Ind. Eng. Chem. Res. 2002, 41, 4435-4438
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Liquid Holdup for Two-Phase Countercurrent Flow in the Packed Column with a Novel Internal Minghan Han,* Hongfei Lin, Jinfu Wang, and Yong Jin Department of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
In the packed column with a novel internal, which is made of several structured porous passages, gas is divided into two branches which meet liquid in countercurrent and cross-current, respectively, so the excessive pressure drop and “flooding” of conventional gas-liquid countercurrent flow can be avoided. A model for predicting dynamic liquid holdup is presented, and it shows a satisfactory agreement with the experimental results. Below the load point, only the superficial liquid velocity and the volume fraction of the internals have evident effects on the liquid holdup. Above the load point, both superficial gas and liquid velocities have great effects on the liquid holdup and so do the parameters of the internal because they can affect gas-flow behavior. 1. Introduction For the operation of gas-liquid countercurrent flow in a packed column, it is important to avoid excessive pressure drop and “flooding”; reactive distillation (RD), which combines reaction and distillation, is a typical example. To implement a RD application, it is essential to meet some of the practical issues,1 such as efficient contacting of liquid with catalyst particles, good vapor/ liquid contacting in the reactive zone, low pressure drop through the catalytically packed reactive section, sufficient liquid holdup in the reactive section, and easy installation and removal of the RD equipment and catalyst. Numerous patents and research reports illustrated catalyst loading methods to meet the above practical requirement; some of the most popular catalyst loading methods are as follows: (1) catalyst baskets on trays, (2) catalytic random packings, (3) catalyst-containing bales or structured catalyst supports. Although some of such catalyst loading methods have been applied in industry, they have some drawbacks. For example, it is difficult to manufacture the catalyst structures properly and to change and recover the deactivated catalysts. To solve the above problem, a new RD device2 with a novel internal has been developed. For the new device, the catalyst particles are loaded in the same way as they are loaded into a fixed-bed reactor, so it is much easier to change the deactivated catalysts in comparison with the conventional catalyst loading methods. The experiments3,4 show that the RD column with the novel internal has advantages such as low pressure, simple structure, low operating cost, easy installation and removal of catalyst, and large catalyst loading fraction. Liquid holdup is one of the most important parameters for gas-liquid countercurrent flow in a packed column, and it can make effects on pressure drop, mass transfer, and chemical reaction. In this present work, a semiempirical model to compute dynamic liquid holdup has been developed not only for better under* To whom all correspondence should be addressed. Telephone: 86-10-62781469. Fax: 86-10-62772051. E-mail: hanmh@ ihw.com.cn.
Figure 1. Schematic drawing of the novel internal, catalyst loading method, and fluid flow: 1, spiral spring (reatining screen passage); 2, baffle; 3, catalyst pellets; 4, column wall; 5, liquid flow; 6, gas flow; 7, frame.
standing the characteristics of the new RD device but also for developing the necessary information that could be used for design and scale-up purposes. 2. Experiments Experimental details are similar to those of Lin at al.5 When steady-state conditions have been established, the dynamic liquid holdup is measured by stopping the gas and liquid supply and collecting the liquid in the catalyst bed. From the collected liquid mass, the dynamic liquid holdup could be calculated. A schematic drawing of the structure of the novel internal and the catalyst loading method is shown in Figure 1. The internal functions as porous passages that form gas and liquid flow channels. These passages are mounted in a frame and placed into the column vertically. The catalyst particles are dumped into the column
10.1021/ie010858c CCC: $22.00 © 2002 American Chemical Society Published on Web 07/24/2002
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Table 1. Main Geometric Parameters of the Different Spiral Spring Internals N Φ, m
F
l b, m
5 0.025 0.159 0.125 7 0.025 0.223 0.125 0.0625 9 0.025 0.287 0.125 0.250
uB,0/uG N Φ, m 0.267 0.182 0.317 0.131 0.049
F
) 0 -
lb, m uB,0/uG
5 0.035 0.313 0.125 3 0.045 0.310 0.125
0.184 0.256
hd 1-F
(1)
When the liquid load is above the load point, liquid fills in both the catalyst bed and internal, the void fraction in the catalytic bed is supposed to be the same as that in the internal. So, the void fraction of the irrigated catalytic bed can be calculated by
) F + 0(1 - F) - hd
(2)
The liquid holdup is a function of the physical properties of density and viscosity expressed by the Reynolds and Froude numbers.6-8 For liquid loads up to the load point, the dynamic liquid holdup hd can be calculated from the equation
hd ) aFrLbReLcuBd(1 - F)e(H/n)f
(3)
where a, b, c, d, e, and f are fitting parameters and Fr, Re, dh, uL, and uB can be calculated by
uL2 gdh
(4)
FLdhuL µL
(5)
0 2 0 ) d a 3 1 - 0 p
(6)
uL,0 1-F
(7)
FrL ) Figure 2. Partial enlarged view of the ideal flow patterns of gas and liquid in the column.
and fill the space between the passages, so it is easy to load and unload the catalyst. Openings are provided in the retaining screens of the passages to allow gas and liquid to flow into or out of the passage. They are sized to prevent the catalyst particles from entering passages. Each passage is separated into several stages by baffles. The baffles are installed alternately between the adjacent passages. In this paper spiral springs are used as the retaining screen of the passages, the opening ratio on the wall of the spiral spring is 50%, and the height of the internals is 1 m. The other geometric parameters of the different spiral spring internals are listed in Table 1. 3. Fundamentals To establish a dynamic liquid holdup model, an ideal flow pattern of gas and liquid in the column is assumed, as shown in Figures 1b and 2. The internal divides gas into two branches: one meets liquid in the conventional countercurrent flow, and the other does in a new crosscurrent flow, so gas and liquid flow in the catalyst bed consists of a conventional countercurrent pattern and a new cross-current pattern. For the new flow pattern, shown in Figure 2, gas flows upward (axially) inside the springs, changes the flow direction, and subdivides uniformly through the wall of the springs into the catalytic bed when it is blocked by the baffles; then, it flows radially through the catalytic bed into adjacent springs; thus, gas contacts liquid in a cross-current pattern in the catalyst bed. After entering the adjacent springs from the catalyst bed, the gas will change its flow direction and flows upward again. When the liquid load is below the load point, the space between the catalyst particles is not totally filled with liquid and capillary effects draw the liquid into the catalyst bed, the void fraction of irrigated catalytic bed , the void fraction of dry catalytic bed minus its liquid holdup, can be calculated by
ReL ) dh ) 4
uL )
uB,0 ) uB )
x
∆rj ru lb G
2
[
x ]
r lb F + (1 - F) lb
∆rj lb
(8)
2
where ∆rj, an equivalent radial distance, can be adopted as9
∆rj )
xN1 R - r
(9)
The liquid holdup at the load point can be calculated by8
(
1 µL u a2 hL,S ) 12 g FL L
)
1/3
(10)
For liquid loads above the load point, hd can be expressed by
hd ) a′FrLb′ReLc′uBd′(1 - F)e′(H/n)f ′ exp(g′uL) (11) where a′, b′, c′, d′, e′, f ′, and g′ are fitting parameters. By fitting the experimental data to the model using a least-squares method, we can obtain the model of liquid holdup below the load point as eq 12 and that above the load point as eq 13.
hd ) 9.5FrL0.376ReL-0.155uB0.198(1 - F)0.764(H/n)0.275 (12)
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Figure 3. Comparison between experimental and calculated dynamic liquid holdup.
Figure 4. Relationship between dynamic liquid holdup and superficial gas velocity for different superficial liquid velocities. 0.231
hd ) 32.3FrL
ReL
-0.692
0.638
uB
-1.31
0.684
(1 - F) (H/n) exp(87.4uL) (13)
4. Results and Discussion 4.1. Verification of the Model. Figure 3 illustrates the comparison of experimental dynamic liquid holdup with calculated values; the model shows a satisfactory agreement with the experimental data. Thus, the model describing the dynamic liquid holdup is applicable, and the assumed ideal flow pattern of gas and liquid in the column is reasonable. 4.2. Effects of the Main Geometric Parameters of the Internals on Gas-Flow Behaviors. Table 1 gives the values of uB,0/uG calculated from eq 8 for the different geometric parameters of the internals. It shows that superficial gas velocity uB,0 for countercurrent flow with the internals is much less than that without internal, which is due to the fact that the internals make a large amount of gas flow in the catalyst bed in a crosscurrent pattern. Because the internal can affect the flow behavior of gas, it will also affect the liquid holdup. 4.3. Effects of the Gas and Liquid Rates on the Liquid Holdup. The relationships between dynamic liquid holdup and superficial gas for different superficial liquids are shown in Figure 4. As indicated in the figures, below the load point, the superficial liquid velocity has an evident effect on the liquid holdup but the superficial gas velocity does not; above the load point, both the liquid and gas velocities have a great effect on the liquid holdup. The experimental results in
Figure 5. Relationship between the dynamic liquid holdup and superficial liquid velocity for the internals with different outer diameters.
Figure 6. Relationship between the dynamic liquid holdup and superficial liquid velocity for the internals with different heights of the stages.
this work are similar to that of the conventional countercurrent packing bed.10 4.4. Effects of the Main Geometric Parameters of the Internals on the Liquid Holdup. Figures 5 and 6 show the relationship between the dynamic liquid holdup and superficial liquid velocity for the internals with different outer diameters and different heights of the stages. When the volume fractions are similar, the diameters of the springs and the heights of the stages have almost no effect on the liquid holdup below the load point; the small differences in Figure 5 were caused by the differences of volume fractions. Above the load point, the liquid holdup increases remarkably with the increase of the diameter or the decrease of the height, which is due to the increase of uB,0 (Table 1). Figure 7 illustrates the relationship between the dynamic liquid holdup and superficial liquid velocity for two catalyst loading methods. One of the methods is in this work; the other is that where catalyst particles are mixed with Cannon rings uniformly and then filled in the RD column.11 It can be seen that the effects of the volume fraction of the internal on the dynamic liquid holdup are contrary to those of Cannon rings. Because capillary effects exist only between the catalyst particles, for the catalyst loading method in this work, the liquid is held mainly in the catalyst bed instead of the internal, but for the catalyst loading method of mixing catalyst particles with Cannon rings, the Cannon rings minimize the capillary effects, so the liquid is held mainly in the Cannon rings instead of the catalyst bed.
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Ind. Eng. Chem. Res., Vol. 41, No. 17, 2002
Figure 7. Relationship between the dynamic liquid holdup and superficial liquid velocity for the different volume fractions of the internals and Cannon rings.
Therefore, with the increase of the volume fraction of the catalyst particles, for the catalyst loading method in this work, the dynamic liquid holdup increases, but for the method of mixing catalyst particles with Cannon rings, the dynamic liquid holdup decreases. Because high liquid holdup in the catalyst bed instead of internal or Cannon rings means a small stagnant liquid zone and a high liquid-solid contacting efficiency, which benefit the RD,12 the catalyst loading method with the internal is better than that of mixing catalyst particles with Cannon rings. 5. Conclusions For two-phase countercurrent flow in the packed column with the novel internal, gas is divided by the internal into two branches which meet liquid in countercurrent and cross-current, respectively. A mathematical model for predicting the dynamic liquid holdup shows a satisfactory agreement with the experimental data, so it is applicable. The effects of the geometrical parameters of the internal, superficial liquid, and gas velocities on the dynamic liquid holdup depend on the flow regime. Below the load point, the superficial liquid velocity and the volume fraction of the internals have evident effects on the holdup, but the superficial gas velocity, diameters of the springs, and the heights of a stage do not. Above the load point, the geometrical parameters of the internal, superficial liquid, and gas velocities have great effects on the liquid holdup. With the increases of superficial gas and liquid velocities, the liquid holdup increases much more greatly than it does below the load point. The internal can change gas-flow behaviors, so it has an evident effect on the liquid holdup above the load point. With the decrease of the volume fraction or the outer diameter or the increase of the heights of the stage of the internals, the effective gas velocity for countercurrent flow decreases, so liquid holdup decreases. For the catalyst loading method in this work, liquid is mainly held up in the catalyst bed; that is contrary to the method of mixing catalysts with Cannon rings. Obviously, high liquid holdup in the catalyst bed means a high liquid-solid contacting efficiency that is wishful for RD. Nomenclature a ) geometrical area per unit volume of packing, m2/m3 a, b, c, d, e, f ) parameters
a′, b′, c′, d′, e′, f ′, g′ ) parameters dp ) diameter of the particles, m dh ) hydraulic diameter of the bed, m F ) volume fraction of the internal Fr ) Froude number g ) acceleration of gravity, 9.18 m/s2 hd ) dynamic liquid holdup in the column, m3/m3 hL,S ) liquid holdup at the load point, m3/m3 H ) height of the column, m lb ) height of the stage between two baffles, m N ) number of springs in the column N ) number of the stages in a spring divided by the baffles R ) radius of the springs, m ∆rj ) equivalent radial distance, m R ) inside radius of the column, m Re ) Reynolds number uG ) superficial gas velocity in the column, m/s uB,0 ) superficial axial gas velocity in the catalyst bed, m/s uB ) effective axial gas velocity in the catalyst bed, m/s uL,0 ) superficial axial liquid velocity in the column, m/s uL ) effective axial liquid velocity in the catalyst bed, m/s uP,0 ) superficial axial gas velocity in porous passages (springs), m/s Greek Letters Φ ) outer diameter of the spring 0 ) void fraction in the dry bed ) effective void fraction in the catalyst bed F ) density, kg/m3 µ ) viscosity, N‚s/m2 Subscripts G ) gas L ) liquid
Literature Cited (1) Taylor, R.; Krishna, R. Modelling reactive distillation. Chem. Eng. Sci. 2000, 55, 5183. (2) Han, M.; Lin, H.; Jin, Y. Catalytic distillation apparatus. CA Patent ZL99107320.7, 1999 (in Chinese). (3) Han, M.; Lin, H.; Wang, Z.; Jin, Y. A Catalytic Distillation Column with a Novel Internal. 2nd International Symposium on Multifunctional Reactors, Nuremberg, Germany, 2001. (4) Han, M.; Lin, H.; Wang, L.; Wang, J.; Jin, Y. Characteristics of the Reactive Distillation Column with a Novel Internal. Chem. Eng. Sci. 2002, 57, 1551. (5) Lin, H.; Han, M.; Wang, Z.; Wang, J.; Jin, Y. Study on a Catalytic Distillation Column with a Novel Internal. Chem. Eng. Commun. 2002, in press. (6) Gelbe, H. Der Flu¨ssigkeitsinhalt und die Rektifizierwirkung beim Vakuumbetrieb in Fu¨llko¨rperschu¨ttungen. Fort. Ber. VDIZeitschrift 1968, 3, 23. (7) Buchanan, J. E. Pressure gradient and liquid hold-up in irrigated packed towers. Ind. Eng. Chem. Fundam. 1969, 8, 502. (8) Billet, R.; Schultes, M. Modelling of pressure drop in packed columns. Chem. Eng. Technol. 1991, 14, 89. (9) Han, M.; Lin, H.; Wang, J.; Jin, Y. Pressure drop for Two Phase Counter-current Flow in the Packed Column with a Novel Internal. Chem. Eng. J. 2003, submitted for publication. (10) Stichlmair, J.; Bravo, J. L.; Fair, J. R. General model for prediction of pressure drop and capacity of countercurrent gas/ liquid packed columns. Gas. Sep. Purif. 1989, 3, 19. (11) Li, D. The synthesis of isopropylbenzene by catalytic distillation. Doctoral Dissertation, University of Petroleum (in Chinese), 1999. (12) Moritz, P.; Hasse, H. Fluid dynamics in reactive distillation packing Katapak-S. Chem. Eng. Sci. 1999, 54, 1367.
Received for review October 17, 2001 Revised manuscript received April 29, 2002 Accepted May 31, 2002 IE010858C
