Ind. Eng. Chem. Res. 1997, 36, 4681-4687
4681
Hydrodynamic Behavior of a Liquid-Lift, External-Loop Bioreactor Using a Spinning Sparger Hedieh Modaressi, Bruce Milne, and Gordon A. Hill* Department of Chemical Engineering, University of Saskatchewan, 110 Science Place, Saskatoon, Saskatchewan S7N 5C9, Canada
The liquid-lift bioreactor is conceptually similar to the familiar air-lift bioreactor. A liquid is sparged into the base of a column containing a second, immiscible liquid of higher density. The two phases rise cocurrently to the top of the column, where they are separated. The dense phase is then recycled to the base of the riser, whereas the light phase is removed from the bioreactor. The hydrodynamic characteristics of a 12 L, liquid-lift, external-loop bioreactor have been investigated using water and oleic acid as the continuous and dispersed phases, respectively. The experimental unit had a working height of 1.7 m and a downcomer to riser area ratio of 0.43. A spinning sparger consisting of six, 1 mm diameter orifices spread evenly on a 4.4 cm diameter circle was incorporated near the base of the riser to allow for enhanced control of the produced droplets. Experimental studies were undertaken at superficial dispersed-phase velocities up to 4 cm/min and sparger spinning speeds up to 350 rpm (maximum orifice tangential velocity of 0.8 m/s). Uniform droplets were produced at diameters ranging from 1 to 5 mm, while liquid holdups and circulation velocities reached up to 2% and 3 cm/s, respectively. The droplet size data were best fit to an empirical model, and the well-known drift-flux theory of Zuber and Findlay was used to predict the dispersed-phase holdup. The circulation velocity of the continuous phase was predicted using an energy balance around the loop. The model was found to provide reasonable predictions of droplet diameter, dispersed phase holdup, and circulation velocity as functions of both the dispersed-phase superficial velocity and the spinning speed of the sparger. Introduction The use of bioreactions for the conversion of low-cost feedstocks to higher valued products is attracting increased attention. One commercial application is fermentation to produce fuel ethanol which helps to reduce the demand for conventional crude oil and is less polluting than existing hydrocarbon-based fuels. However, achieving a high concentration of ethanol by simple fermentation is not possible. Ethanol fermentation is a product-inhibition bioreaction. This implies that as the concentration of ethanol increases, the bioreaction begins to slow down and eventually stops at an ethanol concentration of about 10% by weight. In order to alleviate this problem, many different techniques have been proposed for separating ethanol from fermentation broths. Among them, distillation and extraction are the most popular. In the past few years, researchers have paid more attention to in-situ extraction of ethanol directly from the fermentation broth (Jassal et al., 1994; Bruce et al., 1991; Minier and Goma, 1981). This valuable technique not only increases the productivity of fermentation by lowering product inhibition but is also cost effective since both fermentation and extraction can be handled in the same vessel. The type of solvent used is of great importance for in-situ extraction when dealing with bioreactions. The solvent must be non-toxic to the microorganisms. It should also be immiscible in the fermentation broth so that further separation is not necessary. It should have a high capacity for ethanol in order to minimize the amount of solvent required. Previous studies (Zhang and Hill, 1991; Jassal et al., 1994) showed that oleic acid is a promising solvent for extracting ethanol from water. * To whom correspondence should be sent. Phone: 306-9664760. Fax: 306-966-4777. E-mail:
[email protected]. S0888-5885(97)00089-4 CCC: $14.00
It is a naturally occurring fatty acid which is both nontoxic and harmless to the environment. Oleic acid is highly selective to ethanol over water and is immiscible in water. The boiling point of oleic acid is high, making downstream flash separation from ethanol a simple matter. Tramper et al. (1986) first proposed the use of liquidlift bioreactors for use with nonaqueous enzyme reactions or for product-inhibition fermentations such as ethanol. They proposed several different operating modes depending on the relative densities of the aqueous and organic phases. Van Sonsbeek et al. (1990) studied the hydrodynamic behavior of a liquid-lift, external-loop bioreactor using hexane and water. They obtained drops larger than 3 mm from their static orifices and did not report any information on the drop size distribution. The objective of this work was to study the hydrodynamics of a liquid-lift, external-loop bioreactor using oleic acid as the dispersed phase and a spinning sparger to produce the liquid droplets. The spinning sparger provides better control over drop size characteristics, thereby enhancing in-situ mass transfer. This study represents the first step toward the possible use of the external-loop bioreactor for the in-situ extraction of ethanol. Although this study is a necessary precursor to that work, it is likely that in-situ fermentation will have some effects on these results. For instance, the phenomenon of CO2 production during ethanol fermentation will generate a fourth phase inside the bioreactor. Although these gas bubbles should be evenly distributed throughout the riser and downcomer, high concentrations of CO2 gas will lower the density of the continuous phase and probably modify both the dispersed-liquidphase holdup and circulation velocities from those presented here. During this investigation, dispersed-phase holdup, © 1997 American Chemical Society
4682 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
droplet size, and circulation velocity have been experimentally measured without fermentation. The data have been collected as functions of both the spinning rate of the sparger and the superficial velocity of the dispersed phase. A model for predicting these properties is also presented. Model Development In practice, Sauter mean diameter is often used as a single number to represent a sample of droplets that have a range of diameters. By definition, the Sauter mean diameter is the diameter of a uniform group of droplets with the same specific interfacial area as the real group of droplets and is therefore a suitable scale for representing the mass-transfer characteristics of the original droplets. Mathematically, the Sauter mean diameter is defined as:
dS )
∑i Nidi3 ∑i Nidi2
JDR C0(JDR + JCR) + C1
(3)
where JCR is the superficial velocity of the continuous phase in the riser (m/s), and C0 and C1 (m/s) are arbitrary coefficients. These types of correlations are based on the drift flux, two-phase flow model developed by Zuber and Findlay (1965) and account for both the nonuniform radial holdup in the column and the relative velocity between the two phases. The value of the distribution parameter, C0, in the above correlation is an indication of the extent of radial nonuniformity in holdup. In the case of a radially uniform holdup profile, C0 is equal to 1 and its magnitude increases with an increase in nonuniformity. Van Sonsbeek et al. (1990) observed an unusually high value for the dispersedphase distribution parameter in their liquid-lift bioreactor. They believed this was due to the sweeping effect of the downcomer flow on the droplets emerging from
JDR JDR + JCR + Vt
(4)
In order to estimate the terminal velocity of droplets, Vt, a force balance on a single droplet rising under the influence of a buoyancy force in an infinite medium must be performed. The terminal velocity of a droplet is then estimated by (Coulson et al., 1978)
Vt )
(
)
4g(Fc - FD)dS 3CDFc
0.5
(5)
where CD is the drag coefficient for a spherical droplet and can be calculated using the correlation proposed by Clift et al. (1978):
CD )
3.05(783κ2 + 2142κ + 1080) -0.74 Re (60 + 29κ)(4 + 3κ)
(6)
where κ ) µD/µC. The Reynolds number is defined as
(2)
where C, R, and β are arbitrary coefficients, JDR is the superficial velocity of the dispersed phase in the riser (m/s), and UT is the tangential velocity of the sparger orifice (m/s). The constants C, R, and β are related to the system geometry and the physical properties of the fluids. This equation incorporates the effect of the spinning speed of the sparger but is also applicable to cases where no spinning occurs, i.e., when UT equals zero. In such cases eq 2 reduces to the form frequently found in the literature for static orifices. Many investigators (Hills, 1976; Merchuk and Stein, 1981; Van der Walle, 1985; Shipley, 1984; Philip et al., 1990) have correlated the dispersed-phase holdup with the superficial velocities of the two phases using equations of the form
)
)
(1)
where Ni is the number of droplets in a unit volume and di is the mean diameter of the droplets in that unit volume. In order to predict the Sauter mean diameter of air bubbles produced by a spinning sparger, Fraser and Hill (1993) developed the following empirical correlation:
dS ) CJDRR(1 + UT)β
the sparger orifices. The value of C1 is approximately equal to the terminal rise velocity of a single droplet in an infinite medium. When a spinning sparger is used to produce droplets, the rotational motion of the sparger produces some radial mixing at the location of the spinning disk which enhances homogeneous bubbly flow in the riser. Thus, the produced droplets rise with a uniform radial profile in the riser and there will be a uniform holdup profile. Equation 3 reduces to
Re )
dSVtFc µc
(7)
Knowing the terminal velocity, the time at which the droplets reach their terminal velocity can be calculated from
t)
(
)
1 3(Fc - FD)CDFcg 2 4FD2dS
1/2
(-ln(1 - XVt) + ln(1 + XVt)) (8)
where X is defined by the following equation:
X)
x
3CDFcFD
4(Fc - FD)gFDdS
(9)
From this calculated time, the distance at which the droplets reach their terminal velocity can also be predicted. In order to predict the circulation velocity of the continuous phase, the following equation derived from a force balance around the circulation loop was used (Van Sonsbeek et al., 1990):
1 ∆FghR ) KfFcJCR2 2
(10)
where ∆F is the difference between the densities of the two phases (kg/m3), hR is the height of liquid in the riser (m), and Kf is the single-phase overall friction coefficient in the system. In 1986 Verlaan et al. showed that, for cases where holdup is less than 10-15%, the pressure drop due to friction in loop bioreactors can be estimated by the single-phase flow friction coefficient. The frictional pressure drop in an external-loop bioreactor (∆Pf)
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4683
Figure 1. Schematic of the liquid-lift, external-loop bioreactor.
consists of the pressure drop along the riser (∆PR), the pressure drop in the bends (∆Pb), the pressure drop due to contraction and expansion of cross-sectional areas (∆Pc and ∆Pe), the pressure drop along the downcomer (∆PD), and for this experimental study, the pressure drop in the spacing between the rotating plane of the sparger and the riser wall (∆Pv). The overall friction factor in eq 10 may then be written as (Verlaan et al. 1986)
Kf ) KfR + 4Kfb + Kfc + Kfe + KfD + KfV
(11)
The last term in the above equation is the friction factor caused by the continuous phase flowing through the gap between the riser wall and the sparger which simulates a gate valve in the pattern of flow. In this work, the sparger surface occupies a significant portion of the total flow area in the riser and acts as a severe restriction against the flow from the downcomer to the riser. Hence, it is expected that the frictional pressure drop in this part of the bioreactor is much larger than the frictional pressure drop due to other terms in eq 11, which simplifies eq 11 to
Kf = Kfv
(12)
Experimental Section A schematic diagram of the bioreactor is shown in Figure 1, and some of its important dimensions are listed in Table 1. The bioreactor consisted of two vertical cylinders constructed from acrylic plastic: the riser and the downcomer. Horizontal side arms connected each end of the downcomer to the riser. A window with a flat surface was installed about half way up the riser for a clear, undistorted view of the flow and for photographic purposes. A recycle line was located at the top of the riser to remove the accumulated dispersed phase from the bioreactor. Other accessories for the riser included four pressure taps, three ports which facilitated chemical injections, and sampling and probe ports. The downcomer had three injection ports, one large brass gate valve (left fully open), and a drainage port. The upper side arm was equipped with a bleed line which prevented entrained oleic acid droplets from accumulating in the side arm and flowing down the downcomer. The injection system for the dispersed phase consisted of a rotating sparger constructed from acrylic plastic. The sparger was similar to that described earlier (Hill et al., 1996) and consisted of a flat, 56 mm diameter disk with six evenly placed orifices. Each orifice had a
diameter of 1.0 mm. The sparger disk was mounted on a hollow rotating shaft through which the dispersed phase (oleic acid) entered the bioreactor. The length of the hollow shaft was chosen to locate the sparger above the downcomer inlet, thereby eliminating the sweeping effect observed by Van Sonsbeek et al. (1990). This prevented problems caused by excessive maldistribution of droplets in the riser. The rotation of the sparger was controlled by a variable-speed motor with a pulleydriven, gear system. A holding tank was used to store and collect the recycled dispersed phase. Oleic acid was pumped from the holding tank to the sparger using a variable-speed peristaltic pump. The tubing chosen for the pump was thick-walled, C-Flex tubing (Cole-Parmer, Chicago), which demonstrated good chemical resistance to oleic acid. The flow rate of the dispersed phase was measured using a rotameter located between the pump and the sparger. Five evenly placed baffles were installed in the riser, near the sparger, to prevent the formation of vortices due to the circulatory motion of the spinning sparger. The size of droplets was determined using an image analysis system at 12 different combinations of the two manipulated variables (spinning speed of the orifice and dispersed-phase superficial velocity). In addition, one measurement was duplicated to determine reproducibility characteristics. The location of the 12 measurements was identified using the central rotatable design strategy (Diamond, 1989) which permits quantitative models to be developed from the measured output variables. Videoimages of the droplets were recorded through the small window in front of the riser using a videocamera (COHU, Model 8212-1000/0000) with a macrolens and a 10 mm extension. The videoimages were subsequently analyzed using image analysis software (Mocha 1.0, Jandel Scientific, Mississauga, Canada). In order to eliminate blur caused by the motion of droplets, a stroboscope was used to instantaneously capture the videoimages. A white screen was located behind the riser to evenly distribute the light. The camera was kept close to the front window and was focused on a point inside the bioreactor about 0.5 cm from the window. Glass beads of known sizes were hung by a thread inside the bioreactor, and their sizes were evaluated by Mocha in order to determine the accuracy of droplet size measurements. Comparing the results of this evaluation with the actual size of glass beads demonstrated that Mocha was able to measure the actual sizes within a (2% accuracy. For each operating condition, between 120-150 droplets were manually chosen from the videofilm. Since the Mocha software could not accurately distinguish, the edge of the droplet images (due to insufficient contrast between oleic acid and water and overlap of droplet images), these were manually defined and then droplet diameters were evaluated by the Mocha software. The dispersed phase holdup in the riser column was determined by measuring the hydrostatic pressure drop across the riser using an inverted U-tube manometer. The resolution of measurement of the manometer meant that the holdups could be measured to an accuracy of (0.1%. The dispersed-phase holdup was determined at nine different superficial velocities of the dispersed phase and six different spinning speeds of the sparger for a total of 54 measurements. In order to confirm the reproducibility of the results, the measurements were repeated twice at each operating condition. The circulation velocity of the continuous phase was
4684 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 Table 1. Design Measurements of the Bioreactor description
measurement
description
measurement
riser diameter (mm) downcomer diameter (mm) riser length (m) downcomer length (m)
82 54 1.7 1.9
volume (L) sparger hole diameter (mm) sparger diameter (mm) sparger hole to hole diameter (mm)
12 1.0 56 44
measured using a dye tracer method at the same 54 locations used to determine the dispersed-phase holdup. A water-soluble dye was injected with a slug of water into the downcomer, and the time for it to travel 72 cm in the downcomer was measured. These measurements were the final series of experiments carried out in this study, and it was observed that the dye had no noticeable effect on the circulation velocity data. Each measurement was performed twice in a random fashion, during which time the dye concentration was changing inside the bioreactor. The measured velocities never varied more than 2.5% from each other, and these changes showed no trend toward being lower or higher in value as the dye concentration increased in the bioreactor. Results and Discussion Droplet Size. Ordinary static orifice spargers are inadequate in their ability to produce small air bubbles needed for good oxygen mass transfer in fermentation vessels. Normally they are located at the base of the riser at the central axis and result in radial variations of both gas holdup and bubble diameters. Lippert et al. (1983) measured wall gas holdups of 15% and centerline gas holdups of 35% while the mean bubble diameters varied from 3 to 4 mm at the same locations. Fraser and Hill (1993) have demonstrated that the rotating sparger, on the other hand, could be operated at about 500 rpm, where it produced a swarm of bubbles with narrow diameter distributions and Sauter mean diameters as low as 2 mm. Motarjemi and Jameson (1978) calculated that the best mass-transfer coefficient for oxygen in water occurs at bubble diameters of about 2 mm. Static orifices typically produce air bubbles around 4 mm diameter and larger (Popovic and Robinson, 1987). Such large bubbles cause a 6-fold drop in the interfacial area due to both lower specific interfacial areas and lower gas holdups. Although the optimum droplet diameter for liquid-liquid mass transfer will differ from that for oxygen from bubbles due to differences in mass-transfer coefficients, droplet rise velocities, and chemical solubilities, it is still probable that small droplets with narrow diameter distributions will often be desirable when transferring chemical species in shallow (
