The behaviour of most gas fluidized beds is dominated by the rising gas voids, conveniently termed 'bubbles', which characterize these systems. In analysing the behaviour of bubbling fluidized beds, it is essential to distinguish between the bubble phase (or 'lean phase'), i.e. the gas voids containing virtually no bed particles, and the particulate phase (also known as 'dense phase' or 'emulsion phase') consisting of particles fluidized by interstitial gas. A bubbling bed can conveniently be defined as a bed in which the bubble phase is dispersed and the particulate phase is continuous. The flow regimes observed at high velocity, discussed in Chapter 7, correspond to beds in which the volume occupied by the lean phase is so high that the particulate phase no longer forms a continuous medium between discrete bubbles.
Therising bubbles cause motion of the particulate phase which is the main source of solids mixing in bubbling beds, discussed in Chapter 5. This particle motion in turn causes the temperature uniformity and high bed/surface heat transfer coefficients characte'ristic of fluidized beds and reviewed in Chapter 9. Since the gas in a bubble is not in direct contact with the bed particles, it cannot take part in any reaction between gas and solids. Thus interchange of gas between bubbles and interstitial gas in the particulate phase can determine the performance of a fluidized bed reactor. The influence of bubble characteristics on fluid bed reactors is explained in Chapter 11. Thus an understanding of the behaviour of the bubble phase in fluidized beds is essential for understanding the applications of these devices. Section 4.2 of the present chapter considers the behaviour of individual bubbles and of
53
slugs, i.e. bubbles so large that their shape and rise velocity are determined by the dimensions of the column containing the fluidized bed rather than by their own volume.
The gas which fluidizes the bed and forms bubbles must normally be distributed uniformly over the cross-section of the bed; this is achieved by introducing it through a gas distributor. Design requirements for gas distributors are d' sed in Section 4.3, and the flow patterns observed in the vicinity of the distributo re reviewed in Section 4.4. Finally, the behaviour of continuously slugging an freely bubbling beds is discussed in Sections 4.5 and 4.6, concentrating on prediction of the most important characteristics:
bubble size and flowrate, and bed expansion.
In many respects, bubbles in gas fluidized beds are analogous to gas bubbles in viscous liquids (see, for example, Davidson, Harrison, and Guedes de Carvalho, 1977). This analogy has been of immense value in interpreting the behaviour of bubbling fluidized beds, since bubbles are more readily observable
hi
transparent liquidS, and the analogy is used throughout this chapter. There is, however, an important difference between liquids and fluidized beds. A gas bubble in a liquid is bounded by a distinct interface;material can be transferred across this interface by diffusion but not by bulk flow. On the other hand, the surface of a bubble in a fluidized bed is a boundary between a particle-lean region and a region of high solids concentration which is permeable to gas. Therefore bulk flow can occur between a bubble and the surrounding particulate phase, so that material can be transferred across the boundary by convection as well as by diffusion.
These processes of interphase transfer are considered in detail in Chapter 11..
where Vb is the bubble volume. A bubble in a viscous liquid shows the form of Fig. 4.1 if it is sufficiently large for surface tension forces to be negligible (Clift, Grace, and Weber, 1978), i.e. if
Eo
=
PI d~q g >40(T
where PI and (T are the liquid density and interfacial tension, and the dimensionless group Eo is known as the Eotvos number. Since fluidized beds lack a phenomenon equivalent to inteliacial tension, (T is effectively zero.
Thus bubbles in fluidized beds satisfy Eq. (4.2), and the analogy is reasonable.
The shape of such a bubble can conveniently be described by the 'wake angle' between the nose and the lower rim, Ow in Fig. 4.1. Grace (1970) showed that Ow is a function of the bubble Reynolds number:
where Ub is the bubble rise velocity and JLI the liquid viscosity. Observed shapes of bubbles in liquids are represented (Clift, Grace, and Weber, 1978) by:
Ow
=
50+
190 exp (- 0.62 Re~.4) (Eo> 40, Reb > 1.2) (4.4) where Ow is expressed in degrees. This relationship is shown in Fig. 4.2, with a theoretical relationship derived by Davidson et al. (1977):Reb
= (-2---3-CO-S-o:-+-c-o-s
3-Ow-r
34.2.1 Shapes of Single Bubbles
Figure 4.1shows an idealized bubble, the general shape being well known from photographic studies of bubbles in liquids (see, for example, Clift, Grace and Weber, 1978) and X-ray studies of bubbles in fluidized beds (see, for example, Rowe, 1971). The upper surface of the bubble is approximately spherical, and its radius of curvature will be denoted by r. The base is typically slightly indented. Since r is not readily determinable, it is usually more convenient to express the bubble size as its 'volume-equivalent diameter', i.e. the diameter of the sphere whose volume is equal to that of the bubble:
which is in qualitative agreement with the empirical result. It is worth noting that, for Reb < 100, Ow is constant at 50°, as predicted by Rippin and Davidson t1967); this is the shape observed for spherical cap bubbles in low viscosity liquids such as water. Other parameters of interest are the frontal diameter of the bubble db and the volume of the circumscribing sphere not occupied by the bubble Vw' For reasons explained below, Vw is termed the 'wake volume', and the ratio of wake/sphere volume, that is 3Vw/4nr, is known as the 'wake fraction'
tw.
Figure 4.2shows values of deq/r, dJr, and the wake fraction, calculated assuming that the wake angle is given by Eq. (4.4) and the base of the bubble is flat."Note that the wake fraction is sometimes defined as the wake volume Vwdivided by the bubble volume Vb, in which case it is given the symbol ~w' The relationship between the two is~w =
/.J(1 - /w).
Wake Fraction _
y~---Bubble
volume Vb WakeAngle
8w gO
Wake volume Vw
Quantitative application of these results to fluidized beds is limited by lack of sufficient information on the effective viscosity of the particulate phase, or even on how realistic is the assumption that the particulate phase behaves as a Newtonian medium. However, the effect of viscosity is a convenient starting point for discussing the effect of particle characteristics on bubble behaviour in fluidized beds. The essential feature of Fig. 4.2 is that decreasing the viscosity of the medium surrounding the bubble increases Reb and therefore causes the bubble to become flatter (lower Ow) and the wake fraction to increase. Grace (1970) used this effect to infer the effective viscosity of fluidized beds from bubble shapes reported by Rowe and Partddge (1%5).
Values of Ow ranged from 90 to 134°, corresponding to Reb from 2 to 10, implying effective viscosities from 0.4 to 1.3 N s/m2 (i.e. similar to the viscosity of engine oil). Apparent viscosities have also been measured by more conventional techniques (see Schugert, 1971), involving immersing rotating bodies or surfaces in the bed. Since these techniques disturb the local structure of the bed, the significance of the results is questionable. However, the values obtained are generally consistent with those inferred by Grace.
Hetzler and Williams (1969) have given a semiempirical expression for the effective low-shear viscosityof a fluidized medium. It was derived mainly from data for liquid/fluidized systems and its general applicability to gas/fluidized beds is untested, but it seems to explain some of the differences in behaviour between particle groups. The effective viscosity is predicted to increase with particle diameter for group A powders, to increase weakly withdp in group B powders, and to be high but insensitive to dp in group D powder. The viscosity estimates of Grace (1970) and Schugert (1971) show this general trend. The results given by Rowe (1971) show the corresponding effect on bubble shape : on increasingdp from group A to group B, bubbles become
Shape Parameters
Reb
Figure 4.2 Bubble parameters as a function of Reynolds number.
more rounded and the wake fraction decreases, from 0.4 for 50/-Lm cracking catalyst to 0.28 to 0.3 in group B ballotini. More recently, Rowe and Yacono (1976), working with freely bubbling beds of groups A and B reported that
~article size had no detectable effect on average bubble shape.' However, it is lIkely that the changes of shape resulting from bubble interaction and coales.cence (see Section 4.6) masked any effect of particle characteristics.
Cranfield and Geldart (1974) report that bubbles in group D beds lack a
58 ~ GAS FLUIDIZATION TECHNOLOGY
deeply indented base (that is()w approaches 180°); in terms of Fig. 4.2, this confirms that group D materials display very high effective.viscosity, so that Reb is low. Although theory is lacking, irregular particles are likely to show higher effective vi~osity and therefore lower Reb and wake fraction. Results quoted by Ro~1)971) show exactly this effect: the wake fraction in beds of irregular particles is typically 0.2 compared to 0.28 to 0.3 in beds of spherical material. Increasing bubble size in a medium of fixed viscosity increases Reb and should therefore increase the wake fraction. Rowe and Everett (1972) observed such an effect, and Rowe and Widmer (1973) showed that the results were well correlated by:
below the range for which Eq. (4.7) is strictly valid in liquids. Even so, Eq.
(4.7) has been widely used for fluidized beds, and inaccuracies are no doubt masked by the erratic velocity variations typically observed (Rowe and Yacono, 1976). In terms of the volume-equivalent diameter, Eq. (4.7) can be written:
where the braced term is a weak function of Reb, as shown in Fig. 4.2. For Reb> 100 this term is constant at 0.71, and the resulting expression:
Vb Vw
V =
1-V =
exp (- 0.057db),ph ,ph
where db is the frontal diameter in centimetres. Equation (4.6) was derived from observations of bubbles withdb up to 16 cm, with a range of group B materials; for db larger than 16 cm, it predicts unrealistically low values of Vt/V,ph' In the current stage of the technology, all that can be said about other groups is that the wake fraction is generally larger (up to 0.4) for group A, smaller for irregular group B particles (typically 0.17 to 0.22), and very small for group D.
A spherical cap bubble in a liquid carries a closed circulating wake if Reb<
110 (Clift, Grace and Weber, 1978). Since bubbles in fluidized beds fall in this range, they would be expected to carry closed wakes of particulate phase, and this has been observed (see Rowe, 1971). To a good approximation, the wake volume can be taken as the volume of that part of the circumscribing sphere not occupied by the bubble, Vw (see Figs 4.1 and 4.2). It is important to note that the decrease in wake fraction on moving from group A through group B to group D means that the volume of particulate phase transported per unit bubble volume decreases. This is one cause of the change in particle mixing characteristics between groups, discussed in Chapter 5.
has been widely used to predict the rise velocity of isolated bubbles in fluidized beds (Davidson and Harrison, 1963). However, observed rise velocities are generally smaller than predicted by Eq. (4.9), values of ut/V(gdeq) from 0.5 to 0.66 being typical for groups A and B (see'Davidson, Harrison, and Guedes de Carvalho, 1977). From Fig. 4.2, these values correspond to Reb< 60, broadly consistent with the range inferred from the bubble shape.
For groups A and B, it is possible to estimate bubble rise velocities from the shape, as expressed by the wake fraction V wIV'Ph, and this approach is at least self-consistent. From Eq. (4.8), it follows that:
V2 ( 1
)116
Ub
=
-3 1- V IV V(gdeq)w sph
For rounded group B particles, Eq. (4.6) can be used to estimate VWlVsph' For angular group B particles, the wake fraction is typically 0.2, so that ut/V(gdeq) should be roughly 0.5. The shapes of bubbles in group A particles suggest that Reb is about 10, so that ub/V(gdeq) should befrom 0.5 to 0.6.
For group D particles, Cranfield and Geldart's (1974) results give:
4.2.2. Rise Velocity of an Isolated Bubble
Davies and Taylor (1950) showed that the rise velocityUbof a spherical cap bubble is related to its radius of curvature by:
Ub
=
2/3 V(gr) (4.7)Experimental results show that Eq. (4.7) is reliable for bubbles in liquids if Reb is greater than about 40; below this value, departures from the spherical cap shape have a significant effect on Ub (Clift, Grace and Weber, 1978).
Bubbles in fluidized beds typically have Reynolds numbers of order 10or less,
Sincedb and deq are virtually the same in group D beds, Eqs (4.9) and (4.11) are equivalent. This is unexpected, since observed bubble shapes suggest that group D prticles should be treated as low Reb systems (see Section 4.2.1). In the present state of the technology, all that can be concluded is that treating the dense phase as a Newtonian medium does not explain all features of bubble behaviour and that Eqs (4.9) and (4.11) can be used in group D beds.
4.2.3 Bubble Break-Up
Bubbles in viscous liquids and in fluidized beds break up by the process shown schematically in Fi~.4.3 (Clift and Grace, 1972). An indentation forms on the upper surface ofAhe bubble and grows as it is swept around the periphery by the motio~the particles relative to the bubble. If the curtain grows sufficientlY to reach the base of the bubble before being swept away, the bubble divides. When the surface tension effects are negligible, as in fluidized beds, the growth rate of such a disturbance decreases with increasing kinematic viscosity of the medium surrounding the bubble, so that the maximum stable size a bubble can attain before splitting increases with increasing kinematic viscosity (Clift, Grace and Weber, 1974). Analysis of this process leads to realistic predictions of the maximum stable size of bubbles and drops of conventional fluids (Clift, Grace, and Weber, 1978).
Application to fluidized beds is again limited by lack of sufficient data on effective viscosities, but it does explain the differences betw~n.powder groups. In group A particles the effective viscosity and h6frce-'~aximum bubble size are relatively small, and both increase with particle diameter. For group B particles the effective viscosity and bubble size are larger and less dependent on particle size, while for Group D particles the maximum bubble size is too large to be realized.
that Eq. (4.12) predicts the correct order of magnitude for the maximum bubble size. Matsen(1973) found that Eq. (4.12) underpredicts the maximum bubble size, typically by a factor of 4, the difference being larger for very fine particles. Geldart (1977) suggests that a better fit with experimental data for group A powders is obtained if the terminal velocity in Eq. (4.12) is calculated for particles of size:
d;
=
2.7dp (4.13)wheredp is the mean size of the powder (Eq. 2.8). Figure 4.4 shows(deq)max, for particles of density 2,500 kg/m-', fluidized by air at1and 15bar, and 300 and 1,000 K, calculated from Eq. (4.12) with Vt estimated from the correlations given by Clift, Grace and Weber (1978) (see Fig. 6.7) and using Eq. (4.13). For group D and large group B particles, the maximum stable bubble size is so large that in practice it would not impose a limitation on the size of bubbles present in a bubbling bed. For both group A and group B particles, increasing temperature and, especially, increasing pressure reduces the maximum bubble size, thus tending to make fluidization 'smoother'. This is consistent with observations (see Chapter 3). .
;;1000K
//300K
For quantitative predictions of maximum stable size, a method developed by Harrison et
at.
(see Davidson and Harrison, 1963) must be applied. It was proposed that bubbles split when particles are carried up from the base of the bubble by the circulation of gas within the bubble. The gas was assumed to circulate with velocity of order Ub,so that a bubble breaks up ifUbexceeds the terminal velocity of a bed particle. Since the predictions are at best approximate, Eq. (4.9) may be used to estimateUb' The resulting expression for the maximum stable bubble size is:(deq)max
= -
2v~ (4.12).g
where Vt is the particle terminal velocity. Although the physical process on which Eq. (4.12) is based is now known not to occur, there is some evidence
1mm10!J.m 100!J.m 1000 !J.m
dp
Figure 4.4 Maximum stable bubble size as a function of mean size of powder, and gas pressure or temper-ature (calculated using Eqs 4.12 and 4.13).
Clearly slugs can only exist if the diameter of the largest bubble is greater than q.6D. The question of whether a continuously fluidized bed contains bubbles or slugs is considered in Section 4.6.
4.2.4 Wall Effects: Slugs
Provided that deq is less than about 0.125 times the bed diameter D, the shape and rise velocity ot a bubble are unaffected by the walls. For deqID greater than 0.125, waJlAffects reduce the rise velocity and cause the bubble to be more rounfte«, so that the wake fraction is reduced (Clift, Grace, and Weber, 1978). For deqID between 0.125 and 0.6, the rise velocity can be estimated roughly (Wallis, 1969) by:
Example 4.1:Calculation of the properties of single bubbles
In the following example, bubble properties are estimated for a fluidized bed roaster for zinc sulphide ore. Typical conditions for such an operation are given by Avedesian (1974):
Bed conditions : 1,260 K, 1 bar Off-gas composition (% molar)
O2 : 4.0 N2 : 77.3 H20: 7.8 S02 : 10.9 (deq)
Ub
=
l.13Uboo exp-D
(4.14)where Uboois the rise velocity in the absence of wall effects. For deqlD greater than 0.6, the bubble velocity becomes completely controlled by the bed diameter, and the bubble is then termed a 'slug'. Figure 4.5(a) shows schematically the shape of an ideal slug. The rise velocity of such a slug is given (see Clift, Grace, and Weber, 1978) by:
Usi
=
0.35 Y(gD) (4.15)Slugs sometimes adhere to the wall of the tube, as shown schematically in Fig.
4.5(b); in this case the rise velocity is approximately Y2 times the value from Eq. (4.15).
Figure 4.5(c) shows a rather different type of slug, more accurately termed a 'plug' , or solids slug, which completely fills the column so that particles rain through the void rather than moving around it. For groups A and B, this phenomenon normally occurs only in tubes of small diameter. For coarse, very angular, or cohesive particles, 'plug' flow occurs in beds of much larger diameter and is suppressed by roughening the walls (Geldart, Hurt, and Wadia, 1978).
The bed is operated at velocities many times minimum fluidization, so that it will be assumed to be fully mixed with the off-gas composition also representa~ive of the gas~s within the be~. The bed particles, primarily ZnO, have denSity 5,300 kglm . The calculatlOns are carried through for 30 p,m particles (group A) and 100 p,m particles (group B) . ..The latter is typical for the surface-volume mean diameter of bed particles in such an operation. Two possible beds are considered (Fig. 4.6):
(a) A production plant of large diameter.
(b) A pilot plant 0.2 m diameter.
Solution
(a) Maximum stable bubble size. The properties of the above gas are taken as:
Density: 0.32 kg/m3
Viscosity: 5 x 10-5 N s/m2
Particle diameter: dp 30 p,m
Particle type: Group A
d~(from Eq. 4.13) 81 p,m
CDRe~ 4.72
Ret 0.2
Vt (m/s) 0.42
(deq) from Eq. (4.12) 3.7 cm Frontal diameter (db)max 4.3 crn Figure 4.5 (a) Axisymmetric slugs, (b) asymmetric slugs, (c) solids, square-nosed or
'plug' slugs.
100 p,rn Group B 270 p,rn 174.6
5 3.18 2.06 rn 2.46 rn
Uboo
=
0.51 V(gdeq)=
1.61Vdeq m/s withdeq in mResulting values, appropriate to a bed of large diameter, are shown as curve (a) in Fig. 4.6.
For a bed of diameter 0.2m, wall effects become significant for deq >
2.5 cm (see Section 4.2.4); they are therefore slightly significant for bubbles in the 30/-Lm particles. In a bed of 100/-Lm particles, wall effects must be considered. Curve (b) in Fig. 4.6 shows values calculated from Eq. (4.14) for 2.5 cm<deq <12 cm and from Eq. (4.15) fordeq >12cm.
Clearly the two equations do not match atdeql D
=
0.6. The discontinuity occurs because Eq. (4.14) was developed for bubbles with high Reh, for which Uboo is given by Eq. (4.9). Bubbles in fluidized beds are more 'rounded' (that is 8wis larger), so that for givendeqthey rise more slowly,Clearly the two equations do not match atdeql D