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Phenomenological Simulation Model for the Prediction of Hydrodynamic Parameters of an Internal Loop Airlift Reactor Ragupathy Prabhu Arunkumar and Karuppan Muthukumar* Department of Chemical Engineering, Alagappa College of Technology Campus, Anna UniVersity Chennai, Chennai -600 025, India
Airlift reactors are pneumatically agitated reactors finding wide applications in chemical and biotechnology industries as well as in the treatment of wastewater. The design and scale-up of an airlift reactor is difficult and largely based on empirical approaches. The bubble size, distribution, and concentration are important parameters that influence the gas holdup and interfacial area. However, the influence of bubble size and distribution are not taken into account by any of the empirical correlations. In the present investigation, a phenomenological approach has been developed to predict the gas holdup in an internal loop airlift reactor. This approach considers the effect of bubble dynamics such as bubble breakup and bubble coalescence in the column and employs a population balance approach to determine bubble concentration in the column. From the knowledge of number and size of the bubbles, gas holdup in the reactor was obtained. A reasonably good agreement was observed between the simulation model predictions and the experimental data reported in the literature. 1. Introduction Airlift reactors are employed for a wide range of industrial applications such as wastewater treatment and fermentation because of their ability to achieve high heat and mass transfer rates with low energy input. Sophisticated modeling, complex analysis of the parameters involved, and detailed understanding of the underlying physics of the phenomenon must be used in order to develop models that can adequately describe the observed behavior of the reactors and complexity of the fluid dynamics. On the other hand, the simplicity of their design, construction, better defined flow pattern, and comparatively low power inputs make them attractive.1 Low shear rates, efficient gas phase disengagement, well-controlled flow and mixing, large specific interfacial area, and well-defined residence time make them superior over all other available bioreactors. For the design of airlift reactors, it is essential to have accurate estimates of the phase holdups and liquid velocities in the riser and downcomer.1-3 Most of the literature does not account for the dynamic breakage and coalescence of bubbles which determine the bubble size and its distribution. In general, there are two approaches available to evaluate the gas holdup in a reactor. Empirical correlations have been extensively used for the evaluation of hydrodynamic parameters of reactors but have limited applicability and are bound by scale of the reactors, operating conditions, etc. Moreover, these correlations do not take into account the influence of bubble sizes.4 The bubble size distribution is one of the most important parameter that determines the bubble rising velocity, and henceforth, gas residence time, gas holdup, and interfacial area available for the mass transfer. Thus, the bubble size plays a substantial role in determining the performance, and thus, it is necessary to understand the bubble behavior for the rational design of these reactors. The phenomenological approach, which considers the bubble breakup and coalescence in the column, was first proposed by Prince and Blanch.5 They have developed models to determine * To whom correspondence should be addressed. E-mail:
[email protected]. Phone no.: +91 44 22359153. Fax no.: +91 44 22352642.
the bubble coalescence and breakup rate and reported good agreement between model prediction and experimental data, but their model has not been applied to predict important design parameters for bubble column reactors such as gas holdups and gas-liquid mass transfer rates. Many investigators have developed newer and more accurate models recently for the prediction of the bubble coalescence and breakup rates such as those by Luo,6 Luo and Svendsen,7 Hagesaether et al.,8 Lehr et al.,9 Wang et al.,10 and Chen et al.11 The comparison of various breakup and coalescence models showed that the coalescence model of Lehr et al.9 and the breakup model of Wang et al.10 were found to provide the best results. In order to obtain bubble size distribution, it is necessary to describe the bubble interactions such as bubble coalescence and break-up and the most important deterministic model for carrying out this is the population balance model. Population balance models have been successfully used for the prediction of behavior of particulate systems as well as twophase gas-liquid dispersed systems. Wang et al.12 used the population balance technique to analyze the influence of the bubble coalescence and breakup on gas-liquid flows. Shimizu et al.13,14 studied the phenomenological simulation of a bubble column and an external loop reactor with the models proposed by Prince and Blanch.5 Pohorecki et al.15 employed the model proposed by Prince and Blanch8 to predict the bubble size distribution corresponding to dynamic equilibrium. Bordel et al.4 predicted the variation in bubble size distribution with length in a bubble column using the coalescence model of Lehr et al.9 and the breakup model of Wang et al.10 and reported good agreement between simulated and experimental data. Lehr and Mewes16 implemented the population balance in a commercial computational fluid dynamics (CFD) code to predict the bubble size distribution in bubble columns. Dhanasekharan et al.17 developed a general approach by coupling the bubble dynamics with fluid flow equations for multiphase flow and the population balance coupled with fluid flow equations were solved using CFD to determine the gas holdup. Huh et al.18 also used CFD to predict the interfacial area concentration by coupling the fluid flow equations with number density transport equations.
10.1021/ie900713v 2010 American Chemical Society Published on Web 04/21/2010
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f(Nw) ) 2.9Nw-0.188
Table 1. Configuration of the Reactors Used
column diameter (m) draft tube diameter (m) height of liquid (m) height of draft tube (m) bottom clearance (m) Ad/Ar no. of sparger holes hole diameter (mm)
10.5 L19
32 L19
200 L19
300 L20
0.108 0.070 1.26 1.145 0.030 1.23 25 0.5
0.157 0.106 1.815 1.710 0.046 0.95 25 0.5
0.294 0.2 2.936 2.700 0.061 1.01 90 1.0
0.318 0.216 3.30 3.27 0.040 1.168 40 1.0
From the foregoing brief analysis, it can be observed that little work has been reported on the application of the phenomenological modeling for the prediction of gas holdup in airlift reactors. Shimizu et al.14 reported the phenomenological simulation of external loop airlift reactors but did not consider the recirculation of bubbles in the downcomer. Also, little or no work has been reported for internal loop airlift reactors. The objective of the present investigation was to develop a phenomenological simulation model for an internal loop airlift reactor based on bubble breakup and coalescence to describe the bubble dynamics in an airlift reactor. 2. Simulation Procedure The details and development of population balance, coalescence, and breakup models are given in the Supporting Information. A program was developed in MATLAB to simulate the effect of bubble coalescence and breakup on the initial bubble distribution so as to determine the bubble number density and gas holdup at steady state using the bubble breakup and coalescence rates in the population balance equation. The reactors used by Blazej et al.19 and Merchuk et al.20 are considered for the simulation. The configurations of the reactors are given in Table 1 .The schematic description of airlift reactor used for the simulation is shown in Figure 1. The simulation procedure used by Kawase et al.13,14 for the simulation of the bubble column and the external loop airlift reactor was incorporated in this work for the simulation of internal loop airlift reactor.
f(Nw) ) 1.8Nw0.5 f(Nw) ) 3.6 Nw ) We/Fr1/2 )
1 < Nw e 2 2 < Nw e 4 4 < Nw do1.5UgFlg0.5 σ
(3)
The bubbles entering into the lower compartment tend to move to the upper compartment of the riser at their bubble rising velocity. The bubble size is divided into classes, which facilitates solving the population balance equation by the method of classes. The maximum bubble size is 20 mm and the minimum is 1 mm, this range is divided into 100 classes. The bubble while traveling in the compartment undergoes lot of interactions with the bubbles and coalescence and breakup occur in the compartment. The size and number of bubbles leaving the compartment are determined by solving the population balance equation for the compartment. The newly formed bubbles travel with the bubble rising velocity and will be in the respective compartment at the simulation time. The simulation is repeated for all the compartments in the riser. The bubbles formed in the riser which has the velocity greater than the liquid rising velocity escape out to the gas-liquid separator and the rest of the bubbles are circulated into the downcomer. The annular area of the downcomer was also divided into compartments and was simulated. The bubbles after encountering various interactions in the downcomer area enter the riser through the bottom compartment. Due to this there is an increase in the volumetric flow rate of
The riser is divided into compartments which are considered to be completely mixed. The compartment height (∆H) is chosen such that, the height is greater than the distance traveled by the bubble with its bubble rising velocity as the simulation time interval. The bubble rising velocity of the bubble is given by eq 1 Ubr )
[
2σ + (0.505gdbi) (Fl + Fg)dbi
]
0.5
(1)
The bubbles entering into the lower compartment of the riser is of uniform size, and it varies with the velocity of the gas and the sparger hole diameter. The size of the bubbles formed at the sparger is determined by the equation proposed by Miyahara et al.21 ds ) f(Nw)/(gFl /σdo)1/3
(2)
where f(Nw) ) 2.9
Nw e 1
Figure 1. Schematic description of the simulation model for an internal loop airlift reactor.
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the gas in the riser. The superficial velocity of the gas gets increased due to the recirculation gas and is known as the true superficial velocity of gas,22 which is given by the following equation. Ugt )
(Qgs + Qgd) Qgt ) Ar Ar
(4)
The gas flow rate in the downcomer and the riser were estimated from the bubble data obtained by solving the population balance equation. The further simulation was done by considering the true superficial gas velocity in the riser. The holdup in the riser and downcomer are determined from the number and the size of the bubbles. The simulation is repeated until the holdup reaches a constant value. The liquid circulation in airlift reactor is an important hydrodynamic parameter and the liquid circulation originates from the difference in the bulk densities of the fluid in the riser and the downcomer. The overall liquid circulation velocity1 is given as UL-cir )
circulation path length time taken
Figure 2. Effect of bubble diameter on the coalescence rate.
(5)
The time taken for the circulation is calculated from the liquid velocity in the riser and the downcomer knowing the distance of riser and downcomer. The downcomer liquid velocity is calculated with the help of the Levich equation23 by using the bubble data obtained from the population balance equation. Uld ) 2
∑ ( 1.8 ) gdbi
0.5
(6)
i
The liquid circulation velocity in the riser was calculated from the continuity equation given by eq 7. UldAd ) UlrAr
(7)
As the liquid circulates around the wall of the draft tube, the path length is assumed to be twice of the height of the draft tube.
Figure 3. Effect of breakup fraction on dimensionless breakage function.
3. Results and Discussion 3.1. Specific Coalescence Rate. The coalescence model proposed by Lehr et al.9 was used to simulate the coalescence of bubbles in the reactor, and the variation of specific coalescence rate with bubble size is shown in Figure 2. For very small bubbles, the coalescence efficiency decreased rapidly with an increase in size of the bubble and hence the specific coalescence rate also decreased to a minimum. However, the coalescence efficiency increased slowly with an increase in bubble size and rapid increase was observed for larger bubble diameter. Thereafter, an increase in coalescence frequency increased the specific coalescence rate.24 3.2. Breakage Function and Specific Breakage Rate. The breakup model proposed by Wang et al.10 was used for the simulation, and the breakage rate and bubble size distribution can be obtained with the operating conditions using the model. The breakage kernel is a function of breakup fraction of bubbles, the energy dissipation rate, and the physical properties. Figure 3 shows that the breakage kernel has U-shape and the lowest possibility was achieved with equal sized breakage, which agrees with the results of Hesketh et al.25 The effect of bubble size on the specific breakage rate is shown in Figure 4. The higher specific breakage rate was observed with larger bubble size and
Figure 4. Effect of bubble diameter on specific breakage rate.
the specific breakage rate of very small bubbles is close to zero, since eddies that possess sufficient energy to make them oscillate are too small to make them break.25 3.3. Validation. 3.3.1. Riser Gas Holdup. The riser gas holdup obtained through the simulation was compared with the experimental results of Blazej et al.19 and Merchuk et al.20 Blazej
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Figure 5. Effect of superfical gas velocity in riser on riser gas holdup.
Figure 6. Effect of superfical gas velocity in the riser on downcomer gas holdup.
et al.19 used an internal loop airlift reactor having volumes of 10.5, 32, and 200 L and observed two different regions due to the presence of different flow regimes. In Figure 5, the simulation results are compared with the experimental data and the proposed simulation model predicted the experimental data reasonably well. It can also be observed from Figure 5 that the gas holdup in the 300 L internal loop airlift reactor is also in agreement with the values obtained through the proposed simulation. 3.3.2. Downcomer Gas Holdup. The comparison between experimental data and the values predicted from the simulation with respect to downcomer gas holdup is shown in Figure 6. The downcomer gas holdup increased with an increase in gas velocity, and at very low velocities, bubble recirculation was not observed. At a moderate velocity (Ugr ≈ 0.02 m/s), the gas holdup in the downcomer was found to increase due to the circulation of smaller bubbles. Also a small reduction in downcomer gas holdup was observed at high velocity due to the formation of the large bubbles in the riser. Figure 6 compares the experimental downcomer gas holdup data reported by Blazej et al.19 and Merchuk et al.20 and the data predicted from simulation. From the figure it can be observed that the trend observed shows reasonably good agreement. 3.3.3. Overall Gas Holdup. In Figure 7, overall gas holdup data reported by Blazej et al.19 and Merchuk et al.20 are
Figure 7. Effect of superfical gas velocity in the riser on overall gas holdup.
compared with the simulation model. The model predicted the experimental data reasonably well. 3.4. Overall Liquid Circulation Velocity. Figure 8 shows the comparison of predicted overall liquid circulation velocity with the experimental results of Blazej et al.19 and Merchuk et al.20 The bubble size data obtained through simulation were used to predict the downcomer liquid velocity and in turn riser liquid velocity. By using these data, overall liquid circulation velocity was calculated. The overall liquid circulation velocity increased with gas velocity at low velocity ranges, and the further increase in velocity of gas resulted in the entrainment of the bubbles from the riser to the downcomer which affect the driving force for the liquid circulation. The predictions of the simulation model agree satisfactorily with the experimental data reported by Blazej et al.19 and Merchuk et al.20 3.5. Comparison with Other Models. The liquid circulation velocity obtained using the population balance model was compared with the models proposed by Chisti et al.26 and Chriastel et al.27 Chisti et al.26 proposed a model for the prediction of liquid circulation velocity based on the energy balance and is given as: Ulr )
[ ( ) ( )] 2ghd(εr - εd) Ar 2 1 KB Ad (1 - ε )2
0.5
(8)
d
where KB is the friction loss coefficient which is based on the geometry of the system and is given as KB ) 11.402
() Ad Ab
0.789
(9)
Chriasstel et al.27 developed a model based on the energy flow in the loop and drift flux model and is given as
[
() Ad Ar
2
2(1 - εr)
2
]
+ 1 Uld +
[
hd√g 0.21(1 - εr) 2
]
0.28(1 - εd)
εr Ad + dr Ar
εd U - hdg(εr - εd) ) 0(10) de ld
Figure 9 shows the comparison between these models predictions and values predicted with population balance model. The
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Figure 8. Effect of superfical gas velocity in the riser on overall liquid circulation velocity.
Figure 9. Comparison of population balance model with other models reported for liquid circulation velocity.
results showed that the predictions with the population balance model were almost closer to the other models predictions.
The results can be further applied for the prediction of mass transfer data in an internal loop airlift reactor.
4. Conclusions
Nomenclature
In the present investigation, a steady state phenomenological simulation model based on bubble dynamics has been developed to enumerate the hydrodynamics of an internal loop airlift reactor. The bubble breakup and coalescence are taken into account to predict gas holdups and liquid circulation velocity. The specific coalescence and breakage rate were calculated and anlayzed. The proposed simulation model predicted the experimental data reported in the literature19,20 well. The proposed model was in good agreement with the experimental data for an internal loop airlift reactor having a volume of 300 L. The results obtained are also compared with other model predictions.
Ar ) area of riser (m2) Ad ) area of downcomer (m2) Ab ) area between the riser and downcomer (m2) ds ) diameter of bubbles from the sparger (m) do ) diameter of sparger holes (m) dbi ) diameter of the bubble (m) g ) acceleration due to gravity (m/s2) hd ) gas liquid dispersion height (m) KB ) friction loss coefficient Qgt ) true gas flow rate in riser (m3/s) Qgs ) gas flow rate from sparger (m3/s)
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Qgd ) gas flow rate from downcomer (m3/s) Ugr ) superficial velocity of gases in riser (m/s) Ubr ) bubble rise velocity (m/s) Ugt ) true superficial gas velocity in riser (m/s) UL-cir ) overall liquid circulation velocity (m/s) Ulr ) superficial liquid rise velocity in riser (m/s) Uld ) super liquid velocity in the downcomer (m/s) We ) Weber number Greek Letters ε ) holdup σ ) surface tension (N/m) Fl ) density of liquid (kg/m3) Fg ) density of gas (kg/m3) Subscripts g ) gas phase l ) liquid phase r ) riser d ) downcomer
Supporting Information Available: Details of model development. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Chisti, M. Y. Airlift Bioreactor; Elsevier: New York, 1989. (2) VanBaten, J. M.; Ellenberger, J.; Krishna, R. Hydrodynamics of internal air-lift reactors: experiments versus CFD simulations. Chem. Eng. Process. 2003, 42, 733. (3) Lo, C.-S.; Hwang, S.-J. Local hydrodynamic properties of gas phase in an internal-loop airlift reactor. Chem. Eng. J. 2003, 91, 3. (4) Bordel, S.; Mato, R.; Villaverde, S. Modeling of the evolution with length of bubble size distributions in bubble columns. Chem. Eng. Sci. 2006, 61, 3663. (5) Prince, M. J.; Blanch, H. W. Bubble coalescence and Bubble breakup in air-sparged Bubble columns. AIChE J. 1990, 36, 1485. (6) Luo, H. Coalescence, breakup and liquid circulation in bubble column reactors. D.Sc. Thesis, Norwegian Institute of Technology, 1993. (7) Luo, H.; Svendsen, H. F. Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J. 1996, 42, 1225. (8) Hagesaether, L.; Jakobsen, H. A.; Svendsen, H. F. A model for turbulent binary breakup of dispersed fluid particles. Chem. Eng. Sci. 2002, 57, 3251. (9) Lehr, F.; Millies, M.; Mewes, D. Bubble size distributions and flow fields in bubble columns. AIChE J. 2002, 48, 2426. (10) Wang, T.; Wang, J.; Jin, Y. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chem. Eng. Sci. 2003, 58, 4629.
(11) Chen, P.; Sanyal, J.; Dudukovic, M. P. Numerical simulation of bubble column flows: effect of different breakup and coalescence closures. Chem. Eng. Sci. 2005, 60, 1085. (12) Wang, T.; Wang, J.; Jin, Y. Population balance Model for gasliquid flows: influence of Bubble coalescence and breakup models. Ind. Eng. Chem. Res. 2005, 44, 7540. (13) Shimizu, K.; Takada, S.; Minekawa, K.; Kawase, Y. Phenomenological model for bubble column reactors: prediction of gas hold-ups and volumetric mass transfer coefficients. Chem. Eng. J. 2000, 78, 21. (14) Shimizu, K.; Takada, S.; Takahashi, T.; Kawase, Y. Phenomenological simulation model for gas hold-ups and volumetric mass transfer coefficients in external-loop airlift reactors. Chem. Eng. J. 2001, 84, 599. (15) Pohorecki, R.; Moniuk, W.; Zdrojkowski, A.; Bielski, P. Hydrodynamics of a pilot plant bubble column under elevated temperature and pressure. Chem. Eng. Sci. 2001, 56, 1167. (16) Lehr, F.; Mewes, D. A transport equation for the interfacial area density applied to bubble columns. Chem. Eng. Sci. 2001, 56, 1159. (17) Kumar, M. Dhanasekharan, Jay Sanyal, Anupam Jain, Ahmad Haidari, A generalized approach to model oxygen transfer in bioreactors using population balances and computational fluid dynamics. Chem. Eng. Sci. 2005, 60, 213. (18) Huh, B. G.; Euh, D. J.; Yoon, H. Y.; Yun, B. J.; Song, C.-H.; Chung, C. H. Mechanistic study for the interfacial area transport phenomena in an air/water flow condition by using fine-size bubble group model. Int. J. Heat Mass Transfer 2006, 49, 4033. (19) Blazej, M.; Kisa, M.; Markos, J. Scale influence on the hydrodynamics of an internal loop airlift reactor. Chem. Eng. Proc. 2004, 43, 519. (20) Merchuk, J. C.; Ladwa, N.; Cameron, A.; Bulmer, M.; Pickett, A. Concentric-tube airlift reactors: effects of geometrical design on performance. AIChE J. 1994, 40, 1105. (21) Miyahara, T.; Hamaguchi, M.; Sukeda, Y.; Takahashi, T. Size of bubbles and liquid circulation in the bubble column with draught tube and sieve plate. Can. J. Chem. Eng. 1986, 64, 718. (22) Siegel, M. H.; Merchuk, J. C.; Schugerl, K. Airlift Reactor: Interrelationships between Riser, Downcomer, and Gas-Liquid separator behaviour, including gas Recirculation Effects. AIChE J. 1986, 32, 1585. (23) Chisti, M. Y.; Halard, B.; Young, M. M. Liquid Circulation in airlift reactors. Chem. Eng. Sci. 1988, 43, 451. (24) Ramkrishna, D. Population Balances; Academic Press: San Diego, 2000. (25) Hesketh, R. P.; Etchells, A. W.; Russell, T. W. F. Bubble breakage in pipeline flow. Chem. Eng. Sci. 1991, 46, 1. (26) Chisti, M. Y.; Halard, B.; Young, M. M. Liquid Circulation Velocity in airlift reactors. Chem. Eng. Sci. 1988, 43, 451. (27) Chriastel, L.; Kawase, Y.; Znad, H. Hydrodynamic Modelling of Internal Loop Airlift Reactor Applying Drift-Flux Model in Bubbly Flow Regime. Can. J. Chem. Eng. 2007, 85, 226.
ReceiVed for reView May 3, 2009 ReVised manuscript receiVed March 14, 2010 Accepted March 31, 2010 IE900713V
