Znd. Eng. Chem. Res. 1990,29,1031-1042
2,g-xylenol and rearrangement of 4-methylphenyl tertbutyl ether to 2-tert-butyl-p-cresol. It is possible to selectively remove p-cresol by low-temperature O-alkylation with isobutylene, and the 98:2 mixture of 2,6-xylenol to p-cresol could be refined to 99.802 (w/w). The C-alkylation of 2,6-xylenol took place to a very small extent of about 5%. 2,6-Xylenol of purity higher than 99.8% can be recovered from the xylenol/ether mixture by distillation. The yield of 2,6-xylenol on separation was about 95% as a small amount of 2,6-xylenol was C-alkylated during the process. This method is expected to have wider utility. Conclusions The separation of close boiling point isomeric phenols, such as m- and p-cresols and 2,5- and 2,4-xylenols, was accomplished through a novel strategy of alkylation/dealkylation. From a 5050 mixture of m- and p-cresols, 98% pure m-cresol was recovered; from a 50:50 mixture of 2,5and 2,4-xylenols, 99% pure 2,5-xylenol was obtained. Higher purity materials can be obtained. The product distribution in alkylation of an equimolar mixture of 2,6-xylenol and p-cresol was greatly influenced by the choice of the catalyst. A technical grade 2,6-xylenol containing 98% 2,6-xylenol and 2% p-cresol was refined to give 2,6-xylenol of purity >99.8% by the selective O-alkylation of p-cresol with isobutylene in the presence of acid catalysts. Acknowledgment
B.C.and A.A.P. are thankful to the University Grants Commission, New Delhi, for the award of Senior Research Fellowship. Nomenclature [AMS] = concentration of a-methylstyrene, kmol/m3 [AM& = initial concentration of a-methylstyrene, kmoi/m3 K1 = second-order rate constant in eq 1, m3/(kmol-s) Kz = second-order rate constant in eq 2, m3/(kmol.s) [MC] = concentration of m-cresol, kmol/m3 [MC], = initial concentration of m-cresol, kmol/m3 [OCPC] = concentration of o-cumyl-p-cresol, kmol/m3 [PC] = concentration of p-cresol, kmol/m3 [PC], = initial concentration of p-cresol, kmol/m3 [PCMC] = concentration of p-cumyl-m-cresol, kmol/m3
1031
Registry No. PCP, 599-64-4; AMs,98-83-9; DIB,25167-70-8; pTSA, 104-15-4; Amberlyst 15,9037-24-5; isobutylene, 115-11-7; biphenol A, 80-05-7; m-cresol, 108-39-4; p-cresol, 106-44-5; 2,5xylenol, 95-87-4; 2,4-xylenol,105-67-9; 2,6-xylenol, 576-26-1; p cumyl-m-cresol,27421-06-3; o-cumyl-p-cresol,2675-76-5.
Literature Cited Babin, E. P.; Dzhafarova, N. A.; Fanaliev, Y. M.; Allakhverdiev, M. A. Certain kinetic relationship of cycloalkylation of phenol and ita homologs. Zh. Prikl. Khim. 1985,58 (2), 424-427. Chaudhuri, B.; Sharma, M. M. Paper submitted for publication, 1990. Ciernik, J.; Spousta, E. Czech. Patent 230,842, 1986; Chem. Abstr. 1986,105, 152704. Ciernik, J.; et al. Czech. Patent 240,893, 1988; Chem. Abstr. 1988, 109, 210689. Cislak, F. E.; Otto, M. M. US. Patent 2,432,062,1948; Chem. Abstr. 1948,42, 1967. Engel, K. H. U.S. Patent 2,095,801, 1937; Chem. Abstr. 1937, 31, 88949. Fleischer, J.; Meier, E. Ger. Patent 1,215,726, 1966; Chem. Abstr. 1967,65, 5401. Gaikar, V. G.; Sharma, M. M. Dissociation extraction: prediction of separation factor and selection of solvent. Solvent Extr. Ion Exch. 1985,3,679-696. Gaikar, V. G.; Sharma, M. M. Extractive separation with hydrotropes. Solvent Extr. Ion Exch. 1986, 4, 839-846. Gaikar, V. G.; Sharma, M. M. Dissociation extractive crystallization. Ind. Eng. Chem. Res. 1987,26, 1045-1048. Gurvich, Ya. A.; et al. Zh. Org. Khim. 1985,21,411 (Russian); Chem. Abstr. 1985, 103, 36885. Ludewig, R.; Wilke, H. U.S. Patent 3,193,585, 1965; Chem. Abstr. 1965,63,6262. Orlova, 0. S.; et al. Khim. Prom. SSSR 1975, 1 , 20; Chem. Abstr. 1975,82, 124959. Othmer, D. F.; et al. Composition of vapors from boiling binary solutions. Ind. Eng. Chem. 1949, 41, 572-574. Santhanam,C. J. Br. Patent 1,191,631,1970; Chem. Abstr. 1970,73, 14466. Savitt, S. A.; Othmer, D. F. Separation of m- and p-cresols from their mixtures. Ind. Eng. Chem. 1952,44, 2428-2431. Schnell, D.; Krimm, H. Formation and cleavage of dihydroxydiaryl methane derivatives. Angew. Chem., Int. Ed. Engl. 1963, 2, 373-379. Stevens, D. R. Separation of individual cresols and xylenols from their mixtures. Ind. Eng. Chem. 1943, 35, 655-660.
Received for review August 4, 1989 Revised manuscript received December 4, 1989 Accepted January 4, 1990
Fundamental Model for the Prediction of Sieve Tray Efficiency Miguel Prado and James R. Fair* Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
Fundamental considerations of sieve tray hydraulics, such as hole activity (jet and bubble formation), bubble sizes and rise velocities, and average void fraction have been combined with diffusional mechanisms t o develop a model for predicting mass transfer on an active sieve tray. Experiments were conducted to support model development. A computer-based data acquisition circuitry was designed and built to monitor digitally and simultaneously eight electroresistivity probes, independently located in separate holes of a sieve tray of an air-water simulator. With this monitoring system, it was possible to determine bubble size formation distributions and, importantly, the fraction of active holes that were either jetting or bubbling under a given set of hydrodynamic conditions. In addition, concurrent gas- and liquid-phase resistant mass-transfer efficiencies were measured. The crossflow sieve tray is a common type of device used for vapor-liquid contacting in distillation columns. Its purpose is to promote intimate contacting of the phases and thus to encourage rapid transport of material between 0888-5885/90/2629-lO31$02.50/0
the phases. The transport process is visualized as diffusional movement of molecules to and across the phase boundary, and therefore, the rate of transport is considered to be directly proportional to the extent of the interfacial 0 1990 American Chemical Society
1032 Ind, Eng. Chem. Res., Vol. 29, No. 6, 1990 1.0 t
area as well as to hydrodynamic factors that promote turbulent transport to and from the interface-or to some laminar-like region adjacent to the interface. It is clear that the mass-transfer efficiency of distillation devices is closely associated with the fluid mechanics that prevail in the contacting region, and for certain types of packing devices, this association has been developed profitably (Bravo et al., 1985). However, for tray-type devices, the efficiency models currently available have little relationship with fluid mechanics, other than in rather empirical ways. The purpose of this research was to develop an efficiency-prediction model that is based on more fundamental considerations of the mechanics of fluid-phase contacting. The model would be limited to crossflow sieve trays but might have possible extensions to other crossflow devices such as bubble-cap trays and valve trays. The model would take into account the nature of the two-phase mixture that is generated on the tray and the extent to which interfacial area is created. It would, hopefully, permit the decoupling of the mass-transfer coefficient and the interfacial area terms, so commonly held together because of shortcomings in knowledge of the phase boundary across which material must pass, Previous Efficiency Models The general topic of distillation tray efficiency has been the inspiration of many studies and published reports. Reviews of the literature have been provided by Geddes (1946), Gerster (1963), Fair (1984), and Lockett (1986), among others. The first attempt at fundamental modeling was by Geddes (1946), and others have followed (e.g., Hughmark, 1971; Burgess and Calderbank, 1975; Stichlmair, 1978; Neuberg and Chuang, 1982; Zuiderweg, 1982). All of these models resort to empirical means for dealing with the separate mass-transfer resistances of the vapor and liquid phases, and they do not take into account the different two-phase contacting regimes that can prevail on a crossflow tray. These regimes, ranging from a vapor-continuous “spray” at high vapor/liquid ratios to “froth” and “bubbling” at lower ratios, have been studied by many workers with the object of predicting the type of regime as a function of flow and property parameters. None of the studies, however, have attempted to relate the regime type to the mass-transfer efficiency. As a starting point in the present work, the physical mechanisms underlying the creating of the various regimes were investigated. Contacting Regimes Studies of the nature of the two-phase mixture produced on sieve trays have generally employed the air-water system and have used light-scattering techniques to determine points or zones of phase change. For example, light is transmitted more easily through a spray regime than through a froth regime. An example of the change of light transmission is shown in Figure 1(Ruchirote, 1985). In an earlier paper (Prado et al., 1987),the present authors discussed the studies of others in this connection and contributed data of their own for the air-water, &mineral spirits, and ail-glycerin systems. They then coupled their light transmission experiments with additional experiments to ascertain the nature of vapor evolution from sieve tray holes, to elucidate the connection between initial vapor dispersion and the resulting type of two-phase regime. Their experimental equipment for the latter experiments will be described below. Typical results are shown in Figure 2. It is important to note that a given hole on an operating sieve tray can function in four possible ways:
35
I
t 30 0.1
,QMQ
Fraction of Liquid Entrained
7
e-Q I
-/
25
I /
I
0.01 :
0.001
/
/
y
20
el
15
Transmission Probe Current, mA
+-+-+-
&
+- +-+
Liquid Holdup, \A mm Liquid
10
0.0001 r
5
0.00001 1
-
I
I
I
I
1
1.25
1.50
1.75
0
F - Factor, us pd”, mis (kg/m3f”
Figure 1. Results of experiments showing change of two-phase regime on a sieve tray. Air-water system; hole diameter, 6.35 mm; weir height, 26 mm; tray spacing, 0.61 m; liquid rate, 1.536 m3/(h m of weir); tray open area, 10.1% of active (perforated) area (Ruchirote. 1985).
6
80 Jetting
E
F
m“
c
C
a,
p
40
a,
a
al
Small
5. 20
E
0
1 .o
1.5
2.0
2.5
3.0
3
3
Superficial F - Factor, us pd”, mk (kg/m3f”
Figure 2. Sample percentage of jetting, large bubbling, small bubbling, and liquid cover for a sieve tray with 6.35-mm holes. Airwater system; weir height, 26 mm; liquid rate, 0.0015 m3/(s m of weir) (Prado et al., 1987).
Jetting. A continuous jet is formed, in turn breaking up into bubbles of different sizes. Bubbling. Bubbles are formed at the holes, with distributions tending to be binodal, as “large” and “small” bubble sizes. Liquid Cover. Liquid covers the hole but does not weep through it; the hole is essentially inactive. Weeping. Liquid flows through the hole, not only preventing it from contributing to the mass-transfer process but also creating a recycle of liquid that detracts from the driving force needed in the overall transfer process. An important conclusion of the authors was that there is not a discontinuity in the transitions between jetting and bubbling processes. They found that, at about 5 0 4 0 %
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 1033 Entrainment Baffle
II 1
Entrainment Tray
Table I. Tray Geometries AF, % h ~ m m DH," 12.7 10.7 25.4 12.7 10.7 50.8 76.2 12.7 10.7 12.7 5.9 25.4 12.7 5.9 50.8 12.7 5.9 76.2
D ~ , m m Ap, % 6.35 11.0 6.35 11.0 6.35 11.0 6.35 5.0 6.35 5.0 6.35 5.0
hw,mm 25.4 50.8
76.2 25.4 50.8
76.2
I
Llquid Dlrtrlbutor-+
oo:Q
Brass screws 8 mm
Front view Alr Box
Chamber Volume
=
Front view without front panel
Air Box n
0.042 m3
Stationary
II
+
A
Suctio (entrai hu
500-1 000 rpm
Figure 3. Main body of sieve tray simulator.
jetting, a detectable change in light transmission occurred, and this was consistent among the papers of several authors studying the phase inversion phenomena. For the purposes of the present study of efficiency modeling, this clears the phase regime question from further consideration. Experimental Work This work was carried out in a small +water simulator that could be equipped with any of several different sieve trays. The main body of the simulator had a 0.3-m2cross section. The front face consisted of a transparent and removable acrylic sheet which enabled visual observation of the phase-contacting mechanisms. The lower section consisted of two air boxes which provided for an equal split of the incoming air stream. The chamber volume below the test tray, as indicated in Figure 3, was 0.042 m3. Two heavy mesh screens between the air boxes and the test tray ensured proper air distribution. The test tray inlet downcomer was fitted with a uniform fine hole plate to serve as a liquid distributor. The test tray drain was large enough to accommodate up to 11 m3/(h m of weir). Further details may be found in Prado (1986). Following the recommendation of Jeronimo and Sawistowski (1979), a splash baffle was installed in front of the outlet weir to simulate the conditions present in large columns. To prevent half- and full-wave oscillations, perpendicular to the direction of liquid flow, a screen baffle was placed along the centerline of the liquid flow according to the criterion set forth by Biddulph and Stephens (1974). The tray geometry parameters that could be varied in the simulator were tray hole diameter, tray free area, and weir height. The combinations of tray geometry studied, all of which correspond to commercial-scale designs, are given in Table I. For studies in which the liquid phase offered the controlling resistance to mass transfer, the air-oxygen-water system was used, with oxygen stripped from the water
Side view
All PTFE material
Bats lower energy liquid entrainment away; only air and water vapor are allowed through the suction tube.
Figure 4. Entrainment-free vapor sampler.
stream. An Extech portable digital dissolved oxygen meter was used for these experiments. For gas-phase-resistant mass transfer, the air-water system was used, with water evaporated into a dry air stream. The humidity of the air was determined in a special wet/dry bulb temperature measuring station connected to an Omega 2176A digital thermometer. In order to measure the efficiency of the test tray, it was necessary to separate effectively any entrained liquid from the gas, to minimize the opportunity for further mass transfer. A mesh-type demister device is unsatisfactory for this purpose, since the liquid droplets that collect throughout the device provide additional interfacial area and concentration driving force for mass transfer. To solve this problem, Kastanek and Standart (1967) developed what they called a centrifugal vapor sampler. Their design was later improved by Lockett and Ahmed (1983). This type of passive centrifugal sampler (passive because of the absence of an external driving force) was fabricated and then tested by the present authors under varying entrainment conditions. After short periods of time, liquid water was observed, collecting at the downstream side of the sampler, inside the transparent tube that connected the sampler with the humidity measuring station. Accordhgly, no further use was made of this type of sampler. A new, active-type vapor sampler was then developed that provided improved separation of the entrained liquid from the gas, under similar entrainment conditions, compared with the passive-type centrifugal sampler. This sampler, shown in Figure 4, was fabricated entirely from Teflon (PTFE). The sampler measured 44 mm in diam-
1034 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 3
L = 0.0021 m3/s-mweir L = 0.0028 m3/s-mweir
95
%
0
t?
-
hw = 25.4 mm hw 50.8 mm
95
50 YoJetting
75 1.5 90
2.0
2.5
I
3.0
3.5
4.0
2.0
1.5
2.5
3.0
3.5
4.C
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LI I 80 70
c L = 0.0015 m3/s-mweir L = 0.0021 m3/s-mweir
50 1.5
50 2.0
2.5
3.0
3.5
.
I
.
I
.
I
hw = 25.4 mm hw = 50.8 mm 8 hw = 76.2 mm
.
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.
4.0
F-Factor (Fsa), m/s (kg/m3)”* Operating Conditions: Hole diameter = 12.7 mm Tray free area = 10.7 o/o Weir height = 50.8 mm Figure 5. Murphree tray efficiencies aa a function of the F factor,
with varying liquid flow rate.
F-Factor (Fsa),m/s (kg/m3)l/2 Operating Conditions: Hole diameter = 12.7 mm Tray free area = 10.7 % Liquid Flow rate = 0.0028 m3/s-mweir
Figure 6. Murphree tray efficiencies as a function of the F factor, with varying weir height.
In liquid terms, the Murphree efficiency can be expressed as
by light transmission techniques, occurred when about half of the holes were jetting. Experimental mass-transfer efficiencies are shown in Figures 5-8. The plots show the effect of the different fixed and flow parameters on gas- and liquid-phase mass-transfer efficiencies. The points of 50% jetting are indicated, based on the measurements of hole activity as well as the results of the light transmission studies. The range of variables covered is representative for commercial tray design. It may be noted that there are no indicated discontinuities in the efficiency vs flow rate data, even though distinct changes in character of the two-phase mixture were observed over the range of gas and liquid rates used. Mass-TransferModeling. The two-film mass-transfer model was used in the present work. Some of the key relationships of this model are NG = k$TartG (3)
For the short liquid travel on the tray, these forms are the same for point efficiency and for tray efficency. The use of the splash baffle assured a completely mixed tray where the composition of the liquid was the same, horizontally, throughout the two-phase mass. The gas, on the other hand, was assumed to be perfectly mixed horizontally, upon entering and leaving the tray. The sets of hydraulic data for each experimental run included formation bubble size distribution, aerated mixture height, gas holdup, and pressure drop. Importantly, the data also included a distribution of hole action as indicated in Figure 2. It was found that the observed transitions (inversions) from froth to spray, as measured
When a transfer unit ( N ) is realized, the change in the concentration of a component in a given stream equals the mean driving force over the interval in which that change in concentration occurred. If the separate film resistances are combined in an overall resistance based on either the gas or the liquid phase, the expressions for the number of transfer units can be written as NOG = KoJZTa‘tG (7) NoL = KoLa*tL (8)
eter and the four windows, available for gas flow, measured 12.7 by 9.5 mm. The off-centered baffles extended 12.7 mm away from the limits of the front and back panels. The interior edges of the baffles (those close to the center of the sampler) were sharpened to prevent small liquid droplets from accumulating on them. Tesh showed no accumulation of free water in the sampled vapor downstream of the device. Experimental Results All mass-transfer data were converted to a Murphree efficiency form. In terms of gas concentrations, this efficiency is defined as
EMG=
- Yn-1 Yn* - Yn-1 Yn
Ind. Eng. Chem. Res., Vol. 29, No. 6,1990 1035 where = 6.35 mm
95
90
or related to the number of transfer units for separate film resistance
75
t
701 1.5
The equation that relates point efficiency to the number of transfer units, assuming that liquid composition does not change vertically and that vapor passes vertically in plug flow without mixing, is 1 - E O G = exp(-Nm) (12) In liquid terms and assuming that the gas concentration does not change horizontally while the liquid concentration does change with elevation and distance along the tray, 1 - EOL = exp(-NoL) (13) The dispersion above a sieve tray can be divided vertically into three sections. The section at the bottom and closest to the tray (hole activity zone) corresponds to the activity at the holes (jetting or bubbling), the middle section (bulk froth zone) is composed of gas bubbles dispersed in the liquid, while the top section (spray zone) is gas continuous, with liquid drops and ligaments dispersed throughout. A t high gas rates and low clear liquid heights, the bulk froth zone disappears and the hole activity zone, mainly jets, borders the spray zone. At high gas rates and high clear liquid heights (such as those encountered at high weir heights or in the presence of a splash baffle), the bulk froth zone is highly important, while the spray zone, though present, does not contribute significantly to sieve tray activity. These collapsing zones describe well what is visually observed in sieve tray dispersions. Horizontally, sieve tray activity can also be divided into three different zones: jetting, large bubbling, and small bubbling. These zones were indicated earlier in Figure 2. A two-dimensional representation of the zones is shown in Figure 9, and equivalent expressions for efficiency are shown in Figure 10. Each of the numbered zones in Figure 10 has been modeled separately. In the following paragraphs, all of the assumptions adopted, along with the particular supporting references, are identified. Starting with zone 1 (jetting at the orifice), the standard mass-transfer unit equation is adapted: NL1 = kLa*tL (14) it is also known that PLGf
a*tL = ---;-a'tc. -
PGLf
-
By substituting eq 15 into eq 14 and with tG = to1,
L
2.0
.
I
.
.
I
3.5
3.0
2.5
I
.
4.0
I
I I
50 O h Jetting
"D,, = 12.7mm OH = 6.35mm
60 1.5
2.0
3.0
2.5
3.5
4.0
F-Factor (Fsa),mls (kg/m3f" Operating Conditions: = 50.8 mm Weir height Tray free area = 10.7-11.O % Liquid flow rate = 0.0015 m3/s-mweir
Figure 7. Murphree tray efficiencies aa a function of the F factor, with varying hole diameter.
Substitution of this expression into eq 16, with a'= 4/D1 (where D, is the jet diameter), gives
Lockett et al. (1979) have proposed a correlation for jet height (h,) vs hole Reynolds number (Reh): hl = 0.002853Reh (19) where Reh = DHuH/vG (20) Hai (1980) has proposed a linear correlation for the prediction of the average jet diameter, based on the hole diameter and clear liquid height, which is equal to the height of the static submergence of the hole: D1 = l.lDH 0.25hL (21) The tG1 factor is obtained by dividing the height of the jet (hl)by the jet gas velocity (uj) t ~ =i h / u j (22)
+
where uj =
where tGl is the residence time of the gas in the jet. The kL term, for the jetting contribution, is modeled using Higbie penetration theory (Higbie, 1935). The eddy liquid packet contact time (t3 is taken to be equal to tGl/q. A factor 9 i s introduced to account for multiple surface renewals. Thus, k~ = 1.13((PD~/t~1)'" (17)
II
50 %Jetting
.
UHDH~ (1- FLC)D12
The term FLC denotes the sample fraction of liquid cover on the tray that is needed to adjust the hole velocity (UH) where, according to Prado et al. (1987), FLC = 1836.97uH-1.602L0.524hW0.292 (24) Zone 2 in Figure 9 is assumed to be populated by a bimodal bubble size distribution. Hofer (19831, Kaltenbacher (1984), and Lockett et al. (1979) all reported a
1036 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 a
g$
c
a
