Investigation of the Gas Layer Height in a Multistage Internal-Loop

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Ind. Eng. Chem. Res. 2009, 48, 9278–9285

GENERAL RESEARCH Investigation of the Gas Layer Height in a Multistage Internal-Loop Airlift Reactor Wei Yu, Tiefeng Wang,* Feifei Song, and Zhanwen Wang Beijing Key Laboratory of Green Reaction Engineering and Technology, Department of Chemical Engineering, Tsinghua UniVersity, Beijing 100084, China

A novel multistage internal-loop airlift reactor was realized by using a novel interstage internal. In this reactor, a gas layer is formed below the internal and has important effects on the hydrodynamic behavior. The effects of the opening ratio of the internal for the gas and liquid channels and superficial gas and liquid velocities were experimentally studied in both cocurrent and countercurrent operations. The results show that the gas layer height increases with an increase in the superficial gas velocity for both cocurrent and countercurrent flows. With an increase in the superficial liquid velocity, the gas layer height decreases for cocurrent flow, but increases for countercurrent flow. The opening ratio of the internal for gas channels has a much more significant influence on the gas layer height than that for the liquid channel. A mathematical model for predictions of the gas layer height was proposed based on the balance between the pressure drops of the gas and liquid through the internal. A good agreement was obtained between the calculated and experimental data. This model can be used for the optimum design of the novel multistage internal-loop airlift reactor. 1. Introduction Bubble columns and airlift reactors are widely used in chemical and biochemical processes, especially in the gas-toliquid processes of Fischer-Tropsch synthesis, methanol synthesis, and dimethyl ether synthesis. Compared with the conventional stirred tank reactor, bubble columns and airlift loop reactors have the advantages of simple construction, good heat transfer, and feasible scale-up.1,2 Most work in the literature focused on the single-stage reactor. However, the single-stage reactor has the disadvantages of intense liquid backmixing, thus it is very inefficient for a process that requires a higher conversion of liquid reactants. The use of tanks-in-series can effectively decrease the liquid backmixing, but this will result in more complexity of the operation and control. In our previous works,3,4 a novel multistage internalloop airlift reactor was proposed by analogy with the tanks-inseries concept. This multistage internal-loop airlift reactor achieved excellent performances both in uniform distribution of the solid particles and in decreasing the interstage liquid backmixing,5 showing better performance in the aspect of the uniform distribution of the solid particles than the multistage bubble column,6-11 multistage internal-loop airlift reactor,12 and multistage external-loop airlift reactor13 reported in the literature. The good performance of this novel multistage internal-loop airlift reactor is closely related to the liquid circulation and the special structure of the interstage internal. The interstage internal used was a perforated plate with several tubes, in which the gas flowed through the orifices and the liquid flowed through the long tubes. However, when such an internal is used, a gas layer will be formed below it, which further affects the liquid level and liquid circulation in the stage below the internal. When the liquid level is higher than the upper edge of the draft-tube, there is a liquid circulation, as shown in Figure 1. The liquid circulation is important for a slurry system to homogeneously suspend the solid particles at a relatively low superficial gas velocity. When the liquid level is lower than the upper edge of the draft-tube, the liquid circulation can not be formed, as shown * To whom correspondence should be addressed. Tel.: 86-1062797490. E-mail: [email protected].

in Figure 2. Thus, the gas layer height must be controlled in a certain range for a normal operation. Although the presence of a gas layer between two stages in a multistage reactor were

Figure 1. Flow pattern with liquid circulation when the liquid level is higher than the draft tube.

Figure 2. Flow pattern without liquid circulation when the liquid level is lower than the draft tube.

10.1021/ie9002156 CCC: $40.75  2009 American Chemical Society Published on Web 08/26/2009

Ind. Eng. Chem. Res., Vol. 48, No. 20, 2009

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Figure 3. Schematic of the experimental apparatus.

Figure 4. Structure of the interstage internal.

reported in some published works,12,14,15 all these studies focused on the perforated plate internals and did not systematically study the gas layer height. In this work, we studied the gas layer height in the multistage internal-loop airlift reactor with a novel interstage internal.5 The effects of the opening ratio of the internal for gas and liquid channels and the superficial gas and liquid velocities were experimentally studied for cocurrent, countercurrent, and batch operations. A mathematical model for prediction of the gas layer height was proposed based on the balance between the pressure drops of the gas and liquid through the internal. 2. Experimental Section 2.1. Apparatus. The schematic of the experimental apparatus is shown in Figure 3. The reactor was a vertical Plexiglas column with 0.20 m outer diameter, 0.19 m inner diameter, and 2.85 m height. Two draft-tubes were installed inside the reactor. Each draft-tube was of 0.12 m outer diameter, 0.11 m inner diameter, and 1.0 m height. The experimental apparatus was divided into two stages by an interstage internal. Both stages were internal-loop airlift sections with the annular region being the riser and the draft tube being the downcomer. The structure of the novel interstage internal was a perforated plate with several long tubes, as shown in Figure 4. The orifices were Φ2 mm and had an opening ratio of 0.11% and 0.22%. The tubes were of Φ8 and 300 mm height and had an opening ratio of 0.53%, 1.06%, and 1.60%. The gas flowed mainly through the orifices, and the liquid flowed through the tubes. Air and tap water were used as the gas and liquid, respectively. Air was pumped into the system from the bottom of the reactor, distributed by a perforated plate gas distributor with 30 holes of 3 mm diameter. The difference in gas holdups between the riser and downcomer drove the liquid circulation through the riser and downcomer. Gas was separated from the top of the gas-liquid separator. When the reactor was operated in

cocurrent mode, as shown in Figure 3a, the liquid phase was pumped from the stirred tank into the bottom stage, flowed through the interstage internal to the top stage, and then flowed out of the top stage into the stirred tank. When the reactor was operated in countercurrent mode, as shown in Figure 3b, the liquid phase was pumped by one pump from the stirred tank into the top stage, flowed through the interstage internal into the bottom stage, and then pumped by another pump back into the stirred tank. The rest of liquid in the top stage overflowed into the stirred tank. 2.2. Measuring Methods. 2.2.1. Gas Holdup. The crosssectional average gas holdup was measured at different axial positions by the pressure drop technique. In bubble columns and airlift reactors, the friction pressure drop is usually negligible compared with the static pressure drop.16 The local static pressure drop (∆P) between the two tapping ports vertical distance h0 apart in the gas-liquid system is ∆P ) Flgh0(1 - εg)

(1)

where Fl and εg are the liquid density and gas holdup, respectively. With the measured pressure drop, the gas holdup is determined as εg ) 1 -

∆P Flgh0

(2)

2.2.2. Gas Layer Height. The gas layer height below the internal was measured by visual observation. Three parallel measurements were carried out at a given operating condition, and the average value was used as the final result, with an average discrepancy within (5%. 3. Mathematical Model The formation of the gas layer below the interstage internal is illustrated in Figure 5. The gas layer height refers to the average height between the internal and the liquid surface. In principle, the gas layer height is determined by the balance between the pressure drops of the gas and liquid through the internal. On the basis of this analysis, a mathematical model was proposed to predict the gas layer height. In Figure 5, P0, P1, and P2 satisfy the following relationship: P1 ) P0 - ∆Pd

(3)

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P2 ) P0 + (1 - εg)Flg(h - h1)

(4)

1 ∆Pf1 ) Flkful2 2

For cocurrent flow P1 ) P2 - (1 - εg,T)Flgh - ∆Pf

(5)

ul )

For countercurrent flow P1 ) P2 - (1 - εg,T)Flgh + ∆Pf

(6)

kf ) 4f

where ∆Pd and ∆Pf are the pressure drops through the orifices and the vertical long tubes, respectively, and εg,T is the gas holdup in the long tubes of the internal. For cocurrent flow, substitution of eqs 3 and 4 into eq 5 yields the following: (1 - εg,T)Flgh1 ) ∆Pd - ∆Pf

(7)

For countercurrent flow, substitution of eqs 3 and 4 into eq 6 yields the following: (1 - εg,T)Flgh1 ) ∆Pd + ∆Pf

(8)

When the system is under normal operation elasticity, the gas layer height should satisfy the following condition: 0 < h1 < h - l

( )

2∆Pd u0 ) Cd′ F

Ul ζl

(13)

h d

(14)

f ) 0.0791Rel-0.25 Rel )

(15)

Fldul µl

(16)

where ul is the liquid velocity in the long tube, ζl is the opening ratio of the internal for the liquid channels, and kf and f are the resistance coefficient and friction factor, respectively. For a gas-liquid system at a low gas holdup, f can be safely estimated by the Blasius formula for the single-phase flow.1,2 Substitution of eqs 13-16 into eq 12 yields the following:

()

∆Pf1 ) 0.1582Fl0.75d -1.25

(9)

where h is the length of the long tube and l is the distance from the bottom of the long tube to the top edge of the draft-tube. To predict the gas layer height, the pressure drops ∆Pd and ∆Pf must be determined. The pressure drop through the orifices of a perforated plate was well studied and can be calculated with the following correlation:17

(12)

Ul ζl

1.75

µl0.25h

(17)

In addition, the liquid that flows though the long tube experiences sudden contraction and expansion, then the total pressure drop of the liquid through the long tube is

()

Ul 1 ∆Pf ) 0.1582ζl-1.75Fl0.75d -1.25Ul1.75µl0.25h + kf,CEFl 2 ζl

(18)

1/2

(10)

where u0 ) Ug/ζg is the through-hole gas velocity with ζg as the opening ratio of the internal for gas channels, Cd′ is the resistance coefficient, and F is the gas density. Thus ∆Pd, the pressure drop through the orifices, can be determined as follows: 2 1 u0 ∆Pd ) Fg 2 2 C′

2

(11)

d

The pressure drop within the long tubes can be calculated by the following equations:2

where the second term in the right-hand side of eq 18 is the pressure drop caused by the sudden contraction and expansion and kf,CE is the flowing resistance coefficient of sudden contraction and expansion, which is set 1.5.18 When the system is operated in cocurrent mode, combination of eqs 7, 11, and 18 yields the following: 2 1 u0 (1 - εg,T)Flgh1 ) Fg 2 2 C′

()

d

Ul 1 0.1582ζl-1.75Fl0.75d -1.25Ul1.75µl0.25h - kf,CEFl 2 ζl

2

(19)

When the system is operated in countercurrent mode, combination of eqs 8, 11, and 18 yields the following: 2 1 u0 (1 - εg,T)Flgh1 ) Fg 2 + 2 C′

()

d

-1.75

0.1582ζl

0.75 -1.25

Fl

d

Ul 1 Ul1.75µl0.25h + kf,CEFl 2 ζl

2

(20)

When the system is operated in batch mode, Ul is zero and the gas layer can be calculated by the following: 2 1 u0 (1 - εg,T)Flgh1 ) Fg 2 2 C′

(21)

d

Figure 5. Schematic of the gas layer height below the interstage internal.

The gas holdup in the long tubes of the internal, εg,T, is difficult to measure; therefore, it is estimated by the average gas holdup in the riser of the bottom stage, εg. Such simplifica-


Figure 6. Effects of superficial gas and liquid velocities on gas holdup in riser of the bottom stage for cocurrent flow.

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Figure 7. Effects of superficial gas and liquid velocities on gas holdup in riser of the bottom stage for countercurrent flow.

tion is reasonable because an error of 0.01 in εg,T only causes 1% relative error in the predicted layer height. 4. Results and Discussion 4.1. Parameters in the Model. 4.1.1. Gas Holdup. The gas holdup is an important parameter that affects the gas layer height and depends on the superficial gas and liquid velocities. For the continuous flow operations, the drift-flux model proposed by Zuber and Findlay21 was used to describe the relationship between the gas holdup and superficial gas and liquid velocities. The drift-flux model for the cocurrent flow is Ug ) C0(Ug + Ul) + C1 εg

(22)

Figure 8. Effects of superficial gas velocity on gas holdup in riser of the bottom stage for batch flow.

and for the countercurrent flow, it is Ug ) C0(Ug - Ul) + C1 εg

(23)

where C0 is related to radial uniformity of the gas holdup and C1 is related to the bubble rising velocity. For the batch flow, the gas holdup in the riser of the bottom stage can be calculated by the following correlation: εg ) aUgb

(24)

The gas holdup in the riser of the bottom stage was measured at different opening ratios of the internal and superficial gas and liquid velocities. The results for cocurrent and countercurrent flows are shown in Figures 6 and 7, respectively. It can be seen that the gas holdup increases with an increase in the superficial gas velocity for both cocurrent and countercurrent flows. At low superficial gas velocities, the gas holdup increases

Figure 9. Effect of superficial gas velocity on pressure drop through the gas channels.

almost linearly with the superficial gas velocity because the bubble-bubble interaction is weak in such conditions. While at higher superficial gas velocities, the increase of the gas holdup

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Ug ) 2.092(Ug - Ul) + 0.252 εg

(26)

Figure 8 shows that the effect of the opening ratio of the internal and superficial gas velocity on the gas holdup for batch flow is similar to that for continuous flows. The parameters in eq 24 were determined by fitting the experimental data, and the final correlation for the batch operation is εg ) 1.205Ug0.714

Figure 10. Resistance coefficient of the novel internal.

becomes less notable, due to larger bubbles resulted from bubble coalescence. Similar results were reported by Hibiki and Ishii19 and Wang et al.20 The opening ratio of the internal has an insignificant effect on the gas holdup. The gas holdup slightly decreases with an increase in the superficial liquid velocity for cocurrent flow, but slightly increases with the superficial liquid velocity for countercurrent flow due to an increase in the residence time of gas bubbles. Because the superficial liquid velocity is usually much smaller than the liquid circulation velocity, the influence of the superficial liquid velocity on the gas holdup is insignificant. The parameters of the drift-flux model in eqs 22 and 23 were determined by fitting the experimental data, and the final correlation for cocurrent flow is Ug ) 1.540(Ug + Ul) + 0.273 εg and for countercurrent flow, it is

(25)

(27)

4.1.2. Resistance Coefficient Cd′ . Perry17 reported that with an increase in the through-hole Reynolds number Re, the resistance coefficient Cd′ of the perforated plate increased first, then decreased, and finally remained a constant of about 0.6 when Re > 2000. However, the resistance coefficient Cd′ of the novel internal in this work was not reported in the published literature. The effect of the superficial gas velocity on the pressure drop through the novel internal is shown in Figure 9. It can be seen that the pressure drop shows a quadratic increase with an increase in the superficial gas velocity, similar to that of the perforated plate distributor. The results also show that the pressure drop decreases with increasing opening ratio of the internal for gas channels. By analogy with the perforated plate, the resistance coefficient Cd′ of the novel internal is also correlated by eq 10, but with different parameters. The resistance coefficient of the novel internal is determined from the measured pressure drop and eq 10, and the results as shown in Figure 10. It can be seen that when Re > 2000, Cd′ stays almost constant at 0.8936, 0.8014, and 0.7556 for opening ratios of 0.11%, 0.22%, and 0.33% for gas channels, respectively. 4.2. Cocurrent Flow. The effects of the opening ratio of the internal and superficial gas and liquid velocities on the gas layer height were experimentally studied, and the results for

Figure 11. Effects of opening ratio of the internal and superficial gas and liquid velocities on the gas layer height for cocurrent flow.


Figure 12. Comparison between experimental gas layer heights for cocurrent flow with those predicted with different flow resistance coefficient kf,CE.

cocurrent flow are shown in Figure 11. It can be seen that the gas layer height increases with an increase in the superficial gas velocity and decreases with an increase in the superficial liquid velocity. The opening ratio for gas channels, ζg, has an important effect on the gas layer height. A decrease in ζg results in a significant increase in the gas layer height. The effect of the opening ratio for liquid channel, ζl, is much less notable. With an increase in ζl, the gas layer height only increases slightly. A proper gas layer height can be obtained by adjusting the opening ratio of the internal and superficial gas and liquid velocities. Figure 12 shows the comparison between the measured gas layer heights and those predicted by the mathematical model. The influence of the flowing resistance coefficient of the contraction and expansion, kf,CE, was also considered. A good agreement between the predicted and measured gas layer heights is obtained. The parameter kf,CE has a negligible effect on the gas layer height, because the superficial liquid velocity is in a low range.

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4.3. Countercurrent Flow. The effects of the opening ratios and superficial gas and liquid velocities on the gas layer height for countercurrent flow were shown in Figure 13. The gas layer height increases with an increase in the superficial gas velocity, similar to the results for cocurrent flow. However, different from cocurrent flow, the gas layer height also increases with an increase in the superficial liquid velocity for countercurrent, as shown in Figure 14. The opening ratio for gas channels has a significant effect on the gas layer height, while the effect of the opening ratio for liquid channels is much less notable. On the basis of the different influences of these factors, a proper gas layer height for normal flowing operation can be obtained by adjusting the opening ratio of internal, superficial gas, and liquid velocities. Figure 15 shows the comparison between the measured gas layer heights and those predicted from the mathematical model with kf,CE ) 0, and good agreement is obtained. 4.4. Batch Flow. The effects of the superficial gas velocity and opening ratio for gas channels, ζg, on the gas layer height are shown in Figure 16. It can be seen that the gas layer height increases rapidly with an increase in the superficial gas velocity, and decreases rapidly with an increase in ζg. This is because ζg is inversely proportional to the superficial gas velocity and the pressure drop is proportional to the square of the gas velocity. Thus, it is an effective approach to change ζg for controlling the gas layer height. The measured and predicted gas layer heights were compared in Figure 16, and good agreement is also obtained. 5. Conclusions The hydrodynamics of a multistage internal-loop airlift reactor were studied, with particular interest in the gas layer height and

Figure 13. Effects of opening ratio of the internal and superficial gas and liquid velocities on the gas layer height for countercurrent flow.

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Figure 16. Effects of superficial liquid velocity and opening ratio for gas channel on the gas layer height with batch case (ζl ) 0.53%, Ul ) 0).

velocities. A mathematical model for predictions of the gas layer height was proposed to quantitatively describe the effects of various factors and determine the optimum parameters for a given operating condition. Nomenclature

Figure 14. Effects of superficial liquid velocity on the gas layer height for countercurrent flow.

Figure 15. Comparison between experimental gas layer heights for countercurrent flow with those predicted with flow resistance coefficient kf,CE ) 0.

the pressure drops through the interstage internal. The conclusions are as follows: • The superficial gas velocity and opening ratio of the internal for gas channels have significant effects on the gas layer height, while the superficial liquid velocity and opening ratio of the internal for liquid channels has less significant effects. • For both cocurrent and countercurrent flows, the gas layer height increased with an increase in the superficial gas velocity or a decrease in the opening ratio of the internal for gas channels. • The gas layer height decreases with an increase in the superficial liquid velocity or a decrease in the opening ratio of the internal for liquid channels for cocurrent flow; however, these effects are contrary for countercurrent flow. • The gas layer height should be controlled within an appropriate elasticity. This can be realized by adjusting the opening ratio of the internal and superficial gas and liquid

Cd′ ) resistance coefficient of internal for gas flow d ) diameter of the long tube, m f ) friction factor in the long tube g ) gravitational acceleration, m/s2 h ) length of the long tube, m h0 ) vertical distance between the two tapping ports, m h1 ) gas layer height, m kf ) flowing resistance coefficient in the long tube kf,CE ) flowing resistance coefficient of contraction and expansion Ug ) superficial gas velocity, m/s Ul ) superficial liquid velocity, m/s u0 ) through-hole gas velocity, m/s ul ) liquid velocity through the long tube, m/s ∆P ) static pressure drop, Pa ∆Pd ) pressure drop through the orifices, Pa ∆Pf ) pressure drop through the long tubes, Pa Greek Letters ζg ) opening ratio of the internal for gas channels ζl ) opening ratio of the internal for liquid channels εg ) gas holdup in the riser of the bottom stage εg,T ) gas holdup in the long tubes of the internal µl ) viscosity of the liquid, Pa · s Fl ) density of the liquid, kg/m3 Fg ) density of the gas, kg/m3

Acknowledgment The authors gratefully acknowledge the financial supports by the National Natural Science Foundation of China (No. 20606021), Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 200757), and National 973 Project of China (No. 2007CB714302). Literature Cited (1) Garcı´a-Calvo, E.; Rodrı´guez, A.; Prados, A.; Klein, J. A fluid dynamic model for three-phase airlift reactors. Chem. Eng. Sci. 1999, 54, 2359. (2) Freitas, C.; Fialova, M.; Zahradnik, J.; Teixeira, J. A. Hydrodynamics of a three-phase external-loop airlift bioreactor. Chem. Eng. Sci. 2000, 55, 4961. (3) Yu, W.; Wang, T. F.; Liu, M. L.; Wang, Z. W. Liquid backmixing and pariticle distribution in a novel multistage internal-loop airlift slurry reactor. Ind. Eng. Chem. Res. 2008, 47, 3974.

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ReceiVed for reView February 7, 2009 ReVised manuscript receiVed August 13, 2009 Accepted August 13, 2009 IE9002156

Investigation of the Gas Layer Height in a Multistage Internal-Loop

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