I
PRAMOTE CHAIYAVECH and MATTHEW VAN WINKLE The University of Texas, Austin 12, Tex.
Effect of System Properties on
...
Small Distillation Column Efficiency Use this empirical correlation to predict tray efficiencies in a small distillation column from the system properties variables affecting distillation plate efficiency, or any vapor-liquid contact device efficiency, can be considered in three groups: design variables, operating variables, a n d system property variables. A correlation including all variables and their interactions would be extremely important to engineers concerned with design a n d operation of any vapor-liquid contacting process. -4s yet no such correlation has been developrd. A number of experimental data on efficiency of distillation plates have been reported in the literature (7, 2, 4: 6, 8: 77, 74-76, 78-22, 25, 28, 33-36). Correlations involving some of the variables and their effect on plate efficiency have been presented ( 7 , 8>9, 73, 26, 29). Attempts to derive correlations based solely on so-called fundamental mass transfer models have been unsuccessful primarily because of the difficulty of visualizing a model of multivariant dimensions which would adequately describe the complex two-phase flow phenomena occurring on a vapor-liquid contact plate. In addition, there is some question as to the possibility of solving the mathematical equations derived to describe the model. Apparently the empirical approach offers more possibilities than the theoretical. Hoivever, large quantities of accurately determined d a t a are needed, including all levels of variables tested or observed. This study attempted to evaluate the effect of system variables on perforated plate efficiency in a small-diameter distillation column with all operating a n d design variables maintained constant in so far as possible, subject to experimental limitations. T h e variables included surface tension and relative volatility and viscosity, density, and diffusivity of both liquid and vapor phases. T H E
T h e equation developed satisfactorily correlated experimental data and several sets of lireratiire data. Agreement between predicted a n d actual plate efficiencies was gratifying considering the wide variation of system, type of plate and column, and operating conditions considered. T h e term C of Equation 7 can be determined from a couple of experimental runs in the desired operating range. I t is hoped that in the near future C can be evaluated as a function of operating and design variables. Once its value is established, it can be
used for predicting Murphree plate efficiencies of that column in distilling any mixtures under comparablr operating conditions. The equation should serve as a useful tool in predicting distillation plate efficiency. Because physical properties in the equation a r e those of the liquid phase, it is concluded that in vapor-liquid contacting operations properties of the liquid phase shoiv a predominant effect on plate efficiency.
Experimental Binary sysrems were selected to give a range of values of the properties used in the correlation sufficiently \vide to cover the majority of systems of industrial interest. I t was impossible to vary each property independently since there are fundamental interrelations betLveen
Experimental values for correlation were obtained with this distillation assembly 7. 2.
Reboiler bottle with heaters Perforated plate 3. Overhead thermometer 4. Vapor superheater 5. Overhead condenser 6. Reflux accumulator 7. Reflux rotameter 8. Reflux thermometer 9. Control valve
0. Product rotameter I.
Product sampling line
2. l i q u i d sampling line 3 4.. Vapor sampling line Reflux condenser
5. Powerstats
VOL. 53, NO. 3
MARCH 1961
187
SAMPLE
BOTTLE
_.
6'
Brass perforated plate was used in distillation column Plate diameter Superficial flow a r e a Free area Plate thickness Downcomer area W e i r height Pitch to diameter ratio Hole arrangement
1 in.
0.00545 sq. ft.
9.39%
o f column superficial area in. 6.25y0 of column superficial area ' 1 4 in. 2.0 Equilateral triangle
'is
them. T h e systems selected \\-ere 1propanol-M-ater. n-octane-toluene, acetone-1 -butanol. methanol-l,4-dioxane. ethanol-l,4-dioxane, and carbon tetrachloride-1 -propanol. Equipment. A 1-inch-diameter perforated plate distillation column together Iiith its essential accessories was used ( p , 187). Dimensions of the column a n d plare design details are shown above. T h e perforated plate was made of
l ' ~ inch thick brass. A stainless steel liquid sampling tube of '8-inch diameter \\-as extended through the column ivall onto the plate a t a point close to the outlet \veir. T h e liquid sample draivn a t this point represented liquid leaving the plate through the downcomer. T h e vapor sampling line? of 0.25-inch copper tubing, extended through the column wall to irithin 0.5 inch of the underside of the plate, a t a n angle 15' above horizontal to minimize the effect of differential condensation in the \Tapor sampling line. This vapor sample represented the vapor stream entering The plate. T h e portion of the vapor sampling line extending outside the column was heated by a small heating. coil to prevent any condensation in the line. T h e vapor samples \sithdrawn \\-ere completely condensed in sample collecting bottles immersed in a n ice bath. Because overhead vapor was totally condensed, vapor rate was measured through the calibrated section of the condensate line leading to the reflux accumulator by closing the stopcock in the line and measuring the time required for 10 ml. of condensate to accumulate. Reflux rate was measured by a rotameter in the reflux line; product rate \\-as also measured by a rotameter in the product return line. Condensation of the vapor in the vapor line from the head of the column to the condenser !\-as minimized by installing a heating coil around this section and superheating the vapor slightly. Materials. T h e compounds used were purified until their properties substantially agreed irith those in the literature. Systems \sere selected largely on the basis of difference in physical properties a n d availabi1it)- of reliable physical properties data in the literature. 4 n a l -
ysis of samples by a refractometer \\-as comidered sufficiently accurate. Precision of the Bausch a n d Lomb refractometer \\-as f 0,00003 unil. Relative volatilities of the seven binary systems were calculated from vapor-liquid equilibrium data ( 3 , 5, 7: 72. 77, 27: 32). All physical properties needed, except diffusion coefficients, \\-ere experimental data reported by Ling and Van \Vinkle ( 2 3 ) . Molecular diffusion coefficients in the vapor phase were calculated by the Fair and Lerner generalized correlation ( 70). Pclolecular diffusion coefficients in the liquid phase calculated by the Wilke and Chang correlation (37), \\-ere good for very dilute liquid solutions. For higher solute concentrations. they \yere corrected for concentration effect by the method suggested by Kincaid and others (23) Reid and Sherwood ( 3 0 ) have summarized this method. Procedure. Before each run, the time required to obtain steady-state operation \vas determined. \-apor and liquid rates, expressed \.olumetrically, were kept constant throughout the runs for all systems a n d concentrarions. Test runs were made a t several vapor and liquid rates, and operating characteristics were observed visually for ireeping, flooding? channeling, or any unstable operations. A vapor rate of 1.9 feet per second and a liquid rate of 0.0016 foot per second. based on total cross-sectional area of the column, \\-ere used in all runs? because they gave satisfactor)- stable operation. Before a specific run, the reboiler composition was adjusted to the proper initial value, and the reboiler heaters \rere set a t a predetermined value. .4fter preheating for 2 hours. the heaters on the reflux accumulator and reflux return line \vere adjusted to keep the
70
I*
1
2 0
I
1
1
I
MOLE % LIGHT COMPONENT
MOLE % LIGHT
COMPONENT
Figure 1. Murphree plate efficiency and average liquid compositions were obtained from experimental data A. B. C.
0 1 -Propanol-water X n-Octane-toluene A Acetone-1 -butan0 0 Methanol-l,4-diaxane A Ethanol-l,4-diaxane
X Carbon tetrachloride-1 -propanol
0 1 -Butanol-water MOLE
1 88
INDUSTRIAL AND ENGINEERING CHEMISTRY
?4 LIGHT COMPONENT
D I S T I L L A T I O N C O L U M N EFFICIENCY reflux temperature Lvithin 5" C. of the bubble point, Condensate rate was measured, and reflux rate was adjusted to the desired value by the needle valves in the liquid lines. Liquid level in the reflux accumulator \vas maintained constant by adjusting the needle valve. If the desired vapor rate was not obtained, reboiler heaters were adjusted. Product return rate was read off the product rotameter, and precision of flo\v rate measurement was checked by a material balance. The column was alloived to operate a t steady state for 30 minutes. T h e overhead sample \vas taken first; then samples of liquid leaving the plate and of vapor under the plate were simultaneously draivn. After compositions were determined by refractometer, the hlurphree plate efficiency was calculated by: E = (y. - y9t-
l),'(yn*
- yn-
1)
Experimental data evaluated consisted of temperature, vapor and liquid rates corrected to the operating conditions. overhead composition, composition of vapor entering the plate, composition of vapor in equilibrium Lvith the liquid leaving the plate, and Murphree plate efficiency. Overhead vapor composition \vas taken as an integrated average of vapor compositions on the plate. Arithmetic average values of the compositions of liquid leaving and entering the plate were used to represent the average composition of liquid on the plate. T h e Murphree plate efficiency data are shown as a function of the average liquid composition in Figure 1. Attempts to explain the effect of variation of any physical property on hlurphree plate efficiency were considered useless. .411 physical properties are dependent not only on concentration and nature of the system but also on temperature. T h e counteracting effect of these system variables introduced so many complications that it might be misleading to discuss the effect of any single system variable by itself.
Correlation T h e data obtained were correlated empirically to evaluate the constants in the equation: =
A
80
70
-
f
60
LL
w 50
0
IO
20
(1)
Results
E
90
(PI,V,~ L )( B P LA D L )' x
This is the empirical correlation corresponding to the relation between Murphree plate efficiency and system properties derived by means of dimensional analysis. The method of least squares was used in fitting data to the equation. Equation 2 \vas linearized first
Figure 2.
40
50
EXPERIMENTAL
PLATE
30
70
80
90
I00
Calculated plate efficiencies are compared with experimental values 0
A 0 W V a
-
Experimental d a t a from this study Benzene-toluene (6) Propylene-oil ( 3 6 ) Acetone-benzene ( I 4 ) n-Heptane-methylcyclohexane (35) Methanol-water ( I 5) 3-Propanol-water ( 2 2 )
by means oflogarithms. and themethodof least squares \vas applied using weighted residuals (37) to obtain the same weight for all experimental data points. Attempts to correlate all experimental data points were not successful. Most big deviations in calculated efficiency data were for 1-propanol-water, and these \cere all in the same direction \ \ ith respect to sign. Certain systematic errors xvere believed to exist in the 1-propanol-water data. T h e other source of error might be inaccuracy of vapor-liquid equilibrium data used for this system. All experimental data obtained for 1-propanol-water were then excluded for the correlation and used later in testing the validity of the derived equation. Correlation of the remaining experimental data lcith an IBhI 650 digital computer resulted in Equation 3 with an average absolute deviation of 3.2 efficiency units.
(PD,) -"''(E) rL'
60
EFFICIENCY
"03
(E)
"" (@)0.06
(3)
The terms ( P L 'PA and ( P L P A in Equation 3 may be considered as correction terms since ,ut, p e . p L , and p e appeared once before in the other dimensionless groups of the equation. Also the exponents are small compared with those of other terms. They were, therefore, excluded and the experimental data correlated using Equation 4:
The 128 experimental data points \\-ere correlated by the method of least squares to evaluate the constants in Equation 4:
($i)0'007
(CI)0.056
(3)
The exponent of the Schmidt number for the vapor phase (p, peD,) in Equation 5 was so small that the contribution of this term to the value of E was negligible. The final \corking equation thus became :
Correlation of the experimental data using Equation 6 resulted in an average absolute deviation of 3.35 efficiency units. Application to Literature Data. Because the correlation is empirical and does not involve a range of design and operating variables. i t is good only for the column and plate used in this study. T o apply this equation as a correction for changes in physical properties of s)-stems in other columns and plates under any desired operating conditions, a more general form is:
VOL. 53,
NO. 3
MARCH 1961
189
where C is a constant to be determined for each set of design and operating variables. It should remain constant for these variables no matter what mixture is being distilled. T h e magnitude of C ranged from 0.0101 to 0.0236: except for one system where maximum efficiency reported was 2.0y0 and the calculated C was considered to be of little value. I n the study of plate efficiency, a number of investigators ( 7 , 6, 75, 22, 35, 36) conducted experiments wherein all factors were held constant except system properties. Their data provided a significant test of the validity of the equation obtained in this study. I n selecting literature data, special attention was paid to the wide variety of system, plate, column, and operating conditions. For each set of data selected, design and operating variables were held substantially constant except for a slight variation in vapor velocity. Several sets of data were selected, each set representing a system studied with a type of column and plate design under unique operating conditions. Although several sets of data could be selected for one system, it was desirable to cover as many systems as possible to demonstrate the applicability of the derived equation. Wherever the experimental physical property data were not available, the molal average physical properties were used. X proper value of the term C was assigned to each set of data. The calculated efficiencies are
plotted against the experimental efficiencies in Figure 2. Comparison of Calculated Efficiencies. T h e methods of Drickamer and Bradford ( 9 ) and O’Connell (26) and Equation 7 were used to calculate efficiencies for various systems reported in the literature. Data points were selected randomly and the efficiencies evaluated. Calculated and experimental efficiencies are compared in Table I, which indicates that Equation 7 gives the best results. Nomenclature D = molecular diffusion coefficient, sq. cm./sec. E = Murphree plate efficiency V = superficial velocity based on column cross-sectional area, ft./sec. t* = mole fraction of more volatile component in vapor phase in equilibrium with liquid composition leaving plate y n ! x, = mole fraction of more volatile component in vapor and liquid leaving plate n, respectively yn-l = mole fraction of more volatile component in vapor entering plate n or in vapor sample taken under the plate a = relative volatility, y*(I - x ) / fi
p u
x ( l - y*) = viscosity, cp. = density, grams/cc. = surface tension, dynesicm.
Subscripts g
=
L
= liquid phase
gas phase
Comparison of Calculated Plate Ffficiencies Shows Accuracy of Equation 7 Drickamer and Bradford (9) Present Correlation O’Connell (26) Data Deviation Eoslcd. Deviation Ecalod. Deviation System Source Ecalcd. Eabsd.
Table I.
Benzenetoluene Acetonebenzene n-Heptanemethylcyclohexane Methanolwater 2-Propanolwater CO,-water absorption Propyleneoil %-Octanetoluene Acetone-1butanol Methanol1,4-dioxane Ethanol1,4-dioxane 1-Butanolwater CCla-1propanol Water-1propanol
1 90
64.8 54.1 64.8 69.5 64.0 60.5
1.8 5.1 -13.0 - 18.5 -20.0 - 16.0
62.5 54.0 62.5 67.4 49.5 42.2
-
(1) (86) ($6)
63.0 49.0 77.8 88.0 85.0 76.5
0.5 5.0 -15.3 -20.6 -35.5 -34.3
61.8 50.2 74.0 83.5 80.1 80.7
-1.2 1.2 -3.8 -4.5 -4.9 4.2
(15) (16) (22) (22) (86) ($6)
88.2 96.7 88.0 94.0 1.8 2.2
50.2 50.5 49.5 53.0 5.94 10.8
-38.2 -46.2 -38.5 -41.0 4.14 8.6
48.1 47.9 36.0 38.0 18.0 32.8
-40.1 -48.8 -52.0 -56.0 16.2 30.6
92.5 98.7 91.2 94.4 1.76 1.82
4.3 2.0 3.2 0.4 -0.04 -0.38
(36)
7.4
Exptl. Exptl. Exptl. Exptl. Exptl. Exptl.
21.6 11.0 26.0 26.7 35.1 33.3 34.8 29.5
58.5 62.5 32.5 37.0 31.5 54.0
-14.2 - 9.5 32.5 35.8 - 2.6 3.7 - 3.3 24.5
22.8 3.4 59.0 57.0 38.0 50.5 35.5 45.4
33.0 30.3 2.9 17.2 0.7 15.9
21.2 14.3 25.4 26.1 29.9 33.2 31.0 24.5
-0.4 3.3 -0.6 -0.6 -5.2 -0.1 -3.8 -5.0
Exptl. Exptl.
31.5 28.3
42.5 54.2
11.0 25.9
37.5 43.9
6.0 15.6
29.5 26.1
-2.0 -2.1
Exptl.
24.2
40.0
15.8
31.5
7.3
19.0
-5.0
Exptl. Exptl. Exptl. Exptl.
30.4 35.0 59.9 57.1
38.0 51.1 42.0 50.2
7.6 16.1 - 7.9 - 6.9
27.0 37.5 31.5 31.5
- 3.4
27.1 30.2 58.2 56.0
-3.3 -4.8 -1.7 -1.1
(6) (6) (1)
($6)
1.5
INDUSTRIALAND ENGINEERINGCHEMISTRY
1.2
- 7.6
2.5 -28.4 -25.6
literature Cited (1) Am. Inst. Chem. Engrs., New York, “Tray Efficiencies in Distillation Columns,” 1958. (2) Arnold, D. S.,Planck, C. A., Schoenborn, E. M., Chem. Eng. Progr. 48, 633 (1952). (3) Berg, L., Popovac, D. O., Ibid., 45, 683 (1949). (4) Braulick, W. J., Ph.D. dissertation, University of Texas, Austin, Tex., 1956. (5) Brunjes, A. S., Furnas, C. C., IND. ENG.CHEM.27, 396 (1935). ( 6 ) Carey, J. S., Griswold, J., Lrwis, W. K., McAdams, W. H., Trans. A m . Inst. Chem. Engrs. 30, 504 (1934). (7) Carley, J. F., Bertelsen, L. W.,111, IND.ENG. CHEY.41, 2806 (1949). (8) Clark, J. W., M.S. thesis, University of Texas, Austin, Tex., 1960. (9) Drickamer, H. G., Bradford, J. R., Trans. Am. Inst. Chem. Engrs. 39, 319 /I Od?\
(Id) Fair, J. R . , Lerner, B. J., A.1.Ch.E. Journal 2, 13 (1956). (11) Foss, A. S.,Gerster, 3. A., Chem. Eng. Progr. 52, 285 (1956). (12) Gadwa, T. W., M.S. thesis, Massachusetts Institute of Technology, Cambridge. Mass.. 1936. 3) Gkddes, R: L., Trans. A m . Inst. Chem. Enms. Engrs. 42. 42, 79 (1946). 4) %erstk‘r, Bbnnet, W. E.. J. A,, Bonnet, E., Hess, I., Gerster, J.‘A., Chem. Eng. Progr. 47, 523 (1951). 5) Gerster, J. A , , Koffolt, J. H., Withron, J. R., Trans. A m . Inst. Chem. Engrs. 39, 37 (1943). 6) Gunness, R . C., Baker, J. C., Ibzd., Ibid., 34. 707 I1 938). (17) ’Hopkins, R. N.,Yerger, E. S., Lynch, C. C., J . A m . Chem. Sod. 61, 2460 (1939). (18) Jones, J. B., Pyles, C., Chem. Eng. Progr. 51,424 (1955). (19) Jones, P. D., Van Winkle, M., IND. ENG.CHEM.49, 232 (1957). (20) Karim, B., Nandi, S. K., J . Indzan Chem. Soc., Ind. News Ed. 11, 12 (1948). (21) Keyes, D. B., Byman, L., Univ. Ill. Eng. Expt. Sta., Bull. 328 (1941). (22) Keyes, D. B., Langdon, W. M., IND. ENG.CHEM.35, 464 (1943). (23) Kincaid, J. F., Eyring, H., Stearn. H. E., Chem. Revs. 28, 301 (1941). (24) Ling, T. D., Van Winkle, M., Chem. Eng. Data Ser. 3, 82 (1958). (25) Mayfield, D. F., Church, W. L., Green, A. C., Lee, D. C., Jr., Rasmussen, END.CHEM.44, 2238 (1952). R. W., IND. (26) O’Connell, H . E., Trans. A m . Inst. Chem. Enprs. 42. 741 (1946). (27) PadgGt, F. L., Amis, E. S., Hughes, D. W., J.A m . Chem. SOC. 64, 1231 (1942). (28) Peters, W. A , , Jr., IND.ENG.CHEM. 14, 476 (1922). (29) Quigley, C. J., Johnson, A. I., Harris, B. L., Chem. Eng. Progr. Symposium Ser. 51, No. 16, 31 (1955). (30) Reid, R. C., Sherwood, T. K., “The Properties of Gases and Liquids,” McGraw-Hill, New York, 1958. (31) Scarborough, J. B., “Numerical Mathematical Analysis,” 2nd ed., Johns Hopkins Univ. Press, Baltimore, 1950. (32) Stockhardt. J. S., Hull, C. M., IND. ENG.CHEM.23, 1438 (1931). (33) Umholtz, C. L., Van Winkle, M., IND.END.CHEM.49, 226 (1957). (34) Umholtz, C. L., Van Winkle, M., Petrol. ReJiner 34, No. 7 , 114 (1955). (35) Van Wijk, W. R., Thijssen, H. A. C., Chem. Eng. Sci. 3, 153 (1954). (36) Walter, J. F., Sherwood, T. K., I N D . ENG.CHEM.33, 493 (1941). (37) Wilke, C. R., Chang, P., A.I.Ch.E. Journal 1, 264 (1955).
RECEIVED - . ~ for review March 12. 1960 ACCEPTED-December 9; 1960
