Distillation Sieve Trays without Downcomers: Prediction of

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Ind. Eng. Chem. Res. 2002, 41, 1632-1640

Distillation Sieve Trays without Downcomers: Prediction of Performance Characteristics J. Antonio Garcia† and James R. Fair* Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712

A large amount of performance data on larger-scale trays without downcomers has become available recently, and the data have been examined with a view toward understanding and modeling the contacting mechanisms under distillation conditions. The objective of this paper is to describe new predictive models for efficiency, pressure drop, and flooding of trays without downcomers and to show how they can be applied to distillation separations. Such an effort has not been reported previously. The contacting devices are assigned the generic name of dualflow trays. The models are shown to give reasonable estimates of the performance of these trays in larger columns with open areas in the range of 15-25%, hole diameters in the range of 1225 mm, and tray spacings in the range of 0.3-0.6 m. Bubble trays for distillation columns normally involve liquid flowing between trays through connecting downcomers. Such contacting devices are of the cross-flow type, and vapor flows only through dispersers on the trays such as holes, valves, or bubble caps. Less wellknown and -specified are perforated trays without downcomers, wherein the liquid and vapor flow countercurrently through the same tray openings. These are often called dual-flow trays, but in specialty forms, they have other names such as turbogrid trays and ripple trays. The devices are used for special services, especially when openings of a cross-flow tray might foul. Their less general use appears to have derived from an expected narrow operating range of high efficiency, as well as a general unavailability of design models that can enable reliable prediction of their performance. In the mid- to late-1950s Fractionation Research, Inc. (FRI), undertook an extensive research program on dual-flow trays, obtaining performance data for several different systems but not providing a general, fundamental correlation of the data for pressure drop, efficiency, and flooding. Meanwhile, Shell completed an extensive program of testing its turbogrid trays, similar in characteristics to dual-flow trays. Recently, FRI released all of its dual-flow test results, and these data form a major basis for the modeling in the present paper. Shell has released none of its turbogrid test results. Dual-flow trays have been applied to many situations in which a broad operating range (high turndown ratio) is not essential. In its range of application, the tray provides a very high mass transfer efficiency with low capital investment. Importantly, the application of such devices to fouling systems has been eminently successful, the alternating vapor-liquid passage through the holes providing a self-cleaning action. Previous Work

The published reports cover tests in distillation columns with diameters as large as 2.5 m (8.2 ft). Test data for a 1.0-m (3.3-ft) column containing turbogrid trays have been presented by researchers at the Institute of Process Fundamentals in Prague.3-6 The FRI work was conducted in a 1.2-m (4.0-ft) research column, using several hydrocarbon systems plus water/alcohol and water/ steam. Both Shell and FRI confirmed that the slotted openings of the turbogrids had equivalent performance characteristics to the round holes of dual-flow trays if slots with equivalent diameters were used. The results of the FRI tests have been released to the public and are now available from Oklahoma State University.7 Very little has been done to model the mass transfer performance of dual-flow trays. In the 1950s and 1960s, work in Europe with very small columns led to attempts at dealing with the hydraulics of the trays, but serious scale-up problems were anticipated, and no further work transpired that would aid the commercial-scale designer. The most recently reported attempt to model dual-flow tray efficiency, by Xu et al.,8 appeared in 1994. They studied methanol/water and methanol/2-propanol distillations in a 0.3-m (1.0- ft) column and provided valuable insights into the mass transfer relationships involved. However, they made no attempt to combine their data with those of others to arrive at a more generalized treatment of dual-flow tray efficiency. Perhaps a key finding, although nonquantitative, has been that the insertion of dual-flow trays as replacements for cross-flow trays dramatically alleviates problems with severe fouling. According to Baird,9 his company has “successfully supplied our DualFlo trays to over 70 installations where solids or scaling represented a potential operating problem. These trays, which range from 6 in. to 7 ft (0.15 to 2.1 m) in diameter, stay cleaner longer than other designs and are easier to remove and clean”. Such comments have encouraged designers to use the devices, termed “self-cleaning trays”, without adequate predictive model support.

Very few of the results of Shell’s investigations of turbogrid trays have appeared in the open literature.1,2

Modeling Approach

* To whom correspondence should be addressed. E-mail: [email protected]. † Current address: DuPont Engineering Technology, Brandywine 8226, 1007 Market Street, Wilmington, DE 19898.

Figure 1 shows a schematic of a dual-flow tray. Vapor and liquid flow countercurrently, using the same openings, and a volume of aerated liquid called the froth zone is generated above the tray perforations. It is in this

10.1021/ie010326w CCC: $22.00 © 2002 American Chemical Society Published on Web 02/08/2002

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Figure 1. Schematic of a dual-flow tray showing mass transfer zones.

Figure 3. Efficiency of stamped turbogrid trays, benzene/toluene, atmospheric pressure. Open area ) 14%, tray spacing ) 500 mm, hole diameter ) 12 mm, total reflux. Data from ref 2.

Figure 2. Efficiency of stamped turbogrid trays, methanol/water, 1.0-m column, atmospheric pressure, total reflux. Data from ref 5.

zone that the majority of the mass transfer is presumed to occur. The space above the froth, called the spray zone, is available for additional mass transfer, and this zone differs in performance from the equivalent zone of a cross-flow tray. Observations of operating dual-flow trays reveal a dynamic contacting process in which a given opening alternately passes vapor and liquid. This accounts for the self-cleaning character of the device. At any instant, a certain fraction of the holes are actively passing vapor, either as jets or as bubbles. Efficiency profiles (Figure 2) show a strong modification of the hole dynamics to the extent that there is less self-cleaning potential at lower loadings and clearly less froth volume to accommodate mass transfer needs. At very high loadings, liquid entrainment occurs, thereby reducing the mass transfer efficiency. Figures 2 and 3 (refs 2 and 5) show the sharp efficiency profiles characteristic of dual-flow trays. An effect of column diameter is indicated in Figure 3. Figure 4 shows profiles of both efficiency and pressure drop for representative FRI tests.3 For all of the figures, it is apparent that a “peak efficiency” exists, and in the present paper, an attempt is made to model this efficiency. Depending on the propensity for liquid entrainment upward, the peak appears to be in the

Figure 4. Efficiency and pressure drop of dual-flow trays, cyclohexane/n-heptane, tray spacing ) 0.61 m, hole diameter ) 12.7 mm, column diameter ) 1.2 m, pressure ) 1.63 atm, total reflux. FRI data.

range of 75-90% of the maximum throughput, i.e., where the efficiency becomes very low and the pressure drop becomes very high. Another important objective of the present effort is to develop a generalized relationship for predicting this maximum (“flooding”) condition. Test conditions in the database (Table 1) include the conditions for peak efficiency. The database covers a broad range of physical properties. Flooding. The FRI test data (see Table 1) include measurements of the near-flood condition. As defined by FRI, the flood point is evidenced by a significant increase in liquid holdup (pressure drop). The “true flood” with essentially no separation is at a loading slightly higher than the reported flood point. The flood data have been correlated in the same semiempirical manner used successfully for cross-flow type trays,10 as shown in Figure 5. The plotting method provides a very good fit of the data, and this leads to some insights regarding the mechanics of contacting. The capacity factor, Csb, has been normalized to a tray spacing of 0.61

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Table 1. Database, Tests on Dual-Flow Trays

refa

system

FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI 5 FRI FRI FRI 2 FRI

C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C4 C4 C4 C4 C4 C4 C4 C4 C4 C4 IPA/H2O xylenes xylenes C8/C10 C8/C10 MeOH/H2O MeOH/H2O MeOH/H2O MeOH/H2O Bz/Tol Bz/Tol

a

pressure (kPa)

TS (m)

% open

hole diam (mm)

28 28 28 166 166 166 166 166 345 345 1138 1138 1138 1138 1138 2073 2073 2756 2756 3456 101 16 mm 16 mm 10 mm 10 mm 101 101 101 101 101 101

0.61 0.61 0.61 0.61 0.30 0.91 0.61 0.61 0.61 0.91 0.61 0.30 0.61 0.61 0.91 0.61 0.61 0.61 0.61 0.61 0.61 0.61 0.61 0.61 0.61 0.41 0.41 0.41 0.41 0.51 0.51

13.5 18.9 25.6 13.5 19.1 19.1 18.9 25.6 18.9 29.3 13.5 19.1 18.9 25.6 29.3 13.5 29 13.5 29 13.5 19.1 12.9 17.8 12.9 17.8 10.5 14.2 18.2 23.6 14 14

12.7 25.4 25.4 12.7 12.7 12.7 25.4 25.4 25.4 11.9 0.5 1.0 1.0 1.0 0.47 0.50 0.47 0.50 0.47 0.50 0.5 12.7 12.7 12.7 12.7 b b b b 12.7 12.7

Ep/Fs

Fs flood [m/s (kg/m3)0.5]

peak efficiency (% flood)

79/1.98 75/2.26 63/2.56 83/1.77 55/1.89 57/3.11 81/2.20 55/2.60 98/2.01 67/2.81 121/0.83 90/1.29 115/1.13 92/1.62 96/1.89 114/0.67 91/0.91 150/0.43 87/0.79 >180/0.24 75/2.34 81/2.01 63/2.01 72/2.81 42/2.56 95/1.27 82/1.92 82/1.98 ∼53/∼2.3 87/1.63 80/1.96

2.20 2.59 2.93 2.01 1.98 3.39 2.34 2.89 2.34 3.17 1.43 1.46 1.77 1.73 2.07 0.76 1.01 0.52 0.88 0.33 2.46 3.07 ∼3.3 (3.78) ∼3.2 1.87 2.66 2.78 NA 2.44 2.62

90 87 88 88 96 92 94 90 86 88 58 88 64 94 91 89 90 81 90 74 95 65 61 (74) (81) 68 72 71 NA 67 75

Column diameters: FRI, 1.2 m; ref 5, 1.0 m; ref 2, 0.45 and 2.50 m. b Slots, 4 mm × 150 mm.

Figure 5. Flooding capacity of dual-flow trays based on FRI data, 1.2-m column diameter.

m (24 in.). Thus, the 0.30-m spacing has about 81%, and the 0.91-m spacing about 116%, of the capacity of the 0.61-m spacing. The effect of open area on flooding is evident but not well understood. Apparently, the higher hole velocity for lower open area results in jetting, which increases liquid entrainment. A small effect of hole size on flooding is indicated, with 25-mm holes having about 6% less capacity than the more standard 12.5-mm holes. This difference might be more apparent than real, but it could be a result of the longer jet length for the larger holes. Efficiency at Lower Loadings. The profiles in Figures 2-4 are typical of dual-flow trays, and it is clear

that, at lower loadings, there is a distinct loss of efficiency, much like the case for cross-flow sieve trays operating under conditions of weeping and dumping or the case for packed columns with poor liquid distributions. Observations indicate that, in this region, a definite loss of froth height occurs, fewer holes have intermittent vapor and liquid flow, and the residence time of vapor contacting liquid is shorter. The loss of efficiency for weeping/dumping of cross-flow trays has been interpreted in an approximate way by adapting the Colburn11 relationship for liquid entrainment. The same approach will be used for dual-flow trays, as discussed later. Liquid Entrainment in Vapor. The experimental curves of Figure 2 are representative of the shapes of the efficiency-velocity relationships found for all tests of dual-flow trays. To use these curves as an example, the efficiency at flow rates higher than the peak value are subject to the same type of entrainment analysis as used for cross-flow trays.10,12 The peaks occur at about 1.10 and 1.85 m/s superficial velocity for the 10.5% open and 18.2% open trays, respectively. At higher loadings, the effect of entrainment on efficiency can be approximated by a modification10 of the Colburn relationship

Ew/Ep )

1 1 + EpΨ/(1 - Ψ)

(1)

1-φ φEp + (1 - φ)

(2)

or

Ψ)

where φ ) Ew/Ep, Ew is the “wet” efficiency, Ep is the “dry” efficiency at the peak, and Ψ is the ratio of the

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Figure 7. Effect of hole diameter on tray efficiency and pressure drop of dual-flow trays. Cyclohexane/n-heptane at 1.63 atm and total reflux. Tray spacing ) 0.61 m, open area ) 19.1%. FRI data.

drop curve, indicating the onset of loading where higher vapor velocities cause increased liquid holdup. This is analogous to loading in packed columns. For a pressure balance to be maintained on a given dual-flow tray

ht ) hgd + hL ) hL′ - hLd Figure 6. Fractional entrainment of liquid in vapor. Methanol/ water, 1.0-m-diameter column. Data from ref 5 and Figure 2. The superimposed curve for cross-flow sieve trays is taken from ref 12.

moles of liquid entrained to the total downflow including entrainment recycle. Representative values of Ψ calculated from the experimental data of Figure 2 are shown in Figure 6. Also shown is a composite curve for cross-flow sieve tray entrainment, taken from ref 12. It appears that similar mechanisms for entrainment prevail for the two tray types. Tentatively, the generalized curves for sieve trays can be used for estimating the liquid entrained by the rising vapor of dual-flow trays. This assumes that the vapor breaks through a dual-flow tray froth in the same manner that it breaks through a cross-flow sieve tray froth. A more quantitative assessment of the entrainment effect must await experimental data; however, prudent designs call for an approach to flooding not greater than 80-85%, close to the peak efficiency region, where the entrainment effect is minor. Low Loading Effects. To interpret the loss of efficiency at lower loadings, an “entrainment-in-reverse” approach is used, even though there is no recycle due to entrainment. To take an example from Figure 2, for a superficial velocity of 1.10 m/s (1.10/1.85 or about 60% of the peak loading), the efficiency is 58%, or 70% of the peak value. Using an adaptation of eq 2, one obtains

Ψ′ )

1 - φ′ 1 - 0.70 ) ) 0.34 (3) φ′Ep + (1 - φ′) 0.70(1 - 0.70)

where φ′ is the fraction of the peak efficiency (E/Ep) and Ψ′ is a correlating parameter. Appropriate values of Ψ′ thus enable the total efficiency curve to be established. Pressure Drop. Representative pressure drop data for dual-flow trays of two open areas are shown in Figure 4, and Figure 7 shows the effect of hole size on pressure drop (as well as on efficiency). In the region of peak efficiency, there is an evident break in the pressure

(4)

where ht is the total pressure drop across the tray, height of clear liquid; hgd is the pressure drop for vapor passing through fraction of holes x; hL is the residual pressure loss for vapor flowing through the froth; hLd is the pressure loss for liquid flowing through 1 - x fraction of holes; and hL′ is the liquid head to force liquid through 1 - x fraction of holes. Equation 4 implies that hL′ is greater than hL, because liquid and vapor flow in opposite directions through the holes. The dynamics of the dual-flow tray are such that momentum in the liquid is converted to static head to allow liquid to flow downward against the static pressure gradient. Because the mechanisms of flow are so poorly understood, we will concentrate on the gas flow portion of eq 4

ht ) hdG + hL

(5)

with

hdG )

Ux2FL 2gCv2FG

(6)

where Ux is the linear velocity of vapor through x fraction of total holes and Cv is the orifice coefficient, a function of the hole diameter and effective open area. Orifice Coefficient. For flow through holes in a dualflow tray, the correlation developed originally for sieve trays by Leibson et al.,13 presented originally in graphical form, can be represented analytically by

Cv ) 0.74(Ah/Aa) + exp[0.29(tt/dh) - 0.56]

(7)

where tt is the tray thickness, dh is the hole diameter, and the hole area Ah is based on the holes passing vapor. Orifice coefficients obtained for the tray geometries considered in this work (Table 1) ranged from 0.58 to 0.72. By comparison, for a sieve tray with 12% hole area, 12-mm holes, and a tray thickness of 1.6 mm, the orifice coefficient has a value of 0.80. For the two hole sizes of

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Figure 7, the difference in orifice coefficient accounts for about one-third of the difference in total pressure drop. Liquid Holdup. Earlier work by Kotschering et al.14 provided a correlation for equivalent clear liquid height on dual-flow trays, which was modified later by Xu et al.8 The Xu modification was adapted to the FRI data in the present work as follows

hL ) b1

(LML)n[US(FG/FL)0.5]b2 FL(Ah/Aa)b3 (tt/dh)0.42

(8)

with regressed values of the constants b1 ) 0.01728, b2 ) 1.0, and b3 ) 1.50. In the original work, the exponent n is obtained from the expression

n ) 4.3

() Ah Aa

1.5

(9)

Figure 8. Fraction of holes passing vapor, cyclohexane/n-heptane, 1.63 atm. Tray spacings, open areas, and hole diameters as indicated. FRI data.

Fraction of Holes Passing Vapor. Because there are no measurements of this parameter, it must be deduced from measured pressure drop data for the entire tray (eq 5). After correcting for liquid holdup hL by eq 8, eq 6 is used

hdG ) ht,meas - hL )

Ux2FL 2gCv2FG

(10)

from which

χ)

Q Ah

x

FL

(ht,meas - hL)(2gCv2FG)

(11)

where Q is the volumetric flow rate of vapor. Even though this approach is semiempirical, it is useful for predicting tray pressure drops from the number of active holes. The fraction χ has been correlated as a function of hole area, tray spacing, and approach to flood using the FRI data as

( )( )

χ)A

Ah/At 0.2

0.8

TS 0.610

0.2

[

exp -0.35

(|% floodC - B|)]

Figure 9. Parity plot for the experimental and calculated pressure drops of dual-flow trays. Cyclohexane/n-heptane, ibutane/n-butane, and 2-propanol/water (136 points).

(12) where TS is the tray spacing in meters and A, B, and C are the regression correlation constants (A ) 0.4668, B ) 90, C ) 45). A representative plot of fractional holes passing vapor is shown as Figure 8. Although the trend with loading might seem counterintuitive, until direct measurements are made, the relationships will remain useful for the design process, as shown later in a comparison of calculated and measured overall pressure drop data. Pressure Drop Model Analysis. The approach outlined above was used to develop the parity plot in Figure 9. The plot is based on all of the total reflux FRI experimental data. The mean absolute deviation is 23.0%, and the average deviation is 0%. Of the 136 points, 13 lie above the (25% range. Most of these “outside” points derive from near-flooding conditions, where measurements are not precise. If the water/2propanol system is excluded, leaving only hydrocarbon systems, only 9 of the 122 points are outside the (25% range. In general, pressure drop is underpredicted in the near-flooding zone. A representative performance plot showing the pressure drop fit is given in Figure 10.

Figure 10. Example comparison of predicted and experimental pressure drops for dual-flow trays. Cyclohexane/n-heptane, total reflux, 1.63 atm. Column diameter ) 1.2 m, tray spacing ) 0.91 m, open area ) 19%, hole diameter ) 12.7 mm. FRI data.

The efficiency curve has been included to show the efficiency peak at the pressure drop curve break. Froth Height. A two-phase porosity relationship for dual-flow trays was developed by Mahendru and Hackl15 and used by Xu et al.8 to predict liquid holdup for a 300mm (11.8-in.) column operated with the methanol/water

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and methanol/2-propanol systems. The porosity  (volume fraction of vapor in the froth) determined by Xu et al. is

 ) 1.0 - 0.0946

[ ] Us2FG ghLFL

-0.2

refa

(13)

Accordingly, the froth height for dual-flow trays, hf, can be calculated from the porosity and equivalent clear liquid height

hf )

hL (1 - )

Table 2. Comparison of Calculated and Measured Efficiency for Dual-Flow Trays

(14)

As a note of caution, eqs 10 and 11 should be used only in the vicinity of the peak efficiency, i.e., where the froth is well-developed and stable. At low loadings, the liquid on the tray is not well-aerated. Mass Transfer Efficiency Spray Zone. Previous models (e.g., Xu et al.8) follow earlier work with cross-flow trays and are based on the assumption that essentially all of the interphase transfer occurs within the liquid-continuous froth immediately above the tray floor. However, as pointed out earlier, there can be significant mass transfer in the spray zone above the froth, where all of the downflow liquid comes into contact with the rising vapor (thereby differing from conventional cross-flow trays). Because it is likely that complete horizontal mixing takes place in the froth (in the region of peak efficiency), the additional mass transfer should be taken into account. Because the froth is well-mixed, efficiency in the froth cannot exceed 100% and because FRI obtained efficiencies as high as 150% (Table 1), it is clear that, for some systems, mass transfer in the spray zone can be significant. The liquid flowing through this zone has been observed to flow primarily as streams, with breakup into droplets for low-surface-tension systems such as i-butane/n-butane. The resulting additional interfacial area is available for mass transfer. There appear to be no published data for spray zone mass transfer. Studies by the Separations Research Program have included empty-column contacting of rising vapor with liquid fed through a conventional distributor (430 streams/m2) normally used for packed column work. A maximum of one theoretical stage was obtained at contacting heights in the range of 3.5 m. Clearly, for representative heights of the spray zone in dual-flow trays (less than a tray spacing), one might expect no more than 0.1-0.2 theoretical stages, depending on conditions. At present, any correction with a mass transfer model to account for spray zone transfer must be regarded as empirical. Analysis of the FRI data indicates that up to 0.2 theoretical stages can be achieved in the spray zone, depending on the system and flow conditions. It is prudent, considering the present level of knowledge, to neglect the mass transfer contribution of the spray zone. Froth Zone. Sieve tray mass transfer in the froth zone has been modeled successfully for cross-flow sieve trays. If we assume that mass transfer behavior in a dual-flow froth can be treated the same as in a crossflow froth, as mentioned earlier, then we can estimate the value of the dual-flow efficiency using models developed for cross-flow sieve trays. The point efficiency

FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI FRI

system

C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C4 C4 C4 C4 C4 IPA/H2O xylenes xylenes C8/C10 alcohols FRI C8/C10 alcohols 5 MeOH/H2O FRI MeOH/H2O 2 Bz/Tol

b

hole efficiency, pressure TS % diam peak, calculated (kPa) (m) open (mm) meas (%)b 28 28 28 166 166 166 166 166 345 345 1138 1138 1138 1138 1138 101 16 mm 16 mm 10 mm

0.61 0.61 0.61 0.61 0.61 0.91 0.61 0.61 0.61 0.91 0.61 0.30 0.61 0.61 0.91 0.61 0.61 0.61 0.61

13.5 18.9 25.6 13.5 19.1 19.1 18.9 25.6 18.9 29.3 13.5 19.1 18.9 25.6 29.3 19.1 12.9 17.8 12.9

12.7 25.4 25.4 12.7 12.7 12.7 25.4 25.4 25.4 11.9 12.7 25.4 25.4 25.4 11.0 12.7 12.7 12.7 12.7

79 75 63 83 81 57 81 55 98 67 121 90 115 92 96 75 81 63 72

43 53 54 67 69 71 74 70 75 71 77 71 77 75 74 69 60 62 72

10 mm

0.61 17.8

12.7

42

86

101 101 101

0.41 14.2 0.41 18.2 0.51 14

c c 12.7

82 82 87

80 80 60

a Column diameters: FRI, 1.2 m; ref 5, 1.0 m; ref 2, 0.45 m. Contribution of spray zone not included. c Slots, 4 mm × 150 mm.

model of Garcia and Fair16 was selected as the most recent and extensively tested sieve tray model available. To employ the model, one must utilize a column diameter such that the active (bubbling) area is equivalent (after considering downcomer area) to the total cross-sectional area of the dual-flow tray. The correspondence between modeled and measured peak efficiencies for each system is shown in Table 2. In almost all cases, the predicted value is lower than the observed value, lending some credence to the importance of mass transfer in the spray zone. If a multiplier of 1.2 is used to account for mass transfer in the spray zone, better agreement is obtained, as shown in Figure 11. This multiplier is empirical, based on the earlier discussion, and the modeled efficiency for the froth zone is more fundamental, although more conservative. Clearly, the model prediction must be discounted at lower loadings. The low-load correction is empirical, based on experimental observations. The ratio of corrected efficiency to peak efficiency can be obtained through a rearrangement of eq 3

φ′ )

E ) Ep

1 Ψ′ 1 + Ep 1 - Ψ′

(15)

Values of Ψ′ calculated from experimental data are shown in Figure 12. The scatter indicates that this simplistic approach might neglect some geometric and mechanistic effects. However, prudent tray specifications call for hole sizes in the 12.7-25.4-mm range and open areas in the 15-20% range. The lines in the summary plot (Figure 12d) can be adapted to most practical situations. Tray Geometry Variables In the present study, emphasis has been placed on dual-flow trays with 15-20% open area, 12.7-mm holes,

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Figure 11. Parity plot, predicted vs observed peak efficiency for dual-flow trays.

and tray spacings of 0.5-0.7 m. The reason is that design studies have shown that, for most applications, this is an economical combination of tray geometric variables. For example, Figure 5 shows the capacity advantage of large open area and high tray spacing. However, when mass transfer efficiency and pressure drop are added to the comparison, the extreme cases of geometry might not be optimum. Still, this is a matter for detailed analysis of individual cases. Figure 7 shows the effect of hole diameter on efficiency and pressure drop for the cyclohexane/n-heptane system at 1.63 atm and 19.1% open area. The larger holes have a higher efficiency but also a higher pressure drop. The effect of tray spacing on pressure drop is minor if operation is well below the flood point. Tray spacing can affect the efficiency in that it can provide extra volume for mass transfer in the spray zone. Finally, mention should be made of tray diameter effects. Figure 3 shows a difference between 0.45- and 2.50-m-diameter trays, more in capacity than in efficiency. The importance of maintaining a good liquid

Figure 12. Low-loading discount factor Ψ′ for representative experimental data: (a) 12.7-mm holes, 18-20% open area; (b) 25.4-mm holes, 18-20% open area; (c) 12.7-mm holes or smaller, 13-15% open area; (d) summary plot.

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distribution has been mentioned (spray nozzles are often used to add reflux to the top tray). Zuiderweg et al.2 observed generally higher capacities and lower pressure drops for larger tray diameters, suggesting that the methods given here, largely based on a column diameter of 1.2 m, are somewhat conservative. However, reports of poor dual-flow tray performance for larger diameters and very low flow parameters (as in high-vacuum columns) must be recognized. It is possible that very high volumetric ratios of vapor to liquid create a tendency for the vapor flow to tend toward the center portion of the tray, leading to reduced tray efficiency. Thus, the findings described in this paper should be used with great caution for the low values of the flow parameter LML/VMVxFG/FL. Summary and Conclusions We have proposed a rational method for the analysis and design of dual-flow tray distillation columns. The approach is based on a large number of performance tests under distillation conditions in a large-diameter column. No rational model useful for commercial-scale dual-flow tray column design or analysis has been published previously. We have made suggestions for possible mechanisms of phase contacting in the liquidcontinuous froth as well as in the vapor-continuous spray zone. There is a clear need for additional studies, both experimental and theoretical. The following sequence of steps should be followed in designing or rating dual-flow columns: (1) The column diameter should be determined on the basis of flooding limits and a prudent approach to flooding. (This is the same procedure used for other contacting devices such as cross-flow trays and packings.) An approach to flooding of about 75-80% is in the range of peak efficiency (Table 1). The effect of entrained liquid in the vapor can be used to pinpoint the flooding approach as well as the peak efficiency. (2) The peak efficiency should be modeled by an adaptation of a froth-contacting model for cross-flow sieve trays. To use the model, one needs to know the fraction of holes that are active. Because the model provides only the efficiency in the froth, enhancement of this efficiency can occur through added mass transfer above the froth (spray zone). On the basis of the FRI measurements, the enhanced efficiency can be as much as 1.2 times the modeled efficiency, but until more definitive studies are made, a factor of 1.0 is recommended. (3) The efficiency below the peak point should be obtained by an empirical correction to the peak efficiency. Tentative plots have been provided to enable an estimation of the effect of loading on efficiency. (4) The pressure drop should be calculated on the basis of conventional equations, taking into account the fraction of the total holes passing vapor and the porosity of the froth. This is a pioneering attempt at the modeling of dualflow tray performance. Future studies under distillation conditions might require experimental techniques not yet fully developed, e.g., X-ray tomography to show froth quality changes and the dynamic activity at the holes. Because such work has not yet been effective for the more conventional devices, one might not expect dualflow technology advances soon. Perhaps the work reported here will help reactivate interest in a device that is efficient and inexpensivesand that can operate well under fouling situations.

Acknowledgment This paper would not have been possible without the generous provision of large-scale performance data by Fractionation Research, Inc. (FRI). The authors extend thanks to FRI, as well as to the Separations Research Program at the University of Texas and to Koch-Glitsch, Inc., for providing support for the modeling and analysis effort. Nomenclature A, B, C ) constants in eq 12 Aa ) tray active area, m2 Ah ) tray hole area, m2 At ) total column cross-sectional (superficial) area, m2 Ax ) area of holes open to vapor at any instant ) χAh, m2 b1, b2, b3 ) constants in eq 8 Csb ) Souders-Brown capacity parameter, m/s Cv ) orifice coefficient, eq 6 dh ) hole diameter, mm or m Ep ) peak efficiency, fractional Ew ) efficiency corrected for liquid-in-vapor entrainment, fractional Fs ) vapor F factor based on superficial area, UsFG0.5, m/s (kg/m3)0.5 g ) gravitational constant, m/s2 h ) pressure loss, m of tray liquid hdG ) drop for vapor flow through orifices hL ) residual drop through two-phase mixture hLD ) drop for liquid flow through orifices hL′ ) head required to force liquid through the orifices ht ) total pressure drop for a dual-flow tray ht,meas ) measured total pressure drop for a dual-flow tray hf ) height of froth on the tray, m L ) liquid flow, kg mol/s m ) slope of the equilibrium curve n ) exponent in eq 8 ML, MG ) molecular weights of liquid and vapor, respectively Q ) volumetric flow rate of vapor, m3/s tt ) tray metal thickness, mm TS ) tray spacing, m U ) vapor velocity, m/s Us ) superficial velocity Ux ) velocity through x fraction of total number of holes V ) vapor flow, kg mol/s χ ) fraction of total holes passing vapor at any instant Greek Letters  ) void fraction in the froth λ ) ratio of slopes, equilibrium curve to operating line ) mV/L FL ) liquid density, kg/m3 FG ) vapor density, kg/m3 φ ) ratio of wet efficiency (with entrainment) to dry (peak) efficiency φ′ ) ratio of lower loading efficiency to peak efficiency Ψ ) efficiency discount factor for entrainment in vapor Ψ′ ) efficiency discount factor for lower loadings

Literature Cited (1) Zuiderweg, F. J.; Verburg, H.; Gilissen, F. A. H. Comparison of fractionating devices. Proc. Int. Symp. Distill. 1960, 201. (2) Zuiderweg, F. J.; de Groot, J. H.; Meeboer, B.; van der Meer, D. Scaling up distillation plates. Proc. Int. Symp. Distill. 1969, 5, 78. (3) Huml, M.; Standart, G. The hydraulics of large turbogrid trays. Brit. Chem. Eng. 1966, 11 (11), 1370.

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(4) Kastanek, F.; Huml, M.; Braun, V. Measuring the efficiency of a column of one metre diameter. Proc. Int. Symp. Distill. 1969, 5, 100. (5) Kastanek, F.; Rylek, M. Turbogrid tray efficiencies. Collect. Czech. Chem. Commun. 1970, 35, 3367. (6) Kastanek, F.; Standart, G. Efficiency of selected types of large distillation trays at total reflux. Sep. Sci. 1967, 2, 439. (7) Fractionation Research, Inc., Stillwater, Oklahoma. Research Progress Reports, 1955-1958. Available from Oklahoma State University. (8) Xu, Z. P.; Afacan, A.; Chuang, K. T. Efficiency of dualflow trays in distillation. Can. J. Chem. Eng. 1994, 72, 607. (9) Baird, J. L. Letter to the editor. Chem. Eng. Prog. 1999, 95 (5), 7. (10) Fair, J. R. How to predict sieve tray entrainment and flooding. Petro/Chem Eng. 1961, 33 (10), 45. Also, recent editions of Perry’s Chemical Engineers’ Handbook; McGraw-Hill: New York. (11) Colburn, A. P. Effect of entrainment on plate efficiency in distillation. Ind. Eng. Chem. 1936, 28, 536.

(12) Fair, J. R. Entrainment-efficiency effects on distillation sieve trays. Presented at the AIChE Annual Meeting, Chicago, IL, Nov 15, 1996. (13) Leibson, I.; Kelley, R. E.; Bullington, L. A. How to design perforated trays. Pet. Ref. 1957, 36 (2), 127. (14) Kotschering, N. A.; Oleski, W. M.; Dilman, W. W. Investigation of dualflow tray behavior under distillation conditions. Khim. Prom. 1960, 7, 591. (15) Mahendru, H. L.; Hackl, A. Contribution to the design of sieve trays without downcomers. Inst. Chem. Eng. Symp. Ser. 56 1979, 3.2/35-47. (16) Garcia, J. A.; Fair, J. R. A fundamental model for the prediction of distillation sieve tray efficiency. Ind. Eng. Chem. Res. 2000, 39, 1809 (part 1), 1818 (part 2).

Received for review April 12, 2001 Revised manuscript received December 13, 2001 Accepted December 17, 2001 IE010326W