Predicting binary-solid fluidized bed behavior using averaging approaches Mohammad Asif * Department of Chemical Engineering, King Saud University, PO Box 800, Riyadh-11421, Saudi Arabia Received 15 March 2001; received in revised form 15 April 2002; accepted 15 May 2002 Abstract The present study reports new experimental data on the expansion as well as the layer-inversion behavior of liquid-fluidized beds containing two particle species with almost 10-fold difference in the size and a significant difference in the density. The packing models, which are generally used for predicting the porosity of the packing of particle mixtures, are used here to describe the expansion and the phenomenon of the layer-inversion. Predictions of different averaging models, including the property-averaging model, the serial model, and various packing models, are compared with the present data as well as the layer-inversion data reported in the literature. The overall predictive capability of packing models is found to be superior. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Binary-solid; Liquid-fluidized bed; Expansion; Layer-inversion; Packing model 1. Introduction Liquid-fluidized beds containing two different solid species such that the larger ones are lighter and the smaller ones are denser often reveal interesting hydrodynamic features including the phenomenon of the layer-inversion. This phenomenon is normally associated with the change of the stratification pattern of the two solid species in the fluidized bed due to a change in either the liquid velocity or the bed composition. Recent applications of such binary-solid fluidization have been proposed for simultaneous reaction-adsorption systems where the larger solid species is envisaged to constitute the reactive resident phase of the fluidized bed while the smaller but denser particle species can be used to selectively adsorb the product [1–4]. Another interesting application of the liquid fluidization of binary solids has been recently made in enhancing the mass transfer coeffi- cients by adding smaller but denser inert glass beads in a fluidized bed containing active resin particles [5]. In gas– solid fluidization, the use of binary-solid fluidized beds for thermo-chemical processing of biomass is well established as can be seen from the work of Narvaez et al. [6], Olivares et al. [7] and Berruti et al. [8]. In this application, an inert solid species, often the sand, is used to achieve the fluid- ization of the biomass, improve the heat transfer, and control the residence time. Proper characterization of the hydrodynamics of binary- solid liquid-fluidized beds is an important first step in its effective utilization. In this connection, the applicability of the serial model to predict the overall expansion of the binary- or multi-solid fluidized beds is commonly recog- nized [9,10]. In the case of particle species differing only in size, even the local concentration of individual particle species can be predicted from the information about the local pressure-gradient using the serial model. Using the data of Juma and Richardson [11], this has been demon- strated by Asif [12], and more recently by Epstein and Pruden [13]. Attempts to understand the layer-inversion behavior have been widely reported in the literature. Different approaches have been proposed for its prediction. For example, van Duijn and Rietema [14], Moritomi et al. [15], Epstein and LeClair [16], Moritomi et al. [17], Gibilaro et al. [18], Jean and Fan [19], Funamizu and Takakua [20,21], Asif [22–25], Epstein and Pruden [13] to name a few. A discussion on some of these can be found in the review article of Di Felice [26]. Notable among these approaches appears to be the complete-segregation model of Gibilaro et al. [18], which has been shown to be in good agreement with the available 0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII:S0032-5910(02)00126-2 * Fax: +966-1-467-8770. E-mail address: [email protected] (M. Asif). www.elsevier.com/locate/powtec Powder Technology 127 (2002) 226– 238
Transcript
Predicting binary-solid fluidized bed behavior
using averaging approaches
Mohammad Asif *
Department of Chemical Engineering, King Saud University, PO Box 800, Riyadh-11421, Saudi Arabia
Received 15 March 2001; received in revised form 15 April 2002; accepted 15 May 2002
Abstract
The present study reports new experimental data on the expansion as well as the layer-inversion behavior of liquid-fluidized beds
containing two particle species with almost 10-fold difference in the size and a significant difference in the density. The packing models,
which are generally used for predicting the porosity of the packing of particle mixtures, are used here to describe the expansion and the
phenomenon of the layer-inversion. Predictions of different averaging models, including the property-averaging model, the serial model, and
various packing models, are compared with the present data as well as the layer-inversion data reported in the literature. The overall
predictive capability of packing models is found to be superior.
D 2002 Elsevier Science B.V. All rights reserved.
Keywords: Binary-solid; Liquid-fluidized bed; Expansion; Layer-inversion; Packing model
1. Introduction
Liquid-fluidized beds containing two different solid
species such that the larger ones are lighter and the smaller
ones are denser often reveal interesting hydrodynamic
features including the phenomenon of the layer-inversion.
This phenomenon is normally associated with the change of
the stratification pattern of the two solid species in the
fluidized bed due to a change in either the liquid velocity or
the bed composition.
Recent applications of such binary-solid fluidization
have been proposed for simultaneous reaction-adsorption
systems where the larger solid species is envisaged to
constitute the reactive resident phase of the fluidized bed
while the smaller but denser particle species can be used to
selectively adsorb the product [1–4]. Another interesting
application of the liquid fluidization of binary solids has
been recently made in enhancing the mass transfer coeffi-
cients by adding smaller but denser inert glass beads in a
fluidized bed containing active resin particles [5]. In gas–
solid fluidization, the use of binary-solid fluidized beds for
thermo-chemical processing of biomass is well established
as can be seen from the work of Narvaez et al. [6], Olivares
et al. [7] and Berruti et al. [8]. In this application, an inert
solid species, often the sand, is used to achieve the fluid-
ization of the biomass, improve the heat transfer, and control
the residence time.
Proper characterization of the hydrodynamics of binary-
solid liquid-fluidized beds is an important first step in its
effective utilization. In this connection, the applicability of
the serial model to predict the overall expansion of the
binary- or multi-solid fluidized beds is commonly recog-
nized [9,10]. In the case of particle species differing only in
size, even the local concentration of individual particle
species can be predicted from the information about the
local pressure-gradient using the serial model. Using the
data of Juma and Richardson [11], this has been demon-
strated by Asif [12], and more recently by Epstein and
Pruden [13].
Attempts to understand the layer-inversion behavior have
been widely reported in the literature. Different approaches
have been proposed for its prediction. For example, van
Duijn and Rietema [14], Moritomi et al. [15], Epstein and
LeClair [16], Moritomi et al. [17], Gibilaro et al. [18], Jean
and Fan [19], Funamizu and Takakua [20,21], Asif [22–25],
Epstein and Pruden [13] to name a few. A discussion on
some of these can be found in the review article of Di Felice
[26]. Notable among these approaches appears to be the
complete-segregation model of Gibilaro et al. [18], which
has been shown to be in good agreement with the available
0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.
experimental data by Di Felice et al. [27,28]. An important
feature of their approach consists of using the modified
Ergun equation with its applicability extended to the inter-
mediate regime by introducing a voidage-dependent param-
eter, which was obtained by fitting to the Richardson–Zaki
[29] correlation. In order to account for the presence of two
different particle species in the fluidized bed, the commonly
used surface-to-volume mean diameter was employed in
their modified Ergun equation. This was then equated to the
effective weight of the binary-solid fluidized bed. The
force–balance relationship, thus obtained, when used in
conjunction with the fact that the bottom layer always
possesses the maximum bulk density, yields a unique
solution for the bed composition at a given superficial liquid
velocity. It should be pointed out here that equating the
pressure drop predicted by the modified Ergun equation
with the effective weight of the binary-solid fluidized bed
effectively introduces an averaging rule for the mean density
of the two particle species in the force–balance relationship
of Gibilaro et al. [18].
On the other hand, Asif [24] has recently suggested using
the Richardson–Zaki correlation in conjunction with the
mean particle properties (i.e. diameter and density) for
computing the mean values of the particle terminal velocity
and the exponent ‘n’. Despite being simpler, this model, by
virtue of its direct use of the well-established Richardson–
Zaki relationship, can be used with greater confidence.
Needless to say, the force–balance relationship of Gibilaro
et al. [18] itself makes use of Richardson–Zaki [29]
correlation for the estimation of its voidage-dependent
parameter. While using the mean values of particle proper-
ties as a measure of adherence to the procedure of the
Gibilaro et al. [18], Epstein and Pruden [13] preferred the
Wen and Yu [30] relationship, which has no variable
exponent and applies up to Rei1000, in order to circum-
vent the need for computing the exponent of the Richard-
son–Zaki correlation or the voidage-dependent parameter of
Gibilaro’s model.
Starting from the approach of Gibilaro et al. [18] for the
prediction of the layer-inversion phenomenon, these above-
mentioned approaches can essentially be classified as being
the property-averaging approaches, as they are based on the
averaging of the particle properties. By the same token,
other averaging procedures can also be suggested. One such
example is the serial model, which is based on the harmonic
averaging of solid concentrations of mono-component fluid-
ized beds of individual particle species. The success of any
model will, however, depends upon the accuracy with which
it can represent the expansion behavior of the fluidized bed
containing the binary mixture of solid particles. Another
equally important issue is whether the model in question can
properly describe the bed contraction and the concomitant
increase of the bulk density associated with the mixing of
the solid species at the onset of the layer-inversion.
Using two particle species with a significant difference of
size as well as density, Asif [31] has recently observed a
substantial contraction of the fluidized bed depending upon
the mixing of the two components prevailing in the bed. A
similar behavior has earlier been reported by Chiba [32].
Also, the model of Gibilaro et al. [33] based on the Kennedy
and Bretton type of approach predicted a contraction in the
liquid fluidized bed containing two sizes of equal density
particles. On the other hand, the occurrence of the contrac-
tion phenomena in the packing behavior of particle mixtures
is long known, so are attempts to predict its magnitude [34].
It was, however, interesting to note that models for predict-
ing the porosity of the packing of particle mixtures, hence-
forth simply referred to as packing models, were able to
describe the overall expansion of the fluidized bed better
than the serial model for binary-solids of significant size and
density difference [31]. It is therefore worthwhile to explore
whether these packing models can also predict the phenom-
enon of the layer-inversion with similar accuracy.
In view of the above discussion, experiments were carried
out using two particle species with substantial difference in
size as well as density. The present size ratio of about 10 is
twice the highest size ratio data reported by Moritomi et al.
[15,17] and others [9,16]. The data obtained with such a
binary system can therefore provide an important test of the
predictive capability of any model. The main interest here is
to describe the important hydrodynamic features of binary-
solid fluidization, i.e. the overall bed expansion, the bulk
density of the bed and the layer-inversion. Predictions of
common averaging models, whether based on the physical
properties of the two species or their mono-component
expansion, will be examined in the light of present data as
well as the ones reported in the literature. The main emphasis
will, however, be on packing models.
2. Averaging models
In the following, various types of averaging models are
presented for the sake of comparison. One is based on the
averaging of particle properties as mentioned earlier while
others are based on some kind of averaging of mono-
component bed viodages including the serial model and
particle packing models.
2.1. Property-averaging model
As pointed out earlier, there are several relationships that
can be extended to predict the voidage of binary-solid
fluidized beds using the mean values of particle diameter
and density. Not much difference is, however, expected in
their predictions as long as the same averaging procedures
are applied for the same particle properties. Commonly,
these are surface-to-volume mean particle diameter and
volume-average particle density, given as
d ¼ 1
X1
d1þ ð1�X1Þ
d2
ð1Þ
M. Asif / Powder Technology 127 (2002) 226–238 227
And
qs ¼ X1qs1 þ ð1� X1Þqs2 ð2Þ
Note that other averaging procedures for the mean
particle diameter can also be employed, e.g. the hydro-
dynamic mean diameter suggested by Jinghai [35]. But, any
other averaging procedure for the mean particle density is
not recommended [24].
To represent the class of property-averaging models for
the purpose of comparison in the present work, the well-
known relationship of Richardson and Zaki [29] will be
used with its parameters, Ut and n, defined for their mean
values as [24]
Uo � U ten̄ ¼ 0 ð3Þ
The correlation of Khan and Richardson [36] was employed
here for computing the particle terminal velocities. Not
much difference between its predictions and those of Schil-
ler and Naumann [37] was seen here.
2.2. Serial model
This is by far the most commonly used model to predict
the overall expansion of fluidized bed containing two or
more particle species. Epstein et al. [9] pointed out its
superior predictive capability over the property-averaging
model. In terms of bed void fraction, this model is written as
ð1� eÞ ¼ 1X1
ð1�e1Þ þ1�X1
ð1�e2Þ
" #ð4Þ
which, in terms of the ‘‘specific volume’’, can be written as
V ¼ 1
1� e
� �¼ X1V1 þ ð1� X1ÞV2 ð5Þ
where subscripted variables indicate mono-component val-
ues.
2.3. Packing models
There appears to be a good deal of literature concerning
packing models depending upon the perceived mechanism
of packing behavior of the particle mixture containing two
or more components [38–42]. In the following discussion,
two models based on the Westman equation [34] will be first
considered. The Westman equation is given as
V � V1X1
V2
� �2
þ2GV � V1X1
V2
� �V � X1 � V2X2
V1 � 1
� �
þ V � X1 � V2X2
V1 � 1
� �2
¼ 1 ð6Þ
where the parameter G depends upon the size ratio of the
two components of the packing. It is easy to see that setting
G=1 in the above equation yields the serial model V=
X1V1+X2V2.
Yu et al. [43] have proposed the following functional
form of the parameter G in the Westman equation
1
G¼
1:355r1:566 ðrV0:824Þ
1 ðr > 0:824Þ
24 ð7Þ
where r is the size ratio (smaller to larger) of the two solid
species.
Finkers and Hoffmann [44] have recently suggested
another expression for the parameter G in the Westman
equation. Their approach makes use of the structural ratio
rather than the diameter ratio, and is equally applicable for
both spherical and non-spherical particles. This is given by
G ¼ rkstr þ ð1� e�k1 Þ
rstr ¼ðð1=e1Þ � 1Þr3
1� e2
� �ð8Þ
where a value of exponent k=�0.63 has been recommended
by the authors.
Another model, suggested by Yu et al. [41], is applicable
for predicting the porosity of non-spherical particle mixture
with two or more components. This model, known as the
modified linear-packing model, is given by
V Ti ¼ Vi þ
Xi�1
j¼1
½Vj � ðVj � 1ÞgðrÞ � Vi�Xj
þXnj¼iþ1
½Vj � Vjf ðrÞ � Vi�Xj ð9Þ
V ¼ max½VT1 ;V
T2 ; . . . ;V
Tn � ð10Þ
where V is the overall specific volume of the packing
system, and Vi is the mono-component specific volume of
the ith component. The functions f and g in the above
equation are given by
f ðrÞ ¼ ð1� rÞ3:3 þ 2:8rð1� rÞ2:7
gðrÞ ¼ ð1� rÞ2:0 þ 0:4rð1� rÞ3:7 ð11Þ
where r is the size ratio. For non-spherical particles, Zou
and Yu [45] related
dvi
dpi¼ w2:785
i exp½2:946ð1� wiÞ� ð12Þ
where dvi and dpi are, respectively, the equivalent volume
diameter and the equivalent packing diameters of the ith
component. It can be seen here that the overall porosity of
the packing depends mainly upon three factors: the mono-
component packing behavior, the composition and the size
ratio.
M. Asif / Powder Technology 127 (2002) 226–238228
2.4. Voidage-averaging model
Though without any specific meaning, the following
simple averaging is applied on the mono-component bed
void fractions,
e ¼ 1X1
e1þ 1�X1
e2
" #ð13Þ
The purpose here is to demonstrate how even such an
averaging procedure with no obvious physical meaning
can be used for layer-inversion predictions.
It is worthwhile to point out here that the models
presented above require information about the mono-com-
ponent expansion behavior, except the property-averaging
model. This can be easily obtained using the Richardson–
Zaki equation provided that parameters Ut and n are known.
These parameters can either be obtained with the help of
correlations or deduced directly from the expansion charac-
teristics of the mono-component liquid-fluidized bed. Of the
two options, the latter is preferable in view of better
description of the mono-component expansion by avoiding
errors associated with the correlation predictions.
3. Experimental
The test section of the fluidized bed consisted of a
transparent perspex column of 60-mm internal diameter
and 1.5-m length. The distributor was a 9-mm-thick perfo-
rated plate with 2-mm holes drilled on a square pitch and
4% fractional open area. This configuration gives about 1.3
holes/cm2 (of the distributor area) with sufficient pressure
drop to eliminate the presence of dead zones in the distrib-
utor region even when low-density solid particles are used
in the liquid-fluidized bed [46,47]. Both faces of the
distributor were covered with a fine polypropylene mesh
of 26% open area and negligible pressure drop. Below the
distributor was a 0.5-m-long calming-section packed with 3-
mm glass beads.
Water was used as the fluidizing medium with its temper-
ature carefully controlled at 20 jC. The flow rate of water
was controlled using one of three calibrated flowmeters of
suitable range. An immersion cooler was used to remove the
heat generated by the water pump, and maintain the water
temperature constant in the water tank.
The bed heights were read visually with the help of a
ruler along the length of the column. The pressure drop
along the bed was measured using an inverted air–water
manometer. The observation included measuring the flow
rate, the bed height and the pressure drop across the bed.
3.1. Properties and fluidization behavior of solid particles
The binary system used in the present study consisted of
polyethylene terephthalate (PET) resin and sand. The
slightly cylindrical PET resins sample has the mean vol-
ume-equivalent particle diameter of 2.79 mm, and a
Wadell’s shape factor of 0.85. The sieved sand sample, on
the other hand, was of 300–250-Am range; its mean
diameter was taken as 275 Am.
The fluidization behavior of particle samples was indi-
vidually examined using water at 20 jC. Table 1 reports
parameters Ut and n which were obtained by fitting the
Table 1
Physical properties of particles used
Solid species Diameter (mm) Density (kg/m3) Ut (mm/s) Utl (mm/s) n Umf (mm/s)
PET (1) 2.79 1396 93.7 114.3 2.61 11.80
Sand (2) 0.275 2664 34.6 36.2 3.79 1.0
Fig. 1. Expansion behavior of mono-component fluidized beds of polyethylene terephthalate (PET) resin and sand and their parameters of Richardson and Zaki
correlation.
M. Asif / Powder Technology 127 (2002) 226–238 229
mono-component expansion data with the Richardson–Zaki
equation as shown in Fig. 1. The terminal velocity, Utl, of
each component was computed using the following correc-
tion proposed by Khan and Richardson [48]
Ut
Utl¼ 1� 1:15
d
Dc
� �0:6
ð14Þ
where, d is the particle diameter and Dc is the column
diameter. Note that the value of the correlation coefficient,
R2, for the mono-component expansion data reported in Fig.
1 is over 0.99. This is a good indication of stable particulate
expansion of both solids. Also, no bulk flow pattern was
observed during the fluidization of either the mono-compo-
nent or the binary-solid in the present study.
As can be seen from the Table 1, the lighter PET resins are
almost 10 times larger than the denser sand while the buoyed
density ratio, c, is about 0.24. The cross-over point of the bulkdensities of the two components occurred around 23 mm/s.
A summary of runs is provided in Table 2. A total of
eight runs were made. For the first six runs, the amount of
the smaller component, i.e. sand, was kept constant in the
bed while the amount of the larger component was pro-
gressively increased to obtain the desired bed composition.
For runs 7 and 8, the amount of the larger component was
held constant and the amount of the sand was increased to
get the fractional volumetric concentration of the larger
component (PET), i.e. X1=0.862 and 0.749. This way two
runs were carried out for bed compositions of 0.749 and
0.862 to investigate the effect of solids loading, if any, on
the behavior of the bed. The bed void fractions were
computed from the total mass of each solid species and
the bed height information.
4. Results and discussion
In the following, the capability of the averaging models
to predict the expansion behavior of the binary-solid liquid-
fluidized bed is discussed first. The phenomenon of the
layer-inversion and its dependence on the bulk density is
discussed next. Finally, a comparison is made between
predictions of different models using the available exper-
imental data.
4.1. Prediction of the overall bed expansion
Expansion data of runs 3, 4, 6 and 7 with compositions
X1=0.41, 0.60 and 0.86 are presented in Fig. 2(a–c) along
with predictions of different models. It is clear here that the
serial model generally predicts higher bed expansion, while
the others tend to underestimate it. It should be understood
here that since the serial model is based on the assumption
of complete segregation of the two components, the lower
values of the actual voidage, in fact, indicate a bed con-
traction associated with the mixing of the two components
present in the bed. It is further evident from the figures that
as the segregation tendencies increase in the bed at higher
velocities, the predictions of the serial model show closer
agreement with actual experimental values.
It is seen in Fig. 2(a–c) that predictions of the packing
models are comparable, and, moreover, give better descrip-
tion of the bed voidage than the rest throughout the range of
liquid velocities. The only exception is X1=0.86 for which
predictions of the modified linear-packing model of Yu et al.
[41] are poor. But, nevertheless, the trend is correct.
On the other hand, the property-averaging model also
underestimates the porosity with the difference getting more
pronounced as the liquid velocity increases. Predictions of
the voidage-averaging model show even greater discrep-
ancy. In this case, the model overestimates the bed voidage
at lower liquid velocities and underestimates the same at
higher velocities.
The improved description of packing models looks
surprising at the first instance. But the explanation is simple.
When both components are together in an environment,
there are two possibilities depending upon the size differ-
ence of components. One, the smaller component occupies
the interstitial space of the larger counterpart while retaining
its identity both in terms of the volume as well as the
associated voidage. No contraction is therefore observed in
this case. Second, the smaller component tends to simply fill
the interstices of the larger component. As a result, a
fraction of the smaller component is lost as far as its
contribution to the overall expansion is concerned, thereby
leading to the occurrence of the contraction phenomenon.
The first case is usually a characteristic of an environment
where the two components do not differ significantly in the
size while the latter is normally associated with binaries of
large size difference. At this stage, it becomes clear that the
serial model, which has been frequently shown to describe
the overall expansion quite well for binary-solid fluidized
beds, shows deviations in the present case.
4.2. Layer-inversion behavior and the bed bulk density
In present experiments, either partial or complete mixing
of two components was observed. The PET layer was
always found to contain sand in varying amounts, both
before and after the layer-inversion with complete mixing of
the two components at the onset of the layer-inversion. Even
Table 2
Compositions of binary mixture studied
Run Sand
weight (g)
PET
weight (g)
X1
(vol/vol)
1 528.5 44.5 0.138
2 528.5 97.5 0.260
3 528.5 195.0 0.413
4 528.5 412.0 0.598
5 528.5 825.0 0.749
6 528.5 1723.0 0.862
7 153.3 500.0 0.862
8 320.0 500.0 0.749
M. Asif / Powder Technology 127 (2002) 226–238230
at lower liquid velocities, much before the layer-inversion,
significant amount of sand was seen in the upper PET layer.
The total bed-heights as well as the top of the PET-sand
mixed layers are shown in Fig. 3(a) for different composi-
tions of the bed. It can be seen here that as the fraction of the
larger component increases in the bed, so does the velocity
at which the layer-inversion takes place. This dependence is,
however, relatively weak for lower X1 where not much
increase in the inversion velocity is observed when the
fraction of the larger component is increased from 0.14 to
0.41 in the fluidized bed.
In part (b) of Fig. 3, the effect of the solids loading on the
layer-inversion behavior is shown. Although no difference
is seen between runs 5 and 8 where the bed composition is
Fig. 2. (a) Expansion behavior of binary-solid fluidized bed for composition X1=0.41. (b) Expansion behavior of binary-solid fluidized bed for composition
X1=0.60. (c) Expansion behavior of binary-solid fluidized bed for composition X1=0.86.
M. Asif / Powder Technology 127 (2002) 226–238 231
X1=0.75, a small difference is, however, evident between
runs 6 and 7 for the composition of X1=0.86.
The phenomenon of the layer-inversion is closely related
to the bulk density of the bed. Its values are therefore shown
in Fig. 4 for different velocities and bed compositions. The
bulk densities here are computed as
qb ¼ ð1� eÞ½X1qs1 þ ð1� X1Þqs2� þ eqf ð15Þ
There is a clear trend in the experimental data of Fig. 4(a)
such that there exists a maximum for each bulk density
curve, which might occur at any value of the bulk
composition in the range [0,1] depending upon the liquid
velocity. For the liquid velocity of Uo=15.3 mm/s, the
actual maximum bulk density occurs when the bed com-
position is around X1=0.14. As the liquid velocity is
increased, the value of X1 at which the maximum bulk
density occurs also increases. Note that layer-inversion
velocities obtained from Fig. 3(a and b) agree quite well
with velocities at which the maximum bulk density occurs.
This is due to the fact that the complete mixing of the two
components at the onset of the layer-inversion leads to the
highest degree of bed contraction, which in turn leads to
the maximum bulk density, as recently pointed out by Asif
[31].
The predictions of the serial model are presented in Fig.
4(b). It can be seen here that the maximum always occurs at
the boundary. This means that it is always the mono-
component layer that possesses the highest bulk density;
this being the layer of sand at lower liquid velocities and
the one of PET at higher velocities. Close to the liquid
velocity of Uo=23.6 mm/s, both mono-component layers
have the same bulk density, and will therefore be com-
pletely mixed. Above this velocity, according to the serial
model, the layer-inversion will take place. The PET-layer,
owing to its higher bulk density, will occupy the lower
region of the bed.
Predictions of the packing model of Yu et al. [43] are
shown in Fig. 4(c). It is obvious here that its trend does
conform to the actual bulk density behavior seen in Fig.
4(a). That is, the maximum bulk density might occur at
intermediate values of X1 depending upon the liquid veloc-
ity. Therefore, this model, unlike the serial model, is capable
of describing the composition-dependence of the bed bulk
Fig. 3. (a) Variation of the total bed height and the height of the mixed PET-sand layer with liquid velocity and bed composition. (b) Effect of solids loading on
the layer-inversion behavior.
M. Asif / Powder Technology 127 (2002) 226–238232
density, and, consequently, that of the layer-inversion phe-
nomenon. Predictions of other models are not shown here.
In spite of their poor description of the bed expansion
behavior as seen in Fig. 2, other models can still predict
the composition-dependence of the maximum bulk density
of binary-solid fluidized beds.
4.3. Prediction of the layer-inversion
In order to predict the layer-inversion behavior of binary-
solid fluidized beds, averaging models for describing the
bed expansion can be used in conjunction with the max-
imum bulk density condition. With the serial model, it
Fig. 4. (a) Actual dependence of the bulk density profile on the liquid velocity (experimental data). (b) Predicted (using serial model) dependence of the bulk
density profile on the liquid velocity. (c) Predicted (using the packing model of Yu et al. [43]) dependence of the bulk density profile on the liquid velocity.
M. Asif / Powder Technology 127 (2002) 226–238 233
becomes essentially the approach first used by Pruden and
Epstein [49]. On the other hand, when the property-averag-
ing model is used, it becomes similar to what was first
suggested by Gibilaro et al. [18].
The numerical solution procedure was pursued here.
MATLAB’s minimization subroutine ‘‘fminbnd’’ was used
to obtain the maximum bulk density with respect to the bed
composition X1 while keeping the liquid superficial velocity
constant. Note that the bed voidage in Eq. (15) is a function
of both the liquid velocity as well as the bed composition,
and was evaluated from the different models described
before. Owing to the implicit nature of the Westman
equation, MATLAB’s subroutine ‘fzero’ was employed for
computing the bed voidage. Model predictions, thus ob-
tained, are discussed in the following.
Experimental data along with model predictions are
shown in Fig. 5 for the present case of PET and sand. It
can be seen here that predictions of the serial model are
independent of the bed composition. Moreover, it occurs
around 23 mm/s, much later than actual values, which begin
around 15 mm/s. This early occurrence of the layer-inver-
sion is caused by the penetration of significant amount of
smaller but denser component, i.e. sand in the upper PET-
layer, thereby increasing its bulk density.
Though all other models considered here are capable of
describing the composition dependence of the layer-inversion
phenomenon, the accuracy of their predictions is quite differ-
ent. The description of packingmodels based on theWestman
equation looks much superior. The packing diameter, dpi, of
the non-spherical PET resin in the present case was found to
be 2.77 mm (using Eq. (12)), and incorporated in the
calculation of parameter G in the model of Yu et al. [43].
It is interesting to note that the modified linear-packing
model of Yu et al. [41] shows a rather weak composition-
dependence of the layer-inversion phenomenon, except for
higher values of X1. Its trend is similar to that of the serial
model. There is, however, an important difference. Due to
its capability to account for mixing effects, the modified
linear-packing model correctly predicts the early occurrence
of the layer-inversion.
As far as the predictions of the property-averaging model
are concerned, stronger composition-dependence of the
layer-inversion phenomenon is seen in this case. As the
fraction of the larger component in the bed is increased,
greater difference between predictions and actual values is
observed. Even greater discrepancy is observed in the case
of the voidage-averaging model, which predicts much lower
inversion velocity for smaller X1 and much higher values for
larger X1.
Putting Figs. 2 and 5 together, it becomes obvious that
both the layer-inversion and the bed expansion predictions
of any model have similar accuracy. That is, a model with a
superior description of the bed expansion behavior is also
better at predicting the layer-inversion behavior.
4.4. Comparison with Moritomi et al. [17] data
The widely reported data of Moritomi et al. [17] is now
considered. This involves the fluidization of 775-Am hollow
char and 163-Am glass beads. The physical properties of
their binary system are shown in Table 3. The Richardson–
Zaki correlation parameters, Ut and n, reported in the table
were obtained using their mono-component bed expansion
data as shown in Fig. 6.
The experimental layer-inversion data is presented in Fig.
7. As compared to the case of PET-sand, a slightly stronger
composition-dependence of the layer-inversion data is evi-
dent here. This is apparently due to the difference in the size
Fig. 5. Comparison of model predictions with the layer-inversion data of the present work (binary system of PET and sand).
Table 3
Physical properties of the Moritomi et al. [17] system
Solid species Diameter
(mm)
Density
(kg/m3)
Ut
(mm/s)
n
Hollow char (1) 0.775 1380 46.0 3.00
Glass beads (2) 0.163 2450 14.4 3.98
M. Asif / Powder Technology 127 (2002) 226–238234
ratio, which being 4.75, is half as small as 10.1 of the
former. Model predictions are also shown in Fig. 7. Similar
trend, as seen in Fig. 5 for the PET-sand fluidization, is also
observed here. While the superior predictive capability of
packing models is once again witnessed here, so is the
discrepancy in the predictions of the property-averaging
model at higher X1. At the same time, predictions of the
voidage-averaging model, notwithstanding its simplicity, are
poor. It is worthwhile to point out a mistake in my earlier
work [25], where serial and voidage-averaging models were
mixed up in the computer program, incorrectly identifying
the layer-inversion predictions of the voidage-averaging
model as those of the serial model.
4.5. Comparison of averaging models
In this section, the present experimental data as well as
those reported in the literature are used for the sake of
comparison among different averaging models considered
here. A summary of the size ratio and the reduced-density
ratio of binary systems along with the range of bed compo-
sition used in these works is reported in Table 4. It can be
seen here that the property difference, especially the size
ratio of the binary system used in the present study, is
substantially higher than others.
Fig. 8(a) shows the comparison of predictions of the
packing model of Yu et al. [43]. It can be seen here that the
agreement is good. Only the case of Jean and Fan [19] show
some difference for lower values of X1. This may be due to
significant discrepancy between the experimental and com-
puted value of Ut in Jean and Fan’s [19] work. Since the
predictions of the packing model of Finkers and Hoffmann
[44] are very similar to those of Yu et al. [43], its compar-
ison is not presented here. The comparison with the prop-
erty-averaging model is shown in Fig. 8(b). A clear trend is
seen here. As pointed out before, the predicted layer-
Fig. 6. Expansion behavior of mono-component fluidized beds of 775-Am hollow char and 163-Am glass beads of Moritomi et al. [17].
Fig. 7. Comparison of model predictions with the layer-inversion data of Moritomi et al. [17] (binary system of 775-Am hollow char and 163-Am glass beads).
M. Asif / Powder Technology 127 (2002) 226–238 235
inversion velocities are mostly higher. This discrepancy
increases at higher inversion velocities for the same binary
system. In the case of Epstein and LeClair [16] data, while
predictions are in good agreement for binaries 1–3, in the
case of binary 4, however, the predicted value is much
higher and off the scale.
The comparison with the serial model is presented in Fig.
8(c). As pointed out before, the serial model is not capable
of predicting the composition-dependence of the layer-
inversion behavior. Moreover, it tends to overestimate the
layer inversion velocity. Though the modified linear-pack-
ing model of Yu et al. [41] overcomes both of the afore-
mentioned deficiencies of the serial model as shown in Fig.
8(d), its predictions are poor for higher X1.
5. Conclusions
It becomes obvious from the foregoing that a proper
description of the layer-inversion behavior has two impor-
tant prerequisites. First of all, the model should be capable
of representing the actual bed expansion behavior as closely
as possible. Second, it should account for the occurrence of
the maximum bulk density due to the bed contraction
associated with the complete inter-mixing of the two com-
ponents at the onset of the layer-inversion. A poor descrip-
tion of the expansion behavior leads to poor predictions of
the layer-inversion as seen here for the case of voidage-
averaging and property-averaging models using the present
experimental data. On the other hand, the serial model, in
spite of its reasonable description of the bed expansion,
apparently fails on account of the second condition.
The overall superior capability of the packing models,
based on the Westman equation, to describe the important
hydrodynamic features of the binary-solid fluidized bed is
clearly evident here. It must, however, be noted that that
these models need proper specification of mono-component
expansion behavior for both components. The property-
Table 4
Experimental data used for comparison in Fig. 8
Work Diameter
ratio, r�1
Buoyed
density
ratio, c
Bed
composition,
X1
Present study 10.14 0.238 0.14–0.86
Moritomi et al. [17] 4.75 0.262 0.09–0.84
Matsuura and
Akehata [50]
2.49 0.430 0.20–0.82
Jean and Fan [19] 4.03 0.330 0.16–0.85
Epstein and [16] 5.00 0.212 0.740
LeClair 1.99 0.536 0.618
1.67 0.639 0.493
1.54 0.659 0.563
Fig. 8. (a) Comparison of predictions of the packing model of Yu et al. [43] with experimental data. (b) Comparison of predictions of the property-averaging
model with experimental data. (c) Comparison of predictions of the serial model with experimental data. (d) Comparison of predictions of the modified linear-
packing model of Yu et al. [41] with experimental data.
M. Asif / Powder Technology 127 (2002) 226–238236
averaging model, based on surface-to-volume averaging of
particle diameters, is independent of this requirement.
Symbols used
Dc column diameter (mm)
di diameter of ith particle species (mm)
dvi equivalent volume diameter (mm)
dpi equivalent packing diameter (mm)
n Richardson–Zaki correlation index (–)
f size ratio function defined by Eq. (11) (–)
g size ratio function defined by Eq. (11) (–)
G Parameter G of Westman equation (Eq. (6)) (–)
PET polyethylene terephthalate resin (–)
r size ratio (smaller to larger) (–)
rstr particle structural ratio defined by Eq. (8) (–)
Umf minimum fluidization velocity (mm s�1)
Uo liquid (superficial) velocity (mm s�1)
Ut Richardson–Zaki correlation parameter (Uo=Ut for
e=1) (mm s�1)
Utl particle terminal velocity (mm s�1)
V overall specific volume=[total bed volume/total
solids volume] (–)
Vi mono-component specific volume of ith species (–)
X1 fluid-free volume fraction of particle species 1 (–)
Greek symbols
e overall bed void fraction (–)
ei void fraction of mono-component bed of ith
particle species (–)
c buoyed density ratio=[(qs1�qf)/(qs2�qf)] (–)
qb bed bulk density (kg m�3)
qf fluid density (kg m�3)
qs solid density (kg m�3)
wi shape factor of ith particle species (–)
Subscript
1 larger but lighter component (PET)
2 smaller but denser component (sand)
Acknowledgements
This work was supported by the Research Center,
College of Engineering, King Saud University. The help
of Dr. A. Ibrahim and Engr. A. Ismail with the experimental
work is greatly appreciated.
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