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Journal of Biotechnology 97 (2002) 89101
Mass transfer correlations for rotating drum bioreactors
Matthew T. Hardin a,*, Tony Howes b, David A. Mitchell c
a Chemical and Materials Engineering Department, Uni6ersity of Auckland, Auckland, New Zealandb Department of Chemical Engineering, Uni6ersity of Queensland, St Lucia, Qld 4072, Australia
c Departamento de Bioqumica, Uni6ersidade Federal do Parana, Cx. P. 19046, 81531-990 Curitiba, Parana, Brazil
Received 6 December 2001; received in revised form 18 March 2002; accepted 27 March 2002
Abstract
Evaporative cooling is extremely important for large-scale operation of rotating drum bioreactors (RDBs). Outlet
water vapour concentrations were measured for a RDB containing wet wheat bran with the aim of determining the
mass transfer coefficient for evaporation from the bran bed to the headspace. Mass transfer was expressed as the mass
transfer coefficient times the area for transfer per unit volume of void space in the drum. Values of ka% were
determined under combinations of aeration superficial velocities ranging from 0.006 to 0.017 ms1 and rotation rates
ranging from 0 to 9 rpm. Mass transfer coefficients were evaluated using a variety of residence time distributions
(RTDs) for flow in the gas phase including plug flow and well-mixed and a Central Jet RTD based on RTD studies.
If plug flow is assumed, the degree of holdup at low effective Peclet ( Peeff) numbers gives an apparent under-estimate
of ka% compared with empirical correlations. Values of ka% calculated using the Central Jet RTD agree well with values
of ka% from literature correlations. There was a linear relationship between ka% and effective Peclet number:ka%=2.32103Peeff. 2002 Elsevier Science B.V. All rights reserved.
Keywords: Mass transfer; Rotating drum; Solid state fermentation; Scale-up; Sherwood number
Nomenclature
area available for mass transfer per unit of void volume (m1)a
area available for mass transfer per unit of headspace (m1)a %
dimensionless water concentration calculated from Eq. (13)cC water concentration in dry air (kg kg1)
dimensionless water concentration in headspacecairwater concentration in dry air of headspace (kg kg1)CAIR
cbran dimensionless concentration of water at the bran surface
www.elsevier.com/locate/jbiotec
* Correponding author.
E-mail address: [email protected] (M.T. Hardin).
0168-1656/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 1 6 5 6 ( 0 2 ) 0 0 0 5 9 - 7
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 8910190
cdead dimensionless concentration of water in the dead zone of the drum in the Central Jet RTD
water concentration in dry air entering the drum (kg kg1)CINwater concentration in dry air exiting the drum (kg kg1)COUT
cplug dimensionless concentration of water in the Central Jet of the Central Jet RTD
saturation concentration of water in dry air at the bed temperature (kg kg1)CSATconstant of bed viscosity (dimensionless)CV
D axial diffusion coefficient from the Central Jet RTD (dimensionless)
particle diameter (m)ddrum diameter (m)Ddrum
Dh hydraulic diameter of drum (m)
acceleration due to gravity (ms2)g
h maximum height of the bed (m)
constant in Eq. (3) defined in Eq. (4)K
mass transfer coefficient estimated using the Central Jet RTD (dimensionless)k
area factor used by Stuart (1996) (dimensionless)n
constant of bed porosity (dimensionless)N
effective Peclet number across the surface of the bran (dimensionless)Peeffdegree of exchange between the different regions in Central Jet RTD (dimensionless)QmixReynolds number (dimensionless)Re
s thickness of the mobile layer at the bed surface (m)
Schmidt number (dimensionless)Sc
Sherwood number (dimensionless)Sh
t dimensionless time (number of residence times)
velocity of the particles at the bottom of the moving layer (ms1)u0ueff effective velocity of gas over the surface of the bed (ms
1)
superficial gas velocity through drum (ms1)ugaverage particle velocity in the moving layer (ms1)upvolume of the stagnant region in the Central Jet RTD (dimensionless)Vdeadgas kinematic viscosity (m2 s1)6g
x length along the drum (dimensionless)
rotational speed of the drum (s1)z
h % generic expression for mass transfer area available per unit volume (Eq. (1))
mass transfer coefficient used by Blumberg and Schlunderi
coefficient for fitted correlation of Blumberg and Schlunder
diffusivity of water in air at the particle surface (m2 s1)lgdynamic angle of repose of bed ()k
s generic expression for mass transfer coefficient (Eq. (1))
generic expression for time term (Eq. (1))~
V generic concentration term (Eq. (1))
concentration term in Eq. (1)V1V2 concentration term in Eq. (1)
factor in Eq. (35)x
1. Introduction
Rotating drum bioreactors (RDBs) have poten-
tial to provide better heat and mass transfer
characteristics than solid state fermentation (SSF)
bioreactors with static beds, while providing gen-
tler agitation than bioreactors with internal stir-
rers. Furthermore, the absence of internal moving
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 89101 91
parts for mixing makes design, construction and
operation simpler, and the low pressure-drop
across the bioreactor greatly reduces the operating
costs associated with the aeration system. The
gentle agitation associated with the tumbling mo-
tion of the substrate bed minimises damage to the
substrate particles, and makes RDBs ideal for
those micro-organisms which can tolerate some
shear damage, but which are affected deleteriously
by more vigorous mixing.
A major hurdle that currently prevents wide-
spread use of SSF is the difficulty of regulating
the temperature in large-scale fermentations. In
an RDB, heat exchange, and hence removal of
metabolic heat, is limited to convective cooling
(from the surface of the drum to the surroundings
or from the substrate to the headspace air) and
evaporative cooling. As the fermentations increasein scale evaporative cooling becomes more impor-
tant because the ratio of heat produced to surface
area for convection declines. One of the main
advantages of the mixed bed in an RDB is that it
is practical to add water to the substrate during
the fermentation, for example, by spraying a fine
mist onto the surface of the moving bed (Barstow
et al., 1988). This means that evaporative cooling
can be used as the major mechanism of heat
removal without the danger of restricting growth
due to drying out of the substrate.
Since mass transfer is directly proportional to
the surface area available for particle/gas contact,
it follows that any activity that improves this
surface area will improve mass transfer. Both
increasing the rotation speed and adding lifters
will improve particle/gas contact. Evaporative
mass transfer in rotating drums has been studied
from the point of view of drying (Friedman and
Marshall, 1949) but attempts to develop gener-
alised models are comparatively recent (Riquelmeand Navarro, 1986). There have been few at-
tempts to quantify these effects for SSF. In the
current work, a series of experiments was per-
formed to quantify the mass transfer as a function
of fill depth, rotation speed and air inlet.
Mass transfer is typically characterised by an
equation of the form:
#V
(~=sh %(V1V2) (1)
where V is a concentration of the component in
question (e.g. mass water per unit mass dry air),
V1V2 is the driving force for mass transfer
(both V1 and V2 are concentration terms), s is the
mass transfer coefficient (length per unit time),which characterises the rate at which transportoccurs in response to the driving force, h % is the
area available for mass transfer per unit volume
being transferred into (area per unit volume) and
~ is an expression of time. All of these terms may
be expressed in a variety of units or even in
dimensionless terms (e.g. time expressed as num-
ber of residence times).
For simplicity it is commonly assumed in rotat-
ing drums that the mass transfer coefficient is
constant over the length of the drum (Blumbergand Schlunder, 1996; Jauhari et al., 1998) and
therefore, the challenge lies in establishing the
driving force as a function of axial position within
the drum. In order to estimate the driving force as
a function of position, it is necessary to employ a
model that describes the flow pattern in theheadspace to estimate the concentration of the
species being transported as a function of posi-
tion. Once a model for the concentration profile
down the length of the drum is established, the
mass transfer coefficient can be found easily.For the purposes of this analysis, it assumed
that the moisture content of the substrate is con-
trolled by water sprays (Barstow et al., 1988).
This means that the driving force for evaporation
depends only on the gas phase water concentra-
tion as the substrate surface is saturated with
water. This implies that film resistance from the
liquid to the gas phase limits mass transfer hence,
the system acts as if it is in the constant-rate
drying period. In practice, many SSFs are carried
out in the falling rate period. This means that
evaporative transfer is limited by internal diffu-
sion of water within the substrate and hence, is
greatly affected by substrate composition and
temperature.
This paper describes an investigation of the
effect on the mass transfer coefficient, expressed
as the lumped parameter ka%, of varying the drum
rotation rate and the velocity of the gas, for a
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 8910192
drum operating in the slumping and tumbling
regimes during a constant-rate drying period. It
compares three gas flow patterns; plug flow, per-
fect mixing and the Central Jet residence time
distribution (RTD), derived from earlier experi-
ments in our laboratory (Hardin et al., 2001) with
an empirical correlation from literature (Blum-
berg and Schlunder, 1996).
2. Materials and methods
2.1. Experimental procedure
The reactor was a stainless steel rotating drum
(Fig. 1), with inside dimensions of a radius of 280
mm and a length of 800 mm. A variable speed
drive capable of between 0 and 9 rpm turned thedrum.
For simplicity, no organisms were grown. Since
the rate of metabolic heat and water production
varies with phase of growth of the organism and
substrate composition, the use of organisms
would have added complicating factors, making it
difficult to compare different runs solely on the
basis of drying. Damp Defiance type 2032 wheat
bran (47% water wet weight, 2 mm diameter) was
used to imitate one type of substrate typically
used in these processes (Stuart, 1996; Marsh et al.,2000). The bran and water were mixed in the
drum at full speed (9 rpm) for approximately 1 h.
Many granules of bran formed during this time,
and were broken up by hand before the bran was
used for experimental purposes. The bran was
removed from the drum and, after overnight stor-
age at 4 C, was autoclaved at 121 C for 1 h to
simulate the treatment the substrate normally un-
dergoes. The bran was cooled to approximately
ambient temperature before recording of results
began.
The humidity of the inlet air was measured at
the inlet point of the drum while the bran was
cooling. The inlet humidity was checked prior toeach series of trials. While there was variation in
inlet humidity between series of trials, within each
series the inlet air humidity was constant. The
outlet humidity was measured on-line using an
Electro-tech Model 5612B humidity probe and the
relative humidity logged. The relative humidities
were used to find water concentrations in the gas
streams by use of the Antoine equation.
2.2. Analysis of experimental results
The actual surface area available for the mass
transfer is a function of particle size and exposure
of individual particles to the gas stream. Since this
is extremely difficult to calculate, in this analysis
the surface area per unit volume of headspace, is
combined with the mass transfer coefficient k to
give a ka% term. This is very similar to the way
that oxygen transfer is handled in submerged
liquid culture.
The effect of rotation rate on mass transfer
between the bed and headspace will be related to
the flow regimes that correspond to the various
rotation rates (Fig. 2). As the speed of rotation of
the drum is increased, the regime of flow of the
particles changes. At very low speeds the particles
exhibit slumping flow where the solid bed periodi-
cally slips back down the wall. At higher speeds
the material on the top of the bed tumbles back
down the face of the bed in a continuous cascade.
At still higher speeds material is thrown into the
air before landing again (cataracting). Beyond a
certain critical speed there is sufficient centrifugal
force to hold the bed against the wall. The exact
transition between these regimes is a function of
rotation speed particle size distribution and parti-
cle cohesiveness and is difficult to predict. Flow
regimes beyond tumbling were not observed in the
rotational speed range of these experiments.
Fig. 1. Experimental apparatus. The drum is 800 mm long
560 mm diameter. The humidity probes measure the moisture
content of the air as close as possible (within 50 mm) of the
drum inlet and outlet.
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 89101 93
Fig. 2. Flow regimes in rotating drums showing direction of
rotation (anti-clockwise) and the direction of motion for the
substrate bed.
tion of radial gradients. The thickness of the
mobile layer depends on the material, fill depth
and the rotation speed.
Blumberg and Schlunder (1996) studied mass
transfer in rotating drums and developed an im-
plicit equation for the thickness (s) of this mobile
layer:
pz [Ddrum(hs)(hs)2]Ks5/2
+2pzs(Ddrum/2h+s)=0 (3)
where z is the rotation rate in revolutions per s,
Ddrum is the drum diameter, h is maximum bed
height (Fig. 3) and K is a constant that depends
on the material. This equation can be solved fairly
simply by numerical methods. K is a function of
the porosity of the bed and the dynamic angle of
repose of the material (k). K can be calculated as
follows:
K=2
3gsink
CVd21/2
3
5
12
11N+
18
17N2
12
23N3+
3
29N4
(4)
where N is a dimensionless constant factor of
porosity which is equal to 0.8 for most materials,
CV is a dimensionless constant factor of bed vis-
cosity (0.6 for most materials), g is the accelera-
tion due to gravity (ms
2
), k is the dynamic angleof repose of the bed and d is the particle diameter
in metres (Savage, 1979). Blumberg and Schlunder
(1996) give the full derivation of these equations.
Note that Eq. (4) is different from the equation
given in Blumberg and Schlunder due to a typo-
graphical error in that paper. In the current work
the dynamic angle of repose was measured as
3792 through the Perspex end of the drum.
Blumberg and Schlunder (1996) go on to show
that the average velocity of the particles in the
moving layer can then be calculated from:up=Ks
3/2+u0 (5)
where up is the average flow velocity of the parti-
cles in the moving layer and u0 is the velocity of
the particles in the moving layer in contact with
the non-moving bed and is given by:
u0=2pz(Ddrum/2h+s) (6)
The maximum rotation rate used in the experi-
ments was 9 rpm. This did not allow material to
go beyond the cascading flow regime (Fig. 2).
When material is in the cascading regime there is
a mobile top layer that slides down the face of the
bed (Fig. 3). It is assumed that mass transfer
between the headspace and bed occurs only in this
layer as individual particles in this layer are in
rapid motion with respect to the gas phase. Con-
versely, particles deeper in the bed have little
contact with the gas. Movement of particleswithin the bed ensures that, ultimately, the entire
bed is exposed to the air and minimises the forma-
Fig. 3. Detail of drum in the tumbling regime showing the
direction of travel for the mobile layer as well as the nomen-
clature for equations for calculating the mobile layer thickness.
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 8910194
The effect of superficial air velocity on mass
transfer was also investigated. The air flow rate
is expressed in terms of the superficial velocity
(volumetric gas flow rate divided by unfilled
cross-sectional area). The superficial velocity has
an effect on the RTD of the air in the drum.
The Central Jet RTD of Hardin et al. (2001),
which is summarised below, is used in this paperto determine an estimate for the mass transfer
coefficient based on realistic RTDs. Blumberg
and Schlunder (1996) developed other correla-
tions that are based on the Reynolds number of
the gas flow through the drum and over the
particles. Their correlations are described in Ap-
pendix A.
The overall mass transfer depends on the ef-
fective velocity of the gas over the particles,
which is simply the vector sum of the gas veloc-
ity and the particle velocity (Eq. (5)). If plugflow is assumed, the two are at right angles to
one another for a horizontal drum so the effec-
tive velocity is as given in Eq. (7):
ueff=ug2+up2 (7)
In Blumberg and Schlunder (1996), an effec-
tive Peclet number, Peeff, was calculated on the
basis of the plug flow assumption, regardless of
the real flow pattern. This simplification is help-
ful for scale-up and allows comparison with lit-erature results. The effective velocity is
combined with the diffusion coefficient (lg in
m2 s1) and the particle diameter (d, in m) into
an effective Peclet number, Peeff (Eq. (8)):
Peeff=ueffd
lg(8)
The diffusivities used in this work are derived
from correlations in McCabe et al. (1985).
The Peclet number is a dimensionless group
giving the ratio of convective flow to diffusive
flow. The two extremes for Pe are (represent-
ing a case where diffusion is insignificant) and 0
(representing a case where convective transfer is
insignificant). Peeff is used as a characteristic for
our correlations, as it is a simple description of
the gas flow over the particles. It also allows
simple comparison between the different meth-
ods of estimating ka%. Note, however, that the
gas RTD is far from plug flow and the Peeff is
not a physical quantity within the context of the
Central Jet RTD.
The driving force for the mass transfer is the
most difficult part to estimate accurately because
it depends on the RTD. Two extreme idealised
flow patterns are the plug flow and well-mixedflow patterns. Plug flow assumes a front of gas
moving through the drum with an axial concen-
tration gradient along the drum with no axial
mixing of the gas. The well-mixed distribution
assumes that the gas is uniformly well-mixed
within the drum and the exit concentration of a
substance is equal to the internal concentration
which is the same at every point in the drum.
The flow pattern of the gas affects the concen-
tration of water in the space above the bran.
For the plug flow analysis the concentration ofwater in the air above the bran (CAIR) was esti-
mated as the log mean of the inlet and outlet
driving forces. For the well-mixed case, the out-
let humidity was used to calculate the outlet
moisture content of the air and this value was
used as CAIR. Neither of these RTDs is strictly
true. RTD studies of the system (Hardin et al.,
2001) led to a three-parameter RTD involving a
Central Jet region with axial dispersion, a sur-
rounding stagnant region and a rate of exchange
between the two regions. This Central Jet RTD
accounts for back mixing within the drum, and
is also used to analyse the mass transfer results
obtained in the current work.
The Central Jet RTD can be described by two
partial differential equations:
(cplug
(t=D
(2cplug
(x2
1
(1Vdead)
(cplug
(x
+Qmix
(1Vdead)
(cdeadcplug) (9)
(cdead
(t=
Qmix
Vdead(cdeadcplug) (10)
where c refers to the dimensionless water con-
centration (Eq. (12)), D refers to the axial dis-
persion in the Central Jet, Vdead is the relative
volume of the stagnant region and Qmix is the
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 89101 95
relative rate of exchange between the stagnant
(dead) and jet (plug) regions. The parameters D,
Vdead and Qmix are strictly empirical and depend of
the superficial gas velocity and possibly other
factors including drum geometry. A fuller descrip-
tion of the parameters is found in Hardin et al.
(2001).
If it is assumed that the bran lies entirely withinthe dead region then Eq. (10) can be modified to
describe the transfer of water from the bran (Eq.
(11)). Also the effective Peclet number should be
expressed only in terms of the surface particle
velocity, as this is the only motion of particles
relative to the gas in the dead region. Hence, the
effective Peclet number used in this paper is as given
in Eq. (12).
(cdead
(t=
Qmix
Vdead(cdeadcplug)+ka(cbrancdead)
(11)
Peeff=uPd
lg(12)
The concentrations in the above differential
equations are dimensionless. The dimensional con-
centrations (C) are normalised with the saturation
water concentration at the temperature of the bran
(CSAT) (i.e. assuming that the water activity of the
bran is 1) to give the variable c, where:
c=CSATCAIR
CSATCIN(13)
This implies cbran=0 at the surface of the bran
and cplug=1 at the entry to the drum. The actual
water concentrations, CAIR and CIN, are calculated
from the measured relative humidity. The concen-
tration of water at the surface of the bran particle
is assumed to be equal to CSAT. This must be true
if the steady state analysis is to hold, that is, the
data are collected during the constant-rate drying
period. Tests on the water activity of the bran after
the trials showed this to be so. The saturation
humidity for the temperature is found from the
Antoine equation and by assuming that the air
behaves as an ideal gas.
During the constant-rate drying period, the drum
is at steady state therefore, the left hand sides of Eq.
(9) and Eq. (11) are equal to zero i.e.
0=D(2cplug
(x2
1
(1Vdead)
(cplug
(x
+Qmix
(1Vdead)(cdeadcplug) (14)
0=Qmix
Vdead(cdeadcplug)+ka(cbrancdead) (15)
Combining Eq. (14) and Eq. (15) to eliminate
cdead gives:
0=D(2cplug
(x2
1
(1Vdead)
(cplug
(x
+Qmix
(1Vdead)
Qmixcplug
Vdead+Kcbran
Qmix
Vdead+K
cplug
(16)
which is a second order differential equation of the
form:
0=Ay+By %+f(y) (17)
with the boundary conditions:
x=0, cplug=1 (18)
x=1, cplug=CSATCOUT
CSATCIN(19)
Eq. (17) has the solution:
cplug=Aexp(R1x)+Bexp(R2x) (20)
where A and Bare constants and R1 and R2 are the
roots of the equation
Dy2y
(1Vdead)+
Qmix
(1Vdead)
Qmixy
Vdead+kacbran
Qmix
Vdead
+ka
y
=0 (21)
The second boundary condition is used to elim-
inate either A or B, based on the magnitude of the
roots, with the first boundary condition used to set
the retained constant equal to 1. Arranging the
roots so that the magnitude of R1\0 and R2B0,
the final solution is:
cplug=exp(R2x) (22)
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 8910196
Fig. 4. Conceptual model of water transport from bran bed to stagnant region to central jet region and thence to the exit of the
drum. Note that the bran bed is assumed to be in contact only with the stagnant region.
The outlet concentration is required and is rep-
resented as:
cplugx=1=exp(R2) (23)Rearranging R2 allows the lumped mass trans-
fer coefficient ka% to be calculated from:
NTU=Qmixf
1f(24)
where f is given by the expression:
f=1Vdead
4QmixD
11Vdead
2DlnC*2
1
1Vdead
2n(25)
and NTU represents the number of transfer units.
ka=NTU
Qmix(26)
where ka is in terms of transfer area per unit of
volume of the dead space in m3. Thence
ka%=kaVdead (27)
Conceptually, the movement of water vapour
from the bran to the exit air can be imagined as
shown in Fig. 4.
It can be shown that the NTU will be ln(c) for
plug flow and (1/c1) for the well-mixed case
(Levenspiel, 1999), where c is the water concentra-
tion as defined in Eqs. (5)(13). To calculate ka%
using the Blumberg and Schlunder (1996) correla-
tion, the mass transfer coefficients derived from
the Blumberg and Schlunder (1996) correlations
were multiplied by the flat area of the bed surface
and divided by the void space of the drum.
3. Results
Outlet humidities were measured for the drum
operated under different conditions of aeration
rate, rotation rate and fractional filling. The re-
sults were analysed using four different methods
of estimating the apparent ka% number for each
operating condition. The results of this analysis
are in Table 1. The variation in fill depth changes
the moving layer thickness and the average veloc-
ity of the moving layer. This change is captured in
the effective Peclet number (Peeff), however,
changes in gas flow rate do not substantially
change the Peeff for a given rotation speed. The
calculated Peeff is more sensitive to changes in the
rotation rate, which affect the average velocity of
the particles in the mobile layer.
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 89101 97
Table1
Comparisonofka%derived
fromdifferentmethods
Peeff
Estimatedka%
%Filling
Rotationspeed
Airr
ate
(lmin
1)
(rpm)
Plugflow
Ce
ntralJet
BlumbergandSchlunder(1996)
Well-mixed
correlation
(H
ardinetal.,
2001)
0.0
472
0.0
545
30
21.9
0.0
649
155
0.9
0.0
369
0.0
940
0.0
460
0.0
504
0.0
822
30
1.8
32.9
155
3.6
0.1
323
155
0.1
241
30
49.1
0.1
041
0.0
487
0.1
373
0.1
584
0.0
507
61.7
30
0.1
124
5.4
155
0.0
520
155
0.1
252
0.1
885
30
72.5
0.1
180
7.2
0.1
248
0.0
536
0.2
024
0.2
156
9
155
30
82.3
0.0
505
155
0.0
538
0.0
714
22.5
19.8
0.0
731
0.9
0.0
880
0.0
861
0.0
616
1.8
155
0.1
016
29.5
22.5
0.0
694
155
0.1
337
0.1
125
22.5
43.7
0.1
264
3.6
0.1
400
5.4
0.1
351
155
22.5
54.9
0.1
314
0.0
708
0.1
742
0.1
556
0.0
736
0.1
419
63.9
7.2
155
22.5
0.0
777
155
0.1
141
0.1
741
22.5
72.2
0.1
569
9
0.0
468
155
0.0
449
0.0
570
15
17.3
0.0
630
0.9
0.0
564
0.0
666
0.0
511
0.0
722
1.8
25.6
15
155
0.0
864
0.0
570
0.0
746
0.0
838
3.6
155
15
37.5
0.0
923
0.0
985
0.0
625
5.4
155
0.1
011
46.5
15
0.0
656
155
0.1
164
0.1
114
15
54.1
0.1
095
7.2
0.1
225
0.0
698
0.1
179
0.1
232
155
9
15
60.6
0.1
423
0.1
587
0.0
492
61.3
30
0.1
203
5.4
92.6
0.0
635
118
0.1
286
0.1
587
30
61.8
0.1
562
5.4
0.1
617
0.0
694
0.1
746
0.1
583
5.4
137
30
61.8
0.1
707
0.0
760
0.1
799
0.1
584
155
5.4
30
61.8
0.1
692
0.1
583
30
0.0
837
5.4
174
0.1
852
61.9
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 8910198
Estimating a ka% using either the simple well-
mixed RTD or the plug flow RTD yields values of
ka% quite different from those estimated using the
Central Jet RTD and also quite different from the
values of ka% derived from the correlations of
Blumberg and Schlunder (1996). Blumberg and
Schlunder (1996) validated their correlation with a
large number of different literature values. The
values of ka% estimated using the more complex
flow patterns of Hardin et al. (2001) seem to be
more realistic than those estimated using the plug
flow and well-mixed assumptions, based on their
similarity to the numbers obtained using the ap-
proach of Blumberg and Schlunder (1996). Blum-
berg and Schlunder validated their approach
against a wide range of experimental data, and
therefore, the numbers obtained using their ap-
proach should be reasonably close to the realvalues.
Interestingly, the results of Blumberg and
Schlunder (1996) were for smaller scales (maxi-
mum diameter was 0.3 m) and, in general, higher
length to diameter ratios than the experiments
performed here. The effect of the difference in
geometry on the air RTD probably caused the
slight discrepancies between the estimates using
the Central Jet RTD and the estimates found
using the correlation of Blumberg and Schlunder
(1996). These deviations from plug flow tend toincrease as drums increase in diameter to length
ratio. Scaling up on the basis of a plug flow RTD
is ill-advised as the RTD deviates from plug flow
as scale increases with geometric similarity being
maintained (Mecklenburgh and Hartland, 1975).
The values of ka% estimated from the Central Jet
assumption are probably the most reliable of the
four estimations. They are based on a gas flow
RTD which was experimentally determined for
the drum (Hardin et al., 2001), and not on a plug
flow RTD, which was a key assumption of theapproach of Blumberg and Schlunder (1996). The
method of Blumberg and Schlunder for estimating
the ka% differs from the simple plug flow analysis.
The difference lies in the use of the correlations
described in Appendix A. These modify the plug
flow ka% based on correlations derived from dry-
ing studies.
The similarity, at small drum scales, between
the values of the Central Jet ka% and ka% estimated
using the Blumberg and Schlunder (1996) correla-
tion shows that the convective mass transfer is
independent of the composition of the particle
itself. This is probably to be expected in the
constant-rate drying period where the rate-limit-
ing step is diffusion of water from the saturatedsurface of the particle. The materials used by
Blumberg and Schlunder were mainly uniformly
sized, spherical, inorganic particles. The values of
ka% evaluated in the present trials were performed
using damp wheat bran, which is non-uniform in
size, non-spherical and organic. This similarity in
ka% suggests workers in SSF can access data from
the drying literature, even when it was obtained
with very different particle types, provided they
are operating in the constant-rate drying regime.
Fig. 5 shows ka% estimated on the basis of theCentral Jet flow RTD (solid circles) and also
using the Blumberg and Schlunder correlation
(hollow circles) as a function of effective Peclet
number. The line in the figure is the regression
line for estimates using the Central Jet RTD,
which was forced through the origin. The overall
correlation for estimates of ka% using the Central
Jet RTD is ka%=02.32103Peeff. As can be
seen from Fig. 5 it applies for a wide range of
Fig. 5. ka% vs. effective Peclet number. The estimates using the
Blumberg and Schlunder (1996) method are shown as hollow
circles and the estimates using the Central Jet RTD as solid
circles. The line is the line of best fit for the ka% estimated using
the Central Jet RTD (forced through the origin).
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 89101 99
Peclet numbers with a reasonable correlation
(R2=0.75).
4. Discussion
4.1. Comparison of methods of estimation
The Blumberg and Schlunder (1996) method of
estimating ka% differs from the technique using the
Central Jet RTD developed in this chapter in
three main ways. The two major differing assump-
tions are, firstly, that the area for mass transfer is
simply the flat area of the bed surface, and sec-
ondly, that the gas flow regime through the drum
is plug flow. The third is the use of correlations
from the drying literature (Appendix A).
Calculation of the ka% using the Central Jet
RTD produces a term that includes the wholesurface area available for mass transfer. The cor-
relations from the Central Jet RTD correlation
therefore, include the effect on mass transfer of
increasing mobile layer thickness with increasing
rotational speed. The mobile layer means that the
headspace/bed interface is not something sharp,
but actually has a finite thickness, of the order of
3 cm. This contrasts with the assumption in the
work of Stuart (1996) of a very thin static air
layer of 3 mm thickness where mass transfer was
taking place. Stuarts thin layer was convoluted
by increasing the rotation speed thus, increasing
its surface area, with the fold increase in area
being described by a factor n which varied be-
tween 1 and 5. Note that this assumption (a very
thin layer) was explicit in the work of Blumberg
and Schlunder (1996). The values of ka% estimated
in the current work incorporate the area of mass
transfer so, do not make any assumption as to the
thickness of the layer in which mass transfer
occurs.
The Central Jet RTD is also, by its very nature,
a more realistic assessment of the gas flow regime
and hence, driving force down a given drum axis.
One disadvantage of predicting ka% from the Cen-
tral Jet RTD is there is currently a lack of infor-
mation on how to predict Central Jet parameters
for different drum geometries and sizes. This im-
plies that each different reactor must be character-
ised in terms of its gas flow RTD before any
attempt is made to estimate ka%. Further work is
required to develop correlations for geometry and
scale for Central Jet parameters. However, the use
of an empirical RTD better characterises the gas
flow and accommodates a wide variety of condi-
tions. Characterisation of the RTD using the Cen-
tral Jet RTD allows a more accurate estimate ofka% when back mixing becomes more prevalent.
Also, only one calculation is needed in our ap-
proach whereas, Blumberg and Schlunder require
the worker to calculate four Sherwood numbers
and combine these with a Reynolds-number-
derived factor to produce a predicted Sherwood
number. In our approach, after the RTD in a
drum has been characterised the calculation of
mass transfer coefficients for different conditions
is trivial.
4.2. Implications for design and operation of
RDBs
To date the most complete model of SSF pro-
cesses in RDBs was developed by Stuart (1996).
This model dealt with variations in rotation speed
by a factor n, which varied the surface area avail-
able for mass transfer from the flat area of the top
of the bed (n=1) to a factor of five times this
area for cataracting flow. However, the values
assumed for this factor n were simply educated
guesses and where not based on any theoretical or
experimental evidence. Note that, in the present
work, in which a 56-cm diameter drum was oper-
ated at 9 rpm, cataracting flow of the particles
was not observed. Nine rpm represents 16% of the
critical speed, and as expected, at this speed a
tumbling motion was observed. The correlations
predicted from the Central Jet RTD demonstrate
a much greater effect of rotation speed on mass
transfer than that assumed by Stuart (1996). Sher-
wood numbers increased by a factor of approxi-
mately 4 over the range of rotation speeds from
zero to 9 rpm.
From a design perspective the correlations de-
veloped in this paper (and shown in Fig. 5) give a
mass transfer coefficient for a given Peclet num-
ber. The effective Peclet number takes into ac-
count the fill depth, the gas flow rate and the
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 89101100
rotational speed. This figure allows the worker to
estimate the ka% that corresponds to their calcu-
lated Peeff, and therefore, to calculate the mass
transfer coefficient in their system. This greatly
simplifies design and calculation of mass transfer.
Further work is required to understand the effect
of scale on the Central Jet flow pattern, and
therefore, on the values of the Central Jet RTDparameters. At the moment the correlations for
Vdead, Qmix and D are valid only for the drum as
described in Hardin et al. (2001). Different corre-
lations based on scale and geometry, involving
more RTD trials using different drums, are
needed to improve the usefulness of the method
and to test the ka%-effective Peclet number correla-
tion. If these are found, scale-up on the basis of
mass transfer phenomena within RDBs will be
simplified.
5. Conclusion
The Central Jet RTD correlation offers a sim-
ple yet accurate estimate of Sherwood numbers in
RDBs for Peclet numbers up to 85. This will
allow easy design of RDBs by improving esti-
mates of evaporative cooling. Implicit in this cor-
relation are the assumptions that the observed
effects are independent of temperature and there
are no changes in volume due to mass transfer.
Also, this correlation is only tested for the con-
stant-rate drying period.
Acknowledgements
David Mitchell thanks the Brazilian National
Council of Research (Conselho Nacional de
Pesquisa, CNPq) for a research scholarship and
auxiliary funding.
Appendix A. Brief description of Blumberg and
Schlunder correlation
The effective mass transfer coefficient, ig,eff esti-
mated using the Blumberg and Schlunder correla-
tion is calculated by combining the mass transfer
coefficient around a single sphere, ig,p, and
through a tube in the entrance region, ig,tube,
using the hydraulic diameter of the free cross-sec-
tion of the drum. These values were combined
using:
ig,eff=1.8ig,P+(1)ig,tube (28)
where is evaluated from the fitted equation:
=0.0015ueffd
6g(29)
where 6g is the gas kinematic viscosity. The two
mass transfer coefficients from Eq. (28) are
derived from the following correlations.
Mass transfer around a single sphere:
Shg,P=ig,Pd
lg=2+
Shg,lam
2 +Shg,turb2 (30)
where
Shg,lam=0.664Red(Scg)1/3 (31)
Shg,turb=0.037Red
0.8Scg
1+2.443Red0.1(Scg
2/31)(32)
Red=ugd
6g(33)
Mass transfer for forced convection in tubes:
Shg,tube,lam=ig,tubeDh
lg
=3.663+0.73
+(1.615(ReDScgDh/L)1/30.7)3
+ 2
1+22Scg
1/6(ReDScgDh/L)3
n1/3(34)
Shg,tube,turb=ig,tubeDh
lg=
(x/8)(ReD1000)Scg
1+12.7x/8(Scg2/31)1+DhL2/3n (35)
where:
x= (1.82logReD1.64)2 (36)
and
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M.T. Hardin et al. /Journal of Biotechnology 97 (2002) 89101 101
ReD=ueffDh
6g(37)
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