Ind. Eng. Chem. Res. 1990,29, 251-258
E,,
Here, Qij is the heat duty of match ij,Q is the amount of heat transferred between streams in the 1-2 shell and tube exchanger, and (DT2)& is the temperature difference between the hot and cold streams at the hot end of the 1-2 exchanger. Note that Qij,the heat duty of match ij,may be less than Q the heat transferred between streams in the 1-2 shell and tube exchanger. In this case, A,, is less than zero, indicating that no new exchanger area needs to be purchased. If A,, is greater than zero, then it is equal to the amount of area in the new shell and tube exchanger. Thus, A,, is a lower bound on the total additional area: Xij, 1 Aijn
E,,
The heat load Q $, and temperature difference (DT2)$, can be calculated from a set of equations derived from the rating equation of a 1-2 exchanger to give Qtn
= f P’(ATC)ijn
(DT2)$, = (DT2)ij + (Rij - l)(ATC)ij, Rij = f $ t j / f
,E”
Here, (ATQj, is the temperature rise of the cold stream in the 1-2 shell and tube exchanger, f Fj is the flow rate of the cold stream, and Rij is the ratio of the cold stream flow rate f F J to the hot stream flowrate f y . The temperature rise is obtained from (ATC)ij, =
where
sij,= exp[ -
UijAZx(Ri? + 1)lI2 (1 R&j)f Fj
+
]
Literature Cited Brooke, A.; Kendrick, D.; Meeraus, A. GAMS A Users Guide; The Scientific Press: Redwood City, CA, 1988.
25 1
Ciric, A. R.; Floudas, C. A. A Retrofit Approach for Heat Exchanger Networks. Comput. Chem. Eng. 1989,13(6), 703-715. Floudas, C. A,; Ciric, A. R. Strategies for Overcoming Uncertainties in Heat Exchanger Network Synthesis. Comput. Chem. Enp. 1989, 13 (lo), 1133-1152. Floudas, C. A.; Ciric, A. R.; Grossmann, I. E. Automatic Synthesis AIChE J. of Optimum Heat Exchanger Network Configurations 1986,32, 276-290. Garfinkel, R. S.; Nemhauser, G. L. Integer Programming; John Wiley and Sons Inc.: New York, 1972. Geoffrion, A. M. Generalized Benders Decomposition. J. Optimization Theory Appl. 1972, 10(4), 234-260. Gundersen, T.; Naess, L. The Synthesis of Cost Optimal Heat Exchanger Networks, an industrial review of the state of the art. Comput. Chem. Eng. 1988,12(6), 503-530. Kern, D. Q. Process Heat Transfer; McGraw-Hill Book Co: New York, 1950. Jones, D. A.; Yilmaz, A. N.; Tilton, B. E. Practical Synthesis Techniques for Retrofitting Heat Recovery Systems. AIChE Annual Meeting, Chicago, IL; American Institute of Chemical Engineers: New York, 1985; paper 35c. Jones, D. A.; Yilmaz, A. N.; Tilton, B. E. Synthesis Techniques for Retrofitting Heat Recovery Systems. Chem. Eng. Prog. 1986,82, 28-33. Paterson, W. R. A Replacement for the Logarithmic Mean. Chem. Eng. Sci. 1984,39, 1635-1636. Papoulias, S. A.; Grossmann, I. E. A Structural Optimization Approach in Process Synthesis-11. Heat Recovery Networks. Comput. Chem. Eng. 1983, 7,707-721. Paules, G. E., IV; Floudas, C. A. APROS: An Algorithmic Decomposition Methodology for Solution of Discrete-Continuous Optimization Problems. Oper. Res. J. 1989, 37 (6). Saboo, A. N.; Morari, M.; Colberg, R. D. RESHEX-An Interactive Package for the Synthesis and Analysis of Resilient Heat Exchanger Networks I Program Description and Application. Comput. Chem. Eng. 1986,10,577-589. Tjoe, T. N.; Linnhoff, B. Using Pinch Technology for Process Retrofit. Chem. Eng. 1986, 93, 47-60. Tjoe, T. N.; Linnhoff, B. Achieving the Best Energy Saving Retrofit. AIChE Spring Meeting, Houston, TX; American Institute of Chemical Engineering: New York, 1987; paper 17d. Yee, T. F.; Grossmann, I. E. Optimization Model for Structural Modifications in the Retrofit of Heat Exchanger Networks. Engineering Design Research Center, Report EDRC-06-25-87; Carnegie-Mellon University: Pittsburgh, PA, 1987.
Received for review March 10, 1989 Revised manuscript received September 11, 1989 Accepted October 23, 1989
Simulation of a Dry Fluidized Bed Process for SO2 Removal from Flue Gases Ourania Faltsi-Saravelou* and Iacovos A. Vasalos Chemical Process Engineering Research Institute and Department of Chemical Engineering, Aristotelian University of Thessaloniki, P.O. Box 1951 7, 54006 Thessaloniki, Greece
A fluidized bed reactor model, the large particle fluidized bed model (LPFBM), has been developed in order to predict the performance of a fluidized bed reactor, which operates a t low-to-medium u0/umtratios (uo/ud = 2-5) in the presence of large particles. The LPFB model was applied to simulate a pilot-plant unit of the dry regenerable process of SO2 removal from flue gases, over a wide range of operating conditions. The conversions predicted by the model fit the experimental data reported in the literature satisfactorily. The LPFB model was used to study the effects of the solid sorbent composition and particle size on SO2 conversion. From the simulation, it can be concluded that SO, sorbents containing 5 wt 5% or less of Cu, Na, Fe, Ce, Co, or Ni could be well considered for indistrial applications. Regenerable processes for removing SO2from flue gases are increasingly gaining commercial significance. In a regenerable process, the flue gases are fed to a sorption
* To whom correspondence should be addressed. 0888-5885/90/2629-0251$02.50/0
reactor where SO2reacts with a solid metal oxide sorbent, forming a sulfate that can be in turn regenerated by a reducing gas to form the oxide and a S02/H2Smixture. The feasibility of the regenerable processes depends mainly on the solid sorbent properties and resistance and to a 0 1990 American Chemical Society
252 Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 Table I. Kinetic Data on the SOJMetal Oxides Reaction sorbent k , 11s k,, 11s E, kJ/mol C UO/ A1203" 2.72 x 105 47.4 CuO/A1203' 460 20.1 112.62 CUO 3.98 X 1O'O CuO/A1203" 9.27 NazO/Al2O3' 18.83 Na20/A1203 19.1 8.37 Na20/A1203 3.33 An20/A1203* 111.96 7.54 CeOz 9024.8 33.03 0 4 4.85 x 105 58.2 C0304/A1203" 10 Fez03 4436 38.35 FezO3/Al2O3" 5.5 NiO 9.13 x 104 56.52 NiO/A1203" 7.16 NiO 54.43 Cr203/A1203" 12.83 a
Sorbent prepared by impregnation.
T,O C
n
ref
300-450 350-450 325-482 343 343 300-500 343 130-300 194-262 359-430 343 342-400 343 380-501 343 500-800 343
1 1
Best (1974) Yeh et al. (1987) DeBerry and Sladek (1971) Vogel et al. (1974) Vogel et al. (1974) Kriehnan and Bartlett (1973) Vogel et al. (1974) Bienstock et al. (1967) DeBerry and Sladek (1971) DeBerry and Sladek (1971) Vogel et al. (1974) DeBerry and Sladek (1971) Vogel et al. (1974) DeBerry and Sladek (1971) Vogel et al. (1974) Imgraham and Marier (1966) Vogel et al. (1974)
'13
1 1 1 1 1
2 1 1 l/3
1 l/2
1 1
Experiments in the presence of NO,.
lesser extent to the regeneration gas composition. Various reactor designs have been proposed, including fixed beds, fluidized beds, and radial flow reactors. The Shell copper oxide process, which is the only regenerable process in commercial application to date, is based on a CuO/A1203 sorbent and a cyclic fixed bed reactor design. Numerous metal oxide screening studies have been published that aim at rating the metal oxides (supported on porous carriers or pure metal oxides) according to their ability to capture the SO2 at a sufficient rate and to be regenerated at low enough temperatures. These studies led to selecting sorbents based on the oxides of the following metals: Na, K, Sr, Ca, Cr, and Cu (Vogel et al., 1974); Ce, Co, Cr, Cu, Fe, and Ni (DeBerry and Sladek, 1971); and Ni, Mn, Fe, Co, and Zn (Koballa and Dudukovic, 1978). Although all the metals listed above displayed good reactivity and regenerability, only the sodium and copper oxides supported on porous carriers have been studied more extensively. The pioneering research of the U.S. Bureau of Mines in the late 1960s led to the development of the alkalized alumina process, using a Na20/A1203sorbent in a fluidized bed reactor (Bienstock et al., 1967; Town et al., 1970). This process was finally abandoned, probably due to the high attrition rates of the alkalized alumina sorbent. A t the Pittsburgh Energy Technology Center, a regenerable fluidized bed process using a CuO/A1203sorbent is now under development (Yeh et al., 1985; McArdle et al., 1987). As emphasized by Yeh et al. (1985), the fluidized bed reactor design, while having the disadvantages of higher pressure drop and attrition rates, has the following significant advantages over the fixed bed design: the sulfation/regeneration processes are operated continuously; the production and composition of the regenerator effluent gases are constant; and plugging by fly ash is avoided. Fluidized bed sorption systems of a small scale have been tested also at the Institut de Genie Chimique in France (Barreteau et al., 1978; Barreteau and Laguerie, 1984) and at the University College in England (Best, 1974; Best and Yates, 1977); both research groups used a CuO/A1203sorbent. Meanwhile, a catalytic process was introduced in 1977 by Amoco Co. for the SO2 removal in situ in the FCC regenerator, by simply mixing a metal oxide SO2sorbent with the FCC catalyst as mentioned by Vasalos and Dimitriadis (1987). Since then over 80 patents have been issued that claim sorbent compositions of various metal oxides for reducing the SOz. After the above patent literature,
it seems implausible to restrict the fluidized bed processes for SO2removal from flue gases only to the use of CuO and Na20 sorbents. The objective of this work is to explore the possibility of using in a fluidized bed regenerable process metal oxides other than Na20 and CuO. For this reason, a fluidized bed reactor model has been developed and tested using published data from the pilot plants of the alkalized alumina process (Bienstock et al., 1967) and the fluidized bed copper oxide process (Yeh et al., 1985). Furthermore, this model is used to study the effects of the solid sorbent on SO2 conversion. The model predictions serve as a guide for the development and evaluation of SO2sorbents in our laboratory (Vasalos and Dimitriadis, 1987).
Sulfation Kinetics Sulfation kinetics have been reported for almost all metal oxides for which the sulfation reaction is thermodynamically attainable. The mechanism of the sulfation reaction has mostly been studied for the sulfation of calcium sorbents. At high temperatures, the rate of reaction has been found to be a function of particle size, indicating mass-transfer limitations. The sulfation of the alkali sorbents is probably controlled by a surface reaction (Krishnan and Bartlett, 1973). The sulfation of the copper oxide proceeds via a consecutive reaction path, forming a copper oxysulfate intermediate (Best, 1974). Fortunately, most of the reported rate expressions can be lumped into a pseudo-first-order form which can be easily used in a general purpose fluidized bed reactor model. Although the sulfation mechanism varies for different types of solids, it is possible by using the kinetic expression r = kc(1 - x)" (1) to approximate a number of solid-fluid reaction models, the value of exponent n indicating whether the reaction is controlled by kinetics or diffusion (DeBerry and Sladek, 1971). However, eq 1 can only be used in the same close range of temperatures and operating conditions at which the kinetic parameters have been evaluated in the first place. Some kinetic parameters reported in relation to sulfation kinetics are summarized in Table I. A great variation in the reported data is obvious, which could be explained by the following remarks. a. The method of preparation of the sorbent is a very important factor affecting the reaction rate. Vogel et al. (1974) have shown that alkalized alumina sorbents pre-
Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 253 Table 11. Existing Phases in a Fluidized Bed gas super- velocity void phase fraction exchange ficial gas solid fraction bubble fb uab 1 kbc
cloud
fc
Uuc
u,
emf
uw
unw
(mf
%e
Um
emf
UO
Uno
(b
m
wake emulsion total
fW
f, 1
Oh
k,
Figure 1. Sketch of a gas bubble formed in a fluidized bed.
pared by impregnation have much higher reaction rates than the sorbents prepared by coprecipitation. b. Water or nitrogen oxides, if present, may alter the reaction rate. The water vapor probably promotes recrystallization of the formed sulfate, thus maintaining a more open structure of the sorbent, while the NO is more likely to act as an oxidation promoter (Krishnan and Bartlett, 1973).
Large Particle Fluidized Bed Reactor Model The economic feasibility of the regenerable processes for SO2 removal is highly dependent on the solid sorbent requirements. In order to minimize solid sorbent losses, large particles are used in the fluidized bed reactor. Many fluidized bed reactor models have been published to date, but most of them have been formulated to treat smallto-medium particle fluidization. In this paper, a reactor model, the large particle fluidized bed model (LPFBM), is developed in order to predict the performance of a fluidized bed reactor that operates at low-to-medium uo/umfratios (uo/umf= 2-5) in the presence of large particles. It must be emphasized that there is lack of experimental studies and correlations for the description of the fluidization parameters, applied especially to large fluidized particles. A rigorous approach has been used for the hydrodynamic description of the fluidized bed, in order to assure that no extreme simplifications are made. Additionally, a special technique was used for the formulation and solution of the hydrodynamic equations. This way it was made possible to test the applicability of equations derived for small-to-medium particles to yield a reasonable description of large particles fluidization. The LPFB model combines a revised form of the Partridge and Rowe (1966) model of gas bubbles and essentially the principles of Fryer and Potter (1972) model to describe the various mass balances. Gas Flow Description. In a fluidized bed, one can distinguish four phases. These phases are listed in Table 11,as well as the various symbols used in the present model description. The isolated bubble velocity is given by the well-known relation Ubr
= 22.26Db1I2
(2)
in CGS units. The absolute bubble rise velocity can be obtained by U b = u o - Umf u b r f uso (3) where the plus sign must be used for the concurrent gas/solid feed mode and the minus sign must be used for the countercurrent feed mode. Additionally, the ratio, a, for the characterization of the bubble type is defined as (Kunii and Levenspiel, 1977) a = (Ubrcmf)/Umf (4) Since the LPFB model has been especially developed to treat large particle fluidization, the distinction between
bubble
on
cloud iormation
Figure 2. Phases considered in the large particle fluidized bed model.
“slow”and “fast” bubbles has to be retained, and therefore, two operating regimes can be identified. The first regime, with the characteristics of the Davidson-Harrison (1963) model, consists of two phases, namely, a bubble phase and an emulsion phase. This regime might exist in the bottom of the reactor, near the distributor, and is characterized by small and slow bubbles. When the bubbles reach a certain size, the bubble gas velocity is higher than the dense-phase gas velocity. As a result, clouds and wakes are formed around the bubbles. The bubble is then visualized by the model, as described in Figure 1. The operating regimes and the phases taken into account by the model are shown in Figure 2. The detailed description of the equations used in the LPFBM for the evaluation of the fluidization parameters listed in Table 11, as well as the technique of solution and the various correlations tested, is given in the Appendix. Material Balance Equations. The following assumptions have been made: plug flow of the gas occurs in all phases, the reactor operates at steady state, the reactor is isothermal, the solids in the reactor are fully mixed in all phases, and the reaction between SO2 and the solid sorbent is of pseudo first order:
k’ = k ( l - x ) y l - emf)
(5)
where x is the solid conversion. The solid conversion is obtained by the overall material balance around the fluidized bed and is assumed to remain constant. 1. Two-Phase Regime. mass balance on bubbles
+
mass balance on the emulsion
initial conditions The exit gas concentration is given by
254
Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 =
ch
(UgbCb
+ UgeCe)/Uo
(9)
2. Four-Phase Regime: Emulsion Upflow. mass balance on bubbles
Table 111. Variables Used in Figures 3 and 4 case 1 case 2 Cojr PPm 3000 2100 CuO in sorbent. 70 5.5 3.7 9.2 2.3 645 1600 0.44 0.44 340 449 0.094 0.126 0.34 0.74 4.3 x 10-6 3.3 x 10-5 0.205 0.533 1.04 0.63 614 0.156 eq A8 eq A8 Barreteau et al. (1978) Yeh e t al. (1985) 3000
initial conditions h = hi Ce = Ce,i
Cb
cc
=
=
=
(UgbCb
(-UgeC,,i
+ uoco,i)/ugc (13)
+ (ugc + ugw)cc + UgeCe)/Uo
(14)
mass balance on the cloud and wake
Cc
= (U, - Ugb)Co,i/Ugc
Ce
=0
(17)
The exit gas concentration is ch
=
(UgbCb
- a00 n
- UgbCb,i
3. Four-Phase Regime: Emulsion Downflow. To simulate this regime, a simplified approach proposed by Fryer and Potter (1972) for large reaction rates has been followed. Since the reaction rate for the reaction of SOz with almost all the metal oxides listed in Table I is high (k’> 2), the assumption c, = 0 is reasonable and convenient. This was used, and the following form was given to the mass balance for the case of emulsion downflow. mass balance on bubbles
initial conditions h = hi Cb = Co,i
I See T a b l e I11 1
E
Cbj
where the values c,,~,cb,i, and co,i are calculated from the solution of the two-phase regime equations. The exit gas concentration will be ch
Case [ll
+ (uo - Ugb)Cc)/Uo
(18)
The above sets of first-order differential equations have been solved by a conventional Runge-Kutta procedure. The computational procedure at each height increment is as follows. Start a t the bottom of the reactor, in the two-phase regime. Step 1. Evaluate the bubble size. Evaluate with eqs Al-A4 the fractions and velocities, and solve mass balance equations (6)-(9). Branch to step 6. Step 2. Check a t every length interval the value of a. If a > 1, then go to step 3; otherwise, return to step 1. Step 3. Solve eqs A 5 4 1 2 for the gas and solid balance, and check for emulsion up- or downflow. For emulsion upflow, go to step 4; otherwise, go to step 5. Step 4. Solve eqs 10-14. Branch to step 6. Step 5. Solve eqs 15-18. Branch to step 6.
7 500
------Emulsion
I
2 I 3 I4 ‘6 5 b I9 1 0t Fluidized bed h%ight ICmI Figure 3. SO2 concentration profiles in a fluidized bed reactor, operated in the four-phase regime.
0 :O
l
1
I
Step 6. Check if the desired conversion level has been reached. If yes, then exist; otherwise, go to the next height increment. Results and Discussion The LPFB model was applied to simulate a fluidized bed pilot-plant unit over a wide range of operating conditions. The particle diameter varied from 600 to 2000 pm. The possible reactor operation cases are discussed next. Case 1. The fluidized bed operates completely in the four-phase regime. This happens a t the lower particle sizes ( 4 0 0 0 pm) and larger ratios of uO/ump Case 2. The fluidized bed operates in the two-phase regime at the bottom, while in the upper part of the reactor a four-phase regime is formed. This happens at medium particle sizes (- 1500 pm). Case 3. The fluidized bed operates completely in the two-phase regime, for the larger particles. Typical predicted concentration profiles for cases 1and 2 using the operating conditions given in Table I11 are shown in Figures 3 and 4, respectively. The concentration profiles are as expected for a plug flow model with no flow reversal. The LPFB model was used to simulate the fluidized bed pilot plant data listed in Table IV. The SOz conversions predicted by the model are plotted in Figure 5, with almost all the experimental conversions reported by the investigators listed in Table IV. The mean error was 2%. Experimental data and model predictions are plotted in Figure 6 together with homogeneous plug flow and mixed flow predictions versus the fluidized bed kinetic severity function (k2,/uo). It is apparent that the reported SO2 conversions by alkalized alumina are too high for the reaction kinetics involved. A possible explanation is that the
Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 255 Table IV. Operating Conditions Used in sorbent d,, mm u,/ud 1.6b 2.2-3.2 CuO/Al,O, CuO/A1203 0.645b 2.2-3.5 1.V 1.8 Na20/A1203 (I
the Pilot-Plant Reactor Simulation. See Figures 5 and 6 Hd,m k,"l/s source 0.35-1.15 Yeh et al. (1987) Yeh et al. (1985,1987) 0.05-0.12 Best (1974) Barreteau et al. (1978) 0.22-0.46 Bienstock et al. (1967) Bienstock et al. (1967)and Town et al. (1970)
See Table I for the exact kinetic equations.
Spheres.
Cylindrical pellets 1/16-in.-diameter by 1/16-in.-length.
1600 microns
Bubbles
E
0 c
1500
1000 n microns s
w
c
U 0
N
m
.6
o cn
U L
900-
n
U
01 U U
c U 0
L
n
600-
-I \K
0 en
300-
h
.4
Clouds t wakes1
I
\ I
" I
0
40
L bed height lcml
60
.2 $0
Fluidized Figure 4. SOz concentration profiles in a fluidized bed reactor, operated partly in the two-phase regime and partly in the four-phase regime.
0
I
LE-1
1
Available CuO t o inpuv 0502 molar ratio
Figure 7. Effect of sorbent particle size and Cu/SOz molar ratio on SOz conversion for a CuO/A1,03 sorbent. Table V. Variables Used in Figure 7 O
Barreteau e t a l . 119781 Town e t a l . 119701 Yeh e t a l . Il9E51
d,, fim
.E-
L
m W L
o
o
L W
-2 l200U
c
r
.E
03
c
c O
F
*
.6-
0.193 0.355 0.535
u, (m/s) = 1.036
Hd (m) = 0.89 T ("C) = 450
= 0.44 A, (m2) = 1.2444
A
N cn 0
u d , m/s
600 1000 1600
0
aKinetic rate constants k'(l/s) adapted from Yeh et al. (1985).
1
I
,
.2
0
1
.4
I
.6
1
.E
Experimental SO2 conversion Figure 5. Comparison of experimental and predicted conversions. a 0
0
Experimental and- p r e d i c t e d IBarreteau e t a1..19781 Experimental and- p r e d i c t e d (Town e t a l . . 19701 Experimental and. p r e d i c t e d Neh e t a l . . 19851
c 0 m
L
L 5
.E-
c n U
N
en 0
.6-
D W
U U
.4-
D W L
n
"1
1 I I I I 1 2 3 4 Kinetic severity function Ik'Lmf/Uol Figure 6. Effect of the kinetic severity function k Z d / u , on the SOz conversion.
01 0
high attrition rates reported for this sorbent produced fines that react at higher rates than predicted by the rate equation derived for the pellets, which is the rate equation
used in the simulation. Taking into account the difficulties in obtaining accurate kinetic data, the predictions of the present model must be considered very good. In Figure 7 is shown the effect of the available metal oxide to input SO2 molar ratio in the reactor and the sorbent particle size on the SO2removal, for a CuO/A1203 sorbent. The kinetics used in Figure 7 for a range of particle sizes have been originally derived for the larger particles and are assumed to remain constant in order to obtain only the influence of the bed hydrodynamicson the SO2 conversion. As a result, the conclusions drawn from Figure 7 are practically applicable to sorbents for which the kinetics have a priori been found for the particle sizes in the range of interest. The metal conversion by the overall material balance is directly linked with the sorbent feed rate and the percent active metal in the sorbent. The operating conditions for which the lines in Figure 7 were simulated are listed in Table V. In Figure 7, it can be observed that the performance of the larger particles is better. This can be explained by the fact that, since larger particles have larger umfvelocities, the ratio u,/umf is lower for larger particles. Since this is so, more gas flows through the emulsion and clouds for larger particles, thus enhancing the obtained SO2 conversion. In fact, recent experimental data on sulfur retention by lignite ash during fluidized bed combustion (Yeh et al., 1988) show an enhanced sulfur retention by larger particles and confirm the prediction of the present model. The metal/S02 molar ratio vs SO2 conversion curves for the Cu sorbent have a large slope at the low metal-to-S02 ratios, while at ratios greater than 1 they
256
Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990
Table VI. Variables Used in Figure 8 O metal k’,b 11s
cu
Na Ce
co Ni Fe
4.5, 28 1.3, 6.7 5.1 8.3 2.9 3.3
M ,ka/s 0.0175 0.0127 0.0193 0.0122 0.0162 0.0103
-
“Other conditions the same as in Table V. d, (pm) = 1600. The kinetic rate constants were evaluated from the data of Table I. A mean metal oxide conversion of 0.5 was assumed. Table VII. Empirical Correlations for Bubble Size Prediction proposed equation ref Kobayashi et al. as given in Db = Db + l.4p,d,(u,/um~)h Kat0 and Wen (1969) Mori and Wen as given in Dbmax- Db = exp Kobayashi and Sharma Dbmnx - Dbo (1984) Db = (U,,- U,f)’”(h - h,)3i4/g“4 Rowe (1976) Db = D b + 0.027(u0 - umf)0,94 Geldart (1972)
(-7)
plateau. For the sorbents, where the rate constant (k)is greater, the influence of the metal-to-S02 ratio is less profound, allowing for even lower metal-to-S02 ratios to be remarkably efficient. An analogous behavior is displayed if the factor n in the governing kinetic equation (1) has lower values than unity. Summarizing a more efficient behavior should be expected from sorbents that have higher reaction rate constants (k)or a small dependency of the reaction rate on the solid conversion. In Figure 8 is shown the model prediction of conversion vs the kinetic severity function (k’H,)/u,. The points on the figure are simulated for the conditions listed in Table VI. It is clear that the sorbents based on Cu, Na, Fe, Co, and Ni could be well considered as SO2 sorbents. Attention should be drawn to the fact that there are quite large differences between the results predicted by obtaining rate constants from different kinetic studies. As stated earlier in this paper, kinetic studies should be performed at conditions as close as possible to those in the fluidized bed. Another serious conclusion that can be drawn from the present study is that the Na content of the Na sorbents could be lowered from the 20-30% initially used by Bienstock et al. (1967). A change of this sort is very possible to improve the attrition resistance of the alkalized alumina.
Conclusions A fluidized bed reactor model was developed in order to simulate a fluidized bed process using large particles for the SO2removal from flue gases. The fluidized reactor model fits published pilot-plant data satisfactorily. From the simulation of various operating conditions and sorbent properties, serious conclusions are drawn which could be very useful in solid sorbent/catalysts development. These could be summarized as follows. Large particles have better performance under the same operating conditions if the same kinetic parameters are assumed. There exists a critical sorbent feed rate, or corresponding metal oxide content, above which the fluidized bed performance is not enhanced. This is expected to be lower for higher rate constants and for lower dependency of the reaction rate on the active metal oxide conversion. Other metal oxides than the usual CuO and Na20 could be considered as potential sorbents, possibly the oxides of Ce, Co. Fe, and Ni.
3% ut m 3% ut 0 3% u t 3% u t
cu Na
Ce
co
A
3% ut N i
0
3% w t Fe
.4
0
1
2
3
4
5
7
Kinetic severity function fk’Hmf/Uol
8
9
1
Figure 8. Comparison of various simulated SOz sorbents.
Great care should be taken in kinetic studies to exactly simulate the operating conditions of the fluidized bed reactor.
Acknowledgment This work was partially financed by the EEC’s Integrated Mediterranean Programs. The authors also thank the Hellenic Aspropyrgos Refineries for financial support of this research.
Nomenclature A, = reactor cross-sectional area, m2 c = SOz concentration, mol/m3 D = gas diffusivity, mz/s Db = bubble diameter, m Dbo= initial bubble diameter, m Dbmar= maximum bubble diameter, m d, = particle diameter, m D, = reactor diameter, m E = activation energy, kJ/mol f = phase volume fraction g = gravitational constant, m/s2 h = reactor axial length, m Hmf= height at minimum fluidization, m k = reaction rate constant, based on unit volume of solid, l / s k’ = pseudo-first-order rate constant, based on unit volume of solids at minimum fluidization, l / s k , = preexponential factor of the Arrhenius expression of the rate constant, l / s kbc = bubble to cloud gas interchange coefficient, based on unit volume of bubbles, l / s k , = cloud-to-emulsion gas interchange coefficient based on unit volume of bubbles, l / s M = solid feed rate, kg/s no = number of holes per unit surface area of distributor, l / m 2 r = overall reaction rate based on unit volume of solids, mol/m3/s T = reactor temperature, K u = superficial velocity, m/s Ubr = velocity of rise of a single bubble, m/s u b = velocity of rise of a bubble swarm, m/s umf = velocity at minimum fluidization, m/s u, = gas superficial velocity, m/s u,, = solid superficial velocity, m/s ut = solid particles terminal velocity, m/s W = bed weight, kg n = mean solid conversion Greek Symbols q, =
bed void fraction
emf = bed void fraction at p = density, kg/m3
incipient fluidization
Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990 257 (e.g., f, C 1)for the whole range of the operating conditions of the fluidized bed: f,/fb = 1.17[1 - eXp(1 - U ) ] / ( U - 1) (A7)
Subscripts b = bubble c = cloud e = emulsion eff = effective g = gas h = at height h i = initial o = overall s = solid w = wake
For the evaluation of the wake fraction, the approaches given below can be followed. The Benenati empirical correlation gives in CGS units (Kunii and Levenspiel, 1977) fw/fb = 0.785 exp(-66.3dP)/~,/(1 - emf) (A81
Appendix: Evaluation of Hydrodynamic Parameters for Large Particle Fluidization 1. Two-Phase Regime. For u < 1, the reactor will solely operate in the two-phase regime. Accordingly, the following equations can be written (Partridge and Rowe, 1966):
Uge
= (1 - fb)umf
(A2)
= us,
(A31
= uo - Uge
(A4)
use
2. Four-Phase Regime. In this case, four phases will exist in the fluidized bed. Evaluation of the fractions and gas velocities requires the solution of a set of nonlinear algebraic equations as brought forward by Fryer and Potter (1972) and more recently by Viswanathan (1982). In the present model, however, the gas and solid balances were formulated to yield a set of linear equations. This allows the easy incorporation of various correlations with respect to the hydrodynamic properties of the fluidized bed and greatly facilitates the numerical solution. The fraction of the existing phases in the fluidized bed can be obtained by the following equations. The bubble fraction is by definition fb
= Ugb/Ub
(A5)
Moreover, if the flow through the bubble phase is approximated by u, - umf,the bubble fraction can be obtained by (Kunii and Levenspiel, 1977) f b = (uo - umf)/ub (A6) The cloud fraction is evaluated by the Murray model (Fryer and Potter, 1972), modified by the incorporation of an exponentialterm in order to yield acceptable fcvalues
The last equation gives for large particles a very small wake fraction. On the other hand, the equation of Rowe and Widmer (1973) fw/fb = 1 - exp(-0.057Db) (A91 results in quite large values for fwsince the size of the bubbles formed in large particles fluidized beds is large. Equations A8 and A9, as well as a constant value of 0.2fb) were tested for the wake fraction evaluation. The later two ways resulted in too large wake fractions, so eq A8 was used. The emulsion fraction can be obtained, of course, by f e = 1- f b - f c - f w (A10) For the estimation of the gas and solid velocities, the set of linear eq A l l is solved (Chart I). The coefficients of the linear equations are a function of the phases fractions and are obtained by solving eqs A6, A7, A10, and A8 or A9. From the form of the eq A l l , the major assumptions of the model concerning the gas/solid flows can be clearly seen; the original postulate of the constant relative velocity between gas and solids in the emulsion phase as proposed by Kunii and Levenspiel (1977) has been used. Solving eq A l l for ugeand setting ugeC 0, the flow reversal is predicted by the model equations to start at
(Ai2) Equation A12 is different from the well-known equation of Kunii and Levenspiel (1977)) which can be obtained from eq A12 by setting u,, = 0 and f, = 0, which are the assumptions of the Kunii-Levenspiel model. Evaluation of the Bed Void Fraction. The bed void fraction is evaluated by the following equation: Eb = (1- fb)emf + f b 6413) Evaluation of Bubble Size. For the bubble size estimation, many empirical or semiempirical approaches
Chart I. Set of Linear Equations for the Estimation of the Gas and Solid Velocities in a Fluidized Bed where
A
E
1
:l /l ffbb
0 0
Au = E 1 0 -1lfc%lf 0 0 0
1 0 0 -1lfwcmf 0 0
1 0 0 0 0 0 0 llfecmr
0 1 0 0 0 1 0 0
E=
0 1 0 0
llfc
0 1 0 0 0
258 Ind. Eng. Chem. Res., Vol. 29, No. 2, 1990
have been proposed. Among them, four equations that have been tested in our model are listed in Table VII. The bubble sizes predicted by the four equations of Table VI1 differed a lot for the case of large particles, which was of interest, so the correlation for the bubble size prediction was a parameter in our model. All the equations listed in Table VI1 were used. The equation of Wen and Mori gave the best simulation results with respect to the pilot-plant data taken from Bienstock et al. (1967), Yeh et al. (1985), and Barreteau et al. (1978). Moreover, experimental data on bubble diameters obtained with large particles were reported recently by Glicksman et al. (1987), showing an exceptionally good fit to this equation. So the Wen-Mori equation was finally selected for the prediction of bubble size. The initial bubble size can be obtained by (Doraiswamy and Sharma, 1984)
where G = (uo- umf)/no
(A151
if the distributor is a perforated plate and by Db0 = 0.00376(u0- umf)2
(-416)
if the distributor is a porous plate. The maximum bubble size can be evaluated by the Davidson equation (Kunii and Levenspiel, 1977) Dbmax = ( ~ t / o . 7 1 ) ~ / g
(A17)
or by the Wen-Mori correlation (Doraiswamyand Sharma, 1984) Dbmax= 0.652[A,(uO- Umf)]o'4
(A18)
Gas-Exchange Coefficients ( k b o km).For the evaluation of the gas-exchange coefficients, the expressions suggested by Kunii and Levenspiel (1977) have been adopted:
The effective diffusivity is approximated by Deff =
Em@
(A21)
Registry No. SOz, 7446-09-5; CuO, 1317-380; AZO3, 1344-281; NazO, 1313-59-3; Cu, 7440-50-8; Na, 7440-23-5; Ce, 7440-45-1; Co, 7440-48-4; Ni, 7440-02-0; Fe, 7439-89-6.
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Particles. Fluidization;Cambridge University Press: Cambridge, U.K., 1978. Best, R. J. A Study of a Non-Catalytic Gas-Solid Reaction in Fixed and Fluidized Bed Reactors. Ph.D. Dissertation, Department of Chemical Engineering, Univereity College London, 1974. Best, R. J.; Yates, J. G. Removal of Sulfur Dioxide from a Gas Stream in a in a Fluidized Bed. Ind. Eng. Chem. Process Des. Deu. 1977, 16, 347. Bienstock, D.; Field, J. H.; Myers, J. G. Process Development in Removing Sulfur Dioxide from Hot Flue Gases. Report Inv. 7021; U.S. Bureau of Mines: Washington, DC, 1967. Davidson, J. F.; Harrison, D. Fluidised Particles;Cambridge University Press: Cambridge, U.K., 1963. DeBerry, D. W.; Sladek, K. J. Rates of Reaction of SOz with Metal Oxides. Can J. Chem. Eng. 1971,49, 781. Doraiswamy, L. K.; Sharma, M. M.Heterogeneous Reactions;Wiley and Sons: New York, 1984; Vol. 1. Fryer, C.; Potter, 0. Countercurrent Backmixing Model for Fluidized Bed Catalytic Reactors. Applicability of Simplified Solutions. Ind. Eng. Chem. Fundam. 1972,ll (3), 338. Geldart, D. The Effect of Particle Size Distribution on the Behaviour of Gas-Fluidized Beds. Powder Technol. 1972,6, 201. Glicksman, L. R.; Lord, W. K.; Sakagami, M. Bubble Properties in Large-Particles Fluidized Beds. Chem. Eng. Sci. 1987,42 (31,479. Imgraham, T. R.; Marier, D. Kinetics of the Formation and Desomposition of Nickelous Sulfate. Trans. Metal. SOC.AIME 1966, 236, 1067. Kato, K.; Wen, C. Y. Bubble Assemblage Model €or Fluidized Bed Catalytic Reactors. Chem. Eng. Sci. 1969, 24, 1351. Koballa, T. E.; Dudukovic, M. P. Sulfur Dioxide Adsorption on Metal Oxides Supported on Alumina. AIChE Symp. Ser. 1978, 73, 199. Krishnan, N. G.; Bartlett, R. W. Kinetics of Sulfation of Alkalized Alumina (Naz-A1203).Atm. Environ. 1973, 7, 575. Kunii, D.; Levenspiel, 0. Fluidization Engineering;R. E. Krieger: New York, 1977. McArdle, J. C.; Leshock, D. G.; Williamson, R. R. Sorbent Life Cycle Testing of the Fluidized-Bed Copper Oxide Process. Presented at the AIChE Spring National Meeting, Houston, TX, March 29-April 2, 1987. Partridge, B. A.; Rowe, P. N. Chemical Reaction in a Bubbling Gas-Fluidized Bed. Trans. Inst. Chem. Eng. 1966,44335. Rowe, P. N. Prediction of Bubble Size in a Gas Fluidized Bed. Chem, Eng. Sci. 1976,31, 285. Rowe, P. N.; Widmer, A. J. Variation in Shape With Size of Bubbles in Fluidized Beds. Chem. Eng. Sci. 1973, 28, 980. Town, J. W.; Paige, J. I.; Russell, J. H. Sorption of Sulfur Dioxide by Alkalized Alumina in a Fluidized-Bed Reactor. Chem. Eng. Prog. Symp. Ser. 1970, 66 (105), 260. Vasalos, I. A.; Dimitriadis, V. D. Deactivation of Additives for FCC SO, Control. Presented a t the AIChE Annual Meeting, New York, Nov 15-20, 1987. Viswanathan, K. Semicompartmental Approach to Fluidized Bed Reactor Modelling. Application to Catalytic Reactors. Ind. Eng. Chem. Fundam. 1982,21 (4), 352. Vogel, R. F.; Mitchell, B. R.; Massoth, F. E. Reactivity of SOz with SuDoorted Metal Oxide-Alumina Sorbents. Environ. Sci. Technoi.-1974, 8 (5), 432. Yeh, J. T.; Demski, R. J.; Strakey, J. P.; Joubert, J. I. Combined SOz/NO, Removal from Flue Gases. Environ. Prog. 1985,4 (4), 223.
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Received f o r review April 10, 1989 Revised manuscript received October 3, 1989 Accepted October 16, 1989
