Ind. Eng. Chem. Process Des. Dev. 1984, 23, 814-819
814 T a b l e VI. P e r c e n t O x i d a t i o n V e l o c i t y of 1500 h-’“
cat. Cu2+-zeolite equilibrium conversion for homogeneous reaction
and modification of the catalyst operating conditions. The appropriate option(s) dependb) upon the cause(s) of catalyst deactivation. Although it may be difficult to find a catalyst that yields nearly complete oxidation of the NO at a space velocity of 1500 h-l or greater, it should be possible to achieve 80 to 90% oxidation with a relatively modest effort. Complete oxidation of NO to NOz may not be required for high NO, removal because Nz03can take part in the absorption of NO,. If N203is absorbed at the same rate as Nz04,it should be possible to obtain more than 90% removal of NO, in a wet scrubber if at least 50% of the NO is oxidized in an upstream catalytic reactor.
of NO t o NOz At a Space 400
O F
60 100
500 O 76 92
F
600 OF 70 79
“5% 0,; 63C-640 ppm NO; balance N2 (volume basis).
was 200 OF for the first three catalysts and 550 O F for the Cu2+-zeolite. The first three catalysts exhibited a decreasing activity after 13 to 15 h as shown in Figure 3, and the Cuz+-zeolitewas deactivated much faster. The causes for this deactivation have not been determined. The experimental results are very encouraging. A Fe20,/MnO/Zn0 catalyst yielded over 70% oxidation of NO to NO2 in simulated flue gas at a temperature of 200 OF and a space velocity of 1500 h-l. The optimum temperature for most of the catalysts tested appears to be around 200 O F . This temperature is very suitable for an add-on process since particulates can be removed in a dry collection device ahead of the catalyst bed. The flue gas can then be spray-cooled to 200 O F with water. After catalytic oxidation of NO to NOz, the flue gas can be sent to a limestone scrubber for removal of SO2and NO2. The scrubber will cool the flue gas to its adiabatic saturation temperature of about 125 OF. The experimental results indicate that species such as SO2and H20, which are present in the flue gas, lower the oxidation level considerably. This effect has previously been reported in the literature and may be explained by adsorption of SO2,HzO,etc., on the catalyst surface so that there is a decrease in the number of available active sites. The experimental results have revealed an additional problem with regard to catalytic oxidation of NO in flue gas. After about 14 h of run time, the catalyst activity starts to decrease. Preliminary investigations have revealed that formation of nitrates occurs on the catalyst surface. Additional work is needed to solve the problem of catalyst deactivation as well as to find a more active catalyst. The options for eliminating catalyst deactivation include selection of a catalyst that does not form nitrate and nitrite salts or sulfate and sulfite salts,modification of the catalyst carrier, modification of the catalyst preparation method,
Acknowledgment
The authors are grateful to Dr. Robert A. Ference of the Climax Molybdenum Company for supplying the molybdenum-containing catalysts and to Mr. Masahi Y amada of Tanaka Kikinzoku Kogyo K. K., Tokyo, Japan, for supplying the platinum-containing catalyst. Registry No. Fe203, 1309-37-1;MnO, 1344-43-0;ZnO, 131413-2; MnOz, 1313-13-9; PbO, 1317-36-8; CuO, 1317-38-0; Sbz03, 1309-64-4; Cr2O3, 1308-38-9; NiO, 1313-99-1; COO, 1307-96-6; Moo3, 1313-27-5;BizO3, 1304-76-3;Vz05, 1314-62-1;NO, 1010243-9; NO,, 11104-93-1;Cr, 7440-47-3; Fe, 7439-89-6 Cu, 7440-50-8; Pt, 7440-06-4.
Literature Cited Arai, H.; Tominaga, H.; Tsuchiya, J. “Proceedings, 6th International Congress on Cataiysis”; Chemical Society, Letchworth, England, 1977; p 997. Hattori, H.; Kawai, M.; Egashlra, S.; Sato, G.; Owaki. N.; Hanada, M.; Kuroda, R.; Kutsukake, M.; Annaka, T. Kogal Hakua Shobo 1977, 12(1), 62. Kotera, T.; Ozasa, M.; Takano, T. Japanese Patent 76 44 558, 1976. McKee, R. H. U.S. Patent 1319322, 1921. Miyadera, T.; Kawai, M.; Hirasawa, S.; Mlyajima, K.; Oyama, M.; Kklo, N.; Yamaraki, M.; Hattori, H.; Kobayashi, H. 32nd Spring Term Annual Meeting of the Japan Chemical Society, Tokyo, Japan, April 1975; Japan Chemical Society: Tokyo, Japan, 1975; Paper 2005 (Japanese). Seiji. A. Kogai Hakua Shobo 1975, 10(1), 32. Takayasu, M.; An-nen, Y.; Morita, Y. Mntyo Kyokai-Shi 1975, 54(11), 930. Takayasu, M.; An-nen, Y.; Morita, Y. Was& Daigaku Rikogaku Kenkyusho Hokoku 1976, 72, 17 (English). Takeyama, F.; Masuda, K.; Takahashi, A. Japanese Patent 7562859, 1975.
Received for review April 22, 1983 Accepted January 25, 1984
This work wm supported by the Tennessee Valley Authority under Contract No. TV-52401A.
Prediction of Point Efficiencies on Sieve Trays. 1. Binary Systems Hong Chan and James R. Fair’ Department of Chemical Engineering, The University of Texas, Austin, Texas 78712
A new model for the prediction of mass transfer efficiency on crossflow sieve trays has been developed. The model is based on twwesistance concepts, takes into account axial dispersion of the flowing froth or spray, and is supported by a large bank of performance data on commercial scale sieve tray columns. The model fits the data sample (143 points) with an average absolute deviation of 6.27%, a great improvement over the only other general model available, that of the AIChE Research Committee. For the same data sample, the latter model gives a fit of 22.9% average absolute deviation.
One of the remaining uncertainties in the design of a sieve tray distillation column is the specification of mass transfer efficiency. Methods for predicting vapor and liquid capacity as well as pressure drop seem fairly well 0196-4305/84/1123-0814$01.50/0
in hand and lead to reliable values for design. Other hydraulic parameters, such as entrainment and weeping flow rates, have been treated previously in the literature, and while published methods for their prediction are not 0
1984 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
particularly reliable, it is possible to “design around them” by planning operation comfortably away from the limits of the flood point and the weep point. The prediction of efficiency, however, remains as a rather approximate exercise and one may assume safely that extra trays are specified for sieve tray columns, to cover up for the lack of prediction reliability. The efficiency specification of a distillation column may be approached in several ways. One way is to utilize field performance data taken for the same system in very similar equipment. Unfortunately, such data are seldom available; when they are available, and can be judged as accurate and representative, they should be used as a basis for efficiency specification. Another way to specify efficiency is to utilize laboratory or pilot plant efficiency data; Fair et al. (1983) have shown that if small Oldershaw tray columns are used for the same system, reliable point efficiency data result, and these data can be used for large-scale design. They must be corrected, of course, for vapor and liquid mixing effects if overall tray efficiencies are to be obtained. Still another approach to efficiency prediction is the use of empirical or fundamental mass transfer models. Empirical models have been presented by Drickamer and Bradford (1943), O’Connell(1946), and Bakowski (1969), among others. They have dealt largely with bubble-cap trays and have not always been validated against largescale data; in general, such models can only be used with healthy safety factors. The lack of available large-scale sieve tray data has indeed blocked the development of more fundamental models for efficiency, and only within recent years have such data become available. Now that there are published data on the efficiency of larger size sieve trays, operated under distillation (as opposed to gas-liquid simulation) conditions, it seems appropriate to ascertain whether these data can be represented by a more fundamental mass transfer model. If they can, and if the data sample is considered general enough, then the process designer is provided with a valuable predictive method. The development and validation of such a method is the subject of this paper.
Previous Work In the mid-1950s there was considerable interest in the modeling of bubble-cap tray efficiencies. It was in this era that Fractionation Research, Inc. (FRI) was formed for the purpose of testing and characterizing fractionation equipment, with the results to be the property of the companies supporting the work; thus there was not an intention to disclose the results publicly. It was also in this era that a number of United States companies jointly sponsored a tray efficiency study program under the aegis of The American Institute of Chemical Engineers (AIChE); results from this work were to be placed in the public domain. The FRI and AIChE program proceeded concurrently, the former utilizing bubble-cap trays in 1.2 m diameter column and the latter employing several small bubble-cap tray simulators plus a 0.61 m diameter distillation column containing bubble-cap trays. The AIChE work culminated with the publication of a final report (AIChE,1958a)and a design manual (AIChE, 1958b). The results of the FRI work were not published, except for some raw data donated to the AIChE program. All of the work described above dealt with bubble-cap trays, and ended effectively at the close of the 1950s. Much has happened in distillation tray development during the past 20 years or so. First, the bubble-cap tray has been largely replaced by the sieve tray, the valve tray, and to some extent other contacting devices such as high-efficiency packing elements. The testing and mea-
815
surement of sieve tray hydraulic parameters has been pursued vigorously by a number of investigators, mostly outside the United States, with a view toward improved understanding of the complex vapor-liquid contacting processes occurring on the trays, and several organizations, among them FRI, have published carefully measured efficiencies of relatively large sieve tray columns. Progress has been made to such an extent that a start can be made toward generalizing a rather difficult two-phase phenomenon, a t least for the crossflow sieve tray context. An in-depth consideration of this particular device is attractive because of its nonproprietary nature. It is not within the scope of this paper to review in detail the published developmental work alluded to above. For perspective, however, the reader might wish to consult the proceedings of the last two International Symposia on Distillation, published by the Institution of Chemical Engineers in 1969 and 1979. The book of Stichlmair (1978), in German, provides a review and interpretation of much of the reported work on sieve trays. A more recent paper, by Molzahn and Wolf (1981),also in German, deals with directions that might be taken in research into several distillation areas. Other standard references, such as Kirschbaum (1969), Perry’s Handbook (19731, and the course notes for the AIChE Today course, “Distillation in Practice” (Bolles and Fair, 1982) provide background and references on the state of the art of distillation tray analysis and design.
Data Bank Before undertaking the development of an efficiency model it was first necessary to survey the available larger-scale data in the open literature. Such data would deal with both hydraulic parameters and mass transfer under distillation conditions and would include measurements thought to be reliable. The first reference meeting these requirements was the 1955 paper by Jones and Pyle. The work was done in the duPont laboratories with a 0.46-m test column, using the acetic acid-water system. The column size was thought to be borderline in connection with scaleup validation. In 1962 Kirschbaum published a variety of sieve tray data, largely for the ethanol-water system, in columns ranging up to 0.76 m in diameter. Because of the absence of a detailed description of equipment or test methods, many of the Kirschbaum data could not be included in the data bank. The first extensive data set, covering several types of trays, was published in 1967 by Kastanek and Standart. This work, carried out in Czechoslovakia, utilized a carefully designed and constructed test system (see Huml and Standart, 1966) having a 1-m column; the methanol/water test mixture was used for all studies. Another valuable set of sieve tray data was provided by BASF in Germany and published by Billet and co-workers (1969). The ethylbenzene/styrene test mixture was used, and results were provided for vacuum operation (13.3 P a ) . Hydraulic data for a 1.22-m column were provided in 1972 by Nutter, along with mass transfer data for stripping ammonia from water with air. In a followup paper, Nutter in 1979 furnished hydraulic data for an air-oil system. The most recent, and perhaps most valuable, sieve tray data have come from the FRI laboratories, in two papers. In a 1979 presentation, Sakata and Yanagi reported on two test mixtures, cyclohexane/n-heptane and isobutane/nbutane, at five widely different pressure levels, thus in effect providing data on five systems. The second paper, by Yanagi and Sakata (1982), covered three of the five systems but with a different tray geometry. The FRI data were taken in a 1.22-m column and, as FRI stated, not
816
Id. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
Table I. Data Bank, Sieve Tray Efficiencies
symbol X
9
6 Y
A 4 [Ii
0
a
+ z X
x x x
m
col. tray open pressure, diam, spacing, area, m m % kP a
system cyclohexane/ n-heptane cyclohexaneln-heptane cyclohexaneln-heptane isobutaneln-butane isobutaneln-butane isobutaneln-butane ethylbenzene/styrene ethylbenzene/styrene methanollwater ethanoliwater cyclohexaneln-heptane cyclohexaneln-heptane cyclohexaneln-heptane isobutaneln-butane acetic acidlwater acetic acidlwater ammonialairlwater
1 65 34.5 27.6 1138 2068 2758 13.1 13.1 101.4 101.4 34.5 34.5 165 1138 101.4 101.4 101.4
1.22 1.22 1.22 1.22 1.22 1.22 0.79 0.79 1.0 0.76 1.22 1.22 1.22 1.22 0.46 0.46 1.22
necessarily for geometries that were optimized for the particular test systems. The sources of sieve tray data are summarized in Table I. Except for the Nutter stripping study, all data are for binary mixtures operated a t total reflux conditions. All trays were of the single crossflow type. Reported efficiencies were either overall column (E,) or overall tray (Murphree, Emv).The symbols shown relate to model validation work described in a later section of this paper.
Model Development For data reported as overall column efficiency E,, conversion to Murphree efficiency of tray n utilizes the Lewis (1936) relationship
where = m(GM/LM)
m=
(2)
an
(3)
[1 + ( a n - 1)xn12 Yn* = Knxn
(4) and x, is the mole fraction of light key in the liquid leaving tray n. Conversion of Murphree efficiency to point efficiency requires models for mixing of vapor and liquid. Examination of test tray geometries led to the conclusion that the vapor was likely to be well-mixed between trays, since trays spacing to diameter ratios were relatively large; a departure from this assumption would not have a large effect on the ultimate model (Diener, 1967). Liquid mixing effects may be accounted for by an eddy diffusion model (AIChE, 1958a)
(5)
nt=
0.61 0.61 0.61 0.61 0.61 0.61 0.50 0.50 0.40 0.15 0.61 0.61 0.61 0.61 0.30 0.46 0.61
8 8 8 8 8 8 13.6 13.6 4.8 9.8 14 14 14 14 8.7 8.7 7.9
hole diam, weir mm h t , c m 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 4.1 2.5 12.7 12.7 12.7 12.7 3.2 3.2 12.7
5.1 5.1 5.1 5.1 5.1 5.1 3.8 1.9 4.0 2.0 5.1 2.5 5.1 5.1 3.8 3.8 5.1
source Sakata and Yanagi (1979) Sakata and Yanagi (1979) Sakata and Yanagi (1979) Sakata and Yanagi (1979) Sakata and Yanagi (1979) Sakata and Yanagi (1979) Billet et al. (1969) Billet e t al. (1969) Kastanek and Standart (1967) Kirschbaum (1962) Yanagi and Sakata (1982) Yanagi and Sakata (1982) Yanagi and Sakata (1982) Yanagi and Sakata (1982) Jones and Pyle (1955) Jones and Pyle (1955) Nutter (1972)
and length of travel Z l is taken as the distance between inlet and outlet weirs of the test tray. For very low values of Pe (high diffusive backmixing), eq 5 reduces to the completely mixed form, Emv/Eov= 1. For very high values of Pe, eq 5 reduces to a plug flow form In (m,, + 1) (8) Eo, =
x
The eddy diffusion coefficient XIE in eq 7 must be measured experimentally. For the present work the experimental correlation of Barker and Self (1962) was chosen as appropriate X I E = 6.675(10-3)Ua1.44 + 0.922(10-3)hL- 5.62(10-3) (9) This correlation is based on work with a rectangular simulator in which air and water were contacted on sieve trays with 4.8 mm diameter holes. Diffusion coefficients were measured by means of a dye tracer technique, and liquid holdup was measured by means of floor manometers. These workers also presented a correlation for liquid holdup hL, but it was considered less general than other available correlations. Thus, eq 9 was used directly; while it does not account for stagnation effects, such effects apparently do not affect efficiency in round columns of the size included in the data bank collection (Porter et al., 1972; Yanagi and Scott, 1973). The average liquid residence time fL in eq 7 is based on holdup in the tray froth
Although several methods have been developed for estimating values of hL, by far the most complete and reliable method is that of Bennett et al. (1983) which is based on studies a t Air Products and Chemicals, Inc., of a broad range of sieve tray holdup data. Components of the model are as follows:
e2( [ 1 + 2]1’21) (6)
where the dimensionless Peclet number is defined as
212 Pe = -
BE~L
(7)
4e = e~p[-12.55K,0~’] C = 0.0327 + 0.0286e-1.378hw K, =
(12)
(13)
ua(L)’” PL - Pv
The second part on the right side of eq 11 is a variant of the Francis weir formula for liquid flow, and takes into
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 817
account the case of froth flowing over an outlet weir. The effective relative froth density 4e is based on an effective froth height that is lower than the observed froth height $e = hL/Zf (15) This is in accordance with observations that (a) the froth is not of uniform height and may peak a t some location on the tray (Hausch, 1964; Andrew, 1969) and (b) the froth has a nonuniform vertical density gradient (e.g., Pinczewski and Fell, 1977). While the Barker and Self holdup values were not included in the study by Bennett et al. (detailed hL values were not reported), the correlation of holdup by Barker and Self was used separately for efficiency calculations and was found not to have any significant effect on the deduced point efficiencies. Once the point efficiency has been deduced from the foregoing relationships it can be re-cast in the form of transfer units No, = -In (1 - Eo,) (16) l/Nov= l/Nv X/NL (17) Equations 16 and 17 are based on transfer unit definitions plus the assumption of upward plug flow of vapor in the froth. Also based on transfer unit definitions Nv = kvuifv (18) NL = k L ~ i f L (19) where the interfacial area ai is taken as the same for both phases. Because the resistance to mass transfer in the liquid phase is normally lower than that in the vapor phase (for distillation), an available correlation is used to obtain values of the volumetric mass transfer coefficient for the liquid, kLai. The correlation selected is that based on the work of Foss and Genter (1956),and presented in modified form in the AIChE final report (1958a) kLai = (0.40Fva+ 0.17)(197a)L1/2) (20) where kLai = volumetric mass transfer coefficient, s-', Fva = active area F-factor, = Uap:/2,m / ~ ( k g / m ~ ) 'and / ~ , .BL = molecular diffusion coefficient, cm2/s. This correlation is based on oxygen-air-water studies in a simulator containing small-hole (4.8 mm) sieve trays with varying weir heights. It is thought to be the most reliable correlation available for predicting liquid phase coefficients. An eddy diffusion coefficient correlation, similar to that of Barker and Self, was used by Foss and Gerster to correct measured tray efficiencies to point efficiencies. Equations 10 and 17-20 may be used to deduce values of the vapor phase volumetric mass transfer coefficient
+
An effective froth porosity may be defined as = 1-
(22) and the average vapor residence time in the froth or spray is n €e
*f
f" = €e -
loova
From eq 15
Finally, by eq 21 1
1
c
0.1
r.2
0.3
0.4 c . 5 f
-
3.6
3.7
c.e
0.9
:c
U&at
Figure 1. General correlation of vapor phase mass transfer coefficients. (See Table I for identification of symbols.)
The foregoing approach provides experimentally based values of the vapor phase coefficient k v q . The next step is to find a method of correlating this coefficient against system, geometry, and flow variables. The interfacial area ai appears not to be a simple function of gas rate and weir height. For the froth regime only, Burgess and Calderbank (1975) and Calderbank and Pereira (1977) found that ai increased with gas rate up to an Fvavalue of about 1.22 m/s (kg/m3)1/2and then leveled off or possibly decreased a t higher rates. Neuberg and Chuang (1982), in work with large sieve trays, found that ai definitely decreased with increasing weir height. Raper et al. (1979) found that in the spray regime interfacial area was largely unaffected by tray geometry variables. On the basis of the above, and at least for the froth regime, it was concluded that the volumetric coefficient kvai should have the following functional dependence kvai = function(.B,, OV, h,, Fva) (25) where OV is the Higbie exposure time for the vapor phase. In fact, for Higbie penetration theory, kvai should be a function of the square root of a),/B,, and 8, should be dependent in some way on gas rate. The weir height dependence in eq 25 should be changed to a liquid holdup dependence to allow for operation under zero-weir conditions; as may be seen from eq 11-13, h, and hL are related, and the latter is strongly influenced by gas velocity
u,.
With this reasoning as a basis, several combinations of the eq 25 variables (with h, replaced by hL) were studied using regression-fit computer routines. The best fit was found with the simple relationship a)v'/2(1030f- 867f2) kvai = (26) (hL)'/2 where f = Ua/ Ud, or fractional approach to the active area gas velocity a t flooding, U,. A plot of the model relationship is shown in Figure 1. For most of the data bank efficiency determinations, liquid entrainment values were not measured. Approximations of the effect of entrainment on efficiency, using the generalized correlation of Fair (1961,19731, agree with the decline of the model curve at gas rates above an approach to flood off = 0.60. This, in turn, indicates that on an entrainment-free basis the curve should be essentially flat (zero slope) a t the higher gas rates. Studies underway a t the University of Texas are aimed a t the reliable prediction of liquid entrainment from sieve trays and should in time permit a more precise correction of "wet" efficiencies to dry efficiencies. Validation of Model The model relationship, eq 26, was obtained from the data plot, Figure 1. The points cover all of the data bank
818
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
... c u r i e ‘rcm Fig 1
u a,
r ‘ A
O
’
2 21
yc,i U
21
; a1
f
u,
baf
Figure 2. Comparison of Nutter data, for ammonia stripping, with general correlation.
d i,
ai 0
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7 3 . 8
0.9
1.0
Eov, o b s e r v e d Figure 4. Parity plot for valid distillation data, present model. (See Table I for symbol identification.)
72
a, f
Le ua
4
a,
Figure 3. Comparison of Yanagi and Sakata data, for pressure operation and high open area trays, with general correlation.
with exceptions as described below. The abscissa is the fractional approach to entrainment flooding as reported by the investigators or, of not reported, based on the highest gas throughout when accompanied by significant entrainment. The flood point as used here is not the true flood condition indicated by a very low efficiency. Rather, it might be regarded as an “incipient flood” that might originate by downcomer backup (for the higher pressure cases) as well as by heavy entrainment. The data of Jones and Pyle included in Figure 1 are for f = 0.5 and greater. A special splash baffle was used to increase liquid holdup at lower gas rates, according to the authors, and the resulting increase efficiencies are judged to be inappropriate for the present correlation for sieve trays not having additional aids for increasing holdup. The data of Nutter are shown in Figure 2. Clearly, the data do not fit the correlation and appear to be based on conditions presenting an unusually high gas phase resistance, or possibly an unexpected liquid phase resistance. A comparison of the Nutter efficiencies with those found in AIChE study (1958a) for ammonia absorption on a tray with small (37 mm diameter) bubble caps shows the latter to be 1.2 to 1.6 times higher, for equivalent weir heights, gas rates, and liquid rates. Had the Nutter data checked the AIChE data, they would have been represented quite well by the present correlation. Yanagi and Sakata reported data on a sieve tray with 14% open area. By all standards this area is much too high for pressure distillation (aswas pointed out by the authors; one purpose of their paper was to show that a large open area would not be optimum for all pressure levels), and relatively poor performance was reported by the authors. A plot of the pressure runs in Figure 3 shows the expected low values of the mass transfer coefficient group. The only other data not originally fitting the correlation are those of Sakata and Yanagi for isobutaneln-butane at 2068 and 2758 kPa. However, these data were found by Hoek and Zuiderweg (1982) to be influenced severely by the entrainment of vapor with the downflow liquid at these high pressures. The correction factors proposed by Hoek
-E
0 E
> 0 W
o u 0 0.1
0.2 0.3 0.4 0 . 5 0.6
0.7
0.8
0.9
0
Eov, observed
Figure 5. Parity plot for valid distillation data, AIChE model. (See Table I for symbol identification.)
and Zuiderweg were applied to the data, and the corrected parameters are now included in Figure 1. Accordingly, the curve of Figure 1, or eq 26, can be regarded as a tentative design method. As mentioned earlier, the lower efficiencies at absicissa values of 0.6 and higher might be attributed to entrainment, and a separate correction for entrainment could be made after assuming a zero slope above f = 0.6. A point efficiency parity plot is shown in Figure 4, covering the data of Figure 1. The plot includes 143 points and the fit is f20% except for six points. The average absolute deviation is 6.27%. The standard deviation is 0.051 based on (Eov,obsd - Eov,modeled)
std dev = L
no. observations
I”‘ J
The only comparable model previously available for estimating k p i was developed in the AIChE program (1958b) for bubble-cap trays. This was an empirical model combining the volumetric coefficient with vapor residence time kvaiE, = N , = [0.776 + 0.O457hw- 0.24Fv, + 104.64,] SC[’/‘ (27) The same data represented in Figure 4 were used to compute point efficiencies using eq 27 (instead of eq 23 and 26), and the resulting parity plot is shown in Figure 5. For this case the average absolute deviation is 22.9% and the
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 819
standard deviation is 0.179. It is clear from a comparison of Figures 4 and 5 that the present model is a better representation of experimental measurements than is the AIChE model.
Conclusions A generalized correlation of vapor-phase mass transfer rate of crossflow sieve trays has been developed, and because of the way in which the rates were deduced, the correlation should be general for the prediction of point efficiency. For use in design, an approximate f20% accuracy is expected for the efficiency prediction. Correction of the point efficiency to overall column efficiency should follow the steps described here, i.e., use of the eddy diffusion mixing model (with coefficients from the Barker and Self correlation) and use of the Lewis equation. Because of the complex mechanism governing the transfer of mass on sieve trays, the correlation must be regarded as tentative and subject to modification as more data become avaliable. However, as shown in Table I, a reasonable range of property, flow, and geometry variables has been covered in the present work, and it appears that the correlation is better than any other available in the open literature. Acknowledgment The authors wish to thank Dr. D. L. Bennett of Air Products and Chemicals, Inc., for making available to them the results of a comprehensive study of sieve tray pressure drop, liquid holdup, and effective froth density.
Nomenclature ai = interfacial area for mass transfer, m2/m3 A , = active, or bubbling, area of tray, m2 C = coefficient in eq 11 (see eq 13), dimensionless BE = eddy diffusion coefficient, m2/s DL = molecular diffusion coefficient, liquid, cm2/s D , = molecular diffusion coefficient, vapor, cmz/s E,, = Murphree tray efficiency, vapor concentration basis, fractional E , = overall column efficiency, fractional E,, = point efficiency, vapor concentration basis, fractional f = fractional approach to flooding, U,/U, F,, = F factor (= Udvl/z)through active area of tray, (kg/ m)'l2/s GM = molar mass velocity of vapor, kg-mol/(s m2) hL = liquid holdup on tray, cm h, = weir height, cm k L = mass transfer coefficient, liquid, m/s k , = mass transfer coefficient, vapor, m/s K = vapor-liquid equilibrium ratio K , = capacity parameter = U a [ p V / ( p-~ P,,I'/~, m/s LM = molar mass velocity of liquid, kg-mol/(s m ) m = slope of equilibrium line, dimensionless n' = term defined by eq 6 NL = number of liquid transfer units No, = number of overall transfer units, vapor concentration basis N , = number of vapor transfer units P e = Peclet number, dimensionless q L = liquid flow rate per unit length of overflow weir, m3/s m Q = liquid rate, m3/s
Sc, = Schmidt number for vapor, dimensionless EL = average liquid residence time, s E, = average vapor residence time, s U, = vapor velocity through active area of tray, m/s Uaf = vapor velocity through active area of tray at flood, m/s x , = mole fraction of light key in the liquid leaving tray n y, = mole fraction of light key in the vapor leaving tray n yn* = mole fraction of light key in the vapor, in equilibrium with exit liquid from tray n Zf = effective height of froth, cm Zl = length of liquid travel, m Greek Letters a, = relative volatility on tray n e, = effective froth porosity, fractional 0, = exposure time for vapor, s X = ratio of slopes of equilibrium line to operating line p L = liquid density, kg/m3 pv = vapor density, kg/m3 4, = effective relative froth density, fractional Literature Cited American Institute of Chemical Engineers (AIChE), "Tray Efficiencies In Dlstiliation Columns", Final report from the University of Delaware, by Gerster, J. A.; Hill, A. B.; Hochgraf, N. N.; and Robinson, D. G.; New York, 1958a. American Institute of Chemical Engineers (AIChE), "Bubble Tray Design Manual"; New York, 1958b. Andrew, S.P. S . I . Chem. E . Symp. Ser. No. 32 1969, 2-49. Bakowskl, S. Br. Chem. Eng. 1969, 74, 945. Barker, P. E.; Self, M. F. Chem. Eng. Sci. 1962, 77, 541. Bennett, D. L.; Agrawal, R.; Cook, P. J. AIChE J. 1983, 29, 434. Billet, R.; Conrad, S.;Grubb, C. M. I . Chem. E . Symp. Ser. No. 32, 1969, 5-111. Bolles, W. L.; Fair, J. R. "Distillation in Practice" (course notes); American Institute of Chemical Engineers: New York, 1982. Burgess, J. M.; Calderbank, P. H. Chem. Eng. Sci. 1975, 30, 743, 1107. Calderbank. P. H.; Pereira, J. Chem. Eng. Scl. 1977, 32,1427. Diener, D. A., Ind. Eng. Chem. Process Des. D e v . 1967, 6 , 499. Drickamer, H.; Bradford, J. R. Trans. AIChE 1943, 39, 319. Fair, J. R., PetrolChem Eng. 1961, 33(10) 45. Fair, J. R. I n "Chemical Engineers' Handbook", 5th ed.,Perry, R. H.; Chiiton, C. H., Ed.; McGraw-Hill: New York, 1973; p 18-13. Fair, J. R.; Null, H. R.; Bolles, W. L. Ind. Eng. Chem. Process D e s . D e v . 1983, 22, 53. Foss, A. S.;Gerster, J. A. Chem. f n g . Prog. 1956, 52(1) 284. Hausch, D. C. Chem. Eng. Prog. 1964, 60(10) 55. Hoek, D. J.; Zuiderweg, F. J. AIChE J. 1962, 28(4) 535. Huml, M.; Standart, G. Br. Chem. Eng. 1966, 77(7) 708. Instltutlon of Chemical Engineers I . Chem. E . Symp. Ser. No. 32,titled "Dlstlllatlon-1969"; Rugby, U.K., 1969. Institution of Chemical Engineers I . Chem. E. Symp. Ser. No. 56, title "Distillatlon-1979"; Rugby, U.K., 1979. Jones, J. B.; Fyle, C. Chem. Eng. Prog. 1955, 57, 424. Kastanek, F.; Standart, G. Sep. Scl. 1967, Z(4) 439. Klrschbaum, E. Chem. Ing. Tech. 1962, 3 4 , 283. Klrschbaum, E. "Destillier- und Rektlfizlertechnlk", 4th ed.; Springer Verlag: Berlin, 1969. Lewis, W. K. Ind. Eng. Chem. 1936, 28, 399. Molzahn, M.; Wolf, D. Chem. Ing. Tech. 1981, 53(10) 768. Neuberg, H. J.; Chuang, K. T. Can. J. Chem. Eng. 1982, 60(4) 504. Nutter, D. AIChE Symp. Ser. No. 724 1972, 68, 73. Nutter, D. I . Chem. E . Symp. Ser. No. 56, 1979, 3.2147. O'Connell, H. E. Trans. AIChE 1946, 42, 741. Perry, R . H.; Chiton, C. H., Ed. "Chemical Engineers' Handbook", 5th ed.; McGraw-Hill: New York, 1973; Section 18. Plnczewski, W. V.; Fell, C. J. D. Trans. Inst. Chem. Eng. 1977, 55, 46. Porter, K. E.; Lockett, M. J.; Lim, C. Trans. Inst. Chem. Eng. 1972, 5 0 , 91. Raper, J. A.; Hal, N. T.; Pinczewski, W. V., Fell, C. J. D. I . Chem. E . Symp. Ser. No. 56 1979, 2.267. Sakata, M.; Yanag!, T. I . Chem. E. Symp. Ser. No. 56 1979, 3.2121. Stichlmalr, J. Die Grundlagen des Ga-Flusslg-Kontaktapparates Bodenkolonne", Verlag Chemle: Weinhelm, 1978. Yanagl, T.; Scott, B. D. Chem. Eng. Prog. 1973, 69(10) 75. Yanagi, T.; Sakata, M. Ind. Eng. Chem. Process Des. Dev. 1982, 27, 712.
Received for review June 2, 1983 Accepted November 28, 1983
