Ind. Eng. Chem. Res. 2000, 39, 1809-1817
1809
A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 1. Database Development J. Antonio Garcia* and James R. Fair Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
A mechanistic model has been developed for the prediction of sieve tray point efficiency for both aqueous and hydrocarbon systems. A forerunner of the model was developed from fundamental relationships by Prado and Fair (Ind. Eng. Chem. Res. 1990, 29, 1031) and was based on gasliquid transfer in systems predominantly air and water. The earlier model has now been modified and extended. Contacting on a sieve tray is considered analogous to gas-liquid contacting in a mechanically agitated vessel, and supporting research has been adapted to the tray-contacting case. Studies in bubble columns have provided information on bubble size distribution and bubble stability at high pressure; these studies coupled with isotropic flow theory have formed the basis for correlating bubble size distribution as well as the fraction of small bubbles in the sieve tray froth. New tray efficiency data taken on a semi-industrial scale have been combined with published data as well as new data released by Fractionation Research, Inc. to form a large database suitable for model testing. This work is covered in part 1. In part 2, details of the new model will be presented along with comparisons of predicted and measured efficiencies. Predicted efficiencies were found to be within (25% of the measured (or deduced) values of the same efficiency. Comparisons are included showing the fit of the same data bank to the earlier model of Chan and Fair. Introduction The cross-flow sieve tray is a popular phase-contacting device for commercial distillation columns. Its nonproprietary nature, simplicity of design, and effectiveness of contacting are some of the attractive features of this device. In addition, technology associated with sieve trays may usually be extended to related devices such as valve trays. The major challenge to more reliable designs of sieve trays is the difficulty of understanding the complex two-phase contacting phenomena that result from varying flow rates of liquid and vapor to and from the tray. The mass-transfer efficiency of a sieve tray is a crucial factor in the analysis of sieve tray columns because it relates theoretical stages to real plates. The first step in the usual procedure for design is the prediction of required theoretical stages to satisfy the target separation; this is normally accomplished with the aid of rigorous models, readily available as components of computer-aided design packages. The next step is the conversion to real plates, which involves evaluating point efficiency (“local efficiency”) followed by translation to an efficiency for the entire plate (“Murphree efficiency”). From the latter efficiency, the required real plates in the column can be calculated readily. While much effort has gone into the prediction of theoretical stages for a required separation, relatively little attention has been given to the conversion to real stages (or plates). In part, this results from the rather formidable problem of understanding the contacting mechanisms in the complex two-phase zone. Point efficiency should be properly based on vapor-liquid mass-transfer fundamentals, whereas conversion to tray * To whom correspondence should be addressed. Dr. Garcia is with Koch-Glitsch, Inc., 4900 Singleton Blvd., Dallas, TX 75212. E-mail:
[email protected].
efficiency is largely a matter of geometry and hydraulics. It is not uncommon for the tray efficiency to be 1.2-1.4 times greater than the point efficiency in larger distillation columns. It is unfortunate that a unit operation as well studied as distillation suffers from the largely unsolved problem of efficiency prediction. This problem has been termed the “last frontier” in the development of distillation technology. Empirical and semiempirical methods have been proposed for the determination of point efficiency, but they have not been based on a fundamental understanding of the transport between phases in the context of the turbulent, two-phase dispersion that occurs on an operating sieve tray. A pioneering effort to understand the mass-transfer mechanism in the dispersion was made by Prado.1 His work elucidated the connection between mass transfer and hydraulics and was summarized in two journal articles.2,3 However, his coverage was limited to systems with air-water properties and has not been extended to nonaqueous systems. The purpose of the present undertaking was to explore possible extensions of the Prado model to cover distillation systems in general. Research Objectives. Modifications of the Prado model were to be based on the following tasks: (1) Compile an external database of sieve tray efficiencies measured in larger scale equipment and covering a range of physical properties. (2) Provide new experimental point efficiency data, obtained in semi-industrial scale equipment, using two well-known test mixtures at several operating conditions. (3) Use a combination of the external and measured data to develop a mechanistic model for point efficiency. The model would be based on a fundamental fluid mechanic and diffusional mechanism and would be generally applicable to distillation column design.
10.1021/ie990875q CCC: $19.00 © 2000 American Chemical Society Published on Web 05/12/2000
1810
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000
Regimes on Sieve Trays. The manner by which liquid and vapor contact each other on a tray determines the interfacial area for mass transfer. Contacting occurs in a vapor-liquid dispersion, the character of which can vary according to the relative flow rates and properties of the phases. It is convenient to describe these dispersions in terms of two-phase regimes. The froth regime is most commonly found, especially in distillation, and is the principal focus of the present work. It is characterized by a liquid-continuous mixture containing a variety of vapor bubble sizes that provide the necessary interfacial area for mass transfer. The bubbles circulate rapidly, undergo coalescence and breakup, and have a wide range of nonuniform shapes and sizes. For unusually high flow ratios of liquid to vapor, a free-bubbling or emulsified regime occurs; this regime may be considered a simple extension of the froth regime because it is liquid-continuous and is comprised of bubbles with decreased mixing energy. For unusually high ratios of vapor to liquid, the dispersion is inverted to a vaporcontinuous mixture, called the spray regime. Here, the liquid entering from the downcomer is atomized by the high energy of the vapor, with coalescence and recirculation feeding the atomization process across the tray. These regimes appear to be an approximate function of the dimensionless flow parameter,
Flv )
( )( ) L FG G FL
1/2
(1)
as discussed by Hofhuis and Zuiderweg4 and analyzed in detail by Lockett.5 The parameter represents a ratio of liquid-to-vapor kinetic energies, and approximate ranges for the regimes are
spray (vapor continuous):
equilibrium between the vapor and liquid at some point on the tray. More specifically, the equilibrium relationship is made between the exit vapor from the liquid froth above the point and the vertical-average liquid composition at the same point. It is usually assumed that the liquid is well mixed vertically, in which case the point efficiency cannot be greater than 1.0. Clearly, the equilibrium can vary across the tray, as the liquid composition varies, so one can visualize a number of different values of point efficiency if there is a variation of liquid composition on the tray. The other efficiency, overall tray efficiency, is often called “Murphree efficiency.” This parameter has a rather arbitrary definition: the approach to equilibrium is based on the average total vapor composition leaving the froth and the total liquid composition leaving the tray. Because of this arbitrariness, the overall tray efficiency value can exceed 1.0. When the liquid and vapor are completely mixed on the tray, with uniform compositions of each, the point efficiency and the tray efficiency are the same. The dilemma facing the researcher in distillation efficiency is that the point efficiency is a much more fundamental criterion of mass transfer, whereas the overall tray efficiency is the value that can be measured, especially for the larger scale distillation columns of interest to the present work. Accordingly, any methodology for predicting large column efficiency must take both of these efficiencies into account, and the major problem can be divided into two parts: (1) Understanding the basic mechanism associated with point efficiency. (2) Determining the concentration gradients across the tray. Point Efficiency. The point efficiency of tray n is expressed by
Flv < 0.01
EOG )
froth (liquid continuous): 0.01 < Flv < 0.10 emulsion or free bubbling:
(
yn - yn-1 yn* - yn-1
)
(2)
point
The efficiency concept is based on two-resistance theory, and is usually expressed in terms of the molar rate of diffusion:
Flv > 0.10
N ) kG′ai(yi - y) ) kL′ai(x - xi)
The transition between spray and froth regimes has been the object of many studies, with the zone of phase inversion usually detected by light-scattering techniques. Prado et al.2 analyzed their own phase inversion data, coupling light-scattering results with bubble frequency measurements, and concluded that the frothspray transition occurs (for increasing gas/liquid ratios) when about 60% of the holes are passing jets rather than bubbles. They also found that parameters such as liquid holdup and pressure drop did not show discontinuities when the regime shifted between froth and spray. As noted earlier, the model for mass transfer presented here is based on a froth, with bubbles in a continuous liquid phase.
Assuming phase equilibrium at the interface, the overall mass-transfer coefficient can be obtained by the sum of mass-transfer resistances represented by the following relationship:
Tray Efficiency Definitions The mass-transfer efficiency of contacting trays may be expressed in several ways, but in this paper only two efficiencies will be used, point efficiency and overall tray efficiency. The former deals with the approach to
1 m 1 ) + KOG kG kL
(3)
(4)
Considering a mass balance across a differential element in the froth of a sieve tray, the expressions for the vapor- and liquid-phase mass-transfer units are
NG ) kGai′tG
(5)
NL ) kLai′tL
(6)
and
It may be noted that kGai′ and kLai′ are volumetric coefficients and are used when the interfacial area ai cannot be determined, and residence times tG and tL depend on the nature and volume of the dispersion as
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000 1811
well as the flow direction of the gas. The number of overall transfer units, based on gas concentrations, follows from the individual phase units:
1 λ 1 ) + NOG NG NL
(7)
Thus, from the above one can see that a continuous contacting approach (use of transfer units) is employed. The point efficiency is next computed from the value of NOG:
EOG ) 1 - exp(-NOG)
(8)
Overall Tray Efficiency. The overall tray efficiency, EMV, is expressed by
EMV )
[exp(λEOG) - 1] λ
(9)
The point and overall efficiencies are the same when the phases in the froth are completely mixed. One might expect this to be the case for small columns and for very high gas-to-liquid ratios for larger columns. When the liquid is in plug flow, the overall efficiency is greater than the point efficiency. If one is to deduce point efficiency values from measured overall efficiency values, then the model involving mixing tendencies must be available. This is discussed in a later section of this paper. Column Efficiency. In practice, this is the efficiency most used and understood. It is simply the ratio of theoretical stages, as determined from the observed separation, to the actual number of plates or trays installed in the column. Recognition can be taken of the ability of a partial condenser or reboiler to produce the equivalent of one or two theoretical stages. At total reflux, column efficiency and overall tray efficiency have values very close to each other. For finite reflux, a relationship developed by Lewis6 may be used to deduce one from the other. Previous Work Several attempts have been made to develop a method for the reliable prediction of distillation column efficiency. Most have been purely empirical (e.g., refs 7 and 8) and have not discriminated between point efficiency, tray efficiency, and column efficiency. They have been useful, however, for quick estimates during process development research. The process designer has used them for orientation purposes, but has relied more heavily on experience or tests with similar systems. This has been the approach of many designers with access to the experimental data of Fractionation Research, Inc. (FRI). An early attempt at a mechanistic model was made by Geddes,9 where bubbling was taken into account, but the bubbles were assumed to rise individually through a quiescent liquid that would in no way resemble the turbulent froth found on operating sieve trays. In later work, Calderbank and associates10,11 sought to identify interfacial area, but the experimental method used could not be extended to systems with nonelectrically conducting liquids. The need for a more reliable efficiency model was felt strongly by the chemical and petroleum industries, and to satisfy this need research at three U.S. universities
was supported by a large consortium of companies, under the aegis of the AIChE; the result was the well-known AIChE model.12,13 This model is based on experiments with small bubble-cap trays using mostly air and aqueous liquids. It is based on the two-film approach, and no attempt has been made to identify the effective interfacial area; hence, volumetric masstransfer coefficients (kGa′ and kLa′) are used. The AIChE work has been reviewed extensively by others (e.g., refs 5, 14, and 15). By 1983 a moderately sized database of commercialscale sieve trays efficiencies could be compiled, some of the data from FRI, and this enabled Chan and Fair16 to extend and modify the AIChE approach to cover sieve tray point and overall tray efficiencies. They also used volumetric coefficients because the effective interfacial area could not be identified. This model has found widespread use and has provided a good fit to a number of larger scale experimental studies (e.g., refs 17 and 18), but its empiricism clearly confines it to systems such as hydrocarbons and light organics. Of special interest to the present work is the research of Prado and colleagues at The University of Texas,1-3 who conducted many tests with small sieve trays using air and water. Mass transfer was measured by oxygen stripping (liquid phase) and dry air humidification (gas phase). They evaluated bubbling and jetting using electrical conductivity probes and looked at several different contacting regimes that could occur on a conventional cross-flow sieve tray. This was a pioneering effort to elucidate the contacting mechanisms and enabled the identification of separate values of interfacial area and mass-transfer coefficients. Different zones of the froth were considered to make different contributions to the overall transfer process. Unfortunately, the experimental technique could not be extended to cases with electrical nonconducting liquids. The basic approach of Prado et al. has been followed in the present work, as stated earlier. The adaptation of that approach to represent systems other than air/ water is elaborated below under Model Development. Efficiency Database Experimental Work. A semi-industrial-scale test system, located at The University of Texas at Austin, was used to provide a base set of point efficiency data. The system has been described previously (e.g., ref 19) and consists of a 0.429-m i.d. column with a full set of auxiliaries including a distributed control system. The trays tested were installed through a top column flange and were arranged as a tray bundle. Proper precautions were made to ensure tight seals at the peripheries of the trays. Tray dimensions are included in Table 1 and Figure 1. It may be noted that a special splash baffle was used, to prevent liquid short circuiting and to promote back mixing of the liquid. For the total reflux experiments, the cyclohexane/nheptane system was used at pressures of 33.3, 165, and 414 kPa. Eight trays were used, located such that the contacting action could be observed through viewing windows. For the stripping experiments, the system water/ethylene glycol was used at pressures of 6.67 and 13.3 kPa. For these tests, five trays were used. Further details of the equipment may be found elsewhere.20 Information on the materials used is given in Table 2. A Fischer-Porter DCI-5000 distributed control system was used for monitoring and control.
1812
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000
Table 1. Dimensions/Geometry of Trays Testeda inside diameter of column, mm tray spacing, mm perforated sheet, material perforated sheet, thickness, mm edge of hole facing vapor flow hole diameter and spacing, mm × mm outlet weir, height × length, mm × mm liquid flow path length, mm inlet weir clearance under downcomer, mm single-downcomer area, m2 effective bubbling area, m2 hole area, m2 splash baffle, width × height, mm × mm
429 457 304 stainless steel 1.5 sharp 4.8 × 14.3 50.8 × 264 (178 × 264)a 241 none 38.1 (140) 0.0104 0.1235 0.0125 278 × 356 (none)a
a Annotations between parentheses correspond to the second set of tests with the cyclohexane/n-heptane system.
Figure 2. Test column and auxiliaries.
Figure 1. Diagram of tray used in distillation and stripping studies. Table 2. Characteristics of Materials Used chemical
ingredients
CAS number
cyclohexane
cyclohexane related compounds
110-82-7 various
n-heptane
n-heptane dimethylcyclopentane isooctane methylcyclohexane other heptanes
142-82-5 28729-52-4 26635-64-3 108-87-2 various
ethylene glycol ethylene glycol diethylene glycol water
67-42-5
wt % >99.0 99.0 0.5 (max) 0.2 (max)
(1) Procedure. When operations were lined out for a specified operating condition, samples were taken at the entrance of the reflux to the top tray and at the seal pan below the bottom tray. Figure 2 provides a general
flow diagram for the experimental system. Steady state was ascertained from hourly samples; generally, 3-4 h was needed to achieve steady state. For cyclohexane/n-heptane, analyses were made with a gas chromatograph (Gow-Mac 550) equipped with a TCD and coupled with a Shimadzu Chromatopac C-R3A data processor, used to analyze the liquid samples. Helium was the gas carrier. The GC column was 10% DC200/500 Chromosorb P. The liquid samples of the water/ethylene glycol system were analyzed with a Hayes Sep D packed column. On the basis of calibrated standards, concentrations were determined within (0.2 wt % for cyclohexane/n-heptane and (0.1 wt % for water/ethylene glycol. (2) Experimental Results. For the cyclohexane/ n-heptane system, theoretical stages were computed rigorously, using equilibrium data recommended by Lenoir and Sakata.21 Efficiencies for total reflux operation are shown in Figure 3. The indicated flood points are based on the entrainment-effect method of Fair.22 Figure 4 shows a comparison between the cyclohexane/ n-heptane data and those for the same system taken in a small Oldershaw column.23 Because the latter are accepted as point efficiencies, it appears that the column used in the present work, with its splash baffle, provided point efficiency data directly. Figure 5 shows efficiencies for the water/ethylene glycol system, with equilibrium data taken from Gmehling et al.24 The same correspondence with small-scale data follows if the results are compared with those of Calderbank and Pereira11 for oxygen/glycerol/water and of Mahiout and Vogelpohl25 for ethylene glycol/air. A few runs were made with a weir height of 177.8 mm using the cyclohexane/n-heptane mixture. As shown in Figure 6, the overall efficiency for these tests was ≈0.40 for F-factors below 2.0 (m/s)‚(kg/m3)0.5. This low efficiency resulted from heavy weeping and vapor flow up the downcomers. However, the efficiency for F-factors above 2.0, when a hydraulic seal had been achieved, reached values similar to those obtained at a weir height of 50.8 mm (around 0.60). Apparently, froth residence times for a vapor and a liquid did not change materially with the 3.5-fold increase in weir height. This has implications for situations where a high liquid residence time is needed for chemical reaction. Details of these tests, including pressure drop results, may be found in Garcia.20
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000 1813
Figure 4. Comparison between efficiencies obtained for different sizes of equipment. Cyclohexane/n-heptane system at total reflux. Data from Nutter and Perry, Sakata and Yanagi, and Yanagi and Sakata corrected to point efficiencies from reported overall tray efficiencies using the method of Bennett and Grimm.34
Figure 5. Efficiencies obtained for stripping tests, water/ethylene glycol system. Weir height ) 51 mm. For other tray dimensions, see Table 1.
Figure 3. Total reflux efficiencies, cyclohexane/n-heptane mixture. Weir height ) 51 mm. For other tray dimensions, see Table 1. (a) 33.3 kPa. (b) 165 kPa. (c) 414 kPa.
Other Data. Most of the efficiencies reported by others are Murphree tray efficiencies, it being difficult to sample locations within a tray to obtain point efficiencies. By far, the simplest and most straightforward experimental approach is to use samples taken from clear liquid at the bottom of downcomers. The resulting overall tray efficiencies are then converted to
Figure 6. Total reflux efficiencies, cyclohexane/n-heptane, 165 kPa, weir height ) 178 mm. Below FA ) 2.0 (m/s) (kg/m3)0.5 downcomers were not sealed. For other tray dimensions, see Table 1.
point efficiencies using an available model. Attempts to take vapor samples on trays have not been successful because of the ever-present liquid.
1814
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000
Table 3. Summary of Tray Efficiency Database source
system
pressure (kPa)
column diameter (m)
tray spacing (mm)
hole area (%)
hole diameter (mm)
weir height (mm)
0.457 0.457
305 457
8.35 8.35
3.18 3.18
38.1 38.1
ref 28
acetic acid/water
101.4 101.4
ref 26
methyl isobutyl ketone/water
101.4
0.457
610
10.7
3.18
14.3
ref 36
2-propanol/water o-/p-xylenes
13.3 2.1
1.220 1.220
610 610
12.7 12.7
4.80 4.80
25.4 25.4
ref 36
n-octanol/n-decanol
1.3 8.0 2.1
1.220 1.220 1.220
610 610 610
13 13 13
12.70 12.70 12.70
25.4 25.4 25.4
ref 29
methanol/water
101.4
0.976
400
4.8
4.00
40.0
ref 30
ethylbenzene/styrene
13.3 13.3
0.788 0.788
500 500
13.6 13.6
12.50 12.50
19.0 38.0
ref 27
ammonia/air/water
ref 31
cyclohexane/n-heptane
o-/p-xylenes
isobutane/n-butane
101.4
1.220
610
7.9
12.70
50.8
27.6 165 1138 2068 2758
1.220 1.220 1.220 1.220 1.220
610 610 610 610 610
8 8 8 8 8
12.70 12.70 12.70 12.70 12.70
50.8 50.8 50.8 50.8 50.8
34 34 165 1138
1.220 1.220 1.220 1.220
610 610 610 610
14 14 14 14
12.70 12.70 12.70 12.70
25.4 50.8 50.8 50.8
0.600 0.600 0.600
340 340 340
12.7 12.7 12.7
4.80 4.80 4.80
50.0 50.0 50.0
ref 32
cyclohexane/n-heptane
ref 17
methanol/water 1-propanol/water methylcyclohexane/toluene
101.4 101.4 101.4
ref 33
cyclohexane/n-heptane
101.4
0.500
610
14
12.70
50.8
present work
cyclohexane/n-heptane
33.3 165 414 165 6.7 13.3
0.429 0.429 0.429 0.429 0.429 0.429
457 457 457 457 457 457
10 10 10 10 10 10
4.80 4.80 4.80 4.80 4.80 4.80
50.8 50.8 50.8 177.8 50.8 50.8
isobutane/n-butane
ethylene glycol/water
Descriptions of tray geometries used for compiling the database are given in Table 3. The test mixtures and operating conditions are summarized in Table 4. All the operating data are for binary systems operated at total reflux, except for the stripping data of Rush and Stirba26 and Nutter.27 Use of total reflux data is not a limiting condition, however, because liquid/vapor flow ratios are accounted for in straightforward relationships. All the trays represented in the database have single cross-flow of the liquid. Jones and Pyle28 published performance data for sieve and bubble-cap trays used to separate water and acetic acid at atmospheric pressure. An important element of their tray geometry was a splash baffle located just upstream of the overflow weir on each tray, designed to prevent incoming liquid from splashing or shortcircuiting the contacting zone and to maintain a constant seal depth. In a follow-up study with the same equipment, Rush and Stirba26 stripped methyl isobutyl ketone (MIBK) from water with steam, at atmospheric pressure. The liquid-to-vapor ratios were high, in the range from 8:1 to 40:1. Kastanek and Standart29 measured the efficiencies of several common tray devices, including sieve trays. An industrial-scale test column of 0.976 m i.d. was operated with the methanol/water test mixture at atmospheric pressure. Billet, Conrad, and Grubb30 reported results for vacuum (13.3 kPa) distillation of the ethylbenzene/styrene system in a 0.788-m column. Total reflux efficiencies were reported for 19- and 38-mm weir heights. Nutter27 published stripping efficiency and hydraulic data for air/ammonia/water at atmospheric
pressure in a 1.22-m column; weeping and entrainment were also investigated. In two important papers Sakata and Yanagi31 and Yanagi and Sakata32 presented data from Fractionation Research, Inc. (FRI) taken in a 1.22-m sieve tray column using the cyclohexane/n-heptane and i-butane/n-butane systems. Five pressures were used to give a broad range of physical properties. Korchinsky et al.17 reported efficiency data for methanol/water, 1-propanol/water and toluene/methylcyclohexane taken at atmospheric pressure in a 0.61-m column. They reported point efficiencies based on average conditions on the trays and used their results to make comparisons between several published models for predicting efficiency. Nutter and Perry33 presented total reflux efficiency data for a cross-flow sieve tray as well as for a fixed valve tray (MVG) using cyclohexane/n-heptane at atmospheric pressure and a 0.50-m column. Weeping and entrainment data were included in their paper. Well after the initiation of the present work, FRI elected to release older experimental results, and these included sieve tray total reflux efficiency data for three systems: n-octanol/n-decanol at 1.33 and 8.0 kPa, ortho/ para xylenes at 2.13 kPa, and 2-propanol/water at 13.3 kPa. All tests were made in the 1.22-m column described by Sakata and Yanagi and Yanagi and Sakata. Because this release made available a rather large body of important test data, the present research program was delayed long enough to include an analysis of the data and insertion into the data bank. (1) Conversion of Overall Efficiencies to Point Efficiencies. For data reported for columns operating
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000 1815 Table 4. Physical Properties and Operating Conditions of Tray Efficiency Database
source
pressure (kPa)
system
liquid density (kg/m3)
gas density (mPa‚s)
liquid viscosity (mPa‚s)
gas viscosity (mPa‚s)
surface tension (mN/m)
gas velocity (m/s)
weir load (m3/h‚mweir)
ref 28
acetic acid/water
101.4
949
0.63
0.289
0.013
55 55
0.76 0.94
4.24 4.51
0.80 0.97
4.41 4.67
ref 26
methyl isobutyl ketone/water
101.4
959
0.59
0.289
0.013
36
0.87 2.59 1.28 2.64
2.50 4.30 2.53 5.01
13.13 7.87 4.85 3.00
37.89 13.05 9.60 5.70
ref 36
2-propanol/water o-/p-xylenes
13.3 2.1
802 845
0.27 0.12
1.562 0.515
0.009 0.007
21 26
1.64 2.04
4.10 7.87
2.74 1.28
6.83 6.20
ref 36
n-octanol/n-decanol
1.3 8.0 2.1
775 750 847
0.07 0.34 0.11
1.170 0.655 0.532
0.007 0.008 0.007
19 17 27
2.58 0.60 1.83
7.77 4.35 6.76
0.89 1.94 1.10
4.26 9.03 4.35
101.4
940
0.83
0.380
0.011
39
0.51
1.35
1.37
3.64
13.3
850 847
0.48 0.48
0.377 0.377
0.008 0.008
25 25
0.93 0.95
4.27 4.24
1.80 1.85
9.42 9.27
o-/p-xylenes ref 29
methanol/water
ref 30
ethylbenzene/styrene
ref 27
ammonia/air/water
101.4
998
1.17
1.000
0.018
71
0.54 1.28 1.24
2.92 2.82 2.90
13.08 26.16 25.75
13.08 26.16 26.54
ref 31
cyclohexane/n-heptane
27.6 165
715 658
0.94 5.05
0.370 0.271
0.007 0.008
20 14
0.65 0.32
2.63 1.45
2.95 7.66
14.91 36.49
ref 31
isobutane/n-butane
493 424 430 374 388
28.04 57.58 54.93 88.11 81.44
0.090 0.065 0.065 0.050 0.050
0.010 0.010 0.010 0.011 0.011
5 3 3 1 1
0.07 0.04 0.04 0.03 0.02
0.40 0.14 0.14 0.07 0.07
13.86 18.60 17.87 21.28 14.01
75.59 63.03 56.99 54.34 45.64
714 708 649 490
1.14 1.15 5.09 28.93
0.340 0.377 0.264 0.090
0.007 0.007 0.008 0.009
19 19 14 5
1.38 1.91 0.16 0.07
1.38 2.93 1.66 0.40
5.99 9.01 4.01 13.80
5.99 15.37 39.04 76.35
1138 2068 2758
ref 32
cyclohexane/n-heptane
34 165 1138
isobutane/n-butane ref 17
methanol/water 1-propanol/water methylcyclohexane/toluene
101.4 101.4 101.4
895 875 760
0.96 1.06 3.01
0.455 0.300 0.257
0.011 0.012 0.009
30 27 18
2.15 1.54 1.09
2.65 2.31 1.20
2.04 1.33 4.60
3.07 1.80 5.27
ref 33
cyclohexane/n-heptane
101.4
666
3.05
0.302
0.009
15
0.40
1.81
3.29
15.08
present work
cyclohexane/n-heptane
33.3 165.0 414.0 165 6.7 13.3
0.340 0.271 0.179 0.271 1.444 1.114
0.007 0.008 0.009 0.008 0.012 0.012
17 14 10 13 41 39
0.72 0.39 0.23 0.92 4.57 2.98
2.00 0.82 0.43 1.00 10.67 5.15
2.16 5.05 7.81 12.26 6.51 8.30
6.25 10.6 14.4 13.43 13.61 14.29
ethylene glycol/water
664 661.321 607.376 661 1049 1040
1.19 5.01732 12.1754 5.02 0.08 0.16
at other than total reflux, conversion of overall column efficiency to overall tray efficiency requires use of the following relationship,6
EMV )
[
]
λEOC - 1 λ-1
(10)
where
Gm λ)m Lm
improvements over earlier models: it has a phenomenological basis, not limited to air/water, and when it is compared with axial mixing data, it gives significantly lower average actual and relative errors, and a lower standard deviation of the actual error, than the other models. An eddy diffusion coefficient is needed and is taken as a function of the height of the two-phase (froth) layer:
De ) 0.02366[h2φ]3/2[g]1/2 (11)
and m is the slope of the equilibrium curve. For many cases, the average slope of the curve is about unity, and because for total reflux Lm ) Gm, the value of EOC is not greatly different from EMV. When one is converting from Murphree efficiency to point efficiency, a relationship is needed that properly takes into account concentration gradients caused by vapor and liquid mixing. For the present work, neither complete mixing nor plug flow was assumed, and the relationship of Bennett and Grimm34 was adopted. The Bennett/Grimm model was selected because it offers two
(12)
The value of h2φ is determined from individual heights of vapor-continuous and liquid-continuous regions, obtained by the method of Bennett et al.35 The average residence time of the liquid, tL, on the tray is based on a hold-up correlation given in that paper. The eddy coefficient is used in determining the dimensionless Peclet number,
PeL )
[ ] LT2 DetL
(13)
where LT is the length of travel across the tray. Clearly, short travel lengths and high eddy diffusion coefficients
1816
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000
promote back mixing, and as PeL f 0, EOG ≈ EMV. When the liquid is in pure plug flow, De ) 0 and PeL approaches infinity. In this case,
EMV )
[exp(λEOG) - 1] λ
(9)
For intermediate cases (between plug flow and complete mixing), the back-mixing model developed by the AIChE distillation research program is used (see ref 12.) Values of the resulting point efficiency, EOG, backcalculated for all database points according to the procedure outlined above, will be shown later where they are plotted against the vapor kinetic energy term called the F-factor, defined as follows,
FA ) UAxFG
(14)
where UA is the superficial vapor velocity over the active area, with the volumetric flow determined below the tray bundle, and FV is the vapor density. Summary and Conclusions A database has been compiled on the basis of experimental efficiency studies representing a variety of test mixtures, column sizes, sieve tray designs, and operating conditions. The data have been restricted to larger diameter tests columns, 0.4 m and greater, so that a resulting correlation of the data might readily be useful for commercial design purposes. As will be shown in part 2, reported efficiencies have been converted to point efficiencies, to satisfy the need for fundamental masstransfer analysis. One important source of the data is the experimental work of the authors, taken in equipment which provides direct values of the point efficiency. The database of 233 efficiency values has been checked carefully and is the basis for checking predictions from a new efficiency model, to be described in the second part of this paper. Acknowledgment This work was funded by Grant 63172 from the Consejo Nacional de Ciencia y Tecnologı´a (CONACYT) and by the Separations Research Program at The University of Texas at Austin. Assistance in the experimental work was provided by Joe Snyder, Robert Montgomery, and Steve Orwick. The authors are grateful for these supporting contributions. Nomenclature ai ) interfacial area for mass transfer, m2 ai′ ) interfacial area per volume, m2/m3 AA ) active (bubbling) area on tray, m2 De ) eddy diffusion coefficient, m2/s EMV ) overall tray efficiency (“Murphree efficiency”), fractional EOC ) overall column efficiency, fractional EOG ) point efficiency (gas concentrations), fractional EOG,dry ) point efficiency (gas concentrations), no entrainment or weeping, fractional Flv ) flow parameter (eq 1), dimensionless FS ) F-factor based on total (superficial) cross section of column, (m/s)‚(kg/m3)0.5 FA ) F-factor based on active (bubbling) area of column, (m/s)‚(kg/m3)0.5
g ) gravitational constant, m/s2 G ) gas mass flow rate, kg/s Gm ) molar flow rate of gas, kg‚mol/s h2φ ) height of two-phase layer on tray, m kg ) gas-phase mass-transfer coefficient, m/s kg′ ) gas mass-transfer coefficient, kg‚mol/s‚m2 kL ) liquid-phase mass-transfer coefficient, m/s kL′ ) liquid-phase mass-transfer coefficient, kg mol/s‚m2 KOG ) overall mass-transfer coefficient, gas concentration basis, kg‚mol/s‚m2 L ) liquid mass flow rate, kg/s Lm ) molar flow rate of liquid, kg‚mol/s LT ) length of liquid path across tray, m m ) slope of equilibrium curve, dy*/dx N ) molar flow rate, kg‚mol/s NG ) number of gas-phase mass-transfer units NL ) number of liquid-phase mass-transfer units NOG ) number of overall transfer units (gas concentration basis) PeL ) Peclet number, (eq 13), dimensionless tG ) residence time of gas in the two-phase mixture, s tL ) residence time of liquid in the two-phase mixture, s UA ) gas velocity based on active area, m/s y ) mole fraction in gas y* ) mole fraction in gas, in equilibrium with liquid concentration x x ) mole fraction of liquid Subscripts i ) interface n ) tray n n - 1 ) tray above tray n Greek Letters λ ) ratio of slopes, equilibrium to operating line ) m/ (LM/GM) FG ) gas density, kg/m3 FL ) liquid density, kg/m3
Literature Cited (1) Prado, M. The Bubble-to-Spray Transition on Sieve Trays: Mechanisms of the Phase Inversion. Ph.D. Dissertation, The University of Texas at Austin, Austin, TX, 1986. (2) Prado, M.; Johnson, K. L.; Fair, J. R. Bubble-to-Spray Transition on Sieve Trays. Chem. Eng. Prog. 1987, 83 (3), 42. (3) Prado, M.; Fair, J. R. Fundamental Model for the Prediction of Sieve Tray Efficiency. Ind. Eng. Chem. Res. 1990, 29, 1031. (4) Hofhuis, P. A. M.; Zuiderweg, F. J. Sieve Plates: Dispersion Density and Flow Regimes. Inst. Chem. Eng. Symp. Ser. 1979, 56,2.2/1. (5) Lockett, M. J. Distillation Tray Fundamentals; Cambridge University Press: Cambridge, UK,1986. (6) Lewis, W. K. Plate Efficiency of Bubble Cap Columns. Ind. Eng. Chem. 1936, 28, 399. (7) Drickamer, H. G.; Bradford, J. R. Overall Plate Efficiency of Commercial Hydrocarbon Fractionating Column as a Function of Viscosity. Trans. AIChE 1943, 39, 319. (8) O’Connell, H. E. Plate Efficiency of Fractionating Columns and Absorbers. Trans. AIChE 1946, 42, 741. (9) Geddes, R. L. Local Efficiencies of Bubble Plate Fractionators. Trans. AIChE 1946, 42, 79. (10) Burgess, J. M.; Calderbank P. H. The Measurement of Bubble Parameters in Two-Phase Dispersions. I. The Development of an Improved Technique. Chem. Eng. Sci. 1975, 30, 743; Chem. Eng. Sci. 1975, 30, 743; II. The Structure of Sieve Tray Froths. Chem. Eng. Sci. 1975, 30, 1107. (11) Calderbank, P. H.; Pereira, J. A Micro-Processor System to Monitor Plate Efficiencies. Applications to the Study of Surface Tension and Viscosity Effects. Inst. Chem. Eng. Symp. Ser. 1979, 56, 2.3. (12) American Institute of Chemical Engineers. Bubble Tray Design Manual; AIChE: New York, 1958.
Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000 1817 (13) American Institute of Chemical Engineers, Research Committee. Tray Efficiencies in Distillation Columns; AIChE: New York, 1958. (14) Kister, H. Z. Distillation Design; McGraw-Hill: New York, 1992. (15) Klemola, K. T.; Ilme, J. K. Tray Efficiency Prediction of an Industrial Distillation Column. In Acta Polytechnica Scandinavica; Chemical Technology Series No. 250; Finnish Academy of Technical Science: Espoo, Finland, 1997. (16) Chan, H.; Fair, J. R. Prediction of Point Efficiencies on Sieve Trays. 1. Binary Systems. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 814. (17) Korchinsky, W. J.; Ehsani, M. R.; Plaka, T. Sieve Plate Point Efficiencies: 0.6 m Diameter Column. Trans. Inst. Chem. Eng. 1994, 72A, 465. (18) Klemola, K. T.; Ilme, J. K. Distillation Efficiencies of an Industrial-Scale i-Butane/n-Butane Fractionator. Ind. Eng. Chem. Res. 1996, 35, 4579. (19) Fair, J. R.; Bravo, J. L. Distillation Columns Containing Structured Packing. Chem. Eng. Prog. 1990, 86 (1), 19. (20) Garcia, J. A. Fundamental Model for the Prediction of Sieve Tray Efficiency: Hydrocarbon and Aqueous Systems. Ph.D. Dissertation, The University of Texas at Austin, Austin, TX, 1999. (21) Lenoir, J. M.; Sakata, M. The Correlation of Vapor-Liquid Equilibria Used To Determine Tray Efficiencies. Ind. Eng. Chem. Fundam. 1978, 17, 71. (22) Fair, J. R. Distillation. In Handbook of Separation Process Technology; Rousseau, R., Ed.; John Wiley: New York, 1987; pp 286-287. (23) Fair, J. R.; Null, H. R.; Bolles, W. L. Scale-up of Plate Efficiency from Laboratory Oldershaw Data. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 53. (24) Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt, Germany, 1977 (continuing series). (25) Mahiout, S.; Vogelpohl, A. Mass Transfer of Highly Viscous Media on Sieve Trays. Inst. Chem. Eng. Symp. Ser. 1987, 104, A495.
(26) Rush, F. E.; Stirba C. Measured Plate Efficiencies and Values Predicted from Single-Phase Studies. AIChE J. 1957, 3, 336. (27) Nutter, D. E. Ammonia Stripping Efficiency Studies. AIChE. Symp. Ser. 1972, 124, 68. (28) Jones, J. B.; Pyle, C. Sieve and Bubble-Cap Plates. Chem. Eng. Prog. 1955, 51, 424. (29) Kastanek, F.; Standart, G. Studies on Distillation. XX. Efficiency of Selected Types of Large Distillation Trays at Total Reflux. Sep. Sci. 1967, 2, 439. (30) Billet, R.; Conrad, S.; Grubb, C. M. Some Aspects of the Choice of Distillation Equipment. Inst. Chem. Eng. Symp. Ser. 1969, 32, 5:111. (31) Sakata, M.; Yanagi, T. Performance of a Commercial Scale Sieve Tray. Inst. Chem. Eng. Symp. Ser. 1979, 56, 3.2/21. (32) Yanagi, T.; Sakata, M. Performance of a Commercial Scale 14% Hole Area Sieve Tray. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 712. (33) Nutter, D. E.; Perry, D. Sieve Upgrade 2.0sThe MVG Tray. Presented at the Spring 1995 AIChE Meeting, Houston, TX, 1995. (34) Bennett, D. L.; Grimm, H. J. Eddy Diffusivity for Distillation Sieve Trays. AIChE J. 1991, 37, 589. (35) Bennett, D. L.; Agrawal, R.; Cook, P. J. New Pressure Drop Correlation for Sieve Tray Distillation Columns. AIChE J. 1983, 29, 434. (36) Fractionation Research, Inc. Research Progress Reports for June and July 1966. Obtainable from Oklahoma State University Archives, Stillwater, OK.
Received for review December 2, 1999 Revised manuscript received April 5, 2000 Accepted April 8, 2000
IE990875Q
