I
R. S. RAMALHO,' F. M. TILLERf2W. 1. JAMES, and D. W. BUNCH University of Missouri,
School of Mines and Metallurgy, Rolla, Mo.
( A Rapid Method for Obtaining Vapor-Liquid Equilibrium ~ a t a )
Theoretical Aspects This method offers promise toward materially reducing time required to obtain isobaric vapor-liquid equilibrium d a ta, p a rticula r Iy with muItico mponent systems
v' The
experimenter can obtain three points per hour V' No highly specialized equipment is required v' Reliability is equivalent to that of conventional methods
1
NVESTIGATIONS of vapor-liquid equilibrium data form an important segment of chemical literature. Although techniques have differed among experimenters, methods now being employed depend basically upon analyzing liquid and vapor samples taken simultaneously. I n conventional apparatus, vapors are condensed and returned to the liquid in a cyclical manner, and a single point on the equilibrium curve is determined in each run. Theoretically, the ideal procedure consists of vaporizing the condensate and returning it to the liquid at as close to saturation conditions as possible. Maintenance of a sufficiently large volume of liquid in proportion to the rate of vaporization minimizes the change in concentration produced on mixing the condensate with the liquid charge. The chief difficulty with the present methods centers on performing a large number of experiments to get the complete equilibrium curve. The method proposed in this paper can be used for obtaining the entire equilibrium curve in a single experiment lasting about 2 to 3 hours. I t may be considered to have its roots in the dynamic distillation technique first proposed by Brown in 1879 ( 1 ) . The only method in the literature that is faintly similar is that of Rosanoff, Bacon, and White ( 3 ) . Fundamentally, the new method depends upon performing a simple distillation with continuous determination of concentration of either the liquid or vapor. One stream is analyzed; the composition of the other is found by a material balance. The vapor concentration is ultimately calculated from the slope of a curve which differs slightly for various methods of operation. I n
Present address, Department of Chemical Engineering, University of Rochester, Rochester, N. Y . Present address, Cullen College of Engineering, University of Houston, Houston, Tex.
the most direct procedure, a simple distillation is carried out, and the Rayleigh equation ( 2 ) for differential distillation is used. Only a portion of the equilibrium curve can be determined with accuracy in a single run. By batchwise or preferably continuous feed additions, the entire equilibrium curve, including azeotropes, can be obtained in one experiment. Method of Simple Distillation
The Rayleigh differential equation for simple distillation may be used directly for calculating the vapor concentrations. Suppose that W, units of a binary solution is vaporized in such a manner that the vapor is maintained in equilibrium with the liquid. As the vapor comes from the pot, it is condensed differentially; and the weight is continuously determined. If a differential amount dW of the liquid is vaporized, a material balance for the more volatile component vields (1)
If W and x are known, by graphing Wx us. W , it is possible to obtain y from the slope of the curve by any convenient numerical method. I t is necessary to determine either the liquid concentration or the vapor composition. These can be related by material balance :
w*= woxo - VIYl (2) An important limitation of the batch method lies in the difficulty of encompassing the entire isobaric curve in one run, as the amount of liquid remaining in the flask will become quite small. As the liquid residue approaches the bottom of the flask, the apparatus generally becomes inoperative. Method of Continuous Distillation
A number of modifications can be made in the experimental procedure,
including continuous feed addition, batch feed addition, and simultaneous feed addition and residue withdrawal. The most promising of these methods consists of continuous addition of feed of constant composition a t a fixed rate. The mathematical analysis of the modified process depends on the application of a differential material balance similar to Equation 1. If a t an arbitrary time during the operation an amount of feed Z with concentration t of the more volatile component has been added to the initial charge WO,while an amount V has been distilled, a n over-all material balance yields
w=
Wo+Z-v (3) The differential of this expression is dW = d Z - dV (4) A material balance with respect to the more volatile component gives d(Wx) dZ y = - ~ + Z ~ v (5) For binary systems, the least volatile component would normally be fed into the system. For this case z is equal to zero and Equation 5 becomes
eliminating W , when Z = V y =
-
dx wo dV
Equation 6 represents perhaps the most useful form for determination of y. Beginning with the most volatile component in pure form in the flask, the pure least volatile component is fed at a constant rate approximating the rate of distillation. The slopes of the curve Wx us. ( W - Z ) yield the vapor concentrations. As a pure component enters the pot, the concentration gradually approaches zero-with respect to the more volatile component-regardless of intermediate azeotropes. Thus it is possible to determine the entire concentration range irrespective of intermediate maximum or minimum boiling points. Multicomponent System
Either the batch or continuous process can be adapted for multicomponent systems. For a three-component system, A, B, and C, Equation 1 becomes VOL. 53, NO. 11
NOVEMBER 1961
895
B
To calculate y a and yb, it is necessary to analyze either the vapor or the liquid for two components. Analysis of the vapor might be more convenient with multicomponent systems. The equations with continuous feed are analogous to Equations 5 through 7. A possible method of feed addition is illustrated on the triangular diagram a t right. Starting with pure A in the flask, solution a t 1 is added until point D is reached. A new feed with composition at point 2 is then started, and distillation is continued to point E. By changing feed composition at appropriate points, the entire isobaric curve can be obtained in a single run. Distillate Analysis Method
For a binary system where the least volatile component is fed into the system, Equation 6 is used as the basic equation for calculation of vapor compositions. The weight of the residue in the flask at any arbitrary time is
this condition. Equation 6 becomes - WlXl - woxo v = VI - vo where y represents the average value of the distillate sample taken. The average liquid composition x is given by
consequently one
point of the vapor liquid equilibrium curve is thus established. The application to a ternary system is essentially the same using Equation 5 as the basic equation for calculation of vapor compositions.
A possible method of feed addition for multicomponent systems i s illustrated by use of this triangular diagram
readily obtained from Equation 2. The composition of the distillate is determined by any suitable method. The calculation of the amount of volatile component in the residue PYX is then obtained from a material balance. If a sufficiently small interval of the curve represented by Equation 6 is chosen, this value will be the slope of the straight line connecting the end points of the interval. The assumption is made that successive samples satisfy
Literature Cited (1) Brown, E. P., Trans. Chem. SOC.35, 547 (1879). (2) Robinson, C . S., Gilliland, E. R., “Elements of Fractional Distillation,” 4th ed., p. 108, McGraw-Hill, New York, 1950. ( 3 ) Rosanoff, M. A., Bacon, C. It’., White, R. H., J . Am. Chem. Soc. 36, 1803 (1914).
RECEIVED for review January 3, 1961 ACCEPTED July 17, 1961 This article is a condensation of a Ph.D. thesis by R. S. Ramalho, Vanderbilt University, Nashville, Tenn., 1953. Microfilm available through University Microfilm, Inc., Ann Arbor, Mich.
( A Rapid Method for Obtaining Vapor-Liquid Equilibrium Data)
Simple and Continuous Distillation Methods C O N V E ’ I T I O N A L METHODS for the determination of vapor-liquid equilibrium data require approximately 2 to 3 hours to establish a single equilibrium point. Xormally, about 10 points are necessary to construct a suitable curve for a binary system and 30 to 50 points are needed for a ternary system. With this new method, approximately 30 points may be established in a 3-hour period. However, an additional 6 to 8 hours are required when analysis of the distillate is necessary including the time of calculation of results. T h e time of calculation of results can be, however, considerably shortened by use of computers. Therefore, using conventional methods, an experimenter can obtain a point per 3 hours of effort as compared to at least three points per hour using this rapid method. The reliability of the data as shown is a t least equivalent to that of conventional methods. Furthermore, the method requires no highly specialized equipment, and the equipment can be easily modified and fabricated out of suitable materials for the study of corrosive systems or for studies covering \vide ranges of pressure. The time saved by this method for determining vapor-liquid equilibrium data
896
for multicomponent systems is obvious. I t is necessary to know the liquid concentration x as a function of W if Equation 1 is to be employed for calculating y. Two techniques are described for accomplishing this purpose: boiling point and distillate analysis. Boiling Point Technique
If the boiling points of a binary mixture are known as a function of the concentration, it is convenient to determine the boiling temperature during the course of a simple distillation. With the temperature known as afunction of theweight distilled, it is possible to construct the TWx us. W curve needed. A number of problems arise, some of which are the same as those encountered in conventional methods and others which are peculiar to the method described here. As in other procedures, it is necessary to avoid entrainment and refluxing. Proper design of the vapor space suffices for elimination of entrainment which is usually not a serious problem. Refluxing may be avoided by maintaining the walls of the flask a t a temperature slightly in excess of the boiling temperature. Another factor involved in equilibrium between the vapor and the
INDUSTRIAL A N D ENGINEERING CHEMISTRY
liquid is the effect of the rate of vapor production on the time of contact between the vapor and liquid. Higher rates of vapor production will tend to produce a vapor less rich in the more volatile component than lower rates. These problems are equivalent in both conventional and the proposed methods, and the solutions lie in adequate mixing, low vapor velocities, and proper insulation or wall heating. To determine the slopes as dictated by Equation 1 lvith sufficient accuracy, it is necessary to obtain the temperature with a precision of 0.005 to 0.01” C., thus making reproducibility of temperature measurements essential to the success of the method. The necessary precision of temperature control depends upon the boiling point range of the components involved and upon the shape of the curve. Among the difficulties causing temperature fluctuations are pressure variation, hydrostatic head effects, superheating, and radiation. Pressure control within approximately 0.1 mm. of mercury is important to prevent boiling point variations. A Cartesian manostat (5) can be conveniently employed provided the proper precautions are observed. Once the pressure has been set in the manostat,
V A P O R - L I Q U I D EQUILIBRIUM temperature changes result in pressure variations. Therefore, the manostat must be placed in a thermostat where the temperature can be controlled within approximately 0.05' C. If the temperature is allowed to creep up slowly, as may occur in the course of a typical day, the pressure will also increase in accord with the ideal gas law. Immersion of the temperature measuring element in the boiling liquid leads to objectionable hydrostatic effects which vary as the liquid level changes throughout the distillation. To remain within 0.1 mm. of mercury variations, the liquid level would have to be constant to approximately 1.5 mm. The use of a Cottrell pump ( 4 ) serves to reduce the problem of hydrostatic head, although a t the same time introducing the possibility of superheating. The Cottrell pump produces a vapor lift which causes the liquid to flow in an almost continuous stream onto the temperature measuring element. A thin film of liquid is maintained on the thermometric element, and hydrostatic effects are eliminated. Pulsation and superheating may be encountered if the heat input and shape of the Cottrell pump are not properly adjusted. Since the instantaneous value of the weight W in the residue is needed, holdup in the condenser must be minimized. With the use of a metal condenser in place of glass (shortened lines), the time-ofsampling error may be reduced to a small value. The ratio of the holdup to the residue in the flask must be small if errors are to be avoided. Distillate Analysis Technique
As previously mentioned, fractionation and entrainment must be avoided as this will affect the composition of the condensate. The composition of the boiling solution is gradually changed as the vapor-richer in the more volatile fraction-is evolved, thus also affecting the composition of the vapors. The subsequent analysis of the condensate
!%yd:dgr6 trates the experimental setup for a rapid method of obtaining vapor-liquid equilibrium data
$1
A, 6. C. D.
Reservoir Self-zeroing burets Heating mantle Cottrell pump E. Thermometric element F. Condenser G. Distillate receiver
+ PRESSURE
REGULATOR
66 VARIAC
from the vapor gives the average composition of the vapor, but analysis of the sample of liquid taken either before or after distillation of the condensate sample analyzed gives a value too high or too low in the more volatile fraction. This error, referred to as time-of-sampling error, may be reduced by analyzing essentially instantaneous samples and by applications of the differential Rayleigh equation in the calculations. Apparatus
The experimental apparatus is shown in Figure 1. A 3-liter round-bottomed flask-the necks removed to within 1 inch of the spherical portion of the flask to reduce €ractionation-is heated by a combination of an electric mantle at the bottom and heating tape at the top, Separate variable transformers are used for controlling these heating elements which are primarily for prevention of condensation and fractionation. A third coil is located around the vapor outlet tube leading to the condenser. The main heating load is carried by an internal heater located within the funnel of the Cottrell pump. Vapor formed by the internal heater rises and carries liquid in jets onto the thermometric element. The vapor line is made as short as possible, and the stainless steel condenser need only be about 2 to 3 inches long. The condensate passes
into a sample bottle which is connected to the pressure control system. The temperature measuring element may consist simply of a Beckman thermometer which was used successfully in spite of the short 6' C. range. I n the main portion of the experimental work, however, a platinum resistance thermometer (Leeds and Northrup, No. 8164) was operated in conjunction with a Mueller bridge (Leeds and Northrup, No. 8067) and a galvanometer (Leeds and Northrup, No. 2420~). The absolute value of the temperature was not of importance, while reproducibility of measurements was essential. The apparatus employed appeared to give satisfactory results. The self-zeroing burets shown in Figure 1 are a modification used whenever continuous feed addition is used. Experimental Procedure
Boiling Point Technique. The experiments were performed in two stages. The first stage consisted in boiling point determination needed to establish the boiling point us. liquid compositions curve. The equipment used was basically the same shown in Figure l except that a vertical reflux condenser was used instead of the metallic one. The upper extremity of this reflux condenser was connected to the Cartesian manostat system. The self-zeroing burets were also absent. First, a weighed charge
0.1700
0,1300
34.0 0.00
0.05
0.10
035
0.20
0'0500 aoioo
X
Figure 2. A graph of liquid composition ( X ) vs. resistance for the methanolwater system is made as a first step in the boiling point technique.
Figure 3. A graph of residue W/Wo vs. resistance for the methanol-water system is prepared for the second step in the boiling point technique
t E
0.5
0.C
0.7
0.8
0.9
A 1.0
11
w/ w,
Figure 4. A plot of residue W/ WOvs. Wx/Wo is obtained by eliminating the resistance in Figures 1 and 2 VOL. 53, NO. 11
NOVEMBER 1961
897
1.o
0.7
1 .o
-
0.8
0.5
0.6
>.
h
0.3
0.4 Our d a t a 0.1
0.2
Y
I
0.00
0.05
I
I
030
015
C
X
Figure 5. The boiling point technique yields x - y data (weight for the methanol-water system in good agreement with the literature
yo)
of the most volatile component was introduced in the still. The boiling point curve was then determined as successive weighed quantities of the least volatile component were introduced. This procedure was continued until the final solution in the still was essentially the pure high boiling component. This required some occasional withdrawal of part of the still contents and continued addition of successive weighed batches of the least volatile component. The second stage of the experiment consisted of the actual distillation for determination of the equilibrium data. After the desired amount of least volatile component had been added, the distillation could be begun without the necessity of making up a new solution. Initial weights ranged from 1000 to 3000 grams with vapor samples varying from 10 to 30 grams. I n the first runs, the 0.1 C. thermometer employed was unsatisfactory. Substitution of a Beckman thermometer gave data which checked well with literature values provided precautions were taken to minimize bumping and small temperature fluctuations. The use of an internal heating coil, boiling chips. and a boiling bell ensured satisfactory temperature measurements. Practically, the internal coil was the most important factor in eliminating fluctuations. Under adverse conditions in which the liquid level in the Cottrell pump becomes too low, the pumping is irregular and results in erratic temperature measurements; for good temperature measurernents, it is necessary that the boiling liquid be continuously squirted onto the thermometric bulb. Distillate Analysis Technique. The need for precise determination of temperatures can be a limiting factor in the usefulness of the method. Accordingly. the distillate may be analyzed and the composition of the mixture in the still established by material balance. A weighed quantity of the more volatile component was placed in the still and the system brought to standard
898
0.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
X
Figure 6. This plot compares x - y data (weight %) obtained b y the boiling point technique for the acetone-methanol system with the literature
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.4
x
0.6
0.8
Figure 7. Vapor-liquid equilibrium data for the methanol-water system, obtained b y the distillate analysis technique, compare favorably with the literature
atmospheric pressure. Heat was supplied to the still, and the solution was agitated by a magnetic stirrer. When the first drop of condensate appeared in the receiver, the addition of the less volatile component was started. The feed was metered through two, 50-ml. self-zeroing burets filled from a reservoir by gravity flow (Figure 1). The burets were used alternately in order that readings could be taken, and burets were refilled without disruption of the feed addition. When the proper amount of distillate was collected, the feed was stopped from the first buret and started from the second. The stopcocks on the distillate and pressure-equalizing lines were closed, the receiver was removed, and the temperature recorded. An empty receiver was then inserted onto the distillate line, and the stopcocks on the distillate line and the pressure-equalizing line were opened.
Table 1.
0.2
'I0
7
0.0
0.2
0.4
0.6
0.8
Figure 8. The boiling points for the methanol-water system are shown as a function of the weight fraction of methanol in the liquid
Vapor-Liquid Equilibrium Data for the Methanol-Water System (Run
No. 1 1 ) Original change equals 3126 grams
No.
1 2 3 4 5 6
7 8 9 10 21 22 23 24 25 26 27 28 29 30 41 42 43 44
1.0
Weight Fraction. Methanol
Ohms
Distillate, Grams
34.20 34.23 34.26 34.29 34.32 34.35 34.38 34.41 34.44 34.47 34.80 34.83 34.86 34.89 34.92 34.95 34.98 35.01 35.04 35.07 35.40 35.43 35.46 35.49
132.48 82.19 49.27 56.13 50.36 45.93 38.06 40.35 41.99 35.53 30.89 28.95 31.75 27.70 28.61 29.10 30.16 29.10 31.04 30.70 57.90 52.14 57.56 101.35
w
1
Grams 2994 2912 2862 2806 2756 2710 2672 263 1 2589 2554 2194 2165 2133 2106 2077 2048 2018 1989 1958 1927 1505 1453 1395 1294
w/W" 1.138 1.106 1.088 1.066 1.047 1.030 1.015 1.000
0.9840 0.9705 0.8338 0.8228 0.8107 0.8002 0.7893 0.7782 0.7668 0.7557 0.7440 0.7323 0.5718 0.5520 0.5302 0.4917
X
0.1900 0.1840 0.1780 0.1720 0.1665 0.1610 0.1553 0.1497 0.1443 0.1390 0.0868 0.0826 0.0785 0.0741 0.0700 0.0660 0.0617 0.0579 0.0542 0.0505 0.0126 0.0098 0.0067 0.0047
Wx/ Wa 0.2161 0.2036 0.1936 0.1834 0.1744 0.1658 0.1577 0.1497 0.1420 0.1349 0.0724 0.0680 0.0636 0.0593 0.0553 0.0514 0.0473 0.0438 0.0403 0.0370 0.0072 0.0054 0.0035 0.0023
VAPOR-LIQUID EQUILIBRIUM 1.0
r
m
-
105
ae-
I
1.o
I
t
0.8
0.6
- Literature ( 6 )
-Literature (6) e Our doto, least squares 85
t
00 0.0 X
Figure 9. Vapor-liquid equilibrium data for the n-propyl alcohol-water system,obtained by the distillate analysis technique, compare favorably with the literature
The weight of the distillate and the volume of the feed were determined and recorded. This procedure was continued until the temperature approached the normal boiling point of the less volatile component. Using pycnometers the specific gravities of the distillate samples were then obtained from which the vapor-liquid compositions were determined. Experimental Results
Boiling Point Technique. I n general, the first few points were discarded in order to avoid any possibility of error while the apparatus was reaching smooth operation. I n Table I, a summary of a run on the methanol-water system is presented. Some data were omitted for the sake of brevity. To obtain the vapor concentrations, it is necessary to plot Wx us. W in accord with Equation 1. I n Figure 2, a graph of the liquid composition us. ohms of the platinum resistance thermometer for the first stage of the experiment is illustrated. I n Figure 3, the weight of residue W/Wo is plotted against the reading on the platinum resistance thermometer as determined
Table
II.
Vapor-Liquid Methanol in
Liquid, wt. %
Vapor,
5.1
28.5 32.2 35.5 39.1 43.0 46.3 50.1 52.8 55.7 77.7 79.7
6.0 7.0 8.2 9.5 10.9 12.4 14.0 15.7 40.9 43.3
wt.
%
0.2
0.2
0.4 0.6 0.8 Weight, Froction,n-propyl Alcohol
Figure 10. Boiling points for the n-propyl alcohol-water system are shown as a function of the weight fraction of alcohol in the liquid
in the second phase of the run. With the data from Figures 2 and 3, it is possible to eliminate the resistance which serves simply as a parameter. I n Figure 4, the desired curve of Wx/Wo us. W / W o is given. With the aid of numerical methods for differentiation, the slopes found from Figure 4 yield values of the vapor concentration. I n Figure 5 , the data as obtained for the system methanol-water are compared with values (7) taken from the literature. The agreement is satisfactory. Similar data were obtained in the same manner for the system acetone-methanol, and again the agreement is satisfactory as evidenced by Figure 6. Distillate Analysis Technique. The vapor liquid equilibrium data obtained for the system methanol-water are presented in Table 11. These are shown graphically in Figure 7 and compared with the data of Cornell and Montanna ( 3 ) . The boiling point curve is shown in Figure 8. The vapor-liquid equilibrium data for the system n-propyl alcohol-water, as calculated by numerical differentiation, are presented graphically in Figure 9 where they are compared with the data of Gadwa (6). The boiling point
Equilibrium Data for Methanol-Water at 760 Mm. Hg Temp., O
c.
95.2 94.5 93.7 92.8 91.8 90.9 90.0 89.1 89.2 78.8 77.6
Liquid, wt. % 45.7 48.2 50.7 53.3 55.7 58.2 60.6 90.7 93.3 95.9
Methanol in Vapor,
Temp.,
79.7 80.6 81.9 82.6 83.7 84.9 85.4 96.3 97.9 98.7
77.6 76.9 76.2 75.7 75.1 74.6 74.0 67.2 66.6 65.7
wt. %
c.
o’oO.O
1.0
0.2
0.4
0.6
0.8
1.0
Figure 1 1 , Vapor-liquid equilibrium data for the n-propyl alcohol-water system, calculated from least squares equation, are compared with the literature
curve is given in Figure 10. The data, as calculated by fitting a curve to the experimental data by the method of least squares and subsequent differentiation, are shown in Figure l l . Nomenclature
bl
weight of vapor in a typical vapor sample V = total weight of vapor distilled W = weight of liquid in flask W , = initial weight of liquid in flask x = weight percentage of more volatile component in liquid xu = weight percentage of component A in liquid xb = weight percentage of component B in liquid xg = initial value of x y = weight percentage of more volatile component in vapor yu = weight percentage of component A in vapor yo = weight percentage of component B in vapor v i = weight percentage of more volatile component in typical sample z = concentration of more volatile component in feed Z = total weight of feed =
literature Cited
(1) Bergstrom, H., “Chemical Engineer’s Handbook,” J. H. Perry, ed., p. 1361, McGraw-Hill, New York, 1941. (2) Chu, J. C., “Distillation Equilibrium Data,” Reinhold (1950). (3) Cornell, L. W., Montanna, K. E., IND.ENG.CHEM.25, 1331 (1933). (4) Daniels, F., others, “Experimental Physical Chemistry,” 4th ed., p. 77, McGraw-Hill, New York, 1949. (5) Emil Greiner Go., Brochure on Cartesian Manostat. (6) Gadwa, T. A., “Chemical Engineers’ Handbook,” J. H. Perry, ed., p. 1367, McGraw-Hill, New York, 1941. (7) Othmer, D. G., Benenati, F. R., IND.ENG.CHEM.37, 299 (1945). RECEIVED for review January 3, 1961 ACCEPTEDJULY17, 1961 VOL. 53, NO. I 1
NOVEMBER 1961
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