Table II. Dialysis of Acids from Salts
Solution Dialyzed 2 . 4 N FeS04-1.3N HzSOa
0.64N M g ( N 0 a ) r 1.55~\'"03
Table 111.
Acid
Fraction Dialyzed Acid Salt 0.65 0.023 0.59 0.28
Membrane Tyke Anion exchange0 Nonionic*
Anion exchangeC Nonionicb
0.008 0.50
0.90
0.88
Change in Volume of Concentrated Solution 1 . 5 yo decrease 70y0 increase
5y0 decrease 55y0increase
by the addition of SPVT to a sulfuric acid solution (Figure 2) can be explained in the light of Schlogl's theory also. SPVT is strongly ionized into protons and the negatively charged polymer molecule. The protons from SPVT partially satisfy the electrical neutrality requirement of the diffusing HzSO4 species, thereby lessening the attraction between the diffusing protons and bisulfate ions and thus increasing the membrane potential which gives rise to the anomalous negative osmosis.
Conductance of Acids Equivalent Concentration, Conductance, 1V Ohms-' 0.1 350.6 346,4 0.1 233.3 0.1 0.1 95.7
literature Cited
greater than for "03, the observed anomalous negative osmosis for H N O , is less than that for HCl. This difference may be due to membrane interactions, as the attraction of the anion exchange membranes is greater for NOa- than for C1-, as reflected in the greater selectivity for N O S - than for C1-. The selectivity of strong base anion exchange resins for N 0 3 over C1- is 3.80 (Wheaton and Bauman, 1951). T h e increase in anomalous negative osmosis brought about
Grim, E., Sollner, K., J. Gen. Physzol. 40, No. 6, 887-99 (1957). "Handbook of Chemistry and Physics," 38th ed., Chemical Rubber Co., Cleveland, Ohio, 1956. Mindick, M., Oda, R., Symposium on Innovations in Separation Processes, North Jersey Section, ACS, 1958. Schlogl, R., 2. Physik. Chem. (Frankfurt) 3, 73 (1955). Wheaton, R. M., Bauman, W. C., Znd. Eng. Chem. 43, 1088-93 (1951). RECEIVED for review January 19, 1967 ACCEPTEDJuly 13, 1967
ADSORPTION EQUILIBRIA IN THE METHANE-PROPANE-SILICA
GEL SYSTEM
A T HIGH PRESSURES JOHN J. H A Y D E L ' A N D R l K l KOBAYASHI Defartment of Chemical Engineering, William Marsh Rice University, Houston, Tex.
Further improvements and application of the chrorriatographic technique for obtaining adsorption equilibrium data have been made. Adsorption data have been obtained a t high pressure for methane, propane, and several of their mixfures on silica gel, by using radioactive tracer pulsing. A method of obtaining adsorbedphase volumes is introduced. The data are represented analytically using a two-dimensional virial equation of state truncated after the third virial coefficients.
general chromatographic method for determining the adsorption of gases on adsorbents was recently introduced by Gilmer and Kobayashi (1965), who presented the theory by which component and total adsorption of gases from mixtures on an absorbent could be determined by a per-
A
1
546
RATHER
Present address, Shell Oil Co., Houston, Tex. I&EC FUNDAMENTALS
turbation or chromatographic technique. Experimental adsorption data were obtained on the methane-propane-silica gel system to verify the proposed method. The present work was undertaken to extend the application of the method over a wider range of compositions, temperatures, and pressures and to make other modifications that would further generalize the procedure.
Despite the increasingly widespread application of adsorption to recover gases from multicomponent gas streams, only a limited amount of high pressure adsorption data for mixtures have been presented (Lewis et al., 1950; Mason and Cooke, 1964; Payne, 1964; Ray and Box, 1950; Ray, 1954; Rowley and Ray, 1940; Sturdevant, 1966). Experimental adsorption data are needed for the development of methods for predicting adsorption equilibria of various types of gases and their mixtures on a specific adsorbent at elevated pressures. Experimental Apparatu:;
T h e apparatus used with this technique is similar to that described by Koonce ansd Kobayashi (1965), with the following modifications: Substitution of a column of appropriate length packed with silica gel for the gas-liquid column which had been used previously. Introduction of a switching valve to allow the carrier gas to be diverted around thse packed column. (This provides a convenient means for correcting for the system dead volume outside the column and :for the detector response time.) Introduction of a small metering valve downstream from the expansion valve to permit greater sensitivity in the adjustment of the carrier gas flow rate. Construction and installation of a small 2.34-m1. ionization chamber as the radioactive sample detector to eliminate the need of a purge gas. [The small chamber produced satisfactory peak resolution a t flow rates under consideration (50 to 100 cc. per minute), enabling the carrier gas flow rate to be measured directly \vith a bubble meter.] Insertion of a carrie.r gas water saturator just before the flowmeter to improve the metering accuracy using the bubble flowmeter. Materials Used
The methane used for the pure component isotherms and for the preparation of the mixtures was donated by the Tennessee Gas Transmission Co. and the Associated Oil and Gas Co. T h e analysis of the dried gas as determined by mass spectroscopy was:
Ethane
Mole % 99.6 0.06
COP Nitrogen
0.23 0.1
Methane
Instrument grade (99.5f mole % minimum) propane was obtained from the Phillips Petroleum Co., Bartlesville, Okla., and used for the pure propane isotherms as well as for preparation of the mixtures. T h e gas mixtures were prepared by metering liquid propane into cylinders of kno1z.n volume containing methane. T h e inixture compositions were analyzed by gas chromatography. Radioactive methane and propane were obtained from the New England Nuclear Co. Tritium-tagged compounds were used because they are considerably cheaper than carbon-14labeled ones and within the limit of accuracy of this study the retention volumes of both are identical to that of the pure component. T h e silica gel obtained from the Davison Chemical Co. was Grade 15 with a nominal surface area of 800 sq. meters per gram. The surface area was determined by the Esso Research and Engineering Co. laboratories a t Baytown, Tex., and found to be 803.5 sq. meters per gram. T h e mesh size was 35 to 60, and the bulk density was stated as 42 pounds per cu. foot. This mesh size was used to obtain a favorable ratio of particle to column diameter. Otherwise the gel was very similar to Grade 03, which is the type frequently used in commercial hydrocarbon recovery units. T h e gel was regenerated for 2 hours at 300 to 350' F. before use.
Theory of Ideal Chromatography
T h e chromatographic equation developed by Martin and Synge (1941) relates the retention volume of a sample injected into a chromatographic column to the gas volume of the column and the partition coefficient of the sample between the fixed and flowing phase. This equation was developed by considering the column to be composed of a large number of equilibrium stages. The usual expression is:
where V R = volume of carrier gas a t column pressure evolved from the column from the time of sample injection to the appearance of the peak centroid a t the column exit V, = total gas volume of column V , = volume of stationary phase in column H = equilibrium partition coefficient, concentration in mobile phase/concentration in stationary phase Equation 1 finds wide application because of its simplicity, but is valid only under such conditions that the adsorbate sample is a t infinite dilution in the carrier gas, or follows a linear isotherm, or is a radioactive analog with the same physicochemical properties as the corresponding component in the carrier gas. This equation cannot be used in general for multicomponent adsorption where elution gas concentration perturbations are used for samples, as shown below. The following derivation applies to a chromatographic column operating under the following conditions: An ncomponent gas floivs through a bed of adsorbent particles under conditions of constant temperature and pressure. The velocity is uniform across the diameter of the column. Adsorption equilibrium exists between the gaseous components and the solid. The total volume of the column consists of the solid volume, the gas volume, and the volume of the adsorbed phase. T h e adsorbed phase volume cannot always be neglected. The continuity equation states that in any section of the column the change in the number of moles of a given component is equal to the net flux into the section by convection.
where
and (3)
-0
Summing over all components and a t constant temperature and pressure (C = constant) :
Equation 3 becomes:
This equation will be applied to three situations: (A) a binary carrier gas, (B) component i absent from carrier gas and infinitely dilute in sample, and (C) a multicomponent carrier gas with a radioactive tracer for the sample a t a finite VOL. 6
NO. 4
NOVEMBER
1967
547
concentration. I n all cases considered diffusional and mass transfer effects are neglected, as justified by Stalkup and Deans (1963). A. Binary Carrier Gas. At a given temperature and pressure, the amount of each component adsorbed is a function of the gas-phase composition.
e, = e,
i = 1, 2
(CI,CP)T,P
This function can be simplified by the restriction
+
c = c1 cz to
This equation shows how the retention volume of a concentration perturbation in a binary gas is related to the slopes of the isotherms of each component in the gas phase. Conversely, a knowledge of the isotherms enables the retention volume to be predicted. However, derivation of the individual isotherms for each component from retention volume data alone is impractical. For systems of three or more components the equation becomes too complex to be of any use in determining adsorption isotherms. Equation 7 can be used, however, as a check on the consistency of isotherms obtained by other methods by comparing predicted and observed retention volumes. A good check also verifies the applicability of the equations presented here for ideal chromatography.
B. Component i Absent from Carrier Gas and Infinitely Dilute in Sample. If the carrier gas composition does not include component i, and if a sample of component i at a very low concentration is injected into the column, the retention volume of the sample is determined as follows. Since Ci is essentially zero for this case, the term
therefore
de1 bC1
ac1 -
acl
at
at
ae, _ -- _ be, - -ac1 ac,
at
at
in Equation 4 drops out, and the following equation may be obtained in a manner similar to case A:
Equation 4 may be rewritten as
u
ac1 -
az
= 0
(5)
for component 1 and in a similar fashion for component 2. After rearranging, Equation 5 becomes
+
at
ac1
ba
= 0
(6)
If the total differential of Cl, which is a function oft and t , is equated to zero
Equation 8 allows the determination of the initial slope of the isotherm for component i in any carrier gas. Since all isotherms become linear a t low concentrations, the isotherm can be approximated by a straight line for a short distance from the origin. The usefulness of Equation 8 depends upon the range of linearity of the isotherm.
C. Multicomponent Gas. Finite Elution Gas Concentration, Radioactive Sample. The use of radioisotopes as samples instead of concentration perturbations simplifies the determination of adsorption isotherms. Equation 2 may be written for those molecules of component i which are identifible through their radioactive property. The following nomenclature will be used :
+ ci* e, 6," + e,* c,
=
and by comparison with Equation 6,
(dz/dt),, is the rate of travel of a zone of constant composition through the column, or the characteristic slope in the z,t plane. This velocity, known as the characteristic velocity, will be different from the carrier gas velocity because of the symmetric term in the denominator. This equation may be rearranged, using the ratio (dZ/dt)Cl -_ U
= C,"
vu -VR
that is, the total concentration of component i in each phase is the sum of the concentrations of radioactive (*) and nonradioactive (") molecules. If the sample which is injected a t the column entrance has the same chemical composition as the carrier,
cj (sample)
=
C, (carrier) j = 1, n
Even though some of the molecules of component i are tagged, the chemical composition of the system will not be disturbed. The total amount adsorbed, 6, will not be a function of time, since the gas-phase composition of each component is constant. This allows the term
and by expressing the adsorbate concentration as moles adsorbed per gram of adsorbent w, =
6, V,/m
in Equation 4 to be dropped, even though C1* is not a t infinite dilution. T h e retention volume is therefore:
to
(7) 548
I&EC F U N D A M E N T A L S
(9)
Thus, retention volume measurements yield the slope of the radioactive isotherm a t the concentration of the radioactive component in the carrier gas. At temperatures on the order of 300’ K., chemical isotopes possess the same physical properties. At a fixed total concentration of a particular chemical species, with the large number of molecules involved in macroscopic systems, the expected value of the fraction of a given isotope will be equal in each phase a t equilibrium, or
mine the volume, VG,helium in the absence of a n adsorbing gas was used to obtain V,. At these temperatures helium may be assumed nonadsorbed to a high degree of approximation (Masukawa, 1966). This volume, VG,is called the Gibbs gas volume and is equal to the total volume minus the adsorbent volume, while V , refers to the total volume minus the adsorbent and adsorbate volumes. In order to determine the amount of a given substance adsorbed by either definition, consider a nonflow adsorption system in which a known amount of this substance is metered into the system, and the pressure and temperature are recorded a t equilibrium. A material balance requires that the total number of moles added is equal to the number of moles in the gas phase plus the number of moles adsorbed, n, =
or
This relation is independent of concentration, and radioactive samples d o not have to be at infinite dilution but can be anywhere in the range 0 < Ci*< Ci,as long as Ci is held constant. Substituting Equation 10 into 9 VR*
=
vo + mc wYat
- -
Thus, Equation 9 can be used to determine w for any component of a n n-component system with the use of radioactive tracers. Equations 8 and 9 are very similar and may be used to validate the assumption that isotopes have the same adsorption characteristics. Equation 8 gives the retention volume of an infinitely dilute sample and Equation 9 gives the retention volume for a radioactive tracer. If the retention volume of an infinitely dilute radioactive tracer is the same as a n infinitely dilute concentration perturbation, the relationship
n t + n$
(1 2)
where k equals A or G. This equation is valid for either definition, and superscript A or G will denote whether application is made to absolute or Gibbs adsorption. Thus, by Gibbs’ definition: nuG = n , - noG =
n,
= nt
- VG/v, - V,/u, - Va/v,
The amount adsorbed is calculated by subtracting from the total number of moles present the number of moles in the gas phase plus a number of moles of adsorbed molecules, corresponding to the number of gas molecules which would be present near the surface if there were no adsorbed phase. “Absolute adsorption,” which is thought to be more descriptive and physically accurate, defines adsorbed molecules as those which are confined to a region very near the adsorbate surface. These molecules possess a lower energy than the gas molecules, and do not contribute to the total gas pressure. Applying Equation 12
nuA = n, = n,
- noA - Vo/vo
(13)
Since nuA = Va/ua,Equation 13 becomes will be established, verifying the identity of the physical and chemical properties of the isotopes. Another check on th(e use of tracers is the prediction of a concentration peak in a binary gas (Equation 7 ) from the isotherms obtained using tracers. Equation 11 also can be used to obtain pure component isotherms, where y t = 1. Isotherms obtained in this manner can be compared to those obtained by classical techniques to verify assumptions about the validity of the chromatographic approach. Equation 11 was used in this study for the deterrnination of all isotherms. Adsorbed Phase Volume
Gibbs defined adsorbsed molecules as those molecules which are present in the system which would not be there if the solid were inert. This definition is widely used and is adequate for most adsorption studies (Young and Crowell, 1962). For the reasons explained below, a n alternative definition, “absolute adsorption” (Mason and Cooke, 1964), was employed here, as it is more appro:priate a t high gas-phase densities. I n order to apply Gibb’s definition, the number of molecules which would exist in the system if the solid were inert must be determined. But the substitution of a n inert solid of exactly the same volume as the adsorbent is not possible. To deter-
This equation relates the two definitions, and nuG is a function of the gas and adsorbent densities. At high pressure, Gibbs’ isotherms go through a maximum and then start decreasing. Thus it may appear that dnaG/dp < 0, even though dnuA/d/p 2 0. Another problem is that some points are double-valued because of the maximum in the isotherm, which makes adsorption correlations and equations of state difficult to handle and interpret. Absolute adsorption is not usually used, because most adsorption data are obtained a t low pressures, where there is essentially no difference in nu calculated by either method, and vu, the molar volume of the adsorbed phase, is hard to estimate for most substances. With the chromatographic technique, both definitions could be used, for V , could be determined a t the actual adsorption conditions from the retention volume of a helium sample in the adsorbing carrier gas. This allowed Vu to be approximated from the equation
vu = v, - v, and vu = Va/naA VOL.
6 NO. 4
NOVEMBER 1 9 6 7
549
An advantage of using absolute adsorption in this work may be seen by rearranging Equation 11 for a flow system. This nuA =
nR
-
equation corresponds to Equation 12 with n 2 for a static system equivalent to nR for a flow system. Since Equation 11 allows the amount adsorbed to be determined from the total moles of carrier gas leaving the column and the number of moles in the gas phase, these quantities can be measured a t atmospheric conditions. Calculation a t column conditions is not necessary, eliminating the need for compressibility data on a high pressure mixture. Only atmospheric compressibility data which can be calculated more accurately are required. O n the other hand, if Gibbs' definition is used, V," must be calculated from
VO" =
v,c
);( );( )(;
where superscripts a and c refer to ambient and column conditions, respectively. Thus, Gibbs' definition is actually more difficult to use in chromatography than the definition of absolute adsorption.
Physical adsorption is a phase transition which is accompanied by a latent heat comparable to condensation in a vaporliquid system. However, since adsorption possesses one more degree of freedom than a vapor-liquid system, the heat of adsorption may be defined in several ways: integral, differential, isothermal, adiabatic, and isosteric. Ross and Olivier (1964) have explained the relationships among the various definitions. The isosteric heat of adsorption is defined in a form similar to the Clapeyron equation :
v,)(dP/dT),
(1 5 )
T h e derivative is evaluated a t a constant number of moles adsorbed. This is equivalent to a constant volume adsorbed; hence the name isosteric. This heat of adsorption is a differential molar quantity which is related to fundamental thermodynamic quantities and can be calculated from the temperature dependence of the isotherm. Heat is given off during adsorption, but as defined X is a positive quantity. Equation 15 may be rewritten as
or
where t = z(p,T)(1
-dug)
The quantity 7 is usually taken to be equal to 1 for adsorption a t low pressures. In this work this approximation was found to be adequate for propane adsorption, but not for methane. Equation 16 was used to determine the heat of adsorption for pure methane and propane for various values of n,. The initial isostere was determined by using methane and propane in helium a t infinite dilution. Since P/n, # 0, as nu + 0, Equation 16 yields
550
I&EC FUNDAMENTALS
The mixture adsorption data were fitted to a two-dimensional virial equation of state for the adsorbed phase with the series truncated after the third virial coefficient. The two-dimensional virial equation of state is expressed as:
$A/RT =
wi
f
+ w z+ B i i ~ +i ~B i * ~ i wfs B ~ z z fL ' ~ ~ iC ~ Z W I EfZC22zwza ~
C i i i ~ ~ iC~i i 2 w i 2 ~ ' z
+ ..
,
(18)
where 4 is the two-dimensional spreading pressure, the twodimensional analog of fluid pressure. For convenience, the area concentration is expressed as moles per gram of adsorbent, and is related to the moles per square centimeter through the specific surface area of the solid. The coefficients with mixed subscripts are those due to the interaction of the unlike adsorbed molecules; those with repeated subscripts account for the interaction of like adsorbed molecules. A two-dimensional equation of state cannot be applied until it is converted into a form utilizing measurable physical quantities. This is done through the use of the Gibbs-Duhem equation for the adsorbed phase, also known as the Gibbs adsorption isotherm.
{ ( A m ) d$' =
Thermodynamic Treatment of Data
X = T(v0 -
Analytical Representation of Data
(19 )
nl dfiilT,P
For a binary mixture this may be Lvritten as
This transformation leads to an isotherm for each component in a binary mixture as follows:
+ -21
CllS~lWZ
C122Z'lZeZ
+ 21
c122w22
- c112w12
+ . . .)
(21)
+
(22)
. .)
with the introduction of two more constants, A1 and A2. These are related to the initial slopes of the pure component isotherms for components 1 and 2, respectively, and are characteristic of the adsorbate-adsorbent interactions. The virial coefficients are characteristic of the adsorbate-adsorbate interactions. Thus, nine parameters were evaluated from the experimental data. Each isotherm has six, three of which are repeated. Extremely accurate data are necessary to evaluate "true" two-dimensional virial coefficients, as is the case with the virial coefficients for three-dimensional gas mixtures. With adsorption this problem is even more pronounced because of the extra degree of freedom involved. The value of this approach is that the isotherm equations are of the correct form to be transferred into a two-dimensional equation of state. The physical significance of the virial coefficients may be illustrated by a consideration of the second coefficient, B. If the molecules behave as rigid disks confined to a two-dimensional area, it can be shown that the second virial coefficients are related to the square of the diameter of the disks. The mixed coefficient is related to the pure component mefficients by the relation
expressing the fact that. the closest approach between two unlike circular molecules is equal to the sum of their radii. T h e pure component coefficients can be calculated from the three-dimensional van der Waals constant by converting the volume to a projected area. However, a correction may be necessary in some cases because of orientation of the adsorbed molecules. I n the gas phase a nonspherical molecule such as propane possesses a n effective van der Waals diameter. When confined to a two-dimensional phase, the area occupied depends on the orientation of the molecule relative to the surface. A correction factor must then be applied to the projected area predicted from the van der Waals constant. Estimoiion of Moximum Experimeniol Error
Equation 11 may be rewritten as follows:
T h e uncertainty in each of the above quantities will be reflected in the accuracy of ( w / y ) ( . T h e effect of small errors in each quantity can be estimated from the total derivative of (w/y)i in Equation 24. A(wJ~J/(Wtl~= J ALdL'
AS/S
Quantity L1 L2 LS
L4 S q
P T
z
m
+ ALz/L' + ALu'L' + ALdL' +
+ AP/P + Aq/q + A4.z + AT/T
Methane Propane
-I- A m / m
Uncertainty in Measurement 0.02inch 0.02 inch 0.02 inch 0.02inch Negligible 0.001ml./min. 0.001inchHg 0.1"K.
Approximate Magnitude L ' inches L ' inches L' inchcs L' inches 2 inchea,/min. 50 ml./min. 30 inches Hg 300" K . 1 .o
0,001
0,0005g. 0.0005g.
2.492g. 0.561 g.
(25)
Relative Uncertainty (Uncertainty/ Magnitude) 0.02/L' 0.02/L' O.O2/L' O.O2/L' 0.000 0.0002 0,0003 0.0003 0,001
0.0002 0.001
Discussion
T h e pure component isotherms, calculated from Equation 11, are presented in Table I. Absolute adsorption is essentially equal to Gibbs' adsorption for propane because of low gas densities involved at the temperatures of this study, but methane adsorption differs significantly. Adsorbate molar volumes were calculated from the changes in column void volume for pure methane and propane adsorption (Table 11). The molar volumes fall within the range of the liquid volumes and are close to the van der Waals volume. The agreement with the van der Waals volume is not surprising, since the adsorbate volume is a volume not accessible to the gas molecules in the system. Initial slopes for the pure component isotherms were obtained from the retention volume of infinitely dilute samples of methane and propane with helium as the carrier gas (Table 111). Isosteric heats of adsorption were obtained from initial slopes data as well as for the pure component isotherms a t finite coverages, using Equations 7 and 16. T h e values are shown in Table IV. T h e initial heats are higher than those a t finite coverage, indicating that there are
Adsorption of Methane and Propane on Silica Gel Propane Methane, w , abs., w , MmoleslGram Pressure, Pressure, mmolesl P.S.Z.A. Abs. Gibbs p.s.i.a. gram
Table 1.
o o c. 101 302 600 1000
0.9050 2.0461 3.075 3.647
0.8903 1.950 2.805 3.148
102 303 600 1000
0.7989 1.762 2.735 3.320
10" c. 0.7826 1.695 2.483 2.961
101 305 500 700 1000
0.6975 1.543 2.159 2.578 2.978
20" c. 0.6862 1.487 2.031 2.367 2.578
102 304 600 1000
0.5947 1.357 2.140 2.750
30' C. 0.5840 1.317 1.980 2.577
102 300 600
0.4785 1.190 1.932 2.550
40" C. 0.4238 1.175 1.818 2.422
Summing the right-hand column:
+ 0.0020 for methane = O.08/Lf + 0.0028 for propane
A ( w / y ) t / ( z l / y ) i = O.O8/L'
Thus, the relative error is a function of L', which is proportional to ( V , - V g ) . The most unfavorable conditions were those in which L' was a minimum; this occurred a t 40' C., 100 p.s.i.a., and y 3 = 0.80978. T h e most favorable conditions occurred a t 0' C., 1000 p.s.i.a., andya = 0.000. L', Inches Maximum Minimum Methane Propane
2.84 9.8
0.78 2.0
A ( w / r ) / ( w / v ) , 70 Maximum Minimum 15.15 f1.5 11.05 12.15
T h e uncertainty in (w/y) was greater for methane than for propane because of the smaller retention volumes obtained with methane. This uncertainty can be improved upon by increasing the mass of adsorbent. There is a practical upper limit to the retention times hhich may be used, however, because gas-phase diffusi.on tends to make the peak maximum difficult to define for very wide peaks.
1000
25.2 42.0 60.5
3.554 4.203 4.390
25.0 41.6 60.0 91 . O
2.900 3.753 4.141 4.360
21 31 41.5 51.4 60 71.2 80.8 90.6 100.2 116.5
2.180 2.713 3.220 3.580 3.790 4.01 4.133 4.220 4.239 4.346
28.4 50.0 77.2 99.4 119.8
2.117 2.998 3.708 4.023 4.166
29.4 51.6 82.4 99.8 121 . o
1.787 2.565 3.387 3.667 3.923
Table II. Molar Volume, Adsorbed Phase
Methane Propane Din ( 7967).
*
van der Waals Liquid Volume, Constant, Cc./Molea Cc /Moleb 36 4-98 7 42 8 70-195 7 84 4 Ross and Olivier (7964).
VOL. 6
NO. 4
Av. Adsorbate Val., V,,, Cc./Mole 42.9 85 8
NOVEMBER 1 9 6 7
551
Initial Slope of Methane and Propane Isotherms
Table 111.
[( dw /dY 1I w-
0,
Moles / Gram Methane 6 . 1 2 x 10-5 3.01 x 10-5 1 . 8 0 x 10-6 1 . 1 4 x 10-5 0.7555 x 10-5
T , C. 40 20 0 20 40 O
-
Propane 8 0 . 0 x 10-5 4 9 . 0 x 10-5 2 9 . 0 x 10-5 1 9 . 2 x 10-5 1 2 . 5 x 10-6
0 10 20 30 40 Table IV. w , MrnoleslGram
Isosteric Heat of Adsorption A / q , Cal./Mole
Methane
n
3757
0"
1.o 1.5 2.0 2.5
3571)
Propane 7888 7900
0 0" 2.0 2.5 3.0 3.5 4.0 q = Z( 1
I::::
5513/ Av. 5470 5548 1 5427J
- V,/V,)~
Kiselev ( 1964), who used a silica gel with a specific surface area of 715 sq. meters per gram. a
high energy adsorption sites on the solid which are the first to be filled. Afterwards the surface is more homogeneous and the heat of adsorption is essentially constant. T h e retention volume of a concentration perturbation from isotherms determined by radioactive tracers was estimated (Table V). T h e data were obtained on two samples of silica gel which had different properties than the sample used for most of the adsorption studies reported here. T h e good agreement which was obtained for two different temperatures,
Table V. Y3
0.0000 0.0994 0.1627
Ac knowledgment
The authors thank the National Aeronautics and Space Administration and the National Science Foundation for support of this work, the Tennessee Gas Transmission Co. and the
Prediction of Characteristic Velocity of Concentration Perturbation from Radioactive Perturbation
( V , - V o ) ,Cal./Mole X lo3 Methane Propane P = 220 p.s.i.a. 1.21 24.73 0.8356 14.50 0.778 12.27
1.54 1.45 1.330 1.210 1 ,0804
aw/+ x 103 w x 103 Methane Propane Methane Propane T = 40" C. Methane sample at infinite dilution 1.21 0 ... 24.73 0.7567 1.369 2.75 10.37 0 6513 1.993 1.125 8.25
( V R - V o ) ,Cal./Mole X 70' Predicted 0 bsd.
p.s.i.a. T = 20' C. Propane sample at infinite dilution 32.2 1.54 0 ... 32.2 27.95 1.44 0.2426 18.5 24.7 23.10 1.282 0,6679 8.15 20.0 19.8 1.131 1.1927 4.50 15.0 17 .OO 0.9834 1 ,6434 3.00 10.0 Observed ( V , - V,) cal./mole mass peak. Predicted y l ( d w ~ / d y ~ 24-) YZ ( d w l / d y l ) .
P
0.0000 0,0087 0.0290 0.0579 0.0978
pressures, and ranges of composition justifies assumptions made earlier, that diffusion and mass transfer effects were unimportant under the conditions of the foregoing experiments and that bw,*/byy,*= w i / y t a t all concentrations. The mixed adsorption data are reported as w/y rather than as w because w / y varies more slowly with y than w (Table VI). The limiting value of a l l y asy approaches zero is finite, though w approaches zero. The coefficients obtained from the correlation of the mixture data are presented in Table V I I . The gas-phase fugacities were calculated from the BenedictWebb-Rubin equation of state. The advantages of using chromatography in the determination of phase equilibria are those which have made it such a widely accepted analytical technique-Le., simplicity, speed, versatility, and sensitivity. The advantage of this technique is most pronounced in the case of multicomponent gas adsorption. With standard volumetric and gravimetric adsorption equipment the determination of multicomponent isotherms involves the analysis of the gas phase a t equilibrium and the calculation of the amount absorbed by the use of a material balance and the compressibility factor of the mixture. The data are obtained by adding one component incrementally to the system, changing the pressure and the gas-phase composition. Considerable crossplotting is then required to obtain the isotherms a t a constant pressure andlor composition. Moreover, obtaining accurate data a t low concentrations of a component in the mixture becomes very difficult. The chromatographic method, when used in conjunction with radioactive tracers, allows the isotherms for each component in an n-component mixture to be determined a t constant pressure and gas-phase composition without knowledge of the mixture compressibility a t system conditions. I n addition, accurate low concentration data are easily determined even approaching infinite dilution. Infinite dilution data are very useful, since they allow adsorption phenomena a t zero concentration to be observed directly. Where a linear isotherm may be approximated, such as a t low pressures or concentrations, infinite dilution data alone may be sufficient to determine the isotherm in that region.
I&EC FUNDAMENTALS
24.73 9.25 6.84
32.2 24.64 19.66 14.62 10 17
32.2 24.6 19.05 15.09 10.64
= 320
(dwi/dyyi)obtained from isotherms determined by tracers at various values of y,.
552
24 73 9.65 7.09
Table VI.
oo c. WIV.
mrnohsl gram
p, p.s.i.a.
Adsorption of Methane-Propane Mixtures
loo c.
p, p.s.i.a.
20°
W/Y, mmolesl gram
p, p.s.i.a.
c.
30' C.
40' C.
~
W/Y, mmolesl gram
p, p.s.i.a.
WlY, mmolesl gram
p, p.5.i.a.
mmoles/ gram
W/Y,
- -- (VR* - V,) C / m for Methane CHIT Y
124 313 604 972
1.007 1.911 2.794 3.361
102 307 61 6 970
0.7457 1.682 2.602 3.075
y2 = 0.00870 104 0.6689 308 1.450 603 2.323 945 2.831
121 303 61 1 946
0.6683 1,300 2.111 2.611
121 303 604 929
0.5804 1.151 1.909 2.422
121 304 610 961
0.8993 1.601 2.516 3,101
123 304 602 963
0.7972 1.497 2.261 2.872
y2 = 0.0290 119 0.6946 304 1.330 61 1 2.131 975 2.680
112 300 602 978
0.581 1.225 1.961 2.541
114 313 605 980
0.5403 1.121 1.780 2.402
114 303 607 913
0.701 1.422 2.242 2.811
103 303 601 932
0.6239 1.345 2.110 2,692
y2 = 0,0579 107 0.5818 303 1.210 607 1.961 910 2.501
115 303 606 950
0.5692 1.127 1.821 2.412
103 310 602 999
0.481 1.074 1.701 2.427
0.6473 1.220 1.865 2.720
104 314 606 994
0.5457 1.164 1.799 2.648
106 303 610 979
119 318 620 979
0.5509 1.091 1.738 2.523
120 31 3 61 2 963
0.5191 1.037 1.671 2.431
~2
112 306 609 993
W
Y
27.0 41 . O 45.4 39.1
= (VR*
-
= 0,0978
0.5642 1 ,0804 1.774 2.573
V,) C/m for Propane, C8H,T
y2 = 0.0000 110 18.5 301 32.2 599 35.1 997 32.7
109 304 599 992
38.0 54.5 56.4 47.6
108 303 601 992
109 304 61 1 989
31.4 46.7 49.8 41.55
105 301 600 1000
99.5 304 604 996
23.8 38.2 42.9 36.6
110 303 601 993
18.3 29.5 34.3 32.1
107 303 602 996
110 308 610 999
20.6 32.4 35.0 31 . 9
116 304 599 998
16.6 25.4 29.5 27.7
100 303 604 1000
107 316 604 996
13.2 21 . o 24.0 23.5 0.000).
106 303 622 996
~2
y2
100 303 601 997
12.5 24.1 29.0 28.3
102 301 600 994
9.1 18.7 24.0 25.0
11.2 21.3 25.2 25.6
107 302 605 995
8.7 16.4 20.6 22.5
106 303 599 996
10.6 19.0 23.0 23.5
106 306 602 993
8.0 15.4 19.8 21.5
105 302 603 997
9.8 16.8 20.9 21 .o
113 305 602 992
8.0 14.2 17.7 18.4
110 309 602 991
8.3 14.5 18.5 17.8
114 314 602 995
6.9 12.5 16.4 16.3
= 0,0087
= 0,0290
13.7 23.1 27.5 26.9
Y Z = 0,0579
~2
107 17.0 26.0 301 29.3 601 27.0 997 0 See Table I for pure methane
(y2 =
12.0 19.8 24.2 24.2 = 0.0978
10.1 17.0 21 .o 20.7
= second virial coefficient, grams/millimole = third virial coefficient, (gram/millimole)2
Associated Oil and Gas 120. for the donation of methane gas, the Phillips Petroleum Co. for the donation of propane, the Davison Chemical Co. fcr the donation of silica gel samples, the Monsanto Chemical Co. for analytical help, and the Esso Research and Engineering Co. for determination of the adsorbent surface area.
f H
=
Nomenclature
L;
=
A = specific surface area of adsorbent, sq. meters/gram A I , A Z = integration constants in isotherm Equations 13 and
L1
=
LZ
=
14
Bij Cijk C
C
=
gas phase concentration, moles/cc. phase concentration, moles adsorbed/cc. adsorbent gas phase fugacity, p.s.i.a. equilibrium partition coefficient, gas phase concn./ solid phase concn. distance in inches measured on recorder chart paper from point of sample injection to peak centroid; i = 1,4 L for radioactive sample through column, inches L for radioactive sample through bypass, inches
= solid =
VOL. 6
NO. 4
NOVEMBER 1 9 6 7
553
La
= = =
rn
= mass of adsorbent, grams
n P
= =
?!
=
R S t T
=
Va
VR
= = =
vu
=
V.
= =
Wi
Yi
= =
t
=
Z
=
Xi
+
= = = =
U 00
+
L for helium sample through column, inches L for the helium sample through bypass, inches (L1- L2) - (La - L4)
L4 L'
moles pressure, p.s.i.a. or inches Hg flow rate, cc./min. gas constant, 1.987 cal./mole chart speed, inches/minute time temperature carrier gas velocity specific volume of adsorbed phase, cc./mole specific volume of gas phase, cc./mole retention volume, volume of carrier gas evolved from column from sample injection to appearance of peak centroid a t column exit, corrected for system dead volume, cc. volume accessible to gas molecules, helium retention volume, cc. volume occupied by adsorbent, cc. moles or millimoles adsorbed per gram of adsorbent; asterisk denotes radioactive isomer mole fraction component i in adsorbate mole fraction component i in gas phase; asterisk denotes radioactive isomer length gas compressibility factor, PV/RT
GREEKLETTERS = standard deviation of experimental values of (f/w)i from correlated values 4 = two-dimensional spreading pressure of adsorbed phase, force per unit length parallel to surface 17 = Z(1 - u,/z'y) = isosteric heat of adsorption, cal./mole X
7 l
I
+
+
SUPERSCRIPTS a = ambient conditions C = column conditions 0 = nonradioactive isotope * = radioactive isotope A = absolute adsorption G = Gibbs' adsorption
J
+ $
+
+ +
a0
m8
i3 L
sa
-
E
c
-
II
II
h
h
N
a --. 3 5
SUBSCRIPTS = adsorbed, adsorbed phase = gaseous or gas phase g t = total 1 = component 1, methane 2 = component 2, propane a
L
00000
literature Cited
. . . . .
00000
*m
. . . . .
00000 h
12
554
IhEC FUNDAMENTALS
Din, F., "Thermodynamic Functions of Gases," Butterworth, Washington, D.C., 1961. Gilmer. H. B., Kobayashi, R., A.I.Ch.E. J . 10, 6, 797 (1964); 11, 4(1965). Kiselev, A. V., Nikitin, Y . S., Petrova, R. S., Shcherbakoua, K. D., Yashin, Y. I., Anal. Chem. 36,1526 (1964). Koonce, K. T., Kobayashi, R., A.I.Ch.E. J . 11, 259 (1965). Lewis, W. K., Gilliland, E. R., Chertow, B., Cadogon, W. P., Ind. Eng. Chem. 42, 1326 (1950). Martin, A. J. P., Synge, R. L. M., Biochem. J. 35,1358 (1941). Mason, J. P., Cooke, C. E., Preprint 34a, 57th Annual Meeting, A.I.Ch.E., Dec. 6-10, 1964. Masukawa, S., private communication, 1966. Payne, H. K., Ph.D. dissertation, Rice University, Houston, Tex., 1964. Ray, G. C., Box, E . O . , Ind. Eng.Chem. 42,1315 (1950). Ray, N. H., J . Appl. Chem. (London) 4,21,82 (1954). Ross, S., Olivier, J. P., "On Physical Adsorption," Interscience, New York, 1964. Rowley, H. H., Ray, N., Prod. Iowa Acad. Sci. 47,165 (1940). Stalkup, F. I., Deans, H. A., A.I.Ch.E. J . 9,118 (1963). Sturdevant. G. A , , Ph.D. dissertation, Rice University, Houston, Tex., 1966. Young, D. M., Crowell, A. D., "Physical Adsorption of Gases," Butterworths, London, 1962. RECEIVED for review May 31, 1966 ACCEPTED June 20, 1967
