Correlation of adsorption isotherms of hydrocarbon gases on activated carbon

Correlation of adsorption isotherms of hydrocarbon gases on activated carbon

Carbon Vul 22. No. 6, pp. 493-495. hited I” the U S.A 1984 OOOE-6223184 $3.00 + .oO Pergamon Press Ltd CORRELATION HYDROCARBON OF ADSORPTION ISOTH...

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Carbon Vul 22. No. 6, pp. 493-495. hited I” the U S.A


OOOE-6223184 $3.00 + .oO Pergamon Press Ltd



T. V. LEE, J.-C. HUANG,* D. ROTHSTEIN and R. MADEY Department of Physics, Kent State University, Kent, Ohio 44242, U.S.A. (Received 6 Janual?;


Abstract-A single curve of the adsorbate volume W in the adsorbed phase versus the reduced adsorption potential # correlates adsorption isotherms of saturated hydrocarbons of low molecular weight (viz. ethane, propane, and n-butane) at pressures from 0.034 to IO mm Hg on Columbia 4LXC 12128 activated carbon at 25 and 30°C. This correlation is based on the Polanyi-Dubinin adsorption potential theory and the use of the PengRobinson equation of state to calculate thermodynamic properties. This correlation can be represented analytically by expanding the logarithm of W in terms of a quadratic polynomial in 4. 1. ~TRODU~ON

on solid adsorbents is a process of interest for application to the purification of gases. The literature contains few references to adsorption of hydrocarbon gases on activated carbon in the low-pressure regime corresponding to concentrations in the range from a few parts per million @pm) to about ten thousand ppm. The objective of this paper is to correlate adsorption isotherms for some hydrocarbon gases (viz., ethane, propane, and n-butane) on activated carbon at low pressures in the range from 40 to 1.3 x 104ppm (i.e. 0.034 to 10 mm Hg) by a method based on the Polanyi [ 1,2] and Dubinin [3,4] potential theory of adsorption. Adsorption

of gases at low pressures


peratures are su~~mposable on a single reduced characteristic curve. Since the adsorbate on a solid surface is treated as a liquid-like state. Grant and Manes[S] suggested that the molar volume Y of the saturated liquid at a vapor pressure equal to the adsorbate partial pressure P be used as the correlating divisor fl, Also, it is convenient[6] to express the adsorbate volume Was the product of number of moles N adsorbed per unit mass of solid adsorbent and the saturated molar volume V. For most (nonideal) gases, the fugacity is used to replace the pressure in the expression for the chemical potential[7]; therefore, Eqn (2) can be rewritten as NV=F


According to the potential theory of adsorption of Polanyi[ 1, 21, the energy transfer (or the adsorption potential) E of adsorbate molecules from the gas phase to the solid surface is t =RTInc


where R is the gas constant, P” is the saturated vapor pressure of the adsorbate molecules at absolute temperature T, and P is the partial pressure of the adsorbate gas. Dubininj3, 41 suggested that the adsorbate volume W for similar types of compounds can be expressed as a function of the ratio of adsorption potential E to a quantity 8, called the affinity coefficient:

plnf” [ v f’1


Here f, is the fugacity of the saturated liquid adsorbate at the adsorption temperature, and f is the fugacity at the adsorption partial pressure and temperature for the gaseous adsorbate. It is possible to correlate the adsorption isotherms of similar types of compounds on a given adsorbent by plotting the volume of adsorbed adsorbate (viz., W = NV) versus the reduced adsorption potential Cp,which is the adsorption potential E divided by a correlating divisor /j’. If the selection of correlating divisor p is adequate, a single curve correlates all of the data points for various adsorbates at different temperatures.




To subs~ntiate the correlation prescribed in Eqn (3), it is necessary to determine the fugacities (fand f,) and the molar volume V of the saturated liquid. W=FL (2) According to the law of corresponding states, the P liquid molar volume V may be calculated from a According to Dubininj41, the purpose of using an chart of the compressibility factor Z( = PV/RT), and affinity coefficient appropriate to each adsorbate is the fugacities may be obtained from a chart of the that all characteristic curves of W vs t for various fugacity coefficient[8]. Because these charts were conadsorbates on a given absorbent at different temstructed by fitting the experimental data of many substances, usually they are not accurate enough for estimating properties of a specific substance; in addi*Present Address: Dept. of Plastics Engineering, University of Lowell, Lowell, MA 01854. tion, the determination of thermodynamic properties




T. V. LEEet Table



Parameters for Chakravarti-Dhartype isathetms of ethane. propane, and n-butane on Columbia 4LXC 12/28 activated carbon. --

Gas Adsorbatr

Temperature ("C)

Gas-Phase Concentration,Co (ma tig)



j10m8 mole/c&

j10m3 mole/cm31

110' cm3/mole) 10.6

v (dltnens+onlessl



0.034 -10

0.18 -54




0.036 - 7.6

0.21 -41




0.078 - 7.9

0.41 -42







1.9 -45








'From Ref. [18].

by reading from the charts inevitably introduces additional errors. Equations of state (EOS) can be used to calculate thermodynamic properties of hydrocarbons and related substances. The use of EOS for this purpose has become attractive because of the availability of computing machines. Several thermodynamic EOS are available for calculating fugacities with accuracy; for example, the Benedict-Webb-Rubin (BWR) [9], the BWR-Starling (BWRS) [lo], the Redlich-Wwong (RK) [I 11, the Soave-Redlich-Kwong (SRK) [12], and the Peng-Robinson (PR) [13] EOS are widely accepted both in the academic and industrial areas. The PR EOS was selected in this study because it is capable also of predicting[l3, 141 the liquid-phase density. It is noted that the liquid density can be converted into the liquid molar ,volume V directly.

for ethane, propane, and n-butane at 25°C and propane at 30°C on activated carbon are summarized in Table 1. These isotherms are plotted as solid lines in Fig. 1. The experimental and calculated isotherms are in agreement. 5. RESULTS AND DISCUSSION

We correlated the adsorption isotherms of ethane, propane, and n-butane in the low-pressure region (viz. 0.034-10 mm Hg) on (Columbia 4LXC 12/28) activated carbon by plotting the adsorbate volume (viz. W =NV) in the adsorbed phase vs the reduced adsorption potential 4. As shown in Fig. 2, a single curve of In W vs 4 correlates the isotherms for three i


We used a dynamic method[lS] to measure the transmission of hydrocarbon gases passing through an adsorber bed of Columbia 4LXC 12128 activated carbon. Transmission is the ratio of the concentration at the outlet of the adsorber bed to that at the inlet. A detailed description of the experimental apparatus and the flow system used in this study was given previously[l5]. The amount of adsorbate q,, on the activated carbon was extracted from the transmission curves by using a mass-balance equation[l6]. The adsorption isotherms for ethane, propane, and nbutane were represented by a three-parameter formula of the Chakravarti-Dhar type[l7]: % -= %”

(ru,Co) 1 + KGlY








Here C,, is the adsorbate concentration in the gas phase, q,, is the adsorbate concentration in the adsorbed phase, the parameter qosis the adsorbed-phase concentration for a monolayer coverage of the adsorbate, and the coefficient K,,,and the exponent v are the two other parameters. Values of the parameters

Fig. I. Adsorption isotherms for some hydrocarbon gases on Columbia 4LXC 12/28 activated carbon.


of adsorption



Fig. 2. Correlation

of adsorption

of hydrocarbon


hydrocarbons at 25°C and for the same hydrocarbon (viz., propane) at two temperatures (viz., 25 and 30°C). The success of this correlation justifies the selection of the molar volume of the saturated liquid as a correlating divisor. The logarithm of the adsorbate volume in the adsorbed phase can be represented by a quadratic polynomial function in the reduced adsorption potential b:


with a, = 6.856, a, = -6.797 x 10m4, and a2 = -6.211 x lo-*. In eqn (5), the adsorbate volume W is expressed in units of cm3/kg, and 4 is

expressed in atmospheres. This result [viz. Eqn (5)] can be used for the design of adsorption systems and, as shown by Grant and Manes[5], for predicting the adsorption equilibrium behavior of binary and/or multicomponent gaseous mixtures on activated carbon. Acknowledgement-This

by the Department

m= y

isotherms for some hydrocarbon activated carbon.


In W = a, + a,4 + a&*


gases on activated

work was supported in part of Energy.






gases on Columbia



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