Adsorption Equilibria HYDROCARBON GAS MIXTURES W. K.LEWIS, E. R. GILLILAND, B. CHERTOW',
KWI) W.
P. CADOGAN2
Massachusetts Institute of Technology, Cambridge, Mass.
The vapor-adsorbate equilibria
for binary mixtures of the lower gaseous hydrocarbons o n silica gel and several activated adsorption carbons have been studied. Pressures from a few hundred millimeters absolute to as high as 20 atmospheres were covered and temperatures from 0" t o 40" C. were studied. In all cases mutual interference was foundthat is, the amount of a given gas adsorbed at a given partial pressure was always less in the mixture than it would have been if the other gaseous component had not been present. Several correlations t o predict the vapor-adsorbate equilibria based on pure gas isotherms were studied.
T
I
HE potentiality of separating gas mixtures by adsorption via procedures that are strilringly analogous to distillation led to an integrated study of the equilibria involved between hydrocarbon gas mixtures and adsorbents such as silica gel and activated carbon. Because gases like methane and ethylene can exist as a "condensed" phase a t ordinary temperatures and pressures when in contact with adsorbents, adsorption separation techniques are attractive. To handle the same gases by distillation would require high pressure units with refrigerated condensers; these are expensive in both initial investment and operating charges. Since this work began, commercial application became fact in the hypersorption process ( I ) wherein hydrocarbon gas mixtures are separated by continuous countercurrent movement of both gas and adsorbent. I n conjunction with the determination and corFigure 1. relation of the adsorption isotherms of the light hydrocarbons reported in the companion article (4), work was undertaken to collect and correlate data on the equilibration of gas mixtures at constant total pressure and temperature with commercially available adsorbents. Specifically, the adsorption equilibria of gaseous hydrocarbon mixtures were investigated, 35 vapor-adsorbate equilibrium diagrams being obtained. All the systems investigated are listed in Table I. There are two ternary systems. Pressure was investigated for three systems, the range being 0.33 to 19.2 atmospheres absolute; temperature was investigated over the range 0' to 40' C. for two systems. For the remainder, the conditions are 25' C., 1 atmosphere absolute. PROCEDURE AND APPARATUS Since the details of procedure and some of the original data have been published elsewhere (5),only the outlines of the procedure are presented. High grade hydrocarbons and tested analytical procedures were employed. Known quantities (volumetric) of each of the constituents of the binary or ternary mixtures were introduced to the adsorbent and were permitted to equilibrate under isobaric and isothermal conditions. The unadsorbed gas was analyzed (the volume of the so-called dead space around the adsorbent was known by previous determinaPresent address, Bristol Laboratories, Inc., Syracuse, N. Y. Present address, Standard! Oil Company (Indiana), Whiting Reaearch Laboratory, Whiting, Ind. 1
2
,~~,c*~rE 2s MM.
EAPIL'IP"
GLASS iUdlN0
Circulating Apparatus for Determining Vapor-Adsorbate Equilibrium tion with helium), a n d by material balance both s,y diagrams (where x and are the mole fractions in the adsorbate and vapor, respectively) and the quantity of the mixture adsorbed were calculated. As an experimental check on the calculated balances, the adsorbate was pumped off and its volume and analysis determined. To ascertain the attainment of equilibrium, either of the gases of the mixture was permitted to contact the adsorbent first; in this manner the equilibrium could be approached from two sides. Two general types of equipment were built, the "reversepass" apparatus, Figure 1 of (4), and the circulating apparatus, Figure 1 of this paper. Another reverse-pass type unit, Figure 2, was employed for all the high pressure investigations. Essentially, amixture,formed by either premixing in the premix chamber or by admitting first one gas to the adsorption zone and then the other, was passed back and forth over the adsorbent in the reverse-pass apparatus. Gas mixing was achieved by manipulation of the magnet-washer sets in the glass apparatus and b y thermo-siphon heating in the metal, high pressure units. Becaum of the large length to diameter ratio in the glass units, the mixing was poor; hence the equilibration required the order of 40 to 60 minutes. With the development of the circulating apparatus, this poor mixing was eliminated. The circulation is obtained by causing mercury to drop from a fine capillary into
1319
1320
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 42, No. 7
Table I. S u m m a r y of Binary and T e r n a r y S y s t e m s Investigated
1
Gas Mixture 2
1.
2. 3.
4.
5. 6.
7.
8.
9. 10.
..
11. 12. 13.
17.
C&-C3Ha C2Hs-CsHs
(0" C.) (40' C . )
..
~-
~~~~~
GLC
. . . . . . . . . . . .
. . .
. . . . . . . . . . . . . . . . . .....
2.75/2.55
. . .
......
. . . .
3.8413.3s
.......
. . . . .
Systems Involving Hydrocarbons of Same Degree of Saturation and Different 1\Iolecular Weights CIHI .. 7.7 .. 1.5713.18 ...... &HI CIHI 6.6 12:s , , 1.01/2.28 ....... CSHL .. 6.1 .. .. 0.7111.78 ....... CrHs CnHi 4.8 3:6 .. 0.60/1,54 2.43/3.35
3.58/5.02
.......
. . . . . ...... . . . .
iCiHI0
1 4 . C2H1-CaHs 15. CeHh-CaHa 16.
(Temp. 25' C.; total pressure, 1 atm. except where indicated) More Volatile Components Relative Volatility a t z = 0.50 .vi /x; ..... ____ ___ SG Carbon r P C C CGC .GLC YG PCC COC S y s t e m Involving Hydrocarbons with Same Number of Carbon Atoms per Molecule CzHz 3.0 1.4 .. .. 1.82/1.01 2.01/2.15 . , .. , . . 3.0 .. .. 0 . 4 7 i O . 25 ....... ....... CIHI 2.7 .. i:j .. 1.01/0.60 ....... 3,58/8.90 .. 3.0 .. .. .. 1.15/0.73 ....... . . . . . .. 2.2 .. .. 1.60/1,10 ..... . . . . . .. 1.8 .. .. 2.60/2,20 ....... . . . . . .. 1.6 .. 3.50/3,35 . . . . . . . . 4.4 .. 1.42/0.74 ...... ....... CiH8 3.1 .. i:i i'i 2.28/1.54 ....... 5.02/4.48 .. 3.1 .. .. 2.56/1.71 ....... ...... 2.2 2.1
3.1
3.85i3.40
..
i:5
4.65/3.95 3.30i2.53
.......
..,.,.,
....
..
.......
.......
.......
. . . .
......
Systems Involving Different JIolecular Weights a n d Different Degrees of Unsat.iration 1.15j3.58
18. 19. 20.
.......
3,38/1.48 4.55/5,1 5.75j5.30
21. 22.
.......
23.
2
24. CeHa-CaHa-CsHs
, , . .
. .
. , . , .
.
.
. .
. .
Ternary Systems Relative Volatilities SG CGC
Gas Mixture 1
..
. .
. . .
3
e12
CeHi
C~HI
2.0
a23
a12
an
3.4
13
13
the reservoir, B , trapping thereby a slug of gas mixture and causing it to circulate through C D F A B . Data obtained from both types of apparatus were in excellent agreement. The adsorbents employed mrere the following: silica gel, SG (Davison Refrigeration Grade, 14/20 mesh); activated carbon, PCC (Pittsburgh Coke and Chemical Company, designation No. EY-Sl-C, 30/60 mesh); activated carbon, GLC (Godfrey L. Cabot Company, Black Pearls 11, 30/60 mesh); activated carbon, CGC (Columbia G, 8/14 mesh). RESULTS Table I contains a summary of all the results obtained to date. For purposes of graphical presentation only a few of the data are shown and these are selected only for purposes of succinctness. The contents of Figures 3 to 8 summarize the trends observed. Figures 3 to 8 and Table I demonstrate obvious differences between silica gel and activated carbon in their preferences for the hydrocarbons investigated. I n Figure 3, for example, s the more volatile gas of the mixture when the adsorbent gel; it is less volatile when the adsorbent is activated carbon. Since other systems also exhibit significant differences and since these differences are believed due to several factors, the first part of the following discussion deals with the influence of molecular structure, molecular weight, and liquid boiling point on preferential adsorption on carbon and silica gel.
the more strong!y adsorbed gas. Figure 4 gives similar data on the system isobutane-1-butene. In this case isobutane has a higher vapor pressure at a given temperature than does 1-butene, and thus the effect of vapor pressure and the preference for the unsaturated structure supplement each other, making isobutane the more volatile compoqent both on PCC carbon and on silica gel. The greater preferential action of silica gel for an olefin as compared to the activated carbons is shown in Figure 4 by the greater selectivity indicated by the silica gel curve. Similar effects are shown for the systems acetylene-ethylene and propylene-propane given in Table I. I n both systems the silica gel indicates a strong preferential a,ction for the more unsaturated compound, and greater selectivities are obtained than with the activated carbon as adsorbent. For all four pairs at 1 atmosphere the relative volatility, OL = ( y ~ x ~ / y ~where s ~ ) , yl and y 2 are mole fractions in the vapor for the two components and nl and x2 are mole fractions in the adsorbate, over silica gel is approximately 3. Considering only the olefinpara& pairs, as the molecular weight goes up, the olefin passes from the component which has the lower liquid boiling point to the one vhich has the higher. Thus if both structure and
SYSTEMS INVOLVING HYDROCARBONS WITH SAME NUMBER O F CARBON ATOMS PER MOLECULE Several systems were investigated that involved components containing the same number of carbon atoms to the molecule but having different degrees of unsaturation. In such systems, the vapor pressures of the two components are approximately equal, and the effect of the differences in structure has the opportunity to be dominant. Figure 3 summarizes the data for the system ethane-ethylene for both activated carbon and silica gel. I n a normal vapor-liquid equilibrium, ethylene is the more volatile component; this is also true for the data with carbon, but with silica gel the selectivity, with respect to molecular structure, is sufficient to reverse the volatilities and make ethylene
Figure 2.
High Pressure E q u i p m e n t for Adsorption Equilibria
A t o atmosphere vacuum pump, gas cylinder, or volumetric and analytical burets; B t o manometer gage; C = adsorption ohamber and heating coil; a n d D = adsorption U-tube
July 1950
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INDUSTRIAL A N D ENGINEERING CHEMISTRY
adsorbents, there i s a structural difference which is strongly exhibited on the silica gel but not strong enough to upset the net preference for propane. The net effects can be seen in the relative volatilities at 1 atmosphere; over silica gel 2.1; over both PCC and CGC carbons 13.6. (The value 13.6 parallels the value of 12.5 for the system ethylene-propylene. Since propane and propylene are so similar in both molecular weight and liquid boiling point, ethylene behaves about the same with each of them over carbon, thereby demonstrating the small influence of hydrocarbon structure on carbon.) I n the methane-ethylene system (Table I ) all the factors discussed above combine to yield a greater relative volatility over silica gel than carbon, in view of the silica gel preference for the olefin on the basis of both structure and boiling point, whereas only the latter is of great importance on carbon.
s
0
0.2 0.4 0.6 0.8 1.0 MOL FRACTfON CzH, fN ADSORBATE 0 V 0
--
SIL I C A G&L 0.93 ATM. ABS. I 1 . 0 A7M. ABS. V /.S2 ATU. ABS.
-
2.95 A T U . ABS. 7.8s ATU. ABS. 10.2 ATM. ABS.
u,
3
COL OMBIA 6 CARBON A I A T M . ABS.
-
Figure 3. Vapor-Adsorbate Equilibria for Ethylene-Ethane Mixtures at 25" C. liquid boiling point can combine to favor the preferential adsorption of the olefin as in the four-carbon-atom pair, the question arises as to why the relative volatility is not much greater than for ethane-ethylene where structure and boiling point are in opposition. The answer probably lies in the fact that with increasing number of carbon atoms, the members of a pair are more similar in molecular weight (and hence size), and the influence of the double bond becomes more diffuse over the olefin molecule. As the structural factor is growing more diffuse, the boiling point factor becomes more favorable, the net effect being to hold the relative volatility about constant.
SYSTEMS INVOLVING HYDROCARBONS OF SAME DEGREE OF SATURATION AND DIFFERENT MOLECULAR WEIGHTS
.
Several binary mixtures were investigated, both components of which were either olefins or paraffins differing in molecular weight. The data for the system ethylene-propylene on silica gel and Columbia G carbon are given in Figure 5 . On both adsorbents ethylene is the more volatile constituent, the relative volatility being about 6.6 on silica gel and 12.5 on carbon. The lower selectivity in the case of silica gel is probably the result of the greater effect of the double bond in the small ethylene molecule as compared to the large propylene molecule. Similar data for the system ethane-propane are given in Table I. Ethane is the more volatile component but in this case the selectivity with silica gel is greater than with activated carbon at concentrations above 0.2 ethane. Probably because the liquid volatilities for the paraffin pair are closer than for the olefin pair, the adsorption volatilities for the latter are greater on both types of adsorbent.
SYSTEMS INVOLVING DIF?EFE"I' MOLECULAR WEIGHTS AND DIFFERENT DEGREES OF UNSATURATION I n the ethylene-propane system of Figure 6, the roles played by the combined influences of structure, molecular weight, and liquid boiling point on both types of adsorbent are demonstrated. With a large difference in both molecular weight and boiling point favoring the selective adsorption of propane on both
MOL FRACTION CgHro /N ADSORBATE A - P C C CARBON 0
- SILICA
GCL
Figure 4. Vapor-Adsorbate Equilibria for Isobutane and 1-Butene Mixtures a t 25" C. and 1 Atm. Absolute
The results of the investigation of the ternary system ethylenepropane-propylene, Figures 7 and 8, on both types of adsorbent are entirely in line with the qualitative observations above.
INFLUENCE OF PRESSURE I n Figures 3 and 6 the influence of pressure on the x,y equilibrium curve is shown. Increasing the pressure from 0.33 to 19.2 atmospheFes absolute in the system ethane-ethylene-silica gel serves to effect significant lowering of the relative volatility as shown in Table I. Over the range 1 to 7.4 atmospheres absolute the same effect is shown for the system ethylene-propane-carbon (Figure 6) and propane-propylene-silica gel (Table I). Hence the same influence is observed over both types of adsorbent. Further, the pressure influence parallels that of vapor-liquid equilibrium with the difference Sbeihg that the adsorption condition is isothermal whereas in vapor-liquid systems the temperature falls &lo?@;with the pressure. Since the adsorption conditions are isothermal, as the pressure is increased capillary condensation can occur. I n the three systems investigated with regard to pressure influence, the vapor-liquid relative volatility is much lower than the vapor-adsorbate relative volatility, both compared at 25" C. When capillary condensation occurs, the equilibrium should shift in the direction of the vapor-liquid equilibrium-that is, for the three cases studied, in the direction of lower relative ,volatility. Observation of the influence of
1322
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 42, No. 7
1.0
w
3
0.8
3
w
$ 0.6 %
E?CI
0.4
$
0.2
F
0
0
0
0.2 0.4 0.6 0.8 70 MOL fRACT/ON C2 H4 /N ADSOR5AT.E
0.2 0.4 0.6 0.8 1.0 MOL FRACTION Cg f f 4 IN ADSORBATE SILiCA GEL 0 O F A 2S°C. 0 40°C
--
SILICA GEL
CVLUU8iA G CARBON
-
0
esoc.
Figure 5. Vapor-Adsorbate Equilibria for Ethylene-Propylene Mixtures a t 1 Atm. Absolute pressure on a system where the vapor-liquid CY is greater than the vapor-adsorbate 01, a t the same temperature, would show whether the influence of increasing pressure may be generalized as always adverse (as thus far observed), or whether it is merely headed toward the vapor-liquid equilibrium.
INFLUENCE OF TEMPERATURE Only two systems were investigated, both over the narrow range 0' to 40" C. I n both instances, ethylenepropane-silica gel (Figure 6) and ethylene-propylene-silica gel (Figure 5 ) ) the relative volatility was depressed slightly by increasing the temperature. For the former system, the vapor-liquid 01 is greater than the vapor-adsorbate CY (at the same temperature); for the latter system the reverse is true. The data on these two systems are not sufficient to make generalizations relative to the effect of temperature. ADSORBENT CAPACITY FOR GAS MIXTURES I n Figure 9 there are plotted the adsorption isotherms of both pure propane and propylene, and the adsorption isotherm of each component when it is adsorbed a t constant total pressure in mixtures with the other. Two generalizations have been drawn from study of such plots:
In all 35 mixtures investigated, it was observed that the gas which is preferentially adsorbed in mixture is that pure gas for which the adsorbent has the higher capacity. (There is one a p parent exception, ethylene-propane-CGC at 7.40 atmospheres absolute, in which instance the pure gas isotherm cross at about 4 atmospheres; above this pressure ethylene is adsorbed at greater capacity than propane, where capacity is expressed as the mg. moles adsorbed per gram. If the capacity were expressed on the basis of weight adsorbed per gram, the capacity for propane would be.the higher.) At a given partial pressure, the adsorption of each gas is suppressed relative to the adsorption isotherms of the pure component-that is, each gas interferes with the capacity of the adsorbent for the other. Mutual interference has been observed for all 35 systems; this is in full accord with the thermodynamics of adsorption of gas mixtures (2). CORRELATION OF QUANTITY OF MIXTURE ADS0RBED The variation of total quantity adsorbed is not linear with composition expressed as mole fraction in the adsorbate. Rather it has been found that a plot of Nl against NQyields a satisfactory
0
-
, IAThf. ooc. 25 c. 4O0C.
COLUMB/A C CARSOhJ,.?5'f: A / A T M ABS.
P Ca
-
-
Z25ATM A B . 7 . 4 A T M ABS
Figure 6. Vapor-Adsorbate Equilibria for Ethylene-Propane Mixtures straight line for all the systems investigated, where .VI and ATz are the moles of eac,h component adsorbed from the mixture. The terminal values of the line are N ; and N6, the capacities for the pure components. The equation of the straight line may be written N J N ; f N2/hri = 1 (for the case of the ternary N , 4- N a system, = I). The data are plotted in Figure N : i- 7 iV, AT; 10 as N J N ; against N2IN;. This relation has been found to yield mixture adsorption values which are within 6% of the experimental value with the exception of methane-ethylene on silica gel; the empirical correlation is t'herefore considered very satisfactory.
N.
CORRELATION OF ADSORPTION RELATIVE VOLATILITY A number of different methods were tried for predicting the adsorption relative volatilities. None of those tested was really satisfactory. This is not surprising in view of the small amount of progress that has been made in predicting vapou-liquid equilibria. However, some of the methods are helpful for engineering approximat,ionsand are discussed below. Constant Relative Volatility. A study of all the mixture data indicated that' for a given system the value of the adsorption relative volatility, CY, was fairly constant with respect to composition. This method was tested for sixteen of the mixtures by taking a single dat'a point for each mixture and calculating the complete r , y diagram on the basis of a constant value of CY. In 80y0 of the cases the calculated values of y at a given 5 u'(?re within 5% of the experimental values. Van Laar Equation. An attempt was made t o fit equationR of the Van Laar (6) type to the adsorption equilibrium d a h , and it was concluded that the method was not satisfactory, although in a few cases reasonable agreement \vas obtained. Thermodynamic Method. In a thermodynamic analysis of the adsorption of gas mixtures Broughton's (8)equations state the relationship between the curves of Figure 10 as follons:
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
July 1950
1323
Table 11. Ekperimbntal against Calculated Relative Volatilities x = 0.60
0.8 Silioa Gel
0.6
Exptl. 19
Calculated (Thermodynamic
Method)
3.0
2.7
Y/
6.6
2.1 4.8 3.1 3 .O
0.4
0.2
0
0
0.2
0.6
0.4
Z 1
J
0.8
1.0
XI E7HYLEN.C PROPANE PROPYLENE
Figure 7. Vapor-Adsorbate Equilibria for Ethylene-Propylene-Propane Mixturw Columbia G carbon at 1 atm. a n d 25' C.; figures are values of the parameter, d x e xr
+
PCC Carbon C~H~-CIH~ CIHI-CIH~ CaHe-CvHu dC4Ha-GHa-1 Columbia G Carbon CHI-CZH~ CsH4-CnHs CaH&-cJHs CsHd-CsHe C:He-CrHs
1.4 13.6 3.6 1.5
8.3 4.5 1.8 8.3 2.9 4.1 3.1 3.2
24.0
1.3
0.9 5.5 3.6 1.1
. t .
... ...
...
15.4 1.5 12.5 13.6 1.1
Calculated (Adsorp!io nPoBenCal Method) 4.3 2.7 4.5 1.9 3.9
2.3 2.6
...
4.0 1.4 4.5
...
1.2
...
...
5.6
the terms without superscript the following relationships were employed : pl
+ pz =
Tr
(2)
r. o 0.8
Equation 2 is a physical restraint on the mixture; Equation 3 is an empirical observation discussed above; and Equation 4 ie an assumption based on the observation noted above. Properly combining all four equations yields
0.6 93
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1.0
x.9
I C S
--- crnyLEM
PROPAN€ PROPYLENE
Figure 8. Vapor-Adsorbate Equilibria for Ethylene-Propylene-Propane Mixtures Silica gel at 1 atm. and 25O C.; figures are values of the parameter, X I / X I 22
+
(The primes refer to the isotherms of the pure gas, and the absence of superscript refers to the adsorption isotherm of each component in a mixture with the other component such that the total pressure, T, is constant.) From proper experimental botherm data on the pure gases, two of the integrals can be evaluated. For the systems listed in Table I1 the isotherm data had t o be extrapolated to zero and the following methods were employed.
If the lowest experimental point was a t or below 0.15 mg. mole adsorbed per gram, a linear extrapolation of p against N was made to zero; if the lowest data points were between 0.15 and 1.0 mg. mole per gram, the Langmuir adsorption equation was fitted to the low pressure points and used for the extrapolation to zero; where the lowest values were above 1.0 mg. mole er P a m , no satisfactory method of extrapolation wa8 found. %o integrate
where 3 = N : / N i . The only unknown value in the above equation ie 01 for which a unique solution can be obtained by trial; ail other terms are known from the isotherms of the pure gases. The application of Equation 5 to the isotherms of Lewis e l al. (3) yielded the results in Table I1 under Thermodynamic Method.
A comparison of the experimental and calculated values indicates that agreement for the nine cases listed is only fair and the assumption of a Freundlich-type adsorption equation instead of the Langmuir type yielded no better results. Where no calculated values are given, the isotherm for the pure gases did not extend down to 1.0 mg. mole per gram of adsorbent. The lack of agreement is undoubtedly due to the methods employed for extrapolating the pure isotherm data to low pressure and to the assumption of constant relative volatility. However, on the basis of the systems so far studied, it is believed that this method has some utility for estimating the relative volatilities for the mixtures based on the data for the pure components. Adsorption-Potential Method. Another technique for using only the isotherms of the pure gases to predict adsorption relative volatilities was based on a modification of the Polanyi equation. It waa wsumed that the adsorption potential for each gtbs in the mixture could be pbtained from the Polanyi-type curve for the pure gases, Figures 7 and 8 of reference (4). Since the correlations for the pure gases had indicated that a t constant temperature the most important factor in determining adsorption potential was the amount adsorbed, it was assumed that, in mixtures, the potential value of the individual componenta waa determined by the total amount of adsorbate.
1324
I N D U S T R I A L A N D E N G 13 E E R I N G C H E M I S T R Y
l
?
0
0.2
0.4
N2 LESS 0
200 400 600 800 P c ~ Hor~ Pc,H,, MM. Hg ABS. A, A
e, 0 0.0
lo00
250 UM. He U . 760 MM, 'H A B t .
Vol. 42, No. 7
l
0.6
l
l
0.8
l
/.O
VOLATILE
N;
F i g w e 10. Total Adsorption Correlation for Silica Gel and Activated Carbons P C C Carbon
Silica Gel
Columbia G Carbon
1000 MU. Ug ABS.
Figure 9. Mixture Isotherms on Silica Gel at
25" c.
The potential value was used to calculate fp/jfor each of the components and the value of the vapor composition was calculated employing the Lewis and Randall type fugacity rule. For example, assume that it was desired to calculate the vapor composition in equilibrium with a given adsorbate composition for a two-component system of A and B . By the use of the pure gas isotherms and the correlation given in Figure 10, the actual moles of A and B adsorbed per unit weight of the solid can be estimated. The total volume of the adsorbate was then calculated by summing the product of the moles of each constituent adsorbed times its molecular volume as a saturated liquid a t the adsorption pressure. This total volume adsorbed was then used with the Polanyi-type correlation curves to obtain the adsorption potential values for each component. If both components are on the same correlation curve, the same value of the adsorption potential will be obtained but if they correlate on different lines, such as olefins and paraffins on silica gel, different potential values \?ill be obtained. I n order to evaluate the composition of the vapor from the adsorption potential values i t is necessary to employ some value of the molecular volume and there me several possibilities. For example, the molecular volume for each constituent can be employed with its potential or an average molecular volume for the mixture can be used for all Components. One method gave the best result in some cases, and the other appeared to be more satisfactory for other mixtures. Using either one of these methods for the molal volume allows the value of j s / j to be calculated for each component, These fugacities were related to composition by the Lewis and Randall type fugacity equation. Thus, f. was taken equal to the fugacity of the pure saturated liquid a t the temperature in question times the mole fraction of that component in the adsorbate. The values o f f so calculated for each component were used & determine the vapor composition by assuming that the fugacity for a component was equal to its mole fraction in the vapor times its fugacity as a pure vapor a t the same temperature and total pressure RS the mixture. The
calculation is trial and error to determine the total pressure that will give values for mole fractions in the vapor that add to 1. If this value of the total pressure is significantly different from the value used to determine the amount of adsorbate by Figure 10, the calculation must be repeated. I n making the calculations for Table 11, the pressure was originally assumed to be 1 atmosphere and, in thirteen out of the seventeen cases, the calculated pressure was within +5% of this value, and rec~alculationswere not made, The results of calculations based on the adsorption potential method using an average molecular volume for the mixtuie are given in Table I1 under Adsorption-Potential Method. In the systems involving silica gel given in Table 11, the agreement is reasonably good. The results for the activated carbons are not as satisfactory. With the two carbons the agreement is reasonably good if the two adsorbed components contain the same number of carbon atoms to the molecule, but where the molecular R eights of the constituents differ appreciably, the results are considerably in error. In fact, for this latter case, with the exception of the ethane-propane system, the calculated values are all low by a factor of about 3. Use of the molecular volume of the individual components instead of the average values gives much better results and such a modification does not significantly alter the values for the systems containing the same number of carbon atoms, but it does place the ethane-propane system considerably out of line. The use of the individual volumes also gives poor results for most of the silica gel systems. Additional data are needed to determine why the volatility of ethylene-Cs and the ethane-Cd systems differ so greatly. Until this difference is evaluated it is not clear whether the low values of the predicted relative volatilities are due to structural or molecular weight factors. When the two components have the same adsorption potential this method of calculation gives relative volatilities that appear similar to those for vapor-liquid equilibrium but differ because fi corresponds t o the saturation pressure of the liquid but j corresponds to a much lower pressure. This method gives relative volatilities that are independent of the composition for systems
INDUSTRIAL AND ENG INEERING CHEMISTRY
July 1950
k \
1325
14.0
4.0 P
P
8i=
82
10.0 3*0
.
2.0
(A)
6.0 0
0.2
0.4
Q T
2
i=
0.6
0.8
1.0
XI
J.0
4.0
P
0
cz@
0 L
2
d
0 01
5
10
PRESSURE
15
20
25
,A TM.
(0)
0
0.2
0.4
0.6
0.8
1.0
0.6
0.8
1.0
XI
Figure 11. Relative Adsorption Volatility for EthaneEthylene Mixtures on Silica Gel a t 25" C. 4.0
that give equal adsorption potentials for the two components. However, if the adsorption potential of the two components differ, the calculated relative volatility will be a function of the composition. Predicting Ternary Systems or Other Binary Combinations. The extension of these relations to either other binaries or ternary systems is possible because of the following observation: The relative volatility of any two components of the ternary mixture is approximately the same as the relative volatility of those two components in a binary mixture. For the silica gel system (call ethylene 1, propane 2, propylene 3), the 0112 found in ternary mixtures is 2.0; in the binary system it is 2.1 (Table I). For the carbon ternary ay13is 13.0, for the binary, 12.5. Since N3 5 Nz -5 = 1 for the ternary (critical examinations show
N:
+ N, +
the, relationship holds within 3%, with most of the sums being slightly less than l),2's and y's can be obtained. For most cases the a for a binary mixture can be calculated from two known binary systems in which one component is common, the other components being those to comprise the new binary. Thus for propane-propylene-silica gel CY = 3.1; for ethylene-propane-silica gel CY = 2.1; for ethylene-propylene 01 = 6.6 observed, 6.5 calculated. The value of such a procedure is obvious. Effect of Pressure. Two methods are presented to permit interpolation and extrapolation of the influence of pressure. Once the data have been obtained at two or more pressures a plot similar to Figure 11 permits ready interpolation of the values of 01 as both pressure and composition of the adsorbate vary. When data are desired at pressures different from that employed in the determination of an z,y diagram one may use a correlation similar to that of Figure 12. ;Relative volatilities varied essentially inversely as the ratio of N , / N ; , and the value of the relative volatility at any other pressure could be obtained from the value a t 1 atmosphere by multiplying the latter by the ratio of N : / N : for the two pressures. The agreement for the three systems that were studied at various pressures is shown in Figure 12. Summary of Recommended Correlations. The quantity of the mixture adsorbed per gram of adsorbent as a function of the adsorbate composition can be predicted satisfactorily from a knowledge of the quality of each pure gas adsorbed a t the temperature and total pressure of the mixture. For this prediction, a plot of N1 against N2 through the two known points is a11 that is required for binary mixtures. A method based on a modification of the adsorption potential theory is suggested for a rough estimate of the adsorption relative volatility.
d#
2.0 0
(a
0.2
0.4 XI
Figure 12. Correlation of Relative Volatility with Total Pressure at 25" C. Ethylene-Propane Mixtures Ethane-Ethylene Mixtures on on Columbia C3 Carbon Silica Gel 0 = 1atm. = 2.25atm. 0 = 1 atm. A = 7.85atm. A 7 . 4 atm. W = 2.55at.n. ' I= 19.2atm. Propane-Propylene Mixtures on Silica Go1 = 1 atm. X = 4 . 1 atm. V = 7 . 2 atm.
-
+
If an experimentally determined value of the adsorption relative volatility is available, the assumption that it is independent of composition is satisfactory in most of the cases. If a complete z,y equilibrium diagram is available through either experimentation or the use of the above correlations and if adsorption isotherms of the pure components are known, the influence of total system pressure may be estimated by the correlation of Figure 12. SUMMARY AND CONCLUSIONS 1. In the adsorption of gas mixtures, the factors of molecular weight, molecular structure, and liquid boiling point are involved in the phenomenon of referential adsorption. 2. At constant morecular weight and boiling point, molecular structure of the mixture constituents is of greater significance when the adsorbent is silica gel rather than activated carbon. 3. At constant molecular structure and molecular weight difference-that is, when the gas mixtures contain numbers of homologous series, the greater the boiling point difference the greater the relative volatility for adsorption on both activated carbon and silica gel. 4. When there is interplay of all the above factors, activated carbon adsorbs higher molecular weight gases; silica gel preferentially adsorbs on the basis of both liquid boiling point and gas structure and polarity. 5 . The pure gas for which the adsorbent exhibits the higher capacity is the gas preferentially adsorbed from a mixture. 6. At constant partial pressure there is less of a given hydrocarbon adsorbed from a mixture than from the pure gas-that is, each component interferes with and decreases the adsorption of the other components. 7 . At constant total pressure, the quantity of gas mixture adsorbed per gram of adsorbent lies between the values for each pure gas at the pressure of the mixture. 8. A satisfactory correlation of the quantity of mixture adsorbed is obtained from the correlation equation
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I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
9. For silica gel, an empirical correlation has been obtained for the prediction of adsorption relative volatility from a knowledge of the isotherms of the pure gases comprising the mixture. 10. When a complete x,y diagram has been obtained a t a given total pressure, the relative volatility may be estimated a t other pressures by means of the correlation of Figure 12 and a knowledge of the pure gas isotherms. 11. The relative volatilities of any two components of a multioomponent system appear to be equal to values obtained from a binary mixture of the gases under question. 12. The N1 against IV, correlation coupled with the assumptions of constant relative volatility (determined by the investigation of one mixture composition) yields satisfactory x,y diagrams in many cases. 13. Although the several activated carbons employed have different adsorption capacities, they yield essentially the same equilibrium diagram for a given mixture.
NOMENCLATURE fugacity of gas fugacity of gas a t saturation pressure of liquid a t temperature of adsorption quantity adsorbed from gas mixture per gram of adsorbent quantity adsorbed, as in pure gas isotherms] mg. moles per gram of adsorbent partial pressure of gas in equilibrium gas mixture, mm. Hg. abs. or Ib./square inch abs.
p'
=
z
= = = =
y 01
T
Vol. 42, No. 7
partial pressure as in pure gas isotherm, mm. Hg. abs. or Ib./square inch abs. mole fraction in adsorbate a t equilibrium mole fraction in gas a t equilibrium relative volatility, y ~ x z l y z x= ~ p,Nz/pz-li total pressure
Subscripts 1, 2, etc. = components 1, 2, etc. Adsorbent designations SG = silica gel PCC = activated carbon, Pittsburgh Coke and Chemical Company CGC = activated carbon, Columbia Carbon, grade G GLC = act,ivated carbon, Godfrey L. Cabot Company LITERATURE CITED (1) Berg, Clyde, Trans. Am. Inst. Chem. Engrs., 42,665-51 (1946). (2) Broughton, D. B., IND. ENG.CHEM.,40,1506-8 (1948). (3) Lewis, W. K., etal., J . Am. Chem. Soc., 72,1153, 1157, 1160 (1950).
(4) Lewis, W. K., Gilliland, E. R., Chertow, B., and Cadogan, W. P., IR'D.EBG.CHEY.,42, 1326 (1950). (5) Van Lam, Z . Physik. Chem., 72,723 (1910); 83,599 (1913). RECEIVED February 6, 1950.
(Adsorption Equilibria) PURE GAS ISOTHERMS W. K. LEWIS, E. R. GILLILAND, B. CHERTOW', AND W. P. CADOGANZ Massachusetts Institute of Technology, Cambridge, Mass. T h e adsorption equilibria for eight of the lower hydrocarbons from methane to C4's were measured for silica gel and several activated adsorption carbons. Most of the data were obtained at 25" C. and at pressures up to 1 atmosphere. In addition, i n several cases the effect of temperature was investigated up to approximately 250" C. and pressures up to 20 atmospheres were studied. The adsorption isotherms were correlated by a modification of the Polanyi adsorption potential theory.
T
HE use of solid adsorption for the separation of hydlocarbon mixtures has been proposed for a number of years, but has not gained wide acceptance because of the mechanical difficulties involved in the intermittent cyclical process that has been employed. Recent developments in the techniques of employing solids in continuous operation have revealed new posaibilities for making separations by adsorption. The main advantages of adsorption as a separation technique as compared to absorption, distillation, or extractive distillation are that in many cases much higher selectivity can be obtained by adsorption than by any of the other techniques, and adsorbents have a relatively high capacity for volatile materials even at low partial pressure. The feature of higher selectivity promises more effective separations, while high adsorbent capacity allows the use of higher temperatures and lower pressures than would usually be required with conventional separation methods. The present study has been devoted to obtaining fundamental data on the adsorption of hydrocarbon gases on activated carbon and silica gel. The first portion of the experimental program was concerned with the determination of the isotherms for individual pure gases on various adsorbents. The data for the individual systems are published elsewhere (7, 9, IO), and the summarized results for a number of the systems are presented Present address, Bristol Laboratories Inc., Syracuse, N. Y. Present address, Standard Oil Company (Indiana), Whiting ResedlLh Laboratory, Whiting, Ind. 1
2
in this paper together with the methods developed for correlatirig the data.
APPARATUS AND PROCEDURE A schematic diagram of the apparatus employed in the adsorption isotherm studies is given in Figure 1. A weighed sample of the adsorbent was placed in the U-tube. Prior to every run, the adsorbent was prepared by a standard degassing procedure consisting of evacuation for 1.25 hours while the adsorbent U-tube was held a t 150" C. At the end of this period, the adsorption chamber pressure as measured by a SICLeod gage was about 5 microns. The apparatus "dead space" associated with a given adsorbent was the volume of the adsorption chamber confined between the stopcock on the adsorption gas-measuring buret, the stopcock leading to the vacuum pump, and the manometer zero reference mark. It represented the adsorbent pore volume, the interparticle void space, and the volume of the apparatus capillary lines which could not be purged by filling with mercury. Dead space was determined by introducing measured amounts of helium into the evacuated adsorption chamber and noting the corresponding pressure. Adsorption of helium was assumed to be negligible under these conditions. Adsorption isotherms were obtained by admitting successive
