Biotechnol. Prog. 1994, 10, 543-547
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Dynamic Mixing and Oxygen Transfer in Small, Airlift Loop Bioreactors: Model and Experimental Verification Randall D. Fraser, Brian J,Ritchie, and Gordon A. Hill' Department of Chemical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada, S7N OW0
A mechanistic model for mixing and mass transfer in both airlift bubble column and loop bioreactors is described. The model is a useful design tool to improve oxygentransfer characteristics. It is shown that the model fits mixing and mass-transfer experimental data closely. The model confirms that the overall oxygen-transfer coefficient in the riser of a loop airlift fermentor is similar to that in bubble columns and that lower measured transfer rates are due solely to the dead volume in the downcomer. The effects of parameters such as mass-transfer coefficient, aeration rate, dispersion coefficient, sparger rotation speed, and liquid circulation velocity are presented in terms of both the liquid- and gas-phase oxygen concentrations.
Introduction and Background Airlift bioreactors are now a common configuration used to carry out many kinds of bioreactions (Chisti and Moo Young, 1987). Because of their popularity, ease of construction, and low cost of operation, they are frequently used in both small-scale laboratory studies and large-scale industrial applications. There are both geometric and operating factors that govern the hydrodynamic and mass-transfer performance of any airlift bioreactor. If the airlift bioreactor is a circulating loop type, the key geometric factor is the area ratio of the riser column to the downcomer column. The key operating factor is the rate of supplying gas (usually air) to the riser column. Other operating parameters can involve the opening of a valve in the downcomer (Verlaan et al., 1989) or the rate of rotation of a spinning sparger (Fraser and Hill,1993) at the base of the riser. The steady-state conditions of gas hold-up, liquid circulation velocity, gas riser velocity, gas bubble size, liquid axial dispersion, and oxygen mass-transfer rate have been studied extensively as functions of operating parameters for many bioreactor designs (Merchuk and Stein, 1981; Bello et al., 1984, 1985a,b; Chisti, 1989 (p 73); Joshi et al., 1990; Glennon et al., 1993). Recently, Fraser and Hill (1993)reported on a novel sparger design that allowed localized shear to be generated at the sparger orifices, resulting in improved hydrodynamic conditions in a circulating, airlift bioreactor. Traditional empirical and semiempirical correlations were found to reasonably predict the following measured parameters: gas hold-up, OGR
interfacial area, a
liquid riser superficial velocity
axial dispersion in the riser The first three parameters are seen to be affected by both the aeration rate and the rotation speed of the sparger, while axial dispersion was found to be independent of the sparger speed. Thus, enhanced hydrodynamics occurred as the sparger spinning speed was increased without causing increased mixing, which might lead to the destruction of shear-sensitive cells. It is commonly reported that bubble columns have higher mass-transfer coefficients than circulating loop airlift bioreactors (Weiland and Onken, 1981). Bello et al. (1985a)b) have reported that the volumetric ratio of riser to downcomer is a key factor causing this decline and have developed empirical correlations based on this ratio. It was suggested that the decline in the masstransfer rate is due to the removal of the downcomer liquid from the active mass-transfer conditions of the riser. Andre et al. (1983) modeled the dynamic oxygen build-up in small airlift bioreactors using a tanks-inseries model. They reported that the measured masstransfer coefficient,which assumes the well-mixed model, is essentially correct for small, circulating airlift vessels with low mass-transfer coefficients and cycle times. In this work, a distributed model is used to predict the dynamic oxygen transfer into a bubble column or circulating loop bioreactor. This model is solved using a finite difference formulation and linear algebra. It is shown that the predictions fit mixing and mass-transfer data generated here and elsewhere, but that the measured mass-transfer coefficient must be corrected by the ratio of total bioreactor volume to riser volume.
Model Development
* Author to whom correspondence should be addressed.
The differential equations governing the component balances of a substance flowing through a column reactor have been presented by Rice (1990). Applying this
8756-7938/94/3010-0543$04.50/00 1994 American Chemical Society and American Institute of Chemical Engineers
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the liquid phase by dispersion, into the liquid phase by mass transfer, and out of the gas phase by mass transfer. To convert eqs 5 and 6 to a finite difference model, eq 7 is first substituted to remove c* from both equations. Forward differencing was employed for the time dimension, and central differencing was used for the space dimension. The discretized, algebraic equations become
4 YN
-(A,
+ B,)c,”-+; + (1+ 2AL + EL)c,”+l- ELy,nf’/H (AL - BLk,”;
A B C
D
- 02773
I
I
ULR
UOR
--- Sdt -
-BG>;”-:’- VGC;” f (1+ VJH>y,”’l
Injection Port Conductivity Probe Conductivit Probe +2 Dissolved xygen Probe
= c,” (8)
+ Bd;;;
=
’
yJ(9)
where
d
A, = DLAt/(hz)2
BL = U ~ ~ h t / ( 2 h z )
JGR
Figure 1. Schematic diagram of the E difference grid.
EL = K,a,At
approach to two separate phases and allowing mass transfer to occur between the phases result in a separate differential equation for each component in both phases. The two equations governing oxygen concentrations in the liquid and gas phases become
ac = D, a2c - U ac + KLa,(c* - c ) at az2 LR az
(5)
In writing these equations, it has been assumed that the operating conditions (gas flow rate, spinning sparger speed) are being held constant, so that the dispersion, liquid and gas velocities, gas hold-up, and mass-transfer coefficient are at constant values determined by empirical correlations such as eqs 1-4. Equations 5 and 6 ignore flow and dispersion in the radial and angular directions, and eq 6 assumes that the gas travels in plug flow. Also, the solutions presented here are made for only a small-scale bioreactor and for the low solubility component oxygen; therefore, the variation of UGRwith respect to hydrostatic pressure and oxygen concentration has been ignored. The mass transfer is controlled by a liquid film, such that the concentration of the component in the liquid phase right at the interface is given by Henry‘s law: y = Hc*
B, = u~&/(2hz)
M showing the finite
(7)
Since the model is written only for mixing and masstransfer predictions, eqs 5 and 6 do not contain any nonlinear (bio)reaction terms. Thus, the equations are linear and are solvable by numerical finite differencing and matrix mathematics. Significant mass transfer only occurs in the riser section at low aeration rates because (as mentioned earlier) negligible gas hold-up exists in the downcomer. The riser is therefore divided into a total of J finite difference elements, as shown in Figure 1. The downcomer is treated as a plug flow column containing only liquid. In the riser, the liquid and gas streams conceptually can be considered as two separate elements, as shown in the magnified box in Figure 1. Oxygen flows into and out of each phase by convection, into and out of
VG
= KLarAt(l - @GR)/@GR
Equations 8 and 9 are applied from j = 1 to J , where J represents the total number of space increments into which the riser column is subdivided (see Figure 11,and from n = 0 to N , where N is the final time increment. Before the final coeficient matrix can be assembled, three boundary conditions need to be incorporated. At the inlet for a liquid circulating bioreactor, a modified version of the Danckwertz boundary condition was applied (Nauman and Buffham, 1983):
+
+
(1 2AL EL)$+’ - E&+l/H - (A, - BL@’
CY + BLcI, + ALcI,
=
(10)
This equation includes the inlet convection flow from the downcomer, which has a concentration given by CIN. The second boundary condition is applied a t the exit, where it is assumed that there is no change in the liquid concentration once it exits the top of the riser:
-(A,
+ B,)C:!; + (1+ A, + BL + E,)C:?;
-
Eo:+@ = c Z I (11) The third and final boundary condition is for the gas entering the riser:
B&+l = y ; +
BGYIN( 12)
Equations 8-12 then represent a fully defined linear algebra problem. The matrix A is very sparse, so that the conjugate gradient method was used to iterate to the correct solution. The downcomer was treated as a pure time delay component in these simulations. There is essentially no gas hold-up in the downcomer, thereby eliminating mass transfer and liquid mixing (dispersion) as compared to the riser. For pure mixing calculations, the liquid concentration for the appropriate location in the downcomer was set equal t o an impulse value at the initial time step. No mass transfer was allowed since the mixing chemical was a nonvolatile salt. The same equations and computer program were then used to
Biotechnol. Prog., 1994, Vol. 10, No. 5 2.5
,,
1
-Model
00.0.
2.0
545
-
Tracer Data
#4
1.5
0 1.0
0.4
-
y0.3 0
-
0.2
0.0
II 3 I
l’0
Ti rr
Q
1
Figure 2. Comparison of salt concentration profiles in the E M to the model with JGR= 1.6 cm/s and UT= 0.99 m/s.
0.1
0.0
Time (s) Figure 3. Comparison of experimental to model dynamic dissolved oxygen concentrations (JGR= 0.84 c d s , UT = 0.99 dS).
generate time history predictions for the liquid concentration exiting the riser. This history profile remains the same (although shifted in time) for each point in the downcomer.
Experimental Section Mixing and mass-transfer studies were carried out in an experimental external loop airlift bioreactor (ELAB), as described elsewhere (F’raser and Hill, 1993). The riser had a cross-sectional area of 52.8cm2 and contained a liquid volume of 7.92L, while for the downcomer these values were 22.9 cm2 and 4.35L. The operating parameters included both the rate of aeration and the rotation speed of the sparger. The results reported here are for low aeration rates, such that no air was carried back through the downcomer. As reported earlier (Fraser and Hill, 1993),the high rates of sparger rotation compensate for the low aeration rates by providing greater interfacial areas and gas hold-ups, thereby improving the oxygen mass transfer. The tracer injection port was located 0.44m from the downcomer entrance, while two conductivity probes were located 0.65 and 1.35 m from the entrance (see Figure 1). Five milliliters of a saturated sodium chloride/ distilled water solution was injected into the downcomer at time zero, and the NaCl concentration was detected at the two probe locations. Two in-house conductivity probes were used to make these measurements. Dissolved oxygen was measured using a polarographic oxygen probe (Cole Parmer, Chicago, Model 5946-50)) which had a response time of 3.0 s. The probe was mounted 0.29m above the sparger in the riser column, as shown in Figure 1. The meter gave a linear reading for oxygen concentration between 0 and 8.1ppm (saturation).
Results and Discussion Mixing. Since the Bodenstein number earlier had been found to be independent of both the aeration rate and the sparger rotation rate (Fraser and Hill, 19931,it is clear from eq 4 that, for an ELAB of fixed length, the dispersion coefficient is directly proportional to the liquid circulation rate. Figure 2 compares the predicted and experimental dimensionless NaCl profiles at high aeratiodsparger rotation rates. The operating conditions were JGR= 1.6 c d s and UT= 0.99d s . The values of parameters in the model were computed from eqs 1-4. The first response occuring at approximately 2 s in Figure 2 is due to the as yet undiluted, impulse injection of salt
and is not counted as a peak for mixing studies. Once the impulse enters the riser, it begins to become diluted and spreads out due to the enhanced mixing caused by the two-phase flow. The slug circulates about every 7 s. The close agreement between the model (solid line) and the tracer data clearly demonstrates that the dispersion coeficient is quantitatively well represented by eq 4. High Bodenstein numbers (49.4in eq 4)infer that the circulating liquid does not encounter any severe shearing regimes, which could mechanically damage sensitive cells. Mass Transfer. Andre et al. (1983)predicted that, a t normal values of KLa, treating a circulating loop airliR bioreactor as a well-mixed tank would result in accurate measurements of the mass-transfer coefficient. In that case, a semilog plot of 1 - X versus time results in a straight line for which linear regression gives the numeric value of KLa (Chisti, 1989 (p 302)). The dissolved oxygen data generated here were found to follow this kind of semilog linearity very closely. Figure 3 demonstrates that incorporating the measured value for KLa into the model (0.0088 s-l in this case) resulted in a severe underprediction of the real-time dissolved oxygen concentration (solid line in Figure 3). The measured masstransfer coefficient, KLa,, is based on the total liquid volume, while the model computes mass transfer only in the riser. Thus, &a, must be increased by the ratio of the total bioreactor volume to the riser volume, or
For the ELAB studied here, this volume ratio was 1.55, yielding a KLa, value of 0.0136s-l. When this value was incorporated into the model, an almost perfect fit of the experimental data was achieved, as shown by the dashed line in Figure 3. This correction indicates that KLa, remains constant (i.e,, independent of the downcomer size) and the KLa, value falls due to the dead volume of the downcomer. Bello et al. (1985b)came to the same conclusion after plotting KLa, for a wide range of experimental downcomer to riser area ratios. This correction factor has also been used recently by Pigache et al. (1992) for a large-scale airlift fermentor. Figure 4 shows comparison of the model to dissolved oxygen data published by Kamp et al. (1987)using an ELAB described in detail by McManamey et al. (1984). A linear regression of their published data yields a KLa, of 0.021s-l. The figure demonstrates that, in this case,
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I
0.8
-I
.---I KLar = 0.03
0.8
0.5 0.6
-
0.4
0
0
0 0.4
-
"0.3 0.2 0.1
0.0
I
4b
$0
dl
1 0
0.0
Time (s)
Figure 4. Comparison of the data of Kamp et al. (1987)to the
predicted dynamic dissolved oxygen concentrations.
both this value (solid line) and the KLa, value (short dashed line) fall well below their experimental data. The reason for this is that the dissolved oxygen data of Kamp et al. demonstrated a sharp discontinuity in slope about 15 s into their run. They were using a porous disk sparger, which resulted in tiny air bubble formation. A significant quantity of these bubbles was carried down the downcomer and entered back into the riser after about 15 s of operation. This new source of bubbles likely was depleted of oxygen, resulting in a lower masstransfer driving force throughout the riser, sharply reducing the oxygen-transfer rate. Using their early dissolved oxygen data, a KLa, value of 0.038 s-l was calculated, and it can be seen that with this value (long dashed line) the model slightly undershoots the data at early times, but then overshoots the data at later times when the unaccounted bubbles enter the riser. Having determined that the model predicts well both mixing and mass transfer in an ELAB, we then determined the effects of parameter changes on the predicted dynamic oxygen concentrations. It is clear that experimentally it is difficult (but not impossible) to vary one parameter at a time due to the many variable interactions that occur in an E M . However, the mechanistic model allows parameter effects to be studied without having to conduct extensive experimental work, such that one can determine which variables are most crucial to improved oxygen transfer. The largest factor affecting the mass-transfer rate was found to be the value of KLa,. A change in KLa, from 0.007to 0.04s-l (typical low and high values reported in the literature) resulted in a tripling of the rate of reaching 6 ppm dissolved oxygen in the bioreactor. Using typical values of dispersion coefficients (Joshi, 1983), no significant effects were observed on the rates of oxygen transfer in bubble columns or E m s . Simulations comparing bubble columns to E M S clearly showed that bubble columns always have faster dissolved oxygen build-ups, as is observed experimentally. This is due to the fact that, in an E M , liquid is always not being aerated while it travels through the downcomer. It was also discovered that, a t early times (around 4 s after aeration commences), the dissolved oxygen concentration is highest in the middle of the riser column. This is because the liquid at the base of the riser is continuously being diluted by the mixing of unaerated liquid entering from the downcomer. At later times (around 40 s), this discrepancy disappears and the dissolved oxygen profile becomes flat throughout the riser
Time (s) Figure 6. Comparison of experimental to predicted dynamic dissolved oxygen concentrations and effects of sparger rotation
speed and aeration rate. and the downcomer. The residence time of the air phase in the 1.5-m-high riser was 3.7 s. Simulation runs indicated that after the air rises completely through the column, the oxygen concentration in the air leaving the top of the ELAB reaches 16% 20 s after aeration commences. This is in agreement with the experimental observations of Kamp et al. (19851, who measured exit gas concentrations from a 1.1-m-high riser. Figure 5 demonstrates that the model accurately predicts the dynamic oxygen-transfer enhancements measured in the ELAB due to increased aeration and increased orifice speed. It is seen that as the orifice speed is increased from a low value of 0.30 m/s to a high value of 0.99 m/s, the time required for the dissolved oxygen to reach 30% of its saturation value drops from 81 to 45 s. Further, by increasing the aeration rate (JGR)from 0.48to 0.84c d s , the time taken to reach the 30% level of saturation drops by another 10 s to 35 s. The increased orifice speed improves KLa dramatically by reducing air bubble size and increasing gas hold-up, while the increased aeration rate increases gas hold-up (Fraser and Hill, 1993).
Conclusions A mechanistic model has been developed that accurately simulates both the mixing and mass-transfer capabilities of airlift bioreactors. The model has been used to demonstrate that the overall volumetric transfer coefficient in the riser, KLa,, of an ELAI3 remains constant and similar to the values measured in bubble columns. The drop in oxygen-transfer rates in ELABs is solely due to the removal of liquid from the aerated riser during its return in the downcomer. The model is useful for predicting design improvements in E M S , such as the effects of downcomer residence times or improved air sparging techniques.
Notation interfacial area in bioreactor (m2/m3) dimensionless finite difference parameters (eqs 8 and 9) downcomer cross-sectional area (m2) riser cross-sectional area (m2) dissolved oxygen concentration (g/L) equilibrium dissolved oxygen concentration (g/L)
dissolved oxygen concentration entering riser (g/L)
Biotechnol. Prog., 1994, Vol. 10, No. 5
initial dissolved oxygen concentration (g/L) dispersion coefficient (m%) gravitational acceleration (m/s2) Henry's law coefficient (eq 7) height of liquid in riser without aeration (m)space counter superficial gas velocity ( d s ) superficial liquid velocity ( d s ) overall volumetric transfer coefficient (9-l) measured KLa (8-l) riser KLa (s-l) length of loop in bioreactor (m) finite difference time counter time(s) interstitial liquid velocity in the riser ( d s ) interstitial gas velocity in the riser ( d s ) tangential velocity of sparger orifices ( d s ) volume of downcomer liquid (m3) volume of riser liquid (m3) (c* - c)/(c* - C I M T ) gas-phase oxygen concentration ( g L ) gas-phase oxygen concentration entering riser Cg/L) axial distance u p the riser (m)
gas hold-up in the riser
Acknowledgment This w o r k was funded by a grant from the Natural Sciences a n d Engineering Research Council of C a n a d a .
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