GAS AGITATION OF LIQUIDS L. H . L E H R E R Department of Chemical Engineering, Monarh Uniuersity, Victoria, Australia For agitated aqueous solutions in vessels with ratio liquid height a t rest/diameter N 1, experiments have been carried out to obtain mixing time and heat transfer data for paddle stirrers and spargers, operating in nearly identical systems. To compare agitator performance, mixing times and heat transfer coefficients have been correlated with applied power; different spargers also have been compared on the basis of air flow rate. Calculated applied power ranged from 0.1 3 to 2.60 ft.-lb.r/lb.,-sec. Sparger configuration strongly influenced performance. Some results could b e explained by use of published data on gas discharge into liquids. For the cases considered here, mixing time in sparged systems could b e described by relations based on gas flow rate and system geometry.
from agitation by gas that occurs in liquids with boiling, and with mass transfer in sparged contactors, gas jets and bubbles could be considered as suitable agitators in a number of liquid mixing applications. However, saturation of liquid and gas must be permissible., and chemical reaction between gas and liquid must be absent, or tolerable. I t seemed of interest to compare the mixing performance of spargers with that of a well-investigated type of agitator.
A
PART
Experimental
T o estimate the gas agitation performance that could be expected in a vessel with ratio Liquid height a t rest =1 diameter two-bladed flat paddles in a baffled tank and a number of different spargers were used as agitators in trials in which the criteria of mixing performance were: dispersion time of a solute and heating rate of vessel contents. For dispersion, the criterion was a mixing time 0, which was the time required to reduce a suddenly created concentration difference between two positions in the vessel contents to less than 0.2y0 of the average concentration. T h e liquid was a dilute solution of potassium chloride, in which the sudden concentration difference resulted from rapid injection of a small amount of concentrated potassium chloride solution a t a given location in the vessel. The concentration difference was observed by measuring the electrical conductivity of the solution a t two widely spaced positions, one of which was near the point of injection of the concentrated solution. Injection and the adjacent probe were located in what appeared to be least agitated regions, so that the possible existence of "dead space" could be eliminated from consideration (Figures 1 to 3). T h e agitating effect of the injection itself was insignificant. Injection time was approximately 0.25 second, and thus much shorter than the lowest measured mixing time. With the solutions and instrumentation that were used (shown on Figure 6), the choice of 0.2Yo final concentration difference between probes provided a recorded mixing time approximately equal to actual mixing times, taking instrumental lag into consideration. Mixing times were estimated from recorder charts that showed millivolt values based on the difference of electrical conductivity of the fluid a t the two probes. T h e time between start of the pulse injection and permanent return of the record to within the bounds set by the 0.2% difference criterion was taken as the mixing time, 0. T h e measuring error of each meter was 105, power number qi is constant in a baffled vessel (Rushton et al., 1950). With ratio LILv = paddle length/paddle width = 5.81 (A7, Figure 3), = 1.9 can be estimated from data shown by Rushton et at. (1950, p. 469 and Table 6). For L / L v = 4.36, 4 = (1,35)(1,9) was used (Rushton et al., 1950; Bates et al., 1963). For air agitation, the pressure a t PI6 (Figure 5) is that required to provide a n air flow rate w through the sparger. Thus the power required to deliver w a t that pressure can be regarded as the power P A applied to the system to provide agitation. Since P A in Equation 1 is the net power delivered to the stirrer shaft, the use of a theoretical compression requirement seems justified. T h e adiabatic case provides a conservative value that was not excessive, considering that that maximum pressure readings were below 20 p.s.i.g. Thus, for the spargers, power was estimated from
+
Figure 6. Measurement of difference of electrical conductivity and description of solutions and equipment Measuring cells 6/ls-inch diom. X 1 inch Indicating and transmitting conductivity measuring bridge,
1000 c./s.
Wiring Test solution Pulse injection
Resistances, various values, but R1 = Rz Multirange, multispeed, mv. recording measuring bridge, full-scale 25 cm.; 95% scale balancing time 1 sec. max. chart speed 1 cm. per sec., min. range 1 mv. Screened cables 4 7 0 g. KCI in 6.54 cu. ft. town water, TL varying from 5 l o t o 7 1 " F. 20 g. KCI in 200 cc. of town water
(Perry, 1963, pp. 6-16) with factor C appropriate for the units used and where p l = compressor intake pressure, here taken as atmospheric pressure p z = air pressure a t entry to sparger, as read a t air supply line a t top of tank, PI/6, downstream of any valves or other restrictions (Figure 5) Mixing time 0 and heat transfer coefficient hi were related to power P A by
OpAnl =
c1,
hipAne =
cz
For the sparger, 0 and hi were also related to air mass flow rate, w , by XY" = constant, with X = 0 or hi,Y = w . T h e spread of values of 0 and hi was larger in sparger-agitated vessels than in stirrer-agitated ones. Dispersion of Solute
Figure 7. Measurement of temperature, description of vessel content, and equipment
rcl AT [XI R T [XI
Ti Test liquid Test heating interval
Thermocouples, copper-constantan,
20 g. Same os C[X]R (Figure 6) mv. potentiometer Mercury-in-glass thermometer 392 Ib. town water 100' to 156' F.
Correlated Variables
T h e mixing time 0 and heating time t F were obtained from recorder charts. Using tF, the heat transfer coefficient hi was evaluated as shown later. Mixing times and heat transfer coefficients obtained with air spargers were compared with those resulting from stirrer agitation a t the same net applied power, PA. 230
I&EC PROCESS D E S I G N A N D DEVELOPMENT
Probability of correlation between mixing time 0 and applied power PA was less than 9970 for systems A l , A2, and A3, but exceeded 99.9% for A4, A5, Ab, A7, A8, and A9 (Figures 1 to 3). A l , A2, and A3 were not considered further. Using all experimental 0 values, the least-squares lines shown in Table I were obtained. Figures 8 and 9 illustrate the correlation lines. T h e difficulty of obtaining reproducible end points in highly turbulent systems could be illustrated by the standard deviation of 0Le., s(O)-obtained in the stirrer-agitated systems (Table 11). Kramers e t al. (1953) mention standard deviations of "about 15%" with 45,000 < R e < 200,000. For the experimental conditions: Paddle length was significant (Table I, A7, compared with A8 and A9). However, over the experimental range, correlated mixing time values 0 for A7, A8, and A9 differed by less than 3070 a t equal applied power P A . Relative location of Drobes and iniection were not significant (A8 us. A9). In sparged systems, those providing distributed gas injection, with downward discharge sweeping the vessel floor, yielded shorter mixing times B Fhan c e i t r a i spargers operating a t the same power P A (A4 us. Ab).
-
-~
Table 1.
System A4
A5 A6 A7 A8 A9
Mixing l i m e as Function of Applied Power and Supertlcial Velocity 95% Confidence Interval of Slope Equation (Rounded Of) ePA0"' = 22 .70 0.093 to 0.047 < P A < 2.21 0.247 OPAO." 8.83 0.07 to 0.16 0.019 < P A < 1 . 2 8 0~~0.= 1 78.22 0.13 to 0.20 0.025 < P A < 2.95 0 P ~ o . 3=~ 6 . O O 0.25 to 0.36 0.131 < P A < 1.99 OPAO,~~ = 7.60 0.19 to 0.27 0,039 < P A < 1 . 7 OP~o.24= 7 . 4 0 0 . 1 9 to 0.29 0.038 < P A < 1 . 8
7.32
0.12 to 0.26
3 .71
0.35 to 0 . 4 9
A5
evuQ.19 =
0.029
< u, < 0.34
A6
Ou00.42
=
0.021
< u, < 0.26
Comparing results for stirrer-agitated systems with those of Kramers et al. (1953) where N O = constant was proposed, it could be expected that for the higher R e range used here, ,Ye a 0PA0,33for a given system. Only for A7, with 0PAo,31= constant, the 95% confidence interval spans the 0.33 value (Table I). Siemes and Weiss (1957) and Argo and Cova (1965) discussed mixing in bubble columns of large and various LID ratios, respectively. Although a three-dimensional model is used for the tank systems discussed in this report, a n order of
1
1
1
1
1
Re 673,000 322,000 546,000 157,000 566,000 430,000 156,000
System A7
A8 A9
10
28.5 11.8 18.1 10.6 13.3 29.5 16.1
10
15 10 9 14 8
~
magnitude comparison could be attempted. Assume diffusion from a point source of mass m placed a t the center of a sphere a t time t = 0, into a quarter sphere, with reflection a t planes of section. If concentration c t is a function of time t and radius Y only, and D is a turbulent mixing coefficient, then
[!.4 ?)]
% at = D
At equal power PA, sparger A5 with higher gas rate yielded 0 values which did not differ very much from those obtained with AB: but a t equal gas rates w ,the high exit velocity sparger A6 yielded much lower 0 values than A5 (Figure 9). This may be of interest, since often air quantity, rather than pressure, is a limitation. The high energy sparger A6 provided narrower 957, limits than A4 and A5.
L
Table II. Standard Deviation of Mixing limes for Paddle Stirrers at Various Reynolds Numbers Related to Mean
r2 b r
(Bird et al., 1962, p. 559)
(.2
which can be proved by differentiation ~t =
m =
Act
Jm
+
cto
Acinr2dr
With r2/4 Dt = p2, substituting for Ac, yields m = 8 rD1.K'l
lm p2 exp(-p2)dp
which by use of the identity (Lamb, 1347, p. 230)
for n
>1
becomes, with n = 2,
1
1
I
I
l
I
l
VOL. 7
NO. 2
APRIL
1968
231
Variation of Calculated Mixing Coefficient with Possible Measuring Error Maximum Error per 1% of Full 0.570 of Full Conductivity Meter Scale Scale
Table 111.
0.286
DO,sq. ft. Dl0 = 10 seconds, sq. ft. per hr.
0.501 180
0.565 1.1 396
Table IV. Values of Mixing Coefficient D (Sq. cm. per second. u, assumed to be referred to approximately same pressure and temperature) From DO = From Siemes and Weiss, uo 0.501 Table 2, Series D 0.053 29 5.1 0.105 49 12 0.158 58 34 0.210 63 65
Pia'
Figure
9. Mixing time 0 vs. superficial velocity v o Correlation lines for systems A5 and A6
> 99%,
Pii'
> 99.970,
P I Z ' < 90%
T h e relations found by linear regression are given in Table V. T h e spread of hi values is illustrated by the standard deviation s ( h i ) for A10. No. of 0bservatzons 4 4 4 4
Re 728,000 532,500 481,000 295,000
Substituting for CI,
100 s(hi) him
>%
18.5 10.4 9.5 12.6
m c* =
~
T h e following boundary conditions could be used :
t
< 0, CI = 0, c 2 = cto for all r t = O,ci =
03
atr = 0
c2 = cto a t r =
t = 8, c t 2 (Aci ct
5
(Act
T h e spread of values can be compared with those indicated a t equal R e in reports by Brooks and Su (1959), Cummings and West (1950), and Strek (1963). T h e heat transfer coefficient, hi, was obtained from
R
Q
UAAT,
(12)
and
+ cto) a t r = 0
+ cto) a t r = R
where R = distance between remote probe and injection, and e = mixing time. Then,
Enthalpy increase of vessel contents during time t p was 21,950 B.t.u. Allowing for heat loss, the following values were used for calculations: Qtp
= 22,000 B.t.u. for the stirrer-agitated vessel
Q ' t p = (22,000
With the measurement of two conductivities to establish the difference, the value of the mixing coefficient D is highly dependent on the accuracy of the conductivity meters. For the conditions of experiment, the following are indicative (Table 111). I n view of such possible variation of D values, apart from dissimilar geometry, only qualitative and order of magnitude comparisons with the data of Siemes and Weiss (1957) seem warranted (Table IV). Heat Transfer
T h e stirrer configuration A10 and sparger arrangements A l l and A12 were tested. Correlation probabilities between heat transfer coefficient hi and applied power PA, Re, and gas mass flow rate were: 232
=
I&EC PROCESS DESIGN A N D DEVELOPMENT
Es
=
+ Ea) B.t.u. for the sparged vessels
enthalpy increase of air between entry to sparger and exit from vessel contents; this was evaluated in six intervals between 100' and 156' F. by E s = w Z(t[&t - &D~,.]).
Table V. Heat Transfer Coefficient as Function of Power Input, Reynolds Group, or Superflcial Velocity Equation B.f.71. Evaluated at 128' F . System hi' Hr.-sq.ft.-' F.' A1 0 A1 1 A1 2 A1 0 A1 1
A12
T h e simplifying assumption of saturated and dry air seemed justified by saturation obtained in trial runs on weigh scales with warm water, and a n air supply that was cooled below 20' C. a t 100 p.s.i.g. T h e jacket side heat transfer coefficient, h,, was estimated by a Nusselt equation (Bird et al., 1962, p . 417, 13.6.-4). At the highest and lowest observed heat transfer rates, calculated values of h, would be 1240 and 1485 B.t.u. per (hr.)(sq. ft.)(' F.) respectively. T h e use of a constant value
h, = 1325 B.t.u. per (hr.)(sq. ft.)(" F.) decreased the maximum calculated h, value by less than 5% and increased the minimum one by less than 270. Other simplifying assumptions were : No allowance for a dirt factor was necessary in the clean stainless steel vessels. Equal heat transfer areas, 11 sq. feet. for both sparger and stirrer agitation, and for h, and h,, the ratio D,/D, being 1.026. After estimating heat losses by a number of methods, all except the enthalpy increase of sparged air were taken into account by adding 50 B.t.u., making Qtr = 22,000 B.t.u. At high power input, heating rate due to viscous dissipation was not negligible, but was not deducted from the total supply, since it could be regarded as a characteristic part of the system. A constant value of d / k = 0.0026 (hr.)(sq. ft.)(" F.)/B.t.u. was used. T h e value of the temperature difference, AT,,, was taken as Temperature of steam saturated a t condensing pressure of 40 p.s.i.g. i.e., AT, = 287"
-
1-1
mean temperature of vessel contents over test interval 100" to 156' F.
Comparing A10 and A1 1, the sparger performed considerably better than the paddle a t equal applied power, but part of the transferred heat left as enthalpy of the saturated exit gas, and this part is usually not useful. Comparing A l l (Table V) with the sparged systems discussed by Fair et al. (1962) for which h , = 1200 uo'J.** was proposed, the difference between 0.22 and 0.38 is significant a t the 90% probability level only, indicating the wide spread of the 95% C I of the slope of the regression line for system A411. I n the range of superficial velocity used here-Le., 0.034 to 0.243 foot per second-heat transfer coefficients for A l l and A12 would be lower than those obtained with the equation proposed by Fair et al., whose Figure 7 seems to imply representation of a much wider range of superficial velocity. Probably the significant difference between the configurations discussed by Fair et al. and the systems in this work is the height/diameter ratio. Discussion Agitation Effect of Gas Jets. T h e comparison of spargers differing only with respect to efflux velocity a t equal air rates showed that shorter mixing times could be expected from the sparger with the higher discharge velocity (A5 us. Ab). Abramovich (1963) discussed the discharge of gases into liquids in some detail. From this reference, for an axisymmetric jet:
A plot of theoretical dynamic pressure distribution a t the jet axis LIS. distance along the jet axis shows that
R, =
128' F. = 159' F.
No heat transfer data for directly comparable stirrer systems \\ere found. Thus, comparisons with earlier literature were made only to check approximate magnitudes. After allowing for geometry and blade number, experimental results shown in Figure 10 are of a magnitude which would be calculated from previously published work. iyith regard to the low exponent n of Re, the h , - r.p.m. relation for water shown by Cummings and il'est (1950) indicates also the decrease of n in hi a Re" with increasing Re.
Figure 10.
dR
with ' dz
+
' e2 0.06 PPv2 -
0 for 2
for 3 = 18
N
> 18 (Abramovich, 1963, Figure 12.44)
distance from origin along jet radius of sparger hole
' ( =
pm
= fluid density a t axis of jet
u,
= fluid velocity a t axis of jet
Experimental points plotted on the same figure indicate the possibility that
Heat transfer coefficient hi vs. applied power PA, for systems A1 0,A1 1 , and A1 2 VOL. 7
NO. 2
APRIL 1 9 6 8
233
R, = 0.1 a t
dR, dz
= 18, again with - + 0 a t 3
> 18
Further, from Abramovich (1963, p. 605) for the main region of an axisymmetric jet,
5=
3.85
VY
(2)
= 3.85
c:y
where
Considering arrangements A5 and A6 only, with the calculated ro values and sparger hole spacings of 0.75 inch along the distribution tubes, some overlapping of the jets would be expected along the axes of the tubes. T h e additional energy dissipation due to this is not considered in the following. The term (wv,2/2 gc) could be used to estimate the ratio mixing time for A5/mixing time for A6 = 8 5 / 8 6 a t equal air mass flow rate w . Thus
S, = cross-sectional area a t orifice So = jet cross-sectional area when r = ro Let
Say that R, = 0.5 a t r = 0.4 ro (Abramovich, 1963, Figure 12.43.) Assume that a t any x ,
R, = exp(-u2r2) and p m = p a t
(17)
= 18
S:
r exp(- 1.5 u2r2)dr
Power ofjet = irpmvma
(18)
The dynamic pressure ratio R, decreases rapidly a t distances from jet origin f smaller than 18 and very slowly for z greater than 18. Since z is small compared with the dimensions of the fluid volume, it could be argued that energy dissipated in the jet region a t f < 18 does not contribute significantly to agitation in the remainder of the vessel. Thus,
1
Fraction of power transmitted to vessel contents outside jet region
l=I
(24)
Then from the foregoing relations: 2
-
TPL(1 - €)una [I 3 u2
represents approximately the power dissipated by the air stream outside the actual jet region. The power dissipated near the sparger exits is (1 - 7) wv,2/2 g,. T h e short air jets broke to form a conical cluster of small bubbles. In a manner similar to that for calculating a stable maximum drop diameter in a turbulent medium (Grassmann, 1961, p. 782) a hypothetical stable maximum bubble diameter is given by
a t 5 = 18
where w = povpSQ
7WU,2 ~-
where pl and p2 are the absolute pressures a t sparger exit and liquid surface respectively-i.e., ( p l / p 2 ) = 1.06. T h e values calculated from Equation 23 are shown in juxtaposition to correlated values in Figure 11. The term
- exp(-1.5
uzrO2)]
(20)
Assuming turbulent conditions that justify a constant value for the friction factor, f,values of DBmax for the jet region and for the remainder of the vessel could be estimated, with the result that some energy recovery from bubble coalescence outside
where pL
= density of clear liquid,
E
=
fractional gas holdup =
(VTot
-
b'o)/V~ot 2.0
V T , , ~= total volume of fluid V , = volume of clear liquid For A6, a t approximately maximum power input per unit mass of sparger air, sparger hole exit velocity vo = 1100 feet per second, assuming a flat velocity profile. Sparger hole diameter D , = 2 ru = ' / I 6 inch, density of air a t sparger exit p p = 0.08 lb., per cu. foot,
Et /
A2 i
I power of air jet I a t sparger exit ,
',I
With R, = 0.1, rO2 = 0.00206 sq. ft., u2 = 2095, E
= 0.2, pr, = 62.4 lb., per cu. ft., urn = 13.9 feet per second,
Wv2
7 - e
2 -
irpL(l
i.e., 7 = (22)/(21)
-
E)vm3 E
3 u'
2.1 ft.-lb.f per second
(22)
0.06
T h e fluid density p m as used here depends on the actual gas holdup a t 5 = 18, and this may differ from the holdup (VTot - b'o)/V~ot = E which applies to the whole of the fluid contents. However, the term 7(.171,2/2) is independent of pm provided pg, v g are constant, and also for constant pg, To, 7 = constant. This can be proved from the foregoing relations. 234
l&EC PROCESS DESIGN A N D DEVELOPMENT
I= 0
0.1
ft "0
Figure 11. velocity, vo
0.1
;5;
Ratio of mixing times 1-1
3 es - 73 .. 73 12
05/06
v ~ ( - ~ . ~ ~ ) v0(-o.4*)
(Table I)
vs. superficial
the jet region could be expected. However, calculated values of energy recovery did not assist in explaining the variation of 0 with w and u g . Comparing systems A4 and A6 a t equal power, the localized criterion of 8 may admit the following argument: T h e injection volume represents a target, to be destroyed by fluid motion. Assuming that
e
1 intensity
a
~
1
a r2
~
power unit area
(25)
e4 r4' --- a t equal power e6 r62 From Figures 1 and 2, taking r from sparger exit wall to the injection region, and a t equal power input, 84
-
---I
86
127
r42
=-
= 2.71
47
r6m2 w s l l
T h e log 8 us. log hp. correlations yield e4/e6 = 2.76 (Table I). I n general, the downward discharge-two bar sparger which caused distributed bubble traffic in most of the vessel was superior to the central sparger. T h e (mixing time) - (applied power) relations for A5 and A6 were 8 P ~ ' . l l = 8.83 and 0PA0.l7= 8.22, respectively. Values of 8 thus obtained could be related to a directly evaluable mechanical energy balance from which relatively insignificant terms had been omitted. Thus : 7 9
Assuming bubble velocity U B approximately equal to settling velocity U B S , and further assuming turbulent conditions that allow use of a constant friction factor f = 2.6 (Grassmann, 1961, Table 10.12.1., p. 752),
DE =
(4s7r)n*r feet
when Q is in cubic feet per second. Air flow rates were well above the minimum calculated for bubble chain formation a t upward facing orifices; however, the downward-facing holes with reflection a t the vessel floor do not provide an easily described system. Rising bubble beds emanating from various spargers over a range of flow rates were observed in a tall transparent tank. I t seemed that for an order-of-magnitude estimate, the turbulent two-phase region could be compared to a bubble chain in gross outline. For a sparger with central downpipe-e.g., arrangement A4-one could envisage a number of bubbles surrounding the central tube. Assuming a four-bubble configuration, similar to a clover leaf, the diameter of individual bubbles would be approximately: Air flow rate, lb.,/min. DB (sphere), ft.
1 .8 0.29
3.6 0.39
For 32 holes and no overlap, the diameter of individual bubbles would be: Air flow rate, Ib.,/min. DB (sphere), ft.
1 .8 0.13
3.6 0.17
dimensions, as well as system characteristics, have been used to describe mixing times (Uhl and Gray, 1966). For systems A?, A8, and A9, actual displacement of the two-bladed stirrer = X.v(7r,VL2Lv/240) cu. feet per second. X,. may be a is function of L , N , and other variables. Vessel contents turnover time = V J l J = t ' , where V , = 6.54 cu. feet for dispersion experiments. 'Table V I was drawn up with X, = 1. Probably by chance, turnover times t' thus calculated agree well with 8 values obtained from correlation, though this applied to the high-speed range only for systems A8 and A9 (Table I). T o use the displacement concept in the sparged systems, one could proceed as follows: T h e rising bubble bed, consisting of disintegrating and coalescing bubbles, could be described with aid of the bubble chain model. I n a bubble chain
!I
Gas residence time in two-phase region
1
ZTot
= _ - UB
-
TDB~ZT~~ 6Q
(27)
where Z,,, = height of fluid bed = volumetric gas flow rate Q D E = bubble diameter Table VI.
Vessel Contents Turnover Time, t' at Maximum Power System A7 A8, A S K,r.p.m. 248 350 L , ft. 1.33 1 .oo 0.229 0.229 Lv, f t . V , cu. ft./sec. 1.32 1 .05 t' = V , / V , seconds 4.95 6.22
0.9 0.097
T h e horizontal cross-sectional area of the bubble bed, SB, could be estimated for various systems approximately as follows : 1. Sparger hole pitch x p in horizontal direction
Pumping Capacity of Bubble Bed. Agitator speed and
0.9 0.22
> D E , then
SB = (number of sparger holes)(bubble area) =
n BT ( DB ) * 4 (29)
~
This could apply to arrangement A2 :
2. x P
< DB.
Allowing for the presence of two sparger pipes, this could apply to arrangements A3, A5, Ab, and A1 1. 3. xI, = 0, downward discharge: I t could be assumed that the bubble bed is that formed by four bubbles in cloverleaf formation a t the same gas rate; then A
SB = 4 (2 DE)'
=
*(DE)'
(31)
This could apply to arrangements A l , A4, and A12. Using values of DB listed above, Table VI1 shows horizontal cross-sectional areas for bubble rise regions near bubble bed formation level.
Table VII.
Bubble Rise Horizontal Cross-Sectional Areas,
SB, for Two Main Sparger Geometries at Three Gas Rates Air Flow Rate, Lb.,/Min. 3.6 1.8 Basis Arrangements Al, A4, A12 Spherical bubble diameter D E , (4 bubbles) ft. 0.39 0.29 S B , sq. ft. 0.476 0,264 Basis Arrangements A3, .45, Ab, A l l Spherical bubble diameter 0.13 D B (32 bubbles), f t . 0.17 0.376 0.271 S B , sq. ft.
VOL. 7
NO. 2
0.9
0.22 0.152
0.097 0.197
APRIL 1968
235
Considering the rising bubble bed when pitch x p = D B , and also when there is almost complete overlap of bubbles, the gas holdup in the rising bubble bed could be estimated by: Et
=
log10 ( 1
+
A
where E = power input per unit mass of vessel contents-Le.,
E)
resulting from applied power P A shown on the figure, T h e fractional gas holdup E for the vessel as a whole approaches that due to the rising bubble bed-Le., c ’ S B / ~ as air flow rate decreases, and consequently agitation and downward entrainment of bubbles are reduced. Then assume that liquid flow rate in the rising bubble bed a t the sparger exit is
As defined here, the bubble rise velocity Q / e ’ S B is independent of sparger exit velocity, although the latter influenced mixing time significantly (Table I, Figures 9 and 1 1 ) . Assume momentum transfer a t the sparger exit so that velocity u is given by
E
=
WTOt
fractional gas holdup =
- VO)
-
VTot
cu. ft. 1 where Q = total gas flow rate, __ sec. 170’ F., 1 ata. and experimental values of E were estimated from averaged measurements of the height of a 20-inch diameter, 0.75-inch thick, perforated plastic foam float. For the case of homogeneous isotropic turbulence in a given liquid-gas system a t constant pressure and temperature, and with some simplifying assumptions,
EO.2 a
(34)
from Equation 24
DB-0.5
Also, for turbulent conditions generally, Since the mass of gas holdup in the vessel contents is relatively small, mass of vessel contents = p L y o , so that with Equation 33 turnover time would be t’ = V J V . Allowing for the geometric factor ( T / R )applicable ~ at the injection site (Equation 25),
uBS
a
DBO.6
Equation 36 can then be equated to Oa
work done by buoyancy forces rate of work of kinetic forces
(35) Figures 12, 13, and 14 show that t ’ ( r / R ) 2is of the same order of magnitude as mixing time 0 a t the corresponding values of PA. (39)
Also shown on Figures 12, 13, and 14 is the equation
e=
i o . 2
(1
- E)
(a>’
Figure 12.
provided acceleration a is constant. With E as ft.-lb.f/lb.,-sec.,
Mixing time 0 vs. applied power P A , observed values of
X
236
Least-squares valuer
I&EC PROCESS DESIGN A N D DEVELOPMENT
e, A4
2-2 X
-
('>2
SBV(1"O e') R least-squares values
(35)
50 40
ao
I
pa, "P
Figure 14.
Mixing time 0 vs. applied power
X
PA, observed values of 8, A6
Least-squares values
VOL 7
NO. 2
APRIL 1 9 6 8
237
DB = DBmex[200
c. =
13.7 X 10-3
i-O.4
ft.
(24)
and with uBS = 4.06 DB0.5 feet per second and a = 0.033 ft./ sec.2-i.e., proportional to specific volume only,
= heat transfer coefficient, B.t.u./hr.-sq. ft.-O F. = horsepower
h hP.
k L
m
N n Figure 12 shows that the plot of this equation is almost parallel to the least-squares lines for systems A4, A5, and Ab. In all this, there has been no allowance for variation of holdup with specific power input E a t equal air flow rates. Observed differences between A4, A5, and A6 were relatively small in the few holdup determinations that were carried out here, and holdup data found in previously published literature are not consistent. Holdup was based on observations with system A5. Comparing the least-squares equations (Table I ) with Equation 40 on Figure 12, it can be seen that while the slopes are approximately equal in all three cases shown, the lines for A5 would show approximate coincidence also. T o obtain coincidence with systems A4 and Ab, the term (1 - E ) would have to decrease. This increase of holdup E at equal gas rate would be expected, since A4 and A6 provide higher energy dissipation rates than A5.
P PA
P
Q Q,Q’
R R
Ei r.p.m. r
S S
T t tP
t’
U V
P U
Conclusions
As a consequence of selected criteria and geometry, relative performance of stirrers and spargers in heat transfer differed from that in solute dispersion. As agitator, A10 corresponds to A8 and A9, while A l l corresponds to A6. While the stirrers provided shorter mixing times over most of the range, the sparger provided higher heat transfer coefficients, although part of the transferred heat is used to saturate the exit gas, which is often only an undesirable side effect. I n general, in the short vessels, sparger configuration was an important parameter. A sparger providing bubble traffic in most of the vessel by suitable spacing and discharge sweeping the vessel floor provided nearly the same agitation as the shorter twobladed paddle, but was inferior to the longer one a t equal power PA. Sparger performance can be improved by providing higher power input without increase of total mass flow rate-Le., by increasing exit velocity. Estimates of discharge rate a t a given pressure drop are given by orifice equations such as (5-9), p. 5-8 of Perry’s handbook (1963). T h e calculated correlations are valid for the described experiments only, and mixing time values are merely relative.
UO
1
W
x, X,Y, XN
2
= function
GREEKLETTERS angle, O ratio of specific heats difference, appropriate units fractional holdup of gas in fluid fractional efficiency mixing time, seconds kinematic viscosity, sq. ft./sec. = fluid density, lb.,/cu. ft. = surface tension, lb.{/ft. = power number
= = = = = = =
cy
Y
A E
9
e V
P U
4
SUBSCRIPTS
A B BS
= =
=
g
i
Nomenclature
A a a
c c C
CI
D
D d E J$
f: g
G
:A’ 238
area, sq. ft. = acceleration, ft./sec.2 = constant, l/ft. = constant = conversion factor, hp.-sec./ft.-lb.f = concentration, moles, cu. ft. = confidence interval = characteristic length, diameter, ft. (inches in Figures 1, 2, 3) = mixing coefficient, sq. ft./hr., sq. cm./sec. = thickness, ft. = energy, B.t.u. = power per unit mass, ft.-lb.Jsec.-lb., = friction factor = gravitational acceleration, ftJsec.2 = conversion factor, lb.,-sq. ft./hp.-seca = conversion factor, lb.,-ft./lb.f-sec.2 = conversion factor, lb.,-ft. /lb.f-min.2 = specific enthalpy, B.t.u./lb., =
I&EC P R O C E S S D E S I G N A N D DEVELOPMENT
thermal conductivity, B.t.u./hr.-ft.-O F. “diameter” of stirrer paddle, length, ft., (inches in Figure 1) = quantity of pulse injection, moles = stirrer speed, revolutions per minute = number, parameter, constant = power, ft.-lb.f/sec., h p = applied power, hp. = fluid pressure, p s i . , 1b.Jsq. ft. = volumetric flow rate, cu. ft./sec. = rate of energy flow, B.t.u./time = ratio = radius, ft. = specific gas constant, ft.-lb.f/lb.,-O R., hp.-set./ lb.,-O R. = revolutions per minute = radial distance, linear distance in horizontal plane, ft. (inches in Figures 1, 2, 3) = cross-sectional area, sq. ft. = standard deviation, appropriate units = temperature, O F., O R . = time, seconds, minutes, hours = heating time interval, minutes, hours = turnover time, seconds = over-all heat transfer coefficient, B.t.u./hr.-sq. ft.-O F. = volume, cu. ft. = specific volume, cu. ft./lb., = velocity, ft./sec. = superficial velocity based on mass flow a t 70’ F., 1 atm., ft./sec. = mass flow rate., lb.,/sec. ... = distances, ft., inches = =
L max m 0
r Tot x
1, 2,
, ,
.
= = = = = = = = = =
applied bubble bubble settling gas a t sparger orifice inside; with reference to component i liquid maximum average; mass; a t centerline ofjet superficial; jacket side; outside; initial radial total fluid axial a t position 1, 2, . . . or pertaining to system 1,2, . . .
OTHER
li If
= dV/dt, cu. ft./sec. =
evaluated a t i
literature Cited
Abramovich, G. N., “Theory of Turbulent Jets,” M. I. T. Press, Cambridge, Maw., 1963. Argo, W. B., Cola, D. R., IND.END. CHEM.PROCESS DESIGN DEVELOP. 4, 352 (1965).
Bates, R. L., Fondy, P. L., Corpstein, R. R., IND. END. CHEM. PROCESS DESIGN DEVELOP. 2,310 (1963). Bird, R. B., Stewart, W. E., Lightfoot, E. W., “Transport Phenomena.” 2nd Printing. Wilev. New York. 1962. Brooks, G., Su, G. Jz‘Chem.‘Eng. Progr. 55, No. 10, 54 (1959). Cummings, G. H., West, A. S., Znd. Eng. Chem. 42,2303 (1950). Fair, J. R., Lambright, A. J., Anderson, J. W., IND.ENG.CHEM. PROCESS DESIGN DEVELOP. 1,33 (1962). Grassmann, P., “Physikalische Grundlagen der Chemie-Ingenieur-Technik,” Sauerlander & Co., Aarau & Frankfurt Am Main, 1961. Kramers, H., Baars, G. M., Knoll, W. H., Chem. Eng. Sci. 2, 35 (1953).
Lamb, H., “Infinitesimal Calculus,” Cambridge University Press, Cambridge, 1947. Perry, J. H., ed., “Chemical Engineers’ Handbook,” 4th ed., McGraw-Hill. New York. 1963. Rushton, J. H.,’Costich, E.‘W., Everett, H. J., Chem. Eng. Progr. 46, No. 8, I, 395, No. 9, 11, 467 (1950). Siemes, W., Weiss, W., Chem.-Zng.-Techn. 29, No. 11, 727 (1957). Strek, F., Intern. Chem. Eng. 3, No. 4,533 (1963). Uhl, V. W., Gray, J. B., eds., “Mixing,” Vol. I, Chap. 4, Academic Press, New York, London, 1966. RECEIVED for review May 8, 1967 ACCEPTED November 7, 1967
DEVELOPMENT OF A SURFACTANT SYSTEM FOR ELIMINATING DROP STICKING IN A DEWAXING CRYSTALLIZATION TOWER N. N. LI Central Basic Research Laboratory, Esso Research and Engineering Co., Linden, N . J .
A water-soluble additive system consisting of two surfactants and two colloids is effective in preventing the sticking and disintegration of oil droplets in a brine medium inside a dewaxing crystallization tower.
a crystallization chilling tower. T h e coolant, which is usually brine, is introduced a t a temperature below the wax crystallization temperature of the feed. T h e feed, a waxy oil diluted with a solvent (such as hexane or liquid propane), enters the tower above its wax crystallization temperature in the form of a dense dispersion of droplets which move in the tower countercurrently to the continuous-phase coolant (Torobin, 1966) (Figure 1). As the dispersed-phase feed is gradually cooled to its wax crystallization temperature by direct contact with the coolant, wax crystals grow within each droplet. T h e adhesion of these crystals growing on the surfaces of impinging drops causes drop sticking, which drastically reduces the heat transfer area between oil and brine and thus reduces the over-all heat transfer efficiency (Figure 2). I n the severest cases droplets adhering to one another form rigid connecting networks of wax, which plug the tower. Until recently the only way to prevent sticking was to operate with expensive high solvent dilution and crystal modifier concentrations in the oil. Stirring unfortunately
W
AX may be separated from oil in
COOLANT (COLD)
I7 EF,lU :GE DENAXED OIL
(CONTINUOUS PHASE)
does not prevent drop sticking because of droplets sticking to the stirrer. Three schemes to use brine additives to prevent drop sticking consequently were investigated : the adsorption of surfactant film by oil droplets, colloidal dispersion in brine, and the formation of protective surface film by additive complexes. Brine additives have the inherent advantage over oil additives of remaining in the system and thereby reducing operating cost. I n this work, the waxy oil used was Solvent 100 Neutral (S100N). It is a middle distillate, having an average molecular weight (by osmometer) of 386.5, a cloud point of 93’F., and a pour point of 90’F. Its gravity is 0.836 gram per cc. between 18’ and 140’F. and its kinematic viscosities are 8.20 centistokes a t 150’F. and 4.02 centistokes a t 210’F. T h e additive system developed is applicable to not only SlOON but also other kinds of oil. T h e basic principle employed in developing the additive system can be used to develop other additive systems for preventing drop sticking in two-phase flow columns.
7 COOLANT (COLD BRINE) CLUSTERS OF STUCK DROPLETS POOR H E A T TRANSFER
CHILLING TOWER
, o o o ~ ~ o of-o
Figure 2. tower
DISCRETE O I L DROPLETS
Drop sticking in a crystallization
VOL 7
NO. 2
APRIL 1968
239
