I n d . Eng. Chem. Res. 1987,26, 82-86
82
Studies on Mixing Time in Bubble Columns with Pseudoplastic (Carboxymethy1)cellulose Solutions M. W. Haque, K. D. P. Nigam,* and V. K. Srivastava Department of Chemical Engineering, Indian Institute of Technology, New Delhi 110016, India
J. B. Joshi Department of Chemical Technology, University of Bombay,t UDCT, Matunga Road, Bombay 400019, India
K. Viswanathan Particle Technology Consultants, Research Centre, B-11312, East of Kailash, New Delhi 110065, India
Experimental mixing time data are reported in a 1.0-m-diameter bubble column employing highly viscous pseudoplastic CMC ((carboxymethy1)cellulose)solutions with a clear liquid height to diameter ratio of 1and 2, respectively. T h e number of circulations required for complete mixing has been determined to be 2.7 and 2.0 for H J D equal to 1 and 2, respectively. The liquid mixing behavior is explained in terms of the average liquid circulation velocity. The equivalent path lengths for lag time, bulk mixing time, and diffusion time are found to be (0.50 + H),(0.50 + H),and 50, respectively. Pharmaceutical, food processing, and biotechnological processes constitute a wide spectrum of chemical industries where bubble columns are used to process highly viscous media. The rheological behavior of viscous pseudoplastic non-Newtonian solutions can be fairly well simulated by the solutions of (carboxymethy1)cellulose(CMC) (Godbole et al., 1984). The gas holdup, interfacial area, and mixing are interrelated parameters. Mixing time is thus an important design parameter for bubble columns. The knowledge of mixing time also gives information regarding the liquid-phase flow pattern. Haque et al. (1985a) have pointed out that the knowledge of mixing time and fractional gas holdup data may be used for optimum sparger design in large-diameter bubble columns. Mixing time also helps in the determination of overall rates of reactions and estimations of wall heat and mass-transfer coefficients in bubble columns (Pandit and Joshi, 1984). Practically no information is available in the literature on mixing time in large-diameter bubble columns (low H I D ) employing non-Newtonian liquids. Ulbrecht and Baykara (1981) appear to have been the first to measure mixing time; they used a 0.10-m-diameter bubble column employing non-Newtonian liquids (aqueous solutions of CMC and polyethylene oxide). Pandit and Joshi (1983) studied liquid-phase mixing by employing non-Newtonian liquids in 0.20-m-diameter bubble columns that employ viscous CMC solutions. In all the above cases, the H,/D ratio was high (>3). In the previous paper, Haque et al. (1985b) reported gas holdup data in a 1-m-diameter column employing CMC solutions and concluded that the invicid circulation model of Viswanathan and Rao (1983, 1984) can successfully predict such data. An attempt is made in this paper to present a systematic method of the determination of mixing time from electrolyte concentration response data, to present experimental data from a 1-m-diameter bubble column employing CMC, and to interpret the results in terms of a mathematical model.
Theoretical Section For inviscid liquid circulation, the final theoretical expressions for gas holdup and liquid circulation velocity
* To whom correspondence should be addressed. Where experimental work was carried out.
0888-5885/87/2626-0082$01.50/0
were derived by Viswanathan and Rao (1983, 1984) as
U, = ubr(gRUG/~
~r3)~.~
(2)
Rearranging eq 1 gives eq 3. From eq 2 it follows that Ubr can be obtained from the slope of the plot of UG2vs. t2,5 (Haque et al., 1985b). UG2
= 4Ubr(gD)05t2.5
(3)
The length of the path for a circulation cell equals twice the sum of the column radius and the dispersed liquid height. The liquid circulation time, therefore, is given by eq 4 or 5. Mixing time in a bubble column can be defined t , = 2(H + R ) / U , (4)
t, = (D/U,)(l + 2H/D)
(5)
as eq 6 where N is the number of circulations required for complete mixing. The value of N can be obtained from the slope of the plot of the experimental mixing time against the circulation time.
t, = Nt,
(6)
Experimental Section The schematic diagram of the experimental setup is shown in Figure 1. This is the same as described previously (Haque et al., 1985b), the only addition being the concentration measurement system. The bubble column was of 1.0-m diameter and 2.4-m height. Air and CMC solutions were used as the gas and liquid phases, respectively. A single-ring sparger (ring diameter = 580 mm, number of holes = 148, hole size = 2.0 mm) was used in the study. The clear liquid height was maintained at either 1.0 or 2.0 m. Experiments were carried out in a semibatch manner. The column was filled with the desired liquid up to a predetermined level. The air flow rate was measured with a precalibrated rotameter. The values of gas holdup were determined from the clear liquid height and the height of the dispersion. The values of mixing time were measured by using a pulse technique. A pulse of electrolyte solution 0 1987 American Chemical Society
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 83 A
B BC
C CM
CR CV 0 P
R
5
"
-
AGITATOR B Y P A 5 5 TANK BUBBLE COLUMN CONDUCTIVITY PROBE - CONDUCTIVITY METER - CHART RECOROER - CHECK VALVE - DRAIN - PUW - ROTAMETER - SPARGER FOR GAS VALVE
. .
Figure 1. Schematic diagram of the experimental setup.
Figure 2. Typical response curves for low and high CMC concentrations.
Table I. Physical Properties of Aqueous CMC Solutions CMC flow consisliquid surface concn, behavior tency index density, tension, % wt indexn k,Pa.sn kg/ms N/m 0.1 0.80 0.012 1000 0.073 0.5 0.70 0.061 1003 0.072 1.0 0.67 0.102 1006 0.070
(NaC1 solution) of known volume and concentration was added at the top of the dispersion. The conductivity probe was placed near the bottom of the column (other end). The conductivity response was recorded with the help of a strip chart recorder. I t has been reported (Pandit and Joshi, 1983) that the ratio of the volume to the total liquid volume (u/ V) of pulse has no effect when v / V is greater than 1/100. Experiments were performed accordingly. Since the presence of electrolyte is likely to affect the gas holdup and mixing time, a fresh liquid batch was used for each experiment. This made the experimentation quite costly, for fresh solution of a given CMC concentration had to be prepared for each experiment. This can possibly be avoided by using a thermal response technique (in which case the rheological behavior has to be obtained at the increased temperature). The CMC solutions were prepared by dissolving CMC powder (CEPOL, M/s Cellulose Products of India Ltd.) in tap water. The rheological properties of CMC solutions were sensitive to the mixing techniques. Hence, these were checked several times to ensure constant consistency index and flow behavior index for the same concentration (5% wt) of CMC solution. The rheological properties were measured with a Couette viscometer (Haake). The physical and rheological properties of CMC solutions are given in Table I.
Results and Discussion Typical response curves for both low and high CMC concentrations are shown in Figure 2. For both of the cases the concentration of the electrolyte in the control volume around the measurement probe equals zero for a finite initial "lag time" (t,) taken by the electrolyte (tracer) to traverse the distance between the point of addition and the point of measurement. For low CMC concentrations, the tracer (electrolyte) concentration in the control volume begins to increase at t = tl, and the concentration leaving the control volume due to bulk mixing and diffusion does not increase at the same rate as that entering, leading to concentration buildup which appears as a peak in the response curve. The time from the beginning of the increase in concentration to the peak may be called the "bulk mixing time" (tb). Once the concentration reaches the maximum level, diffusion of the electrolyte from the control volume may be assumed to begin (although, diffusion of the electrolyte occurs also during tb). This continues until complete mixing is achieved. The "diffusion time"
la4
Figure 3. U Gvs. ~
tZ5
x
c25
for 1.0-m-diameter column and HID = 1.
is defined in Figure 2. The total mixing time is t , = t , + t b + td. However, for high CMC concentrations, the
(td)
concentration in the control volume never builds up to such an extent as to show a peak (probably due to high apparent viscosity and low diffusion). Therefore, for high CMC concentrations, t b and t d cannot be separated, and we have simply t , = tl + ( t b t d ) , where t b + t d is shown in Figure 2. Since the response curve has an inherent fluctuation, a sound basis for evaluating t,, tb, and t d would be to linearize the measured response curve as shown in Figure 2, the time periods between the points of intersection of different lines giving tl, t b , and td. This method is adopted here. A similar method is usually adopted to predict the minimum fluidization velocity in fluidized beds (Kunii and Levenspiel, 1969). For the calculation of the average liquid circulation velocity (U,) and circulation time (t,), Ubr values are necessary. As explained elsewhere (Haque et al., 1985b), it is obtained from a plot of UG2vs. measured t2.5. Typical data given by Haque et al. (1985b) are reproduced in Figures 3 and 4. These Ubr values are used in further calculations. The average liquid circulation velocity corresponding to the different experimental runs calculated from eq 2 is shown as a function of superficial gas velocity in Figure 5. The experimental mixing time data are shown as a function of gas velocity in Figures 6 and 7. It can be seen that mixing time is more sensitive to gas velocity at low UG. The dependency of mixing time on CMC concentration is shown in Figure 8. It can be seen that the effect of CMC is greater at higher H I D values. The correlation for experimental mixing time with calculated circulation time (eq 6) for all the data is shown
+
84
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 ,a
fi
,/
/' ,/
I Ub,Z
0365
,'0."7
^.I48
006m 5
, '
i
30 ;
y,'
3
,"
40
.04 x 1 2 5
Figure 4. UG2vs.
f2.5
us l m l i i
for 1.0-m-diameter column and
HID
= 2.
Figure 6. Mixing time vs. superficial gas velocity for HID = 1.
'01 HID: 2
p
y 9
5
T 01 05
0
/ 2 3
'
,0..4 , - .i_.-----I__
-
t
001
0 32
3c3
33'
u5 l m l s l
Figure 7. Mixing time vs. superficial gas velocity for HID = 2.
21-
O J
//
0
0 01
002
003
0 34
0 05
0 06
d~ I m i i :
Figure 5. Average liquid circulation velocity vs. superficial gas velocity.
in Figure 9. As already explained, the slope gives the number of circulations required to achieve complete mixing. It is interesting to note in Figure 9 that the data for H I D = 1 and 2 fall distinctively around two separate straight lines with slopes of 2.7 and 2.0, respectively. Therefore, mixing time can be predicted as t, = Nt,
(7)
where
N = 2.7
for
H,/D = 1
(8)
N = 2.0
for
H,/D = 2
(9)
The predictions of eq 7-9 are also included in Figures 6-8. It can be seen that the comparison of predictions with the data is reasonably good.
Figure 8. Mixing time vs. CMC concentration by weight.
The liquid circulation pattern can be in either of the following two ways. (1) Bubbles from all the nozzles approach the central region and travel upward in a bubblerich zone, leading to the liquid circulation pattern as shown in Figure 10A. (2) Bubbles move toward the wall, leading to the liquid circulation pattern as shown in Figure 10B. A similar pattern has also been observed for solid circulation near the grid region ofa fluidized bed (Viswanathan, 1983).
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 85
20 -
slope
siope :2 ?
:2
G
S
-_--
C Symbol
H I D '/. CMC
S
I '
- Complete - Start
01
05 2
1 Circulation
6
a
I0
10
;2
time , IC [51
Figure 9. Mixing time vs. average liquid circulation time.
However, it is interesting to note that for both of the above patterns, the average liquid circulation velocity and the mixing time are the same, only the direction of the liquid circulation being different. It may be interesting to estimate the path lengths for complete mixing. This is given by 2N (R + H) from eq 8 and 9, and it follows that the path lengths for HJD = 1 and 2 are 8.10 and lOD, respectively. Though the number of circulations is higher for HJD = 1,the path length for complete mixing for this case is smaller. It is proposed that the path length equivalent for lag time is (R + H), the bulk mixing time accounts for another ( R + H) and the diffusion time for the rest of the total path length (which is 5.10 and 5.00, respectively, for HID = 1and 2). This independence of the equivalent path length for t d can be used to predict the time of circulation required for complete mixing (eq 10). The mixing time can be predicted from eq 7 and 10.
LT 2(R+H) +5D N = - - LC 2(R + H) = 1 + 5D/(D + 2H) = 1 + 5/(2H/D + 1)
(10)
Conclusions An expression was developed to predict the circulation time in bubble columns. The time required for complete mixing of the liquid was assumed to be proportional to circulation time, the proportionality constant being the number of circulations required. A new method, avoiding any systematic bias, was presented to determine the mixing time from experimentally measured response to a pulse input of tracer. Experimental mixing times thus obtained in a 1.0-m-diameter bubble column employing pseudoplastic CMC solutions were reported. It was found that the total mixing time is comprised of a lag time, a bulk mixing time, and a diffusion time. The
(0)
Figure 10. Liquid circulation pattem. Path lengths: (- - -) lag, (-- -) bulk mixing, (-) diffusion.
equivalent path lengths were found to be (R + H),( R + tb, and t d , respectively. The number of circulations required for complete mixing was found to be 2.7 and 2.0 for H I D = 1 and 2, respectively. It was found to be independent of all other parameters. Thus, the mixing time can be predicted from eq 5, 7, and 10 as t , = (1 + 5/(2H/D + l))(D/U,)(l + 2H/D) = (H/D + 3)2D/U, (11)
H), and 5 0 for tl,
Nomenclature D = column diameter, m g = gravitational acceleration, m/s2 H,= clear liquid height, m H = dispersed height, m k = fluid consistency index, P a 4 LT = defined in eq 10 L, = defined in eq 10 N = number of circulations required for mixing n = flow behavior index R = column radius, m tb = bulk mixing time, s t , = one circulation time, s t d = diffusion time, s tl = lag time, s t , = total mixing time, s U, = average liquid circulation velocity, m/s U , = superficial gas velocity, m/s Ubr = single bubble rise velocity, m/s Greek Letter t
= gas-phase holdup
Ind. Eng. Chem. Res. 1987,26, 86-91
86 Registry
No. CMC, 9000-11-7.
Literature Cited Godbole, S. P.; Schumpe, A.; Shah, Y. T.; Carr, N. L. AIChE J. 1984, 30, 213. Haque, M. W.; Nigam, K. D. P.; Joshi, J. B.Chem. Eng. J., in Press. Haque, M. W.; Nigam, K. D. P.; Viswanathan, K. Ind. Eng. Chem. Process Des. Deu. 1985b, in press. Kunii, D.; Levenspiel, 0. Fluidization Engineering; Wiley: New York, 1969.
Pandit, A. B.; Joshi, J. B. Chem. Eng. Sci. 1983, 38, 1189. Pandit, A. B.; Joshi, J. B. Rev. Chem. Eng. 1984, 2, 1. Ulbrecht, J. J.; Baykara, L. E. Chem. Eng. Commun. 1981, IOU-31, 165. Viswanathan, K. Ph.D. Thesis, Indian Institute of Technology, New Delhi, 1983. Viswanathan, K.; Rao, D. S. Chem. Eng. Sci. 1983, 38, 474. Viswanathan, K.; Rao, D. S. Chem. Eng. Commun. 1984, 25, 133.
Received for review August 8, 1985 Revised manuscript received April 24, 1986 Accepted May 30, 1986
Studies on Gas Holdup and Bubble Parameters in Bubble Columns with (Carboxymethy1)cellulose Solutions M. W.Haque and K. D. P. Nigam* Department of Chemical Engineering, Indian Institute of Technology, New Delhi 110016, India
K. V i s w a n a t h a n Particle Technology Consultants, Research Centre, B - I I 3 / 2 , East of Kailash, New Delhi 110065, India
J. B. J o s h i Department of Chemical Technology, University of Bombay,' L'DCT, Matunga Road, Bombay 400019, India
Experimental data are reported on the gas holdup in 0.20-, 0.38-, and 1.0-m-diameter bubble columns employing highly viscous pseudoplastic (carboxymethy1)cellulose (CMC) solutions. Although the liquid employed is viscous, it is shown that the inviscid circulation model explains the data extremely well. A new method is developed to obtain the isolated bubble rise velocity and the volume-to-surface mean bubble diameter from gas holdup data. The bubble size increases with HID until HID = 3, after which it becomes constant, and it increases with the CMC concentration. It is the characteristic feature of pseudoplastic systems that the bubble size decreases with increasing gas velocity due to increasing shear. It is well-known that bubble columns are widely used in process industries as absorbers, strippers, gas-liquid reactors, etc. Biotechnology, food processing, and pharmaceutical processes constitute a wide spectrum of chemical industries where bubble columns are used and highly viscous media are processed. The rheological behavior of such viscous pseudoplastic non-Newtonian solutions can be fairly well simulated by the solutions of (carboxymethy1)cellulose (CMC) (Godbole et al., 1984). In bubble columns gas holdup is one of the most important parameters that characterizes the hydrodynamics. Gas holdup in gas-liquid systems gives the volume fraction of the gas phase and hence the gas residence time. Further, the gas holdup in conjunction with the knowledge of the mean bubble diameter allows the determination of interfacial area and mass-transfer rates between the gas and liquid phases. Thus, quantitative relationships among these factors are required, such relationships are available for Newtonian systems (Viswanathan and Rao, 1983,1984), but for CMC solutions available information is scarce for large-diameter columns. The gas holdup, the values of effective interfacial area, and the values of mixing are directly dependent etc. the bubble sizes. Bubble size and its distribution and bubble rise velocity have a direct bearing on the performance of bubble columns. Many methods are available to determine bubble sizes. Photographic techniques are widely used
* To whom correspondence should be addressed. 'Where experimental work was carried out.
because of their simplicity. Though the original bubble size distributions obtained from various measurement techniques differ markedly, the volume-to-surface mean bubble diameters evaluated consequently differ only slightly (Shah et al., 1982). However, it may be pointed out that photographic, electrical, and optical techniques give reliable results only in the bubbly flow regime, whereas the churn-turbulent regime is the most commonly encountered regime in the industrial bubble columns (Bach and Pilhofer, 1978). All the techniques stated above are direct measurement techniques. They have the disadvantage that special arrangements are necessary and that, further, the results may not be reliable. Liquid circulation induced by bubble movement has been experimentally measured by many investigators, and these results have etc. critically discussed (Viswanathan and Rao, 1984). Some investigators (Rietema and Ottengraf, 1970; Crabtree and Bridgewater, 1969) have analyzed circulation created by gas bubbling in viscous liquids. However, most of the literature data is for air-water-like systems. For such systems, viscous effects are negligible under normal operating conditions, and hence, inviscid theory is a reasonable approximation. Viswanathan and Rao (1983, 1984) proposed a model to calculate inviscid liquid circulation in cylindrical columns, and the resultant equations were analytical in nature. They also proposed a theoretical equation for gas holdup. The experimental information available on circulation in bubble columns with pseudoplastic solutions (CMC) are those of Franz et. al. (1980), Schugerl(1981),and Schumpe 1987 American Chemical Society
