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Liquid circulation in a draft-tube bubble column
Chemical EngineeringScience Printed in Great Britain.
Vol. 40. No. 3. pp. 449-462.
1985
ooo9-2509/85 53.Gtlt .Oa m 1985 Pergamon Press Ltd.
LIQUID CIRCULATION DRAFT-TUBE BUBBLE Department
of Chemical
IN A COLUMN
A. G. JONES
and Biochemical Engineering, University College London, London WClE 7JE, England
(Received
5 December
Torrington
Place,
1983; accepted 14 February 1984)
study of liquid circulation in a draft-tube bubble column (250 mm diameter, 60 1. capacity) using a flow-follower technique is reported. It was observed that annulus liquid circulation velocity increased to a maximum with air flowrate and a maximum in the volumetric liquid circulation rate occurred at a tube: column diameter ratio of about 0.5. A simple model based on air-lift pump theory is used to predict liquid circulation velocity using either pressure drop or air flowrate data. Reasonable agreement is found for narrow draft-tubes ( 5 121 mm) at low gas flowrates ( I 400 ml./s) but with significant deviations occurring with larger draft-tube diameters. These are thought to be due to secondary liquid flow within the draft-tube reducing primary liquid circulation. At higher gas flowrates bubble entrainment into the annulus becomes increasingly significant at all diameter ratios and the simple air-lift model is then inapplicable. Abstract-A
INTRODUCTION
Bubble columns are widely used in the processing industries to mix and aerate liquids. The introduction of the gas phase induces liquid circulation and the flow obtained can be stabilised using a central drafttube to create a primary liquid circulation pattern. Bubbles rising through the draft-tube (riser) are disengaged at the top (head) and at higher velocities some bubbles may be entrained into the annulus (down-comer) with the circulating liquor. Since liquid mixing rates are dependent on fluid velocities a knowledge of the flow characteristics of such vessels is required if their performance as chemical reactors or fermentors for example is to be predicted. Bubble columns both with and without draft-tubes have been the subject of increasing interest in recent years. One of the earliest studies of the draft-tube bubble column (DTBC) was by Lamont[l] who predicted the liquid circulation rates in a “Pachuca tank” using air-lift pump theory[2]. In this semiempirical model the energy transferred as the air expands in rising through the vessel is corrected for energy dissipation due to bubble “slip” and the remainder gives rise to velocity heads associated with liquid flow in the vessel. Reitma and OttengrafU] later presented a theoretical model based on minimum entropy production and a momentum balance was developed to predict the diameter of the “bubble street” and laminar liquid circulation velocities in a gas sparged column filled with glycerol. Freedman and Davidson[4] also modelled the liquid circulation in a DTBC based on an energy balance and measured gas hold-up but not liquid circulation velocities. Dussap and Gros[5] considered the kinetic energy transfer in 449
a DTBC fermentor in addition to gas expansion but neglected bubble slip. A number of other studies of liquid circulation in draft-tube bubble columns have been reviewed recently by Blenke[6] and by Reitma[q. The present paper presents data of the internal liquid circulation rate in a DTBC in which compressed air provided the motive force to promote circulation of water in essentially turbulent flow over a range of draft-tube diameters and gas flowrates[8]. It then compares them with the predictions of a simple model developed from air-lift pump theory applying to conditions prior to bubble entrainment which is solved using either pressure drop data or gas flowrate data coupled to expressions for bubble size and rise velocity.
THEORY
Energy
balance
The work done in promoting liquid circulation is equal to isothermal work done by the bubbles of gas expanding through the liquid contents of a vessel and is approximately given by:
W =
V,Q, Iwe
P, + p&L PI
(1)
where PI is the pressure of gas at the column head, Q, is the volumetric gas flowrate, P,,, is the density of the two-phase mixture of height H,,, and q is the efficiency of energy transfer. At higher gas flowrates the kinetic energy of the gas may become significant[S] but may be neglected at the lower flowrates employed in the present study.
A. G. JONES
450
In effect, the introduction of the gas phase to the draft-‘tube creates a density gradient which induces circulation between the riser and the downcomer sections. This density gradient is clearly due to the gas void fraction and this in turn depends on the relative velocity of gas and liquid. In general the gas rises faster than the liquid and the greater is this ratio the lower is the gas voidage fraction and hence driving force for circulation at a given gas flowratc. Slip velocity
The principle of the DTBC is similar to that of the air-lift pump. In these devices not all of the energy in the compressed gas is transferred to cause liquid motion but some is “lost” due to “slip” i.e. due to the relative velocity between gas and liquid resulting in turbulent energy dissipation[l, 2,9, lo]. Nicklin has shown[9] that the efficiency term is then simply related to the relative flowrates of liquid and gas and this can be given here by an expression of the form:
reversal’* as the fluid leaves the annulus and drafttube respectively:
z = (u,’ + Vd2)/%
where v, is the annular liquid velocity. Entrance, exit and pipe friction losses etc. are ignored as they are generally less significant[9]. It is implicit that the DTBC bc designed such that constrictions to flow at the base and head are avoided by suitable geometric arrangement, i.e. by maintaining an adequate crosssectional area for flow at all points in the loop. The work done to create the total hydraulic head by promoting liquid circulation is also given by:
w= wgz
p,+p,
where vd is the liquid velocity in the draft-tube and v, the slip velocity. Thus for the DTBC the work done to promote liquid circulation in the absence of bubble recirculation into the annulus (i.e. e., = 0) is given by: (3)
ci&v, = p&4&
Ld =
the liquid fraction may pressure gradient by:
where us is the gas velocity. Or, in terms of superficial gas velocity, us and draft-tube voidage, &,,:
(1 -+)=
v, = -% -
Ho _= Hf?l
i.e.
Q* -
(10)
(11)
be simply related to the
-g
(12)
v,j
Ed
a* = -
,,(Lq.z).
Hm-Ho Xl
(4)
Vd
-
Alternatively, since gas voidage in the draft-tube is defined by the expression:
By definition the slip velocity is given by the expression: v, = us -
(9)
where w is the mass flowrate of liquid. Hence combining eqns (7), (8) and (9) and noting that pm = p,( 1 - ~3 since plr< Pe a relationship is obtained between the liquid velocities and gas void fraction:
PlneL
PI ‘YHm)}(&).
(8)
0,
+d
where A, is the cross-sectional area of the draft-tube. Thus substituting for v, in eqn (3) gives: (7) Total head The work done by the bubble phase creates a head
of flowing fluid. Freedman and Davidson[4] have proposed that the total hydraulic head of liquid, Z, may be simply defined from Bernoulli’s equation as the sum of the liquid velocity heads in the draft-tube and annulus respectively, i.e. the “head loss due to
--= dh dH
fld
(13)
where fld is the dimensionless pressure gradient in the draft-tube. Thus eliminating cd and H,,, between cqns (10) and (13) gives: P,lOL(l
+55=p&+J(5.!+L).
(14)
which relates the work done by the expanding gas to the head of flowing liquid. Liquid
circulation
velocity
Since there is no nett flow from the column the primary liquid mass flowrates in draft-tube and annulus are equal and so from continuity: P,Q, = P&d
(15)
451
Liquid circulation in a draft-tube bubble column
or in terms of liquid velocities and column geometry: (16)
%%I = (1 - 0%&Y
i.e. the draft-tube and annulus liquid velocities are related by the expression: (17) where u is the annulus: draft-tube area ratio. Equations (14) and (17) may now be combined to give the relationship between the liquid velocity in the annulus and the pressure gradient in the draft-tube:
Hence, the annular liquid velocity, v,,, may now be predicted from eqn (21) for a given superficial gas velocity, s, single bubble rise velocity, v~, and drafttube: column diameter (or area) ratio (i.e. a). Bubble rise velocity Thus the remaining unknown quantity is the bub-
ble rise velocity, v,, and this may be predicted by the method of Mendleson [12], for example, from the expression:
C-W where d, is the equivalent bubble diameter in the liquid. This quantity may be obtained for perforated plate gas dispersers used here from several equivalent correlations, e.g. that due to Koide et al.[13]:
Hence if the pressure gradient, fld (or alternatively voidage, ~3, is known for a particular DTBC the resulting annular liquid circulation velocity, V, (or alternatively rod)may be predicted. This theory may now be extended by eliminating the pressure gradient, fid, from eqn (18) by use of the voidage-velocity relationship for two-phase bubbly flow. Unfortunately there is as yet no agreement on a general model but the simplest expression of this type relates system voidage, ed, to the superficial gas velocity, us, liquid velocity, u,, and rise velocity of a single bubble, vSbrin the form[l I]: u,( 1 - cd, - U&j = U&, = rY&( 1 - 6&1
(19)
where it is assumed that v& is independent of e which is reasonable as 6 + 0 although clearly a development could include a voidage dependency at high gas hold-up. Solving for ~~ gives: E,,= @(c,
+ od) = 1 - &.
(20)
Substituting for cd in eqn (18) and noting that for bubbly flow /Id N 1 then the following cubic equation in v, results: a3vm3+ a2v,’ + a,v, + a, = 0
Thus the liquid circulation velocity may now be predicted simply as a function of gas flowrate within a DTBC of given geometry. Bubble
entrainment
Freedman and Davidson[4] found that while at low velocities essentially clear liquor circulates down the annulus, bubble entrainment occurs when the superficial velocity of the downflowing liquid equals the bubble rise velocity. The voidage and velocity are then uniquely defined for a given bubble size and a graphical method of solution was proposed based on the expression due to Marrucci[lrl]. Plainly, when bubbles are entrained down the annulus the gas is compressed in a manner analogous to the expansion up the draft-tube. Thus some work is effectively recovered by the gas reducing that transferred to promote liquid circulation and eqn (7) can then be written as:
w =
PJlog(P’ +~ff~))EdAdud
(21)
- P,(lo&(p’
+~Ho))~nA~v.
(28)
where: or, as &+O: %=
-:+oge(l
+~)}uJ(l
+cr2)
(22) W = P,(lo&(p’
+THo)}
(cd -
EJA,~,
(29)
= 2gH,u,l(1 + a *) a, = 0
(23)
a, = v,
(24)
a3 = a.
(25)
A further simplification can be made to eqn (29) if it is noted that for pogHo/P, < 1 then lo&(1 + p,gH,/P,) = p&Ho/P, and thus eqn (14) becomes of the form: H&E
=
(V,’
+
V,‘)/&
(28)
452
A.
G.
and is then in a form similar to that of Freedman and Davidson [4] where de = e,+- E,. Thus the presence of bubbles entrained into the annulus (i.e. at values of co > 0) will tend to offset the head difference i.e. the driving force for liquid circulation. However, this is beyond the scope of the present paper since facility was not available to determine annulus void fraction. The present study is largely concerned with low velocity single phase flow in the annular downcomer (i.e. L, = 0) and it determines the conditions at which the transition to entrained flow commences. Further development will concern prediction of the annular voidage at higher flowrates and its effect on liquid circulation. EXPERIMENTAL
Description of apparatus The apparatus used is shown schematically in Fig; 1. The column (60 1.) was constructed from six 250mm i.d. QVF pipe sections each having two 38 mm i.d. horizontally opposed side arms inclined downwards at 30” to the horizontal. The column sections were bolted together vertically using QVF flanges and compressed asbestos fibre gaskets. The base of the column was a 250/38 mm pipe reducing section. The draft-tubes (44 mm, 70 mm, 96 mm, 121 mm, 146mm i.d.) were constructed from cast perspex tubes of 3 mm wall thickness and 1.22 m in length. Each tube was fitted with 3 support legs made from 6 mm thick Perspex sheet. The legs were shaped in order to fit the curvature of the inside of the base of the column so as to locate the draft-tube in a central position 100 mm above the base. An adjustable spider clamp made from 25 mm brass strip was fitted to the top of the draft-tube and was made 6rm by screwing the arms outward to make firm contact with the internal wall of the column. In this way each of the five draft-tubes could be firmly located centrally in the column and could be easily removed. Each of the tubes was drilled with four 13 mm diameter holes at 262 mm intervals to provide an entry into the two-phase region inside the draft-tube for the manometer probes. Four manometer tubes were made from 6mm bore glass tubing and were connected by means of rubber pressure tubing to the manometer probes via the column side arms. The side arms were fitted with rubber bungs which were bored and had a short piece of glass tubing passed through them in order to connect the manometer tubes on the outside to the manometer probes on the inside. The probes were made from the same bore glass tubing as were the manometer tubes. The probes were bent to provide a vertical upwards directed end in the centre of the draft-tube and passed through the four holes in the draft-tube wall which were fitted with rubber grommets to provide a seal and support to the probes. The gas disperser was made from a 76 mm dia. stainless steel disc (3 mm thick), perforated with twenty-five 2.4mm holes on a triangular pitch. The chamber was 13 mm deep and was mounted on a Neoprene rubber gasket. The disperser was con-
JONES
nected to the air supply via a 13 mm i.d. stainless steel pipe which passed through a rubber bung in the base of the column. Plasticine was used to fill the dead space in the base below the level of the disperser disc. The air was supplied from a compressor delivering 600 kNm-’ and reduced to 50 kNme2. The air flowrate was measured with a rotameter which was calibrated using a continuous flow meter and passed via a non-return valve to the disperser.
Procedure The column was filled with 60 1. of soft Manchester tap water which provided an initial depth of 1.33 m. Bath experiments were conducted for each of the five draft-tubes. The manometers were allowed to fill with water and any air was removed from their lines. The air was turned on and passed through the disperser and up the draft-tube and left via the disengaging section at the top of the column. When a liquid circulation pattern had established itself the liquid velocity down the annulus was measured. The range of air flowrates used was 100-575 ml./s equivalent to 0.24-1.38wm, i.e. substantially below that (2wm) required for significant kinetic energy contribution [5]. The liquid circulation velocity in the annulus was measured using a “flow follower*’ made from a piece of Nylon tubing 13 mm long x 6.5 mm bore. Each end of the tube was plugged with rubber and its density adjusted to that of tap water by injecting water from a syringe into the space created by the rubber blocking each end of the tubing. In this way small changes in density could be compensated for thus making the flow follower the same density as the water at ambient temperatures. This is important since if the flow follower is either too heavy or too light it will sink or rise relative to the liquid flowing leading to erroneous results. Care was taken to ensure that the flow-follower was well-wetted and it was observed to flow at the same velocity as tiny bubbles in the liquid. The flow-follower was timed between two unobstructed positions in the annulus in a vertical line. Each time the flow follower passed a chosen reference point in the annulus a digital clock was started and then stopped when it passed a second reference point. About 50 such readings were taken at each volumetric air flowrate in order to obtain the mean velocity of the liquid circulation in the annulus. It was considered that for turbulent flow this procedure would give a reasonable estimate of mean velocity but unfortunately estimates of dispersion are not available. The pressure gradient in the two-phase section (inside the draft-tube) was obtained by measuring the height of the liquid in the manometer tubes above their datum. The head of liquid thus obtained was plotted against the height of the manometer datum above the disperser, h, the slope of these graphs being the pressure gradient in the two-phase section of the column
Liquid circulation in a draft-tube
bubble
453
column
-I-)C manometers
3
-
disengagement z0ne (head)
draft-tube (riser)
liquid flow (downcomer)
1
I
t
&as
disperser
+ Air
inlet
Drain
Fig. 1. Schematic diagram of the apparatus.
454
A. G. JONES
I
0.1
I
0.
0.
0.1
8 I
0.L
p 3 c
.o
z
L
P 0
0.0
z >
0 i7
0.0
g
Drafttube Diameter
0.0.
Area Ratio
0.02 I +
121 146
2.5 1.3
0.01
I””
L””
3””
400
Fig. 2. Effect of air flowrate on draft-tube gas voidage fraction.
500
600
455
Liquid circulation in a draft-tube bubble column
I
I
l
Equation
l
I
I
I
I
l
21
Equation
18
/
entrainment
l
Experimental
Fig. 3. ElTect of air flowrate on liquid circulation velocity (d = 44 mm).
456
A.G.JoNEs
8
l
l l l
l
.
.
.
Experimental
0
I
100
1
200
I
300
I
400
I
500
Fig. 4. Effect of air flowrate on liquid circulation velocity (cI = 70 mm).
I
600
Liquid circulation in a draft-tube bubble column
24,
18
+ 0
l
15
4
l
large bubble \ 12
entrainment
0
l l l
:/
9
/
l l
6_
l
Experimental
/
I
100
I
200
1
300
1 400
I
500
Fig. 5. Effect of air flowrate on liquid circulation velocity (d = 96 mm).
IL-
61 oo
A. G. JONES
458
I
I
-
I
Equation
I
I
I
21
. entrainment
. 0
l
0
100
200
Experimental
300
400
500
Fig. 6. Effect of air flowrate on liquid circulation velocity (d = 121 mm).
600
Liquid circulation in a draft-tube bubble column
I
I
I Equation
21
and
I
I
I
26 bubble
\ 24_
459
rise
velocity
-
l
0
oeo**,
l 0 l
l
large bubble
I
entrainment
0
Experimental
3
0
I
I
I
I
I
I
100
200
300
400
500
600
Fig. 7. Effect of air flowrate on liquid circulation velocity (li = 146 mm).
A. G. JONES
Air
o-3
o-4
II&/S
575
A
o-2
Flowrate
0
325
v
250
D
200
o-5
O-6
0’7
Fig. 8. Effect of diameter ratio on volumetric liquid circulation rate.
Liquid circulation in a draft-tube bubble column DISCUsSION of gas flowrate When the air was
OF RESULTS
Eflect
turned on the contents of the column naturally rose to accommodate the volume of air introduced into the liquid. A noticeably convex section of high gas holdup was created above the level of the top of the draft-tube where the air disengaged from the water. A pressure gradient was developed in the range 0.90-0.99[8]. Draft-tube voidage calculated from eqn (12) is shown as a function of gas flowrate in Fig. 2. A circulation pattern was quickly established with the air/water two-phase mixture flowing up the centre in the draft-tube and the water flowing downwards through the annulus to be drawn into the draft-tube again by the air entering the column at the base. It was interesting to note that although the internal diameter of the smallest draft-tube was less than the diameter of the disperser, all the air was drawn inwards and passed through the draft-tube with the liquid. Calculation of annulus Reynolds numbers Re indicated turbulent flow existed in all runs except those with the largest diameter draft-tube. Bubble diameters were calculated to be in the range 8.5-9.7mm with corresponding rise velocities approximately constant at 250 mm/s (not shown here) [S]. At high superficial gas flowrates and for large diameter draft-tubes (with correspondingly high liquid velocities) air bubbles were entrained into the annulus and were held virtually stationary by the drag of the downwards flowing liquid. It was observed that as expected bubbles of decreasing diameter were drawn further down the annulus than large bubbles. Near the top bubbles of ca. 10 mm dia. were held stationary while below about 600 mm from the top of the draft-tube only tiny bubbles were observed ( -z 1 mm) and only at high superficial gas velocities and thus it was decided that the “flow follower” measurements of the annular liquid velocity should be made below this point. The effect of air flowrate on liquid circulation velocity for each drafttube diameter is shown in Figs. 3-7. The largest diameter draft-tube (d = 146 mm) gave the highest liquid circulation velocity in the annulus. However, this did not correspond to the highest volumetric flowrate of circulating liquid (see later). The volumetric liquid circulation flowrate increased with increasing gas flowrate for all draft-tube diameters. For the smallest draft-tube (d = 44 mm) the rate of increase was slight compared with that of the largest tube. In all cases there was a point after which any increase in the volumetric gas flowrate produced no increase in the liquid circulation rate. It was approximately after this point that there was a steadily increasing number of large bubbles entrained into the annulus and the accuracy of the flow follower measurements became doubtful. Similar bubble entrainment behaviour has been reported recently by Fields and Slater[l5] in a study of mixing in a 152 mm dia. DTBC using 95 mm dia. draft-tubes of various lengths.
Eflect
of draft-tube
461 diameter
It is apparent that there would exist a diameter of draft-tube at which there is a maximum volumetric liquid circulation. The two intermediate sized drafttubes used (d = 96 mm and 121 mm) allowed the most liquid to circulate through the annulus at any given volumetric gas flowrate. The effect of the d/D ratio (where D is the diameter of the column) on liquid circulation at constant volumetric gas flowrate can be most clearly seen in Figure 8 where the “optimum”, i.e. maximum flowrate, appears at about d/D = 0.5, i-e. where the diameter of the draft-tube is equal to the hydraulic diameter of the annulus. This compares with an optimum diameter ratio of 0.59 reported by Blenke[6] for a jet loop reactor, i.e. a DTBC with a gas nozzle (rather than disperser). (For single phase flow the optimum circulation would occur at d/D - 0.71[16]). Circulation models The simple circulation model described above was
solved numerically using a NAG routine and was tested over the range of operation used experimentally. Thus eqn (18) was tested using the pressure gradient data determined in this work[S] and the extended
model incorporating
the relationship
eqn (21).
for bub-
was also tested over the same range of operation. The physicai property data used are given in Table 1. The predictions for these methods are also summarised in Figs. 3-7 where the experimental annular liquid velocity is compared with that predicted for each of the five draft-tube diameters as a function of gas flowrate. At low velocities the predictions from eqn (21) compare fairly well with those of eqn (18). However, for the smallest diameter draft-tube (d = 44 mm) the experimental circulation velocity at low gas flowrates was higher than that predicted, as shown in Fig. 3. It is thought that for this case where the circulation velocities are low compared with those for larger tubes at the same volumetric air flowrate the flow pattern may have been significantly hindered by the manometer probes passing through the annulus to the draft-tube. The majority of flow follower measurements were taken in that part of the annulus where its flow path was unhindered by the manometers with correspondingly higher liquid velocities. For d = 70 mm the velocity predictions are within approx. + 20% as shown in Fig. 4. For d = 96 mm both methods predict circulation velocities approx. 33% higher than those obtained experimentally as shown in Fig. 5. As the draft-tube diemeter is increased the models predict increasingly higher values and the predictions are finally limited here by the single ble velocity,
Table 1. Physical Property Data
A. G. JON=
462
bubble rise velocity eqn (26) which is clearly an overestimate as shown in Figs. 6 and 7. Hence for dfD < 0.5 and 44mm -z d -z 121 mm the predicted values of liquid circulation using eqns (18) and (21) are within + 33%. Where d > 121 mm the models predict much higher liquid circulation than was obtained experimentally. This deviation from theory is thought to be largely due to two main reasons. Firstly, as mentioned earlier, air distribution is an important factor of determining the amount of liquid circulated and the predictions for the two larger diameter draft-tubes (d = 121 mm and 146 mm, d/D > 0.5) indicate that a secondary circulation pattern occurred within the draft-tube itself and some liquid was thus not entering the annulus. It .should also be noted that the diameter of the air disperser was not increased as draft-tube diameter was increased_ If it had been it is possible that circulation within the draft-tube would have been suppressed and a better agreement between experiment and theory obtained at this extreme of diameter ratio. Secondly, bubble entrainment into the annulus was more significant at larger diameter ratios and at higher gas flowrates thereby reducing the driving force for circulation. On the larger scale pipe friction losses may also become significant but cannot be considered further here.
NOTATION
cross-sectional area, m* internal diameter of draft-tubes, m equivalent bubble diameter, m perforated plate hole diameter, m internal diameter of column, m manometer level, m depth of liquid in column, m pressure, N/m’ volumetric flowrate, m’/s superficial velocity, m3/m2s absolute velocity, m/s volume of gas per liquid volume, per min[5], min-’ mass flowrate, kg/s work, W total hydraulic head, m
A d d, dh D h H : u V vvm
W
W Z Greek a
b L p o p
symbols
ratio of annulus: draft-tube cross-sectional areas dimensionless pressure gradient gas voidage density, kg/m’ surface tension, J/m2 viscosity, Ns/m2
Subscripts CONCLUSIONS
has been shown that in a draft-tube bubble column in which an air/water mixture rises through the draft-tube and the water circulates downwards through the annulus the volumetric liquid circulation rate and circulation velocity are dependent on the inlet gas flowrate and the diameter of the draft-tube. It has been found experimentally that increasing gas flowrate increases annular circulation velocity to a maximum for each draft-tube diameter and the maximum liquid circulation occurs at a diameter ratio d/D = 0.5 in the column studied. This corresponds to equal hydraulic diameters. The simple model used in predicting the annular liquid velocity is satisfactory for the small draft-tubes (d I 121 mm) at low gas flowrates (Qb I 400 mL/s) but at larger diameter ratios the model predicts increasingly excessive liquid circulation. These deviations are thought to be due to the wider draft-tubes having poorer uniformity of air dispersion and a secondary flow pattern occurs within the draft-tube itself at the expense of primary liquid circulation. At higher flowrates and for narrower annulus hydraulic diameters (corresponding to wider draft-tubes) bubble entrainment into the annulus increasingly reduces the driving force for primary liquid circulation and the simple air-lift model is then inapplicable. It
Acknowledgement-The
original data were collected at the
Department of Chemical Enaineering. UMIST. under the sq&vision of Dr. G. T. Clegg and Dr. C. G. Sinclair. AGJ was supported by an SRC research studentship.
z zi g
annulus bubble phase continuous phase draft-tube
1 m S
sb Re 0
1
gas liquid two-phase mixture slip single bubble Reynolds number = pod/p ungassed at column head REFERENCES
Lamont A. G. W., Can. J. Chem. Engng 1958 8 153. Cook M. W. and Waters E. D., AEC R & D Rept. HW
39432, Handforth Atomic Products Operation 1955. Rietma K. and Ottenpaf S. P. P., Trans. Inst. Chem. Engrs 1970 48 T54. Freedman W. and Davidson J. F.. Trans. Inst. Chem. Eners 1969 47 T25 1.
Dussap G. and Gros J. B., Chem. Engng J. 1982 25 151
Blenke H.. A&an. Biachem. Engng - - 1979 13 121. Rietma K:, Chem. Engng Sci. 1982 37 8 1125. Jones A. G., M.Sc. Thesis, UMIST, Manchester 1969. Nicklin D. 3., Trans. Inst. Chem. Engrs. 1963 41 29. Nicklin D. J., Chem. Engng Sci. 1962 17 693. Turner J. C. R., Chem. Engng Sci. 1966 21 971. Mendleson H. D.. A.I.Ch.E.J. 1967 13 2 250. Koide K., Kata S., Tanaka Y. and Kubota H.. J. Chem. Engng Japan 1968 1 5 1. Marrucci G., Ind. Engng Chem. Fundis 1965 4 224. Fields P. R. and N. K. H., Chem. Engng. Sci. 1983 38 647. Jones A. G. and Mullin J. W., Chemy Znd. 1973 8 387.
Vol. 40. No. 3. pp. 449-462.
1985
ooo9-2509/85 53.Gtlt .Oa m 1985 Pergamon Press Ltd.
LIQUID CIRCULATION DRAFT-TUBE BUBBLE Department
of Chemical
IN A COLUMN
A. G. JONES
and Biochemical Engineering, University College London, London WClE 7JE, England
(Received
5 December
Torrington
Place,
1983; accepted 14 February 1984)
study of liquid circulation in a draft-tube bubble column (250 mm diameter, 60 1. capacity) using a flow-follower technique is reported. It was observed that annulus liquid circulation velocity increased to a maximum with air flowrate and a maximum in the volumetric liquid circulation rate occurred at a tube: column diameter ratio of about 0.5. A simple model based on air-lift pump theory is used to predict liquid circulation velocity using either pressure drop or air flowrate data. Reasonable agreement is found for narrow draft-tubes ( 5 121 mm) at low gas flowrates ( I 400 ml./s) but with significant deviations occurring with larger draft-tube diameters. These are thought to be due to secondary liquid flow within the draft-tube reducing primary liquid circulation. At higher gas flowrates bubble entrainment into the annulus becomes increasingly significant at all diameter ratios and the simple air-lift model is then inapplicable. Abstract-A
INTRODUCTION
Bubble columns are widely used in the processing industries to mix and aerate liquids. The introduction of the gas phase induces liquid circulation and the flow obtained can be stabilised using a central drafttube to create a primary liquid circulation pattern. Bubbles rising through the draft-tube (riser) are disengaged at the top (head) and at higher velocities some bubbles may be entrained into the annulus (down-comer) with the circulating liquor. Since liquid mixing rates are dependent on fluid velocities a knowledge of the flow characteristics of such vessels is required if their performance as chemical reactors or fermentors for example is to be predicted. Bubble columns both with and without draft-tubes have been the subject of increasing interest in recent years. One of the earliest studies of the draft-tube bubble column (DTBC) was by Lamont[l] who predicted the liquid circulation rates in a “Pachuca tank” using air-lift pump theory[2]. In this semiempirical model the energy transferred as the air expands in rising through the vessel is corrected for energy dissipation due to bubble “slip” and the remainder gives rise to velocity heads associated with liquid flow in the vessel. Reitma and OttengrafU] later presented a theoretical model based on minimum entropy production and a momentum balance was developed to predict the diameter of the “bubble street” and laminar liquid circulation velocities in a gas sparged column filled with glycerol. Freedman and Davidson[4] also modelled the liquid circulation in a DTBC based on an energy balance and measured gas hold-up but not liquid circulation velocities. Dussap and Gros[5] considered the kinetic energy transfer in 449
a DTBC fermentor in addition to gas expansion but neglected bubble slip. A number of other studies of liquid circulation in draft-tube bubble columns have been reviewed recently by Blenke[6] and by Reitma[q. The present paper presents data of the internal liquid circulation rate in a DTBC in which compressed air provided the motive force to promote circulation of water in essentially turbulent flow over a range of draft-tube diameters and gas flowrates[8]. It then compares them with the predictions of a simple model developed from air-lift pump theory applying to conditions prior to bubble entrainment which is solved using either pressure drop data or gas flowrate data coupled to expressions for bubble size and rise velocity.
THEORY
Energy
balance
The work done in promoting liquid circulation is equal to isothermal work done by the bubbles of gas expanding through the liquid contents of a vessel and is approximately given by:
W =
V,Q, Iwe
P, + p&L PI
(1)
where PI is the pressure of gas at the column head, Q, is the volumetric gas flowrate, P,,, is the density of the two-phase mixture of height H,,, and q is the efficiency of energy transfer. At higher gas flowrates the kinetic energy of the gas may become significant[S] but may be neglected at the lower flowrates employed in the present study.
A. G. JONES
450
In effect, the introduction of the gas phase to the draft-‘tube creates a density gradient which induces circulation between the riser and the downcomer sections. This density gradient is clearly due to the gas void fraction and this in turn depends on the relative velocity of gas and liquid. In general the gas rises faster than the liquid and the greater is this ratio the lower is the gas voidage fraction and hence driving force for circulation at a given gas flowratc. Slip velocity
The principle of the DTBC is similar to that of the air-lift pump. In these devices not all of the energy in the compressed gas is transferred to cause liquid motion but some is “lost” due to “slip” i.e. due to the relative velocity between gas and liquid resulting in turbulent energy dissipation[l, 2,9, lo]. Nicklin has shown[9] that the efficiency term is then simply related to the relative flowrates of liquid and gas and this can be given here by an expression of the form:
reversal’* as the fluid leaves the annulus and drafttube respectively:
z = (u,’ + Vd2)/%
where v, is the annular liquid velocity. Entrance, exit and pipe friction losses etc. are ignored as they are generally less significant[9]. It is implicit that the DTBC bc designed such that constrictions to flow at the base and head are avoided by suitable geometric arrangement, i.e. by maintaining an adequate crosssectional area for flow at all points in the loop. The work done to create the total hydraulic head by promoting liquid circulation is also given by:
w= wgz
p,+p,
where vd is the liquid velocity in the draft-tube and v, the slip velocity. Thus for the DTBC the work done to promote liquid circulation in the absence of bubble recirculation into the annulus (i.e. e., = 0) is given by: (3)
ci&v, = p&4&
Ld =
the liquid fraction may pressure gradient by:
where us is the gas velocity. Or, in terms of superficial gas velocity, us and draft-tube voidage, &,,:
(1 -+)=
v, = -% -
Ho _= Hf?l
i.e.
Q* -
(10)
(11)
be simply related to the
-g
(12)
v,j
Ed
a* = -
,,(Lq.z).
Hm-Ho Xl
(4)
Vd
-
Alternatively, since gas voidage in the draft-tube is defined by the expression:
By definition the slip velocity is given by the expression: v, = us -
(9)
where w is the mass flowrate of liquid. Hence combining eqns (7), (8) and (9) and noting that pm = p,( 1 - ~3 since plr< Pe a relationship is obtained between the liquid velocities and gas void fraction:
PlneL
PI ‘YHm)}(&).
(8)
0,
+d
where A, is the cross-sectional area of the draft-tube. Thus substituting for v, in eqn (3) gives: (7) Total head The work done by the bubble phase creates a head
of flowing fluid. Freedman and Davidson[4] have proposed that the total hydraulic head of liquid, Z, may be simply defined from Bernoulli’s equation as the sum of the liquid velocity heads in the draft-tube and annulus respectively, i.e. the “head loss due to
--= dh dH
fld
(13)
where fld is the dimensionless pressure gradient in the draft-tube. Thus eliminating cd and H,,, between cqns (10) and (13) gives: P,lOL(l
+55=p&+J(5.!+L).
(14)
which relates the work done by the expanding gas to the head of flowing liquid. Liquid
circulation
velocity
Since there is no nett flow from the column the primary liquid mass flowrates in draft-tube and annulus are equal and so from continuity: P,Q, = P&d
(15)
451
Liquid circulation in a draft-tube bubble column
or in terms of liquid velocities and column geometry: (16)
%%I = (1 - 0%&Y
i.e. the draft-tube and annulus liquid velocities are related by the expression: (17) where u is the annulus: draft-tube area ratio. Equations (14) and (17) may now be combined to give the relationship between the liquid velocity in the annulus and the pressure gradient in the draft-tube:
Hence, the annular liquid velocity, v,,, may now be predicted from eqn (21) for a given superficial gas velocity, s, single bubble rise velocity, v~, and drafttube: column diameter (or area) ratio (i.e. a). Bubble rise velocity Thus the remaining unknown quantity is the bub-
ble rise velocity, v,, and this may be predicted by the method of Mendleson [12], for example, from the expression:
C-W where d, is the equivalent bubble diameter in the liquid. This quantity may be obtained for perforated plate gas dispersers used here from several equivalent correlations, e.g. that due to Koide et al.[13]:
Hence if the pressure gradient, fld (or alternatively voidage, ~3, is known for a particular DTBC the resulting annular liquid circulation velocity, V, (or alternatively rod)may be predicted. This theory may now be extended by eliminating the pressure gradient, fid, from eqn (18) by use of the voidage-velocity relationship for two-phase bubbly flow. Unfortunately there is as yet no agreement on a general model but the simplest expression of this type relates system voidage, ed, to the superficial gas velocity, us, liquid velocity, u,, and rise velocity of a single bubble, vSbrin the form[l I]: u,( 1 - cd, - U&j = U&, = rY&( 1 - 6&1
(19)
where it is assumed that v& is independent of e which is reasonable as 6 + 0 although clearly a development could include a voidage dependency at high gas hold-up. Solving for ~~ gives: E,,= @(c,
+ od) = 1 - &.
(20)
Substituting for cd in eqn (18) and noting that for bubbly flow /Id N 1 then the following cubic equation in v, results: a3vm3+ a2v,’ + a,v, + a, = 0
Thus the liquid circulation velocity may now be predicted simply as a function of gas flowrate within a DTBC of given geometry. Bubble
entrainment
Freedman and Davidson[4] found that while at low velocities essentially clear liquor circulates down the annulus, bubble entrainment occurs when the superficial velocity of the downflowing liquid equals the bubble rise velocity. The voidage and velocity are then uniquely defined for a given bubble size and a graphical method of solution was proposed based on the expression due to Marrucci[lrl]. Plainly, when bubbles are entrained down the annulus the gas is compressed in a manner analogous to the expansion up the draft-tube. Thus some work is effectively recovered by the gas reducing that transferred to promote liquid circulation and eqn (7) can then be written as:
w =
PJlog(P’ +~ff~))EdAdud
(21)
- P,(lo&(p’
+~Ho))~nA~v.
(28)
where: or, as &+O: %=
-:+oge(l
+~)}uJ(l
+cr2)
(22) W = P,(lo&(p’
+THo)}
(cd -
EJA,~,
(29)
= 2gH,u,l(1 + a *) a, = 0
(23)
a, = v,
(24)
a3 = a.
(25)
A further simplification can be made to eqn (29) if it is noted that for pogHo/P, < 1 then lo&(1 + p,gH,/P,) = p&Ho/P, and thus eqn (14) becomes of the form: H&E
=
(V,’
+
V,‘)/&
(28)
452
A.
G.
and is then in a form similar to that of Freedman and Davidson [4] where de = e,+- E,. Thus the presence of bubbles entrained into the annulus (i.e. at values of co > 0) will tend to offset the head difference i.e. the driving force for liquid circulation. However, this is beyond the scope of the present paper since facility was not available to determine annulus void fraction. The present study is largely concerned with low velocity single phase flow in the annular downcomer (i.e. L, = 0) and it determines the conditions at which the transition to entrained flow commences. Further development will concern prediction of the annular voidage at higher flowrates and its effect on liquid circulation. EXPERIMENTAL
Description of apparatus The apparatus used is shown schematically in Fig; 1. The column (60 1.) was constructed from six 250mm i.d. QVF pipe sections each having two 38 mm i.d. horizontally opposed side arms inclined downwards at 30” to the horizontal. The column sections were bolted together vertically using QVF flanges and compressed asbestos fibre gaskets. The base of the column was a 250/38 mm pipe reducing section. The draft-tubes (44 mm, 70 mm, 96 mm, 121 mm, 146mm i.d.) were constructed from cast perspex tubes of 3 mm wall thickness and 1.22 m in length. Each tube was fitted with 3 support legs made from 6 mm thick Perspex sheet. The legs were shaped in order to fit the curvature of the inside of the base of the column so as to locate the draft-tube in a central position 100 mm above the base. An adjustable spider clamp made from 25 mm brass strip was fitted to the top of the draft-tube and was made 6rm by screwing the arms outward to make firm contact with the internal wall of the column. In this way each of the five draft-tubes could be firmly located centrally in the column and could be easily removed. Each of the tubes was drilled with four 13 mm diameter holes at 262 mm intervals to provide an entry into the two-phase region inside the draft-tube for the manometer probes. Four manometer tubes were made from 6mm bore glass tubing and were connected by means of rubber pressure tubing to the manometer probes via the column side arms. The side arms were fitted with rubber bungs which were bored and had a short piece of glass tubing passed through them in order to connect the manometer tubes on the outside to the manometer probes on the inside. The probes were made from the same bore glass tubing as were the manometer tubes. The probes were bent to provide a vertical upwards directed end in the centre of the draft-tube and passed through the four holes in the draft-tube wall which were fitted with rubber grommets to provide a seal and support to the probes. The gas disperser was made from a 76 mm dia. stainless steel disc (3 mm thick), perforated with twenty-five 2.4mm holes on a triangular pitch. The chamber was 13 mm deep and was mounted on a Neoprene rubber gasket. The disperser was con-
JONES
nected to the air supply via a 13 mm i.d. stainless steel pipe which passed through a rubber bung in the base of the column. Plasticine was used to fill the dead space in the base below the level of the disperser disc. The air was supplied from a compressor delivering 600 kNm-’ and reduced to 50 kNme2. The air flowrate was measured with a rotameter which was calibrated using a continuous flow meter and passed via a non-return valve to the disperser.
Procedure The column was filled with 60 1. of soft Manchester tap water which provided an initial depth of 1.33 m. Bath experiments were conducted for each of the five draft-tubes. The manometers were allowed to fill with water and any air was removed from their lines. The air was turned on and passed through the disperser and up the draft-tube and left via the disengaging section at the top of the column. When a liquid circulation pattern had established itself the liquid velocity down the annulus was measured. The range of air flowrates used was 100-575 ml./s equivalent to 0.24-1.38wm, i.e. substantially below that (2wm) required for significant kinetic energy contribution [5]. The liquid circulation velocity in the annulus was measured using a “flow follower*’ made from a piece of Nylon tubing 13 mm long x 6.5 mm bore. Each end of the tube was plugged with rubber and its density adjusted to that of tap water by injecting water from a syringe into the space created by the rubber blocking each end of the tubing. In this way small changes in density could be compensated for thus making the flow follower the same density as the water at ambient temperatures. This is important since if the flow follower is either too heavy or too light it will sink or rise relative to the liquid flowing leading to erroneous results. Care was taken to ensure that the flow-follower was well-wetted and it was observed to flow at the same velocity as tiny bubbles in the liquid. The flow-follower was timed between two unobstructed positions in the annulus in a vertical line. Each time the flow follower passed a chosen reference point in the annulus a digital clock was started and then stopped when it passed a second reference point. About 50 such readings were taken at each volumetric air flowrate in order to obtain the mean velocity of the liquid circulation in the annulus. It was considered that for turbulent flow this procedure would give a reasonable estimate of mean velocity but unfortunately estimates of dispersion are not available. The pressure gradient in the two-phase section (inside the draft-tube) was obtained by measuring the height of the liquid in the manometer tubes above their datum. The head of liquid thus obtained was plotted against the height of the manometer datum above the disperser, h, the slope of these graphs being the pressure gradient in the two-phase section of the column
Liquid circulation in a draft-tube
bubble
453
column
-I-)C manometers
3
-
disengagement z0ne (head)
draft-tube (riser)
liquid flow (downcomer)
1
I
t
&as
disperser
+ Air
inlet
Drain
Fig. 1. Schematic diagram of the apparatus.
454
A. G. JONES
I
0.1
I
0.
0.
0.1
8 I
0.L
p 3 c
.o
z
L
P 0
0.0
z >
0 i7
0.0
g
Drafttube Diameter
0.0.
Area Ratio
0.02 I +
121 146
2.5 1.3
0.01
I””
L””
3””
400
Fig. 2. Effect of air flowrate on draft-tube gas voidage fraction.
500
600
455
Liquid circulation in a draft-tube bubble column
I
I
l
Equation
l
I
I
I
I
l
21
Equation
18
/
entrainment
l
Experimental
Fig. 3. ElTect of air flowrate on liquid circulation velocity (d = 44 mm).
456
A.G.JoNEs
8
l
l l l
l
.
.
.
Experimental
0
I
100
1
200
I
300
I
400
I
500
Fig. 4. Effect of air flowrate on liquid circulation velocity (cI = 70 mm).
I
600
Liquid circulation in a draft-tube bubble column
24,
18
+ 0
l
15
4
l
large bubble \ 12
entrainment
0
l l l
:/
9
/
l l
6_
l
Experimental
/
I
100
I
200
1
300
1 400
I
500
Fig. 5. Effect of air flowrate on liquid circulation velocity (d = 96 mm).
IL-
61 oo
A. G. JONES
458
I
I
-
I
Equation
I
I
I
21
. entrainment
. 0
l
0
100
200
Experimental
300
400
500
Fig. 6. Effect of air flowrate on liquid circulation velocity (d = 121 mm).
600
Liquid circulation in a draft-tube bubble column
I
I
I Equation
21
and
I
I
I
26 bubble
\ 24_
459
rise
velocity
-
l
0
oeo**,
l 0 l
l
large bubble
I
entrainment
0
Experimental
3
0
I
I
I
I
I
I
100
200
300
400
500
600
Fig. 7. Effect of air flowrate on liquid circulation velocity (li = 146 mm).
A. G. JONES
Air
o-3
o-4
II&/S
575
A
o-2
Flowrate
0
325
v
250
D
200
o-5
O-6
0’7
Fig. 8. Effect of diameter ratio on volumetric liquid circulation rate.
Liquid circulation in a draft-tube bubble column DISCUsSION of gas flowrate When the air was
OF RESULTS
Eflect
turned on the contents of the column naturally rose to accommodate the volume of air introduced into the liquid. A noticeably convex section of high gas holdup was created above the level of the top of the draft-tube where the air disengaged from the water. A pressure gradient was developed in the range 0.90-0.99[8]. Draft-tube voidage calculated from eqn (12) is shown as a function of gas flowrate in Fig. 2. A circulation pattern was quickly established with the air/water two-phase mixture flowing up the centre in the draft-tube and the water flowing downwards through the annulus to be drawn into the draft-tube again by the air entering the column at the base. It was interesting to note that although the internal diameter of the smallest draft-tube was less than the diameter of the disperser, all the air was drawn inwards and passed through the draft-tube with the liquid. Calculation of annulus Reynolds numbers Re indicated turbulent flow existed in all runs except those with the largest diameter draft-tube. Bubble diameters were calculated to be in the range 8.5-9.7mm with corresponding rise velocities approximately constant at 250 mm/s (not shown here) [S]. At high superficial gas flowrates and for large diameter draft-tubes (with correspondingly high liquid velocities) air bubbles were entrained into the annulus and were held virtually stationary by the drag of the downwards flowing liquid. It was observed that as expected bubbles of decreasing diameter were drawn further down the annulus than large bubbles. Near the top bubbles of ca. 10 mm dia. were held stationary while below about 600 mm from the top of the draft-tube only tiny bubbles were observed ( -z 1 mm) and only at high superficial gas velocities and thus it was decided that the “flow follower” measurements of the annular liquid velocity should be made below this point. The effect of air flowrate on liquid circulation velocity for each drafttube diameter is shown in Figs. 3-7. The largest diameter draft-tube (d = 146 mm) gave the highest liquid circulation velocity in the annulus. However, this did not correspond to the highest volumetric flowrate of circulating liquid (see later). The volumetric liquid circulation flowrate increased with increasing gas flowrate for all draft-tube diameters. For the smallest draft-tube (d = 44 mm) the rate of increase was slight compared with that of the largest tube. In all cases there was a point after which any increase in the volumetric gas flowrate produced no increase in the liquid circulation rate. It was approximately after this point that there was a steadily increasing number of large bubbles entrained into the annulus and the accuracy of the flow follower measurements became doubtful. Similar bubble entrainment behaviour has been reported recently by Fields and Slater[l5] in a study of mixing in a 152 mm dia. DTBC using 95 mm dia. draft-tubes of various lengths.
Eflect
of draft-tube
461 diameter
It is apparent that there would exist a diameter of draft-tube at which there is a maximum volumetric liquid circulation. The two intermediate sized drafttubes used (d = 96 mm and 121 mm) allowed the most liquid to circulate through the annulus at any given volumetric gas flowrate. The effect of the d/D ratio (where D is the diameter of the column) on liquid circulation at constant volumetric gas flowrate can be most clearly seen in Figure 8 where the “optimum”, i.e. maximum flowrate, appears at about d/D = 0.5, i-e. where the diameter of the draft-tube is equal to the hydraulic diameter of the annulus. This compares with an optimum diameter ratio of 0.59 reported by Blenke[6] for a jet loop reactor, i.e. a DTBC with a gas nozzle (rather than disperser). (For single phase flow the optimum circulation would occur at d/D - 0.71[16]). Circulation models The simple circulation model described above was
solved numerically using a NAG routine and was tested over the range of operation used experimentally. Thus eqn (18) was tested using the pressure gradient data determined in this work[S] and the extended
model incorporating
the relationship
eqn (21).
for bub-
was also tested over the same range of operation. The physicai property data used are given in Table 1. The predictions for these methods are also summarised in Figs. 3-7 where the experimental annular liquid velocity is compared with that predicted for each of the five draft-tube diameters as a function of gas flowrate. At low velocities the predictions from eqn (21) compare fairly well with those of eqn (18). However, for the smallest diameter draft-tube (d = 44 mm) the experimental circulation velocity at low gas flowrates was higher than that predicted, as shown in Fig. 3. It is thought that for this case where the circulation velocities are low compared with those for larger tubes at the same volumetric air flowrate the flow pattern may have been significantly hindered by the manometer probes passing through the annulus to the draft-tube. The majority of flow follower measurements were taken in that part of the annulus where its flow path was unhindered by the manometers with correspondingly higher liquid velocities. For d = 70 mm the velocity predictions are within approx. + 20% as shown in Fig. 4. For d = 96 mm both methods predict circulation velocities approx. 33% higher than those obtained experimentally as shown in Fig. 5. As the draft-tube diemeter is increased the models predict increasingly higher values and the predictions are finally limited here by the single ble velocity,
Table 1. Physical Property Data
A. G. JON=
462
bubble rise velocity eqn (26) which is clearly an overestimate as shown in Figs. 6 and 7. Hence for dfD < 0.5 and 44mm -z d -z 121 mm the predicted values of liquid circulation using eqns (18) and (21) are within + 33%. Where d > 121 mm the models predict much higher liquid circulation than was obtained experimentally. This deviation from theory is thought to be largely due to two main reasons. Firstly, as mentioned earlier, air distribution is an important factor of determining the amount of liquid circulated and the predictions for the two larger diameter draft-tubes (d = 121 mm and 146 mm, d/D > 0.5) indicate that a secondary circulation pattern occurred within the draft-tube itself and some liquid was thus not entering the annulus. It .should also be noted that the diameter of the air disperser was not increased as draft-tube diameter was increased_ If it had been it is possible that circulation within the draft-tube would have been suppressed and a better agreement between experiment and theory obtained at this extreme of diameter ratio. Secondly, bubble entrainment into the annulus was more significant at larger diameter ratios and at higher gas flowrates thereby reducing the driving force for circulation. On the larger scale pipe friction losses may also become significant but cannot be considered further here.
NOTATION
cross-sectional area, m* internal diameter of draft-tubes, m equivalent bubble diameter, m perforated plate hole diameter, m internal diameter of column, m manometer level, m depth of liquid in column, m pressure, N/m’ volumetric flowrate, m’/s superficial velocity, m3/m2s absolute velocity, m/s volume of gas per liquid volume, per min[5], min-’ mass flowrate, kg/s work, W total hydraulic head, m
A d d, dh D h H : u V vvm
W
W Z Greek a
b L p o p
symbols
ratio of annulus: draft-tube cross-sectional areas dimensionless pressure gradient gas voidage density, kg/m’ surface tension, J/m2 viscosity, Ns/m2
Subscripts CONCLUSIONS
has been shown that in a draft-tube bubble column in which an air/water mixture rises through the draft-tube and the water circulates downwards through the annulus the volumetric liquid circulation rate and circulation velocity are dependent on the inlet gas flowrate and the diameter of the draft-tube. It has been found experimentally that increasing gas flowrate increases annular circulation velocity to a maximum for each draft-tube diameter and the maximum liquid circulation occurs at a diameter ratio d/D = 0.5 in the column studied. This corresponds to equal hydraulic diameters. The simple model used in predicting the annular liquid velocity is satisfactory for the small draft-tubes (d I 121 mm) at low gas flowrates (Qb I 400 mL/s) but at larger diameter ratios the model predicts increasingly excessive liquid circulation. These deviations are thought to be due to the wider draft-tubes having poorer uniformity of air dispersion and a secondary flow pattern occurs within the draft-tube itself at the expense of primary liquid circulation. At higher flowrates and for narrower annulus hydraulic diameters (corresponding to wider draft-tubes) bubble entrainment into the annulus increasingly reduces the driving force for primary liquid circulation and the simple air-lift model is then inapplicable. It
Acknowledgement-The
original data were collected at the
Department of Chemical Enaineering. UMIST. under the sq&vision of Dr. G. T. Clegg and Dr. C. G. Sinclair. AGJ was supported by an SRC research studentship.
z zi g
annulus bubble phase continuous phase draft-tube
1 m S
sb Re 0
1
gas liquid two-phase mixture slip single bubble Reynolds number = pod/p ungassed at column head REFERENCES
Lamont A. G. W., Can. J. Chem. Engng 1958 8 153. Cook M. W. and Waters E. D., AEC R & D Rept. HW
39432, Handforth Atomic Products Operation 1955. Rietma K. and Ottenpaf S. P. P., Trans. Inst. Chem. Engrs 1970 48 T54. Freedman W. and Davidson J. F.. Trans. Inst. Chem. Eners 1969 47 T25 1.
Dussap G. and Gros J. B., Chem. Engng J. 1982 25 151
Blenke H.. A&an. Biachem. Engng - - 1979 13 121. Rietma K:, Chem. Engng Sci. 1982 37 8 1125. Jones A. G., M.Sc. Thesis, UMIST, Manchester 1969. Nicklin D. 3., Trans. Inst. Chem. Engrs. 1963 41 29. Nicklin D. J., Chem. Engng Sci. 1962 17 693. Turner J. C. R., Chem. Engng Sci. 1966 21 971. Mendleson H. D.. A.I.Ch.E.J. 1967 13 2 250. Koide K., Kata S., Tanaka Y. and Kubota H.. J. Chem. Engng Japan 1968 1 5 1. Marrucci G., Ind. Engng Chem. Fundis 1965 4 224. Fields P. R. and N. K. H., Chem. Engng. Sci. 1983 38 647. Jones A. G. and Mullin J. W., Chemy Znd. 1973 8 387.