- Email: [email protected]
On the estimation of effective shear rate in external loop airlift reactors: non-Newtonian fluids
let~-lLl~elh
comx, vati~ ELSEVIER
Resources, Conservationand Recycling18 (1996) II 24
On the estimation of effective shear rate in external loop airlift reactors: non-Newtonian fluids W.A. A1-Masry, M.
Chetty*
Department of Chemical Engineering, University of Durban- Westville, Private Bag X54001, Durban 4000, South Africa
Abstract The determination of shear rate in column bioreactors is an important step to estimate the cell damage rate in shear-sensitive biosystems as well as for correlating hydrodynamic and mass transfer parameters. Due to the complexity of local shear rate measurement, it has been widely assumed that an average shear rate exists and is proportional to superficial gas velocity. The most serious shortcoming in the analysis of non-Newtonian behaviour in airlift reactors is the lack of a reliable method for determining a shear rate and an effective viscosity appropriate to the airlift geometry. Recently Shi et al. (Chem. Eng. Commun. 1990; 89: 22-35) presented an empirical correlation of effective shear rate as a function of superficial gas velocity and based on downcomer liquid circulation velocity. The external loop airlift reactor used by Shi et al. was 1.4 m in height, 0.194 m in riser diameter and 0.06 m in downcomer diameter. To validate Shi's et al. promising approach, this work has been carried out in a larger reactor of 6.5 m in height and 0.225 m in both riser and downcomer diameter. However, the rheological properties of the studied liquids and the superficial gas velocities were similar to those used by Shi et al. Copyright © 1996 Elsevier Science B.V, Keywords: Airlift reactor; Effective shear rate; Non-Newtonian fluids; Hydrodynamics
I. Introduction Biotechnology research has a d v a n c e d b o t h o n a l a b o r a t o r y a n d o n a n industrial scale, with a large variety o f m i c r o - o r g a n i s m s being genetically engineered for possible use in p r o d u c t i o n processes. Various types o f bioreactors are currently Abbreviations: ALR, airlift reactor; CMC, carboxymethyl cellulose; HV, high viscosity. * Corresponding author. Tel: +031 8202754; fax: +031 8202187; e-mail: [email protected]. 0921-3449/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PI1 S0921-3449(96)0 1 164-0
12
W.A. dl-Masry, M. Chetty I Resources, Conservation and Recycling 18 (1996) 11 24
being used, but recently airlift gas-liquid-solid bioreactors have been found to be well suited to biotechnology processes. Airlift loop reactors are replacing conventional reactors for use as aerobic fermenters, because of their simple construction, low power input, good mass and heat transfer characteristics, and better defined flow patterns [2]. Shear rate is one of the indispensable parameters used in the design of aerobic fermenters for viscous non-Newtonian systems. Shear rate in airlift reactors has been investigated on a limited scale using correlations designed for bubble columns, Shear fields resulting from the fluid physical properties and the hydrodynamics may cause physical damage to fragile micro-organisms. Effective viscosity (#~f0 is one of the design parameters widely used in the literature to correlate mass transfer and hydrodynamic parameters for viscous non-Newtonian systems. There are many discrepancies in the literature concerning the effective viscosity of a non-Newtonian fluid. The Ostwald de Waele relation (or commonly known Power Law) is often used to describe the fluid"s dependence on the shear rate: rL =
k~ ~
(1)
Eq. (1) can be written in the following form: /xess = k7 n - ~
(2)
In a given bioreactor, shear rate (y) is a function of position, and actual measurement of local shear rate is complex. There are many methods in the literature for estimating shear rate for non-Newtonian systems. The most reliable method of analysis is the analogical analysis which was first suggested by Metzner and Otto [3]. It is based on operating two identical stirred tank reactors, one containing Newtonian fluid and the other non-Newtonian fluid, under the same conditions, i.e. temperature, superficial gas velocity, impeller speed, etc. If these fluids are agitated in the laminar region, with the same impeller speed used in each, and one varies the viscosity of the Newtonian (by diluting or thickening) so that power measured at each impeller is the same, then, since all other variables are the same in both systems, one may say that the average viscosities are the same for both reactors. Nishikawa et al. [4] used the heat transfer coefficient from an immersed cooling coil and a jacketed wall in a bubble column as the measurable parameter, For the Newtonian system heat transfer coefficient (h) curves which are functions of the superficial gas velocity (Vsg) and the viscosity (/x) were constructed for all solutions. Similarly, for the non-Newtonian system h versus Vsg was developed for each solution. By keeping h and Vsg constant in the Newtonian and non-Newtonian system the effective viscosity was taken to be equal in both systems. The effective shear rate was calculated as a function of superficial gas velocity by: yeff = BPsg
(3)
The constant 'B' was calculated to be 5000 m - 1. The above equation is valid for the range 0.04 < Vsg < 0.1. The Nishikawa correlation (Eq. (3)) has been used exclusively in the literature for bubble columns with gas-liquid and gas-liquid-solid
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) I 1-24
13
viscous systems. It is important to note that heat transfer in bubble column reactors is controlled by the thin boundary layer on the reactor wall or coil, while mass transfer between bubble and liquid is controlled by the resistance in the liquid film around a bubble, thereby making the above correlation unsuitable for mass transfer studies [5]. In another study by Henzler [6] and Schumpe and Deckwer [7], the constant B was found to be 1500 and 2800 m 1, respectively. Shi et al. [1] adopted the analogical analysis to find a correlation for shear rate in a 0.04 m 3 airlift loop reactor. The liquid circulation velocity in the downcomer of the airlift reactor was chosen as the measurable parameter because of its relationship to shear rate. Glycerol solutions were used as the Newtonian medium and CMC (carboxymethyl cellulose sodium salt) and xanthan gum solutions for the non-Newtonian medium. The authors proposed the following quadratic equation for effective shear rate:
(4)
Yezr= 14800V2~ - 3511Z~g + 3.26
The experimental data were scattered along the fitted curve (Fig. 1). For lower Vsg the values fitted the curve closely, but not for the higher values of Vsg. There is still a need for verification in the higher range of Vsg. The scattering in the upper region of the curve could also suggest that another parameter besides V~g could be influencing the effective shear rate. Henzler and Kauling [8] proposed that the effective shear rate depends on the specific power input: 40
+
0.404-< n < 0.937 30
0.122 -< k_< 0.333
20
f
10 ¸
A
0.04
0.02
V~ (nls -1) Fig. 1. Effective s h e a r r a t e versus superficial g a s velocity b y Shi et al. [1].
0.06
I
14
W.A. Al-Masry, M. Chetty Resources, Conservation and Recycling 18 (1996) 11-24
Table 1 Summary of analyses for estimation of effective shear rate Reactor
Authors
Correlation
Bubble column
~eff = 5 0 0 0 V s g 7eft = 1500Vsg
Stirred tank and bubble column
Nishikawa et al. [4] Henzler [6] Schumpe and Deckwer [7] Henzlerand Kauling [8]
Airlift reactor
Shi et al. [1]
Yerr= 14800V~g-351Vsg+3.26
Y~rf =
+ Ugplg
~erf= 2800V~g
7err = ((--~ +
0.5
V~gPsg)l/x.sr)
(5)
fief);
The terminal velocity of bubbles of viscous non-Newtonian solutions is difficult to determine. The above equation was derived intuitively, and since the proposed equation has not been experimentally justified, it therefore cannot be considered. A summary of the various analyses and the resulting correlations are presented in Table 1.
2. Experimental procedure A 700-1 external loop airlift reactor was used for this experimental study. The main component of the reactor is QVF borosilicate glass sections with the test sections fabricated from PVC. The experimental set-up is illustrated in Fig. 2 with a summary of the reactor dimensions shown in Table 2. The non-Newtonian solutions used in this reactor, were sodium salt of carboxymethyl cellulose (Sigma Chemical Co., C8758, C4888, C5013) and xanthan gum (Sigma Chemical Co., practical grade, G1253). Glycerol (technical grade) solutions were used as the Newtonian medium. N o r m a l tap water was used to make up the experimental solutions. The rheological properties of the solutions were examined using a Brookfield (USA) digital cylindrical spindle viscometer (Model L V D V I I + ). A Brookfield small sample adapter' was used for the high viscosity solutions and the Brookfield ultra low adapter was used for low viscosity solutions. Table 2 Summary of reactor dimensions Item Riser diameter Downcomer diameter Downcomer to riser cross-sectional area (AjAr) Dispersion height Nominal riser length Nominal downcomer length
0,7 (m3) ALR 0.225 (m) 0.225 (m) 1,0 6,2 (m) 7.5 (m) 9.6 (m)
W.A. Al-Masry, M. Cherty / Resources, Conservation and Recycling 18 (1996) 11-24
DO,INtOnER
15
tlSER
[]
m
[]
I
[]
J
°
T
-
ml
I
p
EXTERNAL REACTOR LOOPAIRLIFT Fig. 2. Schematic of the experimental set-up. (1) Air shut-off valve; (2) pressure regulator and filter; (3) turbine flowmeter; (4) control valve; (5) sparger; (6) electromagnetic flowmeter; (7) inverted U-tube manometer; (7a,b) pressure tappings; (8) conductivity probe; (9) conductivity meter; (10,11) pressure tappings.
16
W.A. AllMasry, M. Chetty/ Resources, Conservation and Recycling 18 (1996) 11-24
Table 3 k and n for xanthan g u m solutions Wt% of xanthan gum solution
n
k
0.15 0.20 0.25 0.30 0.35
0.3956 0.3206 0.2922 0.2649 0.2355
0.2696 0.5187 0.8365 1.2039 1.6664
Table 4 k and n for carboxymethyl cellulose (high viscosity) solutions Wt% of C M C (HV) solution
n
k
0.30 0.35 0.40
0.9296 0.8097 0.799
0.1472 0.1742 0.2629
0.8
0,6
• Vsg = 0.0018 m/s
1 Vsg = 0.0073 m/s
• Vsg = 0.0128 n~s
• Vsg = 0.0179 m/s
o Vsg = 0.0229 m/s
• Vsg = 0.0287 m/s
+ Vsg = 0.0337 m/s
• Vsg = 0.0396 m/s
¸
.4 ¸
0.2
t
t
0.1
0.2
0.3
~ ( m . s -~) Fig. 3. Liquid circulation curve for glycerol solutions.
0.4
W.A. Al-Masry, M. Chetty /Resources, Conservation and Recycling 18 (1996) 11-24
17
Compressed air was filtered and then passed through a turbine flow meter (GH Flow Automation, UK) which was used to determine the volumetric flowrate of air. Air was sparged with a circular perforated plate with holes of 1 mm diameter on a 11 mm pitch. The liquid velocity in the downcomer was measured using an electromagnetic flowmeter (Flowmetrix, RSA). The electromagnetic flowmeter measured the liquid velocity through the available area [9], hence the liquid circulation velocity is: (6)
Vid = (VId)MFM(1 -- Ed)
The gas hold-up in the riser was measured using a Hitachi (Japan) differential pressure cell with pressure tappings 3.32 m apart. Gas hold-up in the downcomer was estimated from an inverted U-tube manometer (filled with water) connected to tappings 1.1 m apart.
3. Results and discussion
According to the analogical analysis discussed earlier, if two systems are operating under the same conditions, e.g. V~g, temperature, pressure, and if one measurable and characteristic parameter is identical, it can be said that the effective viscosity in both systems is equal. In this work, the liquid circulation velocity was chosen as the measurable parameter because of its relationship to the shear rate. Shear rate is a function of the relative velocity both between the bubble and the 0.8
0.6
,® ~o.4 >
CMC(nV)
0.2
n - - 0.8007 k = 0.1742
0.0" 0.00
I
r
0.03
0.06
P
P
0.09
0.12
V~ (m.s ~) Fig. 4. Liquid circulation velocity in the downcomer versus superficial gas velocity.
0.15
18
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11-24 200
160
120
80
¸
40 @
@
•
O
y
J
t
!
•
•
•
$ •
0
0.02
I
0.04
0.06
V~ (m.s -l) Fig. 5. C a l c u l a t e d effective shear rate as a function o f the superficial gas velocity.
liquid, and between the liquid and the reactor wall. Liquid circulation is induced by the difference in gas hold-up between the riser and the downcomer, which in turn is determined by the superficial gas velocity. When the velocity of the bubble is increased, the residence time within the reactor is reduced, leading to a lower gas hold-up, hence the relationship between Vsl and the speed of the rising bubble. The wall and the change in direction of fluid as it goes around the loop are the main resistance to liquid circulation, therefore the relationship between shear rate and liquid circulation velocity appears logical. The rheological properties of the nonNewtonian solutions used in this work are presented in Tables 3 and 4. The effective viscosity of the xanthan gum and CMC is based on the analogical comparison with solutions of glycerol. VIa versus V~g was plotted for each solution of glycerol and by keeping the viscosity constant, points for the V~g curves in Fig. 3 were derived. For the xanthan gum and glycerol solutions there was foaming at the high gas flowrates, which led to fluid loss through the top of the reactor, and a reduction in the liquid circulation velocity. The upper range of the superficial gas velocity used was thus limited by the foaming. The flow behaviour index (n) and the fluid consistency index (k) of the solutions of CMC and xanthan gum solutions used by Shi et al. [1] ranged from 0.404-0.937 for n and 0.078-0.33 for k. Experiments were carried out with solutions having n and k falling in the above ranges, but most of the data could not be used as the liquid circulation velocity was too high, and did not fall in the range of the glycerol curve constructed in Fig. 3. This could be attributed to the difference in reactor geometry between this work (AJAr = 1) and Shi et al. (Ad/Ar = 0.11). Popovic and
W.A. AI-Masry, M. ChetO, / Resources, Conservation and Recycling 18 (1996) I1-24
19
Robinson [10] reported an increase in Vs~ by a factor of 3, as Ad/A r was increased from 0.111 to 0.444 for the same operating conditions and rheological behaviour as in this work. For this work the difference in reactor geometry is the reason for the high shear rate in comparison to Shi et al. [1]. The range of n and k therefore had to be extended to accommodate the Vsj range of the reactor and the range for glycerol in Fig. 3. For each solution of CMC and xanthan gum, a curve of V~d versus V~g (see Fig. 4) was constructed for analogy with the glycerol system in Fig. 3. By keeping V~e and Vsg constant for the non-Newtonian system and for the glycerol system, the effective viscosity was taken to be equal for both systems. Using Eq. (3) the effective shear rate was calculated using the experimental values of k and n, and in this way the shear rate was correlated for each Vsg. Fig. 5 shows a plot of the calculated effective shear rate as a function of the superficial gas velocity. According to Shi et al. [1] the effective shear rate was independent of the rheological properties of solutions used in their work. From Fig. 5 it is clear that a single correlation does not explain the data adequately. The effective shear rate for xanthan gum and CMC was plotted separately as a function of V~g in Figs. 6 and 7, respectively. Therefore two correlations were derived, one for CMC and the other for xanthan gum. The following correlations describing the effective shear rate as a function of V~g are proposed for xanthan gum solutions (Eq. (7)) and for CMC solutions (Eq. (8)): 21111
1611
12o
8O
40
+ o
0.02
0.04
V~ (nzs -1) Fig. 6. Effective shear rate for x a n t h a n g u m solutions.
0.06
20
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11-24 200.
160
120
"
'& 811
•
t
•
40 $ t
I
~
I
i
0.01
0.02
0.03
0.04
0.05
0.06
W, (m.s-]) Fig. 7. Effective shear rate for carboxymethyl cellulose solutions (high viscosity).
7~r = 14795V~x + 128.76V~ + 0.4996 0.2355 < n < 0.3956
and0.2697 < k < 1.6664
(7)
7eF/= 27625V~ + 358.32V~.g + 22.54 0.7991 < n < 0.9296
and 0.1472 < k < 0.2629
(8)
Both correlations are valid for 0.002 _< Vsg _< 0.06 and A~/Ar = 1. The correlations derived in this work are compared to Shi et al. in Fig. 8. The effective shear rate for this work is larger than that predicted by the S h i e t al. correlation for a given Vsg, for both xanthan gum and CMC solutions. As mentioned above the effect of term (Ad/Ar) reported by Popovic and Robinson [10] can be used to explain the higher, shear rate for this reactor geometry. As Ao/A r increases, Via increases for the same V~g, hence the effective viscosity determined from the glycerol curve (Fig. 3) is lower for this work. From Eq. (2), if the/1elf is decreased for the same k and n, the shear rate increases, thereby explaining the higher shear rate in this work. The shear rate correlations for this work are compared to the available correlations in the literature for bubble columns and external loop airlift reactors (see Fig. 9). The most widely used correlation proposed by Nishikawa et al. [4] shows the effective shear rate to be higher than the works of Henzler [6] and Schumpe and Deckwer [7]. Although the results of calculations of effective shear rate in bubble
21
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (I996) 11-24
columns are different from each other, it was found that the effective shear rate is lower in external loop airlift reactors, except for the work of Henzler [6] which falls below the C M C curve for this work. Henzler obtained a value of B (Eq. (3)) to be an adjustable parameter to be fitted by regression analysis of the mass transfer data. This method of analysis has no physical meaning, therefore Eq. (3) has to be experimentally verified for comparison as done with the curves in Fig. 9. For bubble columns, circulation comprises an upward flow with the liquid relatively rich in entrained bubbles and compensating downward flow with liquid p o o r in bubbles. This countercurrent flow increases the relative velocity between the liquid and the bubbles; and hence increases the effective shear rate. For airlift reactors, the cocurrent flow of gas and liquid, both in the riser and the downcomer, reduces the relative velocity between the bubbles and the liquid. This leads to lower effective shear rates in airlift reactors than for bubble columns. Therefore external loop airlift reactors are more appropriate than bubble columns for the cultivation of plant and animal cells which are sensitive to high shear rates.
4. C o n c l u s i o n s
Two new correlations for effective shear rates in A L R s are presented. The available hydrodynamic correlations that are applicable to external loop airlift
150
100
50
0
0.02
0.04
0.06
V~ (nxs-1) Fig. 8. Comparison of effectiveshear rate correlation derived in this work with Shi et al. [1], for xanthan gum and CMC.
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11 24
22
300 = Shi et al. • Nishikawa • Henzler o Schtmq~e & Dcclover x "I~is work (for xanthan gum) 200
+ This work (for CMC)
-?
f
100
0 0.00
0.02
0.04
0.06
0.08
V~ (m.s-I) Fig. 9. Effective s h e a r rate c o m p a r i s o n for b u b b l e c o l u m n s a n d external loop airlift reactors.
reactors have a serious shortcoming in that they are based on effective shear rate correlations for bubble columns. Use of these correlations overestimates the effective shear rate in external loop airlift reactors. Effective shear rate was found by this work and Shi et al. to be lower in airlift reactors than bubble columns. The reactor geometry (Aa/Ar) had a significant effect on the effective shear rate and the hydrodynamic parameters. This work predicted higher effective shear rate (Aa/Ar = 1), when compared to lower reactor geometries in the range 0.11 < A a / Ar _<0.69.
5. N o m e n c l a t u r e
Ad, downcomer cross-sectional area [m2] At, riser cross-sectional area [m 2] B, probability constant in Eq. (3) [ - ] d,D, diameter [m] g, acceleration due to gravity [m.s 2] h, heat transfer coefficient [kJ.m-2.s-1.°C] h,H, height [m] k, consistency index [Pa.s n]
W.A. AI-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11-24
23
kla, mass transfer coefficient [1.s- l] n, flow behaviour index [ - ] P, total pressure [ N . m - 2 ] P, power [W] Q, volumetric flow rate [m3.s-1] t, average time [s] T, temperature [°C] u, bubble velocity [m.s 1] Ug, gas velocity [m.s 1] V, reactor volume [m 3] VEd, d o w n c o m e r liquid circulation velocity [m.s ~] V~g, superficial gas velocity in the riser [m.s 1] z, height [m] 5.1. Greek letters
E, y, /1, p,
gas hold-up [ - ] shear rate [s l] viscosity [Pa.s] density [ k g . m - 3 ]
5.2. Subscripts
av, average b, bubble d, d o w n c o m e r eff, effective g, gas 1, liquid r, riser
References [1] Shi, L.K., Riba, J.P. and Angelino, H., 1990. Estimation of effective shear rate for aerated non-Newtonian liquids in airlift bioreactors. Chem. Eng. Commun., 89:22 35. [2] Siegel, M.H. and Robinson, C.W., 1992. Applications of gas-liquid-solid reactors in biotechnology. Chem. Eng. Sci., 47:3215 3229. [3] Metzner, A,B. and Otto, R.E., 1957. Agitation of non-Newtonian fluids. AIChE. J., 3:3 10. [4] Nishikawa, M., Kato, H. and Hasimoto, K., 1977. Heat transfer in aerated tower filled with non-Newtonian liquid. Ind. Eng. Chem. Proc. Des. Dev., 16: 133-137. [5] Kawase, Y. and Moo-Young, M., 1987. Heat transfer in bubble column reactors with Newtonian and non-Newtonian fluids. Chem. Eng. Res. Des., 65:121 126. [6] Henzler, H.J., 1980. Begasen hoherviskoer klussinkeiten. Chem.-lng. Tech., 52: 643-652. [7] Schumpe, A. and Deckwer, W.D., 1987. Viscous media in tower bioreactors: hydrodynamics characteristics and mass transfer properties. Bioprocess. Eng., 2:79 94. [8] Henzler, H.J. and Kauling, J., 1985. Scale-up of mass transfer in highly viscous liquids. In: 5th European Conference on Mixing, Wurzburg, Germany, paper 30, pp. 303-312.
24
W.A. AI-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11 24
[9] Pillay, M., 1996. Estimation of effective shear rate in an external loop airlift reactor: Non-newtonian systems. MSc Thesis, University of Durban-Westville. [10] Popovic, M. and Robinson, C.W., 1989. Mass transfer studies of external loop airlifts and a bubble column. AIChE. J., 35:393 405.
comx, vati~ ELSEVIER
Resources, Conservationand Recycling18 (1996) II 24
On the estimation of effective shear rate in external loop airlift reactors: non-Newtonian fluids W.A. A1-Masry, M.
Chetty*
Department of Chemical Engineering, University of Durban- Westville, Private Bag X54001, Durban 4000, South Africa
Abstract The determination of shear rate in column bioreactors is an important step to estimate the cell damage rate in shear-sensitive biosystems as well as for correlating hydrodynamic and mass transfer parameters. Due to the complexity of local shear rate measurement, it has been widely assumed that an average shear rate exists and is proportional to superficial gas velocity. The most serious shortcoming in the analysis of non-Newtonian behaviour in airlift reactors is the lack of a reliable method for determining a shear rate and an effective viscosity appropriate to the airlift geometry. Recently Shi et al. (Chem. Eng. Commun. 1990; 89: 22-35) presented an empirical correlation of effective shear rate as a function of superficial gas velocity and based on downcomer liquid circulation velocity. The external loop airlift reactor used by Shi et al. was 1.4 m in height, 0.194 m in riser diameter and 0.06 m in downcomer diameter. To validate Shi's et al. promising approach, this work has been carried out in a larger reactor of 6.5 m in height and 0.225 m in both riser and downcomer diameter. However, the rheological properties of the studied liquids and the superficial gas velocities were similar to those used by Shi et al. Copyright © 1996 Elsevier Science B.V, Keywords: Airlift reactor; Effective shear rate; Non-Newtonian fluids; Hydrodynamics
I. Introduction Biotechnology research has a d v a n c e d b o t h o n a l a b o r a t o r y a n d o n a n industrial scale, with a large variety o f m i c r o - o r g a n i s m s being genetically engineered for possible use in p r o d u c t i o n processes. Various types o f bioreactors are currently Abbreviations: ALR, airlift reactor; CMC, carboxymethyl cellulose; HV, high viscosity. * Corresponding author. Tel: +031 8202754; fax: +031 8202187; e-mail: [email protected]. 0921-3449/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PI1 S0921-3449(96)0 1 164-0
12
W.A. dl-Masry, M. Chetty I Resources, Conservation and Recycling 18 (1996) 11 24
being used, but recently airlift gas-liquid-solid bioreactors have been found to be well suited to biotechnology processes. Airlift loop reactors are replacing conventional reactors for use as aerobic fermenters, because of their simple construction, low power input, good mass and heat transfer characteristics, and better defined flow patterns [2]. Shear rate is one of the indispensable parameters used in the design of aerobic fermenters for viscous non-Newtonian systems. Shear rate in airlift reactors has been investigated on a limited scale using correlations designed for bubble columns, Shear fields resulting from the fluid physical properties and the hydrodynamics may cause physical damage to fragile micro-organisms. Effective viscosity (#~f0 is one of the design parameters widely used in the literature to correlate mass transfer and hydrodynamic parameters for viscous non-Newtonian systems. There are many discrepancies in the literature concerning the effective viscosity of a non-Newtonian fluid. The Ostwald de Waele relation (or commonly known Power Law) is often used to describe the fluid"s dependence on the shear rate: rL =
k~ ~
(1)
Eq. (1) can be written in the following form: /xess = k7 n - ~
(2)
In a given bioreactor, shear rate (y) is a function of position, and actual measurement of local shear rate is complex. There are many methods in the literature for estimating shear rate for non-Newtonian systems. The most reliable method of analysis is the analogical analysis which was first suggested by Metzner and Otto [3]. It is based on operating two identical stirred tank reactors, one containing Newtonian fluid and the other non-Newtonian fluid, under the same conditions, i.e. temperature, superficial gas velocity, impeller speed, etc. If these fluids are agitated in the laminar region, with the same impeller speed used in each, and one varies the viscosity of the Newtonian (by diluting or thickening) so that power measured at each impeller is the same, then, since all other variables are the same in both systems, one may say that the average viscosities are the same for both reactors. Nishikawa et al. [4] used the heat transfer coefficient from an immersed cooling coil and a jacketed wall in a bubble column as the measurable parameter, For the Newtonian system heat transfer coefficient (h) curves which are functions of the superficial gas velocity (Vsg) and the viscosity (/x) were constructed for all solutions. Similarly, for the non-Newtonian system h versus Vsg was developed for each solution. By keeping h and Vsg constant in the Newtonian and non-Newtonian system the effective viscosity was taken to be equal in both systems. The effective shear rate was calculated as a function of superficial gas velocity by: yeff = BPsg
(3)
The constant 'B' was calculated to be 5000 m - 1. The above equation is valid for the range 0.04 < Vsg < 0.1. The Nishikawa correlation (Eq. (3)) has been used exclusively in the literature for bubble columns with gas-liquid and gas-liquid-solid
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) I 1-24
13
viscous systems. It is important to note that heat transfer in bubble column reactors is controlled by the thin boundary layer on the reactor wall or coil, while mass transfer between bubble and liquid is controlled by the resistance in the liquid film around a bubble, thereby making the above correlation unsuitable for mass transfer studies [5]. In another study by Henzler [6] and Schumpe and Deckwer [7], the constant B was found to be 1500 and 2800 m 1, respectively. Shi et al. [1] adopted the analogical analysis to find a correlation for shear rate in a 0.04 m 3 airlift loop reactor. The liquid circulation velocity in the downcomer of the airlift reactor was chosen as the measurable parameter because of its relationship to shear rate. Glycerol solutions were used as the Newtonian medium and CMC (carboxymethyl cellulose sodium salt) and xanthan gum solutions for the non-Newtonian medium. The authors proposed the following quadratic equation for effective shear rate:
(4)
Yezr= 14800V2~ - 3511Z~g + 3.26
The experimental data were scattered along the fitted curve (Fig. 1). For lower Vsg the values fitted the curve closely, but not for the higher values of Vsg. There is still a need for verification in the higher range of Vsg. The scattering in the upper region of the curve could also suggest that another parameter besides V~g could be influencing the effective shear rate. Henzler and Kauling [8] proposed that the effective shear rate depends on the specific power input: 40
+
0.404-< n < 0.937 30
0.122 -< k_< 0.333
20
f
10 ¸
A
0.04
0.02
V~ (nls -1) Fig. 1. Effective s h e a r r a t e versus superficial g a s velocity b y Shi et al. [1].
0.06
I
14
W.A. Al-Masry, M. Chetty Resources, Conservation and Recycling 18 (1996) 11-24
Table 1 Summary of analyses for estimation of effective shear rate Reactor
Authors
Correlation
Bubble column
~eff = 5 0 0 0 V s g 7eft = 1500Vsg
Stirred tank and bubble column
Nishikawa et al. [4] Henzler [6] Schumpe and Deckwer [7] Henzlerand Kauling [8]
Airlift reactor
Shi et al. [1]
Yerr= 14800V~g-351Vsg+3.26
Y~rf =
+ Ugplg
~erf= 2800V~g
7err = ((--~ +
0.5
V~gPsg)l/x.sr)
(5)
fief);
The terminal velocity of bubbles of viscous non-Newtonian solutions is difficult to determine. The above equation was derived intuitively, and since the proposed equation has not been experimentally justified, it therefore cannot be considered. A summary of the various analyses and the resulting correlations are presented in Table 1.
2. Experimental procedure A 700-1 external loop airlift reactor was used for this experimental study. The main component of the reactor is QVF borosilicate glass sections with the test sections fabricated from PVC. The experimental set-up is illustrated in Fig. 2 with a summary of the reactor dimensions shown in Table 2. The non-Newtonian solutions used in this reactor, were sodium salt of carboxymethyl cellulose (Sigma Chemical Co., C8758, C4888, C5013) and xanthan gum (Sigma Chemical Co., practical grade, G1253). Glycerol (technical grade) solutions were used as the Newtonian medium. N o r m a l tap water was used to make up the experimental solutions. The rheological properties of the solutions were examined using a Brookfield (USA) digital cylindrical spindle viscometer (Model L V D V I I + ). A Brookfield small sample adapter' was used for the high viscosity solutions and the Brookfield ultra low adapter was used for low viscosity solutions. Table 2 Summary of reactor dimensions Item Riser diameter Downcomer diameter Downcomer to riser cross-sectional area (AjAr) Dispersion height Nominal riser length Nominal downcomer length
0,7 (m3) ALR 0.225 (m) 0.225 (m) 1,0 6,2 (m) 7.5 (m) 9.6 (m)
W.A. Al-Masry, M. Cherty / Resources, Conservation and Recycling 18 (1996) 11-24
DO,INtOnER
15
tlSER
[]
m
[]
I
[]
J
°
T
-
ml
I
p
EXTERNAL REACTOR LOOPAIRLIFT Fig. 2. Schematic of the experimental set-up. (1) Air shut-off valve; (2) pressure regulator and filter; (3) turbine flowmeter; (4) control valve; (5) sparger; (6) electromagnetic flowmeter; (7) inverted U-tube manometer; (7a,b) pressure tappings; (8) conductivity probe; (9) conductivity meter; (10,11) pressure tappings.
16
W.A. AllMasry, M. Chetty/ Resources, Conservation and Recycling 18 (1996) 11-24
Table 3 k and n for xanthan g u m solutions Wt% of xanthan gum solution
n
k
0.15 0.20 0.25 0.30 0.35
0.3956 0.3206 0.2922 0.2649 0.2355
0.2696 0.5187 0.8365 1.2039 1.6664
Table 4 k and n for carboxymethyl cellulose (high viscosity) solutions Wt% of C M C (HV) solution
n
k
0.30 0.35 0.40
0.9296 0.8097 0.799
0.1472 0.1742 0.2629
0.8
0,6
• Vsg = 0.0018 m/s
1 Vsg = 0.0073 m/s
• Vsg = 0.0128 n~s
• Vsg = 0.0179 m/s
o Vsg = 0.0229 m/s
• Vsg = 0.0287 m/s
+ Vsg = 0.0337 m/s
• Vsg = 0.0396 m/s
¸
.4 ¸
0.2
t
t
0.1
0.2
0.3
~ ( m . s -~) Fig. 3. Liquid circulation curve for glycerol solutions.
0.4
W.A. Al-Masry, M. Chetty /Resources, Conservation and Recycling 18 (1996) 11-24
17
Compressed air was filtered and then passed through a turbine flow meter (GH Flow Automation, UK) which was used to determine the volumetric flowrate of air. Air was sparged with a circular perforated plate with holes of 1 mm diameter on a 11 mm pitch. The liquid velocity in the downcomer was measured using an electromagnetic flowmeter (Flowmetrix, RSA). The electromagnetic flowmeter measured the liquid velocity through the available area [9], hence the liquid circulation velocity is: (6)
Vid = (VId)MFM(1 -- Ed)
The gas hold-up in the riser was measured using a Hitachi (Japan) differential pressure cell with pressure tappings 3.32 m apart. Gas hold-up in the downcomer was estimated from an inverted U-tube manometer (filled with water) connected to tappings 1.1 m apart.
3. Results and discussion
According to the analogical analysis discussed earlier, if two systems are operating under the same conditions, e.g. V~g, temperature, pressure, and if one measurable and characteristic parameter is identical, it can be said that the effective viscosity in both systems is equal. In this work, the liquid circulation velocity was chosen as the measurable parameter because of its relationship to the shear rate. Shear rate is a function of the relative velocity both between the bubble and the 0.8
0.6
,® ~o.4 >
CMC(nV)
0.2
n - - 0.8007 k = 0.1742
0.0" 0.00
I
r
0.03
0.06
P
P
0.09
0.12
V~ (m.s ~) Fig. 4. Liquid circulation velocity in the downcomer versus superficial gas velocity.
0.15
18
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11-24 200
160
120
80
¸
40 @
@
•
O
y
J
t
!
•
•
•
$ •
0
0.02
I
0.04
0.06
V~ (m.s -l) Fig. 5. C a l c u l a t e d effective shear rate as a function o f the superficial gas velocity.
liquid, and between the liquid and the reactor wall. Liquid circulation is induced by the difference in gas hold-up between the riser and the downcomer, which in turn is determined by the superficial gas velocity. When the velocity of the bubble is increased, the residence time within the reactor is reduced, leading to a lower gas hold-up, hence the relationship between Vsl and the speed of the rising bubble. The wall and the change in direction of fluid as it goes around the loop are the main resistance to liquid circulation, therefore the relationship between shear rate and liquid circulation velocity appears logical. The rheological properties of the nonNewtonian solutions used in this work are presented in Tables 3 and 4. The effective viscosity of the xanthan gum and CMC is based on the analogical comparison with solutions of glycerol. VIa versus V~g was plotted for each solution of glycerol and by keeping the viscosity constant, points for the V~g curves in Fig. 3 were derived. For the xanthan gum and glycerol solutions there was foaming at the high gas flowrates, which led to fluid loss through the top of the reactor, and a reduction in the liquid circulation velocity. The upper range of the superficial gas velocity used was thus limited by the foaming. The flow behaviour index (n) and the fluid consistency index (k) of the solutions of CMC and xanthan gum solutions used by Shi et al. [1] ranged from 0.404-0.937 for n and 0.078-0.33 for k. Experiments were carried out with solutions having n and k falling in the above ranges, but most of the data could not be used as the liquid circulation velocity was too high, and did not fall in the range of the glycerol curve constructed in Fig. 3. This could be attributed to the difference in reactor geometry between this work (AJAr = 1) and Shi et al. (Ad/Ar = 0.11). Popovic and
W.A. AI-Masry, M. ChetO, / Resources, Conservation and Recycling 18 (1996) I1-24
19
Robinson [10] reported an increase in Vs~ by a factor of 3, as Ad/A r was increased from 0.111 to 0.444 for the same operating conditions and rheological behaviour as in this work. For this work the difference in reactor geometry is the reason for the high shear rate in comparison to Shi et al. [1]. The range of n and k therefore had to be extended to accommodate the Vsj range of the reactor and the range for glycerol in Fig. 3. For each solution of CMC and xanthan gum, a curve of V~d versus V~g (see Fig. 4) was constructed for analogy with the glycerol system in Fig. 3. By keeping V~e and Vsg constant for the non-Newtonian system and for the glycerol system, the effective viscosity was taken to be equal for both systems. Using Eq. (3) the effective shear rate was calculated using the experimental values of k and n, and in this way the shear rate was correlated for each Vsg. Fig. 5 shows a plot of the calculated effective shear rate as a function of the superficial gas velocity. According to Shi et al. [1] the effective shear rate was independent of the rheological properties of solutions used in their work. From Fig. 5 it is clear that a single correlation does not explain the data adequately. The effective shear rate for xanthan gum and CMC was plotted separately as a function of V~g in Figs. 6 and 7, respectively. Therefore two correlations were derived, one for CMC and the other for xanthan gum. The following correlations describing the effective shear rate as a function of V~g are proposed for xanthan gum solutions (Eq. (7)) and for CMC solutions (Eq. (8)): 21111
1611
12o
8O
40
+ o
0.02
0.04
V~ (nzs -1) Fig. 6. Effective shear rate for x a n t h a n g u m solutions.
0.06
20
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11-24 200.
160
120
"
'& 811
•
t
•
40 $ t
I
~
I
i
0.01
0.02
0.03
0.04
0.05
0.06
W, (m.s-]) Fig. 7. Effective shear rate for carboxymethyl cellulose solutions (high viscosity).
7~r = 14795V~x + 128.76V~ + 0.4996 0.2355 < n < 0.3956
and0.2697 < k < 1.6664
(7)
7eF/= 27625V~ + 358.32V~.g + 22.54 0.7991 < n < 0.9296
and 0.1472 < k < 0.2629
(8)
Both correlations are valid for 0.002 _< Vsg _< 0.06 and A~/Ar = 1. The correlations derived in this work are compared to Shi et al. in Fig. 8. The effective shear rate for this work is larger than that predicted by the S h i e t al. correlation for a given Vsg, for both xanthan gum and CMC solutions. As mentioned above the effect of term (Ad/Ar) reported by Popovic and Robinson [10] can be used to explain the higher, shear rate for this reactor geometry. As Ao/A r increases, Via increases for the same V~g, hence the effective viscosity determined from the glycerol curve (Fig. 3) is lower for this work. From Eq. (2), if the/1elf is decreased for the same k and n, the shear rate increases, thereby explaining the higher shear rate in this work. The shear rate correlations for this work are compared to the available correlations in the literature for bubble columns and external loop airlift reactors (see Fig. 9). The most widely used correlation proposed by Nishikawa et al. [4] shows the effective shear rate to be higher than the works of Henzler [6] and Schumpe and Deckwer [7]. Although the results of calculations of effective shear rate in bubble
21
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (I996) 11-24
columns are different from each other, it was found that the effective shear rate is lower in external loop airlift reactors, except for the work of Henzler [6] which falls below the C M C curve for this work. Henzler obtained a value of B (Eq. (3)) to be an adjustable parameter to be fitted by regression analysis of the mass transfer data. This method of analysis has no physical meaning, therefore Eq. (3) has to be experimentally verified for comparison as done with the curves in Fig. 9. For bubble columns, circulation comprises an upward flow with the liquid relatively rich in entrained bubbles and compensating downward flow with liquid p o o r in bubbles. This countercurrent flow increases the relative velocity between the liquid and the bubbles; and hence increases the effective shear rate. For airlift reactors, the cocurrent flow of gas and liquid, both in the riser and the downcomer, reduces the relative velocity between the bubbles and the liquid. This leads to lower effective shear rates in airlift reactors than for bubble columns. Therefore external loop airlift reactors are more appropriate than bubble columns for the cultivation of plant and animal cells which are sensitive to high shear rates.
4. C o n c l u s i o n s
Two new correlations for effective shear rates in A L R s are presented. The available hydrodynamic correlations that are applicable to external loop airlift
150
100
50
0
0.02
0.04
0.06
V~ (nxs-1) Fig. 8. Comparison of effectiveshear rate correlation derived in this work with Shi et al. [1], for xanthan gum and CMC.
W.A. Al-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11 24
22
300 = Shi et al. • Nishikawa • Henzler o Schtmq~e & Dcclover x "I~is work (for xanthan gum) 200
+ This work (for CMC)
-?
f
100
0 0.00
0.02
0.04
0.06
0.08
V~ (m.s-I) Fig. 9. Effective s h e a r rate c o m p a r i s o n for b u b b l e c o l u m n s a n d external loop airlift reactors.
reactors have a serious shortcoming in that they are based on effective shear rate correlations for bubble columns. Use of these correlations overestimates the effective shear rate in external loop airlift reactors. Effective shear rate was found by this work and Shi et al. to be lower in airlift reactors than bubble columns. The reactor geometry (Aa/Ar) had a significant effect on the effective shear rate and the hydrodynamic parameters. This work predicted higher effective shear rate (Aa/Ar = 1), when compared to lower reactor geometries in the range 0.11 < A a / Ar _<0.69.
5. N o m e n c l a t u r e
Ad, downcomer cross-sectional area [m2] At, riser cross-sectional area [m 2] B, probability constant in Eq. (3) [ - ] d,D, diameter [m] g, acceleration due to gravity [m.s 2] h, heat transfer coefficient [kJ.m-2.s-1.°C] h,H, height [m] k, consistency index [Pa.s n]
W.A. AI-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11-24
23
kla, mass transfer coefficient [1.s- l] n, flow behaviour index [ - ] P, total pressure [ N . m - 2 ] P, power [W] Q, volumetric flow rate [m3.s-1] t, average time [s] T, temperature [°C] u, bubble velocity [m.s 1] Ug, gas velocity [m.s 1] V, reactor volume [m 3] VEd, d o w n c o m e r liquid circulation velocity [m.s ~] V~g, superficial gas velocity in the riser [m.s 1] z, height [m] 5.1. Greek letters
E, y, /1, p,
gas hold-up [ - ] shear rate [s l] viscosity [Pa.s] density [ k g . m - 3 ]
5.2. Subscripts
av, average b, bubble d, d o w n c o m e r eff, effective g, gas 1, liquid r, riser
References [1] Shi, L.K., Riba, J.P. and Angelino, H., 1990. Estimation of effective shear rate for aerated non-Newtonian liquids in airlift bioreactors. Chem. Eng. Commun., 89:22 35. [2] Siegel, M.H. and Robinson, C.W., 1992. Applications of gas-liquid-solid reactors in biotechnology. Chem. Eng. Sci., 47:3215 3229. [3] Metzner, A,B. and Otto, R.E., 1957. Agitation of non-Newtonian fluids. AIChE. J., 3:3 10. [4] Nishikawa, M., Kato, H. and Hasimoto, K., 1977. Heat transfer in aerated tower filled with non-Newtonian liquid. Ind. Eng. Chem. Proc. Des. Dev., 16: 133-137. [5] Kawase, Y. and Moo-Young, M., 1987. Heat transfer in bubble column reactors with Newtonian and non-Newtonian fluids. Chem. Eng. Res. Des., 65:121 126. [6] Henzler, H.J., 1980. Begasen hoherviskoer klussinkeiten. Chem.-lng. Tech., 52: 643-652. [7] Schumpe, A. and Deckwer, W.D., 1987. Viscous media in tower bioreactors: hydrodynamics characteristics and mass transfer properties. Bioprocess. Eng., 2:79 94. [8] Henzler, H.J. and Kauling, J., 1985. Scale-up of mass transfer in highly viscous liquids. In: 5th European Conference on Mixing, Wurzburg, Germany, paper 30, pp. 303-312.
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W.A. AI-Masry, M. Chetty / Resources, Conservation and Recycling 18 (1996) 11 24
[9] Pillay, M., 1996. Estimation of effective shear rate in an external loop airlift reactor: Non-newtonian systems. MSc Thesis, University of Durban-Westville. [10] Popovic, M. and Robinson, C.W., 1989. Mass transfer studies of external loop airlifts and a bubble column. AIChE. J., 35:393 405.