-
Chemical Engineering Science. Vol. 48, No. 23. pp. 40234035,
1993. 000-2509,93 S6.W + 0.M Printed in Gnnc Britain. 0 1993
Pergamon Press Ltd
AN AVERAGE GAS HOLD-UP AND LIQUID CIRCULATION VELOCITY IN
AIRLIFT REACTORS WITH EXTERNAL LOOP
Z. KEMBLOWSKI. J. PRZYWARSKI and A. DIAB Department of Chemical
Engineering, Faculty of Process and Environmental Engineering,
Technical
University of L6di Wblczahska 175.90-924 L&IS% Poland
(First received 7 July 1992; accepted in revised form 12
February 1993)
Abstract-Experimental investigations were carried out in model
airlift reactors with external loops. Two reactors of laboratory
scale (height 1.95 m, internal diameter 0.1 m, volume 0.08 m3) and
pilot-plant scale (height 7.1% m, internal diameter 0.2 m, volume
0.7 m3) were used. The influence of reactor geometry, gas sparger
design, liquid properties (both Newtonian and non-Newtonian) and
the amount of introduced air was investigated. The influence of gas
sparger design on gas hold-up and liquid velocity was found to be
negligible. A modified method for the prediction of liquid
circulation velocity-based on the energy balance of the reactor-was
proposed. An original dimensionless correlation for gas hold-up
prediction involving superficial velocities of gas and liquid,
cross-sectional areas, as well as Froude and Morton numbers, was
obtained.
1. INTRODUCTION
During the last two decades a large number of papers concerning
airlift loop reactors have appeared. The principles of operation as
well as the advantages and disadvantages of this type of reactors
are discussed in the review papers (Chisti and Moo-Young, 1987;
Blenke, 1979, 1983; Schiigerl et al., 1977).
The basic hydrodynamic design parameters of an airlift loop
reactor are the average gas hold-up and liquid circulation
velocity.
1.1. Literuture survey Severai important papers dealing with the
two in-
terrelated parameters of average gas hold-up and liquid
circulation velocity have been published (Bell0 et aI., 1984, 1985;
Calve, 1989, Chisti et a& 1988; Chisti and Moo-Young, 1988;
Hills, 1976; Hsu and DudukoviC, 1980; Jones, 1985; van der Lans,
1985; Merchuk and Stein, 1981; Nicol and Davidson, 1988a,b; Philip
et al., 1990; Popovii: and Robinson, 1984, 1989; Roberts, 1979;
Vatai and Tekib, 1986; Verlaan et al., 1986a). Most of them
describe experi- mental investigations carried out for water-like
media in various model reactors of different geometries and mostly
laboratory scale [except the data presented by Hills (1976), van
der Lans (1985) and Nicol and Davidson (1988a, b)]. Only a few
papers concern highly viscous and non-Newtonian liquids (Chisti and
Moo-Young, 1988; Popovil: and Robinson, 1984; 1989; Philip et al.,
1990; Vatai and TekiC, 1986).
Some correlations for gas hold-up prediction have been proposed
in the literature (Bell0 et al., 1984, 1985; Hills, 1976; Hsu and
Dudukovie, 1980; Merchuk, 1986; Nicol and Davidson, 1988a,b;
Popovii: and Robinson, 1984, 1989; Roberts, 1979; Vatai and
Teki& 1986; Weiland and Onken, 1981). The greatest disadvantage
of most of the reported correla- tions is their dimensional form,
which means that the constants of the equations depend on the
geometry
and properties of the system. Only the correlations proposed by
Hsu and DudukoviC (1980) and Vatai and TekiC (1986) seem to be more
general than the others because they contain dimensionless
parameters such as Froude, Reynolds and Weber numbers, and
superficial velocities ratio of gas and liquid. However, there is a
lack of evidence showing that they have been applied for other
geometries. According to some re- searchers there is an obvious
need for studies of large- scale reactors (Blenke, 1979; Bello et
al., 1984).
Various equations for liquid velocity prediction have also been
reported in the literature, generally for water or similar liquids.
Most of them are simple correlations involving two or three
parameters (Be110 et al., 1984; Nicol and Davidson, 1988a,b,
Popovii: and Robinson, 1988; Roberts, 1979; Vatai and TekiC, 1986).
Some of them are semitheoretical model equa- tions derived from
energy or pressure balance equa- tions. They take into account most
of the known factors that influence liquid circulation but not all
of the terms involved are known or may be easily estim- ated for
calculations (Chisti et al., 1988; Chisti and Moo-Young, 1988; Hsu
and DudukoviE, 1980). There are also some very simple correlations
available de- rived from drift flux model but they take into
account neither the properties of gas and liquid nor the geometry
of the reactor (Calvo, 1989; Nicol and Davidson, 1988a, b).
Therefore, reported results are mostly limited to particular cases
for which they were obtained.
It follows from the above-mentioned literature data that there
are two main approaches to the modelling of liquid circulation
velocity in an airlift loop reactor. One of them begins with a
pressure balance over the circulation loop (Blenke, 1979, Hsu and
Dudukovik, 1980; Kubota et al., 1978; Merchuk and Stein, 1981;
Verlaan et al., 1986b). The other one begins with a total energy
balance of the reactor (Chisti et al., 1988; Chisti and Moo-Young,
1988; Calvo, 1989; Young et al., 1991).
4023
-
4024 2. K~MBLOWSKI et al.
Only the model proposed by Chisti and Moo- Young (1988),
concerning both Newtonian and non- Newtonian liquids, will be
discussed further because this approach seems to be more
convincing. The authors wrote the energy balance of the reactor in
the following form:
Ei=E,+ED+E,+ET+EF (1)
where Ei is the energy input due to isothermal gas expansion
E, is the energy dissipation due to wakes behind bubbles in the
riser,
E. = Ei -_p&,VLx&e~ (3)
I?,, is the energy dissipation due to stagnant gas in the
downwmer,
.% = PLgh, VU&&, (4)
& is the energy dissipation due to fluid turn around at the
bottom of the reactor,
z P&(1 -ed VLD 2
-AD (5) (1 -eD)
E, is the energy dissipation due to fluid turn around at the top
of reactor,
z PU --El!) VLR 2 (1 -.5x) AR (@
and finally EP is the energy loss due to friction in the riser
and the downcomer.
EF = APFa VLx AR + APp, VLD AD. (7)
Applying complicated experimental correlations for wall shear
stress in tube flow of gas-liquid mixture, given by Sokolov and
Metkin (1981) and Metkin and Sokolov (1982), Chisti and Moo-Young
(1988) de- veloped an equation for the prediction of liquid circu-
lation velocity (see Table 1). For the prediction of gas
hold-up-which is necessary for the calcula- tions-they recommended
the correlation proposed by Popovii: and Robinson (1984). This
correlation was obtained for power-law liquids in a laboratory-
scale model reactor.
Summing up, it follows from the literature review that
-the reported investigations were concerned mainly with
Newtonian liquids of low viscosity,
-the majority of the published data were obtained in
laboratory-scale model reactors, and
-the results of measurements were usually pres- ented in the
form of dimensional dependencies.
1.2. Scope of the work Taking into account the above statements
our in-
vestigations were concerned with highly viscous Newtonian and
non-Newtonian fluids. The experi-
ments were carried out in two external-loop model airlift
reactors of distinctly different geometries. The purpose of the
work was to develop
-a dimensionless correlation for the prediction of average gas
hold-up, and
-a simple method for the prediction of liquid circulation
velocity.
2. A MODEL FOR PREDICTION OF AVERAGE GAS
HOLD-UP AND LIQUID CIRCULATION VELOCITY
2.1. Gas hold-up It was decided to develop a classical
dimensionless
correlation for gas hold-up prediction in order to avoid the
modelling of gas-liquid interaction in a two- phase flow. Reported
results concerning the influence of various physical factors on the
hydrodynamics of an airlift reactor are often contradictory and
strongly affected by system properties. Therefore, they have
limited general importance [e.g. Nicol and Davidson (1988a,b) and
contradictory conclusions on surface tension influence reported by
Wachi et al. (1991)]. Let US consider a generalized Newtonian
liquid (i.e. purely viscous fluid with shear-rate-dependent
viscosity) whose rheological properties can be approximated by the
power-law model of Ostwald-de Waele. We as- sume, on the basis of
literature data and our own considerations, that the average gas
hold-up in the riser, &R, is a function of superficiti
velocities of gas, V,,, and liquid, VLR, densities of gas, Pc, and
liquid, pL, liquid rheological parameters, n and k, surface
tension, crL, height of the liquid head, H, cross-sec- tional areas
of the riser, AR, and downcomer, Ar,, total cross-sectional area of
holes or nozzles of the gas sparger, A,, and acceleration due to
gravity, g:
ER = I(v,R, VLR, PC, PL, n, k OL,, H, AD, AR, Ag).
(8)
A dimensional analysis leads to the following rela- tion between
gas hold-up and dimensionless moduli:
where the Froude number is defined as
Fr = (VLR + vGR)2 gdn
and the Morton number is defined as
(10)
4(n-1) / 3n + 1 14
\ 4n I *
A classical relation of Morton well-known numbers is as
follows:
Eo Wet MO=-
R&R
(11) number to other
(12)
-
Tab
le I.
Sele
cted lit
era
ture
corr
ela
tions f
or
the p
red
icti
on
of
gas h
old
-up
an
d li
qu
id c
ircu
lati
on velo
city
in a
irlif
t re
act
ors
Auth
or
Pro
pose
d co
rrela
tion
Exueri
menta
l range
Belle
et a
l., 1
984
Bell0
et a
l., 1
985
Ch
isti
et
al., 1
988
ER
=
,.I,(
I +
+s)
($>
VLR
=
Ch
isti
an
d M
oo-Y
ou
ng
, 1989
I +
~P&
&
_+L
!!
s ir
( >I
(I
-es)
* (1
-~
a)*
A
,,
-0
L
where
Ap =
4 D
7,
For
lam
inar
flow
:
ah
vt
Re,. 2000)
0.0792 f=- Ret
(18)
(19)
where the Reynolds number of the liquid is defined in the case
of the riser by eq. (15) and in the case of the downcomer by the
following equation:
ReL1, = VtDdh
* (20)
8m-,k
The above ranges of laminar and turbulent flow were proposed by
Hsu and DudukoviC (1980).
Combining eqs (l)-(6) and (17) for riser and down- comer
columns, a general equation for the prediction of the liquid
superficial velocity in the riser is ob- tained:
If the phases are almost completely separated at the top of the
reactor, gas hold-up in the downcomer is often less than 1%. In
this case eq. (21) can be re- written in the form
-
An average gas hold-up and liquid circulation velocity 4029
Equation (22) incorporates the geometrical dimen- sions of the
reactor, the Fanning friction factors in the riser and downcomer,
frictional loss coefficients at the top and bottom of the reactor,
and the gas hold-up in the riser. The geometry of the reactor is
known, the Fanning friction factors may be assumed roughly and
checked after calculations, and the frictional loss coef- ficients
at the top and bottom of the reactor may be taken from the
literature. The only unknown para- meter is the average gas
hold-up, which should be predicted separately.
3.1. Media 3. EXPERIMENTAL
Both Newtonian (tap water without and with added surfactants,
glycol, sugar syrup) and non- Newtonian media (power-law CMC
solutions) were used for investigations concerning verification of
energy balance approach. The following ranges of media properties
were obtained:
-liquid density pL = 998-1286 kg/m, - surface tension oL =
0.0420-0.08 16 N/m, -power-law parameter n = 0.758-1, -power-law
parameter k = 0.001-0.261 Pa s.
The properties of the experimental media for which the data
points presented in Figs 4-12 were obtained are summarized in Table
2.
3.2. Apparatus and procedure Two mode1 reactors were used for
the experiments.
One, of laboratory-scale, was 1.95 m high, of 0.1 m internal
diameter of the riser and the downcomer, and 80 dm3 volume. The
other one, of pilot-plant scale, was 7.18 m high and had a riser of
0.2 m internal diameter. It had two possible geometrical arrange-
ments, with the downcomer internal diameter equal to 0.15 or 0.2 m.
The total volume of the second reactor was 700 dm.
Liquid circulation was directed through one of the two
downcomers of the pilot-plant scale reactor by butterRy valves
placed in the bottom connections of the reactor. There were only
two possible positions of
the valves applied in the experiments-one totally open and the
other completely closed. The schematic views of the reactors and
the photograph of the upper part of the pilot-plant scale apparatus
are shown in Figs l-3.
Compressed air was introduced only through the bottoms of the
reactors by means of various gas spargers. There were gas spargers
containing porous plates made of glass beads of three different
size ranges: 100-160, la-250 and 250-500~. Each of them was applied
with three diameters: 30, 50 and 70 mm. Single-nozzle gas spargers
of six dia- meters-l, 1.4, 2, 2.8, 3 and 4 mm-were also used. For
the pilot-plant scale reactor only the 3 mm gas sparger was
applied.
Air flow rate, average gas hold-up in the riser and downcomer,
liquid velocity in the downcomer, pres- sure of compressed air,
temperature of the system and atmospheric pressure were measured
during the ex- periments. For each run properties of the liquid
phase were carefully determined. Rheological properties were
measured by means of the rotational rheometer Rheotest 2. Surface
tension was determined by the classical stalagmometric method.
Average gas hold- up was determined by means of the manometric
tcch- nique described by Hills (1976). The following equa- tion was
applied for the estimation of the average gas hold-up:
Ah, s=-
AZ
where Ah,,, is the difference of manometer readings and AZ is
the vertical distance between the connec- tions of manometers to
the column.
Liquid circulation velocity was measured in the downcomer
according to the flow follower method, described previously by
Jones (1985) and Philip et al. (1990), and modified by Diab (1991).
Separation of phases was complete at the tops of the model
reactors. Therefore, only a single-phase flow existed in the
downcomers. In this way, it was possible to determine the liquid
superficial velocity in the riser applying the continuity equation
for liquid flow. The procedure for evaluation of the mean linear
velocity of the liquid in the downwmer was as follows:
Table 2. Properties of experimental media used for data
presentation in Figs 4-12
Figure
4
5, 8
6, 9
7, 10
Medium
Glycol solution
Water Water with surfactant Glycol Glycol solution Sugar syrup
CMC solution
Water CMC solution
Water
Power-law parameters Density Surface tension k b/m) V/m) n (Pa
s)
1011 0.0699 1 0.0015
1000 0.0735 1 0.001 997 0.0690 1 0.001
1115 0.0420 1 0.0176 1011 0.0699
: 0.0015
1284 0.0814 0.141 1010 0.0769 0.758 0.261
998 0.0726 1 0.001 1018 0.0802 0.855 0.212
998 0,0726 1 0.001
-
4030 Z. KEMBLOWSKI et a/.
Fig. 1. Schematic diagram of the laboratory scale airlift model
reactor with external loop.
- The velocity of small thin aluminium flakes floating in the
liquid was measured in the down- comer 10 to 15 times in order to
obtain the maximum velocity in the axis of the column,
- According to the velocity profile determined previously as a
function of Reynolds number of the liquid in the downcomer, the
mean linear velocity was calculated. All details were given by Diab
(1991).
4.1. 4. RESULTS AND DISCUSSION
Gas spargers The influence of gas sparger geometry on the
aver-
age gas hold-up in our model reactors, despite the changes
offlow regime from uniform bubbly to chum- turbulent flow, has
proved to be negligible during the experiments. Figure 4 presents
some experimental data obtained in the model reactor of laboratory
scale for ethylene glycol solution and for various gas spargers.
For other media the results are similar. Therefore, the correlation
obtained for gas hold-up prediction, proposed below, can be
regarded-as a first approximation-as being independent of gas
sparger geometry.
4.2. Gas hold-up The gas hold-up data obtained in our two
model
reactors-as well as other complete data available in the
literature (Bell0 et al., 1985; Merchuk and Stein, 1981; Roberts,
1980) concerning airlift external-loop reactors with complete phase
separation at the top-were applied in order to obtain a
dimensionless correlation for gas hold-up prediction. The final
form
Fig. 2. Schematic diagram of the pilot-plant scale airlift model
reactor with external loop.
of the equation is
(24)
The range of experimental data used to develop eq. (24) was as
follows:
Ea = 0.002-0.21
V,, = 0.001-0.50 m/s
V,, = 0.07-1.3 m/s
V -YE = l-153 V CR
Fr = 0.00-14.1
MO = 2.47 x lo- -0.390
AD - = 0.11-l. AR
Additionally, geometrical parameters not included in the
correlation were of the following ranges:
H - = 10.2-22s DR
A AR = (5.60-360) x lo- 5
ReLR = 40-130,000.
-
An average gtts hold-up and liquid circulation velocity
Fig. 3. View of the upper part of the pilot-plant scale airlift
reactor with external loop.
The exponent of the Morton number in eq. (24) is actually very
small. One may, therefore, expect that the Morton number is
negligible. However, the range of numerical values of this number
for the experi- mental data is so wide that even taking the power
to be 0.012 it changes from 0.746 to 0.989.
Plots presenting the dependencies of the experi- mental values
of the average gas hold-up as a function of gas superficial
velocity, obtained in our model reactors, are shown in Fig. 5. They
illustrate a strong influence of liquid properties and reactor
geometry on
the results obtained. The values of the experimental average gas
hold-up in the riser are plotted against those calculated using eq.
(24) in Figs 6-8. Their com- parison shows a satisfactory validity
of eq. (24) with up to f20% deviation.
4.3. Liquid circulation velocity Hots presenting the
dependencies of the experi-
mental values of the liquid superficial velocity in the riser as
a function of gas superficial velocity, obtained in our model
reactors, are shown in Fig. 9. They
-
2. KEMIILOWSKI et al. 4032
0.07
O.Ci5
0.05
0.04
I -=0.03
0.02
O.oi
n
A 4A 0
0
0.00 L 0.00 0.06 0.10 O.i5
OR Imlsl
Fig. 4. Experimental values of the average gas hold-up in the
riser column of the laboratory model airlift reactor obtained for
various gas spargers (experimental medium-glycol solu- tion);
single-nozzle spargers: (0) 4 mm; (A) 2.8 mm; (I) 2 mm; (A) 1.4 mm;
(Cl) 1 mm; porous-plate spargers: (0)
3Omm;(+)50mm;(V)70mm.
J
V, Lm/sl
Fig. 5. Experimental values of the average gas hold-up in the
riser column of model reactors; laboratory scale model reac- tor
(single-hole gas sparger 2.8 mm), experimental media: (0) water;
(0) water with added surfactant; (A) glycol; (A) glyml solution; (
W) sugar syrup; (Cl) CMC solution; pilot- plant scale model reactor
(single-hole gas sparger 3 mm), water: (0) AD/AR = 1; (V) AD/AR =
0.56; CMC solution:
(+) AD/AR = l;(V) AD/AR =0.56.
illustrate a strong influence of liquid properties and
reactor geometry on the results obtained. Fig- ures lo-12
present a comparison of the proposed model with our experimental
data and the data given by Roberts (1979). One may see that over a
large range of reactor size and liquid properties, the pro- posed
model predicts liquid superficial velocity in the riser with up to
+ 20% error. The higher deviation of the calculated values observed
in the range of small velocities (i.e. in the laminar region) may
be caused by the assumption that friction loss coefficients at the
top and the bottom of the reactor do not depend on the superfkial
Reynolds number of the liquid. Therefore,
0.06
1 0.04
1 Ox)3 . 0.02 S
0.0 1
0.00 0.00 0.0 1 0.02 0.03 0.04 0.06 0.06
en. predicted 1-l Fig. 6. Comparison of the experimental values
of the aver- age gas hold-up in the riser column of the laboratory
model airlift reactor with those. predicted by eq. (20);
single-hole gas
sparger 2.8 mm (symbol; asin Fig. 5).
J 0.00 0.0 1 0.02 0.03 0.04
6, Cxedlcted I-l
Fig. 7. Comparison of the experimental values of the aver- age
gas hold-up in the riser column of the pilot-plant model airlift
reactor with those predicted by eq. (20); single-hole gas
sparger 3 mm (symbols as in Fig. 5).
slightly too conservative values of these coefficients are used
in the calculations in the laminar region (the values of the
coefficients actually used are sum- marized in Table 3).
Two basic equations [eqs (22) and (24)] enable the
prediction of the liquid circulation and gas hold-up in airlift
external loop reactors with almost complete phase separation at the
top. These parameters can be predicted provided the geometry of the
reactor, the liquid properties and the amount of gas to be intro-
duced are known. The procedure for the prediction of the gas
hold-up and liquid circulation velocity in the riser can be
summarized as follows:
(1) Assume liquid superficial velocity in the riser. (2)
Estimate gas hold-up using eq. (24). (3) Predict liquid velocity
using eq. (22) and other
related equations.
-
An average gas hold-up and liquid circulation velocity 4033
-I
0.20 0.30 0.40
en. aedcted f-1
Fig. 8. Comparison of the experimental values of the aver- age
gas hold-up in the riser column of airlift reactor, pub- lished in
the literature, with those predicted by eq. (20) (experimental
medium-water); Be110 et al. (1985): (A) AD/AR=0.25; (V) AD/AR =
0.11; Roberts (1979), AD/AR = 1: (0) ID 75 mm; (I) ID 25 mm; (0)
Merchuk
(1986), AD/AR = 1.
I
Fig. 9. Experimental values of the liquid superficial velocity
in the riser column of model reactors (symbols as in Fig. 5).
(4) If the assumed and calculated values of the liquid velocity
do not agree satisfactorily, then return to point (2) with the last
calculated value of the liquid velocity until sufficient agreement
is obtained.
5. CONCLUSIONS
The results of the experimental investigations pres- ented lead
to the following conclusions:
-The influence of the gas sparger geometry on the average gas
hold-up proved to be negligible, despite the observed changes of
flow regime from uniform bubbly to churn-turbulent flow.
-The liquid circulation velocity cannot be directly related to
the gas superficial velocity because it depends also on reactor
geometry and gas and liquid properties.
Fig. 10. Comparison of the experimental values of the liquid
superficial velocity in the riser column of the laboratory model
airlift reactor with those predicted by the proposed
model (symbols as in Fig. 5).
f ,
-1 0
, v o 0 _-,f-p 0 ,e*
, 4
I #I
, , I 1 ii/
_- ,.*~~,o
,* , ,?-
-
4.034 Z. KEMFJLOWSKI et al.
Table 3. Values of the local friction factors applied in the
calcu- lations, according to Maksimov and Orlov (1949)
Experimental data obtained in/by
Laboratory scale model reactor 1.8 1.3 Pilot-plant scale model
reactor, 200/200 mm 2.95 1.3 Pilot-plant scale model reactor,
200/150 mm 3.01 1.43 Roberts, 1979 2.4 2.4
-The same conclusion is valid for the average gas hold-up.
-The simple model [see eqs (H-(22)] proposed for the prediction
of the liquid circulation velo- city in an airlift reactor with
external loop gives satisfactory results in a relatively wide range
of physical and geometrical parameters for both Newtonian and
nun-Newtonian liquids.
-The proposed dimensionless correlation for the prediction of
the average gas hold-up in the riser column of an airlift reactor
with external loop [see eq. (24)] also gives satisfactory results
for a relatively wide range of physical and geometri- cal
parameters for both Newtonian and non- Newtonian liquids.
Acknowledgement~The authors acknowledge the financial support
provided by the Polish State Committee of Scientific Research
(Grant no. 3 1266 9101).
A d E Eo
f Fr
9 h, H k L MO
;
Q Re
V We Ah
AP AZ
NOTATION
cross-sectional area, m* internal diameter, m energy dissipation
or input rate, W Eijtvijs number, defined by eq. (13) Fanning
friction factor Froude number, defined by eq. (10) acceleration due
to gravity, m/s2 height, m power-law parameter, Pa s length of the
tube, m generalized Morton number for power-law liquids, defined by
eq. (11) power-law parameter pressure, Pa gas flow rate, m3/s
Reynolds number, defined by eqs (15) and
(20) superficial velocity, m/s Weber number, defined by eq. (14)
height difference, m pressure drop, Pa vertical distance of
manometer connec- tions, m
Greek letters & gas hold-up,
e friction loss coefficient
p viscosity, Pas
P density, kg/m3 d surface tension, N/m
Subscripts B bottom of the reactor d gas-liquid dispersion D
downcomer et7 effective F friction G gas phase h head space i input
L liquid phase m manometer
: nozzle or hole of the gas sparger riser
T top of the reactor
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