Ind. Eng. Chem. Res. 1995,34, 4003-4008
4003
Transition from Bubbling to Turbulent Fluidization H.T.Bi, J. R. Grace,* and K. S.Lim Department of Chemical Engineering, University of British Columbia, Vancouver, Canada V6T 124
Two types of transition to turbulent fluidization are proposed on the basis of bubble-bubble interaction. A relatively sharp transition (type I) is triggered when bubbles grow t o such a size t h a t following wakes become open and turbulent. The type I1 gradual transition occurs when the wake is closed at the transition point. A mechanistic model is developed to predict the type I transition and is found to be consistent with experimental results obtained in a column of 102-mm diameter and with extensive data from the literature. The model also successfully predicts the variation of U,with particle properties, measurement location, and system pressure.
Introduction Although extensive studies have been carried out to quantify the transition to turbulent fluidization (see Bi and Grace (1995)), the flow patterns in turbulent fluidized beds are still not well understood. Previous experimental work using a variety of techniques and indices has indicated that there are at least two different types of transitions to turbulent fluidization: Type I is a relatively sharp transition to a hydrodynamic regime which is physically distinct from other regimes. This kind of transition has been reported, for example, by Kehoe and Davidson (1970), Yerushalmi et al. (1978),Crescitelli et al. (1978),Yang and Chitester (1988), and Tsukada et al. (1993). Type I1 is a gradual transition involving intermittent sluglike structures interspersed with periods of fastfluidization-like behavior, the latter becoming predominant with increasing superficial gas velocity. This type of transition has been viewed, for example,by Crescitelli et al. (1978), Rowe and MacGillivray (1980), and Brereton and Grace (1992). Both of these modes of transition need to be accounted for in any model which seeks to explain the behavior of fluidized beds operating in the turbulent regime or to predict the onset of turbulent fluidization. In addition, any model should be consistent with the observed parametric effects of various operating variables on the superficial velocity, U,,which is usually assumed to correspond to the beginning of the transition. These variables and their respective influences on U, are summarized in Table 1, together with relevant references. It has also been noted (e.g., Yang and Chitester (1988)) that there are differences between two-dimensional and three-dimensional beds, and these differences should again be explainable in terms of any model. Empirical equations have been suggested by a number of workers for predicting U, (see Bi and Grace (1995)). While they may correlate data over restricted ranges, none of these equations accounts for the effects of particle size distribution (PSD) and height above the distributor, while important variables like bed diameter, pressure, and temperature are also omitted in some of these equations. Previous mechanistic attempts to explain the onset of turbulent fluidization have not led to fully satisfactory models or predictive equations. Yang (1984) explained the transition in terms of clusters of particles obeying laws similar to those governing the behavior of indi-
* To whom correspondence should be addressed.
vidual particles fluidized in a homogeneous manner and in terms of propagation of continuity waves in fluidized beds. The transition from bubbling to turbulent fluidization was defined as the point where the continuity wave speed reached a maximum. Rhodes and Geldart (1986) accounted for U,in terms of the transport of material from the interval between two pressure taps. Sun and Chen (1989) defined the transition as the point where bubbles reached a maximum size at a certain distance above the distributor. Cai et al. (1990) postulated that bubble splitting dominated over coalescence beyond the onset of turbulent fluidization. While these ideas are generally helpful, they fail to explain the full range of observations reported in the literature. Each of these criteria relates the transition process to a change of bubble behavior. Bubble behavior at high gas velocities, however, is not well understood due t o severe distortion caused by bubble-bubble interactions. A key point in seeking the transition mechanism is t o model void behavior a t high gas velocities. In this paper, a transition mechanism is proposed on the bais of a simple and idealized model of bubble-wake interaction. The model is compared with experimental results obtained in our laboratory (Sun, 1991; Bi, 1994) and other literature data.
Transition Mechanism 1. Transition Modes. The transition from welldefined bubble flow to turbulent flow has often been attributed to coalescence and splitting of bubbles. Bubble instability may occur naturally or be induced by nearby bubbles. Bubbles in gas-solid fluidized beds are generally of spherical-cap shape and accompanied by laminar closed wakes (Clift et al., 1978). However, turbulent open wakes are present for large bubbles in low viscosity media. For liquids it has been found (e.g., Crabtree and Bridgwater (1971) and Komasawa et al. (1980)) that open turbulent wakes give much more disturbance to following bubbles than closed laminar wakes and often cause trailing bubbles to break up. Therefore, one may postulate that bubbles in fluidized beds become unstable when they grow to such a size that their wakes undergo a transition from closed to open. This is consistent with X-ray observations (Rowe and MacGillivray, 1980)showing that wakes in fluidized beds become more and more turbulent with increasing bubble size and rising velocity. Turbulent open wakes may also be responsible for reported “maximum stable bubble sizes” in fluidized beds of fine particles. In gasliquid systems, bubbles with open turbulent wakes tend t o rupture on collision (Komasawa et al., 1980; DeKee
0 1995 American Chemical Society Q888-5885/95/2634-4QQ3~Q9.QQ/Q
4004 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 Table 1. Factors Influencing the Onset of Turbulent Fluidization variable increased
effect on
bed diameter distance above distributor mean particle diameter breadth of particle size distribution sphericity of particles absolute pressure temperature
U,
source Thiel and Potter (19771, Cai (1989) Grace and Sun (1991), Bi and Grace (1995) Yerushalmi et al. (19781,Jin et al. (1986) Grace and Sun (1991) Judd and Goosen (1989) Yang and Chitester (1988), Cai et al. (19891, Tsukada et al. (1,993) Cai et al. (1989)
decrease decrease increase decrease decrease decrease increase
Table 2. Relationship between Maximum Stable Bubble Size and Reynolds Number, Estimated on the Basis of Equations 1 and 2, Which Determines the Nature of the Following Wake source
particles
Morooka et al. (1972) Matsen (1973)
FCC
PP?
m pm kg/m3
DBmax, mm
ReB,max
0.20 59
830
55
95
0.60 26 70 70 90 catalyst 0.14 59
2080 2080 2080 2080 880
25 64 127 >152 100
24 74 209 2261 163
0.80 54 1800 64 1800 0.20 64 1850
110 130 75
182 225 98
Coke
Rowe and MacGillivray (1980) SunandChen(1989) FCC Asaietal. (1990)
D , dp,
FCC
et al., 1986). Table 2 shows the maximum stable bubble size obtained in large columns by Matsen (1973), Sun and Chen (19891, and Asai et al. (1990). Reynolds numbers corresponding t o the maximum bubble size have been estimated as
where the bubble rise velocity is estimated by UB= 0.71 x ( ~ D B , ~ There ~ ) ~ .is~no. satisfactory correlation for the prediction of the kinematic viscosity of the dense phase. The data for spherical particles evaluated from bubble size and shape (Grace, 1970) and from a rotating cylinder viscometer (Schugerl et al., 1961) can be correlated (in SI units) by vd
= 0.000374Ar0.0764
Falling-sphere data have not been included because the kinematic viscosity measured by the falling-sphere method is a strong function of the diameter of the falling sphere due to the compaction of the emulsion phase near the sphere. As shown by Kai et al. (19911, Vd from the falling-sphere method is about an order of magnitude smaller than those from the bubble shape and rotating cylinder viscometer methods. In addition, the effect of dense phase voidage is not included, although it is clear that Yd decreases with increasing dense phase voidage (Bagnold, 1954; Kai et al., 1991). The transition from a laminar closed wake to a turbulent open wake depends on the Reynolds number and hence on the dense phase viscosity. This transition occurs for ReB x 130 for bubbles in liquids (Clift et al., 1978). Such a criterion can be extended to gas-solid systems if the dense phase viscosity can be estimated (Davidson et al., 1977; Clift et al., 1978). Table 2 indicates that the Reynolds number corresponding t o the maximum stable bubble size is almost always of the same order as 130. While there is considerable scatter, not surprising given the difficulty in measuring DB,max and the approximate nature of the kinematic viscosity correlation, the results suggest that laminar closed
Table 3. Comparison of the Type of Transition to Turbulent Fluidization with DB,,,ID Predicted on the Basis of Rf?Bmmar = 130 ~ p , dp, D, transn /D source kg/m3 pm mm D B , ~ ~ ~mode" Kehoe and Davidson (1970)
Massimilla (1973) Thiel and Potter (1977) Crescitelli et al. (1978) Yerushalmi and Cankurt (1979) Abed (1984) Schnitzlein and Weinstein (1988) Mori et al. (1988) Kai et al. (1991) Grace and Sun (1991) Perales et al. (1991) Horio et al. (1992)
1100 2200 2200 1100 1100 1100 1000 930 930 930 940 1400 1550 1670 1070 1450 850 1400
22 22 22 26 55 55 50 60 60 60 60 60 95 33 49 49 55 59
100 100 50 100 100 50 156 51 102 218 152 152 152 152 152 152 152 152
0.75 0.78 1.56 0.77 0.86 1.72 0.54 1.71 0.85 0.40 0.56 0.58 0.63 0.53 0.55 0.57 0.56 0.58
I I I I I I1 I I I I I I I I I I I I
729 2400 770 1440 1715 1000
56 78 55 60 80 60
50 50 82 100 92 200
1.68 1.88 1.02 0.88 1.02 0.44
I1 I1 I I I I
I, type I sharp transition; 11, type I1 gradual transition.
wakes behind bubbles transform into turbulent open wakes at about the same condition as that where bubbles reach their maximum stable size. To distinguish the type I sharp transition to turbulent fluidization from the type I1 gradual transition, the bubble size, the bubble shape, and the column size need t o be considered. As bubbles grow, their wakes also increase in size. Note that bubbles may be elongated and have stunted wakes when restricted by the walls of the column (Clift et al., 1978). As a result, wakes following slugs are still laminar and closed for ReD up to 500 (Campos and Guedos de Carvalho, 1988). The ReB = 130 criterion therefore requires that the maximum stable bubble size be much smaller than the column diameter. This suggests that the type I sharp transition should only be attainable in columns of sufficient size. Table 3 compares the turbulent transition mode observed using small type A particles and the ratio DB,max/D with D B ,estimated ~ ~ ~ by setting ReB,max = 130, where ReB,max and Vd are given by eqs 1and 2. It is seen that, except for one system used by Thiel and Potter (1977), the sharp transition was indeed observed for small particles with DB,,/D generally smaller than about unity, while the type I1 transitions all correspond to higher values of this ratio. On the basis of these considerations, we propose the following transition criterion: Transition from bubbling to turbulent fluidization is postulated to occur when the bubble spacing becomes close enough that following bubbles are strongly influenced by the wakes of leading bubbles. If the bubble wakes at this transition point
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4005 Table 4. Local and Overall Time-AverageVoidage and Void Phase Volume Fraction at U,from the Literature source
column size, mm
Lanneau (1960)
100
Abed (1984) Lancia et al. (1988)
152 100
Yang et al. (1990) Asai et al. (1990) Tsukada et al. (1993)
114 152 100
Bi and Grace (1995) Canada et al. (1978)
102 305 x 305
Yerushalmi and Cankurt (1979)
152
Schnitzlein and Weinstein (1988) Mori et al. (1988)
152 50
Sun and Chen (1989) Yang et al. (1990) Lee and Kim (1990) Grace and Sun (1991) Horio et al. (1992)
800 800 114 100 102 50
Brereton and Grace (1992) Tsukada et al. (1993)
152 100
Svensson et al. (1993) Mei et al. (1993) Chehbouni e t al. (1994) Bi (1994)
1420 x 1470 300 82 102
d,, pm
pp, kg/m3
70 70 54.8 257 700 67 64 46.4 46.4 46.4 60 650 2600 33 49 49 268 59 56 134 54 64 67 362 60 60 106 158 46.4 46.4 46.4 320 3180 130 60
2000 2000 850 2650 2650 1480 1850 1780 1780 1780 1580 2480 2920 1670 1070 1450 2650 1450 729 2400 1800 1800 1480 2500 1580 1000 2600 2480 1780 1780 1780 2600 1100 2650 1580
C B ~
0.41 0.41 0.36 0.41 0.52 0.39 0.28 0.40 0.35 0.30 0.38 0.51 0.51 0.55 0.49 0.29 0.53 0.38 0.34 0.60 0.31 0.33 0.40 0.42 0.42 0.51 0.67 0.31 0.42 0.36 0.36 0.31 0.49 0.25 0.27
CC
P, kPa
methoda
0.68 0.68 0.62 0.68 0.74 0.67 0.61 0.68 0.65 0.65 0.66 0.73 0.73 0.87 0.72 0.63 0.74 0.66 0.64 0.78 0.62 0.63 0.67 0.68 0.68 0.73 0.82 0.62 0.68 0.65 0.65 0.62 0.72 0.59 0.60
170 520 100 100 100 100 100 100 350 700 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 350 700 100 100 100 100
CP CP CP CP CP OP OP OP OP OP OP DP DP
AP AP AP AP AP DP
AP DP
AP AP AP DP DP DP DP
a AP,absolute pressure fluctuation measurements; DP, differential pressure fluctuation measurements; CP, capacitance probe; OP, optical fibre probe.
are turbulent and open (i.e., Rep, > 1301, the transition is then expected to be sharp (denoted as type I above). Otherwise, the transition is a gradual process (denoted above as type 11). 2. Simplified Model for Transition in Type I Systems. To predict the transition velocity to turbulent fluidization, a bubbling fluidized bed is divided into two regions, one primarily occupied by bubbles and the other by the dense phase. According to the modified twophase theory (Clift and Grace, 19851, GB = Y(U- Urnf).A
(3)
where Y I 1. Y is typically about 0.8 in bubbling systems of fine group A particles (Baeyens and Geldart, 1986). For group B particles a correlation for Y was given by Baeyens and Geldert (1986)
Y = 2.27Ar-0.21
(4)
From a mass balance on the bubble phase
while the bubble rise velocity is given (Grace and Harrison, 1969) by (6)
uc= urn,+ o.711~Bc(gDBc)1’2/(Y -6
~
~
) (8)
For type I systems, bubble wakes are required to be open and turbulent at Uc(Le., ReB 2 130). Bubbles are then assumed to reach their maximum stable size when ReB reaches 130 for a freely bubbling bed. Therefore, (9) Because bubbles are already well deformed and interacting when U,is reached, it is necessary to base the corresponding bubble volume fraction on experimental evidence. To estimate E B ~ ,all literature data on local and overall voidage and void phase volume fraction at U = Ucfrom capacitance probes, optical fiber probes, and absolute and differential pressure fluctuation measurements are listed in Table 4. In general, bubbles are larger and following wakes proportionally smaller for larger particles (Rowe and Partridge, 1965) so that e~~ tends to be higher in systems with larger particles. Such a trend is evident when all available E B ~data in Table 4 are plotted against Ar in Figure 1. It is seen that e~~ranges from 0.30 to 0.50. Given the scatter, only a linear fit is justified. A least squares fitting of the data in Figure 1 leads to eBc= 0.30Ar0.04
Combining eqs 3, 5, and 6 gives
(10)
Substituting eqs 9 and 10 into eq 8, one obtains At Uc,eq 7 becomes
+
Uc= Urn, 1.2IAr0.04(g~d)1’3/( Y - 0.3Ar0.04) (11)
4006 Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995
0 A
0.8
Sed expansion Visual observation
I
I.
I
0.6 i W
E
0.4
a
o'2
t
ioo
10'
io2
?
.
io3
Equation (10)
10'
lo5
lo6
I.
I
9 10'
10'
100
1o4
102
Ar
Ar Figure 1. Local and spatial average void phase volume fraction a t U = U, as a function of Ar: (open symbols) local void phase
Figure 2. Effect of particle properties on transition velocity U, based on literature data listed in Table 1 of Bi and Grace (1995)
volume fraction from optical and capacitance probes; (solids symbols) spatial average void phase volume fraction from differential pressure measurements. Data sources are listed in Table 4.
and model predictions. '
1.2
with Y = 0.8 for group A particles or estimated by eq 4 for groups B and D particles, while Y d can be estimated by eq 2 for spherical particles. It is seen from eq 11 that Uc tends to increase dramatically and goes to infinity with (Y - 0.3Ar0.04) approaching zero a t Ar = 3280. This sets the upper limit of the present model and is consistent with the type I systems because type I transitions only occur in large columns with group A and fine group B particles when bubble growth is restrained by the maximum stable bubble size.
I
,
'
,
,
I
-
(13)
\(Equation
I
,
,
Bi (1994), Hmt=0.6rn +Sun ( 1 9 9 1 ) , H,,=0.7 rn
I
Equation (11) I
\
0
0
02
. .- -
-I
,
- _- - - - - - - - _ _ _ _ _ _ _ _
0.4
0.6
08
1
z, m Comparison of Model Prediction with Experimental Data
Figure 3. Effect of axial location on the transition velocity U,
1. Effect of Particle Properties. In the proposed model (eqs 8 and ll),the minimum fluidization velocity increases with increasing particle size and density. The second term on the right hand side of eq 11 also increases due to the increase of dense phase viscosity (see eq 2) and the decrease of Y (Baeyens and Geldart, 1986)with increasing particle size and density. Ucthus increases with particle size and density. Figure 2 shows a comparison of this model with the literature data under ambient pressure and temperature conditions (see Bi and Grace (1995) for sources of data). There is seen to be reasonable agreement between the model and the literature data, although there is wide scatter. Accurate estimation of the effective dense phase viscosity is required to improve the present model. Equation 11also predicts that Ucvaries with particle size distribution. For particles of wide size distribution, the dense phase viscosity is lower than for particles of narrow size distribution (Matheson et al., 1949). This is consistent with the finding that bubbles are smaller for particles of wide size distribution (Matsen, 1973; Sun, 1991). As a result, Uc is expected to be smaller for wide PSD particles, in agreement with experimental findings (Grace and Sun, 1991). Consistent with the experimental data of Judd and Goosen (19891, eq 8 also predicts that particles of irregular shape and rough surface give a higher Uc,because of smaller wake fraction (Rowe and Partridge, 1965) and higher dense phase viscosity (Grace, 1970).
2. Effect of Column Size and Static Bed Height. For given particles, the column size is expected t o have little effect on Ucso long as DBJD is much smaller than unity. This is consistent with the experimental data of Cai (1989) which demonstrate that U, does not vary with column diameter for D > 0.1 m and group A particles. Consistent with eq 11,static bed height seems to have little influence on Uc in tall columns (e.g., Hmf > 1 m) where fully developed bubbly flow is established in the upper region. This is supported by experimental data (Grace and Sun, 1991; Cai, 1989). In short beds of large particles (e.g., HmdD < 21, Ucdetermined from absolute pressure fluctuations tends to increase with static bed height (Canada et al., 1978; Dunham et al., 1993). 3. Effect of the Axial Location. Figure 3 shows transition velocity Uc data of Sun (1991) and Bi (1994) obtained from differential pressure fluctuation measurements. These show a small decrease in U, with increasing height. There is some evidence (e.g., Yates and Cheesman (1992)) that gas is progressively transferred from the dense phase to the bubble phase with increasing height. This should lead to some increase in Y,and this may account (see eq 11) for the small decrease of Ucwith increasing z . When the average bubble size is estimated for fine particles by the Darton et al. (1977) equation
from differential pressure fluctuation measurement.
D, = 0.54(U - Umf>0,4(2 + 4S, 1/2)0.8g -0.2
(12)
Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 4007 the gas velocity, U l , required for bubbles to grow to D B ~ can be calculated on the basis of eqs 9 and 12 as a function of z. After some algebra this gives
ul = urn,+ 2.75 x 10 Yd513/(z + 4
112 2 1/3
)g
(13) This is shown for FCC particles used by Sun (1991) and Bi (1994) by the broken line in Figure 3. The gas velocity required for bubbles to grow to their maximum size is predicted to be much smaller than 0.4 m / s at a level 0.4 m above the distributor, consistent with the present model where bubbles are required not only to grow to a size where their wakes become open and turbulent but also to be close enough together to trigger significant interactions. 4. Effect of Pressure. U, has been found to decrease with increasing system pressure (Cai et al., 1989; Tsukada et al., 1993) for group A particles. As the pressure increases, the dense phase voidage, ce, has been found to increase for fine Group A particles (Subzwari et al., 1978; Weimer and Jacob, 1986). This must cause the dense phase viscosity to decrease (Bagnold, 1954; Kai et al., 1991). D B is~ then expected to be reduced in pressurized systems. This is consistent with the experimental finding that bubbles are smaller in high pressure systems (Subzwari et al., 1978; King and Harrison, 1980). A decrease of U, with increasing pressure would be predicted by eq 11 if the effect of pressure on the dense phase viscosity could be accounted for properly. Conclusion A mechanism for transition from bubbling to turbulent fluidization is proposed on the basis of bubblebubble interaction and coalescence. A relatively sharp transition to turbulent fluidization takes place when (i) the wake is open and turbulent (Le., ReBc > 130), (ii) the bubble size at U, is much smaller than the column diameter (i.e., DB,
