Ind. Eng. Chem. Res. 1994,33,2180-2186
2180
GENERAL RESEARCH Liquid Mixing in Internal Loop Airlift Reactors Wen-Jang L u a n d S h y h - J y e Hwang' Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.
Chun-Min C h a n g Department of Biotechnology, Union Chemical Laboratories, ZTRZ, Hsinchu, Taiwan 30043, R.O.C.
Liquid mixing in the riser and downcomer of two- and three-phase internal loop airlift reactors as well as the overall liquid mixing were studied. Tracer was injected into the airlift reactors, and pH sensors were employed to measure the variations of tracer concentration in the riser, downcomer, top, and bottom sections. The Bo number in individual sections of the airlift reactors were obtained by time domain analysis of these concentration variations. It was found that the degree of mixing in the riser was higher than that in the downcomer. Moreover, mixing in the two-phase system was superior to that in the three-phase system, and the degree of mixing of the calcium alginate system was lower than that of the polystyrene system. Minimum values of the overall axial dispersion coefficient existed in the relationship between the overall axial dispersion coefficient and solids loading. Introduction The airlift reactor is a promising reactor for two- and three-phase reactions due to its advantages of high fluid circulation, mass and heat transfer, short mixing time, low shear stress, and energy consumption. It has been widely applied in biochemical fermentation, chemical reactions, and biological wastewater treatment processes. An airlift reactor consists of four distinct sections, riser, downcomer, top, and bottom sections. Each section exhibits different hydrodynamic and mixing behavior. Hence, for reactor design purpose it is necessary to understand the hydrodynamic and mixing behavior in individual sections of the airlift reactor. Tracer injection and response method has been used to study the mixing characteristics of reactors. Techniques such as the moment (Hatch, 1973), weighted moment (Anderssen and White, 1977),Laplace and Fourier transform domain analysis (Gangwal et al., 19711, and time domain analysis (Verlaan et al., 1989;Mills and Dudukovic, 1989) have been employed to analyze the tracer response data. Fahim and Wakao (1982) suggested that time domain analysis was the best method for the evaluation of mixing parameters. Verlaan et al. (1989) investigated mixing behavior in individual sections of an external loop airlift reactor by time domain analysis. They showed that the liquid flow in the riser and downcomer were close to plug flow and the top section was fairly well-mixed. Fields and Slater (1983) also reported that the top section approached well-mixedness at high aeration rate. Merchuk and Siege1 (1988) used a simple model for split airlift reactors, which was represented by two plugflow zones for the riser and the downcomer and a completely mixed zone for the top section. This model could reasonably describe the mixing behavior in the well-mixedtop section, but it neglected the effect of axial dispersion in the riser and downcomer.
* To whom correspondence should be addressed.
Immobilized enzyme reactions and cell biocatalyst particle fermentations are often used in biochemical processes, so the investigation of the influence of solids loading on the mixing behavior of the airlift reactors is important. Verlaan and Tramper (1987) and Kennard et al. (1991)studied the mixing behavior in three-phase airlift reactors. Verlaan and Tramper (1987) found Bo number increases with increasing solids loading in an external loop airlift reactor. Kennard et al. (1991) showed that the effect of solids loading on mixing were unpredictable. Moreover, study of the effect of solids loading on liquid mixing in individual sections of three-phase internal loop airlift reactors is still lacking. The purpose of this study was to investigate the hydrodynamic and mixing behavior including liquid mixing and velocity in the riser and downcomer, and the overall liquid mixing characteristics of internal loop airlift reactors. The Bo number was estimated by time domain analysis. The distinctions in the mixing behavior between two- and three-phase airlift reactors were discussed. Effects of operating parameters including draft tube length, aeration rate, and solids loading on liquid mixing in the internal loop airlift reactors were extensively examined. Materials and Methods Experimental Equipment. The apparatus for investigating liquid mixing in two- and three-phase internal loop airlift reactors is shown in Figure 1. A dimensioned elevation sketch of the reactor is shown in Figure 2. The reactor is constructed by Plexiglas, and the inside diameter and height of the airlift reactor are 18 and 250 cm, respectively. The diameter and thickness of the draft tube are 12 and 0.5 cm, respectively, which makes the ratio of the cross-sectionalarea of the riser to the downcomer equal to 1. Both the draft tube and the reactor consist of four sections, and they can be taken apart and rearranged to obtain the desired height. Unless specified otherwise,the
0 1994 American Chemical Society oaaa-5aa519412~33-2~a~~~4.5010
Ind. Eng. Chem. Res., Vol. 33, No. 9, 1994 2181 Table 1. Physical Properties of Solids Used in the Experiments solid polystyrene Ca-alginate
Ei /I
7
? 1
A,?-
'?
1. outer column
2. 3. 4. 5. 6.
Draughttube Gessparger Tracer injection port pH electrodes pHtransmittem
7. Data acquisition system 8. Computer 9. Ressure regulator 10. Mass flowmeter 1 1. Pressure gauge 12. Drain
Figure 1. Schematic diagram of experimental apparatus.
D,,
Ps,
vt,
mm
g/cm3
cm/s
hardness
characteristics
2.4 2.4
1.05
3.9 2.4
rigid soft
hydrophobic hydrophilic
1.03
signals of all pH sensors are transmitted to a computer by the data acquisition system. The pH values of the liquid in the riser and the downcomer sections were recorded every 0.1 s by the computer, and the measured pH values were then converted to actual concentrations through a calibration curve. The computer recording was synchronized manually with the introduction of every pulse of 1 mL of 10 N NaOH solution through the injection port located at 5 cm above the bottom of the reactor. Air and water were used as the gas and liquid phases, respectively, and solids used in the experiments were polystyrene cylinders and calcium alginate beads. Calcium alginate beads were produced by dropping method (Hulst et al., 1985). The properties of the solids are given in Table 1. Determinationsof the Degree of Liquid Mixing and MixingTime. Many researchers used an axial dispersion model to describe the overall mixing phenomena in airlift reactors (Frohlich et al., 1991; Kochbeck et al., 1992).The mathematical expression can be shown as
ac, -_---a%, ac, _ a?
BO
az2
az
where Bo is the Bodenstein number, a dimensionless mixing parameter defined as
Bo = VLID lOcm
120cm
C, is the dimensionless concentration, CIC,, z is the dimensionless length, xlL, 7 is the dimensionless time, tlt,, L is the distance between two measured points, and t, is the circulation time. Note that tc is obtained by the average time difference between adjacent peaks of the tracer response curve. The liquid linear velocities in the riser and downcomer are obtained by the following equations:
v, 1Ocm
-
1Ocm J
y
t
,
c
m
Figure 2. Dimensioned elevation sketch of airlift reactor.
length of the draft tube used in this study is 110 cm, and the draft tube is located 10 cm above the base of reactor. The gas is dispersed by a ring sparger located a t the bottom edge of the draft tube. The sparger is a circular steel pipe with pipe and ring diameters of 0.5 and 9 cm, respectively. There are sixteen 1-mm holes on the upper side of the sparger with equal space (about 1.6 cm) between two holes, and four 1mm holes on the lower side of the sparger with equal space (about 6.9 cm) between two holes. The aeration rate is measured by a mass flowmeter. Four pH sensors linked to the RTI-820 AID and D/A data acquisition system are located in the riser and downcomer sections, two in each section. The response time of the pH sensors is 0.1 s within pH = 7-10. The
(2)
= L,/t,
(3) (4)
where L, and& are the distances between two pH sensors in the riser and downcomer, respectively, and t, and td are the differences in response time between two pH sensors in the riser and downcomer, respectively. In this paper, the time domain analysis method is used for the estimation of the Bo number in individual sections of two- and three-phase airlift reactors. This method was first employed by Verlaan et al. (1989) to obtain the Bo number in individual sections of an external loop airlift reactor. Figure 3 shows the algorithm for the prediction of the Bo number. In Figure 3 the transfer function F(iw) is obtained from Verlaan et al. (19891, and the discrete Fourier transformation and inverse discrete Fourier transformation were evaluated by subroutines FFT (fastFourier transformation) and IFFT. The variance for a reactor is equal to the sum of the variances in individual sections, so the variance in an airlift reactor as a whole can be obtained by (Levenspiel, 1972) (5)
2182 Ind. Eng. Chem. Res., Vol. 33, No. 9, 1994 Start
b y FFT
New Bo and TW
P r e d i c t e d r e s p o n s e Yp(t)
Compare Yp(t) w i t h experimental o u t p u t response Y ( t )
k=l
I
1
The O D t i m u m Bo
1
Figure 3. Algorithm for prediction of Bo number.
Note that the variance is calculated by
where K t C ( t ) dt (7)
P=
somC(t)dt Moreover, the relationship between the Bo number and the variance of a system is (Levenspiel, 1972)
In order to minimize the error associated with a nondelta pulse, Aris (1959) and Bischoff (1960) proposed a method for the determination of the dispersion coefficient over a regime of finite length. According to their method, the tracer concentration should be measured at two points in the system, and the difference in concentration variances, Au2 = uz2 - u12, is substituted for u2 in eqs 5 and 8 to reduce error due to a finite injection pulse. After the Bo numbers of individual sections were obtained by time domain analysis, the difference in variances of individual sections could be calculated by eq 8. The overall Bo number of the airlift reactor could then be estimated from eqs 5 and 8. The mixing time in the airlift reactor is defined in this study as the time required for the homogeneity to reach 0.01, which is a typical value used for design purposes in agitated vessels. Note that the homogeneity, h, is defined as
Results and Discussion Parts a, b, and c of Figure 4 show the comparison of the output response curves and the predicted curves in the
riser, top and downcomer sections, respectively. As shown in these figures, the predicted curve matches the output response curve for each section. Therefore, accurate Bo values of individual sections could be obtained by time domain analysis. The Bo numbers in the top, riser, downcomer, and bottom sections and the overall Bo number for 5 vol 5% polystyrene system are shown in Figure 5. It is seen in this figure that the Bo numbers are 20-30 in the riser, 40-70 in the downcomer, about 10 in the top section, and 10-20 in the bottom section. Thus, the mixing in the riser is better than that in the downcomer, and the mixing in the top is highest among all sections. Moreover,the mixing is also very intensive in the bottom section due to rapid flowing and turning around of the fluid and impingement of downflow fluid at the bottom of the reactor. Axial dispersion coefficientsin the reactor and individual sections for the whole range of aeration rates used in this . study are shown in Figure 6. Solids loading is 5 ~ 0 1 5 %As shown in this figure, the axial dispersion coefficients are 100-220 cm2/sin the riser section and 30-70 cm2/s in the downcomer section for Hd = 110 cm. Thus, the mixing in the riser section is about 3 times as much as that in the downcomer section. The overall axial dispersion coefficient lies between those at the riser and downcomer sections, but is closer to that at the riser section. This is due to the contributions of highly mixed top and bottom sections. It should be noted in the figure that the axial dispersion coefficient increases with increasing aeration rate. Figure 6 also shows the influence of draft tube length on the axial dispersion coefficient. The top clearance is 20 cm. It is found that the axial dispersion coefficients in the riser and the downcomer sections with Hd = 170 cm are higher than those with Ha = 110 cm. This is due to the fact that longer draft tube results in higher liquid circulation velocity, which gives rise to higher axial dispersion coefficient. However, the overall axial dispersion coefficientdecreases with increasingdraft tube length. Although the top clearance is the same for both draft tubes, the liquid volume of the top section for Hd = 110 cm is 15.1 9% relative to total liquid volume, while it is 11.4%for Hd = 170 cm. Therefore, the contribution of the top section
Ind. Eng. Chem. Res., Vol. 33, No. 9, 1994 2183 100 40
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Figure 5. Eo number in individual sections and overall Eo number (5 vol % polystyrene, Hd = 110 cm, Ht = 140 cm).
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Figure 6. Influence of aerationrate on D a~ a function of draft tube length (5 vol % polystyrene, top clearances = 20 cm).
00 0
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Time, sec
Figure 4. (a, top) Comparison of output response curve of the riser and the predicted one (Eo = 28). (b, middle) Comparison of output responsecurve of the top and the predicted one (Eo = 7). (c, bottom) Comparison of output response curve of the downcomer and the predicted one (Eo = 55).
to the overall axial dispersion coefficientfor a shorter draft tube is substantially higher than that for a longer draft tube, which leads to a higher overall dispersion coefficient for a shorter draft tube system. It should be noted that the effect of draft tube length on the overallaxial dispersion coefficient found in this study is similar to that reported by Fields and Slater (1983). In this paper, polystyrene cylinders and calcium alginate beads, which exhibit different properties, are used to study the influence of solid on the degree of mixing. Figure 7a shows the Bo number in the riser section as a function of aeration rate for two-phase and three-phase systems. The solids loading for three-phase system is 5 vol 7%. It is
shown in this figure that the Bo number for the polystyrene system is close to that for the two-phase system. However, the Bo number for the calcium alginate system is higher than that for the two-phase system. It was observed that the liquid velocityin the calcium alginate system was lower than that in the two-phase system (Figure 7b), which would lead to lower mixing and higher Bo number for the calcium alginate system. However, polystyrene particles are hydrophobic so that small bubbles adhere easily to the surface of the polystyrene particles. Thus, the average density of polystyrene particles is lower than that of water. This makes the liquid velocity in the riser of polystyrene system close to that of the two-phase system (Figure 7b). Thus, the Bo number for the polystyrene system is similar to that for the two-phase system. Comparison of the Bo number in the downcomer between two- and three-phase systems is shown in Figure 8a. Since the liquid velocity of the two-phase system is higher than that of the three-phase systems (Figure 8b), the Bo number for the two-phase system is lower than that for the three-phase systems. In addition, the Bo number for the polystyrene system is lower than that for the calcium alginate system due to enhancement of mixing by bubble-attached polystyrene particles in the polystyrene system. It should be noted that the Bo number in the riser is lower than that in the downcomer. This is similar to that observed in the two-phase system. Comparison of the overall Bo number between two- and threephase systems is given in Figure 9. As shown in this figure, the two-phase system has the lowest Bo number, and the
2184 Ind. Eng. Chem. Res., Vol. 33, No. 9, 1994 50
TWOPhase 5%PS 5% Alginate
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i: t
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Figure 7. (a, top) Comparison of riser Bo number between twophase and three-phase systems (Hd= 110 cm, Ht = 140 cm). (b, bottom)Comparisonof riser linear liquidvelocitybetweentwo-phase and three-phase systems (Hd= 110 cm, Ht = 140 cm).
calcium alginate system has the highest Bo number. The Bo number for the polystyrene system lies between those for the the calcium alginate system and the two-phase system. Another indicator of the degree of mixing is the mixing time. The higher the degree of mixing, the shorter the mixing time. Figure 10shows the comparison of the liquid mixing time between two- and three-phase systems. It is found that the liquid mixing time is the highest for the calcium alginate system, followed by the polystyrene system, and the mixing time for the two-phase system is smallest. These results are consistent with those for the overall Bo number shown in Figure 9; i.e., the Bo number is larger when the mixing time is longer. Effect of solids loading on the overall axial dispersion coefficient of polystyrene system is shown in Figure 11.It is noted that the overall axial dispersion coefficient decreases with initial addition of solids. It reaches a minimum value and then increases with increasing solids loading. During the experiments, it was observed that the collision of solids increased as solids loading was increased. These collisions generated liquid vortices, which probably led to better mixing in the reactor. However, the gas holdup decreased as solids loading was increased, which would lead to a decrease in liquid mixing. These two counteracting effects gave rise to the results shown in Figure 11. The mixing time in the polystyrene system as a function of solids loading for various aeration rates was reported elsewhere (Chang et al., 1993). It was observed that the
I 80
I
Qg , limin
Figure 8. (a, top) Comparison of downcomer Bo number between two-phase and three-phase systems (Ha= 110 cm, Ht= 140 cm). (b, bottom) Comparison of downcomer linear liquid velocity between two-phase and three-phase systems (Hd= 110 cm, Ht= 140 cm). 95 A
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-. m y
go
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TwoPhase 5%PS 5% Alginate
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c-
I 10
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' 50
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Qg , llmin
Figure 9. Comparisonof overaUBo number between two-phaseand three-phase systems (Ha= 110 cm, Ht= 140 cm).
mixing time increased with increasing solids loading up ' . When solids loading was increased beyond to 15 vol % 15 vol 7%, the trend was reversed. Those results are also consistent with the results for the overall axial dispersion coefficient shown in Figure 11. Conclusions Experiments were conducted to study liquid mixing behavior in two- and three-phase airlift reactors. Time
Ind. Eng. Chem. Res., Vol. 33, No. 9, 1994 2185 Nomenclature 85
75 t
i \\
Two phase 5% PS 5% Alginate
-0-
-0-
-A-
m 55
c ._ x
50 45
30 0
10
20
30
40
50
60
70
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90
100
110
Qg , t h i n
Figure 10. Comparisonof mixing time between two-phase and threephase systems as a function of aeration rate. 1 00 0 95
Subscripts b = bottom section c = whole reactor d = downcomer 1 = liquid r = riser t = top
0 90 0 85 0 80
.
Bo = VL/D, Bodenstein number, dimensionless C = tracer concentration, mol/L Cm = homogeneous tracer concentration, mol/L C, = C/C,, dimensionless concentration D = axial dispersion coefficient, cm2/s D, = equivalent diameter, mm F = transfer function h = homogeneity, dimensionless Hd = length of draft tube, cm Ht= height of static liquid, cm i = i 2 = -1 L = characteristic length, cm t = time, s t = mean residence time, s t, = circulation time, s V = linear fluid velocity, cm/s V, = terminal velocity, cm/s x = axial distance, cm z = x/L, dimensionless length
075
070 -0-0-
-A-
Qg=30 llmin Qg-50 llmin Qg=70 llrnin
0 55 0 50 0
5
10
15
20
25
Greek Symbols = mean of residence time distribution function, s 02 = variance, s2 7 = t/t,, dimensionless time w = frequency, rad/s p
30
PS% , -
Figure 11. Effect of solids loading on overall axial dispersion coefficient of polystyrene system (Hd= 110 cm, Ht = 140 cm).
domain analysis was used to obtain the Bo number in individual sections of the airlift reactors. It was found that the overall axial dispersion coefficient increased as aeration rate was increased for the two-phase system, but it decreased as draft tube length was increased. However, the axial dispersion coefficient in the riser and the downcomer increased with an increase in aeration rate or draft tube length. The overall Bo number and the Bo number in the downcomer of the three-phase system were higher than those of the two-phase system, and they were higher in the calcium alginate system than in the polystyrene system. In addition, the Bo number in the riser of the calcium alginate system was higher than the two-phase system, but that of the polystyrene system was close to the twophase system. For the polystyrene system, the overall axial dispersion coefficient decreased initially with increasing solids loading, reached a minimum value, and then increased with increasing solids loading. Moreover, the results of liquid mixing time were consistent with those for the overall Bo number.
Literature Cited Anderssen, A. S.; White, E. T. Parameter estimation by the weight moments method. Chem. Eng. Sci. 1977,26,1203-1221. Ark, R. Notes on the diffusion-type model for longitudinal mixing in flow. Chem. Eng. Sci. 1959,9,266267. Bischoff, K. B. Notes on the diffusion-type model for longitudinal mixing in flow. Chem. Eng. Sci. 1960,12, 69-70. Blenke, H. Loop reactors. Adu. Biochem. Eng. 1979, 13, 121-214. Chang, C. M.; Lu, W. J.; Own,K. S.; Hwang, S. J. Operation conditiona affectingtheperformanceofairliftreactorsfor immobilizedenzyme reactions. Biotechnol. Tech. 1993, 7,317-322. Chisti, M. Y. Airlift Bioreact0rs;Elsevier Sci. Pub.: New York, 1989. Fahim, M. A.; Wakao, N. Parameter estimation from tracer response measurements. Chem. Eng. J. 1982,25, 1-8. Fields, P. R.; Slater, N. K. H. Tracer dispersion in a laboratory airlift reactor. Chem. Eng. Sci. 1983,38,647453. Frbhlich, S.; Lotz, M.; K o a , T.; Labbert, A,; Schwerl, K.; Seekamp, M. Characterization of a pilot plant airlift tower loop bioreactor. I: Evaluation of the phase properties with model media. Biotechnol. Bioeng. 1991,38,43-55. Gangwal, S. K.; Hudgins, R. R.; Bryson, A. W.; Silveston, P. L. Interpretation of chromatographic peaks by Fourier analysis. Can. J. Chem. Eng. 1971,49,113-119. Hatch, R. T. Experimental and theoretical studies of oxygen transfer in the airlift fermenter. Ph.D. Thesis, Massachusetts Institute of Technology, 1973. Hulst,A. C.;Tramper, J.;Van’tRiet,K.; Westerbeek,J. M. M.Anew technique for the production of immobilized biocatalyst in large quantities. Biotechnol. Bioeng. 1985, 27, 87+876. Kennard, M.; Janekeh, M. Two- and three-phase mixing in a concentric draft tube gas-lift fermentor. Biotechnol. Bioeng. 1991, 38,1261-1270.
Acknowledgment This work was supported by the National Science Council under Grant NSC 81-0402-007-590.
Kochbeck, B.; Lindert, M.; Hempel, D. C. Hydrodynamics and local parameters in three-phase-flow in airlift-loop reactors of different scale. Chem. Eng. Sci. 1992,47, 3443-3460. Levenspiel, 0. Chemical Reaction Engineering. John Wiley, New York, 1972.
2186 Ind. Eng. Chem. Res., Vol. 33, No. 9,1994 Merchuk, J. C.; Siegel,M. H. Airlift reactor sin chemicaland biological technology. J. Chem. Technol. Biotechnol. 1988,41,105-120. Mills, P.L.; Dudukovic, M. P. Convolution and deconvolution of nonideal tracer response data with application to three-phase pached-beds. Comput. Chem. Eng. 1989,13,881-898. Rousseau, I.; Bu'lock, J. D. Mixing characteristics of a simple airlift. Biotechnol. Lett. 1980,2,475-480. Verlaan, P.; Tramper, J. International Conference on Bioreactors andBiotransformations,Moody,G.W.,Baker,P. B.,Eds.;Elsevier Sci. Pub.: London, 1987;pp 363-373.
Verlaan, P.; Van Eijs, A. M. M.; Tramper, J.; Van't Riet, K.; Luyben, K. Ch. A. M. Estimation of axial dispersion in individual sections of an airlift-loop reactor. Chem. Eng. Sci. 1989,44,1139-1146.
Received for review August 30, 1993 Revised manuscript received May 24, 1994 Accepted June 15, 1994O *Abstract published in Advance ACS Abstracts, August 1, 1994.
