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Holdup and Liquid Circulation Velocity in a Rectangular Air-Lift Bioreactor Mesenia Atenas and Mark Clark* Department of Civil Engineering, University of Illinois, 205 North Mathew Avenues, Urbana, Illinois 61801
Valentina Lazarova Lyonnaise de Eaux, Cirsee, 38 rue du President Wilson, 78230 Le Pecq, France
Gas holdup and circulation velocity in a rectangular, pilot-scale air-lift reactor were studied as a function of superficial gas velocity. As the gas velocity increases, the gas holdup in the riser and downcomer increase, although the gas distribution in the downcomer remains quite inhomogeneous even at the highest gas velocity studied. Also, as the superficial velocity increases, the distribution of gas in the reactor becomes more homogeneous, with the difference in holdup between the riser and downcomer approaching an asymptotic value. Liquid circulation velocity was estimated by fitting batch tracer data to an N tanks-in-series recirculation model. Liquid circulation velocity increases with the superficial gas velocity and approaches a constant value, which corresponds to an asymptotic difference in holdup between the riser and downcomer. Measured liquid circulation velocity compared favorably with a model of Chisti et al. (Chem. Eng. Sci. 1988, 43 (3), 451-457). Introduction Gas holdup is one of the most frequently studied parameters in air-lift and bubble column reactors. This parameter is related to both the fluid dynamics and the mass transfer between gas and liquid. There is quite a bit of variation in experimental data and correlations for holdup in the literature (Freedman and Davidson, 1969; Merchuck, 1986; Shah et al., 1982). This is probably because gas holdup depends on several parameters such as liquid velocity, reactor geometry, and the fluid density and viscosity. The relationship between the superficial gas flow rate and holdup is generally presented in the form of a power law. Chisti (1989) examined the relationship between gas holdup and flow rate in an air-lift reactor, taking into account continuity and the drag force acting on the air bubbles. The resulting generic expression for the gas holdup () was
) Rugβ
(1)
The empirical constants R and β depend on fluid properties and the flow regime. It has also been found that the gas hold up changes depending on the position of the bubble sparger (Siegel et al., 1986). In addition to the gas holdup, the liquid circulation velocity represents one of the most important hydrodynamic parameters in the design of bubble columns and air-lift reactors.The liquid circulation velocity depends on several reactor characteristics but in particular on the superficial gas velocity. The relationship between these two quantities has been described in many papers as a power law (Chisti, 1989; Merchuck, 1986; Siegel et al., 1986):
ul ) AugM * Fax: 217 333-9464. E-mail:
[email protected]).
(2)
Figure 1. Schematic of reactor.
where A is a function of the reactor geometry and fluid properties and M is a parameter determined by the flow regime and reactor geometry. The purpose of this paper is to examine gas holdup and liquid circulation in a pilot scale, rectangular airlift reactor. Description of the System The reactor used in this study is a rectangular tank, 1.27-m tall with a cross sectional area of 0.18 × 0.18 m (Figure 1). The liquid volume is 0.0418 m3. The reactor is divided by an internal baffle located 0.07 m from the bottom. The reactor is filled with water to 1.12 m from the bottom, leaving a 0.15-m free space at the top of the reactor. The tank is operated as a closed system, with no circulation of fluid into or out of the reactor. Air is injected on one side of the baffle, which modifies the bulk density of the fluid in the riser. Because of the difference in fluid density in the riser and downcomer, water circulation is induced around the internal wall or baffle. The air is introduced through the bottom of
10.1021/ie980052l CCC: $18.00 © 1999 American Chemical Society Published on Web 02/04/1999
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the tank using a porous rubber membrane provided by Lyonnaise des Eaux, Le Pecq, France. An air compressor connected to the reactor through a 1/4-in. plastic tubing system supplies the air. A 150-mm brass flowmeter, a variable-area model with standard valves, is located between the air compressor and the reactor to control the amount of air going into the reactor. The range of air flow rates examined in the system varied from 0.15 to 2.91 cm/s. All of the physical characteristics of the system such as the dimensions of the reactor, the position of the baffle with respect to the bottom of the tank, and the water volume were fixed in this study. The only variable was the air flow rate. Gas Holdup. For the complete range of superficial gas velocities studied here, more air is contained in the riser than in the downcomer. When the air flow rate was increased, the amount of air reaching the downcomer increased, and the distance the air bubbles travel down the downcomer increased. The distribution of air inside the reactor is characterized by the gas holdup. Because of the spatial distribution of gas in the riser and downcomer, it is important to compute the global gas holdup, the partial gas holdup, and the manner in which gas is distributed in the riser and downcomer lanes. Gas holdup is computed using the piezometric and bed-expansion methods. The local gas holdup is computed using the piezometric readings and the distance between the piezometer taps:
g )
∆h ∆z
(3)
where ∆h is the difference in readings and ∆z is the distance between piezometers. Equation 3 can also be used to compute the partial gas holdup in each lane by considering the first and the last piezometer in each lane. Ten 1/4-in.-diameter piezometers were used to measure pressure. The piezometers are connected to a piezometer board by 1/4-in.-diameter plastic tubing. The piezometers are numbered from 1 to 5 in the riser lane and from 6 to 10 in the downcomer lane. A schematic of the piezometer distribution is shown in Figure 2. The bed-expansion method is the main method for measuring global holdup here. This method requires the measured reactor volume with and without air bubbles, Vd and Vl, respectively. The expansion of the volume due to the presence of bubbles (Vd - Vl) divided by the volume of the water with air bubbles (Vd) gives the global holdup in the system (Chisti, 1989):
g )
Vd - Vl Vd
Figure 2. Distribution of piezometers.
(4)
Liquid Circulation Velocity. The average velocity in the reactor is estimated using a tracer test. To perform a tracer test, a conductivity probe is placed in downcomer lane, 20 cm from the bottom of the reactor. Tracer is injected at the top of the riser, at a point midway between the baffle and the outside wall. The apparatus used to measure the response of the system to the injected tracer consists of a CDM230 conductivity meter (Radiometer, Copenhagen), a CDC641T conductivity cell (Radiometer), a Macintosh computer with a data acquisition card, and data acquisition software (LabVIEW, version 3.1, National Instruments).
Figure 3. Definition of turnover time.
After a value is set for the air flow rate, the conductivity meter is allowed to reach a stable output in order to characterize the initial conditions. The tracer is then injected at the top of the riser lane. The experiment lasts until a new stable signal is obtained. During this time, the variations in conductivity are saved to the computer. In Figure 3, a typical response of the system to a tracer injection is shown. The ending (steady) signal is higher than the initial signal because the conductivity of the water inside the reactor has increased because of tracer dissipation. The same procedure is repeated for each air flow rate. The usual procedure is to start the experiment using the lowest air flow rate and gradually increase the rate up to the largest value. After each run is completed, the water is changed. This procedure was completed six times in order to compute the final correlations between liquid circulation velocity and superficial gas velocity. The tracer was comprised of 5 mL of 4 M NaCl. The amount and concentration of the tracer was determined by trial and error, keeping in mind that the main goal was to have fast injection and good detection of the tracer. The main objective behind a fast injection is to mimic a pulse injection. Holdup experiments were done
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independently of the velocity measurements, so there was no effect of salt on interfacial tension or holdup. The acquired data were used to fit a batch, N tanksin-series, recirculation model. This model starts with the classic analysis of exit age distribution in a continuous flow, N tanks-in-series reactor system. Linear superposition is applied to derive a final expression for the variation of the concentration of the tracer inside the batch system (Levenspiel, 1972): -t/thi
ht iC ) e
∞
∑
(t/thi)mN-1
m)1(mN
- 1)!
(5)
where m is the number of loops in the recycle model. A typical concentration response is reproduced in Figure 9. To fit this model to the experimental tracer data, the parameters N and hti are adjusted to reproduce the experimental data. The critical fitting criteria are the maximum and minimum values of the concentration response, the time of their occurrence, and the final or asymptotic value of the tracer concentration. In the fitting procedure, values for hti and N are varied, and the model response is computed using eq 5. This response is then compared to the experimental data using a spreadsheet. If the two responses are not the same, the parameters are adjusted to reduce the discrepancy. For instance, the value of the maximum concentration is modified by adjusting the value of N, and the value of the final concentration is modified by adjusting the value of hti. This procedure is continued until the error between the data and model is minimized. Once good agreement between model and data is reached, the turnover time (tT ) htiN) is determined; this corresponds to the time needed for the tracer to travel one complete loop inside the system. Values of tT calculated in this way were generally within 10% of the peak-to-peak values shown in Figure 3. The characteristic circulation velocity is therefore computed as
Ul )
L tT
(6)
where Ul is the superficial liquid circulation velocity, tT is the turnover time, and L is the mean distance traveled by the tracer during circulation around the reactor. L was considered to be the length of the average flow path around the reactor; i.e., L ) 2.34 m. Riser and downcomer cross-sectional areas were the same, so Ul can be considered to characterize superficial velocity in both the riser and downcomer. Results Global Holdup. Results for global gas holdup computed by the bed-expansion method are shown in Figure 4. The straight line is from a least-squares fit to the logarithm of the global gas holdup () versus the logarithm of the air flow rate (ug), or
) 0.020‚ug0.691
(7)
with a correlation coefficient of r2 ) 0.972. The units of the air flow are cm/s. (Global gas holdup was also calculated by averaging the partial holdups in the riser and downcomer. These values were almost identical to
Figure 4. Global gas holdup as a function of superficial air flow rate.
Figure 5. Comparison of results of Chisti et al. (1989) and present study. SF is solids fraction.
those calculated form the bed-expansion method for the three highest gas flow rates but were lower than the bed expansion estimates for the three lowest flow rates; see Atenas, 1997). Chisti (1989) presents an expression which relates and the air flow rate (ug) for a reactor of similar characteristics (rectangular cross section). This expression is
) (1.49 - 0.496Cs)ug0.892(0.075
(8)
where the air flow rate is in units of m/s and Cs is the concentration of solids. If we consider Cs ) 0 as in this study, Chisti’s equation reduces to
) 1.49ug0.892(0.075
(9)
To compare eqs 7 and 9, the former has to be recomputed because its units are different from eq 9. The new version of eq 7 with ug in units of m/s is
) 0.473ug0.691
(10)
A comparison of eqs 9 and 10 show that the exponent values are not too dissimilar. However, the values of the constants are quite different. Another way to compare these two expressions is to plot our experimental results and the summary results presented by Chisti (see Figure 5). It should be noted that the experimental range for the flow rates in our experiment
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Figure 6. Partial gas holdup versus air flow rate, riser and downcomer.
is just a fraction of that used by Chisti. Plotted together, the results of this study conform well with those of Chisti (1989). Differences between eqs 9 and 10 could be related to the fact that even though the geometry of the two systems is similar (rectangular cross-sectional area), the larger reactor used by Chisti had two internal baffles, whereas the reactor used in this research had only one baffle. Another important difference between the two studies is the way in which the air is injected into the reactor. In the reactor examined here, the air is injected only at the bottom of the riser, whereas in Chisti’s reactor, the air is injected from the bottom of the two external lanes. (Most of the other holdup relations in the literature were developed for bubble column reactors and are therefore not comparable to the system used in this study.) Partial Gas Holdup. The purpose of computing the partial gas holdup is to determine the distribution of air inside the reactor. The piezometric method was used to compute the partial gas holdup. The piezometers used in this analysis are numbers 1 and 5 for the riser and 6 and 10 for the downcomer (Figure 2). Figure 6 illustrates the partial gas holdup for the riser and the downcomer lanes. As in the case of the global gas holdup, the lines represent the least-squares fit of the experimental data. The agreement between the experimental data and the empirical relationship for the riser is quite good, with a correlation coefficient, r2, of 0.982. The expression of the best fit is
r ) 0.0234ug0.713
(11)
where the units of superficial gas velocity are cm/s. Figure 6 also shows the total gas holdup for the downcomer lane. In this case, the relationship between the total gas holdup and the air flow rate is approximated by a linear function:
d ) 0.0144ug - 0.00 304
(12)
in which the correlation coefficient is equal to 0.975. Figure 6 shows that as the air flow rate increases the difference between the gas holdup in each lane approaches a constant. Figure 7 compares the distribution of gas holdup in each lane, expressed as a percentage of the global holdup. From this figure, it can also be seen that as the
Figure 7. Gas holdup in riser and downcomer as percentage of global holdup.
Figure 8. Gas holdup distribution. (a) Riser and (b) downcomer lane.
air flow rate increases the distribution of air tends to become more homogeneous. Distribution of the Gas Holdup. To compute the variation in holdup along each lane, the piezometric method was used. Parts a and b of figure 8 show how the gas holdup is distributed in the riser and downcomer lanes, respectively. This shows that in the riser the air can be considered approximately homogeneously distributed. On the other hand, in the downcomer, the air bubbles are located preferentially at the top of the reactor. As the air flow rate increases, the amount of air in the downcomer increases, as observed in Figure 8b (see also Chisti, 1989). From Figure 8b, it is clear
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Figure 9. Response of system to a tracer test at ug ) 1.97 cm/s.
that air bubbles do not reach the bottom of the downcomer lane, even for the highest air flow rate studied here. Liquid Circulation Velocity. Figure 9a shows a sample system response to tracer injection for an air flow rate of 1.97 cm/s. Fitting of these data to eq 5 was performed by modifying the number of tanks (N) and the mean residence time parameter (thi) in such a way that the model reproduces the maximum and asymptotic values of the tracer concentration response. Figure 9b compares the experimental and model responses. To obtain the turnover time, the final or asymptotic value of the tracer concentration is most important. To reproduce the maximum values observed in the responses, the value of N is changed as required. However, to reproduce the first maximum value, the N had to be set as high as 200, which was felt to be unrealistic. We also felt that by trying to fit the first peak, we would be expecting an unrealistic correspondence between initial conditions and assumptions of the model and the actual experimental conditions. For example, the model used here assumes that the tracer injection is instantaneous and that its concentration is homogeneous across a reactor section. Also, the model assumes that the injection of the tracer is at the beginning of the conceptual system, whereas the actual tracer injection takes place at a position (top of the riser) which corresponds to a place somewhere near the middle of the conceptual system. The injected NaCl travels only about a half loop before its first detection by the probe, which probably explains the large initial peak in the tracer concentration. This problem tends to die out once the tracer has dispersed sufficiently. As a result, we decided to approach this analysis by reproducing the experimental data starting with the second maximum or peak value. When the first peak was ignored, the fitting procedure outlined above yielded turnover times of 18.4, 14.0, 11.7,
Figure 10. Liquid circulation velocity as a function of air flow rate. Curve 1: ul ) 24.8 ug0.342; curve 2: ul ) 21.6 ug0.0494; curve 3: ul ) 25 - 20exp(-3.0ug).
9.52, 9.88, and 10.6 s for air flow rates of 0.14, 0.28, 0.58, 0.97, 1.94, and 2.91 cm/s (respectively) for a typical experiment. After the turnover times are computed, the liquid circulation velocity can be determined as the distance traveled divided by the turnover time. The travel distance simply was estimated as the mean path around the reactor, which was found here to be 2.34 m. Plots of all of the liquid circulation velocities measured in this study are presented in Figure 10, along with some fitted curves. A theoretical relationship between gas holdup and liquid circulation velocity was developed by Chisti et al. (1988) for air-lift configurations such as ours with equal cross-sectional areas in the riser and downcomer:
Ul ) [2ghD(r - d)(1 - d)2/KB]0.5
(13)
Here g is the acceleration of gravity, hD is the of the gas-fluid dispersion depth, and KB is the loss coefficient in the bottom of the reactor. Equation 13 was tested using experimentally determined partial gas holdups and gas-liquid dispersion heights for the six flow rates studied. KB was left as a fitting parameter which was determined by minimizing the variation between measured and computed circulation velocities. Figure 11 is a result of this exercise, for which the best fit was found for KB ) 16.6. The correspondence between the measured and predicted values is fairly strong, although there is some overshoot of the predictions in the experiments corresponding to the lowest superficial gas flow rates. Chisti et al. (1988) tested several forms of eq 13 with eight data sets for different reactors. For equal riser and downcomer cross-sectional areas, their correlation suggested KB ) 11.402. However, it is notable that the gas flow rates used in our study were lower than in any of the data sets used in developing their
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with the experimental work. Several anonymous reviewers were very helpful in improving the paper. Notation
Figure 11. Comparison of superficial liquid velocity measurements with a model from Chisti et al. (1988).
correlation for KB. Also from Figure 1 of Chisti et al. (1988), one notes a much greater scatter between measured and predicted liquid flow rates at the lowest flow rates. So our value of KB) 16.6 may not be unreasonable. Conclusions Three different aspects of holdup were studied: the total amount of air inside the reactor (global holdup), the amount of air in each lane (partial holdup), and the distribution of the air in the riser and downcomer. Two different methods, piezometric and volumetric, were used to compute these values. The measurements of global gas holdup agreed fairly well with the power law relationships found in the literature. Regarding the relative distribution of gas between the riser and downcomer, it was observed that as the air flow rates increase, the difference in holdup between the two lanes approaches a constant value. In the riser lane, the air is quite homogeneously distributed, whereas in the downcomer lane, the air is present mainly at the top of the reactor. It was also observed that even for the highest air flow rates studied here, there was no significant recirculation of air bubbles. An N tanks-in-series batch recycle model was used to fit the experimental data for the liquid circulation velocity. The turnover time, which here is the characteristic time to traverse the reactor once, was estimated from the fitted tracer circulation model. The results show that up to a point the liquid circulation velocity increases with the superficial gas velocity but then approaches a plateau value. These results were found to be consistent with previous studies (Chisti et al., 1988; Cockx et al., 1997), which showed that the circulation velocity is proportional to the square root of the difference in holdup in the riser and downcomer. Acknowledgment This work was supported by Lyonnaise des Eaux, Le Pecq, France. We thank Jennifer Prepejchal for help
A ) constant C ) concentration, mg/L Cs ) concetration solids, mg/L hD ) height of gas-liquid dispersion, cm KB ) constant L ) length of circulation path, cm m ) parameter representing number of loops in tanks-inseries model, dimensionless N ) number of tanks in tanks-in-series model, dimensionless Ul ) characteristic circulation velocity, cm/s hti ) mean residence time in subsystem of tanks-in-series model, s tT ) turnover time, s Vd ) volume of air-water dispersion, cm3 Vl ) volume of water, cm3 ug ) superficial liquid velocity, cm/s R ) constant β ) constant ∆z ) distance between piezometers, cm ∆h ) difference in piezometer readings, cm ) holdup, dimensionless d ) holdup in downcomer, dimensionless g ) holdup, dimensionless r ) holdup in riser, dimensionless
Literature Cited Atenas, M. Characterization and Modeling of Flow in a Rectangular Air-Lift Reactor. Master’s Thesis, University of Illinois, Urbana-Champaign, 1997. Chisti, M. Y. Airlift Bioreactors; Elsevier Applied Science: London, 1989. Chisti, M. Y.; Halard, B.; Moo-Young, M. Liquid Circulation in Airlift Reactors. Chem. Eng. Sci. 1988, 43 (3), 451-457. Cockx, A.; Line´, A.; Roustan, M.; Do-Quang, Z.; Lazarova, V. Numerical Simulation and Physical Modeling of the Hydrodynamics in an Air-lift Internal Loop Reactor. Chem. Eng. Sci. 1997, 52 (21-22), 3787-3793. Freedman, W.; Davidson, J. F. Holdup and Liquid Circulation in Bubble Column, Trans. Instn. Chem. Eng. 1969, 47, T251. Merchuck, J. C. Hydrodynamics and Holdup in Air-Lift Reactors. Encyclopedia of Fluid Mechanics: Cheremisinoff, N. P., Ed.; Gas-Liquid Flows, Vol. 3; Golf Pub. Co.: Houston, 1986. Levenspiel, O. Chemical Reaction Engineering, 2nd ed.; John Wiley & Sons, Inc.: New York, 1972. Shah, Y. T.; Kelkar, G.; Godbole, P. Design Parameters Estimation for Bubble Column Reactors. A.I.Ch.E. J. 1982, 28 (3), 353. Siegel, M. H.; Merchuk, J. C.; Schugerl, K. Air-Lift Reactor Analysis: Interrelationships between Riser, Downcomer, and Gas-Liquid Separator Behavior, Including Gas Recirculation Effects. A.I.Ch.E. J. 1986, 32 (10), 1585.
Received for review January 29, 1998 Accepted December 7, 1998 IE980052L
