Coal-gasification kinetics derived from pyrolysis in a fluidized-bed reactor

Coal-gasification kinetics derived from pyrolysis in a fluidized-bed reactor

Pergamon PII: S0360-5442(98)00011-5 Energy Vol. 23, No. 6, pp. 475–488, 1998  1998 Elsevier Science Ltd. All rights reserved Printed in Great Brita...

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Pergamon

PII: S0360-5442(98)00011-5

Energy Vol. 23, No. 6, pp. 475–488, 1998  1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0360-5442/98 $19.00 + 0.00

COAL-GASIFICATION KINETICS DERIVED FROM PYROLYSIS IN A FLUIDIZED-BED REACTOR JONG MIN LEE, YONG JEON KIM, WOON JAE LEE and SANG DONE KIM† Department of Chemical Engineering and Energy and Environment Research Center, Korea Advanced Institute of Science and Technology, TaeJon 305-701, Korea (Received 7 July 1997)

Abstract—Coal pyrolysis and gasification reactions were carried out in a fluidized-bed reactor (0.1 m i.d. by 1.6 m height) over a temperature range from 1023 to 1173 K at atmospheric pressure. The overall gasification kinetics for the steam–char and oxygen–char reactions were determined in a thermobalance reactor. The compositions of the product gases from the coal-gasification reactions are 30–40% H2, 23–28% CO, 27–35% CO2 and 6–9% CH4 with heating values of 2000– 3750 kJ m−3. The heating value increases with increasing temperature and steam/coal ratio but decreases with increasing air/coal ratio. Our kinetic data derived from the two-phase theory on coal gasification in a thermobalance reactor and coal pyrolysis in a fluidized bed may be used to predict the product-gas compositions.  1998 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

Conversion of coal to gaseous fuel occurs in systems with integrated gasification combined cycles (IGCCs), which are becoming of increasing importance [1]. Gasification with O2, H2O, CO2 and H2 produces combustibles such as CH4 and CO/H2 mixtures for use as gaseous fuels or chemical feedstocks [2]. Among the coal-gasification processes, the fluidized-bed process with inherent advantages of high heat transfer and easy handling of solids is a natural choice [3,4]. Applications range from the Winkler process, one of the first commercial applications of fluidized-bed technology, to the more recent HTW (high-temperature Winkler) combined-cycle power-generation process. Coal gasification with O2 and H2O in a fluidized-bed reactor involves pyrolysis, combustion and steam gasification. To understand the gasification process, individual reaction steps must be identified. Numerous studies of coal gasification have been reported. In many cases, gasification was carried out with devolatilized chars without considering pyrolysis and combustion [5–7]. In some modeling studies, literature data were used with the assumption that complete combustion occurs very rapidly in a narrow reaction zone [8–12]. Since coal properties differ widely, kinetic data for coal combustion and gasification should be coal-specific. We have used Australian sub-bituminous coal in a thermobalance reactor and have studied pyrolysis in a fluidized-bed reactor. On the basis of these studies, a coal-gasification model in a fluidized-bed reactor is proposed. 2. EXPERIMENTAL STUDIES

2.1. Feed material The char particles for the thermobalance reactor were prepared by devolatilization of Australian subbituminous coal, which was heated from room temperature to 900°C at a rate of 10°C min−1 and then maintained for 30 min at 900°C. The coal-particle diameters for the pyrolysis and gasification reactions



Author for correspondence. Fax: 82-42-869-3910; e-mail: [email protected] 475

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J. M. Lee et al Table 1. Analyses of Australian coal and char preparation.

Proximate analysis

wt%, db

Ultimate analysis

Volatile matter Fixed carbon Ash Heating value (cal g−1 )

26.37 63.91 9.72 6273

C H O N S

Ash analysis (wt%) SiO2 = 60.2 Fe2O3 = 7.1 MgO = 0.2 K2O = 1.7

Al2O3 = 26.8 CaO = 0.4 TiO2 = 1.4 MnO = 0.1

wt%, daf 68.10 4.58 25.38 1.62 0.32

Char preparation Devolatilization temperature = 900°C Soaking time = 0.5 h Heating rate = 10°C min−1 Surface area = 63.9 m2 g−1 (N2 BET)

were 0.25 to 1.0 mm. The physical properties and proximate and ultimate analyses of the coal and char are given in Table 1. 2.2. Facilities and experimental procedure Details concerning the thermobalance reactor and experimental procedure may be found elsewhere [13,14]. To eliminate the influence of diffusion on reaction rate, experiments were performed with varying sample sizes and masses. We gasified 0.3–0.6 g of char in the size range 0.3–1.0 mm in a thermobalance reactor. Pyrolysis and gasification were carried out in a fluidized-bed reactor made of 316 stainless steel (see Fig. 1). The solid particles were supported on a bubble-cap distributor which contained seven bubble

Fig. 1. Schematic diagram of the fluidized-bed reactor: 1, water reservoir; 2, master pump; 3, steam generator; 4, air-flow meter; 5, air box; 6, distributor; 7, main bed; 8, bed drain; 9, overflow; 10, freeboard; 11, screw feeder; 12, coal hopper; 13, cyclone; 14, condenser; 15, collector; 16, dust filter; 17, condenser; 18, gas sampling bottle; 19, I.D. fan.

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caps (4 × 2.0 mm i.d.) that served as air and steam distributors. To measure temperature and pressure, eight pressure taps were mounted flush with the wall at 0.1 m height intervals from the distributor and six K-type thermocouples were similarly mounted along the bed height. A 6 kW electric heater was installed at the reactor wall. Sand of 0.27 mm average size with umf = 0.11 m s−1 served as fluidizing medium with a static bed height of 0.33 m from the distributor. For gasification, the reactor was heated to the ignition temperature of coal ( ⬇ 500°C) by using the electric heater. Thereafter, the electric heater was turned off and coal was fed to raise the bed temperature. When the reactor temperature reached a desired value, steam was introduced. A cyclone (0.076 m i.d by 0.304 m height) was installed at the outlet to collect fine particles. For the study of pyrolysis, the effects of reaction temperature and gas velocity on yield and also the heating value and compositions of the product gas were determined. For gasification, the effects of reaction temperature, gas velocity and air coal and steam coal ratios on yield, heating value and product-gas composition were determined. The product gases were analysed with gas chromatography (GC) with a molecular sieve and Porapak Q columns after removal of tar and condensable gases. The conditions and variables for the pyrolysis and gasification reactions are given in Table 2. 2.3. Modeling of coal gasification in a fluidized-bed reactor The overall gasification process involves pyrolysis in the freeboard region and combustion and steam gasification in the main bed region, where the following reactions occur. Combustion reactions: C + ␣O2 → 2(1 − ␣ )CO + (2␣ − 1)CO2.

(1)

Steam-gasification reactions [7]: C + H2O → CO + H2,

(2)

CO + H2O → CO2 + H2,

(3)

C + 2H2O → CO2 + 2H2,

(4)

C + ␤H2O → (2 − ␤ )CO + ( ␤ − 1)CO2 + ␤ H2.

(5)

Here, ␣ is a mechanism factor [15] which takes the value 0.5 when CO is transported away from the char particle and 1.0 when CO2 is transported away during char combustion. The factor ␣ is a function of char-particle diameter and temperature. For small particles, CO formed during char combustion diffuses out quickly because of rapid mass transfer and burns to form CO2 outside the particle. For large particles, because of slower mass transfer, CO burns within the boundary layer and CO2 is transported out. The values are

␣ = (p + 2)/(2p + 2) for dc ⬍ 0.005 cm

(6)

and Table 2. Experimental conditions and variables for the pyrolysis and gasification reactions. Variables

Pyrolysis

Gasification

Temperature (°C) u0 /umf Coal feed rate (kg h−1 ) Air/coal ratio (kg/kg) Steam/coal ratio (kg/kg)

750–900 1.5–3.0 0.897 — —

750–900 2–5 0.76–2.23 1.5–3.0 0.63–1.26

Coal dp (mm) Static bed height (m)

0.25–1.0 0.33

Sand dp (mm) Sand umf (m)

0.27 0.11

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␣ = (p + 2)/[(2p + 2) − p(dc − 0.005)/0.095] for 0.005 ⬍ dc ⬍ 0.1 cm,

(7)

p = 2500 exp( − 5.19 × 107 /RT).

(8)

where

In Eq. (5), (2 − ␤ )/ ␤ represents the fraction of the steam consumed by reaction (2) and 2( ␤ − 1)/ ␤ represents the fraction of steam consumed by reaction (4). Matsui et al. [7] determined ␤ experimentally to be in the range 1.5–1.1 at 750–900°C. They found that ␤ decreases with increasing temperature. In this study, ␤ from Matsui et al. [7] was used for modeling. Our model is based on the two-phase theory of hydrodynamics for a fluidized bed. The kinetic equations were obtained from the thermobalance reactor and from correlations for product-gas compositions during pyrolysis in a fluidized-bed reactor [16]. The basic equations are summarized in Table 3. The bubble diameter is estimated from a correlation of Mori and Wen [17] for Geldart B and D solids. The assumptions of the model are plug flow in the gas phase and a completely mixed emulsion phase at a uniform reactor temperature. The combustion of product gases is neglected. The model calculations for coal gasification proceed as follows. (1) Initially, the extent of solid conversion (Xt ) in the bed is assumed. (2) The bed hydrodynamic parameters are determined for the input condition. (3) The gas-concentration profile along the bed height is calculated from the hydrodynamic parameters, mass balance and gas reactions at a given Xt. (4) From the gas-concentration profile along the bed height, the extent of solid conversion (Xt⬘) is calculated. (5) An iteration process is repeated until the solid conversion (Xt⬘) converges to the initial conversion (Xt ). (6) With this value for solid conversion (Xt⬘), the product-gas compositions, gas-concentration profile and reactant-gas conversion may be predicted by using the pyrolysis data. 3. RESULTS AND DISCUSSION

3.1. Determination of kinetics in a thermobalance reactor The activation energies and reaction-rate constants for the combustion and steam-gasification reactions are determined from an Arrhenius plot using data obtained with the thermobalance reactor. Kinetic Table 3. Basic equations for modeling coal gasification in a fluidized-bed reactor. 1 Two-phase model parameters (a) Minimum fluidizing velocity [30] ( ⑀mf = 0.5, ⑀m = 0.4, ␳s = 2.4): umf = ( ␮ / ␳gdp )兵[28.72 + 0.0494d 3p␳g( ␳s − ␳g )g/ ␮2 ]1/2 − 28.7其. (b) Bubble-rise velocity with respect to the emulsion phase: ubr = 0.711(gdb )1/2. (c) Bubble-rise velocity: ub = u0 − umf + ubr. (d) Bubble volume fraction: ␦ = (u0 − umf )/(ub − umf ). (e) Interchange coefficient between the bubble and emulsion phases [31]: Kbe = 11/db. 2. Mass-balance equation (a) Definition of total conversion: Xt = 1 − [(discharge rate of coal) − (discharge rate of ash)]/[(feed rate of coal) − (feed rate of ash)], Xt = X1 + X2 + X3, where X1, X2, X3 are conversions for combustion, gasification, and pyrolysis, respectively. (b) Combustion and gasification kinetics (shrinking core model): Combustion-reaction rate = dX1 /dt = k1[exp( − E1 /RT)]PnO2(1 − X1 )2/3, Steam-gasification rate = dX2 /dt = k2[exp( − E2 /RT)]PnH2O(1 − X2 )2/3. (c) Gas-phase reaction rate equations: rO2 = − d[O2 ]/dt = k1PnO2(1 − X1 )2/3( ␳sFC /MB )␣, rH2O = − d[H2O]/dt = k1PnH2O(1 − X2 )2/3( ␳sFC /MB )␤, rH2 = d[H2 ]/dt = − rH2O, rCO = d[CO]/dt = − rO2[2(1 − ␣ )/ ␣ ] − rH2O[(2 − ␤ )/ ␤ ], rCO2 = d[CO2 ]/dt = − rO2[(2␣ − 1)/ ␣ ] − rH2O[( ␤ − 1)/ ␤ ]. (d) Reactant-gas mass balances: − ub d[Ci,b ]/dh = Kbe(Ci,b − Ci,e ), − (1 − ␦ )umf d[Ci,e ]/dh = (1 − ␦ )(1 − ⑀mf )ri,e − ␦Kbe(Ci,b − Ci,e ) (i = O2, H2O, H2, CO, CO2, N2 ), (boundary conditions — Ci,b = Ci0 and Ci,e = Ci0 at h = 0)

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values are calculated by using the rate of conversion with time at different reaction temperatures on the basis of the shrinking-core model shown in Fig. 2(a)Fig. 2(b). It is defined by dX/dt = k exp( − E/RT)Pn(1 − X)2/3,

(9)

where k is the frequency factor and E the activation energy. The carbon conversion is X = (W − Wash )/(W0 − Wash ),

Fig. 2. Conversion fraction of coal char as a function of time: (a) combustion reaction (O2 = 0.03 atm); (b) steam-gasification reaction (H2O = 0.5 atm).

(10)

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where W0 is the weight of coal char measured after completion of devolatilization. The weight of ash (Wash ) was determined after completion of combustion of the residual carbon in the thermobalance reactor. Thus, the slopes of the lines in Fig. 2(a)Fig. 2(b) include the term k exp( − E/RT) from which Fig. 3 is deduced. The activation energy for steam gasification in Fig. 3(b) is 40 kcal mol−1, which is similar to values obtained in previous studies [18–21] for the reaction-controlled regime. The rate of the steam-gasification reaction is so slow that chemical reaction control persists. For the combustion reaction [Fig. 3(a)], the activation energy is 27 kcal mol−1 in the chemical-reaction-controlled regime as obtained in previous studies [15,23,24]. However, with increasing temperature, the activation energy changes since the diffusion rate through the pores of particles or the gas film around particles is slower

Fig. 3. Arrhenius plot of coal char: (a) combustion reaction; (b) steam-gasification reaction.

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than the combustion reaction rate [15,22]. The reaction-rate equations were finally expressed in terms of apparent activation energies and rate constants for the individual reaction steps as follows. For combustion: dX1 /dt = k1[exp( − E1 /RT)]PnO2(1 − X1 )2/3,

(11)

where k1 = 75,785 s−1 atm−1 and E1 /R = 13,523 K for the chemical-reaction-controlled regime; k1 = 0.44 s−1 atm−1 and E1 /R = 3342.4 K for the pore-diffusion-controlled regime; and k1 = 0.046 s−1 atm−1 and E1 /R = 1166 K for the gas-film-diffusion-controlled regime. The steam-gasification reaction is: dX2 /dt = 6474.7[exp( − 19,544/T)]PH2O(1 − X2 )2/3.

(12)

In Eq. (11), n is considered to be 1.0 in view of previous studies [22–24]. For the steam-gasification reaction, n has been reported to be different in some previous studies [20,25]. It is actually 1.0 in the steam partial pressure range 0.25–0.8 atm as shown in Fig. 4. By using the rate equations for combustion [Eq. (11)] and steam gasification [Eq. (12)], the rate of conversion data may be reasonably well predicted as is shown in Fig. 5. 3.2. Coal pyrolysis in a fluidized-bed reactor Coal pyrolysis in a fluidized-bed reactor yields the products H2, CO, CO2 and CH4 for various reaction temperatures and fluidizing velocities. The effect of reaction temperature on product yield (mass%) at different fluidizing velocities is shown in Fig. 6. The mass fractions of H2 and CO increase but those of CH4 and CO2 decrease with increasing temperature. However, yields (g gas/g coal fed) of all compo-

Fig. 4. Effect of the steam partial pressure on the reaction rate for steam gasification; T = 850°C, slope = n = 1.0.

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Fig. 5. Comparison between experimental data and results from the shrinking-core model for the conversion of coal char: (a) combustion reaction; (b) steam-gasification reaction. The lines are calculated data.

nents increase with increasing temperature. This result indicates that H2 and CO are produced more rapidly than CH4 and CO2 with increasing temperature. It may reflect the fact that pyrolysis activated by a temperature increment has a strong influence on the production of H2 and CO in coal and steam– char gasification. With increasing fluidizing velocity, the mass fraction of the product gas does not vary greatly, although the gas yield is expected to increase due to increased mixing in the solids bed that enhances heat transfer. The heating value of the product gas obtained from pyrolysis increases from 920 to 1500 kcal kg−1 of feed and the conversion of coal to pyrolysis gas increases from 12 to 20% when the temperature is increased from 750 to 900°C. Calculated values of the product-gas yield based on correlations for previous studies [26,27] are shown in Fig. 6. The correlation of Loison and

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Fig. 6. Effect of reaction temperature on gas-product yields from pyrolysis at different gas velocities. The dotted curve (· · ·) is from [26]; the dashed curve ( – – – ) is from [27].

Chauvin [26] has been widely used to model coal gasification [10,11,15,28] and to estimate the mass fraction of the most important gaseous products as a function of the volatile content of coal. Ma et al. [27] proposed a correlation to predict the devolatilization yields for New Mexico sub-bituminous coal with variations of the average bed temperature. We find that their correlations [26,27] do not predict our pyrolysis data accurately. Instead, the product-gas yields from pyrolysis are given by yH2 = 8.233 × 10−4T − 0.073, yCO = 2.168 × 10−4T − 0.102, yCO2 = 2.999 × 10−6T + 0.039,

(13)

yCH4 = 2.561 × 10−5T + 0.011,

where T is in K and yi (kg h−1 ) is the gas-yield to coal-feed ratio (kg h−1 ) from pyrolysis on a dry ashfree basis. 3.3. Coal gasification in a fluidized-bed reactor The effect of reaction temperature on product composition is shown in Fig. 7. The solid lines represent values for pyrolysis [26,27] derived from our model. The product gases are 30–40% H2, 23–28% CO, 27–35% CO2, and 6–9% CH4. As the reaction temperature is increased, the yields of H2 and CO increase due to an increase in steam gasification and pyrolysis. At the same time, the CO2 yield decreases with a reduction of combustion reactions. Eqs. (11) and (12) show that the rates of combustion and gasification at 900°C are, respectively, 1.23 and 30.7 times faster than those at 750°C. The yields of CO and CO2 are increased in the product gas since the combustion reaction is faster than the steamgasification reaction. The amount of CH4 decreases with increasing reaction temperature since it is mainly produced by pyrolysis. As may be seen in Fig. 7, our model predicts the experimental data well

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Fig. 7. Effect of reaction temperature on gas composition from coal gasification based on model predictions in a fluidized-bed reactor. The lines are calculated data with (a) our model predictions, (b) from [26] and (c) from [27]. The air/coal ratio (by mass) is 1.5 and the steam/coal ratio (by mass) is 0.63. The lines refer to H2 (—— ——), CO ( – – – ), CO2 (· · ·) and CH4 ( – · – ).

and much better than previously published models [26,27]. We conclude that pyrolysis plays an important role in coal gasification, especially for coals with higher volatile contents. The gas compositions for pyrolysis and gasification with variations of reaction temperature and fluidizing gas velocity are shown in Fig. 8. We see that the yields of H2 and CH4 for pyrolysis are higher than those for gasification, whereas this trend is reversed for CO and CO2 because of char combustion and the production of H2 and CH4 with O2 in coal gasification. On the other hand, the slope of the H2 yield in gasification is steeper than that in pyrolysis, which means that the increase of H2 comes mainly from enhanced steam–char gasification with increasing temperature. The slope of the CO yield in gasification is similar to that in pyrolysis which may be caused by the steam–gas shift reaction. With increasing fluidizing-gas velocity, yields of the product gas increase due to increased mixing in the solids bed that enhances heat transfer. The effects of steam/coal and air/coal ratios on product compositions, together with the predicted values from our model, are shown in Fig. 9(a)Fig. 9(b). With increasing steam/coal ratio, the H2 yield increases slightly due to the increase of steam gasification. Since the reactivity in steam gasification is very low, yields of other components do not change appreciably. The air/coal ratio plays an important role in governing the product-gas quality [see Fig. 9(b)]. The yield of H2 decreases from 40 to 27% and the CO2 yield increases from 31 to 45% due to enhancement of combustion. As may be seen, the calculated values agree reasonably well with the experimental values. The heating value of the product gas is 2000–3750 kJ m−3, which is similar to values obtained in a previous study [29]. It increases with increasing reaction temperature and steam/coal ratio but decreases with increasing air/coal ratio. The heating value of the product gas as a function of carbon conversion is shown in Fig. 10. As the

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Fig. 8. Comparison of gas compositions from pyrolysis and gasification wth variation of reaction temperature and fluidizing gas velocity: closed symbols, pyrolysis; open symbols, gasification.

carbon conversion increases, the heating value increases at first, but then decreases drastically after the conversion exceeds 25%. This result may indicate that pyrolysis converts carbon to gas mainly at low carbon conversions. At high carbon conversions, combustion may govern carbon conversion and the associated reduction in the heating value of product gas. Coal pyrolysis plays an important role in coal gasification, especially for coals with high volatile contents. A comparison between the gas composition obtained from our model and the experimental data of Park et al. [22] and Saffer et al. [11] is shown in Table 4, in which the product-gas yield from pyrolysis is used for the product gas as a function of volatiles in the coals. This finding may represent the influence of temperature and volatile contents. On the basis of the good agreement between our model and the experimental data, we believe that our model is suitable for predicting the performance of fluidized-bed gasifiers. 4. CONCLUSIONS

Coal gasification was carried out in a fluidized-bed reactor over a temperature range from 1023 to 1173 K at atmospheric pressure. Kinetic data for the steam–char and oxygen–char reactions have been determined in a thermobalance reactor. Coal pyrolysis was studied in a fluidized-bed reactor. Our proposed model may be utilized to predict product-gas compositions from coal gasification with good accuracy. Acknowledgements—We acknowledge a grant-in-aid for research from the Hyundai Heavy Industry Co., Korea.

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Fig. 9. Effects of steam/coal ratio (a) and air/coal ratio (b) on gas composition from coal gasification with the model prediction lines in a fluidized-bed reactor; T = 850°C, air/coal ratio = 1.5, steam/coal ratio = 0.63. The lines refer to H2 (—— ——), CO ( – – – ), CO2 (· · ·) and CH4 ( – · – ).

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Fig. 10. Heating value of product gas in coal gasification with increasing carbon conversion.

Table 4. Predictions of the product-gas compositions and of coal conversion from the model. Gas composition (vol%)

Park et al. [22]

Saffer et al. [11]

Temperature = 900°C, S/Ca = 0.78

Temperature = 940°C, S/C = 1.27

A/Cb = 2.85 Experimental results

H2 CO CO2 CH4 Conversion

42.7 36.9 18.3 2.1 —

Predictions from our model 39.7 34.2 22.6 3.5 —

A/C = 3.80 Experimental results

39.9 34.3 24.0 1.8 —

Predictions from our model 37.1 34.1 24.8 3.9 —

A/C = 3.17 Experimental Predictions results from Saffer et al. 30.7 27.4 39.4 2.5 68.7

33.1 32.4 34.0 0.4 71.0

Predictions from our model 34.7 26.6 38.3 0.3 66.1

S/C = Steam-to-coal ratio on a mass basis. A/C = Air-to-coal ratio on a mass basis.

a b

REFERENCES

1. Alpert, S. B., Penner, S. S. and Wiesenhahn, D. F., Energy—The International Journal, 1987, 12, 639. 2. Haag, W. O., Kuo, J. C. and Wender, I., Energy—The International Journal, 1987, 12, 689. 3. Caram, H. S. and Amundson, N. R., Ind. Eng. Chem. Process Des. Dev., 1979, 18, 80.

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4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

J. M. Lee et al

Chatterjee, P. K., Datta, A. B. and Kundu, K. M., Can. J. Chem. Eng., 1995, 73, 204. Matsui, I., Kunii, D. and Furusawa, T., Ind. Eng. Chem. Res., 1987, 26, 95. Purdy, M. J., Felder, R. M. and Ferrell, J. K., Ind. Eng. Chem. Process Des. Dev., 1981, 20, 675. Matsui, I., Kunii, D. and Furusawa, T., J. Chem. Eng., Japan, 1985, 18, 105. Institute of Gas Technology, Prepared for U.S. Dept. of Energy, Contract No. Ex-76-C-01-2286, Report No. HCP/T2286-01, UC-90, 1978. Sundaresan, S. and Amundson, N. R., Chem. Eng. Sci., 1979, 34, 334. Kosky, P. G. and Floess, J. K., Ind. Eng. Chem. Process Des. Dev., 1980, 19, 586. Saffer, M., Ocampo, A. and Laguerie, C., Int. Chem. Eng., 1988, 28, 46. Bilodeau, J. F., Therien, N., Proulx, P., Czernik, S. and Chornet, E., Can. J. Chem. Eng., 1993, 71, 549. Song, B. H. and Kim, S. D., Fuel, 1993, 72, 797. Lee, J. S. and Kim, S. D., Energy—The International Journal, 1996, 21, 343. Rajan, R. R. and Wen, C. Y., AIChE J., 1980, 26, 642. Davidson, J. F. and Harrison, D., Fluidized Particles. Cambridge University Press, Cambridge, 1963, p. 116. Mori, S. and Wen, C. Y., AIChE J., 1975, 21, 109. Veraa, M. J. and Bell, A. T., Fuel, 1978, 57, 194. Schmal, M., Monteiro, J. L. F. and Castellan, J. L., Ind. Eng. Chem. Pro. Des. Dev., 1982, 21, 256. Kasaoka, S., Skata, Y. and Tong, C., Int. Chem. Eng., 1985, 25, 160. Kwon, T. W., Kim, S. D. and Fung, D. P. C., Fuel, 1988, 67, 530. Park, K. Y., Park, Y. C., Son, J. I. and Park, W. H., HWAHAK KONGHAK, 1987, 25, 345. Walker, P. L. J., Pusinko, F. J. and Austin, L. G., Adv. in Catalysis, 1959, 11, 133. Dutta, S. and Wen, C. Y., Ind. Eng. Chem. Pro. Des. Dev., 1977, 16, 31. Chin, G., Kimura, S., Tone, S. and Otake, T., Int. Chem. Eng., 1983, 23, 105. Loison, R. and Chauvin, R., Chimie et Industrie, 1964, 91, 269. Ma, R. P., Felder, R. M. and Ferrell, J. K., Fuel Process Tech., 1988, 19, 265. Yoon, H., Wei, J. and Denn, M. M., AIChE J., 1978, 24, 885. Gutierrez, L. A. and Watkinson, A. P., Fuel, 1982, 61, 133. Wen, C. Y. and Yu, Y. H., AIChE J., 1966, 12, 610. Kobayashi, H. and Arai, H., Kagaku Kogaku, 1967, 31, 239. NOMENCLATURE

Ci,b = Concentration of component i in the bubble phase (mol m−3 ) Ci,e = Concentration of component i in the emulsion phase (mol m−3 ) db = Bubble diameter (m) d¯b = Average bubble diameter (m) db0 = Bubble diameter just above the distributor (m) dbm = Maximum bubble diameter (m) dc = Char-particle diameter (m) dp = Particle diameter (m) dt = Bed diameter (m) E1 = Activation energy of the char–O2 reaction (kcal mol−1 ) E2 = Activation energy of the char–H2O reaction (kcal mol−1 ) FC = Weight fraction of carbon in the bed ( – ) F0 = Feed rate of coal in a fluidized bed reactor (kg h−1 ) h = Bed height (m) H = Bed height at the fluidization condition (m) i = H2, CO, CO2, O2 or CH4 ( – ) k1 = Rate constant for the combustion reaction (s−1 atm−1 ) k2 = Rate constant for the steamgasification reaction (s−1 atm−1 ) Kbe = Gas interchange coefficient (s−1 )

MB = Molecular weight of carbon ( – ) PH2O = Partial pressure of steam (atm) PO2 = Partial pressure of oxygen (atm) r = Reaction rate (s−1 ) t = Time (h) ¯t = Mean residence time of the solid in the bed (h) ub = Bubble-rise velocity (m s−1 ) ubr = Bubble-rise velocity with respect to the emulsion phase (m s−1 ) umf = Minimum fluidizing velocity (m s−1 ) u0 = Superficial gas velocity (m s−1 ) W = Mass of char (kg) Wash = Mass of ash (kg) Wb = Mass of solid in the bed (kg) W0 = Mass of char at completion of devolatilization (kg) X = Conversion of solid ( – ) Xt = Total conversion of coal ( – ) ␣ = Mechanism factor ( – ) ␤ = Product-distribution coefficient ( – ) ␦ = Bubble-volume fraction ( – ) ⑀m = Void fraction in a fixed bed ( – ) ⑀mf = Void fraction in a bed at minimum fluidizing conditions ( – ) ␳g = Gas density (kg m−3 ) ␳s = Solid density (kg m−3 )