Pergamon Chemical Engineering1 Science, Vol. 50, No. 23, pp.

3763 3775, 1995

Copyright' © 1995 Elsevier Science Ltd
Printed in Great Britain. All rights reserved
0009 2509/95 $9.50 + 0.00
0009-2509(95)00202-2

A F L U I D DYNAMIC M O D E L O F THE DRAFT TUBE

G A S - L I Q U I D - S O L I D F L U I D I Z E D BED

LJ. K U N D A K O V I C
Tufts University, Department of Chemical Engineering, Medford, MA 02155, U.S.A.

and

G. VUNJAK-NOVAKOVIC'
Massachusetts Institute of Technology, E25-342, Cambridge, MA 02139, U.S.A.

(First received 8 September 1993; revised manuscript received 27 December 1994; accepted 17 May 1995)

Al~traet--Fluid dynamics of gas-liquid-particle flow in the draft tube and liquid-particle flow in the
annulus were studied for a draft-tube fluidized bed (DTFB) operating in the circulating regime. The local
concentrations and velocities of the continuous liquid phase, solid particles and air bubbles were assessed in
flow visualization studies, using a two-dimensional column, 1 cm thick x 8 cm wide x 105 cm high, with
a 4 cm wide x 83 cm high internal draft tube. The drift-flux model was extended to take into account the
momentum transfer between all phases in the three-phase system studied, and used to describe the
circulating flow in the DTFB. Additional momentum transfer from gas bubbles to solid particles was
identified and attributed to the changes in relative velocities and drag forces induced by bubble motion in
three-phase flow.

INTRODUCTION pressure drop (Merchuk, 1986; Li et al., 1988;

The draft tube fluidized beds (DTFB) are pneumati- Chen and Fan, 1990). Fan (1989) and Chisti (1989)
cally mixed reactors that combine the features of gave excellent reviews of the published data on these
three-phase fluidized beds and circulating bubble re- class of three-phase contactors. However, the range of
actors. The DTFB is also known as the sparged loop application of the reported fluid dynamic models is
reactor with the internal circulation, the internal-loop limited, as they rely on empirical correlations for gas
air-lift reactor or the recirculating fluidized bed. Gas holdup, and consider the whole DTFB as a single
and liquid are both introduced at the bottom of the compartment. So far, there has been no attempt to
column to establish a steady-state circulation of liquid analyze the fluid dynamics of three-phase flow in the
and particles between the draft tube and the annulus; in DTFB. Darton and Harrison (1975) and Chen and
some operating regimes, gas bubbles also recirculate Fan (1990) applied the drift-flux approach to three-
into the annulus (Vunjak-Novakovic et al., 1992a). phase fluidized beds, based on the Wallis' (1969)
Driving force for the circulating flow is generated model for two-phase flow. However, these models
by the difference in densities of fluid-particle mixtures deal only with the gas-liquid drift velocities, and do
in the draft tube (gas-liquid-particle flow) and an- not include the liquid-particle drift flux. Their direct
nulus (liquid-particle flow). For a defined geometry application to the three-phase flow in draft and annu-
(sparger and gas disengagement section design, draft lar regions of DTFB is thus not possible.
tube height and diameter) and physical characteristics Recently, a fluid dynamic model was proposed for
of gas, liquid and particles, gas flow rate basically a DTFB operating in the circulating regime, which
determines the reactor performance. The DTFB has corresponds to the conditions of a steady-state circu-
higher mass transfer coefficients when compared to lation of liquid and particles with no bubble recircula-
air-lift reactors with external circulation, which can be tion into the annulus (Vunjak-Novakovic et al.,
attributed to higher liquid velocities and gas holdups 1992b). This model described gas-liquid-particle flow
(Siegel and Robinson, 1992). in the draft tube and liquid-particle flow in the annu-
Several models were proposed so far to predict the lar region, by extending the drift flux model proposed
fluid dynamic properties of DTFB, such as flow re- by Wallis (1969). Gas flow in the draft tube was
gimes, overall gas holdup, liquid circulation rate, and considered as bubbling flow of discrete non-coalesc-
ing bubbles that are uniformly dispersed in the liquid
phase. Interactions between the two dispersed phases
(i.e. bubbles and particles) were not taken into ac-
*Corresponding author. Tel: 1-617-253-3858; Fax: 1-617- count, and the circulation of liquid and particles was
258-8827; Email: gordana@mit.edu. attributed only to the difference in densities of the
3763
 ~
3764 LJ. KUNOAKOVICand G. VUNJAK-NovAKOVlC
fluid-particle mixtures in draft and annulus. Model
0
19redictions for local liquid velocities in draft and
annulus were systematically higher than the experi-
mental values. Consequently, the model over pre-
dicted superficial gas velocities that are necessary to
maintain liquid circulation at given liquid flow rates.
These results indicated that the proposed model did
not take into account all mechanisms of momentum
transfer in the DTFB. In addition, our previous
studies of the same experimental system (Vunjak-
Novakovic et al., 1992a) demonstrated that the gas /
40
flow in the draft tube basically determined the behav-
ior of DTFB, while liquid flow had only a slight effect
f
on both the flow regimes and liquid circulation rate.
The existence of additional mechanisms of mo-
mentum transfer between gas bubbles and liquid
phase, and gas bubbles and solid particles, was thus 1050
assumed. 830
To test this hypothesis, mechanics of the discrete
particle settling in the draft tube of DTFB was studied
(Kundakovic and Vunjak-Novakovic, 1995). The ob-
served particle settling velocities in three-phase flow
were significantly different from the corresponding
free settling velocities. Effects of gas bubbles and
fluidized bed particles on particle settling were as-
sessed in terms of the effective drag and effective
buoyancy of settling particles. The proposed model
included the additional momentum transfer from gas
bubbles and fluidized bed particles on the settling
particle and gave a good prediction of particle settling 10
velocities in three-phase flow.
In this paper, fluid dynamic studies of the two
major compartments of DTFB, i.e. the draft tube and
the annulus, are presented. Momentum transfer in Fig. 1. Experimental two-dimensional column used in flow
visualization studies (all dimensions are in mm).
three-phase flow in the draft tube was analyzed based
on (a) the liquid-particle and liquid-bubble drift flux,
and (b) the additional mechanisms of momentum column used in this work was a 8 cm ID, 160 cm high
transfer from gas bubbles and solid particles. A model cylinder with an internal draft tube (5.4/5 cm in dia-
of the circulating flow was proposed, to predict local meter, 90 cm high) placed 7 cm above the top of the
phase velocities and holdups in the draft and annulus gas and liquid distributor.
of a DTFB. To test the model, the local flow condi- Water (15°C) was introduced through a central
tions in draft and annular regions were assessed by 3.6cm× 1 cm sparger, while air (1 bar, 20°C) was
flow visualization using a two-dimensional column. introduced through the outer 4 mm wide annular
fritted glass sparger. In a separate series of experi-
ments, bubble diameter was decreased by addition of
EXPERIMENTAL a surfactant to the recirculating liquid. Superficial air
The experimental unit was a two-dimensional velocity was varied from 0 to 1.1 cma/cm 2 s, while
plexiglass column with a conical bottom and an over- liquid superficial velocity was maintained at
flow at the top, operating with air and water (Fig. 1). 0.45 cm3/cm 2 s. At these fluid velocities, a steady-state
The column had inner dimensions 8 cm × 105 cm x circulation of liquid and particles was maintained,
1 cm, and a 4 cm x 83 cm draft tube which was placed with no significant recirculation of gas bubbles into
1.5 cm above the conical bottom. A convergent two- the annular space. Fluid flow rates were measured by
phase injector nozzle was used as air and water dis- rotameters (Cole-Parmer). Solid phase were alginate
tributor; the height and relative positions of air and particles (ds = 2.5 + 0.1 mm, p, = 1040 + 1 kg/m3),
water inlets were adjusted to obtain a monodisperse produced from 2% Na-alginate using a droplet gener-
population of air bubbles. This two-dimensional col- ator (BioLoop, FTM, Belgrade), and subsequently
umn was geometrically similar to full size columns gelated for 30 min in Ca chloride. Volumetric fraction
used in previous fluid dynamic studies (Vunjak- of solids in the reactor volume was varied from 0 to
Novakovic et al., 1992a) and for bioconversion of 20%.
penicillin by immobilized biocatalyst particles (Vun- The local flow conditions in draft and annular
jak-Novakovic et al., 1991). The three-dimensional regions, as well as the hydrodynamics of the DTFB as
 Fluid dynamic model of the draft tube 3765
a whole, were assessed in flow visualization studies 30. 2-0
using liquid and particle tracers. The opaque tracer 13 L ' G 0% • 0%
particles were used that could be easily distinguished o L-Q-S,0~ • 10%
from transparent fluidized bed particles in a side light • L-O-S~0"~ +

(2 x 500 W) on a black background. Neutrally buoy- 20 3-D

ant opaque particles were used as tracers of the liquid + o
4" L-G-S 20% o
flow. A high-speed 16mm camera (Photosonic, _~ x

200 frames/s, exposition 1/800 s) was used for flow

o,
visualization in conjunction with a frame-to-frame 10 B
analyzer, data acquisition system and image process- ÷ • &

ing software. The estimated error of these measure-

ments was < 1%, based on the high speed of the
camera (200 frames/s) when compared to the highest °0.0 o12 0.4 0:6 0:8 10

velocity that was measured ( < 30 cm/s).

Ug Ices]
Local particle velocities were assessed from series of
successive positions of the tracer particle within de- Fig. 2. Local liquid velocity in annulus as a function of the
fined (5ms) time intervals, in a view area of superficial gas velocity and fraction of solids: d~ = 2.5 ram,
4 cm x 15 cm. Each experimental value was an aver- p~ = 1040 kg/m3.
age of 30 independent measurements. Bubble velocity
was assessed as an average from 160 independent
measurements, each representing a bubble velocity 0z5
obtained from six successive bubble positions in 5 ms
time intervals. Bubble frequency was calculated from 0.2o [3 O

the number of bubbles passing through a certain level _7.

within i.5 s time interval. Bubble diameter was as- ~ 01~ • g

sessed as an average of diameters of all bubbles in the

e e
4 cm x 15 cm view area. The local gas and particle :~ = • o

holdups were measured from the respective area frac- ~- 010

e sA ~ $0
tions occupied by gas bubbles and particles. 0.06
• 10% o 10%

RESULTS • ~0% a ~%
0.00
Liquid velocities, bubble properties and phase holdups oo o'.~ o., 0:6 o:. -~o
in the draft and annulus U g (crrVs)

The effect of superficial gas velocity on the local

Fig. 3. Holdup of solid particles in the draft and annulus vs
liquid velocity in annulus of the two-dimensional col- the superficial gas velocity; d~ = 2.5 mm, p~ = 1040kg/m3,
umn is shown in Fig. 2 for various fractions of solids Ut = 0.45 cm/s.
and two bubble diameters. Note that the data for
v~ obtained in a geometrically similar three-dimen-
sional column using tracer-response technique were from the circulating into the turbulent regime
comparable with the corresponding data obtained (Ug = 0.45 cm/s in Fig. 3) had little effect on particle
from flow visualization studies using the two-dimen- holdup. The fraction of solids increased only slightly
sional column. Similar effects of gas velocity, fraction in the draft tube and decreased in the annulus ( < 4%
of solids and bubble diameter on the local liquid within the range of this study) as the result of changes
velocity were observed for the draft tube (data not in the gas holdup when the superficial gas velocity was
shown). As seen in Fig. 2, liquid velocity increased increased.
when gas velocity was increased, up to Ug = 0.45 cm/s The photographs of a 8 cm high section of the
at which a transient from the circulating into the two-dimensional column [Fig. 4(a) and (b)] for the
turbulent regime was observed (Vunjak-Novakovic et system operating with 4 mm gas bubbles show repre-
al., 1992a). A further increase in Ug had little effect on sentative situations of a relatively uniform distribu-
liquid circulation rate. The effect of solids fraction tion of gas bubbles and solid particles in draft and
(0-20 vol%) on vt was not significant, as expected for annular regions. Gas bubbles were somewhat larger in
low-density particles (Ps = 1040 kg/m3). In addition, three-phase flow than in gas-liquid bubbling flow
a decrease in bubble diameter from 4 to 1 mm (Fig. 2, (data not shown), as already reported by Li et al.
open and closed symbols, respectively) had little effect (1988). These findings were attributed to the enhanced
on the annular liquid velocities. coalescence of bubbles in presence of solid particles.
One of the assumptions of the drift-flux model A slight increase in bubble diameter (from 3.5 to
developed in our previous studies for three-phase flow 4.5 mm) was observed when the superficial gas velo-
(Vunjak-Novakovic et al., 1992b) was the uniform city was increased [Fig. 4(c)]. Gas holdup was a linear
distribution of fluidized particles. Experimental data function of the superficial gas velocity, and increased
for particle holdup in draft and annulus support this when the fraction of particles in the three-phase flow
assumption (Fig. 3); in addition, the transient was increased [Fig. 4(d)].
3766 LJ. KUNDAKOVIC and G. VUNJAK-NovAKOVIC

(a)

(b)
Fig. 4. Experimental data for bubble diameter and gas holdup in the draft tube for the D T F B operating
with large ( ~ 4 ram) bubbles; ds = 2.5 ram, Ps = 1040 kg/m 3, U~ = 0.45 crn/s, E, = 0 and 10 vol%. (a) Pho-
tograph of the 8 cm x 8 cm view area at U u = 0.67 cm/s, es = 0 vol%, (b) photograph of the 8 c m x 8 cm
view area at Ug = 0.67cm/s, ~ = l0 vol%, (c) bubble diameter vs the superficial gas velocity, (d) gas
holdup vs the superficial gas velocity.
 Fluid dynamic model of the draft tube 3767
6" that resulted in variable and irregular paths of indi-
vidual bubbles in the draft tube. The experimental
A
5" & data justified the assumption that bubble rise velocity
E &
A 0 can be approximated with only the vertical compon-
4" A
A 0 O O 0 ent of bubble velocity. Significant fluctuations in both
U~x and Uby were observed, as seen from the values of
3.
"o the respective standard deviations given in Table 1.
¢.~
2
These fluctuations could be attributed to the interac-
m tions of bubbles and particles and small variations in
O L-G-S 10% ] bubble diameter. Due to the relatively low gas hold
I A L-G-S20% ups ( ~< 0.04 v/v) the effects of bubble to bubble inter-
actions were not significant. Radial profiles of bubble
o.o 0.2 01, o16 018 1.0 velocities within the draft tube (Fig. 7 ) were consistent
(c) Ug (cm/s) with those reported by Joshi et al. (1990).
Based on the experimental data, a bubbling flow of
0.05 gas in the form of a monodisperse bubble swarm was
0 L-G-S10% ]
assumed as a model of gas flow in the draft tube.
o~ 0.04'
A L-G-S20%
I Bubble rise velocity Ub, was calculated from experi-
A mental data for Ub and v~:
g O
~ o.oa- Ub,.~j = Ub -- vl (1)
o and compared with Ub, for a single spherical bubble
= 0.02 &
rising in liquid (Wallis, 1969).
(.9 o o
& Bubble frequency in the draft tube was calculated as
O.Ol o
&
o
,fb,~l = ego Ao Ub/Vb (2)
o.oo where Ub, Vb and ego were the experimental values for
o.o 0.2 0.4 0.6 o'.8 " 1.o
bubble velocity, mean bubble volume and gas holdup,
(d) ug (cnVs) respectively. Experimental data for bubble frequency
J~ were compared withJ~.c.] to justify the assumption
Fig. 4. (c) and (d). of bubbling flow (Table I).fb andJb.c,l were not signifi-
cantly different except for the higher gas velocity
(Ug = 0.67cm/s) at the highest fraction of solids
Figure 5 shows the data corresponding to those in (es = 0.20). This deviation could be attributed to the
Fig. 4 for a DTFB operating with small (1 mm) gas relatively large bubble diameter observed at those
bubbles. Addition of a surfactant to the liquid phase conditions. Ub, andJ~ in three-phase systems (experi-
resulted in a dominant presence of l mm bubbles, mental data and model predictions for 10% and 20%
with a relatively small fraction of larger (2 mm) of solids in the draft tube, Table l) were only slightly
bubbles. The main population of 0.5 mm bubbles was lower than those for two-phase flow,
mixed with relatively small number of 2 mm bubbles
[Fig. 5(a) and (b)]; about the same relative number Effects of gas bubbles and solid particles on momentum
ratio of smaller and larger bubbles was maintained at transfer in the draft tube
all gas and liquid velocities. The mean bubble dia- The model for the circulating flow of liquid and
meter was not sensitive to changes in superficial gas fluidized particles between the draft and annulus of
velocity and fraction of solids [Fig. 5(c)]. The gas the DTFB which was developed in our previous
holdup was proportional to the superficial gas velo- studies (Vunjak-Novakovic et al., 1992b) over pre-
city [Fig. 5(d)]. dicted the superficial gas velocities needed to establish
Bubble size distribution was assessed for the experi- a steady-state circulation. This model was based on
mental conditions corresponding to Figs 4 and 5 in an extension of the drift-flux model proposed by Wal-
order to check the model assumption of bubbling gas lis (1969), assuming two components of momentum
flow. A relatively uniform bubble size was observed at transfer: (a) between the liquid phase and solid par-
all experimental conditions in both two-phase and ticles, and (b) between gas bubbles and the liquid
three-phase systems. The presence of solid particles phase. The interactions between gas bubbles and solid
resulted in a wider bubble size distribution around the particles were neglected.
mean bubble diameter (Fig. 6). The mean bubble Our subsequent studies demonstrated significant
diameter, calculated from bubble size distribution as contributions of momentum transfer from gas bubbles
a mean diameter of an equivalent sphere, was not and fluidized solid particles to particle settling in
significantly affected by gas or liquid superficial vel- three-phase flow. The effects of bubbles and particles
ocities. on the relative velocity of the settling particle and the
Flow visualization studies demonstrated bubble particle drag coefficient resulted in increased liquid
motion in both the horizontal and vertical direction velocities in the draft tube (Kundakovic and
3768 LJ. KUNDAKOVICand G. VUNJAK-NOVAKOVIC

(a)

(b)

Fig. 5. Experimental data for bubble diameter and gas holdup in the draft tube for the DTFB operating
with small ( ~ 1 mm) bubbles; d~ = 2.5 mm, p~ = 1040 kg/m 3, Ut = 0.45 cm/s, e, = 0 and 10 vol%. (a) Pho-
tograph of the 8 cm x 8 cm view area at Ug = 0.67 cm/s, ~s = 0 vol%, (b) photograph of the 8 cm x 8 cm
view area at U o = 0.67 cm/s, es = I0 vol%, (c) bubble diameter vs the superficial gas velocity, (d) gas
holdup vs the superficial gas velocity.
 Fluid dynamic model of the draft tube 3769
2,0 The friction term ( - Ap/)o was presented as
• L-G

( - Apy)D = 3/4 Co L/d.~ [h GZo ~so (6)

E
1.5'
-O L-G-S10% I
where
v~m = U ; (1 - ~,o) "~- 1 (7)
1.0
is the actual particle to liquid relative velocity in the
draft tube, Co is the corresponding drag coefficient
and UI is the particle settling velocity in the presence
of gas bubbles.
0 . 0 ~
Based on the results of the studies of particle sett-
0.0 0.2 0.4 0.6 0.8 1.0 ling in three-phase flow (Kundakovic and Vunjak-
Novakovic, 1995), the motion of liquid and particles
(c) Ug (cm/s}
in the draft tube was considered in conjunction with
0.05" the bubbling gas flow. The presence of gas bubbles
m L-G ] resulted in a decrease of particle to liquid velocities:
O L-G-S10%
o~ 0.04-
U;= U, Uh'R2 arctan(Ym"----~) (8)
Xmax .}:max \Xmax/
=~ 0.03-
where
O
2 0.02" A X b - - dp
Ymax = Xmax (9)
(5 2
0.01
0
Az U~
Ax~ = (10)
0.00 A
0.0 0.2 0.4 0.6 0,8 t ,0
Equation (8) was derived from Navier-Stokes
(d} Ug (cm/s)
equations as proposed by Clift and Grace (1985) as-
Fig. 5. (c) and (d). suming: (a) uniform distribution of monodisperse gas
bubbles in the draft tube, (b) nonviscous flow of liquid
Vunjak-Novakovic, 1995). A fluid dynamic model for around the bubble, (c) negligible wall effects, (d) negli-
the circulating flow between draft and annular regions gible horizontal component of bubble rise velocity, (e)
in the DTFB should thus take into account this addi- negligible bubble to bubble interactions. These as-
tional momentum transfer between bubbles and par- sumptions were experimentally tested, and were found
ticles. to be fair approximates of the observed behavior.
Bubble to particle momentum transfer was assessed The effect of fluidized particles on particle settling
as a cumulative effect of successive discrete changes in in three-phase flow was considered as a result of
the relative particle to liquid velocity and the particle momentum transfer via elastic particle to particle
drag coefficient, and calculated in terms of the effec- collisions (Kundakovic and Vunjak-Novakovic,
tive drag force. The momentum transfer equation for 1995). The net force acting on the settling particle as
circulating flow between the draft and annulus of a consequence of this additional momentum transfer
DTFB could therefore be presented in a form: can be presented as

Pl (eta -- eta) gL -- ps (eso -- Ga) gL Fps 8sDADX 2msmp (v~ -- vl + Vpl)2. (11)
V, m, + mp

= ( -- Apf)a + ( -- Ap/)o + ( -- Apw) + ( - Apa). The net force calculated from eq. (11) is significant
(3) for particle motion when its diameter or density is
significantly different from those of the fluidized par-
ticles (dp/d, >1 5, [,% - ,oJ ~> 200 kg/m3); for the
Equation (3) represents a balance of the driving
fluidized particles this additional force is zero.
force, i.e. the difference in apparent densities of the
flow in draft and annulus, and the friction losses in the
The model of circulating flow between the draft and
draft tube ( - A p l ) o, annulus (-Apt),4, bottom sec-
annulus of the DTFB
tion ( - Aps) and at the column walls ( - Apw). The
The momentum transfer equation for circulating
friction pressure drop in annulus was calculated as:
flow between the draft and annulus of DTFB was
modified to take into account the pressure drops due
( - Apl)a = 3/4 CoL~d, Pl vs~A ~x,A (4) to wall friction ( - Apw) and flow resistance
where at the bottom of the column ( - A p s ) [eq. (3)].
The wall friction term of the pressure drop ( - Apw)
(5) was calculated as proposed by Joshi et al. (I990)
3770 LJ. KUNDAKOVIC and G. VUNJAK-NovAKOVIC

1.0 1.0
(s) large bubbles; two phase; I (c) small bubbles; two-phase
.
Ug=O.67cm/s ! Ug=O.67cm/s
0.8- 0.8
I
g
'.,=
.~_ .

0.6" ~ 0.6- iiii i

O 0

E= 0.4" 0.4 .... !

-6
>
> I

0.2" 0.2"

I
0.0
. . . . . . . . . 0.0 i ' , ..... , " , '

1 2 3 4 5 6 7
db (ram) db (mm)

1.0 1.0-
(b) large bubbles; 10% of solids; (d) small bubbles;lO% of solids;
Ug=O.67cm/s Ug=O.67cmls
0.8- 0.8-

0.6- ,-- 0.6"

0

0.4 0.4"

0.2" 0-2 •

0.0 ¢ 0.0
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6
db (ram) db (mm)

Fig. 6. Experimental data for bubble size distribution in the draft tube; d+ = 2.5 ram, p, = 1040 kg/m 3,
U, = 0.45 cm/s, U~ = 0.67 cm/s. (a) e+ = 0 v o l % , large ( ~ 4 ram) bubbles, (b) e+ = 10 vol%, large
( ~ 4 ram) bubbles, (c) es = 0 vol%, small ( ~ 1 ram) bubbles, (d) e~ = 10 vol%, small ( ~ 1 ram) bubbles.

Table 1. Experimental data for the diameter, velocity and frequency of gas bubbles, and gas holdup in the
draft tube of D T F B

Fraction of solids (vol%)

0 10 20

G a s velocity, U s (cm/s)
0.49 0.67 0.49 0.67 0.49 0.67

db (ram) 4.1 4.3 3.5 3.7 4.1 5.2

eg 0.025 0.035 0.013 0.018 0.020 0.034
fb(s- t) 99.0 117.2 95.4 91.2 59.4 107.8
STD 20.2 12.0 30.0 24.2 12.8 18.5
fb, c,I (S- t ) 108.6 131.7 79.2 107.6 77.9 67.4
Uby (cm/s) 39.2 39.1 34.5 40.3 35.9 37.0
STD (Ubr) 4.1 3.8 8.6 10.3 7.5 8.9
U ~ (cm/s) - 1.9 - 1.6 - 0.8 0.8 - 0.3 - 2.2
STD (Ub,,) 3.3 2.5 4.4 5.5 4.3 3.3
U~, (cm/s) 23.6 22.9 18.7 22.6 22.5 21.3
Ub,.c,i (cm/s) 24.9 24.4 27.0 26.2 24.9 22.1

Air-water system, d, -- 2.5 ram, p, = 1040kg/m 3, Ut = 0.45 cm/s. Model predictions for bubble fre-
quency and bubble rise velocity are shown for comparison.
 Fluid dynamic model of the draft tube 3771
80" The liquid flow rate in the draft tube was related to
Uby
the annular liquid flow rate and liquid input flow rate:
• °. •= ==
60"
. ~..,%.'-" - /
J t o A o = J I A A a + qt. (19)
,',_: • .._. ,_~."'" . . .
40-
Equations 06) (19), which were derived based on
• . : .,..: the results of previous experimental and modeling
2oi • . • -p, •
studies (Vunjak-Novakovic et al., 1992b; Kundakovic
• ¢!. ,:." •" :4.' "" and Vunjak-Novakovic, 1995) all define the phase
0"
holdups as functions of the corresponding relative

-20-
i Ubx
velocities. These equations strictly refer to the circula-
ting regime in DTFB, i.e. the conditions of steady-
state circulation of liquid and particles between draft
-4C and annular regions with gas bubbles present in the
draft tube only.
x (cm) Equations (16) (19) were solved in conjunction
with eqs (3) and (12) (15) to obtain liquid velocities
Fig. 7. Experimental data for the radial distribution of
bubble diameters in the draft tube; d, = 2.5mm, and phase holdups in the draft and annulus. The effect
p,=1040kg/m 3, Ut=0.45cm/s, e,=10vol%, Ug= of gas bubbles on particle motion was integrated into
0.67 cm/s. the model by predicting the relative velocities vst using
eqs (5) and (7)-(10), and calculating the drag coeffi-
for two-phase flow in the heterogeneous bubbling cient CD as function of v~t.
Figure 8 shows liquid velocities in the draft tube,
regime:
vto, and annulus, via, as functions of the superficial gas
2f pd~o2L velocity, Uo, for one representative series of experi-
( - ap~) ~,~ (12) ments (ds = 2.5 mm, p** = 1040 kg/m 3, Ul = 0.45 cm/s,
D
where and e~ = 10 vol%). Experimental data (points) are
compared with model predictions (lines) for the circu-
2 1 2 gad "~7,/3 ) z lating regime (Ug ~< 0.45 cm/s). Figure 9 shows the
1 - eoo corresponding experimental data and model predic-
(13) tions for gas holdup in the draft tube (ego), and holdup
of solids in the draft tube (e,o) and annulus (e,a).
As reported by Chisti (1989), pressure losses in the
bottom section of DTFB depend only on the column DISCUSSION
geometry, ( - ApB) was thus considered as a function Flow behavior of a DTFB operated in the circula-
of the ratio of cross-section areas of the draft and ting regime was analyzed in terms of the
annulus and calculated using the equation: gas-liquid-particle flow in the draft tube, and
liquid-particle flow in the annulus, with the aim to
(14) develop a physically sound mathematical model of
( - ap,) = . . , - - 5 - this system. The existing theory of the two-phase flow
where proposed by Wallis (1969) was extended to describe
( A A ~ 0"79 the three-phase flow in the draft tube, assuming ho-
Ks = 11.4 \ A n j • (15) mogeneous bubbling flow and homogeneous particle
fluidization. The model takes into account mo-
Equation of the momentum transfer between liquid mentum transfer between (a) gas bubbles and liquid
and fluidized particles in the circulating flow in draft phase, (b) liquid phase and solid particles, and (c) the
and annular regions could be presented as additional momentum transfer from gas bubbles to
solid particles. The latter results from the changes in
Otsojto relative velocities and drag forces which are induced
U,~so(1 - ~,o)"'- '
1 -- ~so by bubble motion in three-phase flow.
Use of a two-dimensional column to study the local
OtsAJt'4 "st- UtOtsA(I -- ~ s A ) ' - 1. (16) flow conditions in the DTFB was justified by findings
I -- asA from our previous studies that showed no significant
A corresponding equation for momentum transfer effects of column geometry (i.e. two-dimensional vs
between gas bubbles and the liquid phase is three-dimensional) on the reactor fluid dynamics
(Kundakovic and Vunjak-Novakovic, 1995). Specifi-
(1 - - Otoo)jgD -- agojlo = Ub, gaO(| -- OtgO)n'. (17)
cally, the local liquid velocities and phase holdups in
A balance equation for the hold up of solids is the draft and annulus of a DTFB were determined
from (a) tracer response experiments using a three-
Vo VA dimensional column, and (b) flow visualization
~'sO"~- + esA'--~- = ~'s" (|8)
studies using a geometrically similar two-dimensional
3772 LJ. KUNDAKOVICand G. VUNJAK-NovAKOVIC
30 particle settlingin thrcc-phasc flow (Kundakovic and
O dr~-ixp~i~mal
--~lu~-m0deprtKllCt~n Vunjak-Novakovic, 1995).
Interaction between solid and liquid phase and gas
20 ¸ and liquid phasc in the draft tube wcrc modeled in
terms of the driftflux [-eqs(16) and (17),rcspcctively].
Particlc-liquid intcractions in draft tube and annulus
10"
wcrc analyzed based on the driftflux modcl which was
extended to take into account thc presence of gas
bubbles in the draft tube. Richardson-Zaki cocfficicnt
used was calculated as proposed by Wallis 0969),
~.0 0.2 0.4 0.6 0.8 1.0 based'on thc particlc free-settlingvelocity. Equation
tJg Icr~sl (16), which dcscribcs particlc-liquid interactions in
the draft tube and annulus rcgion does not includc
Fig. 8. Comparison of experimental data (.....) and model any effectof bubble-particle interaction on solid par-
predictions ( ) for liquid velocities in the draft tube and
annulus; d~ = 2.5 mm, p~ = 1040 kg/m 3, Ut = 0.45 cm/s, ticlcs velocity and hold up. Additional m o m e n t u m
~ = 10 vol%. transfcr from gas bubblcs to solid particles results
from the changes in rclativcvelocitiesand drag forces
that wcrc induced by bubble motion in the three-
column, that was designed as lcm thick slice of the phase flow. Influcncc of gas bubbles was modclcd as
actual three-dimensional column. This thickness of a cumulative cffcct of successive discrete changes in
the two-dimensional column was chosen to minimize the particlevelocity relativeto thc liquid phase and in
the wall effects, allow an insight into the structure and the corresponding drag coefficient[cq. (8)].
dynamics of multiphase flow, and enable translation Expression for the particlesettlingvelocity in pres-
of the obtained results to the cylindrical geometry of ence of gas bubbles [cq. (8)] was derived for a two-
the full-size column. The same two-dimensional col- dimensional bubble, assuming thc potcntial flow
u m n was used in this work to study the mechanisms of around a sphcrical bubble. Equation (8) shows that
bubble and particle motion in multiphase flow, and to the change in particlc settlingvelocity,duc to bubble
assess the local phase velocities and holdups that wcrc risenear the particle,depends on bubble diameter and
needed to test the proposed model. vclocity and particle size.
In our earlier studics (Vunjak-Novakovic et al., Equation (17) was dcrivcd by accounting for thc
1992b) we proposed a model of thrcc-phase flow, related changcs in gas and liquid holdup, and assum-
based on thc assumption of the m o m e n t u m transfer to ing that at low values of gas holdup ( ~< 0.04 in this
the fluidized particlcs from liquid phasc only, while study) particle motion docs not affectbubble motion.
the interactions between the two dispersed phases Shamlou et al. 0994) prcscntcd a model of draft tube
were not taken into account. A poor agreement of air-lift rcactor that takes into account liquid flow
modcl predictions with the experimental data was associated with the bubble wakes.
attributed to the additional m o m e n t u m transfer from Integration of the additional effects of momcntum
gas bubbles which was demonstrated in studies of transfcr from gas bubblcs into the drift-fluxmodcl,

20
Experimental data

IA g a s ; draft t u b e

J0 p a r t i c l e s ; draft t u b e

o~ • particles; annulus
o

10 ........ 0- ....... Model predictions

t......o° ...... .~- .....
/
gas; draft tube

O_ - - particles; draft tube

..... particles; annulus

0 • T , i • i - , - •
0.0 0.2 0.4 0.6 0.8 1.0 1.2

Ug (cm/s)

Fig. 9. Comparison of experimental data (. . . . . ) and model predictions ( ) for phase holdups in the
draft tube and annulus; ds = 2.5 mm, p, = 1040 kg/m 3, Ul = 0.45 cm/s, ~ = 10 vof%.
 Fluid dynamic model of the draft tube 3773
resulted in a close prediction of the observed liquid 300
velocities in draft and annulus of the DTFB operating ---o--- drivingforce
in the circulating regime (Fig. 8). At superficial gas friction losses
velocities approaching the transient from the circula-
ting into the turbulent regime (Ug = 0.45 cm/s for 200
data shown in Fig. 8), gas bubbles start entering into
the annular space. The model assumptions of a
three-phase (gas-liquid-particle) bubbling flow
in the draft tube, and two-phase (liquid-particle) flow 100
in the annular space are not satisfied in this transient o_
region, and the model overpredicts the observed
liquid velocities in draft and annulus. Similar
effects can be seen from Fig. 9 presenting the gas and
particle holdups in the draft and annulus. Somewhat 0 10 15 20
higher phase holdups predicted with the model,
when compared to the experimental data, could be Jlo (cm/s)
attributed to the inaccuracy of the experimental
determination of low gas hold ups, and possibly to the
Fig. 10. Model predictions for driving force and frictional
wall effects on bubble motion in a two-dimensional losses for Ug=0.3cm/s, db=3.5mm, d,=2.5mm,
column. p, = 1040 kg/m 3, UI = 0.45 cm/s, ~ = 10 vol%.
Addition of the surfactant to the liquid phase result-
ed in the formation of a large fraction of small bubbles
(about 1 mm) and a relatively small fraction of large 150-
bubbles (about 2 mm). In this double size bubble dra~ tube / p
population, only large bubbles appeared to generate
the driving force for liquid circulation. On the other
hand, small bubbles were associated with a high
gas-liquid surface area, which might be of interest in ~ ~00
annulus
wall effects. /
biochemical applications with high oxygen mass
transfer requirements. However, the identification of
possible mechanisms of the double peak population of
small and large gas bubbles warrants further studies. ~ 50
Figure 10 shows the model predictions for the o_
liquid circulation driving force and flow resistance as
functions of the superficial liquid velocity. The driving
force for liquid circulation passes through a maximum 0
5 10 15 20
while the overall drag force continuously increases, o
when the superficial liquid velocity is increased. The
maximum of the driving force results from changes in Jlo (cm/s)
relative contributions of individual components to the
Fig. I1. Effects of the liquid flux on the components of
overall drag with the superficial liquid velocity, as
frictional losses. Model predictions for U~ =0.3cm/s,
shown in Figure 1 I. At low liquid velocities, the liquid db= 3.5 mm, d~ = 2.5 mm, p~ = 1040 kg/m 3, U t = 0.45 crn/s,
particle drag has a major contribution to the overall ~;~= 10 vol%.
drag, while at higher liquid velocities the other two
components, i.e. the friction losses at the column bot-
tom and wall friction, become dominant. The effects particle transport by bubble wakes becomes more
of additional momentum transfer from gas bubbles important and a different value of the coefficient nb
are most significant at low liquid velocities. should be used.
In the momentum balance equation the kinetic Relative magnitude of different frictional terms de-
term was neglected since the cross-sectional areas of pends on the column geometry and phase holdups.
the draft tube and annulus are the same, the solid With increasing solid holdup for a fixed liquid circula-
phase holdup is the same (Fig. 3) and consequently tion velocity, liquid-solid frictional losses in draft and
liquid velocities are the same. annulus increase compared to the wall and bottom
The proposed model was strictly derived for homo- friction. Also as the particle size and density increase
geneous bubbling flow in the draft tube at low gas the effect of additional momentum transfer from gas
velocities, and low solid holdups. These conditions are bubbles decreases and particle liquid interactions are
required for most of the biochemical applications of dominant. However, additional momentum transfer
air-lift reactors. As the gas flow rate and holdup from gas bubbles is significant for low particle densit-
increase, a transition to heterogeneous bubbly flow ies and low liquid velocities, which are important for
may occur. Under those conditions the assumption of biochemical applications of air-lift reactors with im-
uniform bubble size distribution is not valid, mobilized cells or enzymes.

CE$50-Z3-H
3774 LJ. KUNDAKOVICand G. VUNJAK-NovAKOVIC
CONCLUSION ms mass of particle, kg
A two-dimensional DTFB operating with low-den- mp mass of tracer particle, kg
sity particles in the circulating regime was experi- nO Richardson-Zaki coefficient for bubbles
mentally studied in terms of the gas-liquid-particle rls Richardson-Zaki coefficient for particles
flow in the draft tube, and liquid-particle flow in the Ap pressure drop, Pa
annulus. Local velocities and holdups of solid par- qt input liquid flow rate, cm3/s
ticles, gas bubbles and the liquid phase were assessed Rb radius of the gas bubble, cm
in flow visualization studies. Flow behavior of the Ub local velocity of the gas bubble, cm/s
DTFB in the circulating regime was basically govern- Ubr bubble rise velocity, cm/s
ed by gas flux and bubble size. Liquid and particle Ug superficial gas velocity, cm/s
velocities in draft and annulus and the gas holdup all Ut superficial liquid velocity, cm/s
increased when the superficial gas velocity was in- U, particle settling velocity, cm/s
creased, while only slight effects of the net liquid flow v relative velocity, cm/s
rate and the particle volume fraction were observed. va liquid to particle relative velocity, cm/s
The existing theory of the two-phase flow proposed V volume of the compartment, cm 3
by WaUis (1969) was extended to describe three-phase Vb volume of a single bubble, cm s
flow in the draft tube by taking into account mo- x horizontal distance, cm
mentum transfer between (a) gas bubbles and liquid AXb mean horizontal distance between two ad-
phase, (b) liquid phase and solid particles, and (c) the jacent bubbles, cm
additional momentum transfer from gas bubbles to Xmax horizontal component of the maximum
solid particles, which was assessed in studies of par- bubble to particle axial distance, cm
ticle settling in three-phase flow (Kundakovic and X fraction of the area of influence of a fluidized
Vunjak-Novakovic, 1995). bed particle on the settling particle
The effects of gas bubbles on liquid and particle y=ax vertical component of the maximum bubble
motion were related to the changes in relative to particle axial distance, cm
velocities and drag forces on fluidized particles, which y vertical distance, cm
are induced by motion of gas bubbles. The overall Az height of the view area, cm
drag force on fluidized particles was significantly dif-
ferent in three-phase flow, when compared to Greek letters
liquid-particle flow. In addition, a decrease in mean at volumetric fraction of gas or solids in liquid
bubble diameter from 4 to 1 mm resulted in lower e phase holdup
momentum transfer from gas bubbles, indicating that p density, kg/m 3
only relatively large bubbles have a significant influ- ~2 two-phase friction multiplier
ence on circulating flow in DTFB. The proposed
model gave close predictions of liquid velocities and Subscripts
phase holdups in draft and annular regions of the A annulus
DTFB operating in the circulating regime. B bottom section
D draft tube
Acknowledgement--This work was supported by Research f friction
Council of Serbia Grant No. G14-03. 1 liquid
g gas
NOTATION p tracer particle
A surface area, cm 2 s solid
An available cross-section area for fluid flow w wall
from annulus into the draft tube, cm 2 x horizontal direction
Cd particle drag coefficient y vertical direction
db bubble diameter, cm 1 continuous phase
d~ particle diameter, cm 2 dispersed phase
D draft tube diameter, cm
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