Table II. Dialysis of Acids from Salts

Solution Dialyzed Membrane Tyke 2.4N FeS04-1.3N HzSOa Anion exchange0

0.64N M g ( N 0 a ) r Nonionic*

1.55~\'"03 Anion exchangeC Nonionicb

Fraction Dialyzed Acid Salt 0.65 0.023 0.59 0.28

0.90 0.008 0.88 0.50

Change in Volume of Concentrated

Solution 1 . 5 yo decrease 70y0 increase

5y0 decrease 55y0 increase

Table 111. Conductance of Acids Equivalent

Concentration, Conductance, Acid 1V Ohms-'

0 . 1

0 . 1 0 . 1

0 . 1 350.6 346,4 233.3 95.7

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.

greater than for "03, the observed anomalous negative osmosis for HNO, 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 NOS- than for C1-. The selectivity of strong base anion exchange resins for N03- over C1- is 3.80 (Wheaton and Bauman, 1951).

The increase in anomalous negative osmosis brought about

literature Cited

Grim, E., Sollner, K., J. Gen. Physzol. 40, No. 6, 887-99 (1957). "Handbook of Chemistry and Physics," 38th ed., Chemical Rubber

Mindick, M., Oda, R., Symposium on Innovations in Separation

Schlogl, R., 2. Physik. Chem. (Frankfurt) 3, 73 (1955). Wheaton, R. M., Bauman, W. C., Znd. Eng. Chem. 43, 1088-93

RECEIVED for review January 19, 1967 ACCEPTED July 13, 1967

Co., Cleveland, Ohio, 1956.

Processes, North Jersey Section, ACS, 1958.

(1951).

ADSORPTION EQUILIBRIA IN THE

METHANE-PROPANE-SILICA GEL SYSTEM

A T HIGH PRESSURES J O H N J . H A Y D E L ' A N D R l K l K O B A Y A S H I

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 at high pressure for methane, propane, and several of their mixfures on silica gel, by using radioactive tracer pulsing. A method of obtaining adsorbed- phase volumes is introduced. The data are represented analytically using a two-dimensional virial equa- tion of state truncated after the third virial coefficients.

RATHER general chromatographic method for determining A the adsorption of gases on adsorbents was recently intro- duced 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-

turbation or chromatographic technique. Experimental ad- sorption data were obtained on the methane-propane-silica gel system to verify the proposed method.

The present work was undertaken to extend the applica- tion of the method over a wider range of compositions, tem- peratures, and pressures and to make other modifications that would further generalize the procedure. 1 Present address, Shell Oil Co., Houston, Tex.

546 I & E C F U N D A M E N T A L S

Despite the increasingly widespread application of adsorp- tion 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 develop- ment of methods for predicting adsorption equilibria of various types of gases and their mixtures on a specific adsorbent at elevated pressures.

Experimental Apparatu:;

The 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 satis- factory peak resolution at 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. The analysis of the dried gas as determined by mass spec- troscopy was:

Methane Ethane COP Nitrogen

Mole % 9 9 . 6

0.06 0.23 0 .1

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 prepara- tion of the mixtures. The gas mixtures were prepared by metering liquid propane into cylinders of kno1z.n volume con- taining methane. The 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-14- labeled ones and within the limit of accuracy of this study the retention volumes of both are identical to that of the pure component.

The 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. The 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. The gel was regenerated for 2 hours at 300 to 350' F. before use.

Theory of Ideal Chromatography

The 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 con- sidering 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 in- jection to the appearance of the peak centroid at 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 n- component 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. Ad- sorption 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. The 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 com- ponent is equal to the net flux into the section by convection.

where

and

- 0 (3)

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 at a finite

V O L . 6 NO. 4 N O V E M B E R 1 9 6 7 547

concentration. In 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 func- tion of the gas-phase composition.

e, = e, (CI,CP)T,P i = 1, 2

This function can be simplified by the restriction

c = c1 + cz to

therefore

ac1 de1 bC1 a t acl a t

be, ac1 ae, a t ac, at

-

_ - _ - - -

Equation 4 may be rewritten as

ac1 u - = 0 (5) az

for component 1 and in a similar fashion for component 2. After rearranging, Equation 5 becomes

ac1 + ba = 0 (6)

at

If the total differential of Cl, which is a function oft and t , is equated to zero

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 vu -_ - - - U V R

and by expressing the adsorbate concentration as moles ad- sorbed per gram of adsorbent

w , = 6, V,/m to

(7)

This equation shows how the retention volume of a concen- tration perturbation in a binary gas is related to the slopes of the isotherms of each component in the gas phase. Con- versely, a knowledge of the isotherms enables the retention volume to be predicted. However, derivation of the in- dividual 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 ob- tained by other methods by comparing predicted and observed retention volumes. A good check also verifies the applica- bility of the equations presented here for ideal chromatog- raphy.

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

in Equation 4 drops out, and the following equation may be obtained in a manner similar to case A:

Equation 8 allows the determination of the initial slope of the isotherm for component i in any carrier gas. Since all iso- therms 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 Concen- tration, 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 identi- fible through their radioactive property. The following nomenclature will be used :

c, = C," + ci* e, = 6," + e,*

that is, the total concentration of component i in each phase is the sum of the concentrations of radioactive (*) and non- radioactive (") 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

in Equation 4 to be dropped, even though C1* is not a t infinite dilution. The retention volume is therefore:

(9 )

548 I & E C F U N D A M E N T A L S

Thus, retention volume measurements yield the slope of the radioactive isotherm at the concentration of the radioactive component in the carrier gas. At temperatures on the order of 300’ K., chemical isotopes possess the same physical proper- ties. At a fixed total concentration of a particular chemical species, with the large number of molecules involved in macro- scopic systems, the expected value of the fraction of a given isotope will be equal in each phase a t equilibrium, or

or

This relation is independent of concentration, and radioactive samples do not have to be at infinite dilution but can be any- where in the range 0 < Ci* < Ci, as long as Ci is held constant.

Substituting Equation 10 into 9

m wt V R * = vo + - - c Y a

Thus, Equation 9 can be used to determine w for any com- ponent of an n-component system with the use of radioactive tracers.

Equations 8 and 9 are very similar and may be used to vali- date 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 radio- active tracer. If the retention volume of an infinitely dilute radioactive tracer is the same as an infinitely dilute concentra- tion perturbation, the relationship

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 iso- therms obtained using tracers.

Equation 11 also can be used to obtain pure component iso- therms, 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 ap- proach. Equation 11 was used in this study for the deterrnina- tion 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, an alternative definition, “ab- solute 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 an inert solid of exactly the same volume as the adsorbent is not possible. To deter-

mine the volume, VG, helium in the absence of an adsorbing gas was used to obtain V,. At these temperatures helium may be assumed nonadsorbed to a high degree of approxima- tion (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 ad- sorbent 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 , = 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 , - VG/v,

= nt - 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, corre- sponding 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 de- scriptive 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, - noA

= n, - Vo/vo (1 3)

Since nuA = Va/ua, Equation 13 becomes

This equation relates the two definitions, and nuG is a func- tion 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 at the actual adsorption conditions from the retention volume of a helium sample in the adsorbing carrier gas. This allowed Vu to be approxi- mated from the equation

vu = v, - v,

vu = Va/naA

and

VOL. 6 NO. 4 N O V E M B E R 1 9 6 7 549

Analytical Representation of Data

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-dimen- sional virial equation of state is expressed as:

$ A / R T = wi + w z + B i i ~ i ~ + Bi*~ iws f B ~ z z L ' ~ ~ f

C i i i ~ ~ i ~ f Cii2wi2~'z i- C ~ Z W I E Z ~ f C22zwza + . . , (18)

where 4 is the two-dimensional spreading pressure, the two- dimensional 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 ap- plied 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$' = n l d f i i l T , P (1 9)

For a binary mixture this may be Lvritten as

An advantage of using absolute adsorption in this work may This be seen by rearranging Equation 11 for a flow system.

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 at atmospheric conditions. Calculation at column conditions is not neces- sary, eliminating the need for compressibility data on a high pressure mixture. Only atmospheric compressibility data which can be calculated more accurately are required.

On 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 condi- tions, respectively.

Thus, Gibbs' definition is actually more difficult to use in chromatography than the definition of absolute adsorption.

Thermodynamic Treatment of Data

Physical adsorption is a phase transition which is accom- panied by a latent heat comparable to condensation in a vapor- liquid 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, differen- tial, 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 :

X = T(v0 - v,)(dP/dT), (1 5 )

The derivative is evaluated at a constant number of moles adsorbed. This is equivalent to a constant volume adsorbed; hence the name isosteric. This heat of adsorption is a differen- tial molar quantity which is related to fundamental thermo- dynamic quantities and can be calculated from the tempera- ture 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 - d u g )

The quantity 7 is usually taken to be equal to 1 for adsorp- tion at 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 at infinite dilution. Since P/n, # 0, as nu + 0, Equation 16 yields

This transformation leads to an isotherm for each component in a binary mixture as follows:

CllS~lWZ + - 1 c 1 2 2 w 2 2 + . . . ) (21) 2

1 2

C122Z'lZeZ + - c112w12 + . . ) (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-dimen- sional 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

550 I & E C F U N D A M E N T A L S

expressing the fact that. the closest approach between two unlike circular molecules is equal to the sum of their radii. The 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. In the gas phase a nonspherical molecule such as propane possesses an effective van der Waals diameter. When confined to a two-dimensional phase, the area occupied de- pends 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:

The uncertainty in each of the above quantities will be re- flected in the accuracy of ( w / y ) ( . The effect of small errors in each quantity can be estimated from the total derivative of (w/y)i in Equation 24.

A ( w J ~ J / ( W t l ~ J = ALdL' + ALz/L' + ALu'L' + ALdL' + AS/S + AP/P + A q / q + A 4 . z + AT/T -I- A m / m (25)

Quantity L1 L2 LS L4 S q P T

m z

Methane Propane

Approximate Magnitude

L ' inches L ' inches L' inchcs L' inches 2 inchea,/min. 50 ml./min. 30 inches Hg 300" K . 1 . o 2.492 g. 0.561 g.

Uncertainty in Measurement

0.02 inch 0.02 inch 0.02 inch 0.02 inch Negligible 0.001 ml./min. 0.001inchHg 0 . 1 " K . 0,001

0,0005 g. 0.0005 g.

Relative Uncertainty

(Uncer- tainty/

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

Summing the right-hand column:

A ( w / y ) t / ( z l / y ) i = O.O8/L' + 0.0020 for methane

= O.08/Lf + 0.0028 for propane

Thus, the relative error is a function of L', which is propor- tional to ( V , - V g ) . The most unfavorable conditions were those in which L' was a minimum; this occurred at 40' C., 100 p.s.i.a., and y 3 = 0.80978. The most favorable conditions occurred at 0' C., 1000 p.s.i.a., andya = 0.000.

L', Inches A ( w / r ) / ( w / v ) , 70 - Maximum Minimum Maximum Minimum Methane 2.84 0.78 1 5 . 1 5 f 1 . 5 Propane 9.8 2.0 12.15 11.05

The 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.

Discussion

The pure component isotherms, calculated from Equation 11, are presented in Table I. Absolute adsorption is essen- tially 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 adsorp- tion (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 surpris- ing, since the adsorbate volume is a volume not accessible to the gas molecules in the system.

Initial slopes for the pure component isotherms were ob- tained 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. The values are shown in Table IV. The initial heats are higher than those a t finite coverage, indicating that there are

Table 1. Adsorption of Methane and Propane on Silica Gel

Pressure, P.S.Z.A.

101 302 600 1000

102 303 600 1000

101 305 500 700

1000

102 304 600 1000

102 300 600

1000

Methane, w , MmoleslGram

Abs. Gibbs

0.9050 2.0461 3.075 3.647

0.7989 1.762 2.735 3.320

0.6975 1.543 2.159 2.578 2.978

0.5947 1.357 2.140 2.750

0.4785 1.190 1.932 2.550

o o c. 0.8903 1.950 2.805 3.148

10" c. 0.7826 1.695 2.483 2.961

20" c. 0.6862 1.487 2.031 2.367 2.578

30' C. 0.5840 1.317 1.980 2.577

40" C. 0.4238 1.175 1.818 2.422

Propane w, abs.,

Pressure, mmolesl p.s.i.a. gram

25.2 3.554 42.0 4.203 60.5 4.390

25.0 2.900 41.6 3.753 60.0 4.141 91 . O 4.360

21 2.180 31 2.713 41.5 3.220 51.4 3.580 60 3.790 71.2 4.01 80.8 4.133 90.6 4.220 100.2 4.239 116.5 4.346

28.4 2.117 50.0 2.998 77.2 3.708 99.4 4.023 119.8 4.166

29.4 1.787 51.6 2.565 82.4 3.387 99.8 3.667 121 . o 3.923

Table II. Molar Volume, Adsorbed Phase Av.

van der Waals Adsorbate Liquid Volume, Constant, Val., V,,,

Cc./Molea Cc /Moleb Cc./Mole Methane 36 4-98 7 42 8 42.9 Propane 70-195 7 84 4 85 8

Din ( 7967). * Ross and Olivier (7964).

VOL. 6 NO. 4 NOVEMBER 1 9 6 7 551

Table 111. Initial Slope of Methane and Propane Isotherms

[( dw /dY 1 I w- 0, Moles / Gram

T , O C. Methane - 40 - 20

0 20 40

0 10 20 30 40

6 .12 x 10-5 3.01 x 10-5 1 . 8 0 x 10-6 1.14 x 10-5 0.7555 x 10-5

Propane 80.0 x 10-5 49 .0 x 10-5 29.0 x 10-5 19 .2 x 10-5 12 .5 x 10-6

Table IV. Isosteric Heat of Adsorption w , MrnoleslGram A / q , Cal./Mole

Methane n 3757 0" 1 .o 1 . 5 2 . 0 2 .5

Propane 0 0" 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0

3571)

7888 7900 ::::I 5513/ Av. 5470 5548 1 5427J

q = Z( 1 - V , / V , ) ~

a Kiselev ( 1964), who used a silica gel with a specific surface area of 715 sq. meters per gram.

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.

The retention volume of a concentration perturbation from isotherms determined by radioactive tracers was estimated (Table V). The 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. The good agreement which was obtained for two different temperatures,

pressures, and ranges of composition justifies assumptions made earlier, that diffusion and mass transfer effects were un- important under the conditions of the foregoing experiments and that bw,*/byy,* = w i / y t at 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 VII . The gas-phase fugacities were calculated from the Benedict- Webb-Rubin equation of state.

The advantages of using chromatography in the determina- tion 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 deter- mination of multicomponent isotherms involves the analysis of the gas phase at 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, chang- ing the pressure and the gas-phase composition. Considerable crossplotting is then required to obtain the isotherms at 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. In addition, accurate low concentration data are easily determined even approaching infinite dilution. Infinite dilution data are very useful, since they allow adsorp- tion 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.

Ac knowledgment

The authors thank the National Aeronautics and Space Administration and the National Science Foundation for sup- port of this work, the Tennessee Gas Transmission Co. and the

Table V. Prediction of Characteristic Velocity of Concentration Perturbation from Radioactive Perturbation

(V , - V o ) , Cal./Mole X lo3 w x 103 aw/+ x 1 0 3 ( V R - Vo) , Cal./Mole X 70' Y 3 Methane Propane Methane Propane Methane Propane Predicted 0 bsd.

P = 220 p.s.i.a. T = 40" C. Methane sample at infinite dilution 0.0000 1 . 2 1 24 .73 1 .21 0 . . . 24.73 24 73 24.73 0.0994 0.8356 14 .50 0.7567 1 .369 2 .75 10 .37 9 . 6 5 9 .25 0.1627 0.778 12.27 0 6513 1 .993 1 .125 8 . 2 5 7 . 0 9 6 .84

P = 320 p.s.i.a. T = 20' C. Propane sample at infinite dilution 0.0000 1 .54 32 .2 1 . 5 4 0 . . . 3 2 . 2 32 .2 32 .2 0,0087 1 . 4 5 27.95 1 . 4 4 0.2426 1 8 . 5 24 .7 24.64 24 .6 0.0290 1 .330 23.10 1 .282 0,6679 8 . 1 5 20 .0 19 .66 19 .05 0.0579 1 .210 19 .8 1 .131 1.1927 4 .50 1 5 . 0 14 .62 15 .09 0.0978 1 ,0804 17 . O O 0.9834 1 ,6434 3 .00 1 0 . 0 10 17 10 .64

Observed (V , - V,) cal./mole mass peak. Predicted y l ( d w ~ / d y ~ 2 ) 4- YZ ( d w l / d y l ) . (dwi /dyy i ) obtained from isotherms determined by tracers at various values of y,.

552 I & E C F U N D A M E N T A L S

p, p.s.i.a.

124 313 604 972

121 304 610 961

114 303 607 913

112 306 609 993

109 304 599 992

109 304 61 1 989

9 9 . 5 304 604 996

110 308 610 999

107 301 601 997

oo c. W I V .

mrnohsl gram

1.007 1 .911 2.794 3.361

0.8993 1 .601 2.516 3 ,101

0.701 1 .422 2.242 2.811

0.6473 1 .220 1 .865 2.720

38 .0 54 .5 56 .4 47 .6

3 1 . 4 46 .7 49 .8 41 .55

23 .8 38 .2 42 .9 36 .6

20 .6 3 2 . 4 3 5 . 0 31 . 9

1 7 . 0 26 .0 2 9 . 3 27 .0

Table VI. Adsorption of Methane-Propane Mixtures loo c. 20° c. 30' C.

p , p.s.i.a.

102 307 61 6 970

123 304 602 963

103 303 601 932

104 314 606 994

108 303 601 992

105 301 600

1000

110 303 601 993

116 304 599 998

107 316 604 996

~

W/Y, W/Y,

gram p.s.i.a. gram p.s.i.a. mmolesl p , mmolesl p ,

- - - (VR* - V,) C / m for Methane CHIT Y

y2 = 0.00870 0.7457 104 0.6689 121 1 .682 308 1 .450 303 2.602 603 2 .323 61 1 3 .075 945 2.831 946

y2 = 0.0290 0.7972 119 0.6946 112 1 .497 304 1 .330 300 2.261 61 1 2.131 602 2.872 975 2.680 978

y2 = 0,0579 0.6239 107 0.5818 115 1 .345 303 1 .210 303 2.110 607 1 .961 606 2 ,692 910 2.501 950

~2 = 0,0978 0.5457 106 0.5642 119 1.164 303 1 ,0804 318 1.799 610 1 .774 620 2.648 979 2 .573 979

W - = (VR* - V,) C/m for Propane, C8H,T Y

y2 = 0.0000 27 .0 110 1 8 . 5 100 41 . O 301 32 .2 303 45 .4 599 35.1 601 39 .1 997 32.7 997

~2 = 0,0087

0 See Table I for pure methane ( y2 = 0.000).

y 2 = 0,0290 1 8 . 3 107 13 .7 106 29 .5 303 23 .1 303 3 4 . 3 602 27 .5 599 32 .1 996 26 .9 996

Y Z = 0,0579 1 6 . 6 100 1 2 . 0 105 25 .4 303 1 9 . 8 302 29 .5 604 2 4 . 2 603 27 .7 1000 24 .2 997

~2 = 0.0978 13 .2 106 10 .1 110 21 . o 303 1 7 . 0 309 24 .0 622 21 . o 602 23 .5 996 20 .7 991

W l Y , mmolesl gram

0.6683 1 , 3 0 0 2.111 2.611

0.581 1 .225 1 .961 2.541

0.5692 1 .127 1 .821 2.412

0.5509 1 .091 1 .738 2 .523

1 2 . 5 24 .1 29.0 28 .3

1 1 . 2 21 .3 25 .2 25 .6

1 0 . 6 1 9 . 0 23 .0 23 .5

9 . 8 1 6 . 8 20 .9 21 . o

8 . 3 1 4 . 5 1 8 . 5 1 7 . 8

40' C.

p , p.5.i.a.

121 303 604 929

114 313 605 980

103 310 602 999

120 31 3 61 2 963

102 301 600 994

107 302 605 995

106 306 602 993

113 305 602 992

114 314 602 995

W / Y , mmoles/

gram

0.5804 1 .151 1 .909 2.422

0.5403 1 .121 1 .780 2.402

0.481 1.074 1.701 2.427

0.5191 1 .037 1 .671 2.431

9 . 1 18 .7 24 .0 25.0

8 . 7 1 6 . 4 20 .6 22 .5

8 . 0 15 .4 19 .8 21 .5

8 . 0 14 .2 17 .7 1 8 . 4

6 . 9 1 2 . 5 1 6 . 4 1 6 . 3

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.

Nomenclature

A A I , A Z = integration constants in isotherm Equations 13 and

= specific surface area of adsorbent, sq. meters/gram

14

Bij Cijk C C = solid phase concentration, moles adsorbed/cc.

f H

L;

= second virial coefficient, grams/millimole = third virial coefficient, (gram/millimole)2 = gas phase concentration, moles/cc.

= 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

adsorbent

L1 LZ

V O L . 6 NO. 4 NOVEMBER 1 9 6 7 553

+ +

+ +

$ a 0 c

+ +

+ +

II II - N h h

a --. 3 5

8 m

s a

I

i

E

J

3

L

- L

00000

. . . . . 00000

* m

. . . . . 00000

h

12

La L4 L' rn n P !? R S t T

V a

0 0

VR

U

vu

V. Wi

X i

Yi

t Z

= L for helium sample through column, inches = L for the helium sample through bypass, inches

= mass of adsorbent, grams = 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 at 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;

= mole fraction component i in adsorbate = mole fraction component i in gas phase; asterisk

= (L1 - L2) - (La - L4)

asterisk denotes radioactive isomer

denotes radioactive isomer = length = gas compressibility factor, PV/RT

GREEK LETTERS l7 = standard deviation of experimental values of (f/w)i

from correlated values

phase, force per unit length parallel to surface 4 = two-dimensional spreading pressure of adsorbed

17 = Z(1 - u, /z 'y) X

SUPERSCRIPTS a = ambient conditions C = column conditions

* = radioactive isotope A = absolute adsorption G = Gibbs' adsorption

SUBSCRIPTS a = adsorbed, adsorbed phase g t = total 1 = component 1, methane 2 = component 2, propane

= isosteric heat of adsorption, cal./mole

0 = nonradioactive isotope

= gaseous or gas phase

literature Cited

Din, F., "Thermodynamic Functions of Gases," Butterworth,

Gilmer. H. B., Kobayashi, R., A.I.Ch.E. J . 10, 6, 797 (1964); Washington, D.C., 1961.

11, 4(1965).

K. D., Yashin, Y. I., Anal. Chem. 36,1526 (1964). Kiselev, A. V., Nikitin, Y . S., Petrova, R. S., Shcherbakoua,

Koonce, K. T., Kobayashi, R., A.I.Ch.E. J . 11, 259 (1965). Lewis, W. K., Gilliland, E. R., Chertow, B., Cadogon, W. P.,

Martin, A. J. P., Synge, R. L. M., Biochem. J. 35,1358 (1941). Mason, J. P., Cooke, C. E., Preprint 34a, 57th Annual Meeting,

Masukawa, S., private communication, 1966. Payne, H. K., Ph.D. dissertation, Rice University, Houston, Tex.,

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,

Ind. Eng. Chem. 42, 1326 (1950).

A.I.Ch.E., Dec. 6-10, 1964.

1964.

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.

Butterworths, London, 1962. Young, D. M., Crowell, A. D., "Physical Adsorption of Gases,"

RECEIVED for review May 31, 1966 ACCEPTED June 20, 1967

554 I h E C F U N D A M E N T A L S