Adsorption of Benzene in Carbon Slurries Dragoslav M. Misic' and J. M. SmithZ University of California, Davis, California 95616
Experimental rates have been measured at 24°C for the solution of benzene from gas bubbles into water and aqueous slurries of activated carbon particles. Batch-type experiments were carried out so that the data at low time values gave from a single-resistance equation the mass transfer coefficient k L from gasbubble interface to bulk liquid. For bubbles whose diameter was 1 .E mm k l was about 4 X 1 O-' cm/sec. The same value was obtained for the solution of benzene in water alone or in aqueous slurries of carbon particles. Rate data were measured for various concentrations of carbon particles in the slurry. Although it was not possible to achieve conditions where mass transfer to the particle surface controlled the rate, data Interpretation of these results in terms were obtained at bubble-to-particle area ratios as high as 1.7-2.7. of two-resistance equations gave k, = 6.3 X cm/sec. This value is 60% greater than that predicted for mass transfer between a spherical particle and surrounding, stagnant liquid. The adsorption isotherm was required for obtaining k, and this was measured at 24°C and for benzene partial pressures from 1.9 to 9.0 X atm.
A c t i v a t e d (high surface area) carbon particles are widely used in gas-solid and liquid-solid systems for purification, decolorization, and deodorization. Interest in using aqueous slurries of carbon particles, a gas-liquid-solid system, for purifying gas streams is more recent. The mobility of the slurry may offer some advantages over gas-solid adsorbent systems for cont'inuous operation. I n order to predict' the performance of slurry adsorbers, rate coefficients or equilibrium constants are required for the various steps in the mass transfer process. While solubility information is usually available, adsorption isotherms for slurries are rare. The objectives of the study reported here were to establish the adsorption capacities of aqueous slurries of carbon particles for benzene and t>oevaluate rate coefficients from transient adsorption measurements. I n studies of adsorption equilibria for such hydrocarbons as CHI, C&, CaHs, and C6& in aqueous slurries of carbon particles, X e h t a and Calvert (1967) found that the adsorpt,ion capacity could be as high as that for the dry particles. Rate data agreed with equations derived on the basis t h a t the mass transfer st'ep from gas bubble-liquid interface to bulk liquid controlled the rate. Recently the same authors jllehta and Calvert, 1970) reported the performance of a porous plate column used as a slurry adsorber. Munemori (1951) found that the isotherm for the adsorption of carbon dioside on aqueous slurries of charcoal particles followed the Freundlich equation. Other equilibrium and rate data for aqueous slurries include the adsorption of hydrogen on a palladium catalyst (Nagy, et al., 1959), of carbon dioxide on charcoal, quartz sand, BaSOd, and CaSOa particles (Pozin, et al., 1957)) and of ethylene on alumina, talc, and carbon (Nagy and Schay, 1955). Insufficient data from which to extract' rate coefficients were reported in all but the first reference. Equations for Transient Adsorption
The experimental method t'hat we have used to measure mass transfer rates is the transient, batch approach de-
' Present Address: California State Polytechnic College, San Luis Obispo, Calif. 2 T o whom correspondence should be sent. 380
Ind. Eng. Chem. Fundam., Vel. 10, No. 3, 1971
scribed by Mehta and Calvert (1 967). Gas bubbles containing the adsorbate are passed vertically through an agitated slurry. The amount adsorbed is obtained from the difference in adsorbate concentrations in the gas stream entering and leaving the slurry. The rate of adsorption depends upon the resistances of the several steps involved in transferring the adsorbate from gas bubble to adsorption site on the carbon particle. Local Rate and Equilibrium Equations. Mass transfer from bulk conditions in the gas bubble to bulk liquid for slightly soluble components is determined by the liquidphase coefficient /cz (Calderbank, 1959). Hence, for the benzene-water system the concentration of benzene in the liquid a t the interface is close to the equilibrium value, C,. If the partial pressure of benzene in the gas bubble is p
C , - Pl - H
and the mass transfer rate may be written
The value of k l S B is frequently low enough for the rate to be significantly influenced by this step (hIehta and Calvert, 1967; Sherwood and Farkas, 1966). I n an agitated slurry with bubbles, the mixing in the liquid phase is expected to be rapid. Then the resistance to mass transport through the bulk region from near the gas bubble to near the particle should be negligible. Thi. conclusion has been confirmed by experimental qtudies (Kolbel and Siemes, 1957; Siemes and Weiss, 1959). The size of adsorbent particleq in slurries is small enough (0.014.1 mm) that the relative velocity between liquid and particle is low. Hence, the resistance t o mass transfer through the liquid immediately surrounding the particle may be significant. -4 decisive parameter is the relative surface areas of the gas bubbles and particles (external surface). The diameter of the bubbles is normally between 1 and 5 mm. Hence, if the volume fractionq of gas and qolld in the adsorber are about the same, the surface area S,for
mass transfer to the particle will be much greater than the area S B for transport from bubble to liquid. Then the resistance of the liquid around the particles would be small. This situation would correspond to the results of Mehta and Calvert (1967), where k l controlled the adsorption rate. However, for a high gas holdup and a very low concentration of particles, the resistance to transport through the liquid surrounding the particles should be considered. The rate equation applicable for this step is 1 dN
V L dt
=
k,S, (C
-
C,)
(3)
Sherwood and Farkas (1966) in studies on the hydrogenation of a-methylstyrene in slurries of palladium block found both k l and k , affected the rate for certain concentrations of slurry. Two additional steps are involved in the overall process: intraparticle transport and adsorption at the interior site. For the small size particles used in slurries, intraparticle diffusion resistance is negligible. For example, since the diffusivity of benzene in water is about 10-5 cm2/sec, the effective diffusivitg in the pores would be, approximately, Dez or 5 X 10W6 cmZ/sec. The analysis of t'he experimental rate data shows (see Results section) t h a t the rate constant for the overall process is about 1 X sec-I. Then a Thielet'ype modulus for a 127-w particle (the largest diameter studied) is 0.3, indicating that the concentration n of adsorbed benzene will be nearly uniform throughout the particles. For benzene and carbon particles, the process a t the site is one of physical adsorption for which the intrinsic rate is very high. This has been confirmed by many studies in gaseous systems, for example, by Shen and Smith (1968) for benzene adsorption on silica gel. They found that equilibrium could be assumed between concentrations in the fluid and on the surface. This assumption would be even better justified for slurry adsorption where the slow diffusion steps in the liquid phase are involved. For a uniform value of n within the particle, and equilibrium conditions a t the adsorption site, the concentration C, at the out'er surface of the particle is related t o n by the adsorption isotherm. For a linear isotherm through the origin this relation is
Absorbent particles: k,S,(C
b -Dl4
Gas bubble:
-vB
(7)
(--) VBP
az
= klSB
(;
-
c)
RT
At low concentrations of benzene (in mixtures with helium) in the bubbles and for constant total pressure, the bubble volume V B will be constant. For the mean bubble size of 1.8 mm corresponding t o our experiments (see Experimental Section), the bubble velocity V B is also constant. Then eq 8 can be integrated, taking p = pa a t z = 0, to give
The partial pressure in the gas leaving the adsorber of height L , in terms of the liquid concentration C, will be
The length-average value for p is obtained by integrating the equation
;s,
L
(4)
The isotherm for benzene a t 24OC on our carbon (Figure 4) i. approximately linear. More importantly, i t closely approaches linearity in the higher concentration range where it is used in the analysis of the rate data. I n summary, for physical adsorption for the small particles normally encountered in slurries, the mass transport from gas bubble to adsorption a t an interior site should be determined by the two liquid-phase diffusion steps: bubble interface-to-bulk liquid and bulk liquid-to-particle surface. Conservation Equations. Assuming t h a t t h e two liquidphase diffusion steps control slurry adsorption, a mass conqervation equation for transient adsorption may be rewritten for each of the three phases
dn dt
= ? u s -~
where p is the average partial pressure of benzeiie in t'he gas bubbles during their vertical travel in the slurry. I n formulating these equations i t is assumed that the gas bubbles pass in plug-flow through a completely mixed [C # f(z), n # j ( z ) ] slurry. Plug flow is a reasonable assumption for the gas stream since the flow is in discrete bubbles which, for a size range of 1-4 mm, have approximately the same velocity (Valentin, 1967). A magnetic stirrer was used in the experimental work to supplement the agitation induced by the bubbles and ensure a uniform concentrat,ion of particles in the slurry. T h e experimental data showed that the time required to transfer benzene from the bubble to the slurry was very large in comparison with the bubble residence time (from 0.1 to 0.7 see). O n t'he other hand, the fractional removal of benzene from an individual bubble in passing through the slurry was large. Therefore, d p b l = parameter defined by eq 13 CY = parameter defined by eq 24 P
*
I
= =
e
P
porosity of carbon particles density of solid phase in porous carbon particles, g/cm3
literature Cited
Arnold, D. S., Plank, C. A,, Erickson, E. E Pike, F. P., Ind. Eng. Chem., Chem. Eng. Data Ser. 3, 253 (1958). Bohon, R. L., Clausen, W. F., J . Arner. Chem. SOC.73, 1571 (1951).
Brian, P. L. T., Hales, H. B., A.I.Ch.E. J . 15, 419 (1969). Calderbank, P. H., Trans. Inst. Chem. Eng. 37, 173 (1959). Calderbank. P. H., Moo-Young, - M. B., Chem. Eng. Sci. 16, 39
:1961). as reDorted bv Green. S. J., Sine. K. S. in 1)L ibinin. hI &I.. “Adsirptioil, ‘Surface Area and l%rosity,’J p 526, Academic Press, Xew York, N . Y . , 1967. Higbie, R., Trans. A.I.Ch.E. 31, 365 (193,5). Roughton, G., Ititchie, P. I),, Thompson, J. A,, Chem. Eng. Sci. 7. 111 (ia;7),. Hughmark , G . A,, Ind. Eng. Chem., Process Des. Develop. 6, 218 11967). Kdbel, H.,Siemes, W., Umschau24, 746 (1957)
w.,
Liebermann, L., J . Appl. Phys. 28, 205 (1957). Livingston, H. K., J . Colloid Chem. 4,447 (1949). Manley, D. M. J. P., Brit. J. Appl. Phys. 11,38(1960). Mehta, D. S.,Calvert, S.,Environ. Sci. Techno!. 1, 32.5 (1967). Mehta, D. S.,Calvert, S., Brit. Chem. Eng. 15, 781 (1970). Munemori, M., Sci. Rep. Tohoku Univ. 35, 165 (1951). Nagy, F., Moger, U., Magy. Kem. Foly. 65,406 (1959). Nagy, F., Scha G., Magy. Kem. Foly. 64, 81 (1958). Pozin, M. E., %bp lev, B. H., Gulyaev, S.P., Trans. Leningrad Teknol. Inst. im Eensoveta 43, 52 (1957).
Ray, A. B., Chem. Met. Eng. 28,977 (1923). Satt>erfield,C. N., “Mass Transfer in Heterogeneous Catalysis,” M.I.T. Press, Cambridge, Mass., 1970. Shen, J., Smith, J. hI.,IND.ENG.CHEY.,FUNDAM. 7, 106 (1968). Sherwood, T. K., Farkas, E . J., Chem. Eng. Sci. 21, 573 (1966). Siemes, W., Weiss, W., Dechema Monogr. 32, 451 (19-39). Valentin, IF. H . H., “Absorption in Gas-Liquid lhpersioris,” E. and 1’.N . Spon Ltd., London, 1967. Young, D. M., Crowell, A. D., “Physical Adsorption of Gases,” Butterworths, London, 1962.
V1,.
RECEIVED for review September 18, 1970 ACCEPTEDMarch 17, 1971
A Generalized Correlation for Henry’s Constants in Nonpolar Systems G. T. Preston’ and J. M. PrausniW Deparfment of Chemical Engineering, University of Caliifornia, Berkeley, Calif. 94720
A generalized thermodynamic expression for Henry’s constants is derived. The derivation is based on the statistical mechanics of dilute liquid solutions in conjunction with Scott’s two-fluid theory and a reduced empirical equation of state; it is applicable to solid as well as fluid solutes. When Henry’s constants are plotted against temperature, the correlation correctly predicts the maximum observed for some systems. The correlation is applied successfully to experimentally obtained Henry’s constants covering seven orders of magnitude for 60 nonpolar binary systems.
Thermodynamic properties of a dilute liquid solution call be determiiied from Henry’s law which says t h a t the fugacity of the solute is proportioiial to its mole fraction in the liquid lilirise. (At lo^ pressures the fugacity of the solute is equal t o its pai,tinl pressure.) The coiistaitt of proportionality, called Heiiry’s coiistant, is a funct’ion of ternperature and, to a 1es;her esteiit, also of pressure. Sumerous workers have studied the therinodyiiamics of dilute solutioiis; we do not give aii exhaustive review here. For eiigiiieeiiiig work, iiotable contributions were made by 1)udge aiid Newtoii (1!337), Eley (1939): Uhlig (1937) and Krishevsky aiid coworkers (1935, 1945). More recent work iiicludes t h a t of Prausnitz and Shair (1961), Hildebrand, et al. (1970), Kobatake arid -4lder (1962), Pierotti (1963, 1965), aiid Miller and I’rausnitz (1969). Many of these and other Ytudier are critically reviewed by I h t t i n o atid Clever (1966). See also the receiit tests of Prausnitz (1969) and King (1 969). For niasimuni utilitj-, a method for correlating Henry’s c-oiistaiits should be applicable to a variety of binary systems Present address, Garrett Research arid Development Co., L a Verile, Calif. 91750. * T(Jwhom correspotideiice should be sent.
over a wide range of temperature. Previous treatments are restricted in their application, often because they rely on some particular description of the liquid state. A method of correlatioii is presented here which, in principle, is not so restricted; for implemeiitation, however, it depends oti a reliable generalized equation of state. 111a binary mixture, the fugacity of cornponelit 2 , the solute, can be written = y2*(P)Z2H2,1(P expJpr ‘)
aY
(1)
where subscript 1 stands for the solvent; y2*(P)is the act’ivity coefficient of the solute in the solution a t pressure P, defined such that yr* + 1 as x 2 + 0; P‘ is the (arbit,rary) reference pressure for Henry’s constant N 2 , 1 ( P ‘ ) , aiid is the part’ial molar volume of the solute in the mixture a t infinite dilutioii, all a t system temperature T . Statistical Mechanics
T o obtain a useful expression for Heiiry’s constant, we ube Hill’s work on the statistical mechanics of dilute solutions (1957) 1960), from which it can be shoivii that Ind. Eng. Chem. Pundam., Vol. 10, No. 3, 1971
389
