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PROCESS DESIGN AND CONTROL Modeling Aerated Fermenters with Computational Fluid Dynamics Pasi Moilanen,* Marko Laakkonen, and Juhani Aittamaa Laboratory of Chemical Engineering, Helsinki UniVersity of Technology, P.O. Box 6100, FIN-02015 HUT, Finland
Various aspects of viscous gas-liquid modeling are discussed. A detailed model is developed for aerated fermenters. Rigorous gas-liquid mass transfer, xanthan bioreaction kinetics, and non-Newtonian hydrodynamics are combined with computational fluid dynamics (CFD). Gas-liquid hydrodynamics is investigated in a 200dm3 laboratory stirred tank and xanthan fermentation is studied in a 70-m3 agitated reactor. Sub-models needed by the CFD simulation are verified against the hydrodynamic and oxygen transfer experiments. Multicomponent gas-liquid mass transfer is modeled based on the Maxwell-Stefan diffusion. A bubble swarm drag correction is developed for viscous shear-thinning fluids with a single bubble size. The laboratory stirred tank simulations predict the cavern and gas slug formation. The “snapshot” fermenter simulations show significant inhomogeneity of gas-liquid mass transfer rate, dissolved oxygen concentration (DO), and apparent viscosity of liquid in the bioreactor. Impeller flooding and poor mixing at the bottom of the fermenter were identified. The developed model can be used for the scaleup and detailed design of aerobic bioreactors. 1. Introduction Mechanically agitated aerobic fermenters are widely used in biotechnology, food, and pharmaceutical industries. Stirred tanks are overwhelmingly dominant in fermentation and cell culture industries.1 In large fermenters, reaction conditions are seldom homogeneous.2,3 Cavern formation is typical for viscous shearthinning fluids.4-6 Low dissolved oxygen (DO) content7 and poor distribution of nutrients8 are likely in the stagnant zones of a reactor. This causes inefficient use of reactor space, may harm the biomass, or may alter the microbiological metabolism.9,10 The physical properties of fermentation broth change during the cultivation. In a typical fermentation, the broth rheology is initially similar to water, but often becomes viscous and non-Newtonian at the end. Insufficient oxygen transfer rates and poor bulk mixing as a rate-limiting step of bioreactor performance has been addressed in many studies.11-15 The lack of suitable physical models and the general complexity of bioreactors is a major obstacle in numerical simulations. Most available models are limited to a specific scale and operating conditions.16,17 Scaleup is still largely performed using empirical knowledge. One of the most challenging tasks in the fermentation industry today is the design of highly shearthinning viscous fermentation broths, where the main limiting factors are bulk mixing and oxygen mass transfer.1 Experimental information from shear-thinning gas-liquid dispersions is widely available; however, most of it is from slightly shearthinning and dilute dispersions. Available studies include information that concerns flow fields,18,19 bubble sizes,20 rise velocities,21 bubble interactions,22,23 local gas holdups,24,25 mass transfer, and mixing.3,26,27 Local information is needed to make detailed investigations of heterogeneous fermenters.16 In this work, gas-liquid hydrodynamics was investigated from gassed * To whom correspondence should be addressed. Tel.: +358 9 451 2648. Fax: +358 9 451 2694. E-mail:
[email protected].
xanthan solutions in a laboratory stirred tank to get information needed for model validation. With computational fluid dynamics (CFD), it is possible to model local conditions in arbitrary vessel geometries. Still, CFD has been used to investigate turbulent, aerated, non-Newtonian flows only in a few studies.16,17,19 In this work, physical scaleindependent models are combined with CFD. Local gas-liquid, mass transfer, and bioreaction28,29 rates are investigated to gain a deeper understanding of reactor gas-liquid hydrodynamics and to develop a model that can be used for the troubleshooting, design, and scaleup of aerobic fermenters. 2. Experimental Section Gas-liquid hydrodynamics was investigated from aqueous xanthan gum (Keltrol BT) in a laboratory stirred tank. The ungassed system is transparent at low xanthan concentrations and not prone to contamination, in contrast to the actual fermentation broths. This simpler model system mimics the actual fermentation broth, allowing a wider range of experimental techniques to be used. Additives were used in the physical property measurements to imitate a real fermentation broth. Local bubble size distributions (BSDs), DO content, bubble rise velocities, and vessel averaged gas holdup were investigated. The power consumption of mixing varied over a range of 0.1-3 W/(kg liquid) and the gas feeds were 0.1-1 vvm. [Here, vvm represents the volume of gas feed per unit volume of liquid per minute.] The dimensions of Rushtonturbine-agitated, fully baffled vessel are as follows: volume, V ) 200 dm3; tank diameter, T ) 0.64 m; height of liquid level, H ) T; diameter of impeller, Dimp ) T/3; clearance of impeller, Cimp ) T/3; baffle width, W ) T/10; and clearance of the baffle, Cbaf ) T/20. Surface baffling was used to avoid surface aeration. The gas was introduced through a ring sparger (Dspa ) 0.75Dimp) that was located below the impeller. 2.1. Physical Properties. Physical properties were measured from the 0.0, 0.25 and 0.75 wt % xanthan solutions with
10.1021/ie060097j CCC: $33.50 © 2006 American Chemical Society Published on Web 11/02/2006
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3. Xanthan Fermentation Modeling
Table 1. Average Bubble Rise Velocities, Sizes, and Xanthan Concentrations xanthan concentration [wt %]
bubble size [mm]
rise velocity [cm/s]
injection rate [1/s]
0.25 0.25 0.40 0.40 0.75 0.75 0.90
3.8 3.4 4.3 3.8 5.6 6.0 9.1
13.1 12.0 7.8 4.2 8.7 11.3 9.0
0.28 0.38 0.30 0.38 0.56 0.34 1.08
µapp - µ∞ ) [1 + (λγtot)2](n-1)/2 µ0 - µ ∞
additives. The additives were as follows: biocide, Na2S2O3 (0.15 wt %); lactose (2.0 wt %); sulfate, (NH)4SO4 (0.25 wt %); phosphate, KH2PO4 (0.25 wt %); and a defoamer, Struktol SB2121 (0.2 mL/L). The surface tension was measured with KSV Sigma 70 tensiometer. Viscosity and yield stress were measured with a Brookfield DV-E viscometer. The density, which was measured with an Anton Paar DMA 512P system, was 1010 kg/m3. The surface tension increased from 0.042 N/m to 0.046 N/m with increasing xanthan concentration (0-0.75 wt %) The additives had little effect on the viscosity of the solution. 2.2. Gas Holdups and Mixing Intensity. The gas holdups and mixing intensity were measured for tap water, as well as for 0.25 wt % and 0.75 wt % xanthan solutions, in the laboratory vessel. The gas holdup was obtained by measuring the change in dispersion height. The mixing intensity was measured with a strain gauge, based on the torque on the impeller. 2.3. Bubble Rise Velocities. Bubble rise velocities were investigated by injecting bubbles through a pipe to stagnant 0.25, 0.40, 0.75, and 0.90 wt % xanthan solutions. Characteristic bubble size was calculated from the air volume flow and the number of generated bubbles. The time for a bubble to rise a distance of 250 mm from the pipe to the surface was recorded. Series of 50 bubbles were recorded at each xanthan concentration with two flow rates. The gas flow rate was varied from 3.3 mL/min to 22.2 mL/min. The average bubble rise velocities are presented in Table 1. 2.4. Local Bubble Size Distributions. Local bubble size distributions were measured from 0.25 and 0.75 wt % xanthan solutions. Because of dense dispersions, photography was possible only near the vessel wall. Pictures were taken at four heights between the bottom and the surface of dispersion at a mid-plane position between baffles. The BSDs were analyzed by identifying 500-1500 bubbles manually as ellipsoids. The particle analysis tool of ImageJ 1.32 freeware was used to convert the ellipsoids from the thresholded images to BSDs. The resolution of the digital camera allowed the detection of bubbles larger than ∼0.1 mm (5 pixels). 2.5. Dissolved Oxygen. Using a Lutron DO-5510 oxygen meter, the amount of dissolved oxygen was measured. The apparatus was inserted at the leeward side of the baffle at a position 0.315 m from the bottom. Determination of the kLa value, based on the changing concentration of the gaseous O2 was considered using a second-order method.30 The liquid concentration and the measurement probe were simulated separately.31 The calculation of the equilibrium values is shown in previous work.32 Mass-transfer coefficients were kLaconverted33 to a temperature of 20 °C, to make the measurements at varying temperatures comparable.
kLa20 )
k La 1.022
θ-20
3.1. Liquid Viscosity. The Carreau model34 was used to describe the apparent liquid viscosity:
(1)
(2)
This model has limiting viscosities, which makes it numerically stable in CFD calculations; however, it neglects the yield stress and elasticity that are observed in viscous xanthan solutions.48,54,55 The widely used power law and Casson35 viscosity models have a problem: at zero shear, the viscosity becomes infinite, which causes numerical instabilities in the CFD simulations. The Carreau model parameters were fitted against viscosity measurements. The fitting is important for the simulations, because, usually, in viscous fluids, the apparent viscosity outweighs the turbulent viscosity. The viscosity at infinite shear was assumed to be that of water (0.001 Pa s). The other parameters were, for 0.25 wt % xanthan solution, λ ) 0.268 s-1, n ) 0.314, and µ0 ) 0.215 Pa s, and, for the 0.75 wt % xanthan solution, λ ) 1.754 s-1, n ) 0.096, and µ0 ) 13.23 Pa s. Yield stress measurements produced values that increased almost linearly from 0.05 Pa to 10.6 Pa when the xanthan concentration increased from 0.25 wt % to 4.0 wt %. 3.2. Bubble Drag. A bubble drag model21 for non-Newtonian fluids is used. It has been developed for individual bubbles in a stagnant shear-thinning liquid.
CD )
24 0.413 (1 + 0.173Re0.657) + Re 1 + 16300Re-1.09 (for Re < 135) (3a) CD ) 0.95
(for Re > 135)
(3b)
where the bubble Reynolds number, Re, is defined as
Re )
UslipFcd µapp
(4)
In traditional correlations52,53 for Newtonian fluids, increasing the particulate or bubble concentration increases drag. Our bubble rise velocity experiments indicate the opposite with the xanthan solution. In the viscous shear-thinning xanthan solutions, individual bubbles rose slower than bubbles in a swarm. This effect became more pronounced at higher injection rates and with increased xanthan concentration. Similar behavior has been observed22 with carboxymethylcellulose (CMC) and polyacrylamide solutions, and the effect has been explained by liquid elasticity. Chhabra36 developed a model for the bubble swarm effects in shear-thinning fluids. The model predicts that slip velocity increases as gas holdup increases if the flow index (n) is 100 mm) were observed to rise out of dispersion in the 0.75 wt % solution. Our simulations51 have indicated similar behavior. It has been suggested that the volume BSDs may be bimodal;20 similar observations have also been made from xanthan fermentation broths.6 The measurement of large bubbles is difficult, because they rarely appear in the near wall areas, where measurement by photography is possible. The largest bubbles rose out in the middle and near the impeller shaft, indicating that the impeller was incapable of dispersing the gas completely. This can mean that the bubble size measured near the vessel wall does not represent the vessel-averaged bubble size. Gas holdups were shown to be time-dependent in our experiments. Seventy minutes were required for a 0.75 wt % xanthan solution to reach a steady holdup of 6.6% at 0.5 vvm and 250 rpm in the laboratory vessel. Similar behavior has been observed in viscous fluids.20,46,47 There remains a residual gas holdup in viscous xanthan solutions even when the mixing has been stopped. The small bubbles are trapped by the viscous liquid and coalesce until buoyancy becomes so large that they separate from the xanthan solution. This phenomenon is hard to reproduce in the CFD simulations with a single bubble size.
Figure 2. (a) Simulated local velocities shown for 0.75 wt % xanthan solution; cavern formation can be seen below the dashed line. (b) Local velocities for pure water. Conditions for both panels: 0.5 vvm, 390 rpm, bubble size of 4 mm. The values are taken from the mid-plane between baffles.
A two-phase simulation was made to fit the value of K in the bubble swarm correction. In the laboratory vessel (390 rpm, d ) 1.8 mm, 0.5 vvm, and 0.25 wt % xanthan solution) the measured gas holdup was 5.4 vol %, whereas CFD simulation yielded 7.3 vol % with K ) 15. The simulated volume-averaged bubble slip velocity was 11.4 cm/s, whereas the experimental value was 12.5 cm/s (3.6 mm bubbles, injection rate of 0.33 s-1). The simulations and experiments are of same magnitude. The rise velocity in an agitated tank may be higher than that in a stagnant medium, because of liquid-flow-induced shear and higher gas holdups. The modeling of bubble size seems to be one of the most critical tasks in the simulation of viscous gasliquid dispersions. It directly influences the bubble slip velocity, the mass transfer area per gas volume, and, thus, the masstransfer rate. Indirectly, it influences gas holdup and flow fields. The CFD simulations showed that the gas begins to accumulate quickly in viscous fluids if a suitable combination of submodels is not used. It seems that the use of population balances (PBs) for bubbles would avoid the tedious iteration of the suitable combination of bubble size, bubble swarm correction, and drag model. Therefore, it has been suggested that PBs for bubbles with appropriate coalescence and breakage models should be used17,51 to predict gas-liquid hydrodynamics in viscous shearthinning fluids. Finally, a 0.75 wt % xanthan CFD simulation of the laboratory vessel with 390 rpm, 0.5 vvm, and a bubble size of 4 mm was made to investigate the behavior of gas slugs and cavern formation. The 4-mm bubble size was used instead of the experimental value, because small bubbles do not separate from the solution (see Figure 1). The simulations with measured bubble (d32 ∼2 mm) size failed. It is probable that the photographed bubbles near the wall of the vessel do not represent the vesselaveraged bubble size. The uneven distribution of shear is the main problem in bioreactors with a shear-thinning medium. Near the impeller, the shear is high, which results in low apparent viscosity and good mass transfer. In the bulk region, a contrary situation is observed.3 Gas slugs or very large gas bubbles are known to exist in pseudoplastic media.49,50 In Figure 2a and b, local velocities are shown for 0.75 wt % xanthan solution and water, cavern formation is observed in Figure 2a. Using the bubble swarm correction, bubbles form gas slugs when the local gas holdup is high enough. The gas slugs penetrate the stagnant area of high viscosity near the vessel surface. The mechanism is inherently transient, so there is not a steady-state solution.
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Figure 3. Depiction of the 25 vol % air isosurface; arrows show gas slugs rising through the stagnant region. Conditions: 0.5 vvm, 390 rpm, bubble size of 4 mm, 0.75 wt % xanthan, 3D calculation. Table 2. Average Feed and Off-Gas Compositions, Local Minimums, Local Maximums, and Vessel-Averaged Concentrations in Both Phases Concentrationa
Composition [wt %] component
gas feed
off-gas
minimum
average
maximum
H2O (g) CO2 (g) N2 (g) O2 (g) N2 (aq) CO2 (aq) O2 (aq)
1.00 0.03 76.97 22.00
1.59 8.98 70.1 19.3
1.05 0.16 69.5 19.0 14.1 54.6 6.94
1.32 7.82 71.3 19.6 15.5 92.5 7.74
1.60 9.88 76.8 21.9 17.0 102.4 8.98
a Units for gaseous components are wt %, whereas those for dissolved components are mg/L.
Gas slugs are illustrated as isosurfaces in Figure 3. In visual observations, large slugs can be seen bursting out in the central parts of the vessel surface, which supports the simulation. The simulation also agrees with the observations that gas holdup is greater near the axis of the vessel.24 4.2. The 70-m3 Fermenter. Four-component gas-liquid mass transfer with xanthan bioreaction kinetics was investigated in the 70-m3 fermenter. The simulations with the experimental 2-mm bubble size failed. A bubble size of 5 mm was used in the mass transfer simulation, because it produced reasonable vessel-averaged gas holdups and bubble slip velocities. The fermentation was simulated for 90 s. The mass balances of the gas or liquid phase did not change because of the bioreaction or mass transfer. This assumption is justified because the gas and liquid volume change due to mass transfer is minute. The bioreaction rates and mass transfer rates were stored as scalars for further evaluation of the results. The compositions of the off-gas, liquid, and gas phases are presented in Table 2. It can be seen that the sparged gas becomes moist, removes CO2 from the bioreactor, and transports oxygen into the liquid. Because the reactor was not at equilibrium in respect of N2, some of the nitrogen is being dissolved into the broth. At the end of the simulation, CO2 and O2 are both being depleted in the liquid phase. It can be concluded that the fermenter has not yet reached a steady state. The computational time required for the steady-
state solution is considerable, but can be decreased via appropriate initialization. Pseudo-steady states can be calculated for the vessel hydrodynamics and mass transfer, because the time scales for these phenomena are on the order of a few minutes. The degree of local variation is shown in the 70-m3 bioreactor in Figure 4a-f at the mid-plane between baffles. Figure 4a shows the shear-dependent apparent viscosity, and Figure 4b shows the resulting local velocities. In the bulk region, viscosities are high, near to the limiting viscosity at zero shear (215 mPa s), and the velocities are low, as expected. The lower Rushton is flooding and does not generate a radial discharge. This reduces the mixing efficiency in the lower part of the reactor. The buoyancy of the gas phase is clearly the driving force near the lower impeller and near the vessel wall above the upper impeller. Figure 4c shows the variation of the local gas-liquid masstransfer rate for oxygen. The majority of the mass transfer occurs near the gas feed and the upper impeller discharge flow. Because of the assumption of a constant bubble size, the mass transfer rate is mainly determined by the local gas holdup, which results in very low mass transfer rates at the bottom of the vessel. A gas slug (signified by an arrow in Figure 4c) can be observed as an area of high mass transfer rate in the upper part of the vessel. The hold-up correction causes the formation of slugs that penetrate the area of high apparent viscosity at the top of the vessel. Figure 4d shows the DO amount as a percentage from local equilibrium that is calculated based on the local partial pressure of oxygen. The percentage of saturation is calculated according to the local gas-phase oxygen concentration. The xanthan production rate (see Figure 4e) in this case is affected only by the absolute DO concentration, because of the perfectly mixed nitrogen source and biomass. The highest xanthan production rate is observed in the vessel midsection. In the midsection, the absolute pressure is moderate and most of the oxygen mass transfer occurs near the impellers, which results in high DO concentrations. At the top of the vessel, there is low absolute pressure, resulting in low DO concentrations. At the bottom, there is almost no mass transfer, because of low gas holdup, so the DO is convected to the bottom from the upper parts of the vessel. During the convection, the bioreaction consumes oxygen, which results in lower DO concentrations at the bottom. At the top, where DO saturation is highest, the xanthan production is the lowest, because of the lower oxygen partial pressure. It is evident that mass transfer limits the performance of this reactor, because the vessel-averaged DO is
