Ind. Eng. Chem. Res. 1996, 35, 4139-4146
4139
Steam Activation of a Bituminous Coal in a Multistage Fluidized Bed Pilot Plant: Operation and Simulation Model Ignacio Martı´n-Gullo´ n,* Manuel Asensio, Antonio Marcilla, and Rafael Font Chemical Engineering Department, Universidad de Alicante, P.O. Box 99, E-03080 Alicante, Spain
A hydrodynamic and kinetic model was developed and applied to simulate the experimental data from a three-stage fluidized bed pilot plant with downcomers. This was used to study the activated carbon production from a Spanish bituminous coal by steam gasification. The steam gasification kinetics, considering the influence of inhibitors, were also determined in a thermobalance. With the kinetic equation and the experimental solids residence time distribution of the pilot plant, the model simulates the overall process that takes place in the reactor. The proposed model is able to reproduce the experimental results satisfactorily. Introduction The University of Alicante has developed a wide research project (funded by the European Union) in order to study the production of activated carbons at pilot plant scale from a bituminous coal [which was selected from previous laboratory-scale studies (Mun˜ozGuillena et al., 1992)], by steam activation. Part of this project was the design, construction, and operation of a three-stage fluidized bed pilot plant with downcomers. The process, to obtain activated carbons, consists of two steps: (i) carbonization of the raw material in an inert atmosphere at moderate temperatures (500-900 °C) and (ii) gasification of the char obtained with an oxidizing agent, e.g., steam (800-950 °C). The process may be carried out in separate reactors and operations or simultaneously in the same reactor in a single process, which is called direct activation. Interest in fluidized beds has grown due to the good solid-gas contact. The steam gasification of chars, which takes place in continuous fluidized bed reactors, has been modeled from thermogravimetrically obtained kinetics by Matsui et al. (1985). The steam gasification reaction rate, when the proccess is carried out at atmospheric pressure, has been studied by several authors, e.g., van Heek and Mu¨lhen (1991), with an apparent constant as a Langmuir-Hisselwood-type equation:
dX ) kap(1 - X)n ) dt
( )
k1 exp -
( )
Ea P RT H2O
(
)
∆H2 ∆H3 1 + K2 exp PH2O + K3 exp P RT RT H2
(1 - X)n (1)
where X is the degree conversion of fixed carbon that equals the burn-off degree. This equation considers the inhibition due to hydrogen. The reaction order, with respect to the nonreacted carbon, is generally 0 for catalyzed gasification, 0.67 under diffusion-controlled kinetics (unshrinking core model), and 1 under chemical-controlled kinetics (uniform conversion model) (van Heek and Mu¨lhen, 1991). Modeling fluidized bed reactors is quite a delicate task, and many different assumptions may be taken into account (i.e., one-, two-, and three-phase models). Le * E-mail:
[email protected].
S0888-5885(95)00759-7 CCC: $12.00
Table 1. Analysis and Characteristics of High Volatile Bituminous Coal from Puertollano Basin (Spain) proximate (wt %) elemental (wt %)
moisture
volatiles
ash
fixed carbon
6
28
8
59
C
N
H
O
60
1.2
3.8
36.9
Bolay et al. (1989a,b) pointed out that the application of the Davidson model (two-phase model) to a steam gasification proccess in the fluidized bed reactor hardly improves the results obtained by a simplified one-phase model. Consequently, the one-phase model is an acceptable aproximation in order to study the steam gasification of coals. No papers have been found considering the simulation of coal gasification in a multistage fluidized bed reactor. In this paper, a model is proposed to simulate the experimental burn-offs of the activated carbons obtained in the three-stage fluidized bed reactor with downcomers, based on previous thermogravimetrycally obtained kinetics, experimental solids residence time distribution, and a fluidized bed model. Steam Gasification Kinetics Materials. Table 1 shows the analysis of the coal used in this work, which is a high volatile bituminous coal from the Maria Isabel mine, Puertollano, Spain. Coal particles with particle size between 1.50 and 0.84 mm (mean 1.13 mm) were used. This coal does not present thermoplastic behavior, and consequently, no air pre-oxidation treatment was necessary to avoid the coke formation. Most of the activations runs done in the pilot plant were carried out by the direct activation method. The char formed in the carbonization was produced at high heating rates, discharging the fresh material into the fluidized bed at 800-900 °C. The steam gasification kinetics were thermogravimetrically determined for a char obtained in similar conditions. Equipment. The experimental equipment used to determine the kinetic constants of the steam gasification process of a char obtained under high heating rate conditions is shown in Figure 1. It consists of a C. I. Electronics MK2 thermobalance equiped with an 800-W electric furnace. The water, fed by the action of an HPLC pump (0.15 g/min), is vaporized in a DMT steam generator at 180 °C, assuring an even steam flow. An H2/CO (50% vol) stream may be mixed with the latter one in order to study the reaction in the presence of inhibitors. This reactive stream is fed at point 1 to the © 1996 American Chemical Society
4140 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
Figure 3. Experimental apparent reaction rate constant vs hydrogen partial pressure at 830, 850, and 870 °C.
Figure 1. Thermobalance equipment used to determine the steam gasification kinetics.
muir-Hisselwood-type eq 1, using the simplex flexible method (Himmelblau, 1970) and obtaining the following equation:
dX ) dt 195447 PH2O RT (1 - X) 372 93510 1 + 6927 exp PH2O + 12.6 exp P H2 RT RT (s-1) (2)
(
3.5 × 109 exp -
( )
)
(
)
The activation energy and the hydrogen adsorption enthalpy values calculated agree with the range of values in literature for the same reaction with similar char materials. Three-Stage Fluidized Bed Pilot Plant with Downcomers Figure 2. Experimental and best fit to first-order kinetics of the natural logarithm of the nonreacted carbon fraction (1-X) vs reaction time, at 850 °C and PH2O ) 1 atm.
thermobalance and is not mixed with the purge gas until the exit of the exhaust gases, which leave the system at point 2. The mass balance data are transfered continuously to a PC-compatible computer. The sample mass used was always around 10 mg. Results. Twenty different runs were carried out at temperatures ranging from 800 to 870 °C at steam partial mole percentage from 64% to 100% (the remaining percentages correspond to the equimolar CO/H2 mixture). All runs were adjusted successfully to the uniform conversion model (yielding correlation coefficients better than 0.99 when correlating ln(nonreacted fixed carbon fraction) linearly vs time), giving a firstorder kinetics with respect to the nonconverted carbon fraction. Figure 2 shows the correlation for one run as an example. Consequently, an apparent constant value, kap, was obtained at each different experimental condition. Figure 3 shows the variation of the apparent firstorder kinetic constant vs hydrogen partial pressure for three different temperatures. It can be observed that the presence of hydrogen strongly inhibits the gasification reaction, yielding apparent constants more than 10 times lower, with only 15% of hydrogen with respect to the apparent constant obtained with pure water vapor. All these apparent constants, with their respective experimental conditions, were adjusted to the Lang-
Experimental Equipment. Figure 4 shows a scheme of the three-stage fluidized bed reactor with downcomers. Coal/char (depending on the experimental run) initially in a hopper is fed by the action of a screw feeder (10-40 kg/day) to the upper fluidized bed, crosses the reactor downwards through the next stages by the downcomers, and finally leaves by a weir to an activated carbon reservoir. On the other hand, the reactive gas, steam generated in an industrial boiler, is introduced into the reactor at the bottom, crosses a preheater (with ceramic balls inside) and the three stages countercurrently to solids, and finally exits at the top into the atmosphere. All stages are identical, with 0.147 m i.d. and 0.75 cm long, each fluidized bed 0.15 m in height, and including a vertical baffle in the middle in order to narrow the overall solids RTD. Two downcomers of 0.021 m i.d. and 0.85 cm long allow the solids transfer bed from the upper bed to the lower one. Perforated plates, with 1-mm orifices, are used as distributors. The perforated plate at the lower stage has 2.36% free area, whereas the middle and upper plates have 7.9% free area. Four independent electric furnaces of 10 kW each supply the heat needed to carry out the process. The furnaces are controlled by the respective thermocouples. The hydrodynamic behavior of the reactor is monitored, measuring the absolute pressure of each stage by the respective manometers. Solids Residence Time Distribution. The solids residence time distribution through the three-stage
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4141
Figure 5. Experimental solids residence time distribution (normalized with respect to dimensionless time) vs dimensionless time. Continuous line shows the best fit to tank in series model.
Figure 4. Continuous three-stage fluidized bed pilot plant with downcomers. Diagram of the experimental equipment: a, hopper; b, screw feeder; c, fluidized bed; d, downcomer; e, activated carbon reservoir; f, preheating stage; g, cyclone; h, burner; i, electric furnaces; j, thermocouples; k, steam generator; l, pressure reductor; m, regulation valve; n, orifice; o, steam preheater; p, sampler; q, steam purge; r, N2 supply; s, control; t, manometers.
fluidized bed pilot plant was determined at room temperature conditions and using air supplied by a compressor as the fluidizing agent. Coal particles of mean size 1.13 mm were used. The residence time distribution was determined by the short pulse technique, using as the tracer 180 g of coal impregnated with CoCl2 (1.21% wt). Samples were collected every 10 min during a 6-h period. The tracer was analyzed by extracting the CoCl2 with 0.1 N HCl and analyzing the Co2+ by atomic adsorption spectroscopy. The solids feed rate was 32 kg/day, and the gas velocity was 0.67 m/s, around 1.5 times the minimum fluidizing velocity. The experimental statistical parameters were
τ)
∑i tiCi∆ti ∑i Ci∆ti
) 2.1 h;
σ2θ )
( ) ∑i ti2Ci∆ti ∑i
τ2
- 1 ) 0.27 (3)
Ci∆ti
Figure 5 shows the residence time distribution (RTD) function, Eθ vs the dimensionless time θ ) t/τ. These experimental data were adjusted successfully to the tanks in series model (Levenspiel, 1979), obtaining as the best fit 3.7 ideal stages, while the pilot plant presented three real stages. As reported by Krishnaiah
et al. (1982), multistage fluidized bed reactors with downcomers present solids RTD, which can be interpretated successfully by the monoparameter tanks in series model, obtaining a higher value of ideal stages than the real ones due to the baffles placed in each stage and the effect of the downcomers, as ocurrs in this case. The increase of 0.7 stages above the three real ones indicates that the effect of the downcomers and the baffles, although significant, is small. On the other hand, considering that the number of stages obtained from the model (3.7) is very close to the real number of stages (3), it can be concluded that the stirring caused by the bubbles in the fluidized bed is quite intense, indicating a behavior of the system close to three wellmixed ideal tank stages. The distributor of the lowest bed has a lesser value of free area, and consequently, the turbulence can be different from that in the two upper beds due to the different size of the bubbles. Nevertheless, the three beds can be considered wellstirred, and consequently the RTDs of the three beds can be considered similar. The differences have not been taken into account since the purpose of obtaining this RTD is to use it in the simulation model, which involves more hypothesis. The feed rate of solids in all the runs of activation was similar or less than that used in the RTD, and the stirring conditions in the activation runs were slightly more intense than in the RTD determination run. In the activation runs, the minimun fluidization velocity was estimated considering the operating conditions and changes of solids density and fluid composition in each bed. The estimated fluid velocity varied from 1.5 to 2-2.5 umf. Consequently, the RTD of the solids at the high temperatures of the activation runs will also be close to three ideal stages, with a small increase in the number of stages exceeding three, taking into acount the baffles and the downcomers as in the cold conditions. In the simulation model described in this paper, the same number of total stages (3.7) has been considered for the activation runs. The increase of the number of stages over 3.7 is not logical, because the beds are more intensively stirred in the activation runs with 2-2.5 umf, due to an increased flow of gas in the bubble phase as compared to the cold RTD determination run with 1.5 umf. Consequently, the reaction system can be approximately considered as an association of three reactors in series, where each reactor is equivalent to 3.7/3 ) 1.23 stages in accordance with the tank in series model.
4142 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 Table 2. Experimental Conditions and Results of Direct Activation Runs
no.
feed
1 2 3 4 5 6 7 8 16
MB850 coal coal coal coal coal coal coal coal
F (kg/ τnominal Tu Tm,l u BOnominal S BOs day) (h) (°C) (°C) (m/s) (%) (m2/g) (%) 30.4 30.4 35.1 25.6 18.3 36.8 15.2 8.3 25.6
1.69 2.01 1.56 2.23 2.66 1.72 3.74 6.23 2.31
850 810 800 820 835 800 800 800 700
850 850 850 850 850 800 800 800 850
0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32
36.1 48.4 42.5 55.0 65.0 10.3 28.3 63.9 29.0
1022 1067 1017 1192 1596 816 1126 1717 1153
33.9 35.9 33.6 41.7 60.2 24.4 38.6 65.8 39.9
Experimental Runs. In this paper, the simulation model (to be commented on later) is applied to eight direct activation runs (carbonization and steam activation in the same process) runs and one steam activation run from a previously carbonized char (obtained in moving bed reactor at 850 °C). These runs are summarized with their corresponding operating conditions and results in Table 2, indicating the raw material, the solids feed rate F, the solids nominal spatial time τ (obtained by dividing the experimental solids holdup, pressure drops between the stages, by the solids feed rate in volatile and moisture free basis), the temperature Tu of the upper bed (where the carbonization mainly takes place), and the temperature Tm,l of both middle and lower fluidized bed stages. The nominal burn-off degree, BOnominal, was obtained analyzing the ash content of the final activated carbons produced. This method was not accurate enough to determine the burnoff due to the fact that the initial coal presents a heterogeneous composition, and consequently, this nominal burn-off can have systematic errors. On the other hand, the activated carbon samples were characterized by the 77 K nitrogen adsorption isotherm (Quantachrome Autosorb 6 sorption apparatus), obtaining the specific surface area (shown also in Table 2) applying the equation of Dubinin-Izotova as shown elsewhere (Marcilla et al., 1995) to the experimental isotherm data. Each run was operated during at least three times the solids nominal spatial time, and different instantaneous samples were collected at different times when the stationary state conditions were attained. Analyzing both the nominal burn-off and the specific surface area (on an ash free basis) for different samples of the same run, it could be observed that the specific surface areas were all very similar (only 2% dispersion among them), whereas the nominal burn-off presented quite a high dispersion (6-10%). This fact revealed that the reactor behaved very stably (as indicated by the good reproducibility of the adsorption capacity). The nominal burn-off dispersion was probably produced due to the heterogeneous proximate composition of the raw material, considering that from a given coal mass the differences in the initial ash content from 7% to 9% may considerably affect to the final nominal burn-off values. For this reason, the burn-off degrees were also analyzed using a correlation obtained from the experimental data of Serrano et al. (1994), who used a batch lab-scale fluidized bed reactor to obtain steam-activated carbons from the same coal at 800 °C (and the burn-offs were determined gravimetrically). The specific surface area obtained in this case presented a good linear correlation coefficient with the burn-off: BOs ) -0.1305 + 0.000459S, where BOs is the burn-off and S is the specific surface area (m2/g).
The main attention of this work was centered on obtaining a stable performance of the three-stage fluidized bed reactor for producing activated carbons, and gas composition through all the system was not monitored. All runs carried out were stable, and the activated carbons obtained have a quite good surface area, similar to those obtained in batch reactors. Simulation Model This model has been developed for steady conditons. Chemical Reactions. In this proccess, two different reactions are involved: (i) carbonization of the coal and (ii) steam gasification of the subsequent char. The carbonization takes place in the upper fluidized bed, and the carbonization time (around 10 min) in relation to the gasification time (hours) has been neglected, which seems to be a reasonable approximation. It has been assumed that the composition of the pyrolysis gas from this coal, in a continuous fluidized bed reactor, is similar to that obtained by Tyler (1980) with a similar coal and conditions. Consequently, it is assumed that, together with the coal feed (on a devolatilized basis), a gas stream of a mean molecular weight of 23 with a 2.38% wt of H2 is introduced to the upper fluidized bed. The steam gasification of chars takes place through the following reactions, the first one being what controls the kinetics:
C + H2O f CO + H2 CO + H2O f CO2 + H2 C + 2H2 f CH4
∆H ) 130 kJ/mol ∆H ) -42.3 kJ/mol ∆H ) -87.5 kJ/mol
The methane formation reaction is very slow at atmospheric pressure and can therefore be neglected. In addition, it has been assumed that the ratio of the homogeneous reaction with respect to the heterogeneous reaction depends on the temperature, as pointed out by Matsui et al. (1984), based on the following overall chemical reaction:
C + RH2O f (2 - R)CO + (R - 1)CO2 + RH2 where R ) 2.95 - 0.0019T (°C). Fluidized Bed Hydrodynamic Parameters. As the activation continues, the particle size remains almost constant, and consequently, the particle density decreases. With the values of particle density corresponding to several activated carbons with different burn-off degrees, the following equation has been used to correlate the particle density as a polinomic function of the burn-off degree (from 0 to 1):
Fs ) 1099 - 3337.58BO + 18197BO2 51818.2BO3 + 68181.8BO4 - 33333.3BO5 (4) The viscosity of the gas mixture at any stage of the reactor is calculated using the Chapman and Enskong theory (Reid et al., 1977). The minimum fluidization velocity of chars at different burn-off degrees is calculated by the Wen and Yu (1966) equation. The fluidized bed voidage is estimated from the Hsiung and Thodes (1977) equation, which was tested previously as the best voidage correlation for this material (Marcilla et al., 1994). The solids fluidized bed height of each fluidized bed with respect to the weir height is obtained from a previously obtained correlation (Martı´n-Gullo´n et al.,
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4143
1995), as a function only of the gas velocity and the minimum fluidization velocity. Fluidized Bed Model. A model to simulate the three-stage fluidized bed reactor to produce activated carbons based on the following considerations has been developed: It is considered that the particles are in permanent contact with gases of the same composition. This assumption has been made based on the following estimations; the pilot plant is operated under the mean experimental conditions: F ) 1.66 kg/h, dp ) 1.13 mm, Fs ) 1000 kg/m3, Tu ) Tm,l ) 850 °C, P ) 1 atm, umf ) 0.18 m/s, mf ) 0.55, u ) 0.32 m/s, hs ) 0.14 m, and fw ) 0.1. Assuming the three-phase Kunii and Levenspiel model, the estimated upward solids flow rate inside the fluidized bed is around 400 kg/h (see Appendix A). The solid particles therefore travel up and down in the fluidized bed many times before exiting by the weir, and thus, it has been considered that the particles are in contact with a gas of a composition that is the average of those at the top and the bottom of each corresponding bed. Appendix A shows the calculations carried out. The mass exchange between the bubbles and the emulsion has been taken into account. Under the conditions outlined in the previous paragraph, the velocity of the bubbles is similar to umf/mf. The cloud phase would therefore occupy all the emulsion phase, and the mass exchange between the bubble phase and the emulsion phase would be high; under such conditions, the emulsion and bubble phases would present quite a similar gas composition. This point is discussed further in Appendix B. Considering that the char gasification in each stage for the particles moving up and down takes place in a changing atmosphere and that the composition of the bubble phase and the emulsion phase are very close; the conversion of the particles for each bed has been calculated on the basis of an average arithmetic gas composition corresponding to the inlet and outlet flows in the corresponding beds. On the other hand, the residence time distribution of solids at each stage is calculated by the tanks in series model, assuming a theoretical number of stages of 1.23 (3.7 theroretical stages divided by 3 real stages) for each stage, in accordance with the following relation:
E(t) )
(
1.23t 1.23t 0.23 1.23 exp τ τ τΓ(1.23)
)
(
)
(5)
Development of Simulation Model. A scheme of the simulation model developed, with all the assumptions commented on previously, is shown in Figure 6. The inputs to the simulation model are the data of the temperature of each bed, the initial steam gas flow rate, and both the coal feed rate and the proximate coal composition. In order to solve the mathematical equations, three initial burn-off degrees (one for each bed) are considered, and the simulation model is as follows: (1) First, considering the burn-off degrees assumed, the mass balances at the three fluidized beds are solved, from the lower fluidized bed, taking into account the chemical reactions involved, the gases formed in pyrolysis, and the gas flow increment at each stage. From these mass balances, gas compositions that leave the corresponding stages are calculated, and from them, the composition inside each fluidized bed can be estimated. The hydrodynamic parameters of each fluidized bed (minimum fluidization velocity, particle density, gas velocity, solids height, fluidized bed voidage) are worked
out with the gas compositions determined previously, calculating finally the solids holdup at each stage. Dividing the solids holdup of each stage by the corresponding char flow rate (from the assumed burn-off degree at each stage), the real residence time at each stage is obtained. The calculation of these parameters are detailed in Appendix C. (2) Second, from the parameters calculated in step 1 (gas composition and real spatial time of each fluidized bed), the burn-off degree at each stage is calculated again but from the kinetic expression (previously determined) and assuming the solids residence time distribution given by the tanks in series theory, for a parameter N ) 1.23. For a particle that remains in the fluidized bed 3 (or upper) for a determined time, t3, the burn-off is obtained by
(
X(3,t3) ) 1 -
(
)
)
195447 PH2O,3 RT3 exp t3 372 93510 1 + 6927 exp PH2O,3 + 12.6 exp PH2,3 RT3 RT3 3.5 × 109 exp -
( )
(
)
(6)
and the mean conversion for a group of particles that stay a residence time distribution E3 with spatial time τ3 is
Xmean(3) )
∫0∞X(3,t3)E3(t3) dt3
(7)
For the middle or second stage, the conversion of a given particle that has remained for a time t3 in the stage 3 and a time t2 in stage 2 is given by
(
X(2,t2,t3) ) 1 - (1 - X(3,t3)) ×
(
)
)
195447 PH2O,2 RT2 exp t2 372 93510 1 + 6927 exp PH2O,2 + 12.6 exp PH2,2 RT2 RT2 3.5 × 109 exp -
( )
(
)
(8)
The mean conversion in stage 2 of the particles that have spent a time t3 in stage 3 is
Xmean(2,t3) )
∫0∞X(2,t2)E2(t2) dt2
(9)
being the mean conversion in stage 2, of all particles coming from stage 3, given by
Xmean(2) )
∫0∞Xmean(2,t3)E3(t3) dt3 ) ∫0∞∫0∞X(2,t2,t3)E2(t2)E3(t3) dt2 dt3
(10)
Analogously, the conversion of chars for the lower bed is straightforward:
(
)
X(1,t1,t2,t3) ) 1 - (1 - X(2,t2,t3)) × 195447 PH2O,1 3.5 × 109 exp RT1 exp t1 372 93510 1 + 6927 exp PH2O,1 + 12.6 exp PH2,1 RT1 RT1
( )
(
)
(
)
(11)
4144 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
Xmean(1) )
∫0∞∫0∞∫0∞X(1,t1,t2,t3)E1(t1)E2(t2)E3(t3) dt1 dt2 dt3
(12)
(3) These last three conversions obtained from the kinetics and RTD distribution, Xmean(3), Xmean(2), and Xmean(1), are compared to those initially assumed. If these values are different, an iteration method is needed to solve the burn-off degrees. The iteration is carried out using the simplex flexible method (Himmelblau, 1970), using as the objective function the sum of the square of the differences between the assumed conversions and those calculated for the three beds. On the other hand, the integral functions are calculated numerically by the Euler method with a time increment ranging from 500 to 2000 s depending on the experimental run. The solution procedure is explained in Appendix C. Results. Figure 7 shows the experimental burn-offs of the carbons leaving the pilot plant at stage 1 (the nominal one by ash gravimetry, BOnominal, and that obtained from the specific surface area, BOs) vs the burn-off calculated by the simulation model. It can be observed that when the burn-off is determined by the ash content procedure, the simulation model is able to approximately interpret the activation process, but shows some scattering around the diagonal line. Nevertheless, when the burn-off is determined by the surface area correlation, the simulation model without any optimizing paremeter is able to satisfactorily correlate the experimental results with a very low scattering. The differences between BOnominal (determined from the ash content) and BO calculated are probably due to the heterogeneity of the raw material. It can be observed that the simulation model is able to reproduce the experimental runs with different operating conditions, such as temperature, solid feed rate, and raw material, without optimizing any parameter. It is remarkable that using the experimentally obtained kinetic expression in TG, the experimentally obtained solids RTD, and the assumptions made (discussed and used previously by other authors) this model is able to simulate the activation process (pyrolysis + gasification) carried out in a three-stage fluidized bed reactor. Conclusions A three-stage fluidized bed pilot plant has been satisfactorily operated for the production of activated carbons from a bituminous coal. A model in order to simulate a three-stage fluidized bed pilot plant with downcomers has been developed, considering the kinetic expression obtained by thermogravimetry, the experimental residence time distribution of solids, and some relationships proposed in the literature. This model, without any parameter to be optimized, satisfactorily reproduced the experimental results obtained. Appendix A Upward Solids Flow Rate inside the Fluidized Bed. For a fluidized bed that is operated under the same conditions as the three-stage fluidized bed reactor, dp ) 1.13 mm, Fs ) 1000 kg/m3, Tu ) Tml ) 850 °C, P ) 1 atm, umf ) 0.18 m/s, mf ) 0.55, u ) 0.32 m/s, h ) 0.14 m, and assuming a wake volume bubble volume ratio, fw ) 0.1, the following varibles have been estimated:
Figure 6. Three-stage fluidized bed model scheme. Gas and solid flow are presented in narrow and thick lines, respectively.
Bubble diameter at a medium fluidized bed height. As the char particles are Geldart D particles, the bubble diameter is calculated by the Cranfield and Geldart equation (1974) (in cgs units):
db ) 0.0326(u - umf)1.11h0.81 ) 2.95 cm ) 0.0295 m (A1) The upward bubble velocity, by the equation proposed by Kunii and Levenspiel (1969, 1991):
ub ) u - umf + 0.711(gdb)0.5 ) 0.52 m/s
(A2)
The bubble phase fraction at the medium fluidized bed height is expressed by the following equation due to ub is between 1 and 5 times umf/mf:
δ)
u - umf ) 0.28 u + umf
(A3)
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4145 Table 3. Calculated Gas Compositions at Different Fluidized Bed Heights from Assumption Developed in Appendix B h (m)
0
0.02
0.05
0.07
0.1
Cb/Ceo Ce/Ceo
0 1
0.35 0.486
0.4024 0.4091
0.4048 0.4056
0.4052 0.4052
Scheme 1
Figure 7. Experimental burn-off degrees, obtained from ash content BOnominal and from surface area BOs vs calculated burnoff with the simulation model.
The solid flow rate that goes upwards in the fluidized bed is given by
Fup ) ubA δfw(1 - mf)Fs ) 0.11 kg/s = 400 kg/h Appendix B Consider the same experimental conditions mentioned in Appendix A. Under these conditions, all emulsion can be considered to be inside the clouds of the bubbles. In this fluidized bed, assume that a trace gas is introduced at the bottom of the fluidized bed but only in the bubble phase in such a way that the initial composition (at the bottom) of the emulsion is zero (Ceo ) 0) and the initial composition of the bubble phase is 1 (Cbo ) 1). The compositions in both the emulsion and bubble phases must be determined at the top of fluidized bed. Applying a mass balance at element dV, corresponding to a fluidized bed height dz
Qb dCb ) Kt(Ce - Cb) dVb )
(
)
QbCb - Cb δA dz (B1) Qe
Kt Ceo -
The previous equation can be written as
[
(
)]
Qb Qb dCb ) Kt Ceo - Cb +1 A Qe
δ dz ) u* bδ dCb (B2)
where u*b is the velocity of the gas that crosses the fluidized bed through the bubbles and not the upwards bubbles velocity. Using as the volumetric transfer coefficient (Kt) the value assumed by the Kunii and Levenspiel (1969, 1991) model and solving the differential equation from the distributor to different heights, both bubble and emulsion compositions are already quite similar at only 2 cm from the distributor, being practically identical at 4 cm above the distributor. Table 3 shows the calculated compositions at different fluidized bed heights. Considering that the bed has a height of around 14 cm and that the mass transfer is very high with small bubbles (as occurs near the perforated plate), it can be deduced that the emulsion
gas and bubble gas take the same composition at any height of the bed. Appendix C A outline of the procedure calculation is presented in Scheme 1. For each bed, the viscosity of the gas mixture is calculated following the equations of Yoon and Thodos and the Wilke approximation for estimating the parameters of interrelation (Reid et al., 1977). The minimum fluidization velocity is calculated by the Wen and Yu equation (Wen and Yu, 1966). The height of the beds Hi is slightly less than the distance between the top of the downcomer, where the solids go downwards, and the bottom of the bed. The correlation used was obtained experimentally (Gullon et al., 1995):
Hi ) 0.15 - [0.066(u - umf)3 - 0.148(u - umf)2 + 0.103(u - umf) - 0.003] (C1) The porosity of each bed was estimated with the Hsiung and Thodes (1977) equation, which satisfatorily
4146 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
correlated the experimental data of porosity and Reynolds number obtained under cold conditions (Gullon et al., 1995). The mass of each bed is obtained considering the volume, the solids density, and the porosity. The residence time of solids is calculated by dividing the mass of solids in a bed by the solids mass flow that leaves the corresponding bed. It was tested using 20 intervals for the RTD of solids the solution was correct. Note the simplex flexible method used is only for solving the different equations of the simulation model. There is no adjustable parameter introduced to approximate the experimental results to those deduced from the model.
Xmean(i) ) burn-off calculated in stage i
Acknowledgment
Literature Cited
The authors thank ECSC (7220-EC-758), OCICARBON (C-23.275), and the Spanish Goverment DGICYT (CE91-0011-C03) for their financial support.
Himmelblau, D. M. Process Analysis of Statistical Methods; Wiley: New York, 1970. Hsiung, T. H.; Thodes, G. Expansion Characteristics of Gas Fluidized Beds. Can. J. Chem. Eng. 1977, 55, 221. Krishnaiah, K.; Pydissetty, Y.; Varma, Y. B. G. Residence Time Distribution of Solids on Multistage Fluidization. Chem. Eng. Sci. 1982, 53, 1371. Kunii, D.; Levenspiel, O. Fluidization Engineering; Wiley: New York, 1969. Kunii, D.; Levenspiel, O. Fluidization Engineering; Heineman Butterworth: New York, 1991. Le Bolay, N.; Languerie, C.; Angelino, H. Kinetic Modelling of the Steam Gasification of Coke in a Fluidized Bed Reactor I. Simplified Approach. Chem. Eng. J. 1989a, 41, 125. Le Bolay, N.; Languerie, C.; Angelino, H. Kinetic Modelling of the Steam Gasification of Coke in a Fluidized Bed Reactor II. Modelling of the Hydrodynamic Behaviour of the Fluidized Bed during Reaction. Chem. Eng. J. 1989b, 41, 139. Levenspiel, O. The Chemical Reaction Omnibook; Wiley: New York, 1979. Marcilla, A.; Martı´n, I.; Font, R.; Asensio, M.; Linares-Solano, A. Activated Carbon in a Continuous Moving Bed Pilot Plant. Proceedings of Carbon ’94; Spanish Carbon Group, Granada, Spain, 1994; p 302. Martı´n-Gullo´n I.; Asensio, M.; Font, R.; Marcilla, A. Stable Operating Velocity Range for Multistage Fluidized Bed Reactor with Downcomers. Powder Technol. 1995, 85, 193. Matsui, I.; Kojima, T.; Furusawa, T.; Kunii, D. Gasification of Coal Char by Steam in Continuous Fluidized Bed Reactor. Fluidization; Kunii, D., Toei, T., Eds.; American Institute of Chemical Engineers: New York, 1984. Matsui, I.; Kojima, T.; Furusawa, T; Kunii, D. Study of the Fluidized Bed Steam Gasification of Char by Thermogravimetrically obtained Kinetics. J. Chem. Eng. Jpn. 1985, 18, 105. Mun˜oz-Guillena, M. J.; Illa´n-Go´mez, M. J.; Martı´n-Martı´nez, J. M.; Linares-Solano, A.; Salinas-Martı´nez de Lecea, C. Activated Carbons from Spanish Coals. 1. Two-Stage Activation. Energy Fuels 1992, 6, 9. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Liquids and Gases; McGraw-Hill: New York, 1977. Serrano, B; Mun˜oz-Guillena, M. J.; Linares-Solano, A.; SalinasMartı´nez de Lecea, C. Proceedings of Carbon ’94; Spanish Carbon Group, Granada, Spain, 1994; p 240. Tyler, R. J. Flash Pyrolysis of Coals. Fuel 1980, 59, 518. van Heek, K. H.; Mu¨lhen, H. J. Chemical Kinetics of Carbon and Char Gasification. In Fundamental Issues in Control of Carbon Reactivity; Lahaye, J., Ehrburger, P., Eds.; Kluwer Academic Publishers: Dordrecht, 1977; p 1. Wen, C. Y.; Yu, Y. H. Predicting the Minimum Fluidization Velocity. AIChE J. 1966, 12, 610.
Notation A ) reactor section, m2 BO ) activated carbon burn-off degree BOnominal ) activated carbon burn-off degree obtained by ash gravimetry BOs ) activated carbon burn-off degree obtained by specific surface area Cb ) tracer TR concentration in the bubble phase Cbo ) initial tracer TR concentration in the bubble phase Ce ) tracer TR concentration in the emulsion phase Ceo ) initial tracer TR concentration in the emulsion phase Ci ) tracer concentration db ) bubble diameter, m (cm in eq A.1) dp ) particle size, mm Ea ) activation energy, J/mol Eθ ) residence time distribution normalized for dimensionless time F ) solid feed rate, kg/day Fup ) upward solids flow rate inside the fluidized bed, kg/s fw ) wake to bubble volumetric ratio Hi ) height of the fluidized bed at bed i, m h ) fluidized bed height, m hs ) solids fluidized bed height, m kap ) apparent kinetic constant, s-1 k1 ) Arrhenius prexponential factor, s-1 Ki ) Equilibrium constant Kt ) volumetric transfer coefficient, s-1 P ) absolute pressure, atm PH2 ) hydrogen partial pressure, atm PH2O ) steam partial pressure, atm Qb ) volumetric gas flow through the bubble phase, m3/s Qbo ) initial volumetric gas flow through the bubble phase, m3/s Qe ) volumetric gas flow through the emulsion phase, m3/s Qeo ) initial volumetric gas flow through the emulsion phase, m3/s S ) specific surface area, m2/g T ) temperature, K t ) time, s or min u ) gas velocity, m/s ub ) upward velocity of bubbles, m/s ub* ) upward velocity of gas which crosses through bubbles, m/s umf ) minimum fluidization velocity, m/s V ) volume, m3 X ) conversion degree, fixed carbon reacted divided by initial fixed carbon (equals burn-off degree) X(i,ti) ) burn-off calculated for a particle which has remained a time ti in stage i
Greek Letters R ) stoichiometric parameter in chemical reactions of steam gasification δ ) bubble fraction with respect to the overall fluidized bed ∆H ) reaction enthalpy in chemical reactions, J/mol ∆Hi ) adsorption enthalpy in eq 1, J/mol mf ) minimum fluidization voidage Γ(x) ) γ-function of number x θ ) dimensionless time Fs ) particle density, kg/m3 σθ ) statistical variance with respect to dimensionless time τ ) spatial time, s or h
Received for review December 15, 1995 Revised manuscript received June 10, 1996 Accepted June 10, 1996X IE950759X
Abstract published in Advance ACS Abstracts, August 15, 1996. X
