Powder Technology, 72 (1992) 31-37 31

Scaling considerations for circulating fluidized bed risers

G. S. Patience*, J. Chaouki
Dkpatiement de Gt!nie Chimique, Ecole Polytechnique de Monttial, Monheal, Que., H3C 3A7 (Canada)

F. Berruti and R. Wong

Department of Chemical and Petroleum Engineering, University of Calgay, Calgary, Alta., T2N IN4 (Canada)

(Received June 10, 1991; in revised form December 27, 1991)

Abstract

The ratio between actual gas velocity to particle velocity in the hydrodynamically fully developed region of
Circulating Fluidized Bed risers (CFB) may be approximated by cp= 1 + 5.6/Fr + 0.47Frp = U&VP. This ratio,
termed the slip factor, is about 2 at operating conditions characteristic of industrial risers several meters in
diameter and agrees with observations of J. M. Matsen (in D. L. Keairns (ed.), Fluidization Technology, Vol. 2,
Hemisphere, 1976, p. 135). The proposed relationship between the gas and solids velocity is an adequate first
approximation to estimate gas and solids residence times, blower capacity and standpipe length.

Introduction two phase model of a bubbling fluidized bed to the

dense phase. Kunii and Levenspiel[7] adopted a similar
Circulating Fluidized Beds (CFB) are being consid- approach and correlated decay constants based on a
ered as alternatives to more conventional Fluidized number of experimental investigations to model the
Bed processes because of their apparent intrinsic ad- decrease in solids hold-up along the riser. Also, mea-
vantages, including short and controllable residence surements of the internal flow structure of the riser
times for the gas and solids, high turn down ratios and by Hartge et al. [ES],Bader et al. [9], and Bolton and
flexibility. Industrial scale plants for coal combustion, Davidson [lo] indicated that large radial gradients exist,
aluminum oxide calcination, catalytic cracking, with significantly higher concentrations of solids near
Fischer-Tropsch synthesis successfully employ this tech- the wall.
nology. Contractor and Chaouki [l] and Gianetto et A complete description of the hydrodynamics of such
al. [2] have discussed a number of potential catalytic a flow structure is difficult. The gas-solid flow is typically
processes that are likely candidates for CFB technology. characterized by large relative velocities between the
The main difference between bubbling, turbulent beds two phases. Two mechanisms have been proposed to
and CFB risers is gas velocity. Typical gas velocities account for the difference in velocity: Yerushalmi et
in CFBs range from 2-10 m s-l. At these velocities, al. [3] suggested that particles agglomerate into clusters
solids are readily entrained by the gas and are carried whose void fraction approaches E,.,,~,whereas Rhodes
to the top of the vessel. Cyclones and rough cut sep- et al. [ll] and Berruti and Kalogerakis [12] postulated
arators separate the solids from the gas phase. The that particles ascend in the core in a dilute phase and
solids are returned to the riser bottom by a standpipe. descend along the wall as a dense annulus. Ishii et aE.
The longitudinal solids hold-up in the riser, discussed [13] have recently incorporated both mechanisms into
by Yerushalmi et al. [3] and by Li and Kwauk [4], a clustering annular flow model.
exhibits a relatively dense region at the solids entry Most of the studies on the hydrodynamics of CFB
point and a dilute phase above it. A number of models systems reported in the literature have been conducted
have been proposed to characterize the riser hydro- using laboratory scale units (i.e. relatively short and
dynamics. Rhodes and Geldart [5] used the entrainment narrow). Scale-up to industrial reactors several meters
model, developed for fluidized beds by Wen and Chen in diameter and tens of meters in height is uncertain
[6], to describe the dilute phase and adapted a classical at best. Experimental rigs. are not only limited by
diameter and height constraints but also by the maximum
*Presently at E.I. du Pont de Nemours & Co., Wilmington, circulation rates attainable. Matsen [14] reported that
DE 19880. USA. typical industrial FCC units operate at solids fluxes

0032-5910/92/$5.00 0 1992 - Elsevier Sequoia. All rights reserved

32

between 500 and 1500 kg m- s-l. The majority of low circulation rates and gas velocities were considered
experimental rigs employ non-mechanical devices and (U,<2 m s-l, G,<20 kg mm2 s-l). Jazayeri [36] de-
Geldart group B particles, which facilitate circulation veloped a graph, based on the data of Van Swaaij et
rate control but may ultimately limit the maximum al. [20], that predicts the suspension density at various
solids fluxes attainable. Although CFB boilers generally gas velocities and circulation rates.
operate at solids circulation rates less than 100 kg m- In the present work, we consider a large pool of
S -I, catalytic reactors require different operating con- data, measured in laboratory and pilot scale risers, to
ditions. develop a generalized scaling criterion.
Despite the growing body of literature, more fun-
damental information on the hydrodynamics of large
scale CFB reactors is needed to assess the potential Slip factor as a scaling law
of this technology and to establish design criteria. Scale-
up parameters are useful for the design of industrial The slip factor is the ratio of the actual gas velocity
CFB units. These parameters should not only estimate to particle velocity,
the overall pressure drop for a given gas velocity and
4p= U&V P (1)
circulation rate, necessary to size compressors and the
standpipe, but also adequately predict reactor per- The average particle velocity, VP, is evaluated based
formance including gas-solids contact efficiency and on the solids circulation rate,
heat transfer characteristics. The internal flow structure
VP= G,/p,(l - 6) (2)
of small experimental units is well understood, but Dry
and La Nauze [15] suggest that the symmetry of the and the void fraction, E, is calculated assuming that
radial solids distribution measured in small units may the time average pressure drop is attributable only to
not apply to large units. However, experiments con- the hydrostatic head of the solids,
ducted in a commercial FCC riser by Saxton and Worley
E= 1 - dpl(p,g dz) (3)
[16] using a radiation attenuation technique, indicate
that a two-phase type flow pattern might adequately Clearly, neglecting the particle acceleration contri-
describe the flow phenomenon. In addition to the bution to the pressure drop restricts the analysis to
uncertainties in scaling-up the riser diameter, few studies the hydrodynamically fully developed region of the riser.
address the effect of height on the hydrodynamics. In Moreover, eqn. (3) ignores the wall shear stress con-
tall risers, differences in the gas velocity between the tribution to the pressure drop, which may be significant
top and bottom of 50% are conceivable at high cir- under certain operating conditions as shown by Van
culation rates. Grace [17] indicates that further com- Swaaij et al. [20] using y-ray absorption. Their results
plications may arise from the exit and entrance effects, indicated that at low riser density conditions the mea-
wall intrusions or roughness and the coefficient of sured pressure drop was systematically higher than the
restitution of the particles. Glicksman et al. [18] doc- hydrostatic head of solids and at high densities it was
umented the increase in the solids void fraction by lower. They showed that the wall shear stress in the
changing the geometry of the exit from a smooth elbow fully developed region is 20-40% of the total pressure
to a sharp one and presented data suggesting that drop at gas velocities greater than 13 m s-l and mass
objects intruding into the riser may significantly influence fluxes greater than 180 kg me2 s-. At gas velocities
the local solids hold-up. below 6 m s-l and circulation rates up to 350 kg m-
Glicksman et al. [18], Ishii et al. [13] and Ishii and S - the contribution of the shear to the measured
Murakami [19] proposed scaling laws to predict the pressure drop was negative and less than 25% of the
behaviour in large scale units. Scale-up criteria were total pressure drop.
derived based on the principles of fluid-particle systems. The slip factor is not commonly reported in the
The criteria were then verified in geometrically similar scientific literature. However, Bolton and Davidson [lo],
small scale lab units. Axial solids hold-up and pressure Yang [22], and Kunii and Levenspiel [7] have used the
fluctuations were generally used as the basis for com- slip velocity as a parameter to model the hydrodynamics
parison. Despite the differences in derivations, Glicks- of experimental risers,
man et al. [18] maintain that the scaling laws proposed
v,, = U,lE - VP (4)
in the literature are not dissimilar. They examined two
units with a 34 mm and 152 mm square cross section. In addition, the slip velocity, VsI, has been used as a
Ishii et al. [13] developed scaling parameters based on parameter for heat and mass transfer correlations.
the Clustering Annular Flow Model and validated the Rhodes and Geldart [5] and Patience and Chaouki [21]
theory experimentally in two geometrically similar units have assumed that Vsl is equal to the particle terminal
200 mm and 50 mm in diameter. However, only very velocity from which the particle velocity is calculated.
 33

5 I I I I 1 I
However, work by Patience et al. [23] clearly shows
V 0 l T
that the latter assumption is not true and better criteria V v oe
are required to evaluate the average solids velocity. 4 - Us= 6 m/s

In large industrial scale FCC risers Matsen [14] wcm 0 Gs= 102 kg/n+
reported that the slip factor cp, is approximately equal l Gs= 108 kg/m s

to 2 and hence the particle velocity equals Ug/2e. u,= 6 m/s

Comparisons between large scale industrial units and
experimental units is complicated not only because of 2 0
V G,= 26 kg/n+
.M I Gs= 07 kg/m s
the differences in geometry but also because of the !z 2
l
differences in operating conditions; high circulation
rates, high temperatures and pressures. Sternerding [24]
showed that the riser pressure drop was independent
of the transport gas properties in the range,
1.4 lo- <p < 3.7 lo- Pa-s
0 100 200 300 400 500 600 700

and P .u,p (kdm3)

Fig. 2. Longitudinal suspension density, Patience [25].

0.33 < pg < 5.0kg rnm3.
However, Findlay and Knowlton [32] suggest that the
solids mass fraction is inversely proportional to the gas W

density to the 0.6 power. More study on the effect of U,= 6 m/s
gas properties on suspension density is required.
0 G,= 102 kg/n+
Van Swaaij et al. [20] reported data with FCC catalyst
l G,= 196 kg/m s
in the developed region of an 0.18 m diameter riser
WI= 6 m/s
at circulation rates up to 500 kg mm2 s-l and their
experimental circulation rates are compared with the V Gs= 26 kg/ms
predicted values assuming a slip factor of 2 in Fig. 1. v G,= 67 kg/ms

Reasonable agreement between the predictions and the

experimental values is evident despite the wide range
of operating conditions. The gas velocity varied between
4.3 to 15.1 m s- and the mass flux from 133 to 514
kg m- s-. l
I , w t C
Figure 2 illustrates the longitudinal solids density at I

02 10 20 30 40
gas velocities of 6 and 8 m s-l and various solids Slip Factor, (p
circulation rates in a riser 83 mm in diameter and 5
Fig. 3. Variation of the slip factor along the riser length.

600 r
op=z
I I I I
m tall as reported by Patience [25]. Sand with a mean
l p = 1+5.6/Fr+0.47Fr,041 diameter of 275 ,um and a density of 2630 kg rnF3 was
E 500 used in all experiments. The suspension density in the
\ riser decays exponentially, reaches a steady value around
r
- 400 the middle of the column and eventually increases
r toward the top. The exit configuration was an abrupt
E:
reducing right angle. Brereton [26] attributes the in-
: 300
4
crease in the density at the exit to internal refluxing
e of solids.
2 200 Experimental data, shown in Fig. 2, are replotted in
2 terms of slip factor, instead of suspension density, in
a
100 Fig. 3. At the entrance, the calculated slip factors are
greater than 20 and at the top of the riser they are
0
greater than 7. However, in the centre of the riser,
0 100 200 300 400 500 600 above the acceleration region, the flow profile is flat
Experimental Mass Flux (kg/ms) and perhaps hydrodynamically fully developed. The
Fig. 1. Data of Van Swaaij et al. [20] compared with predictions slip factor is close to 2 in this region, which agrees
assuming a slip factor of 2, and a slip factor = 1 + 5.6/Fr + 0.47Fr,4. with measurements in risers up to 1.5 m in diameter
34

that operate at elevated circulation rates with Group 10 I I I 1 I I I

_-- (P =
A powders as reported by Matsen [14]. At the entrance, 1+5~3/Fr+0.47Fr,~.~~
the slip factor increases with mass flux, which may be
attributable, in part, to the overprediction of the solids
fraction because the acceleration contribution to the
pressure drop was neglected. Also, the slip factor ap-
pears to be greater at higher gas velocities at the top
of the riser.
In Fig. 4, data measured by Wong [27] in a 3 m tall
riser 50 mm in diameter is shown. The apparent slip
factor in the acceleration region is plotted together
with the actual slip factor in which the acceleration
contribution of the particles is taken into account. The
contribution of particle acceleration to pressure drop, 06
0 2 4 6 8 10 12 14 16
hence density, was calculated based on the work by
up b/s)
Weinstein and Li [30]. The figure indicates that, although
the actual slip factor in the acceleration zone is greater Fig. 5. Slip factors in the hydrodynamically fully developed region
than 2, ignoring the acceleration effect greatly over- at different gas velocities. Data referenced in Table 1.
estimates the slip factor, hence total solids hold-up.
The slip factor calculated in the hydrodynamically Agreement between predicted and experimental cir-
developed region, based on data reported by a number culation rates of Van Swaaijs data [20] using this
of researchers, is plotted against the gas velocity in correlation is good, as shown in Figs. 1 and 5. The fit
Fig. 5. Table 1 summarizes the particle characteristics is superior compared to the single parameter estimate
and riser geometry of each study. Both Geldart A and of rp=2.
B powders were used in the experiments for which the Equation (5) suggests that, at gas velocities much
particle terminal velocities vary between 0.2 m s-l and greater than single particle terminal velocities, the solids
2 m s-l. A slip factor of 2 correlates the data reasonably hold-up increases with diameter, i.e.
at gas velocities between 6 and 12 m s-l. This agrees
with the value reported by Matsen [14] for industrial
4(1- l) = (1 +5.6(Dg)o.5/U, + 0.47Fr,0-41)cG,lUg (6)
risers, which typically operate at velocities greater than The effect of riser diameter on suspension density has
8 m s-l. not been fully explored. Arena et al. [31] studied two
To account for the increase in q with decreasing gas risers 41 mm and 120 mm in diameter and concluded
velocity, as shown in the figure, the following relationship that the density increased with diameter at the same
is proposed: operating conditions. Kato et al. [34] reported that, for
small tubes, the density increased with diameter to the
cp= 1 + 5.6jFr + 0.47Frp4* (5) 0.4 power, whereas a power of 0.2 fit data collected
by Findlay and Knowlton [38] better. Larger riser
6- I I I diameters were used in the latter study. The correlation
0 U = 7.9 m/s
predicts that the solids hold-up is relatively independent
GE = 57 kg/m's
5- d; = 174 /.un of particle characteristics as long as the superficial gas
0 (p experimental velocity is much greater than the particle terminal
0 0 0 corrected for acceleration velocity. Moreover, it suggests that the solids hold-up
9. 4-
i is relatively insensitive to gas properties.
9 0 At high gas velocities, typical of pneumatic conveying,
E0 3- 5.6/Fr tends to zero and cp approaches 1 +0.47Frp41.
0 0
.? 0 Typically, FCC risers operate at slip factors near two;
Ci 2 D
CJ 0 00
Govier and Aziz [37] suggest that in pneumatic conveying
1 < cp< 2, which agrees with the proposed correlation.
Brereton [26] reports large differences in the slip
factor between a smooth exit and an abrupt geometry.
The slip varies between 1.88 and 2.32 for sand particles
1 .o (open squares in Fig. 5) in a CFB with a smooth exit.
Height (m) The slip factor for sand in the same unit with an abrupt
Fig. 4. Slip factors in the hydrodynamically developing region exit geometry (filled squares) varies from 8.2 at low
(acceleration) of a riser, Wong [27]. gas velocities to 3.6. Most of the data reported in the
 35

TABLE 1. References and experimental conditions for the data in Fig. 5

Key Study Riser geometry Particle properties Remarks

D Height Type dP
Cm) Cm) (pm) Zg mm3) (m SC)

V Arena et al. [LB] 0.041 6.4 Glass 88 2600 0.46 Smooth exit
0 Brereton [26] 0.152 9.3 Sand 148 2650 0.99 Smooth exit
n 0.152 9.3 Sand 148 2650 0.99 Abrupt exit
A 0.152 9.3 Alumina 65 3500 0.36 Abrupt exit
0 Patience [25] 0.083 5 Sand 275 2630 1.9 Abrupt exit, 20 < T< 250
+ Rhodes and Geldart [5] 0.152 5 FCC 64 1800 0.2 Abrupt exit
v Stemerding [24] 0.051 2-10 FCC 65 1600 0.18 , Developed region, 15 < T < 500
0 Van Swaaij et al. [20] 0.18 FCC 65 1400 0.16 Developed region
A Wong [27] 0.05 3 Sand 93 2500 0.48 Abrupt exit
0 0.05 3 Sand 174 2500 1.2 Abrupt exit

Estimates.

CFB with the abrupt exit geometry varies between 4 in the experiments with alumina and eqn. (5) fits these
and 6. The slip factor with the alumina particles and data well compared to the experiments with sand where
an abrupt exit geometry (open triangles) lies between the solids circulation rates were made by tracking the
2.1 and 4.7. The large slip velocities reported by Brereton wall velocity in the downcomer.
[36] may be a result of the contribution of two different The general agreement between slip factors reported
phenomena. Firstly, the abrupt exit configuration, in for industrial FCC reactors and experimental risers
this unit, might affect the solids behaviour significantly. suggests that pressure drop predictions may be possible
Secondly, secondary gas was supplied to the column without having to develop large and costly pilot plants.
which extends the acceleration region of the riser. The That is, given the desired residence time of the gas
combination of the abrupt exit and extended accel- and solids, the blower requirements and height and
eration zone may prevent the establishment of a fully diameter of the reactor may be calculated. The insistence
developed flow region. However, experiments by Pa- of geometrical similarity, as suggested by Ishii et al.
tience [25] and Wong [27], conducted in short risers [13] and Ishii and Murakami [19], appears to be too
with abrupt right angle exits, for which the acceleration restrictive. In the present work, the proposed slip factor
zone would presumably affect the solids loading more model is shown to provide a reasonable estimate of
than in taller units, gave much lower slip factors. the average gas and solids residence times. Particle
Whereas values of rp greater than those predicted characteristics do not affect the slip factor as long as
by the proposed correlation are evident in the work the operating gas velocity is significantly greater than
of Brereton [26], smaller values of cp are calculated the particle terminal velocity (in the fully developed
from data obtained in the experimental unit of Arena flow regime of the riser). Van Swaaij et al. [20] and
et al. [28] as reported by Louge and Chang [29] and Stemerding [24] used Geldart Group A powders,
Yang [22]. In this case, the slip velocity approaches whereas Patience [25], Brereton [26] and Wong [27]
the single particle terminal velocity. At gas velocities used Geldart Group B particles. Zhang et al. [35] suggest
of 5 m s-l and circulation rates ranging from 80 to that particle density and particle size distribution of
390 kg rnp2 s-l the slip varies between 1.15 and 1.055. Geldart A materials do not affect the radial voidage
Inaccuracies in the measurement of the circulation rate profile when comparing systems operating at the same
could explain the differences in slip factor as reported suspension density.
by Brereton [26] and Arena et al. [28]. The slip factor
is inversely proportional to the mass flux; hence, under-
estimating the circulation rate will result in large cal- Conclusions
culated slip factors and overestimating the rate gives
low values of q. Patience and Chaouki [33] show that Correlations available in the literature do not seem
using the particle velocity along the downcomer wall, to predict the relationship between the gas and solids
the technique used by Brereton [26] in the experiments velocity adequately. An examination of a large pool of
with sand, can underestimate the circulation rate by data from both experimental laboratory scale CFBs and
up to 40%. Brereton [26] used a butterfly valve technique industrial units indicates that the ratio of interstitial
36

gas velocity to particle velocity, or slip factor, is ap- References

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4
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