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Optimum particle size in a gas-liquid-solid fluidized bed catalytic reactor
Chrmkrrl Enyinvrriny Sciuncc. Printed in Great Britain
Vol. 43. No.
IO, pp. 2741
2750,
1988
CK09 2509/88 $3.00+0.00 R> 1988 Pergamon Press plc
OPTIMUM PARTICLE SIZE IN A GAS-LIQUID-SOLID FLUIDIZED BED CATALYTIC REACTOR KEITH Department
of Chemical
D. WISECARVERt Engineering,
(Received
The Ohio
15 December
and LIANG-SHTH FAN’ Columbus, OH 43210, U.S.A.
State University,
1986; accepted
17 February
1988)
Abstract -The effect of particle
size on the reactant conversion for a pseudo-first-order reaction in a gas-liquid-solid fluidized bed catalytic reactor is rigorously examined based on a comprehensive model developed in this study. The model takes into consideration inherent transport properties of the reactor including gas-liquid and liquid-solid mass transfer, axial liquid dispersion, solids mixing, and phase holdups. The reactant conversion predicted by the model exhibits a maximum with respect to particle size. which is shown to vary with process variables such as gas and liquid velocities, reaction rate constant, and intraparticle ditfusivity. The effect of solids mixing on conversion is shown to be insignificant for a wide range of process variables. Overall reaction rates in the fluidized-bed system are also compared to those predicted for a slurry bubble column utilizing a model based on sedimentation and dispersion of the solids.
INTRODUCTION
Many gas-liquid-solid catalytic reactions are carried out industrially using suspended particle reactors, i.e. gas-liquid-solid fluidized beds or slurry bubble columns. Examples include hydrodesulfurization of oil, cracking of hydrocarbons, Fischer-Tropsch synthesis, and hydrogenation reactions. A reactor operated in the suspended particle state has a number of advantages over fixed-bed operation. These advantages include the excellent contacting between phases occurring in the suspended-particle reactor, which leads to uniform temperature distributions and high mass transfer rates; the ease of on-stream catalyst replacement as compared with the fixed-bed reactor; and the absence of plugging problems associated with the attrition of catalyst particles, the formation of solids, and solid impurities in the influent streams. Operation of three-phase cocurrent-flow suspended-particle reactors has traditionally been divided into the slurry bubble column regime for small particles (less than about 500 I’m) and the gas-liquid-solid fluidized bed regime for larger particles. However, the distinction between these two regimes in the literature is often not clear. Recent work by Fan er al. (1986) attempted to classify three-phase reactors according to the state of motion of the solid phase. According to their classification, cocurrentflow three-phase reactors with liquid as the continuous phase can be divided into three regimes: the fixed-bed regime, in which the drag force exerted by the combined liquid and gas flow is not sufficient to fluidize the particles; the expanded-bed regime, in which the particles are fluidized but the terminal velocity of the particles in the gas-liquid medium is not exceeded; and the transport regime in which the terminal velocity is exceeded, and the solids are trans-
t Present address: Department of Chemical Engineering, University of Tulsa, Tulsa, OK 74104, U.S.A. t To whom correspondence should be addressed. 2741
ported in and out of the reactor with the liquid. If the particle size is increased at a given gas and liquid flow rate, the flow regime of the bed will change from the transport regime to the expanded-bed regime and finally to the fixed bed. Based on the classification of Fan et al. (1986) the gas-liquid-solid fluidized bed operation is conducted in the expanded-bed regime whereas the slurry bubble column operation is conducted either in the expanded-bed regime or the transport regime. Many papers have appeared in the literature regarding the hydrodynamics and modelling of semibatch slurry bubble column reactors (no liquid flow). However, relatively little work has been done in modeling slurry bubble columns with continuous liquid flow (cocurrent-flow slurry bubble columns). Parulekar and Shah (1980) modeled a cocurrent slurry bubble column reactor for hydrocracking (which they referred to as a gas-liquid-solid fluidized bed reactor). They found that yields of all products undergo a maximum as the feed catalyst concentration is varied, due to the competing effects of catalyst concentration and liquidphase holdup. Govindarao and Chidambaram (1983) simulated a catalytic reaction in a cocurrent-flow slurry bubble column reactor using the model differential equations presented by Govindarao (1975) which assume an axially dispersed flow of the gas and liquid phases and a sedimentation-dispersion model for the solid phase. They found that the conversion reaches a minimum with respect to particle size. However, they only considered catalytic reactions occurring on the particle surface; intraparticle diffusion and reaction was not considered in their simulations. Serpemen and Deckwer (1983) modeled the hydrogenation of butynediol in a cocurrent-flow slurry bubble column. They concluded that the nonuniformity of the catalyst distribution has a negligible effect on reactor performance for large column diameters (greater than 30 cm) but that the effect can be considerable for small column diameters.
2742
KEITH
D. WISECARVERand
Relatively few papers have appeared in the literature regarding catalytic reaction in gas-liquidsolid ffuidized beds. Lee et al. (1974) analyzed a gas liquid~solid fluidized bed catalytic reaction by considering a global reaction rate based on resistances to reaction. They calculated an overall resistance based on gas-liquid mass transfer, liquid-solid mass transfer, and catalytic reaction in the solid. The gas-liquid mass transfer resistance decreases with increasing particle diameter due to decreasing bubble size, while the reaction resistance increases with particle diameter due to the larger intraparticle diffusion effect. Lee et al. (1974) showed that this can lead to the existence of an optimum particle diameter for gas-Iiquid-solid fluidized beds. However, their analysis was based onty on a point value for the gtobal reaction rate. They did not consider the bed hydrodynamics or phase holdups and did not quantitatively examine the relationship between the optimum particle size and process variables. Sastri et al. (1983) presented a non-catalytic gas-liquid-solid fluidized bed model for the production of zinc hydrosulfite from sulfur dioxide and particulate zinc in aqueous solution. The model considered the cases of complete mixing, axially dispersed flow, and plug fiow for the liquid phase. Since the gas phase consisted of pure SO,, with constant gas composition throughout the reactor, the gas phase hydrodynamics was not considered. Phase holdups were determined using the generalized wake model of Bhatia and Epstein (1974). The bubble size was assumed to remain constant while the bubble frequency decreased with bed height due to absorption of SOZ. They found that the measured concentration profiles of dissolved SO, and reacted zinc were best predicted by the axially dispersed flow model for the liquid phase. For a three-phase catalytic reaction, the particle size used can have a strong effect on the overall convcrsion. The purpose of this paper is to analyze, based on a comprehensive model, the effect of particle size on the reactor performance in the three-phase fluidized bed reactors for a pseudo-first-order catalytic reaction. The reactor performance is compared with the performance for the slurry bubble column reactors based on the sedimentation-dispersion model. MODEL
In developing a model for the gas-liquid-solid fluidized bed catalytic reactor, the following assumptions are made: (1) The reaction is isothermal and pseudo-firstorder with respect to a single gas phase component. All other reactants are present in excess. (2) The liquid phase is axially dispersed while the gas phase is in plug flow. (3) The gas is sparingly soluble in the liquid phase, so that the gas velocity and interfacial area remain constant throughout the column. In addition to these assumptions, the mixing of the solid phase must be incorporated into the model.
LIANG-SHIH
FAN
Little information is available in the literature concerning solids mixing in gas-liquid-solid fluidized beds, but it appears that the solid phase can exhibit a variety of mixing states ranging from complete solids mixing to no solids mixing, depending on the particle properties and the gas and liquid flow rates (Bickel and Thomas, 1982; Fan et al., 1984). The effect of solids mixing on the conversion will depend on the time associated with the solids intermixing in relation to the rate of reaction. Conceptually, when the reaction rate is much faster than the rate of solids intermixing, then reaction will occur before any significant solids movement can take place, and the rate will be the same as it would be for no solids mixing. For a reaction rate which is very slow with respect to the rate of solids intermixing, complete mixing of solids may occur before any significant reaction takes place, and the solid phase can be treated as being well-mixed. It is therefore desirable to examine the limiting cases of complete solids mixing and no solids mixing as practical models for three-phase fluidization. For the liquid and gas phases, the equations and boundary conditions for the gassliquid-solid fluidized bed can be summarized as follows. s,E,---
d2C, dz’
dC, Ldz + K,u(C,lm
-U
- CJ
-kk,a,E,(C,-CC,)=0 lJgz
c,E,
+ K La(C,/m - C,) = 0
dC,
d-z- + U/,C,,
dC,
z=H
c,=c,,
at z=o
If there is no solids mixing, tion, C,, can be found from k,a,(C,
4
(5)
the surface
concentra-
- C,) = k,rlC,
where q is the effectiveness order reaction, is
where
(2)
at z = 0
= U/,C,
-=Oat dz
factor
(I)
(6)
which,
for a first-
1
is the Thiele modulus. 1 For the case of complete solids mixing, the surface concentration is constant throughout the reactor. C, can therefore be found by making an overall material balance on the reactor: = (d,/6)&,/&
c,= Us(C,o - C,lz=ff)+ U,(C,, k,rlW
- C,l;=,)
(8)
The above model equations [eqs (lW5) and (6) or (S)] were solved analytically for both cases of complete mixing of solids and no solids mixing. The solutions are summarized in Table 1. In order to compare the performance of the reactors
Gas-liquid-solid
Table
1. Solution
to
model equations tluidized bed
for
2743
fluidized bed catalytic reactor
three-phase
Table 2. Solution to sedimentation-dispersion model for slurry bubble cohnnn [from Smith and Ruether (1985)]
Complete solid mixing
6,” = 1.27e,,-( I - cs)
(i.St U + mC, p= C go
C,lJm imiSt-RR, PeSr UR,) c !I0 St2 UKl>.
St(m+U)i.+PeSrUR,
-R,+----x2
transported the volume
No solid mixing
m
St UC,
by the solids is expressed as ~C,E,, times of solids. The resulting equation is
- k,q.+, = y1(m/3, + St U) eoL5 + y,(ma,
+ St U)
- k,r&T, due to particle size effect, conversion for a gasliquid-solid slurry bubble column was also calculated. The sedimentation-dispersion model has been shown to accurately describe the axial distribution of solids for the slurry bubble column (Kato et ul., 1972; Smith and Ruether, 1985), while the liquid phase has been shown to be axially dispersed (Kato et al., 1972). It is assumed here that the gas is in plug flow. Equations (1) and (2) can therefore be used for the gas and liquid phases, respectively. The sedimentation-dispersion model equation for the distribution of solids, assuming constant gas holdup in the column, is as follows (Smith and Ruether, 1985): d’c, de, E v-=0 (9) ‘dz2 ‘dz where E, is the axial dispersion coefficient for the particles and up is the particle velocity defined as 1 --Eg--E,
UL (1 -Eg)(l
-E,/)-
1 -Eg
up
(12)
Combining eqs (9) and (12) results in the following equation for the solid phase:
C 90
VP =
= 0.
(10)
Up in eq. (10) is the velocity of solids relative to the liquid velocity and E,~ is the relative volumetric solids flow rate in the slurry flow, defined as
(11) An equation relating C, to axial distance can be obtained through a material balance on the reactant in the solid phase, where the amount of reactant being
= 0.
(13)
The boundary condition for eq. (13), assuming the feed slurry contains no gas phase reactant, is C, = 0 at z = 0.
(14)
Equation (9) was solved by Smith and Ruether (1985) to yield the solids concentration profile in a slurry bubble column reactor. Their results are summarized in Table 2. Equations (l), (2) and (13) were solved numerically with eqs (3H5) and (14) as boundary conditions. The numerical scheme utilized the “shooting” method with integration via fourth-order Runge-Kutta. MODEL
For model, used to ficient,
PARAMETERS
USED
IN SIMULATIONS
the gas-liquid-solid fluidized bed reactor the correlation of Arters and Fan (1986) was determine the liquid-solid mass transfer coefk,:
kd 2 D,
= 0.228( 1 + 0.0826Re,0~623)Ga0~323S~0~4
x
(
Pp-PL
PL
o:3 1.
The axial dispersion coefficient, E,, was determined from the correlation of Kim and Kim (1983): F
= 20.19(z)1-66
(UL~U,)l-os.
(16)
Phase holdups for gas-liquid-solid fluidized beds can be determined by using a wake model approach or
2744
KEITH
D. WISECARVER
by using empirical correlations. The wake model approach was used successfully by Sastri et al. (1983) for modeling a non-catalytic gas-liquid-solid fluidized bed reaction. There are some uncertainties, however, regarding the wake structures and the values of the parameters required in this approach. Since the gas and liquid velocities can be considered constant in the present study, average values for the phase holdups may also be used. The empirical correlations of Begovich and Watson (1978) were chosen for calculation of phase holdups due to the large data base from a wide variety of particles which they used for their correlation: 5 = E,=
0.048~,0”2d,0~‘6sD;0.‘2~
-o.~l6dp0.*68~~.055D;0,033
EL.= 1 - Eg- E,.
The liquid-phase axial dispersion coefficient was determined from the correlation of Kato et al. (1972): + 8Fr0.85).
E, = 31
(23)
The gas-liquid mass transfer coefficient was calculated using the correlation of Nguyen-Tien et al. (1985): E,
0.58(1-
c9)
(24)
Sanger and Deckwer’s (1981) correlation was used to calculate the liquid-solid mass transfer coefficient:
(17)
1 - o.371u:.Z71 U,o.O4’(p, - PL)
and LIANG-SHIH FAN
(18)
Gas holdup was determined from Hughmark’s (1967) correlation, as recommended by Smith and Ruether (1985) for their sedimentationdispersion model:
(19)
The gas-liquid mass transfer correlations available in the literature for gas-liquid-solid fluidized beds are often in poor agreement. A recent paper by Nguyen-Tien et al. (1985) pointed out that many of these previous researchers failed to account for the liquid-phase axial dispersion in their calculations. The study by Nguyen-Tien er al. properly accounts for the liquid-phase axial dispersion and is based on concentration measurements made throughout the column length; their results were therefore chosen for this study for determination of K,a. For the purposes of this work, their Fig. 9 was correlated by the following equation: K La = 0.Q53d~.709,/<.
Since most of the above correlations are based on an aqueous liquid phase, the physical properties of water were used for the liquid phase in the simulations. The gas properties used are the physical properties of air at 1 atm pressure. These conditions would correspond, for example, to the catalytic oxidation of an aqueous component which is present in excess [e.g. the oxidation of SO2 using activated carbon as reported by Komiyama and Smith (1975)]. The parameters used in the model simulations are summarized in Table 3.
(20)
For the slurry bubble column reactor, the equations of Smith and Ruether (1985) were used to determine the solids axial dispersion coefficient, E,, and the velocity of solids relative to the liquid velocity, U,:
RESULTS
Table 3. Parameters used in simulations Pressure
Temperature Particle density, pp Liquid density, p,_ Gas density, ps Reactor diameter Bed height (for fluid&d bed) or column height (for slurry bubble column) Liquid viscosity, p’r. Gas viscosity, ps Henry’s law constant, m Inlet gas concentration, C,, DitTusivity of reactant in Iiquid, D, Porosity of particle, Ed Surface tension of liquid, 0
AND
DISCUSSION
Figure 1 shows the overall reaction rate (that is, the rate of reactant consumption per volume of reactor) in a gas-liquid-solid fluidized bed catalytic reactor as a function of particle diameter for two different combinations of reaction rate constant and fluid velocities. Curves are given for both the complete solids mixing case and the case of no solids mixing. It can be seen that the reaction rate goes through a maximum with respect to particle size, as was predicted by Lee ef al.
1 atm 293 K 1.5g/cm3 1.O g/cm” 0.0012 g/cm3 15 cm
200 cm 1 cP 0.018 cp 30 8.6 x 10~bgmol/cm3 2.4 x IO-* cm’/s 0.6 72 dyne/cm
Gas-liquid-solid
fluidized bed catalytic
-?
e 2
0.0075
LINE
U,
U,
k,
D
I
4.5
6
I5
0.2
c,o 0
10.0
PARTICLE
&%ETER
(;:I
Fig. 1. Overall reaction rate vs particle diameter for complete solids mixing and no mixing of solids.
At a low particle diameter the terminal velocity of the particle is approached, so the solids holdup is extremely low, resulting in a low overall reaction rate. As the particle diameter is increased, the reaction rate increases due to both the increase in solids holdup and the increase in the gas-liquid mass transfer coefficient, K,u. The increase in K,a with particle diameter is due primarily to the increased bubble break-up occurring with larger particles, resulting in an increased gas-liquid interfacial area. At large particle diameters, this increase in K,_u is offset by the decrease in the effectiveness factor due to the intraparticle mass transfer resistance. These effects result in a maximum reaction rate at an intermediate particle size. It can be seen from Fig. I, however, that the value of this optimum particle size can differ markedly for different values of the process variables. It can be seen from Fig. 1 that there is very little effect of solids mixing on the amount of reactant consumed for the conditions shown. For a low reaction rate constant (0.1 sP ‘) there is a greater relative difference in overall reaction rate for the two extremes of solids mixing, but the difference is still less than 10%. It is noted that complete mixing of the solids results in a slightly higher reaction rate than no solids mixing. If the inlet liquid stream contains no dissolved gas, then the gas must diffuse into the liquid phase at the bottom of the reactor and then into the catalyst particles before any reaction can take place; therefore, the particles at the very bottom of the bed do not contribute to the reaction if there is no solids mixing. If the solids are mixed, then the bottom of the bed contains reactant-rich particles which contribute to the reaction, thereby increasing the rate at the bottom of the bed. However, the particles at the top of the bed have a lower reactant concentration, and therefore a lower reaction rate, than in the case of no solids mixing. Apparently the effect of the increased reaction rate at the bottom of the bed outweighs the effect of the decreased reaction rate at the top of the bed.
(1974).
reactor
2745
It was found that when the liquid feed is saturated with the gas phase reactant (C,, = C,,/m), there is no discernible difference in reactor performance for the two extremes of solids mixing. The effect of solids mixing is relatively more prominent for lower values of reaction rate constant and for lower values of intraparticle diffusivity because the concentration at the surface of the particies, C,, is higher under these conditions, as can be seen from eq. (5). The amount of reactant brought to the bottom of the bed by solids mixing is therefore greater. If k, is large enough that the reaction can be considered instantaneous, it can be seen that solids mixing would have no effect at all on reactor performance, since the surface concentration, C,, would then go to zero and the solid phase would no longer contain any reactant. It is also noted that the effect of solids mixing is influenced by the extent of mixing in the liquid phase. If the liquids were completely mixed, then every catalyst particle would be exposed to the same liquid concentration regardless of the extent of solids mixing, thus resulting in the same reaction rate. The closer the liquid phase is to the plug flow state, the greater should be the importance of solid phase mixing. It was found that the difference in overall reaction rate for the two extremes of solids mixing decreases as UL and U, are increased, corresponding to a higher axial dispersion coefficient for the liquid. For most of the conditions used in this study thcrc was found to be a negligible difference in reactor performance for the two extremes of solids mixing. Since most conditions of operation of gas-liquid-solid fluidized beds appear to involve complete solids mixing (Bickel and Thomas, 1982; Fan rt nl., 1984), only the complete solids mixing case will be considered in the remainder of this study. Figure 2 shows the effect of inlet liquid concentration on the optimum particle size. It can be seen that the optimum particle diameter decreases as the concentration of reactant in the inlet liquid is increased. This is due to the increased concentration of reactant in the liquid phase: since the concentration of absorbed gas is higher, the gas-liquid mass transfer coefficient has less effect on the reaction rate. The effect of intraparticle mass transfer resistance in reducing the reaction rate is therefore more prominent at a lower particle diameter. Note also that, as the particle diameter is increased beyond the optimum, the overall reaction rate decreases from the maximum value much more rapidly when the inlet liquid stream is saturated with the gas reactant. Figure 3 shows the concentration profile in the liquid phase for three different values of the dimensionless inlet liquid concentration, mC,,/C,,. When there is no absorbed gas in the inlet liquid stream, the concentration profile shows a rapid increase in concentration in the lower part of the reactor due to absorption of gas. Note that the concentration at the bottom of the reactor is greater than zero due to the effect of axial dispersion. When the inlet liquid stream is saturated with gas, the concentration decreases
2746
D. WISECARVER
KEITH
and LIANG-SHIH
FAN
LINE
a PARTICLE
DIAMETER
tl~,,l”““““““I 2.5 o~ooo.o
5.0
PARTICLE
(mm)
Fig. 2. Overall reaction rate vs particle diameter for various inlet liquid concentrations (U,=4.5 cm/s, U, = 6 cm/s, k,=loo-‘, D -0.2).
k. (set-‘1
(mm)
Fig. 4. Overall reaction rate vs particle diameter for various reaction rate constants (U, = 4.5 cm/s, U, = 6 cm/s, D = 0.2, c,, = 0).
LINE
LINE
10.0
7.5
DIAMETER
D
mC,/Ceo
g s 00
0.0
““““““““““““, 0.4 0.2 DIMENSIONLESS
Fig. 3. Concentration profile inlet liquid concentrations k,=loos-1,
rapidly
near
reaction
of the absorbed
= 0.5, the nearly tion
the
of
is nearly
offset
the
gas. For
concentration
PARTICLE
in liquid phase for various (U, = 4.5 cm/s, LIB= 6 cm/s, D=O.2).
bottom
flat: the decrease
1.0
0.8 LENGTH
0.6 REACTOR
profile
reactor
due
a value can
be
in concentration
by the increase
to
the
seen
to
be
due to reac-
The
overall
fluidized
bed
intraparticle
rate
calculated
in the
for
tion
gas-liquid-solid
various
values
of
the
rate as
either
particle
reaction
diffusivity
the reaction increases When
in concentration
due to absorption.
reaction
increasing
reaction
seen to increase
rate in
gas-liquid,
k,.
is not This
directly is
liquid-solid,
fer resistances
due
proportional to
the
strong
and intraparticle
on the overall
reaction
to
the
in-
effect
of
mass trans-
rate. The effect of
constant This
rate at higher
particle
particle
Figure 6 shows the effect of reactor performance. Increasing the overall
to the increase
in K,a
size
increases. or the intra-
the particle-side
is decreased.
the actual conversion creases). The increased
particle
diffusivity
rate
size
to the effect of
the optimum
is increased,
the optimum
particle
is similar
intraparticle
the reaction
diffusivity
resistance
creased
on the optimum
5. The effect constant:
the
reaction rate constant is shown in Fig. 4. The optimum particle size can be seen to increase with increasing values of k,. Note that the increase in overall crease
(mm)
Fig. 5. Overall reaction rate vs particle diameter for various values of intraparticle diffusivity (U, = 4.5 cm/s, U, = 6 cm/s, k, = lOOs-‘, C,, = 0).
can be seen in Fig.
of TPuZ,,/C,,
DIAMETER
results
in
diameters,
reacan
inthus
size. gas velocity on the the gas velocity is
rate of reaction
(although
based on the gas phase dereaction rate is due primarily with
gas velocity.
It can also
be
Gas-liquid-solid
fluidized bed catalytic
reactor
2747
LINE
UL(cm/secl
j 2 9 0 0.00
0.0
’
’
’
’
’ ’ ’ 2.5 PARTICLE
’
’
’ ’ ’ 5.0 DIAMETER
’
’
’ ’ 7.5 (mm)
’
’
’
10.0
Fig. 6. Overall reaction rate vs particle diameter for various gas velocities (U,_ = 4.5 cm/s, k, = lOOs_‘, D = 0.2, C,, = 0).
seen from Fig. 6 that the gas velocity has little effect on the optimum particle size. In Fig. 7 the effect of liquid velocity on the reactor performance is demonstrated. Increasing the liquid velocity decreases the reaction rate and increases the optimum particle size. An increase in liquid velocity results in a decrease in solids holdup, thus lowering the reaction rate. The increase in optimum particle size appears also to be due to the decrease in solids holdup: the relative importance of the gas-liquid mass transfer resistance is decreased because of the increase in liquid-solid mass transfer resistance and particle-side reaction resistance with solids holdup, so the effect of the increased K,a with particle diameter is less important. A comparison is made between the overall rates of reaction for the gas-liquid-solid fluidized bed and for the slurry bubble column in Fig. 8. Four values bubble column (i.e. ss,of ESJ for the slurry = 0.01, 0.02, 0.03 and 0.05) are considered. For the conditions shown, it can be seen that the slurry bubble column gives a somewhat higher rate of reaction than the gas-liquid-solid fluidized bed, especially at very iow particle diameters. The reaction rate for the slurry bubble column is seen to decrease monotonically with particle diameter and to increase with increasing inlet solids concentration. Figure9 shows the same comparison for a case of lower reaction rate constant, lower intraparticle diffusivity, and higher gas velocity. The overall rate of reaction for the slurry bubble column is seen to be up to 3 times higher than for the gas-liquid-solid fluidized bed when the inlet slurry concentration is high. The higher reaction rate for the slurry bubble column is due to the larger specific surface area of solids, resulting in a higher liquid-solid mass transfer rate, and the much higher effectiveness factor for small particles. These advantages are partially offset by the gas-liquid mass increased transfer in the
II o-mo.o
2.5 PARTICLE
5.0 DIAMETER
7.5 (mm)
10.0
Fig. 7. Overall reaction rate vs particle diameter for various liquid velocities (U, = 6 cm/s, k, = 100-‘, D = 0.2, C,, = 0).
0.04
r-
‘”
r-4
~o.o~ 5.0
PARTICLE
DIAMETER
7.0
9.0
(mm)
column with Fig. 8. Comparison of slurry bubble gas-liquid-solid fluidized bed (U, = 3.5 cm/s, U/B= 3 cm/s, k, = 200 s - ‘, D = 0.5, C,, = 0).
gas-liquid-solid fluidized bed resulting from bubble breakup with large particles. In general, the performance of the gas-liquid-solid fluidized bed as compared with the slurry bubble column is improved with increasing reaction rate constant, increasing intraparticle diffusivity, and decreasing gas velocity, because the relative importance of gas-liquid mass transfer to the overall reaction rate is higher. The gas-iiquid-solid fluidized bed also fares better when the inlet slurry concentration to the slurry bubble column is low. Under conditions of high pressure and high temin industrial perature, as are often encountered gas-liquid-solid reactions, the bubble size is considerably smaller and the gas holdup is considerably larger
KEITH
2748
D. WISECARVER
and LIANG-SHIH
FAN
ticle diameter and to increase with increasing inlet solids concentration. A comparison between the slurry bubble column simulations and the gas-liquid-solid Auidized bed simulations show that under conditions of high reaction rate constant, high intraparticle diffusivity, and low gas velocity, the slurry bubble column with inlet slurry concentration above 1% gives a somewhat higher rate of reaction than the gas-liquid-solid Auidized bed. As the reaction rate constant and intraparticle diffusivity are decreased and the gas velocity is increased, the difference between reaction rates for the slurry bubble column and the gas-liquid-solid Auidized bed becomes greater. AcknowledgementpThis No.
PARTICLE
DIAMETER
et al., 1986). The difference in reaction rate between the transport reactor and the expanded-bed reactor would therefore be even greater, since there would be less effect of bubble size reduction with increasing particle size. It should be noted, however, that the increased reaction rate in slurry bubble columns as compared with gas-liquid-solid fluidized beds is only one factor to consider in deciding which reactor type to use for a given catalytic reaction. Many process variables enter into such a decision, such as the capital cost associated with each reactor type, the liquid and gas Aow rates required and the associated pumping costs, the ease of catalyst replacement, and the costs associated with separating the catalyst particles from the effluent liquid stream for a transport reactor. In addition, catalyst deactivation would be expected to occur more rapidly for a smaller particle diameter. The relative difference in reaction rates for a given set of process conditions must be weighed against these other factors. (Fan
CONCLUDING
by NSF
grant
A
mPe-StU
%
solids surface area per unit volume of solids (cm- ‘)
b 12 b 23 b 31 c,
C go Cl. c LO C, D DC D eff D, 4 El E2 E3 EL
REMARKS
The effect of bed hydrodynamics and process variables on the optimum particle size in a gas-liquid-solid Auidized bed catalytic reactor was analyzed based on a comprehensive model. The optimum particle size in the reactor as well as the overall reaction rate was found to increase with increases in the reaction rate constant and the intraparticle diffusivity. Reaction rates were found to increase and the optimum particle size to decrease with decreasing liquid flow rate and with increasing inlet liquid concentration. Mixing of the solid phase was found to have a negligible effect on the rate of reaction except at very low reaction rate constants with zero inlet liquid concentration. The reaction rate for the slurry bubble column was found to decrease monotonically with increasing par-
was supported
NOTATION
(mm)
Fig. 9. Comparison of slurry bubble column with gas-liquid-solid fluidized bed (U, = 4.5 cm/s, U, = 6 cm/s, k, = zos-1, D = 0.1, c,, = 0).
work
CBT-8516874.
EP
F,
E,F, - E,F, E,F, - E,F, E,F, - E,F, reactant concentration in phase gas (g mol/cm3) inlet gas concentration (g mol/cm3) reactant concentration in liquid phase (g mol/cm”) reactant concentration in liquid feed (g mol/cm3) reactant concentration at particle surface (g mol/cm3) D&D, column diameter (cm) effective intraparticle diffusivity (cm2/s) molecular diffusivity of gas component in liquid (cm’/s) particle diameter (cm) ~l(m~l + Sr U) ep’ B2(m/32+ St U) es2 f13(m& + St U) es3 axial dispersion coefficient of liquid based on linear velocity of liquid (cm2/s) axia1 dispersion coefficient for particles based on linear velocity of slurry (cm’/s) /?l(/?lm-A)-PeStU
F2
fiz(fi2m -
A) -
Pe St iJ
F3
b3(,!Y3m -
A) -
Pe St U
Fr
Froude
u
G,
number, & &‘, gravitational acceleration [St(m + U) + m/311es1 [St(m + U) + mPz] es2 [St(m + U) + mB3] eSa
Ga
Galileo
9 G, G,
H KLa
number,
(cm2/s)
d;dg
~
Pf bed height (cm) volumetric gas-liquid ficient (s - ‘)
mass transfer
coef-
Gas-liquid-solid
k, k
m P
pseudo-first-order
reaction
rate
constant
(s- ‘) liquid-solid mass transfer coefficient (cm/s) Henry’s law constant (g mol per cm3 in gas/g mol per cm3 in liquid) 3m Pe St(m + mKI + U) + A2 for complete solids mixinR +AZfornosol-
P ids mixing Pe
Peclet number, ~
4
2A3 + 9m Pe St A(m + mKI + U) + 27m2 Pest2 UK~ for complete solids mixing
4
2A3 + 9mPeStA
ELEL
+
27m2 Pe St2 1 + K,
rnKt
m + -+u 1 + Kr UK,
2749
fluidized bed catalytic reactor
>
mCLo y-(E3--4)+b,, II0
b,, + b,, + b,, mCLo
-(El-EE,)+b,, C SO
b23+b,z+ba, holdup of gas phase holdup of liquid phase void fraction of catalyst particle holdup of solid phase average holdup of solid phase holdup of solids at bottom of column holdup of solids at top of column relative volumetric solids flow rate in the slurry flow, defined in eq. (11). effectiveness factor
for no solids mixing
RI
-1.5
( > 4P
cos-1
~
2
R2
Re$ PL
ktl b,, + b,, + b,,
UP&%
Re,
P’s
Pest
u,d,e.
RetJ
PI.
PL
u
-UL
-E,)+b,,
U, UL U, U*I U,
superficial gas velocity (cm/s) superficial liquid velocity (cm/s) velocity of solids relative to liquid velocity superficial slurry velocity (cm/s) terminal velocity of single particle in liquid
UP z
(cm/s) velocity of solids, defined by eq. (t 0) axial distance from bottom of bed (cm)
u,
Greek letters
#O
b2, -
1 mC, 1 go --Ez)+b,, c 1mC,
Pest
St
- E3) c
Pest
U(E,
U(E,
density density density surface Thiele VH P E,
U(E,
c
-El)
go mCLo c + b,, g0
Pest
U(E,
Pest
U(E,
c
viscosity viscosity Z
w
Pest
mc,
4,
--3)+
Schmidt number, ~ PL.D, K,aH Stanton number, UI._
SC
mCLo+
U(E,
- E,)
“CL0 ~
C g0
+b,z--
of gas $&m/s) of liquid (g/cm/s)
of gas (g/cm3) of liquid (g/cm3) of particle (g/cm3) tension (dyne/cm) modulus
REFERENCES Arters, D. C. and Fan, L.-S., 1986,Solid-liquid mass transfer in a gas-liquid-solid fluidized bed. Chem. Engny Sci. 41, 107. Begovich, J. M. and Watson, J. S., 1978, Hydrodynamic characteristics of three-phase fluidized beds, in Fluidization (Edited by J. F. Davidson and D. L. Keairns), p. 190. Cambridge University Press, Cambridge. Bhatia, V. K. and Epstein, N., 1974, Three-phase fluidization: a generalized wake model, in Proc. Inc. Symp. on Fluidces
13:10-n
KEITH D. WISECARVER and
2750
ization
and
its
App1iccrrion.s.
p. 380.
Cepadues-Editions,
Toulouse.
Bickel, T. C. and Thomas, M. G., 1982, Catalyst deactivation in the H-Coal coal liquefaction process. 1. Catalyst residence time distribution. Ind. Eqqnq Chrm. Proce.ss Des. Dev. 21, 377. Fan, L.-S., Chen, S. H. and Muroyama, K., 1984, Solids mixing in a gas-liquid-solid fluidized bed containing a binary mixture of particles. A.I.Ch.E. J. 30, 858. Fan, L.-S., Kreischer, B. E. and Tsuchiva, K., 1986. Advances in gassliquidPsolid fluidization: f&damentals and applications. Paper 28g, presented at the AIChE Annual Meeting, Miami Beach, FL, 2-7 November 1986; to appear in Fluidization (Edited by A. S. Mujumdar and L. K. Doraiswamy). Elsevier. Amsterdam, 1988. Govindarao, V. M. H.. 1975. On the dvnamics of bubble column slurry reactors. Chem. Enyny j. 9, 229. Govindarao, V. M. H. and Chidambaram, M, 1983, On the steady state performance of cocurrent bubble column slurry reactors. Chrm. Enqnq J. 27, 29. Hughmark, G. A., 1967, Holdup and mass transfer in bubble columns. Ind. Engny Chem. Process Drs. Del-. 6, 218. Kato, Y.. Nishiwaki, A., Fukuda, T. and Tanaka, S., 1972, The behavior of suspended solid particles and liquid in bubble columns. J. them. Enqng Japan 5, 112. Kim, S. D. and Kim, C. H., 1983, Axial dispersion characteristics of three-phase fluidized beds. J. them. Engny Japan 16, 172. Komiyama, H. and Smith, J. M., 1975, Sulfur dioxide oxidation in slurries of activated carbon. A.f.Ch.E. J. 21, 664. Lee, J. C., Sherrard, A. J. and Buckley. P. S.. 1974. Optimum particle size in three phase ftuidized bed reactors, in Fluidization and irs Applications (Edited by H. Angclino et al.), p, 407. Cepadues-Editions, Toulouse. Nguyen-Tien, K., Patwari, A. N.. Schumpe, A. and Deckwer.
LIANG-SHIH
FAN
W.-D., 1985, Gas-liquid mass transfer in fluidized particle beds. A.I.Ch.E. J. 31, 194. O’Dowd, W., Smith, D. N. and Ruether, J. A., 1987, Gas and solids behavior in a baffled and unbaffled slurry bubble column. A.1.Ch.E. J. 33, 1959. Parulekar. S. J. and Shah. Y. T.. 1980. Steadv-state behavior of gas-liquid-solid fluidized-bed reactors. Chem. Engny J. 20, 21. Sanger, P. and Deckwer, W.-D., 1981, Liquid-solid mass transfer in aerated suspension. Chrm. Enqnq J. 22, 179. Sastri, N. V. S., Epstein, N., Hirata, A., Koshijima, I. and Tzumi, M., 1983, Zinc hydrosulphite by three phase Ruidization: experiments and model. Can. J. them. Enqny 61, 635. Serpemen, Y. and Deckwer, W.-D., 1983, Influence of nonuniform catalyst distribution on the performance of the bubble column slurry reactor, in Mass Transffr with Chemical Reaction in Multiphase Systems (Edited by E. Alper), Vol. 2, p. 239. Martinus Nijhoff, The Hague. Smith, D. N. and Ruether, .I. A., 1985, Dispersed solid dynamics in a slurry bubble column. Chrm. Engug Sri. 40, 741.
ADDENDUM
The correlation for U,, given in eq. (22), which was taken from the work by Smith and Ruether (1985), was recently shown by O’Dowd et al. (1987) to be in error. The correct equation, as given by O’Dowd et al., should be
Simulation results using the corrected value for U, differ from the results reported in Figs 8 and 9 by a factor of less than 5%.
Vol. 43. No.
IO, pp. 2741
2750,
1988
CK09 2509/88 $3.00+0.00 R> 1988 Pergamon Press plc
OPTIMUM PARTICLE SIZE IN A GAS-LIQUID-SOLID FLUIDIZED BED CATALYTIC REACTOR KEITH Department
of Chemical
D. WISECARVERt Engineering,
(Received
The Ohio
15 December
and LIANG-SHTH FAN’ Columbus, OH 43210, U.S.A.
State University,
1986; accepted
17 February
1988)
Abstract -The effect of particle
size on the reactant conversion for a pseudo-first-order reaction in a gas-liquid-solid fluidized bed catalytic reactor is rigorously examined based on a comprehensive model developed in this study. The model takes into consideration inherent transport properties of the reactor including gas-liquid and liquid-solid mass transfer, axial liquid dispersion, solids mixing, and phase holdups. The reactant conversion predicted by the model exhibits a maximum with respect to particle size. which is shown to vary with process variables such as gas and liquid velocities, reaction rate constant, and intraparticle ditfusivity. The effect of solids mixing on conversion is shown to be insignificant for a wide range of process variables. Overall reaction rates in the fluidized-bed system are also compared to those predicted for a slurry bubble column utilizing a model based on sedimentation and dispersion of the solids.
INTRODUCTION
Many gas-liquid-solid catalytic reactions are carried out industrially using suspended particle reactors, i.e. gas-liquid-solid fluidized beds or slurry bubble columns. Examples include hydrodesulfurization of oil, cracking of hydrocarbons, Fischer-Tropsch synthesis, and hydrogenation reactions. A reactor operated in the suspended particle state has a number of advantages over fixed-bed operation. These advantages include the excellent contacting between phases occurring in the suspended-particle reactor, which leads to uniform temperature distributions and high mass transfer rates; the ease of on-stream catalyst replacement as compared with the fixed-bed reactor; and the absence of plugging problems associated with the attrition of catalyst particles, the formation of solids, and solid impurities in the influent streams. Operation of three-phase cocurrent-flow suspended-particle reactors has traditionally been divided into the slurry bubble column regime for small particles (less than about 500 I’m) and the gas-liquid-solid fluidized bed regime for larger particles. However, the distinction between these two regimes in the literature is often not clear. Recent work by Fan er al. (1986) attempted to classify three-phase reactors according to the state of motion of the solid phase. According to their classification, cocurrentflow three-phase reactors with liquid as the continuous phase can be divided into three regimes: the fixed-bed regime, in which the drag force exerted by the combined liquid and gas flow is not sufficient to fluidize the particles; the expanded-bed regime, in which the particles are fluidized but the terminal velocity of the particles in the gas-liquid medium is not exceeded; and the transport regime in which the terminal velocity is exceeded, and the solids are trans-
t Present address: Department of Chemical Engineering, University of Tulsa, Tulsa, OK 74104, U.S.A. t To whom correspondence should be addressed. 2741
ported in and out of the reactor with the liquid. If the particle size is increased at a given gas and liquid flow rate, the flow regime of the bed will change from the transport regime to the expanded-bed regime and finally to the fixed bed. Based on the classification of Fan et al. (1986) the gas-liquid-solid fluidized bed operation is conducted in the expanded-bed regime whereas the slurry bubble column operation is conducted either in the expanded-bed regime or the transport regime. Many papers have appeared in the literature regarding the hydrodynamics and modelling of semibatch slurry bubble column reactors (no liquid flow). However, relatively little work has been done in modeling slurry bubble columns with continuous liquid flow (cocurrent-flow slurry bubble columns). Parulekar and Shah (1980) modeled a cocurrent slurry bubble column reactor for hydrocracking (which they referred to as a gas-liquid-solid fluidized bed reactor). They found that yields of all products undergo a maximum as the feed catalyst concentration is varied, due to the competing effects of catalyst concentration and liquidphase holdup. Govindarao and Chidambaram (1983) simulated a catalytic reaction in a cocurrent-flow slurry bubble column reactor using the model differential equations presented by Govindarao (1975) which assume an axially dispersed flow of the gas and liquid phases and a sedimentation-dispersion model for the solid phase. They found that the conversion reaches a minimum with respect to particle size. However, they only considered catalytic reactions occurring on the particle surface; intraparticle diffusion and reaction was not considered in their simulations. Serpemen and Deckwer (1983) modeled the hydrogenation of butynediol in a cocurrent-flow slurry bubble column. They concluded that the nonuniformity of the catalyst distribution has a negligible effect on reactor performance for large column diameters (greater than 30 cm) but that the effect can be considerable for small column diameters.
2742
KEITH
D. WISECARVERand
Relatively few papers have appeared in the literature regarding catalytic reaction in gas-liquidsolid ffuidized beds. Lee et al. (1974) analyzed a gas liquid~solid fluidized bed catalytic reaction by considering a global reaction rate based on resistances to reaction. They calculated an overall resistance based on gas-liquid mass transfer, liquid-solid mass transfer, and catalytic reaction in the solid. The gas-liquid mass transfer resistance decreases with increasing particle diameter due to decreasing bubble size, while the reaction resistance increases with particle diameter due to the larger intraparticle diffusion effect. Lee et al. (1974) showed that this can lead to the existence of an optimum particle diameter for gas-Iiquid-solid fluidized beds. However, their analysis was based onty on a point value for the gtobal reaction rate. They did not consider the bed hydrodynamics or phase holdups and did not quantitatively examine the relationship between the optimum particle size and process variables. Sastri et al. (1983) presented a non-catalytic gas-liquid-solid fluidized bed model for the production of zinc hydrosulfite from sulfur dioxide and particulate zinc in aqueous solution. The model considered the cases of complete mixing, axially dispersed flow, and plug fiow for the liquid phase. Since the gas phase consisted of pure SO,, with constant gas composition throughout the reactor, the gas phase hydrodynamics was not considered. Phase holdups were determined using the generalized wake model of Bhatia and Epstein (1974). The bubble size was assumed to remain constant while the bubble frequency decreased with bed height due to absorption of SOZ. They found that the measured concentration profiles of dissolved SO, and reacted zinc were best predicted by the axially dispersed flow model for the liquid phase. For a three-phase catalytic reaction, the particle size used can have a strong effect on the overall convcrsion. The purpose of this paper is to analyze, based on a comprehensive model, the effect of particle size on the reactor performance in the three-phase fluidized bed reactors for a pseudo-first-order catalytic reaction. The reactor performance is compared with the performance for the slurry bubble column reactors based on the sedimentation-dispersion model. MODEL
In developing a model for the gas-liquid-solid fluidized bed catalytic reactor, the following assumptions are made: (1) The reaction is isothermal and pseudo-firstorder with respect to a single gas phase component. All other reactants are present in excess. (2) The liquid phase is axially dispersed while the gas phase is in plug flow. (3) The gas is sparingly soluble in the liquid phase, so that the gas velocity and interfacial area remain constant throughout the column. In addition to these assumptions, the mixing of the solid phase must be incorporated into the model.
LIANG-SHIH
FAN
Little information is available in the literature concerning solids mixing in gas-liquid-solid fluidized beds, but it appears that the solid phase can exhibit a variety of mixing states ranging from complete solids mixing to no solids mixing, depending on the particle properties and the gas and liquid flow rates (Bickel and Thomas, 1982; Fan et al., 1984). The effect of solids mixing on the conversion will depend on the time associated with the solids intermixing in relation to the rate of reaction. Conceptually, when the reaction rate is much faster than the rate of solids intermixing, then reaction will occur before any significant solids movement can take place, and the rate will be the same as it would be for no solids mixing. For a reaction rate which is very slow with respect to the rate of solids intermixing, complete mixing of solids may occur before any significant reaction takes place, and the solid phase can be treated as being well-mixed. It is therefore desirable to examine the limiting cases of complete solids mixing and no solids mixing as practical models for three-phase fluidization. For the liquid and gas phases, the equations and boundary conditions for the gassliquid-solid fluidized bed can be summarized as follows. s,E,---
d2C, dz’
dC, Ldz + K,u(C,lm
-U
- CJ
-kk,a,E,(C,-CC,)=0 lJgz
c,E,
+ K La(C,/m - C,) = 0
dC,
d-z- + U/,C,,
dC,
z=H
c,=c,,
at z=o
If there is no solids mixing, tion, C,, can be found from k,a,(C,
4
(5)
the surface
concentra-
- C,) = k,rlC,
where q is the effectiveness order reaction, is
where
(2)
at z = 0
= U/,C,
-=Oat dz
factor
(I)
(6)
which,
for a first-
1
is the Thiele modulus. 1 For the case of complete solids mixing, the surface concentration is constant throughout the reactor. C, can therefore be found by making an overall material balance on the reactor: = (d,/6)&,/&
c,= Us(C,o - C,lz=ff)+ U,(C,, k,rlW
- C,l;=,)
(8)
The above model equations [eqs (lW5) and (6) or (S)] were solved analytically for both cases of complete mixing of solids and no solids mixing. The solutions are summarized in Table 1. In order to compare the performance of the reactors
Gas-liquid-solid
Table
1. Solution
to
model equations tluidized bed
for
2743
fluidized bed catalytic reactor
three-phase
Table 2. Solution to sedimentation-dispersion model for slurry bubble cohnnn [from Smith and Ruether (1985)]
Complete solid mixing
6,” = 1.27e,,-( I - cs)
(i.St U + mC, p= C go
C,lJm imiSt-RR, PeSr UR,) c !I0 St2 UKl>.
St(m+U)i.+PeSrUR,
-R,+----x2
transported the volume
No solid mixing
m
St UC,
by the solids is expressed as ~C,E,, times of solids. The resulting equation is
- k,q.+, = y1(m/3, + St U) eoL5 + y,(ma,
+ St U)
- k,r&T, due to particle size effect, conversion for a gasliquid-solid slurry bubble column was also calculated. The sedimentation-dispersion model has been shown to accurately describe the axial distribution of solids for the slurry bubble column (Kato et ul., 1972; Smith and Ruether, 1985), while the liquid phase has been shown to be axially dispersed (Kato et al., 1972). It is assumed here that the gas is in plug flow. Equations (1) and (2) can therefore be used for the gas and liquid phases, respectively. The sedimentation-dispersion model equation for the distribution of solids, assuming constant gas holdup in the column, is as follows (Smith and Ruether, 1985): d’c, de, E v-=0 (9) ‘dz2 ‘dz where E, is the axial dispersion coefficient for the particles and up is the particle velocity defined as 1 --Eg--E,
UL (1 -Eg)(l
-E,/)-
1 -Eg
up
(12)
Combining eqs (9) and (12) results in the following equation for the solid phase:
C 90
VP =
= 0.
(10)
Up in eq. (10) is the velocity of solids relative to the liquid velocity and E,~ is the relative volumetric solids flow rate in the slurry flow, defined as
(11) An equation relating C, to axial distance can be obtained through a material balance on the reactant in the solid phase, where the amount of reactant being
= 0.
(13)
The boundary condition for eq. (13), assuming the feed slurry contains no gas phase reactant, is C, = 0 at z = 0.
(14)
Equation (9) was solved by Smith and Ruether (1985) to yield the solids concentration profile in a slurry bubble column reactor. Their results are summarized in Table 2. Equations (l), (2) and (13) were solved numerically with eqs (3H5) and (14) as boundary conditions. The numerical scheme utilized the “shooting” method with integration via fourth-order Runge-Kutta. MODEL
For model, used to ficient,
PARAMETERS
USED
IN SIMULATIONS
the gas-liquid-solid fluidized bed reactor the correlation of Arters and Fan (1986) was determine the liquid-solid mass transfer coefk,:
kd 2 D,
= 0.228( 1 + 0.0826Re,0~623)Ga0~323S~0~4
x
(
Pp-PL
PL
o:3 1.
The axial dispersion coefficient, E,, was determined from the correlation of Kim and Kim (1983): F
= 20.19(z)1-66
(UL~U,)l-os.
(16)
Phase holdups for gas-liquid-solid fluidized beds can be determined by using a wake model approach or
2744
KEITH
D. WISECARVER
by using empirical correlations. The wake model approach was used successfully by Sastri et al. (1983) for modeling a non-catalytic gas-liquid-solid fluidized bed reaction. There are some uncertainties, however, regarding the wake structures and the values of the parameters required in this approach. Since the gas and liquid velocities can be considered constant in the present study, average values for the phase holdups may also be used. The empirical correlations of Begovich and Watson (1978) were chosen for calculation of phase holdups due to the large data base from a wide variety of particles which they used for their correlation: 5 = E,=
0.048~,0”2d,0~‘6sD;0.‘2~
-o.~l6dp0.*68~~.055D;0,033
EL.= 1 - Eg- E,.
The liquid-phase axial dispersion coefficient was determined from the correlation of Kato et al. (1972): + 8Fr0.85).
E, = 31
(23)
The gas-liquid mass transfer coefficient was calculated using the correlation of Nguyen-Tien et al. (1985): E,
0.58(1-
c9)
(24)
Sanger and Deckwer’s (1981) correlation was used to calculate the liquid-solid mass transfer coefficient:
(17)
1 - o.371u:.Z71 U,o.O4’(p, - PL)
and LIANG-SHIH FAN
(18)
Gas holdup was determined from Hughmark’s (1967) correlation, as recommended by Smith and Ruether (1985) for their sedimentationdispersion model:
(19)
The gas-liquid mass transfer correlations available in the literature for gas-liquid-solid fluidized beds are often in poor agreement. A recent paper by Nguyen-Tien et al. (1985) pointed out that many of these previous researchers failed to account for the liquid-phase axial dispersion in their calculations. The study by Nguyen-Tien er al. properly accounts for the liquid-phase axial dispersion and is based on concentration measurements made throughout the column length; their results were therefore chosen for this study for determination of K,a. For the purposes of this work, their Fig. 9 was correlated by the following equation: K La = 0.Q53d~.709,/<.
Since most of the above correlations are based on an aqueous liquid phase, the physical properties of water were used for the liquid phase in the simulations. The gas properties used are the physical properties of air at 1 atm pressure. These conditions would correspond, for example, to the catalytic oxidation of an aqueous component which is present in excess [e.g. the oxidation of SO2 using activated carbon as reported by Komiyama and Smith (1975)]. The parameters used in the model simulations are summarized in Table 3.
(20)
For the slurry bubble column reactor, the equations of Smith and Ruether (1985) were used to determine the solids axial dispersion coefficient, E,, and the velocity of solids relative to the liquid velocity, U,:
RESULTS
Table 3. Parameters used in simulations Pressure
Temperature Particle density, pp Liquid density, p,_ Gas density, ps Reactor diameter Bed height (for fluid&d bed) or column height (for slurry bubble column) Liquid viscosity, p’r. Gas viscosity, ps Henry’s law constant, m Inlet gas concentration, C,, DitTusivity of reactant in Iiquid, D, Porosity of particle, Ed Surface tension of liquid, 0
AND
DISCUSSION
Figure 1 shows the overall reaction rate (that is, the rate of reactant consumption per volume of reactor) in a gas-liquid-solid fluidized bed catalytic reactor as a function of particle diameter for two different combinations of reaction rate constant and fluid velocities. Curves are given for both the complete solids mixing case and the case of no solids mixing. It can be seen that the reaction rate goes through a maximum with respect to particle size, as was predicted by Lee ef al.
1 atm 293 K 1.5g/cm3 1.O g/cm” 0.0012 g/cm3 15 cm
200 cm 1 cP 0.018 cp 30 8.6 x 10~bgmol/cm3 2.4 x IO-* cm’/s 0.6 72 dyne/cm
Gas-liquid-solid
fluidized bed catalytic
-?
e 2
0.0075
LINE
U,
U,
k,
D
I
4.5
6
I5
0.2
c,o 0
10.0
PARTICLE
&%ETER
(;:I
Fig. 1. Overall reaction rate vs particle diameter for complete solids mixing and no mixing of solids.
At a low particle diameter the terminal velocity of the particle is approached, so the solids holdup is extremely low, resulting in a low overall reaction rate. As the particle diameter is increased, the reaction rate increases due to both the increase in solids holdup and the increase in the gas-liquid mass transfer coefficient, K,u. The increase in K,a with particle diameter is due primarily to the increased bubble break-up occurring with larger particles, resulting in an increased gas-liquid interfacial area. At large particle diameters, this increase in K,_u is offset by the decrease in the effectiveness factor due to the intraparticle mass transfer resistance. These effects result in a maximum reaction rate at an intermediate particle size. It can be seen from Fig. I, however, that the value of this optimum particle size can differ markedly for different values of the process variables. It can be seen from Fig. 1 that there is very little effect of solids mixing on the amount of reactant consumed for the conditions shown. For a low reaction rate constant (0.1 sP ‘) there is a greater relative difference in overall reaction rate for the two extremes of solids mixing, but the difference is still less than 10%. It is noted that complete mixing of the solids results in a slightly higher reaction rate than no solids mixing. If the inlet liquid stream contains no dissolved gas, then the gas must diffuse into the liquid phase at the bottom of the reactor and then into the catalyst particles before any reaction can take place; therefore, the particles at the very bottom of the bed do not contribute to the reaction if there is no solids mixing. If the solids are mixed, then the bottom of the bed contains reactant-rich particles which contribute to the reaction, thereby increasing the rate at the bottom of the bed. However, the particles at the top of the bed have a lower reactant concentration, and therefore a lower reaction rate, than in the case of no solids mixing. Apparently the effect of the increased reaction rate at the bottom of the bed outweighs the effect of the decreased reaction rate at the top of the bed.
(1974).
reactor
2745
It was found that when the liquid feed is saturated with the gas phase reactant (C,, = C,,/m), there is no discernible difference in reactor performance for the two extremes of solids mixing. The effect of solids mixing is relatively more prominent for lower values of reaction rate constant and for lower values of intraparticle diffusivity because the concentration at the surface of the particies, C,, is higher under these conditions, as can be seen from eq. (5). The amount of reactant brought to the bottom of the bed by solids mixing is therefore greater. If k, is large enough that the reaction can be considered instantaneous, it can be seen that solids mixing would have no effect at all on reactor performance, since the surface concentration, C,, would then go to zero and the solid phase would no longer contain any reactant. It is also noted that the effect of solids mixing is influenced by the extent of mixing in the liquid phase. If the liquids were completely mixed, then every catalyst particle would be exposed to the same liquid concentration regardless of the extent of solids mixing, thus resulting in the same reaction rate. The closer the liquid phase is to the plug flow state, the greater should be the importance of solid phase mixing. It was found that the difference in overall reaction rate for the two extremes of solids mixing decreases as UL and U, are increased, corresponding to a higher axial dispersion coefficient for the liquid. For most of the conditions used in this study thcrc was found to be a negligible difference in reactor performance for the two extremes of solids mixing. Since most conditions of operation of gas-liquid-solid fluidized beds appear to involve complete solids mixing (Bickel and Thomas, 1982; Fan rt nl., 1984), only the complete solids mixing case will be considered in the remainder of this study. Figure 2 shows the effect of inlet liquid concentration on the optimum particle size. It can be seen that the optimum particle diameter decreases as the concentration of reactant in the inlet liquid is increased. This is due to the increased concentration of reactant in the liquid phase: since the concentration of absorbed gas is higher, the gas-liquid mass transfer coefficient has less effect on the reaction rate. The effect of intraparticle mass transfer resistance in reducing the reaction rate is therefore more prominent at a lower particle diameter. Note also that, as the particle diameter is increased beyond the optimum, the overall reaction rate decreases from the maximum value much more rapidly when the inlet liquid stream is saturated with the gas reactant. Figure 3 shows the concentration profile in the liquid phase for three different values of the dimensionless inlet liquid concentration, mC,,/C,,. When there is no absorbed gas in the inlet liquid stream, the concentration profile shows a rapid increase in concentration in the lower part of the reactor due to absorption of gas. Note that the concentration at the bottom of the reactor is greater than zero due to the effect of axial dispersion. When the inlet liquid stream is saturated with gas, the concentration decreases
2746
D. WISECARVER
KEITH
and LIANG-SHIH
FAN
LINE
a PARTICLE
DIAMETER
tl~,,l”““““““I 2.5 o~ooo.o
5.0
PARTICLE
(mm)
Fig. 2. Overall reaction rate vs particle diameter for various inlet liquid concentrations (U,=4.5 cm/s, U, = 6 cm/s, k,=loo-‘, D -0.2).
k. (set-‘1
(mm)
Fig. 4. Overall reaction rate vs particle diameter for various reaction rate constants (U, = 4.5 cm/s, U, = 6 cm/s, D = 0.2, c,, = 0).
LINE
LINE
10.0
7.5
DIAMETER
D
mC,/Ceo
g s 00
0.0
““““““““““““, 0.4 0.2 DIMENSIONLESS
Fig. 3. Concentration profile inlet liquid concentrations k,=loos-1,
rapidly
near
reaction
of the absorbed
= 0.5, the nearly tion
the
of
is nearly
offset
the
gas. For
concentration
PARTICLE
in liquid phase for various (U, = 4.5 cm/s, LIB= 6 cm/s, D=O.2).
bottom
flat: the decrease
1.0
0.8 LENGTH
0.6 REACTOR
profile
reactor
due
a value can
be
in concentration
by the increase
to
the
seen
to
be
due to reac-
The
overall
fluidized
bed
intraparticle
rate
calculated
in the
for
tion
gas-liquid-solid
various
values
of
the
rate as
either
particle
reaction
diffusivity
the reaction increases When
in concentration
due to absorption.
reaction
increasing
reaction
seen to increase
rate in
gas-liquid,
k,.
is not This
directly is
liquid-solid,
fer resistances
due
proportional to
the
strong
and intraparticle
on the overall
reaction
to
the
in-
effect
of
mass trans-
rate. The effect of
constant This
rate at higher
particle
particle
Figure 6 shows the effect of reactor performance. Increasing the overall
to the increase
in K,a
size
increases. or the intra-
the particle-side
is decreased.
the actual conversion creases). The increased
particle
diffusivity
rate
size
to the effect of
the optimum
is increased,
the optimum
particle
is similar
intraparticle
the reaction
diffusivity
resistance
creased
on the optimum
5. The effect constant:
the
reaction rate constant is shown in Fig. 4. The optimum particle size can be seen to increase with increasing values of k,. Note that the increase in overall crease
(mm)
Fig. 5. Overall reaction rate vs particle diameter for various values of intraparticle diffusivity (U, = 4.5 cm/s, U, = 6 cm/s, k, = lOOs-‘, C,, = 0).
can be seen in Fig.
of TPuZ,,/C,,
DIAMETER
results
in
diameters,
reacan
inthus
size. gas velocity on the the gas velocity is
rate of reaction
(although
based on the gas phase dereaction rate is due primarily with
gas velocity.
It can also
be
Gas-liquid-solid
fluidized bed catalytic
reactor
2747
LINE
UL(cm/secl
j 2 9 0 0.00
0.0
’
’
’
’
’ ’ ’ 2.5 PARTICLE
’
’
’ ’ ’ 5.0 DIAMETER
’
’
’ ’ 7.5 (mm)
’
’
’
10.0
Fig. 6. Overall reaction rate vs particle diameter for various gas velocities (U,_ = 4.5 cm/s, k, = lOOs_‘, D = 0.2, C,, = 0).
seen from Fig. 6 that the gas velocity has little effect on the optimum particle size. In Fig. 7 the effect of liquid velocity on the reactor performance is demonstrated. Increasing the liquid velocity decreases the reaction rate and increases the optimum particle size. An increase in liquid velocity results in a decrease in solids holdup, thus lowering the reaction rate. The increase in optimum particle size appears also to be due to the decrease in solids holdup: the relative importance of the gas-liquid mass transfer resistance is decreased because of the increase in liquid-solid mass transfer resistance and particle-side reaction resistance with solids holdup, so the effect of the increased K,a with particle diameter is less important. A comparison is made between the overall rates of reaction for the gas-liquid-solid fluidized bed and for the slurry bubble column in Fig. 8. Four values bubble column (i.e. ss,of ESJ for the slurry = 0.01, 0.02, 0.03 and 0.05) are considered. For the conditions shown, it can be seen that the slurry bubble column gives a somewhat higher rate of reaction than the gas-liquid-solid fluidized bed, especially at very iow particle diameters. The reaction rate for the slurry bubble column is seen to decrease monotonically with particle diameter and to increase with increasing inlet solids concentration. Figure9 shows the same comparison for a case of lower reaction rate constant, lower intraparticle diffusivity, and higher gas velocity. The overall rate of reaction for the slurry bubble column is seen to be up to 3 times higher than for the gas-liquid-solid fluidized bed when the inlet slurry concentration is high. The higher reaction rate for the slurry bubble column is due to the larger specific surface area of solids, resulting in a higher liquid-solid mass transfer rate, and the much higher effectiveness factor for small particles. These advantages are partially offset by the gas-liquid mass increased transfer in the
II o-mo.o
2.5 PARTICLE
5.0 DIAMETER
7.5 (mm)
10.0
Fig. 7. Overall reaction rate vs particle diameter for various liquid velocities (U, = 6 cm/s, k, = 100-‘, D = 0.2, C,, = 0).
0.04
r-
‘”
r-4
~o.o~ 5.0
PARTICLE
DIAMETER
7.0
9.0
(mm)
column with Fig. 8. Comparison of slurry bubble gas-liquid-solid fluidized bed (U, = 3.5 cm/s, U/B= 3 cm/s, k, = 200 s - ‘, D = 0.5, C,, = 0).
gas-liquid-solid fluidized bed resulting from bubble breakup with large particles. In general, the performance of the gas-liquid-solid fluidized bed as compared with the slurry bubble column is improved with increasing reaction rate constant, increasing intraparticle diffusivity, and decreasing gas velocity, because the relative importance of gas-liquid mass transfer to the overall reaction rate is higher. The gas-iiquid-solid fluidized bed also fares better when the inlet slurry concentration to the slurry bubble column is low. Under conditions of high pressure and high temin industrial perature, as are often encountered gas-liquid-solid reactions, the bubble size is considerably smaller and the gas holdup is considerably larger
KEITH
2748
D. WISECARVER
and LIANG-SHIH
FAN
ticle diameter and to increase with increasing inlet solids concentration. A comparison between the slurry bubble column simulations and the gas-liquid-solid Auidized bed simulations show that under conditions of high reaction rate constant, high intraparticle diffusivity, and low gas velocity, the slurry bubble column with inlet slurry concentration above 1% gives a somewhat higher rate of reaction than the gas-liquid-solid Auidized bed. As the reaction rate constant and intraparticle diffusivity are decreased and the gas velocity is increased, the difference between reaction rates for the slurry bubble column and the gas-liquid-solid Auidized bed becomes greater. AcknowledgementpThis No.
PARTICLE
DIAMETER
et al., 1986). The difference in reaction rate between the transport reactor and the expanded-bed reactor would therefore be even greater, since there would be less effect of bubble size reduction with increasing particle size. It should be noted, however, that the increased reaction rate in slurry bubble columns as compared with gas-liquid-solid fluidized beds is only one factor to consider in deciding which reactor type to use for a given catalytic reaction. Many process variables enter into such a decision, such as the capital cost associated with each reactor type, the liquid and gas Aow rates required and the associated pumping costs, the ease of catalyst replacement, and the costs associated with separating the catalyst particles from the effluent liquid stream for a transport reactor. In addition, catalyst deactivation would be expected to occur more rapidly for a smaller particle diameter. The relative difference in reaction rates for a given set of process conditions must be weighed against these other factors. (Fan
CONCLUDING
by NSF
grant
A
mPe-StU
%
solids surface area per unit volume of solids (cm- ‘)
b 12 b 23 b 31 c,
C go Cl. c LO C, D DC D eff D, 4 El E2 E3 EL
REMARKS
The effect of bed hydrodynamics and process variables on the optimum particle size in a gas-liquid-solid Auidized bed catalytic reactor was analyzed based on a comprehensive model. The optimum particle size in the reactor as well as the overall reaction rate was found to increase with increases in the reaction rate constant and the intraparticle diffusivity. Reaction rates were found to increase and the optimum particle size to decrease with decreasing liquid flow rate and with increasing inlet liquid concentration. Mixing of the solid phase was found to have a negligible effect on the rate of reaction except at very low reaction rate constants with zero inlet liquid concentration. The reaction rate for the slurry bubble column was found to decrease monotonically with increasing par-
was supported
NOTATION
(mm)
Fig. 9. Comparison of slurry bubble column with gas-liquid-solid fluidized bed (U, = 4.5 cm/s, U, = 6 cm/s, k, = zos-1, D = 0.1, c,, = 0).
work
CBT-8516874.
EP
F,
E,F, - E,F, E,F, - E,F, E,F, - E,F, reactant concentration in phase gas (g mol/cm3) inlet gas concentration (g mol/cm3) reactant concentration in liquid phase (g mol/cm”) reactant concentration in liquid feed (g mol/cm3) reactant concentration at particle surface (g mol/cm3) D&D, column diameter (cm) effective intraparticle diffusivity (cm2/s) molecular diffusivity of gas component in liquid (cm’/s) particle diameter (cm) ~l(m~l + Sr U) ep’ B2(m/32+ St U) es2 f13(m& + St U) es3 axial dispersion coefficient of liquid based on linear velocity of liquid (cm2/s) axia1 dispersion coefficient for particles based on linear velocity of slurry (cm’/s) /?l(/?lm-A)-PeStU
F2
fiz(fi2m -
A) -
Pe St iJ
F3
b3(,!Y3m -
A) -
Pe St U
Fr
Froude
u
G,
number, & &‘, gravitational acceleration [St(m + U) + m/311es1 [St(m + U) + mPz] es2 [St(m + U) + mB3] eSa
Ga
Galileo
9 G, G,
H KLa
number,
(cm2/s)
d;dg
~
Pf bed height (cm) volumetric gas-liquid ficient (s - ‘)
mass transfer
coef-
Gas-liquid-solid
k, k
m P
pseudo-first-order
reaction
rate
constant
(s- ‘) liquid-solid mass transfer coefficient (cm/s) Henry’s law constant (g mol per cm3 in gas/g mol per cm3 in liquid) 3m Pe St(m + mKI + U) + A2 for complete solids mixinR +AZfornosol-
P ids mixing Pe
Peclet number, ~
4
2A3 + 9m Pe St A(m + mKI + U) + 27m2 Pest2 UK~ for complete solids mixing
4
2A3 + 9mPeStA
ELEL
+
27m2 Pe St2 1 + K,
rnKt
m + -+u 1 + Kr UK,
2749
fluidized bed catalytic reactor
>
mCLo y-(E3--4)+b,, II0
b,, + b,, + b,, mCLo
-(El-EE,)+b,, C SO
b23+b,z+ba, holdup of gas phase holdup of liquid phase void fraction of catalyst particle holdup of solid phase average holdup of solid phase holdup of solids at bottom of column holdup of solids at top of column relative volumetric solids flow rate in the slurry flow, defined in eq. (11). effectiveness factor
for no solids mixing
RI
-1.5
( > 4P
cos-1
~
2
R2
Re$ PL
ktl b,, + b,, + b,,
UP&%
Re,
P’s
Pest
u,d,e.
RetJ
PI.
PL
u
-UL
-E,)+b,,
U, UL U, U*I U,
superficial gas velocity (cm/s) superficial liquid velocity (cm/s) velocity of solids relative to liquid velocity superficial slurry velocity (cm/s) terminal velocity of single particle in liquid
UP z
(cm/s) velocity of solids, defined by eq. (t 0) axial distance from bottom of bed (cm)
u,
Greek letters
#O
b2, -
1 mC, 1 go --Ez)+b,, c 1mC,
Pest
St
- E3) c
Pest
U(E,
U(E,
density density density surface Thiele VH P E,
U(E,
c
-El)
go mCLo c + b,, g0
Pest
U(E,
Pest
U(E,
c
viscosity viscosity Z
w
Pest
mc,
4,
--3)+
Schmidt number, ~ PL.D, K,aH Stanton number, UI._
SC
mCLo+
U(E,
- E,)
“CL0 ~
C g0
+b,z--
of gas $&m/s) of liquid (g/cm/s)
of gas (g/cm3) of liquid (g/cm3) of particle (g/cm3) tension (dyne/cm) modulus
REFERENCES Arters, D. C. and Fan, L.-S., 1986,Solid-liquid mass transfer in a gas-liquid-solid fluidized bed. Chem. Engny Sci. 41, 107. Begovich, J. M. and Watson, J. S., 1978, Hydrodynamic characteristics of three-phase fluidized beds, in Fluidization (Edited by J. F. Davidson and D. L. Keairns), p. 190. Cambridge University Press, Cambridge. Bhatia, V. K. and Epstein, N., 1974, Three-phase fluidization: a generalized wake model, in Proc. Inc. Symp. on Fluidces
13:10-n
KEITH D. WISECARVER and
2750
ization
and
its
App1iccrrion.s.
p. 380.
Cepadues-Editions,
Toulouse.
Bickel, T. C. and Thomas, M. G., 1982, Catalyst deactivation in the H-Coal coal liquefaction process. 1. Catalyst residence time distribution. Ind. Eqqnq Chrm. Proce.ss Des. Dev. 21, 377. Fan, L.-S., Chen, S. H. and Muroyama, K., 1984, Solids mixing in a gas-liquid-solid fluidized bed containing a binary mixture of particles. A.I.Ch.E. J. 30, 858. Fan, L.-S., Kreischer, B. E. and Tsuchiva, K., 1986. Advances in gassliquidPsolid fluidization: f&damentals and applications. Paper 28g, presented at the AIChE Annual Meeting, Miami Beach, FL, 2-7 November 1986; to appear in Fluidization (Edited by A. S. Mujumdar and L. K. Doraiswamy). Elsevier. Amsterdam, 1988. Govindarao, V. M. H.. 1975. On the dvnamics of bubble column slurry reactors. Chem. Enyny j. 9, 229. Govindarao, V. M. H. and Chidambaram, M, 1983, On the steady state performance of cocurrent bubble column slurry reactors. Chrm. Enqnq J. 27, 29. Hughmark, G. A., 1967, Holdup and mass transfer in bubble columns. Ind. Engny Chem. Process Drs. Del-. 6, 218. Kato, Y.. Nishiwaki, A., Fukuda, T. and Tanaka, S., 1972, The behavior of suspended solid particles and liquid in bubble columns. J. them. Enqng Japan 5, 112. Kim, S. D. and Kim, C. H., 1983, Axial dispersion characteristics of three-phase fluidized beds. J. them. Engny Japan 16, 172. Komiyama, H. and Smith, J. M., 1975, Sulfur dioxide oxidation in slurries of activated carbon. A.f.Ch.E. J. 21, 664. Lee, J. C., Sherrard, A. J. and Buckley. P. S.. 1974. Optimum particle size in three phase ftuidized bed reactors, in Fluidization and irs Applications (Edited by H. Angclino et al.), p, 407. Cepadues-Editions, Toulouse. Nguyen-Tien, K., Patwari, A. N.. Schumpe, A. and Deckwer.
LIANG-SHIH
FAN
W.-D., 1985, Gas-liquid mass transfer in fluidized particle beds. A.I.Ch.E. J. 31, 194. O’Dowd, W., Smith, D. N. and Ruether, J. A., 1987, Gas and solids behavior in a baffled and unbaffled slurry bubble column. A.1.Ch.E. J. 33, 1959. Parulekar. S. J. and Shah. Y. T.. 1980. Steadv-state behavior of gas-liquid-solid fluidized-bed reactors. Chem. Engny J. 20, 21. Sanger, P. and Deckwer, W.-D., 1981, Liquid-solid mass transfer in aerated suspension. Chrm. Enqnq J. 22, 179. Sastri, N. V. S., Epstein, N., Hirata, A., Koshijima, I. and Tzumi, M., 1983, Zinc hydrosulphite by three phase Ruidization: experiments and model. Can. J. them. Enqny 61, 635. Serpemen, Y. and Deckwer, W.-D., 1983, Influence of nonuniform catalyst distribution on the performance of the bubble column slurry reactor, in Mass Transffr with Chemical Reaction in Multiphase Systems (Edited by E. Alper), Vol. 2, p. 239. Martinus Nijhoff, The Hague. Smith, D. N. and Ruether, .I. A., 1985, Dispersed solid dynamics in a slurry bubble column. Chrm. Engug Sri. 40, 741.
ADDENDUM
The correlation for U,, given in eq. (22), which was taken from the work by Smith and Ruether (1985), was recently shown by O’Dowd et al. (1987) to be in error. The correct equation, as given by O’Dowd et al., should be
Simulation results using the corrected value for U, differ from the results reported in Figs 8 and 9 by a factor of less than 5%.