Separation of Hydrocarbons by Liquid Membrane Permeation Norman N. Li Corporate Research Laboratories, Esso Research and Engineering Co., P . 0. Box 45, Linden, N . J . 07036 A novel separation technique based on selective permeation through liquid surfactant membranes was developed for separations of hydrocarbons (as well as aqueous solutions). An emusion-treating technique a n d a method of using membrane-strengthening agent with surfactants before making the emulsion are very effective in generating a stable emulsion having liquid membranes of high selectivity a n d very large surface area. Such a n emulsion can be intensively mixed with wash solvent without drop breakup and solvent emulsification. Historical background, some possible process schemes, and the unique features of this technique and its comparison with extraction are described. The permeation and separation mechanisms are discussed in terms of the effects of temperature, membrane additives, solvent-emulsion mixing intensity, a n d the nature a n d composition of feed a n d surfactant solution.
Liquid membrane permeation is a novel separation technique which gets its selectivity from the relative diffusion rates of feed components through a liquid surfactant membrane surrounding a droplet of the feed. I t gives nearly perfect membrane selectivity for many hydrocarbons. This separation technique was discovered from a laboratory observation that Saponin. a natural surfactant, forms a strong and visible film a t a water-oil interface. The film is so strong, that in a Du Nuoy ring experiment for measuring interfacial tension, the ring can actually hook up the film and suspend it in the top oil phase. The usefulness of this kind of instantly formed film for separation purposes was then considered. The first task was to devise a separation scheme for testing the feasibility of such an idea. The original separation scheme employed a small tower, called a liquid membrane diffusion tower. The tower contained three phases-an aqueous surfactant solution a t the bottom section of the tower, a hydrocarbon solvent in the middle section, and a raffinate solution at the top formed by the drops rising out of the solvent phase (this section of the tower was, of course, initially empty). In the tests, drops of a hydrocarbon feed, usually binary mixtures such as n-hexane-benzene, were bubbled through the aqueous surfactant solution from the bottom of the tower. The aqueous liquid membranes formed instantly around the drops and allowed them to rise through the solvent phase without dissolving in it. The solvent can be any organic compound boiling well outside the range of the permeate because the permeate can then be easily removed by flash distillation. All the solvents used had no significant selectivity for any of the feed components and therefore, were completely miscible with the feed: in this way, the separation obtained was owing entirely to membrane selectivity. The drops, after emerging from the solvent because of density difference, coalesced in the top section of the column to form the raffinate phase. which was analyzed for enrichment in the nonpermeating feed component. The membrane portions of the coalesced drops formed surfactant droplets which descended down to the aqueous bottom phase for re cycle.
The initial tests were successful in showing some degree of separation and in proving that the separation scheme was basically workable. Subsequent single drop experiments showed that liquid membranes have nearly perfect selectivity for many hydrocarbons. However, two very serious problems were encountered. One was partial membrane rupture which produced a low overall selectivity in spite of the high inherent selectivity of the membrane. The other was small surface area which resulted in low overall permeation rate. The small surface area was owing mainly to large drop size (average drop diameter was about 0.3 cm) and drop sticking in the solvent phase. The sticking of droplets produced large clusters of droplets which reduced the overall surface area for mass transfer. Mixing could not be used to break the clusters and to improve drops-solvent contact because the membranes would be ruptured. Without overcoming these major problems, the liquid membrane separation technique would have remained a laboratory curiosity. The breakthrough came when solutions to these problems were found. General Description of the Modified "Liquid Membrane" Separation Technique
The first major improvement was to make emulsionsize feed droplets. Detailed discussion of it has been presented in a separate paper (Li, 19'ila). Briefly stated, it involved emulsifying the feed in the surfactant solution, which resulted in a sharp decrease of the average drop diameter from 0.5 em to 10 em. Both the drop stability and the permeation rate were increased greatly owing to the tremendously increased total surface area of the drops. The emulsion was then mixed with the solvent. Varying the ratio of emulsion to solvent did not vary the selectivity as expected; however, it did change the permeation rate because of the changed concentration gradient across the membrane. Demulsification after solventemulsion contact was achieved by the use of conventional demulsification techniques such as heating or electrostatic coalescence. The other advance was the use of glycerol t o strengthen the membrane as discussed in the next section. The combination of these two techniques makes drop breakup insignificant even when the drops are Ind. Eng. Chern. Process Des. Develop., Vol. 10, No. 2, 1971
215
Experimental Apparatus and Procedure
I
I
1
P R O D L C T 2SE3ARAIOR
8URFd:TAhT
SOLUTION
Figure 1. Process scheme modified b y emulsifying feed
d Q U E O U S SUR-
HYDROCARBON
FACTANT SOLUTION
+
EMULSION
U
The runs with diffusion columns were described elsewhere (Li, 1971a). The laboratory-scale emulsion runs consisted of first making an emulsion of the feed solution to be separated in an aqueous surfactant solution by using an ordinary high-speed mixer or blender. The emulsion thus made and the solvent were then fed into another mixer three in. in diam by one ft long containing a central stirrer which had multiple blades for good mixing. Drop breakup in the mixer was tested by using a dye tracer technique (Li, 1971a). The mixer content constantly flowed into a settler of the same capacity (Figure 2). The mixer-settler unit can be operated either manually or automatically. I n the latter case, a liquid level control in each unit and two pumps for feeding the emulsion and the solvent, respectively, are required. In studying the effects of temperature and the intensity of mixing, batch runs were made with the mixer placed in a heating mantle, which was connected to temperature control instruments. Results and Discussion
MIXER
SOLVENT SETTLER
Figure 2. Single-stage mixer-settler combination
intensively mixed with the solvent. Good separations of many different kinds of hydrocarbon mixtures are achieved therefore. In many cases, separation factors, which are defined as the concentration ratio of a more permeable compound to a less permeable compound in the solvent phase to the concentration ratio of these two compounds in the raffinate phase, were increased more than 25-fold t o values near 100, and permeation rates became much higher than those found in liquid permeation of the same hydrocarbons through one-mil polymeric membranes (Binning et al., 1961; Li and Long, 1970. 1971). Several process schemes are possible with the improved liquid membrane technique. For example, instead of the diffusion columns discussed previously, combinations of mixer and settler can be used as illustrated in Figure 1. Briefly stated, the feed is emulsified by the surfactant solution recovered from the demulsifier, the emulsion thus made is sent to a mixer to be mixed with the solvent, where selective permeation takes place. The emulsion and the solvent continuously flow into a settler where they are separated rapidly into two layers because of their large density difference. The solvent phase is sent to a separator to recover the permeates from the solvent; whereas the emulsion is sent to a demulsifier t o remove the nonpermeable or less-permeable compounds. In addition t o the combination of mixer and settler, combinations of wetted-wall columns, or diffusion column, emulsifier, and demulsifier may be used. 216
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 2, 1971
Elimination of Drop Breakup by Glycerol. Although several surfactant membranes show nearly perfect selectivity for various types of hydrocarbons in single drop experiments, the overall membrane selectivity is low because of drop breakup. Emulsifying the feed droplets does stabilize droplets considerably but does not entirely eliminate breakup. However, glycerol was effective in eliminating drop breakup. Adding glycerol to a membrane increases the water layer viscosity and the surfactant layer strength by the synergistic action between surfactants and glycerol. For instance, as shown in Table I , without glycerol, the life of a stationary feed drop (heptane-toluene) coated with a surfactant (Saponin) membrane in a solvent is about 10 min. Adding glycerol extended the drop life to more than three hr. The demulsification method used can be the same in both cases. In actual runs, without glycerol the overall separation factors are three for separating benzene from hexane and cyclohexane and seven for separating benzene from isohexane, isoheptane, and toluene. Using glycerol increased the separation factors in these two cases for benzene to 95 and 60, respectively (Table 11). The permeation rate is lowered, however, by the use of glycerol, presumably owing to an increase of film thickness. As far as the effect of glycerol is concerned, Table 1. Effect of Glycerol on Membrane Life and Permeation Rate
Surfactant: Solvent for permeates: Feed: Temperature:
Saponin Hexane Toluene-Heptane (A7-nC7) (1-to-1 by wt) 25" c
+
Saponin solvent
Membrane life (life of feed drop), min Permeation rate of A : , g! hr, 100 cm' Time for nCj to appear in solvent. min
Water
10
12.1 10
+
Water glycerol,
Water glycerol,
30%
70%
194
4.2
50
200
0.80
85
I
8 ,
I
Table 11. Effect of Glycerol Concentration on Separation Factor
Run temperature = 25" C Separation factors of permeate (referred to poroffin) at different glycerol concentrotions in water LL
Permeate
Surfactant: Saponin (0.2c'c) Feed I" A,, Feed 11' Feed 111' Feed IVc
A: Ah A: A6 Cyclo CC C,C
C6
0 Yo
30%
70%
0
1
I
I
40
20
60
3.7 2.9 6.1 4.7 2.9 1.2 1.5 2.0
Surfactant: dodecyl sodium sulfate (0.25) Ab 4.4 Feed I" A: 2.6 Feed IIh A6 8.4 A: 5.4
5.8 5.8 8.4 5.0 3.6 1.2
14.3 8.5 60.0 32.1 95 .O 2.7 2.0 4.0
5.3 2.5 7.0 3.9
13.4
Figure 3. Effect of glycerol concentration on permeability dN/di
E
=
PA(C- C) PHASE 2
MONOLAYER
~
22
r n
I.I
28.8 15.0
Feed I, hexane-benzene-toluene. Feed 11, 2,4-dimethyl butane-2,4-dimethyl pentane-benzene-toluene. ' Feed 111, nC6-A6cyclo C6. ' Feed IV, nC6-1-CC-l,5 C , T .
1
I
\
Table Ill. Separation of Aromatics from Virgin Naphtha
Surfactant solution: Run temperature:
I
80
WT % OF GLYCEROL IN SURFACTANT SOLUTION
0.lc;C Saponin water 25" c
c2
+ 70% glycerol + DIRECTION OF DIFFUSION
Components
Feed composition, w t Yo
Permeate composition in solvent phose, wt O h
Total aromatics Total paraffins Total naphthenes
21.2 39.8 39.0
85.3 11.1 3.6
Separation factors of aromatics: Based on paraffins = 14.4; based on naphthenes = 43.7.
70% by weight of glycerol appears t o be its optimum concentration. The actual amount of glycerol used in each application will depend on a balance between selectivity and permeation rate. In an actual process design, the separation data will enable one to calculate the number of stages needed for a given separation and the permeation rate data will enable one to calculate the size of each stage. A potential application of this novel separation technique is to remove aromatics from virgin naphtha. As shown in Table 111, the separation factor of aromatics in reference to paraffin is 14.4 and that to naphthenes is 43.7. Effect of Membrane Thickness and Thinning Rate on Permeability. Permeability and permeation rate, defined by the following mass transfer equation, have been calculated from the data obtained in the single drop experiments with Saponin used as the membrane-forming surfactant.
dN/dt = P A ( C - C )
(1)
As shown in Figure 3, the permeability decreased with increasing glycerol concentration in the surfactant solution. This indicates that mixing glycerol with the surfactant has the effect of thickening the liquid membrane, thereby reducing the diffusion rate. The decrease of permeability
Figure 4. Concentration gradients for diffusion through a monolayer
was rapid up to the glycerol concentration of 70% a t a constant sampling time. This suggests that the membrane had become so viscous a t 70% glycerol t h a t further addition of glycerol did not change the membrane thickness appreciably. The film drainage rate became constant a t the glycerol concentration of 50% because there was very little change of permeability and permeation rate in five min. Permeability discussed here is different from the one used by some researcher in describing diffusion through a monolayer (LaMer, 1962). A mathematical analysis is made to illustrate such difference for the simple case of a solute diffusing from a homogeneous phase, through a monolayer, into another phase. As shown in Figure 4, the diffusion is driven by an overall concentration difference, AC, which is C1 - C2. I n a steady state, if the solute flux across the total distance, Z,, is described by the Fick's Law, it is
(dN/dt)t= DA (C, - C,)/Zt
(2 )
Since Henry's Law for the monolayer can be written as:
C: = H,C, and Ci = H 2 c 2
(3)
The overall diffusion can be broken down into separate diffusion steps for the surfactant monolayer and the solvent phase number 2.
(dN/dt)i = DiA(C: - Ci')/Zi (dN/dt)g = D?A(Ci"- C?)/22
(4)
(5)
I n steady state, the flux as given by Equations 2, 4, and 5 are equal-Le., Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 2, 1971
217
l------
YJ Y
L
1.2
c. 0 z
90
YJ
1.0
z
i
0 z
m
J 3
z
70
z 0
+ z
ii a
2
0.4
L 4
i
=
2
i
0.2
0 0
E o0
I
100
I
200
300
I
400
600
500
700
c
40
,
800
900
I
1000
T I M E lMlN I
i
Figure 5 . Drainage of surfactant solution from a liquid membrane emulsion Temperature, 25" C; surfactant solution: 0.2% Saponin, 29.8% HLO, 70%
i I 10
1
I
1
I
/
-
"
40
50
bO
I
70
Figure 7. Effect of temperature on permeation rate Permeate: toluene; emulsion-solvent mixing rate: 370 rpm; sampling time interval: 10 min
0.01
I
I
0
2
4
H.C. SOLVENT
I
I
,
,
J
b
8
10
12
14
T I M E . MINUTES
Figure 6. Permeation of toluene through lgepal film (for clarity, only the data points on the 5 and 10% acetone lines are shown)
7 V E R Y THICK W A T E R L A Y E R SOLUBILITY hlAY BE CONTROLLING
r V E R Y THIN \VATER L A Y E R DIFFUSION M A Y BE C O N T R O L L I N G
Aqueous solution: 0.1 Y' o lgepal dissolved in water and acetone
Figure 8. Structure of a liquid membrane
0 5%
(H.C. = hydrocorbon)
Acetone concn
A 10%
(dN/dt)t= (dN/dt)i = (dN/dt)z
(6)
From the above equations, we obtain
(Di/Zi)H= ( D ? / z * ) ( D 1 / 2 t ) / [ ( D * / Z(DtiZt)] ?) (7) or
PiH = P;P//(P,'- Pj')
(8)
Pi = DilZi PI = D,/ Z? Pj' = Dt/Zt
(9 )
where
(10) (11)
P;, Pi, and P,' are, therefore, Fick's Law permeabilities. T o relate these parameters to the liquid membrane permeability or overall mass transfer coefficient. one can write the following equation by combining Equations 1 and 2
(dN/dt)t= Pt(Ci - Cz)= P(€i - CI)
(12)
From Equations 8 and 12, one obtains
P = P : P I H / ( P { H+ Pi')[(Ci- C*)/(C- C I ) ] (13) Relationship between Film Drainage and Weight Ratio of Surfactant Solution to Feed. The minimum weight ratio of surfactant solution/ feed necessary for forming a stable emulsion can be determined by two methods. One is to 21 8
I
I
30
20
T E M P E R A T U R E IT1
151 Acetone
-
I
0
E "1
E
t
10
glycerol; feed: toluene-heptane (1 -to-1 by wt)
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 2, 1971
make a series of emulsification tests a t varying surfactant solution to feed ratios. The other is a drainage experiment, which involves making an emulsion with a much higher than necessary surfactant solution-to-feed ratio and measuring the volume of the surfactant solution drained from the emulsion phase under the influence of gravity to determine the final amount of surfactant solution retained in the emulsion phase. Close agreement between these two methods can usually be obtained. For example, for the typical case where the feed was a mixture of 1-to-1 toluene-heptane and the surfactant solution was composed of 0.2% Saponin, 29.8% water, and 70% glycerol. The minimum weight ratio was determined to be 0.45 from the emulsification tests and to be 0.45 from the drainage experiment starting from a ratio of 1.2 (Figure 5 ) . In general, the second method, being much easier to use than the first, is employed to determine the minimum amount of surfactant solution needed t o form a stable emulsion for a given feed-surfactant system. I t should be noted that the drainage curves obtained when plotted as the amount of surfactant solution drained vs. time can be closely approximated by the commonly used drainage equations such as the equation recommended by Davies and Rideal (1963) for slowly draining foams.
d v / d t = B V o / 2 (Bt + l)-''
(14)
Effect of Acetone in Liquid Membrane on Membrane Selectivity. To examine further how the permeation rate is influenced by additives in the water layer in a membrane, mixed solvents of water and acetone were used to dissolve surfactants. No glycerol was used together with acetone. Acetone was chosen because of its good miscibility with water as well as with the hydrocarbon feed. It was hoped, therefore, that the use of acetone in the membrane might increase the permeation rate of hydrocarbons. However, the diffusion rates of toluene and heptane through the liquid membranes formed in such a solution remained constant throughout the acetone concentration range from 0 to 30%, indicating that the presence of acetone in the water layer did not facilitate the transfer of hydrocarbons. This is shown by the relatively unchanged slopes of permeate concentration vs. time curves in Figure 6. The difference between the starting points of any two curves was chiefly owing to feed contamination on the walls of the container used. At acetone concentrations higher than 30%, the membranes around the toluene-heptane drops became highly unstable and ruptured practically at the moment they were formed. Although the exact reasons for the decrease of membrane stability when acetone is added to the membrane are not yet completely clear, viscosity appears to be a major influencing factor. Membrane viscosity and thickness are interrelated because the more viscous the surfactant solution, the thicker the membrane. Thicker membranes give rise to lower permeation rate but higher drop stabilities. Since the viscosity of acetone is smaller than that of water and much smaller than that of glycerol-e.g., a t 60' C. their respective viscosities are 0.24, 0.50, and 100.0 cP-adding acetone t o water will lower the water layer viscosity and, hence, increase the film drainage rate, whereas, adding glycerol to water increases the layer viscosity and thus increases the film stability. Membrane Structure and Temperature Effect. The permeation rate increased exponentially with temperature (Figure 7 ) , whereas the selectivity remained about the same throughout the temperature range studied. As discussed previously (Li, 1971a), the liquid membrane on the surface of a hydrocarbon drop in a hydrocarbon solvent should have, by necessity, two surfactant layers with a water layer containing some free surfactant molecules in between (Figure 8). When the drop undergoes violent mixing motion in the solvent phase, the outer layer of surfactant and portion of the inner water layer are constantly being wiped off the membrane. New outer layers of surfactant apparently can be formed almost instantly by the free surfactant molecules in the water layer. The water layer may eventually become ultrathin and tightly bonded to the hydrophilic ends of the two surfactant layers. For this kind of membrane structure of two surfactant layers with one water layer in between, the permeation rate of a permeate is a function of its solubility in and diffusivity through the membrane. The diffusivities of hydrocarbons through a liquid membrane should be quite close in value as suggested from the known diffusivities of hydrocarbons through water. In comparison, the solubilities of hydrocarbons in water are quite different (McAuliffe, 1966). The solubility of a hydrocarbon in water is therefore the controlling factor in determining its permeation rate and the membrane selectivity (Li, 1971a). I n the case of varying temperature in studying permeation rate, the diffusivity usually increases approxi-
Table IV. Membrane Separation Does Not Depend on Volatility Difference Hydrocarbon mixture
Bp, ' C
Preferentially diffusing comp
n C-
98
A-
110 68
A-
81
Cyclo
nC6 Cyclo
c,
Seporotion per stage
50c; C6
50';
-
99';
76'c
mately linearly with temperature, and the solubility varies to a much lesser degree with temperature. The decrease of membrane thickness, a third factor which does not exist in the case of permeation through a rigid polymeric membrane, therefore, appears t o be the main factor which accounts for the rapid increase of permeation rate with temperature. This is shown by the rate vs. time data a t constant temperature in single drop studies, where the rate always sharply increases near the time of membrane rupture owing to membrane thinning effects (Li, 1971b). For the hydrocarbons studied, their ratios of solubilities in water change very little with temperature within the temperature range studied. This accounts for the relative constancy of membrane selectivity throughout the temperature range studied. Membrane selectivity does not correspond to volatility difference. The two examples given in Table IV show the more permeable components are less volatile (higher boiling point) than the less permeable components. Because a membrane becomes thinner a t higher temperature owing to higher drainage rate, the highest temperature one can study is limited by the membrane stability. This means that a t a certain high temperature, the membrane becomes so unstable that complete membrane rupture occurs. I n an actual process, a balancing point needs to be determined by economics studies, a t which the cost increase owing to temperature increase is offset by the gain in rate increase. Effect of Mixing Intensity. Since the function of the solvent used in contacting the emulsion is t o remove the permeates, intimate contact of solvent with feed drops, therefore, is important. However, because of the surface compatibility among the drops and the density difference between the drops and the solvent, the drops tend to stick together. This reduces the total surface area for mass transfer. Good mixing of the emulsion with the solvent is essential, therefore, in obtaining high permeation rate. This cannot be done if liquid membranes were weak as intensive mixing would break up the membranes. However, since the membrane stability can be increased tremendously by making emulsion-size droplets and by the use of glycerol as a membrane strengthening agent, intensive mixing can be applied. As shown in Figures 9 and 10, both the rate and the separation factor obtained in batch runs increased with increasing stirring speed. The fact that separation factor was also increased shows that drop breakup was insignificant, if not zero. I t was mainly the consequence of the increase of permeation rates of permeates since separation in this membrane technique is entirely based on rate difference. For the same reason, both the separation factor and permeation rate obtained in batch runs will decrease a t times longer than shown in the drawings. They will reach a constant value instead of declining in continuous runs. Ind. Eng. Chem. Process Des. Develop., Vol. 10, N o . 2, 1971
2 19
100
0 z
-
80
I
1
I
I
c
'I 4
in
3 J
e
Y
0 Y Y
Y _1
0 t
a 0 LL m
0 LL
rn
0 m
9
0
d
W a
0 z Y
z 3 Y
c
0
2
a in
0 LL
ae
s
10'
20
TIME (MIN I
Figure
9. Effect of mixing intensity on permeation rate
Run temperature: 40"C; feed: toluene-heptane (1-to-1 by wt); surfactant solution: 0.2% Saponin, 29.8% H20, and 70% glycerol
0 53 rpm
A
170 rpm
30
40
50
0
TIME (h.1IN I
370 rpm
Figure 10. Effect of mixing intensity on separation factor Run temperature: 40" C, feed: toluene-heptane (140-1 by wt); surfactant solution: 0.2% Saponin, 29.8% H,O, and 70% glycerol
0 53
rpm
A
170 rpm
370 rpm
Conclusions
Table V. Effect of Feed Composition on Separation Factor
Run temperature: 25" C Feed composition (A;-nCi)
Permeate composition in solvent (A;-nC:)
Separation factor of A i in reference to nC;
20-80 50-50 70-30
55-45 79-21 96-4
22 51 91
Effect of a Feed Composition on Membrane Selectivity. Both membrane selectivity and permeate composition vary with feed composition. The results in Table V and the previously published results (Li, 1971a) show: The above conclusion is partly owing to membrane structure and thickness varying as a function of the nature of feed because of structure compatibility; and, solubility is a more important controlling factor than diffusivity for permeation as discussed in detail elsewhere (Li, 1971a). However, the effect of diffusivity is still appreciable. Although membrane selectivity is largely dependent on solubility, it is not the absolute values of the solubilities of the permeates, but the relative solubilities, or solubility ratio that determine the relative selectivity. T h e uniqueness of this novel separation technique, therefore, lies in utilizing water (or other solvent for surfactants) as an ultrathin membrane. If water were' used as the solvent in extraction for hydrocarbon separations, a huge amount of water will be needed to get appreciable yield and a tedious separation of the hydrocarbons from water, as solutes, is also necessary; whereas in a liquid membrane process, very little water is needed to achieve the same yield and there is no problem of separating permeates from water because the permeates automatically diffuse out of the water in the membranes owing t o the imposed concentration gradient. 220
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 2, 1971
A novel separation technique involving selective permeation of hydrocarbons through liquid surfactant membranes has been developed. An emulsion-treating technique and a method of using glycerol with surfactants before making the emulsion are very effective in generating a stable emulsion having liquid membranes of high selectivity and very large surface area. Such an emulsion can be intensively mixed with wash solvent without drop breakup and without emulsifying the solvent. The historical background as to how this technique was invented is briefly discussed. Some of the possible process schemes using diffusion columns and mixer-settler combination are described. The unique features of this technique and its comparison with extraction are briefly stated. The permeation and separation mechanism is discussed in terms of the effects of temperature, using glycerol and acetone as membrane additives, solvent-emulsion mixing intensity, and the nature and composition of feed. Acknowledgment
The author thanks K. Kammermeyer of the University of Iowa, E. L. Cussler of Carnegie-Mellon University, and D. A. Saville of Princeton University for their invitations to present the results discussed in this paper in their respective chemical engineering seminars. Discussions in these seminars were helpful in formulating this paper. Nomenclature
A = interfacial area, cm' B = constant used in Equation 14, sec-' C = equilibrium concentration of a feed component in the solvent phase, g/cc C = concentration of a feed component in the solvent phase at a given time, g/cc C' = concentration of a permeating compound a t the surface of a monolayer of a surfactant, g/cc C" = concentration of a permeating compound in the solvent phase near a monolayer of surfactant, gicc
D = diffusion coefficient, cmL/sec H = Henry’s Law constant
N
= amount a feed component permeated, g
P = membrane permeability, cmisec, corresponding to an overall mass transfer coefficient
p’
= permeability used in Fick’s Law diffusion equa-
cmlsec t = time, sec v = volume of the surfactant solution drained from a column of emulsion, cc v, = original volume of a surfactant solution in a column of emulsion, cc distance of permeation, cm
z=
SUBSCRIPTS
Davies, J. T., Rideal, E. K., “Interfacial Phenomena,” Academic Press, New York, N . Y., 1963, p 401. LaMer, Y. K., Ed., “Retardation of Evaporation by Monolayers,” Academic Press, New York, N. Y., 1962. Li, N. N., Long, R. B. in “Progress in Separation and Purification,” Vol. 3, E . S. Perry, Ed., Interscience, New York, N. Y., 1970, p 153. Li, N. N., Long, R. B., “Membrane Processes,” Perry’s Chemical Engineering Handbook, 5th ed., McGrawHill, New York, N. Y., in press, 1971. Li, N. N., A I C h E J . , inpress (1971a). Li, N. N . , manuscript in preparation for “Progress in Separation and Purification,” Interscience, New York, N. Y., in preparation, 1971b. McAuliffe, C., J . Phys. Chem., 70,1267 (1966).
1 = in the surfactant monolayer 2 = in the solvent phase t = for the total system including a surfactant monolayer and solvent phases
RECEIVED for review April 13, 1970 ACCEPTED January 13, 1971
Literature Cited
Binning, R. C., Lee, R. J., Jennings, J. F., Martin, E. C., Ind. Eng. Chem., 53, 45 (1961).
Presented at the Division of Industrial and Engineering Chemistry, 160th Meeting, ACS, Chicago, Ill., September 1970.
A Correlation of Vaporization Equilibrium Ratios for Gas Processing Systems Robert 1. Robinson, Jr.’ and Kwang-Chu Chao’ Pan American Petroleum Corp., Tulsa, Okla. 74103 A correlation of vaporization equilibrium ratios in hydrocarbon mixtures i s developed based on the same structure as the work of Chao and Seader with K = uy/$. A new set of equations i s obtained for the representation of u, the fugacity of pure liquids, in terms of reduced variables from J, = 0.35 to 1.8 and pr to about 6. Activity coefficients in the liquid solutions are expressed as a sum of contributions owing to interaction energy differences and to molecular size differences. Specific binary interaction constants in the regular solution expression for the energy differences are determined for a number of unlike molecular pairs of special interest in gas processing, including pairs involving as one component, methane, ethane, carbon dioxide, and hydrogen sulfide.
A
general correlation of vapor-liquid equilibria for a large class of mixtures is much needed in engineering calculations where generality, reliability, and ease of use are the prime considerations. The present work follows, in structure, the work of Chao and Seader (1961) t o meet these needs. New equations and parameters are introduced in the interest of broadening the scope and improving the accuracy of predictions. Vaporization equilibrium ratios are calculated in the present correlation according to the thermodynamic identity
K , = viyt/J/I
(1)
where the subscript refers to component identity. K , is defined as the ratio of the mole fractions in the equilibrium gas and liquid phases,
’ Present address, Oklahoma State University, Stillwater, Okla. 74074. To whom correspondence should be addressed. - Present address, Purdue University. Lafayette, Ind. 47907
K , = Y,/X,
(2)
The other quantities in Equation 1 are defined by = fLIp =
vi
fugacity coefficient of component i as a pure liquid
(3)
yi = fil ( f Y L X J =
activity coefficient of i in the liquid solution $4
7,
= ti I (PYJ = fugacity coefficient of i in the vapor mixture
(4) (5)
I n this paper, calculations of the three quantities and $ are described.
Y,
Fugacity Coefficient of Pure Liquids
A three-parameter, reduced-states correlation of u is adopted in this work. Following Curl and Pitzer (19581, two generalized functions. Y ” and Y ’ , are introduced, log
u
= log u
“ + w log Y ’
Ind. Eng. Chern. Process Des. Develop., Vol. 10, No. 2, 1971
(6) 221
