Pressure Drop Studies in Bubble Columns - American Chemical Society

chamber volume on the plate performance was also studied. The experimental results ... In bubble column reactors or plate columns using perforated pla...
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Ind. Eng. Chem. Res. 2001, 40, 3675-3688

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Pressure Drop Studies in Bubble Columns Bhaskar N. Thorat, Kamal Kataria, Anand V. Kulkarni, and Jyeshtharaj B. Joshi* Department of Chemical Technology, University of Mumbai, Matunga, Mumbai 400 019, India

The effect of sparger design on dry and wet plate pressure drop was investigated in 0.2 and 0.385 m i.d. bubble columns. Perforated plates were used as spargers. The effect of the gas chamber volume on the plate performance was also studied. The experimental results of dry and wet plate pressure drop were analyzed with the help of a newly developed Ergun-type equation. The Ergun equation constants AW and BW were shown to display a particular trend with respect to the clear liquid height on the plate and the plate parameters such as the percent of free area, hole diameter, pitch to hole diameter ratio, and plate thickness to hole diameter ratio. All of the findings were coherently put together using simple correlation for bubble columns. Introduction Bubble columns are widely used in the chemical process industry and the metallurgical industry as absorbers, strippers, reactors, fermenters, coal liquifiers, visbreakers, etc. This is basically because of simple construction, high rates of mass and heat transfer, and ease with which the residence time can be varied. The hardware consists of a cylindrical vessel and a sparger. The specifications of the former include the dimensions of diameter and height. However, the specifications and description of the sparger are relatively elaborate. There are many types of spargers such as sintered plate, perforated or sieve plate, ring, spider, radial, etc. Further, for each type, we need to specify the hole diameter, their orientation, and the free area. The location of the sparger is also important with respect to the gas inlet nozzle and in many cases liquid inlet/ outlet nozzles. In bubble columns, the entire column volume is divided into two regions: sparger and bulk. In the sparger region, the bubble characteristics (size, shape, and the rise velocity) and hence the column performance are governed by the sparger design. In the bulk region, the bubble characteristics are governed by the flow patterns. The sparger design is known to be important when the height-to-diameter ratio (HD/D) is typically less than 5. For taller columns and the air-water system, the sparger design is known to be unimportant as far as bubble characteristics are concerned.1-3 (For coalescence-inhibiting liquids, it may not hold.4) However, the sparger may contribute major pressure drop and hence power consumption. In bubble column reactors or plate columns using perforated plates as gas/vapor distributors, it is recognized that the pressure drop across the perforated plate differs in the presence and absence of liquid over it. The reason is believed to be due to the modification in the gas flow through the holes in the presence of liquid. Conventionally, the pressure drop across the plate is expressed as the sum of three components. These are (i) the dry pressure drop, (ii) the hydrostatic head of dispersion, and (iii) the residual/excess pressure drop. * To whom correspondence should be addressed. Phone: 0091-22-414 5616. Fax: 0091-22-414 5614. E-mail: jbj@ udct.ernet.in.

Thus, mathematically the total pressure drop is given by the following equation:

∆PT ) ∆PD + ∆PL + ∆PR

(1)

where ∆PD is dry plate pressure drop. ∆PL is the pressure drop due to the hydrostatic head, which is given by the following equation:

∆PL ) HD(LFL + GFG)g

(2)

∆PR is the residual pressure drop. It depends on the hole velocity, hydrostatic head, plate geometry, surface tension, etc. The wet plate pressure drop is the sum of the residual pressure drop (∆PR) and the dry plate pressure drop (∆PD). The subject of dry and wet pressure drops has been extensively investigated in the past 50 years. A brief review is presented below. Dry Plate Pressure Drop (∆PD). For compressible gases, the orifice coefficient is given by the following equation:5

CO )

qm π 2 d R 2∆PDFG 4 O x

(3)

where R is the expansibility (expansion) factor under isentropic condition and is calculated using the following equation:4

∆PD γP1

R ) 1 - (0.41 + 0.35β4)

(4)

where FG is the gas density in the upstream region of the sparger, γ is the isentropic coefficient (for air, it is 1.41), and β is the ratio of the hole diameter to the column diameter. The orifice coefficient and the resistance coefficient are related by

CO ) 1/xξ

(5)

For single hole spargers, ξ is a known function of the hole Reynolds number. For multihole spargers, ξ is influenced by the interaction of gas jets issuing from the holes. In other words, apart from the hole Reynolds number, ξ also depends on % FA or equivalently on P/dO (% FA is related to P/dO as % FA ) k(dO/P)2, where k

10.1021/ie000759j CCC: $20.00 © 2001 American Chemical Society Published on Web 07/12/2001

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depends on the arrangement of the holes).6 The ratio of plate thickness to the hole diameter (t/dO) has the largest influence on ξ. For thin trays (t/dO e 1), the vena contracta of the gas jet lies above the plate, and there is a pressure recovery as the gas slows down from its maximum to its superficial velocity, VG. In contrast, for thick plates (t/dO . 1), the vena contracta lies within the hole itself. The jet partially expands to fill the complete cross section of the hole before emerging, after which it slows down to the superficial velocity. This necessarily means that the pressure recovery associated with a thick plate is greater owing to the two-stage expansion than for the single-stage expansion that occurs in thin plates. Therefore, it can be generalized that thick trays have a lower pressure drop than thin plates. There are more than 20 correlations available in the literature for the orifice coefficient.7-33 Besides these, there are a few related papers which review the available correlations for the dry plate pressure drop. Notable among them are Cervenka and Kolar,6 Chase,35 Thomas and Haq,36 and Lockett.37 The correlations, which have broader validity with respect to % FA, t/dO, and P/dO will be examined in the following text. Kolodzie, Smith, and Van Winkle14,19 found that CO depends on the hole Reynolds number, % FA, plate geometry t/dO, and P/dO. The dependence of the parameter K on t/dO and the Reynolds number was given in a graphical form. The correlation satisfies quantitatively both thick and thin plates. The correlation could be useful within the range covered except for the disadvantage of using the graphical form of the presentation of K. Cervenka and Kolar6 extended their set of data to formulate the correlation. In doing this, they started with the Kolodzie, Smith, and Van Winkle14,19 type correlation with the same theoretical assumption that the resistance coefficient would generally depend on the Reynolds number of the opening and the plate parameters, t/dO and P/dO. From the analysis of the dependence of the pressure drop on gas velocity, they found that for thin plates the effect of the Reynolds number on the resistance coefficient was insignificant. They processed about 78 perforated plates and obtained the following correlation:

1/CO2 ) ξ )

a(1 - φ2) φ0.2(t/dO)0.2

(6)

The drawback of this correlation is that it covers limited ranges of t/dO, typically between 0.1 and 0.8 and a relative free area from 1.5 to 20%. The authors claim for a better analytical character of the correlation because it includes the geometric parameters of the sieve plate. In any way the model falls short of covering the lower free area range. Lockett37 has systematically analyzed 20 available correlations and recommended the use of the Stichlmair and Mersmann31 model. The incorporation of % FA in the correlation for the resistance coefficient is the added feature, and the resistance coefficient was then correlated against t/dO with the Reynolds number as a parameter. Two different equations have been proposed for ξ, one for t/dO < 2 and the other for t/dO > 2. They obtained the predicted curve of the dry plate pressure drop at different values of the F factor (defined as the product of the superficial gas velocity and the square

root of the gas density). They also showed that the other correlations also follow the same shape and form. However, all of the results have been presented in a graphical form. From the foregoing discussion, it is clear that most of the published literature on the dry plate pressure drop is devoted to plates having dO > 4-5 mm and % FA > 7. This results from the large research input in the area of plate distillation columns in the last 50-60 years. The literature on perforated plates with higher t/dO and lower % FA is scarce, and therefore an effort has been made in this paper to highlight this area along with those plates which have been studied extensively. Wet Plate Pressure Drop (∆PW) and Residual Pressure Drop (∆PR). Arnold et al.7 and Mayfield et al.8 were among the first few who found the pressure drop to be influenced by the presence of liquid on the perforated plates. In the case of the air-water system, the wet pressure drop, ∆PW, (calculated as ∆PT - ∆PL) was consistently higher by 2-5 mm of water than ∆PD. This was found to hold regardless of the air flow rate and the depth of the liquid. Hunt et al.10 followed this work on similar lines. They reported that the turbulent expansion loss (under dry conditions) gets modified in the presence of liquid. The difference in ∆PW and ∆PD obtained was 25 mm of water for 3 mm hole plates and less than 25 mm of water for dO > 3 mm. This residual pressure drop was found to increase with an increase in the gas velocity for small perforations, and it remained practically the same for larger perforations. Also, it was consistently higher for plates with lower % FA. Further, the residual pressure drop was found to increase with an increase in the P/dO ratio for a given hole velocity. However, for practical design, they recommended a constant residual pressure drop value of 12 mm, independent of the hole velocity and plate geometry. They have also studied the effect of surface tension on the residual pressure drop and found that a decrease in the surface tension decreases the residual pressure drop. These findings were later corroborated by Hughmark and O’Connell13 and Eduljee.15 McAllister et al.17 studied the effect of t/dO and liquid flow rate on the residual pressure drop. They observed that the residual pressure drop increases with an increase in t/dO and the liquid flow rate for thick plates (t/dO g 1), whereas for thin plates (t/dO < 1), it remained practically constant. Lemieux and Scotti39 studied the pressure drop across a plate with 12.7 and 25.4 mm perforations, both having thicknesses of 3 mm and free areas of 10 and 9.6%, respectively. They observed the total pressure drop to be higher for 25.4 mm plates than 12.7 mm plates. Kupferberg and Jameson40 studied the pressure drop across sieve plates of hole diameters of 3.16 and 6.35 mm. The value of ∆PR was found to increase with an increase in the hole velocity. Payne and Prince41 studied the wet pressure drop in perforated plates having a wide range of hole diameters (3.16, 4.76, 6.35, and 9.35 mm) and chamber volumes of 50-5000 cm3. All of the plates were single hole spargers. These authors made very important observations. First, the interaction between the gas and liquid was found to increase with an increase in the liquid depth, resulting in an increased residual pressure drop. This interaction causes bulk motion of the liquid near the orifice, as the liquid pulses back and forth. The atomization of the liquid increases with increasing depth, and so the residual pressure drop rises to the

Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3677

transition. The peak in the residual pressure drop curve corresponds to the transition from the bubbling to jetting regime. Second, the effect of the surface tension was found to be less important at high gas velocities and liquid depth because surface tension forces under these conditions are small compared with the gravitational and inertial forces affecting the stability of the jet. At low liquid depths and gas velocities, the latter forces are reduced and so the surface tension becomes important, a common phenomenon encountered in plate columns. Davy and Haselden42 have developed the following correlation for wet pressure drop:

∆PW ) 0.5FG(VO/CW)2

(7)

where CW is the wet plate discharge coefficient (CW ) zCO). CO is the dry plate orifice discharge coefficient and z the bubbling factor. However, the dependence of z on the hole diameter (dO), the plate thickness to hole diameter ratio (t/dO), has not been elucidated for the bubble column range. Also, it is much easier to visualize the effect of the tray geometry on the individual pressure drop in terms of eq 1. Thomas and Ogboja43 observed ∆PR to depend on the surface tension and the hole velocity. According to them, the residual pressure drop consists of two components: one is the conventional pressure drop required for the bubble formation (by surface tension forces), given by 4σ/dO, and the other momentum head as introduced by Sargent and Bernard44 [∆PM ) (FG/FL)VG(VO - VG)]. The second term allows for the head loss by vapor/gas leaving the tray holes. Under the circumstances, the contribution of this term was found to be approximately 10-15% of the pressure drop due to surface tension forces. Bennett et al.45 studied the pressure drop for trays with small perforations (dO ) 1 and 3 mm), and these were shown to exhibit large pressure drops. They attributed the entire ∆PR to the bubble formation, and the surface tension force was found to be most important. Prakash and Briens46 were among the first to study the residual pressure drop in porous distributors. They employed porous distributors having an average pore size of 35 µm. They found that the presence of liquid increased the pressure drop by 200-900% at practical gas flow rates of VG < 0.15 m/s. For small bubbles at the beginning of its growth, the surface tension forces were found to be very large. Recently, Biddulph and Thomas34 studied air-water, air-benzyl alcohol, and air-n-propanol systems and found the residual pressure drop to be a strong function of the liquid-phase properties. Notably, for the airwater system, ∆PR increases with an increase in the F factor. They proposed an empirical approach to correlate the residual pressure drop with the F factor, clear liquid height, and surface tension forces. Their conclusive observation was the linear relationship between the residual pressure drop and the above three variables, given as follows:

[ ]

∆PR ) n

σ + R′F + β′HL FLgdO

(8)

According to these authors, the bubbling process appears to be the most important part of the residual pressure drop. The end of the bubbling and then subsequent start of jetting lead to a drop in the residual

Figure 1. Experimental setup.

pressure drop, and it was found to approach zero at sufficiently higher hole velocity. However, eq 8 does not support these observations. From the foregoing discussion, the following points emerge: (i) In the presence of liquid, gas issues either in the form of bubbles or as a jet. Though the force balance during the bubble and jet formation is well documented in the literature (Ra¨biger and Vogelpohl47 and Tsuge48), the same information has not been used in the pressure drop calculations. (ii) When the hydrostatic head is high (particularly in bubble columns), the liquid may penetrate into the holes, effectively reducing the area available for the gas flow. The movement of liquid across the floor of a plate is usually chaotic. Some holes or groups of holes may be discharging rapidly at a given instant, while the others may be temporarily inactive. This means that the orifice velocity is not the same for all of the holes, and hence the pressure drop gets modified. (iii) In plate columns, an increase in the liquid flow rate increases the hydrostatic head and hence the residual pressure drop. However, in bubble columns, the hydrostatic head is not related to the liquid flow rate, and hence the latter does not affect the residual pressure drop. (iv) In most of the published literature, % FA > 5, dO > 3 mm, and clear liquid height < 100 mm. In contrast, for bubble columns, % FA is much smaller, dO < 3 mm, and the clear liquid height is much higher. Further, the effect of the plate geometry (P and dO) has been investigated only qualitatively, and no quantitative relationships are available.

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Table 1. Design Details of Sieve Plate Spargers sparger type SP1 SP2 SP3 SP4 SP5 SP6 SP7 SP8 SP9 SP10 SP11 SP12 SP13 SP14 SP15 SP16 SP17 SP18 SP19 SP20 SP21 SP22A SP22 SP23 SP24 SP25 SP26 SP27 SP28 SP29 SP30 SP31 SP32

% free area 0.136 0.42 1

3 6 20

0.136 0.2 0.3 0.42 1.68

hole diameter, mm

N

pitch of holes

total hole perimeter, mm

1 3 7.4 1 3 12.9 1 3 6 20 3 6 34.6 3 6 49 3 6

A. 0.2 m i.d. Bubble Column 54 triangular 6 triangular 1 168 triangular 19 triangular 1 400 triangular 44 triangular 11 triangular 1 133 triangular 33 triangular 1 267 triangular 67 triangular 1 889 triangular 222 triangular

169.6 56.54 23.25 527.79 179.1 40.53 1256.63 414.69 207.34 62.83 1253.49 622.03 108.70 2516.41 1262.92 153.94 8378.63 4184.60

1 3 14 0.95 1.5 3 1.5 3 3 6 25 1 3 6 50

B. 0.385 m i.d. Bubble Column 201 triangular 22 triangular 1 314 triangular 132 triangular 33 triangular 198 triangular 50 triangular 69 triangular 17 triangular 1 2490 triangular 276 triangular 69 triangular 1

631 207 44 937 622 311 933 471 650 320 78 7822 2601 1300 157

(v) The effect of gas velocity has been investigated up to an orifice Reynolds number of 4000. The behavior of ∆PR at higher Reynolds number is not known in the published literature. In view of the above, it was thought desirable to undertake a systematic investigation of the wet, and hence the residual, pressure drop for the range of parameters encountered in bubble columns. Experimental Section Experiments were carried out in cylindrical bubble columns of 0.2 and 0.385 m i.d. and 1.5 and 3 m height, respectively (hereafter, referred to as BC1 and BC2, respectively). A schematic diagram is shown in Figure 1. Sieve plate spargers were placed between the column and distribution chamber, which had a drain at the bottom and a gas inlet at the side. The pressure drop across the sparger was measured using the DPI 280 Druck pressure probe (England) and also with the help of a U-tube manometer. For BC1, 18 different spargers were employed with hole diameters in the range of 1-49 mm and free areas in the range of 0.13-20%. For BC2, these values were 0.95-50 mm and 0.13-1.68%, respectively, covering 15 spargers. Further details of the spargers are given in Table 1A,B. The superficial gas velocity was measured with the help of a precalibrated anemometer placed at the top (exit) of the column. The error in the measurement of the superficial gas velocity was within 2%. Polypropylene mesh was provided just before this assembly to prevent any water from being entrained to the top. The chamber below the distributor plate was made from mild steel. For BC1, two such gas chambers having different volumes (6 and 18 L) were

P/dO

t/dO

25.8 25.8

6 2 0.81 6 2 0.46 6 2 1 0.3 2 1 0.17 2 1 0.12 2 1

14.7 14.7 9.5 9.5 9.5 5.5 5.5 3.9 3.9 2.13 2.13 25.8 25.8 20.3 20.3 20.3 17.4 17.4 14.7 14.7 7.35 7.35 7.35

6 2 0.81 6.316 4 2 4 2 2 1 0.46 6 2 1 0.3

employed to study the end effects and the effect of chamber volume on the plate performance, whereas for BC2, chamber volumes of 11.6 and 44.8 L were used. For wet pressure drop studies, first the air was introduced at a sufficiently high flow rate and then tap water was introduced from the top until the dispersion height (HD) reached the desired level. For obtaining the required HD, the clear liquid height was varied in the range from 0.1 to 2 m. The superficial gas velocity was varied in the range of 0.01-1.5 m/s, covering both the bubble column and the plate column range. The pressure drop measurements were carried out under no weep conditions. Because the other end of the bubble column and the clear liquid limb were exposed to the atmosphere, the difference in the total pressure drop across the plate and the hydrostatic head gives the value of the wet pressure drop (∆PW). One important point may be noted at this stage. In the range of superficial gas velocities covered in this work, the gas-liquid dispersion was found to be in the heterogeneous regime. In this regime, intense liquid circulation occurs which is upward in the central region and downward near the column wall. As a result, wall shear stress gets developed in the downward direction. Therefore, the actual pressure on the sparger surface is expected to be lower than the hydrostatic head [HD(LFL+ GFG)g]. However, the values of such pressure drops are expected to be negligible as far as the estimation of the gas holdup is concerned. Results and Discussion Dry Plate Pressure Drop. The gas flow from the chamber to the column experiences sudden contraction

Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3679

Figure 2. Velocity profiles and location of vena contracta for (A) t/dO < 1 and (B) t/dO g 1.

and expansion losses, the magnitude of which depend on the hole Reynolds number, t/dO ratio, and P/dO ratio. The contraction and expansion are schematically shown in parts A and B of Figure 2 for thick and thin plates, respectively. As mentioned earlier, for thin plates, the vena contracta lies above the plate, and for thick plates, it lies within the hole itself. Expansion occurs in two stages, as shown in Figure 2B: The first stage is the gas expands partially to fill the complete cross section. The second stage expansion occurs when the jet emerges from the hole and finally attains superficial gas velocity. For the estimation of contraction and expansion losses, knowledge of velocities is needed at the various stages of contraction and expansion. For instance, for thick plates

V12 V22 V32 + ke1 + ke2 ∆PD ) kC 2 2 2

∆PDR2 (t/dO)0.2 A ) +B 0.4 1 ReO 2 (P/d ) O FGV2 2

(11)

where A was obtained in terms of A′, P/dO, and t/dO as follows:

(9)

where kC is the contraction coefficient and ke1 and ke2 are the two stage expansion coefficients. V1, V2, and V3 are the velocities at three stages (Figure 2B). It is obvious that the estimation of kC, ke1, and ke2 cannot be made from first principles particularly for multipoint spargers. Therefore, the following Ergun-type equation was developed:

∆PDR2 A′ ) + B′ 1 ReO 2 FGV2 2

A. Sparger SP2 (dO ) 3 mm and N ) 6) has the highest transition ReO. Alternatively, keeping the same % FA, if the hole diameter is increased by decreasing the number of holes, the transition shifts to higher ReO. A similar trend was observed for spargers with free areas of 0.42 and 1% (SP4-SP10) as shown in Figure 3B,D. Further, as the free area is increased from 0.136 to 0.42-1%, the transition ReO decreases considerably and approaches a value of 5000. Based on the above results, it can be generalized for multihole spargers that the orifice discharge coefficient increases sharply with an increase in ReO up to the point of transition, and thereafter it remains nearly constant. Second, for the sparger plates with t/dO < 1, the orifice discharge coefficient gradually increases with increasing ReO before reaching a constant value. The transition at which this happens is at ReO between 10 000 and 25 000 depending upon the free area. As is seen from Figure 3A-C, as % FA is increased from 0.136 to 1%, the transition Reynolds number also decreases considerably, from about 25 000 to about 10 000. It can be seen from the above results that CO is a strong function of not only the hole Reynolds number but also the plate design parameters, such as t/dO and P/dO. (i) Data Analysis Using the Proposed Correlation. Equation 10 was used to correlate the resistance coefficient with the hole Reynolds number. Constants A′ and B′ were determined for each plate. These constants have a particular trend with respect to the P/dO and t/dO ratios. The dependence has been summarized in Table 2, and these values were further used to obtain the following correlation:

(10)

where A′ and B′ are functions of t/dO and P/dO ratios, respectively. Before developing a quantitative relationship, qualitative observations will be described. The orifice discharge coefficient was calculated using eq 3. For plates with 1 e t/dO e 6, CO increases with an increase in ReO, as shown in Figure 3A-D. The increase is up to a particular hole Reynolds number, beyond which CO was found to increase only marginally. The Reynolds number at which this transition takes place varies between 5000 to 10 000 depending upon the plate geometry. Sparger types SP1 and SP2 appear to have higher transition Reynolds numbers than the other spargers (SP3-SP12) as shown in Figure 3

A ) A′(t/dO)0.5(P/dO)-0.5

(12)

The exponents of the terms t/dO and P/dO in eq 11 were taken as 0.2 and 0.4, respectively, as proposed by Cervenka and Kolar.6 Their study was limited to plates with free areas between 1.5 and 20%. The findings from our study show that the same may be applied for the plates having free areas as low as 0.136% and hole diameters as low as 1 mm. The added feature of this correlation is the applicability of the same for lower ranges of the hole Reynolds number that was not studied earlier. It may be emphasized that the lower range of the Reynolds number is more common for bubble columns. The constants A and B were obtained for both of the bubble columns (BC1 and BC2), each having two sets of chamber volumes to study the effect of the chamber volume. These are shown in Table 3. Essentially, each gas chamber has a particular height-to-diameter ratio, and the constants A and B obtained differ in magnitude depending on the chamber volume. For example, in the case of BC1, constant A is 1844 for a small chamber (VC ) 6 L), whereas it is 2210 for a large chamber (VC ) 18 L). Similarly in the case of BC2, constant A is 4125 for a small chamber (VC ) 11.6 L) and 2664 for a large chamber (VC ) 44.8 L). The effect of the chamber volume on constant B was found to be less as compared to that

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Figure 3. Orifice discharge coefficient (CO) versus hole Reynolds number (ReO) with dO as a parameter for BC1 (chamber volume ) 18 L). (A) % FA ) 0.136: 4, SP1; ], SP2; 0, SP3. (B) % FA ) 0.42: ], SP4; 0, SP5; 4, SP6. (C) % FA ) 1: ], SP7; 0, SP8; 4, SP9; ×, SP10. (D) % FA ) 3: ], SP11; 0, SP12. Table 2. Constants A′ and B′ of Eq 10 % FA

P/dO

t/dO

Table 3. Constants A and B Calculated Using Eq 11 A′

B′

10-3 m3)

0.136 0.42 1

0.136 0.42 1

0.2 0.42

A. 0.2 m i.d. BC (VC ) 18 × 26 6 401 26 2 579 0.81 2333 14.7 6 637 14.7 2 597 0.46 2015 9.5 6 375 9.5 2 410 9.5 1 490 0.3 1854

0.22 0.23 0.124 0.235 0.25 0.173 0.25 0.24 0.23 0.23

B. 0.2 m i.d. BC (VC ) 6 × 10-3 m3) 26 6 459 26 2 550 14.7 6 327 9.5 6 493 9.5 2 326 9.5 1 443

0.18 0.22 0.22 0.25 0.22 0.25

C. 0.385 m i.d. BC (VC ) 44.8 × 10-3 m3) 20.3 4 908 20.3 2 1535 14.7 2 1963 14.7 1 2988

0.27 0.27 0.28 0.27

of constant A. It varies between 0.4 and 0.42, except for the case of BC2 (VC ) 44.8 L), in which case a smaller value of 0.35 was obtained.

type of bubble column

A

B

BC1 (chamber volume ) 6 L) BC1 (chamber volume ) 18 L) BC2 (chamber volume ) 11.6 L) BC2 (chamber volume ) 44.8 L)

1844 2210 4125 2664

0.42 0.4 0.41 0.35

The effect of the chamber volume on the dry plate pressure drop as discussed above can be incorporated in eq 11. The chamber volume is made dimensionless by dividing it with the total hole volume of the plate. The exponent of this dimensionless chamber volume was obtained as -0.08 by a trial and error method, and the following equation was obtained:

AD ∆PDR2 (t/dO)0.2(HCD2/NdO2t)-0.08 ) + BD 0.4 1 ReO (P/dO) FGV22 2

(13)

where AD and BD are new constants obtained as a result of incorporation of the chamber volume in eq 11. The values obtained were 1192 and 0.14, respectively. The comparisons of the orifice discharge coefficients calculated using eq 13 with our experimental values and the other reported correlations are shown in Figure 4A-C. The earlier correlation which suffices for perforated plates with higher free area predicts the orifice dis-

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As found earlier, the constants in eq 11 have two sets of values for the two types of chambers, which are varying in size by a factor of 3 (BC1). The larger chamber volume is 18 L (HC/D ≈ 3), whereas the smaller chamber was of 6 L (HC/D ≈ 1). The orifice discharge coefficient with the larger chamber was found to be slightly lower (≈3-5% less) than the small volume chamber at the same hole Reynolds number (Table 4). This observation was consistent for all of the plates studied here. Because there exist no end effects in the large chamber, the possible reason for additional pressure drop may be attributed to the form drag experienced by the fluid in the chamber. The orifice coefficient for the larger chamber was found to be slightly less than that of smaller chamber, thereby giving higher resistance to the flow. This observation is contrary to what one might expect that in the former case the gas flow might be assumed to have achieved a fully developed profile. On the other hand, in the latter case the flow profile may be underdeveloped, leading to maldistribution of sparged gas. This contradiction may be explained with the help of observations made by Litz.49 Accordingly, the discharge coefficient is independent of the distributor design if the location of the nozzle and the dimensions of the nozzle in comparison with the column diameter satisfies the following conditions:

H g 0.2D + 0.5Dnoz

Figure 4. Comparison of the orifice discharge coefficient calculated using eq 9 with experimental and other reported correlations: (]) experimental, (1) predicted, (2) Tsuge and Hibino,38 (3) Stichlmair and Mersmann,31 (4) Van Winkle,14,19 (5) Kneule and Zelfel,25 (6) Cervenka and Kolar.6 BC1 (VC ) 18 L): (A) SP5; (B) SP9; (C) SP12.

charge coefficient values to be lower than the experimental values, and also it does not give plate behavior at an extremely low hole Reynolds number. Predicted CO using eq 13 matches well with that of experimental CO even at low ReO, as can be seen from Figure 4A-C. The large gas chamber of BC1 has a height-todiameter ratio of 3. Five nozzles attached over the length of the distribution chamber were used to see if there exist any end effects due to the pressure gradient lengthwise. This was done by measuring the pressure at each of the five locations and comparing it with the pressure near the bottom of the vessel. It was found that the pressure in the chamber was uniform throughout.

for Dnoz > D/100

(14)

where H is the distance between the sparger plate and the nozzle center line. In the present study, a nozzle diameter of 50 mm was used. The value of H, calculated using eq 14, is 102 mm, which is smaller than the values employed in the current study, i.e., 510 and 110 mm for larger and smaller distributors, respectively. Thus, the condition given by eq 14 is satisfied in both of the cases. Therefore, the effect of the nozzle location on the plate performance is thus ruled out. It is likely that the upstream flow is relatively more turbulent in the case of the smaller distributor. It has been shown earlier that CO increases with ReO, which is perhaps related to the extent of turbulence.50 In any case, it may be noted that the difference is less than 5%. In the case of a 0.385 m i.d. bubble column, CO was found to be more by about 5% in the case of a larger distributor (VC ) 44.8 L, HC/D ≈ 1) than the smaller one (VC ) 11.6 L, HC/D ≈ 0.3). The smaller chamber does not satisfy the criteria given by eq 14 and hence the maldistribution and the lower CO. The distance between the nozzle center line and the plate was 55 mm, almost half that is required to satisfy eq 14. Wet Pressure Drop. The wet to dry pressure drop ratio (∆PW/∆PD) is plotted against the hole Reynolds

Table 4. Effect of the Chamber Volume on the Orifice Discharge Coefficient (0.2 m i.d. Bubble Column) resistance coefficient (ξ) sparger type

ReO

SP2 (% FA ) 0.136, dO ) 3 mm)

1000 5000 50000 100000 1000 5000 50000 100000 1000 5000 50000

SP5 (% FA ) 0.42, dO ) 3 mm)

SP8 (% FA ) 1, dO ) 3 mm)

VC ) 6 ×

10-3

3.75 1.955 1.55 1.523 2.87 1.38 1.18 1.23 2.367 1.29 1.132

m3

VC ) 18 ×

discharge coefficient (CO) 10-3

4.158 2.139 1.685 1.66 3.3 1.687 1.315 1.32 2.97 1.234 1.132

m3

VC ) 6 × 10-3 m3

VC ) 18 × 10-3 m3

0.516 0.71 0.8 0.8 0.59 0.85 0.921 0.90 0.65 0.88 0.94

0.5 0.68 0.77 0.77 0.55 0.77 0.8721 0.87 0.58 0.9 0.94

3682

Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001

Figure 5. Ratio of the wet pressure drop to the dry pressure drop versus hole Reynolds number with the hole diameter as a parameter, BC1 (chamber volume ) 6 L): ], SP7; 0, SP8; 4, SP9. (A) HL ) 0.1 m; (B) HL ) 0.2 m; (C) HL ) 0.3 m; (D) HL ) 0.4 m, and (E) HL ) 0.5 m.

number with the hole diameter as a parameter. For BC1, a typical plot is shown in Figure 5A-E for five different clear liquid heights varying from 0.1 to 0.5 m. It can be seen that above a certain Reynolds number (ReO,crit) the ∆PW/∆PD ratio increases with increasing hole diameter as the latter is increased from 1 to 3 mm and further to 6 mm. Beyond ReO,crit there is no effect of the hole diameter on the pressure ratio and the wet pressure drop approaches the dry pressure drop. Parts A and B of Table 5 show ReO,crit and the critical superficial gas velocity (VG,crit) for all of the plates, and it can be generalized that VG,crit increases with an increase in the hole diameter for a given free area plate and increases with free area for a given hole diameter. Parts A-C of Figure 6 show the pressure ratio against ReO for a 0.385 m diameter bubble column for 0.2% free area plate and for three different hole diameters, viz. 0.95, 1.5, and 3 mm. Here also, the effect of the hole diameter on the pressure ratio is similar to that for BC1.

As the clear liquid height is varied from 0.3 to 2 m, there is an increase in the pressure ratio at a given orifice Reynolds number below its critical value. For 0.42% FA, similar findings were obtained. The increase in ∆PW/ ∆PD can be attributed to the ingress of liquid into the holes, thus reducing the available free area. With an increase in the clear liquid height, the driving force for the liquid to penetrate into the holes increases and therefore the pressure ratio increases. This phenomenon can be explained in a better way by considering the residual pressure drop. Residual Pressure Drop. The residual pressure drop (∆PR) was obtained by subtracting the dry pressure drop and the hydrostatic head from the total pressure drop (eq 1). Figure 7 shows the plot of ∆PR against the superficial gas velocity, VG, with clear liquid height as a parameter for 0.42% free area plate. The residual pressure drop increases initially, and then it decreases with a further increase in VG. Higher free areas than

Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3683 Table 5. Critical Reynolds Numbers at Which ∆PW/∆PD Approaches 1 (≈1.01) for 0.2 and 0.385 m Diameter Bubble Columns sparger type, % FA, and hole diameter

clear liquid height, m

ReO,crit

VG,crit, m s-1

A. 0.2 m Diameter Bubble Column 0.1 4819 0.2 4819 0.3 5389 0.4 5389 0.5 5946 1%, 3 mm 0.1 15 279 0.2 15 279 0.3 16 255 0.4 17 852 0.5 17 852 1%, 6 mm 0.1 19 976 0.2 19 976 0.3 22 541 0.4 27 020 0.5 27 020 0.42, 1 mm 0.1 2185 0.15 2445 0.2 2690 0.25 3030 0.3 3372 0.42, 3 mm 0.1 22 158 0.15 23 660 0.2 24 972 0.25 26 011 0.3 28 973 0.136, 1 mm 0.1 4343 0.15 5006 0.2 6176 0.25 6176 0.3 7750 0.136, 3 mm 0.1 38 196 0.15 38 196 0.2 46 002 0.25 50 685 0.3 53 401

0.665 0.665 0.746 0.746 0.82 0.71 0.71 0.749 0.82 0.82 0.665 0.665 0.76 0.9 0.9 0.113 0.128 0.139 0.156 0.173 0.49 0.512 0.54 0.577 0.61 0.082 0.088 0.113 0.113 0.139 0.237 0.237 0.271 0.284 0.3

B. 0.385 m Diameter Bubble Column 0.2, 0.95 mm 0.365 3283 0.643 3283 1.313 3283 1.864 4534 0.2, 1.5 mm 0.575 9284 1.235 10 795 1.863 12 708 0.2, 3 mm 0.59 23 248 1.24 27 958 1.962 27 958 0.42, 3 mm 0.325 15 539 0.555 15 539 0.745 20 505 1.03 20 505 1.285 20 505 1.635 20 505 0.42, 6 mm 0.41 26 000 1.295 38 552 1.865 38 552

0.0988 0.0988 0.0988 0.134 0.167 0.19 0.22 0.2 0.24 0.24 0.269 0.238 0.34 0.34 0.34 0.34 0.25 0.35 0.35

1%, 1 mm

0.42% (for example, 1%) also show similar behavior, whereas for lower free areas of 0.2%, it decreases continuously and approaches zero at sufficiently higher VG (Figure 8). Thus, for relatively higher free area plates, the residual pressure drop shows a peculiar behavior, whereas this phenomenon was found to be absent in 0.2% and lower free area plates. This anomalous behavior can be explained with the help of Figures 9 and 10. These two figures show the two possible physical situations. From Figure 9B it can be seen that at lower gas velocity the holes are partially blocked by the liquid, thus reducing the effective hole diameter from dO to dR. This offers additional resistance for the gas to flow through the holes, and hence the residual

Figure 6. Ratio of the wet pressure drop to the dry pressure drop versus hole Reynolds number with the hole diameter as a parameter, BC2 (chamber volume ) 44.8 L): ], SP22A; 0, SP22; 4, SP23. (A) HL ) 0.55 m; (B) HL ) 1.24 m; (C) HL ) 1.9 m.

pressure drop increases. At sufficiently higher gas flow rates, the liquid is completely driven out and dR tends to dO. An alternative physical picture is shown in Figure 10. At low gas velocity, only a few holes are active (Figure 10A) and gas-liquid dispersion prevails in one part of the column. This generates a pressure gradient and hence liquid circulation in the direction of ABCA. At locations such as C, the liquid flow rate is downward and thus creates a low-pressure region. Because the gas always finds the path of minimum resistance, the holes below C become active and the liquid circulation is reversed. Thus, at low gas velocity, only a few holes are active, and the active holes were found to jump from place to place (Figure 10B). As the superficial gas velocity was increased, the number of active holes increased, and at sufficiently high gas velocity, all of the holes became active. When the free area was less (