , gas (g)


30.

YU ET AL.


373

Acknowledgment T h i s work was supported by the E l e c t r i c Power Research Institute.


Literature Cited 1.

Yu, W. C . ; Denn, M. M.; Wei, J. "Radial Effects in Moving Bed Coal Gasifiers," AIChE annual meeting, New Orleans, Nov. 8-12, 1981.

2.

Yu, W. C . ; Denn, M. M.; Wei, J. "Two Dimensional Steady State and Transient Modeling of Moving Bed Coal Gasifiers," report to Electric Power Research Institute, RP-1268-1, in press (1982).

3.

Young, L. L.; Finlayson, B. A. Ind. Eng. Chem. Fundam., 12, 412 (1973).

4.

Guertin, E. W.; Sorensen, J . P; Stewart, W. E. Comp. & Chem Eng., 1, 197 (1977).

5.

Birnbaum, I.; Lapidus, L. Chem. Eng. S c i . , 33, 455 (1978).

6.

Yoon, H.; Wei, J.; Denn, M. M. Chem Eng. S c i . , 34, 231 (1979).

7.

Yoon, H.; Wei, J.; Denn, M. M. AIChE J., 25, 429 (1979).

Received April 27, 1982.


Transient Simulation of Moving-Bed Coal Gasifiers - American

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