EFFICIENCY OF JET TRAYS Air- Water-Triethylene Glycol System RICHARD
A .
KIRSTEN’
A N D
M A T T H E W
V A N
W I N K L E
The University of Texas, Austin, Tex. 78712 A partial statistical study was conducted to determine the relution of four key design variables with jet tray efficiency. The equipment used is large enough to simulate small commercial size equipment with a minimum of wall effects usually encountered in laboratory-scale equipment. Data were also taken on sieve trays of comparable size using the same system. Jet trays are capable of handling higher liquid rates than sieve trays while operating at the same efficiencies. Sieve trays have greater flexibility of vapor-liquid rates at high efficiencies. The range of efficient iet tray operation is shortened as the tab angle is reduced from 90’ to 30’. Of four design variables, weir height and tab angle had a greater effect on efficiency than liquid and vapor rates.
DISTILLATION accounts for a major portion of the fixed asset investments and operating costs in the process industries. Therefore, a simple, efficient, and inexpensive distillation tray is of prime importance to the economics of plant construction and operation. Currently a designer can choose between many types of trays, other than the conventional bubble-cap and sieve tray, to meet the particular needs of a separation at the lowest cost. Little experimental work has been published concerning the directional jet tray. The main advantage claimed for this type of tray is the increased liquid-handling capacity resulting from the transfer of momentum from the vapor to the liquid in the direction of flow. This advantage could be utilized t o overcome overloads in existing equipment or to reduce investment cost caused by large liquid loads in new columns. The main disadvantage with the jet tray is its tendency to lose its normal liquid inventory a t a particular gasliquid rate, when liquid is jetted from the inlet side of the tray to the other side and into the downcomer, the “blow-off point.” This behavior reduces vapor-liquid contact and reduces efficiency. Consequently, the tray and column should be designed to prevent blow-off as well as “weepage,” which occurs at low vapor rates. Previous experimental work on jet trays includes a study of entrainment and pressure drop of the air-water system by Todd and Van Winkle (1967). Forgrieve (1960) reported the results of plant tests in which the efficiencies of jet trays were compared to those of bubble-cap trays. Recently, Rempacek and Van Winkle (1968) published a study of efficiency of jet trays and perforated trays in a 6-inch-diameter column. They concluded that unexpected wall effects peculiar to the laboratory scale equipment would not allow meaningful scale-up to commercial size applications. Therefore, the effect of key design and operating variables on the efficiency effectiveness of phase contact remains to be fully investigated. Although wall effects may influence plate hydraulics and mixing, it is believed that the equipment used in this study is large
‘ Present address, Union Carbide Engineering Center, Houston, Tex. 100
enough to simulate small commercial-size equipment. The purpose of this study was twofold. First, certain jet trays were studied to investigate the tray hydraulics and to determine the effect of four of the most important design variables on tray efficiency. Secondly, data were taken on a sieve tray in order to establish a reference point for comparing jet and sieve tray efficiencies in the same experimental system. Plan of Experiment
The air-water-triethylene glycol system was used because it was possible to get a broad range of gas and liquid rates at atmospheric pressure and room temperature, and the complexity of vapor analysis was reduced to the simple measurement of temperature and the calculation of absolute humidity. This simplicity results from the low vapor pressure a t room temperature of triethylene glycol. Thus, air and water were essentially the only components in the vapor. T o study the efficiency of jet trays and to compare them with sieve trays, the effect of four independent variables (gas mass velocity, liquid mass velocity, weir height, and tab angle) on tray efficiency was studied by using an ideal central composite experimental design in four variables proposed by Box (1954) and Himmelblau (1969) (Table I ) . The use of statistical experimental design and analysis of data is a convenient and time-saving method for obtaining a large amount of information with a minimum of experimentation. Dechman and Van Winkle (1959) have shown the applicability of this design to experimental work on separation efficiency. T o plan the statistical design, it was necessary to conduct exploratory experiments to find a suitable range of vapor and liquid rates a t which to observe tray hydraulics and to make preliminary efficiency experiments. Based on the preliminary work, values for the four variable were set for five design levels. Table I1 defines the uncoded or actual value of the variables a t the five levels. Finally, efficiency data were taken on a sieve tray using the same system, hole diameter, and active area as the test jet tray. Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 1, January 1970
~
~~~
Table 1. Central Composite Design in Four Variables
Run No.
XI
X2
X3
X4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
+1 +1 +1 +1 +1 +1 +1 -1 +1 -1 -1 -1 -1 -1 -1 -1 +2 -2 0 0 0 0 0 0 0 0 0 0
+1 +1 +1 +1 -1 -1 -1 +1 -1 +1 +1 +1 -1 -1 -1 -1 0 0 +2 -2 0 0 0 0 0 0 0 0
+1 +1 -1 -1
+1 -1 +1 -1
+l
+1 -1 +1 +1 -1 -1 +1 -1 +1 -1 +1 -1 0 0
+1 -1 +l -1 +1 -1 -1 +1 +1 -1 -1 0
0 0 0
0 0
+2 -2 0 0 0 0 0 0
0
0 +2 -2 0 0 0 0
Table II. Uncoded Variables at Four levels
Level
G, Lb. H r Sq Ft.
hk, Inches
Tab Angk Degrees
L, Lb. Hr.Sq. Ft.
+2 +1 0 -1 -2
1750 1600 1450 1300 1150
4 3 2 1 0
90 75 60 45 30
11,000 9,500 8,000 6,500 5,000
Efficiency
Equilibrium stage efficiencies are usually studied by measuring the Murphree tray or over-all column efficiencies. For the system under study, the Murphree dry-vapor plate efficiency was applicable to evaluate the effect of liquid rate, vapor rate, weir height, and tab angle on the performance of the jet tray. The Murphree efficiency is given by:
where
E = plate efficiency factor y ; = vapor composition in equilibrium with liquid -
leaving plate = average composition of vapor leaving tray n +1 -
Y"+l
Y"
= average composition of vapor leaving tray n
Thus, the actual vapor enrichment is divided by the theoretical maximum enrichment to obtain the efficiency factor. Experimentally, vapor samples above and below the plate are taken simultaneously with the liquid sample taken from the downcomer. The efficiency factor of 1.0 or 100% is assigned to a vapor-liquid contacting stage Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 1, January 1970
which is designed to give sufficient contact area and time for the attainment of equilibrium between the two phases at all points (Van Winkle, 1967). In this study, where the efficiency of jet trays was studied using the air-water-triethylene glycol system, the over-all Murphree plate efficiency was measured directly in terms of humidity by:
where
E, = over-all plate efficiency factor
E, = g,=
average humidity of the vapor leaving the tray average humidity of the vapor entering the tray H, = saturation humidity or humidity in equilibrium with the average liquid composition on the tray For this particular case, an accurate value for overall tray efficiency could be measured directly. Experimental Apparatus and Procedure
Apparatus. The apparatus consisted basically of a rectangular Plexiglas column (Finch and Van Winkle, 1964) with a stainless steel, jet tray, %-inch hole diameter. The operation simulated a single vapor-liquid contacting stage on which water was desorbed from a triethylene glycol-water solution using atmospheric air. The overall height of the column was 50 inches: 18 inches below the tray and 32 inches above the tray. The upper downcomer was 1% by 6 inches and the lower downcomer was 3 by 6 inches. The bubbling area, A A , of the tray was 1.05 sq. feet. An entrainment eliminator described by Finch and Van Winkle (1964) was used. Air was introduced into the system with a Spencer Turboblower through a Venturi meter into the bottom of the column. The pressure drop across the Venturi was measured using a single-leg inclined water manometer. The water content of the air entering and leaving the jet tray was determined by the use of wet- and dry-bulb temperature probes placed in the ducts where the recommended (U. S. Weather Bureau, 1953) air velocity was reached. A 53 weight 70 glycol mixture of triethylene glycolwater was pumped to the inlet downcomer through a regulating valve and measured by a Fischer-Porter rotameter. The temperature of the tray liquid was measured with a traversing thermocouple mounted in a 2-foot length of copper tubing. Using this temperature measurement, the saturation humidity of the air leaving the jet tray could be read from standard tables. Analysis and Materials. The vapor entering and leaving the jet tray was composed of air and water. It was assumed that no triethylene glycol was present in the vapor, since it had a vapor pressure of approximately 2.5 x lo-' mm. of mercury at 75" F. and 1 atm. The water content of the air was determined by measuring wet- and drybulb temperatures and reading the humidity from standard charts (Zimmerman and Levine, 1945). All temperatures were measured by using calibrated copper-constantan thermocouples accurate to 0.1" C. A typical wet-bulb temperature probe was used to determine the wet-bulb temperature. The liquid composition was analyzed by measuring the index of refraction by means of a Bausch & Lomb precision refractometer. Liquid samples from the column were taken 101
Table 111. Results
Inlet Humidity, H , x 10
Outlet Humidit), H ~ 10 x
Saturation Humidity, H, x
Hu - H , , l\Ha x lo-'
H , - H,, AHr x l o - '
Efiiency ( E )
1 2 3 4
9.20 9.75 9.70 10.00
15.20 16.50 17.30 17.20
18.60 19.80 21.67 21.15
6.00 6.76 7.60 7.20
9.40 10.05 11.97 11.15
64.0 67.2 63.6 64.6
5 6 8
8.65 8.70 9.85 9.65
14.80 15.11 16.15 16.10
20.00 20.15 23.46 23.95
6.15 6.41 6.30 6.45
11.35 11.45 13.61 14.30
54.2 56.0 46.3 45.1
9 10 11 12
8.70 9.20 9.50 9.60
15.75 16.70 17.90 18.00
19.44 19.85 21.77 22.09
7.05 7.50 8.40 8.40
10.74 10.65 12.27 12.49
65.6 70.4 68.5 67.3
13 14 15 16
8.65 8.65 9.60 9.45
15.02 15.85 16.90 17.25
20.14 20.28 23.83 24.85
6.37 7.20 7.30 7.80
11.49 11.63 14.23 15.40
55.4 61.9 51.3 50.6
17 18 19 20
9.50 9.40 9.80 9.75
15.40 17.20 16.85 15.80
20.74 20.59 20.28 22.93
5.90 7.80 7.05 6.10
11.23 11.19 10.48 13.10
52.5 69.7 67.2 46.6
21 22 23 24
10.10 9.75 9.35 9.35
18.30 16.95 16.10 16.43
22.54 24.76 20.75 20.38
8.20 7.20 6.74 7.08
12.44 15.01 11.40 11.03
65.9 48.0 59.2 64.2
25 26 27 28
9.60 9.60 9.75 9.75
16.30 16.40 16.40 16.40
20.56 20.70 20.57 20.52
6.70 6.80 7.10 6.65
10.96 11.10 11.27 10.77
61.2 61.3 63.0 61.7
Run
I
from sample taps along the tray and from the feed tank. A copper-constantan traversing thermocouple was used to measure temperatures along the jet tray. Distilled water, atmospheric air, and 99.9% pure triethylene glycol were used. The index of the refraction of the glycol was 1.4543 a t 25" C. Results
The results of the efficiency experiments based on the central composite experimental design are presented in Table 111. The absolute humidity terms are reported as the ratio of pounds of water vapor per pound dry air. The over-all Murphree tray efficiency was calculated by Equation 2 in per cent units. A total of 28 experimental points was necessary to permit a thorough analysis of variance on the experimental results. T o determine the experimental error, four replicates a t the zero level of the design were taken (runs 25 to 28, Table I ) . Variables. The independent variables measured were vapor rates, liquid rates, weir height, and tab angle. The vapor rate was measured using a Venturi meter with an estimated precision of 10%. The liquid rate was measured using a precision-bore rotameter with a precision of 0.5%. The accuracies of these measurements were estimated to be 2% for the gas rate and 1% for the liquid rate. The design variables of weir height, hole diameter, and tab angle had an estimated accuracy of 0.25, 1.0, and 2.0%, respectively. Murphree tray efficiency was the dependent variable measured. The precision of this measurement is equivalent to the summation of the precisions from the measurement 102
c
of temperature and the calculation of humidity. Numerically, the precision or reproducibility was calculated using the four replicates in the design and was found to be equal to d~0.83efficiency 70. The accuracy of the efficiency can be estimated from the accuracy of the analytical procedures discussed before. A liberal estimate of the accuracy is +3.0 efficiency %. Observations
The hydraulic behavior of jet trays affects efficiency greatly. At low vapor rates, weepage occurs similar to that encountered with sieve trays. At relatively high vapor rates for a given liquid rate, blow-off occurs in which the liquid inventory is blown from the entrance of the tray, to the weir, or to the opposite wall and into the downcomer. To illustrate the hydraulic behavior of the tray, photographs were taken a t a constant liquid rate of 8000 lb./hr.-ft. of weir and a t a vapor rate which was variable from 1150 to 2150 lb./hr.-sq. ft. of active area. A jet tray with a 2-inch weir and 45" tab angle was used as a representative example. Beginning with Figure 1 a t the lowest vapor rate, normal tray inventory with sieve-like bubbling can be observed. As the vapor rate is increased, jetting conditions begin on the first part of the tray (Figure 2), where liquid is actually jetted to the middle part of the tray and beyond. When jetting conditions exist on the tray, much of the liquid-in-vapor entrainment is directed toward the wall in back of the downcomer, where it impinges on the wall and drains into the downcomer. Finally, the blow-off point is reached (Figure 3), where the entire liquid inventory is jetted Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 1, January 1970
I
8
'
ir is common proceduri, 10 assume an arbitrary tuiictim IC, h t , firred t o thr avnilahlr datu. Frequently. rl simple liril -order equarion is t e i i d belor(. going I O ninrr complex functions. Fur rhe rase 01 jet tray etticienry, dihnire rclatiunships I,rrwe?n the variables have nor been e:.rnbli;hcd. However, in previous studies on sieve trays, first- and second-order equations with linear coefficients were found sufficient to correlate data. Based on the above considerations, a five-coefficient, first-order model was tested after collecting the +l and -1 levels in the experimental design. However, an analysis of variance indicated that the model was inadequate to fit the experimental data (12.9% average absolute deviation). This implies that a second-order equation should he tried next. After collecting the remainder of the data in the experimental design, a second-order, 15-coefficient model was assumed. The general form of the equation is
Y = bo -I b,X, + bzX, + baXz ibnXa ibizX,Xz + buXiX3 ibiaXiX4 + bmX2X3 + bz,XZX, + baaXzX4 ibnX: + bzzXi + baaxi + buXi (3) Referring to Table IV, the coded coefficients for Equation 3 and the results from the analysis of variance are summarized. I n the analysis of variance, the variance resulting from the lack of fit (s: Inches
L,
G, Lb lHr
Lb Hr Ft
Sq Ft
% E
Jet
2 2
8000 8000
1450 1750
65.9 64.0
Sieve
2
8000
1500 1300 1450 1750
64.3 62.8 62.6 59.2
Tray T3pe
Acknowledgment
The authors gratefully acknowledge the generosity of the Union Carbide and Chemicals Co. in furnishing the triethylene glycol. Nomenclature
bo, bl,.
Both trays had ‘f4-inchhole diameters and 10 0% active area based on plate
I n both cases, the tab tray was more efficient by an average of 4.0%. Although this is not a great difference, it can be explained by the observation that the tabs at a 90” angle caused a slightly higher resistance to flow across the plate, resulting in more liquid inventory on the plate and more contact area.
..
-
E,E, = G =
h, = H,H, =
L =
bubbling area or active area of column, sq. ft. coefficients in coded regression equation efficiency, Murphree tray efficiency, Murphree point efficiency 76 lb. per hour per sq. ft. weir height, inches humidity, saturation humidity, pounds of water vapor per pound of dry air liquid rate, pounds per hour per foot of weir length
s2, S L , See
xi,
= variance, lack of fit variance, experimental
variance, efficiency 7% squared independent variables in regression equation Y = dependent variable in regression equation Y = mole fraction in vapor
. . --
x2,.
Conclusions
literature Cited
Jet trays are capable of handling higher liquid rates than comparable sieve trays while operating a t the same efficiencies. This results from the transfer of momentum from vapor to liquid in the direction of flow. Sieve trays have greater flexibility of vapor-liquid rates a t high efficiencies. Jet trays have less flexibility due to a decrease in vapor-liquid contact, and thus efficiency, caused by jetting and blow-off conditions occurring on the jet tray. I n addition, the range of efficient jet tray operation is shortened as the tab angle is reduced from 90” to 30”. Because efficiency is more sensitive to the lateral movement of liquid across the jet tray, weir height and, to a lesser degree, tab angle had the greatest effect. The effect of each variable on efficiency was represented by a second-order curve. Efficiency was a linear function of vapor rate in the range studied in the statistical design. However, from exploratory experimentation, it was found that efficiency rapidly decreased when jetting conditions began on the tray. Efficiency was found to be a linear function of and affected least by liquid rate.
Box, G. E. P, Biometrics 10, 16 (1954). Dechman, D. A., Van Winkle, M., Ind. E%. C h e m . 51, 1015 (1959). Finch, R. N., Van Winkle, M., IND.ENG.CHEM.PROCESS DESIGNDEVELOP. 3, 106 (1964). Forgrieve, John, Proceedings of Symposium on Distillation, Brighton, England, 1960, Institute of Chemical Engineers, 16 Belgrave Square, London. Himmelblau, D. M., “Process Analysis by Statistical Methods,” Wiley, New York, 1969. Rampacek, C. M., Van Winkle, M., IND. ENG. CHEM. PROCESS DESIGNDEVELOP. 7,313 (1968). Todd, W. G., Van Winkle, M., IND.ENG.CHEM.PROCESS DESIGNDEVELOP. 6, 95 (1967). U. S. Weather Bureau, “Relative Humidity and Psychrometric Tables,” U. S.Government Printing Office, Washington, D. C., 1953. Van Winkle, M., “Distillation,” McGraw-Hill, New York, 1967. Zimmerman, 0. T., Levine, Irvin, “Psychrometric Tables and Charts,” Waverly Press, Baltimore, 1945.
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 1, January 1970
RECEIVED for review April 16, 1969 ACCEPTED September 10, 1969
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