Ind. Eng. Chem. Fundam. 1981, 20, 28-34
28
Table 111. Parameters and R e l a t e d Data for the Proposed Equation and Wilson Equation
system
proposed eq _ _ I _ _ _ _
A ,..,
1,)
1.418 0.5041 0.04802 0.4498 0.6410 0.7800 0.1862 0.8201 0.6048 0.3714 1.046 0.1415 0,1476 0.1021 0.08501 0.04340 0.3751 0.06906 0.005110 0.002312
0.3092 0.6404 0.3213 0.5391 0.2620 0.8868 0.5253 0.8185 1.330 0.4541 1.864 0.5676 0.9142 0.06728 0.09606 0.1067 0.0 2044 0.4431 0.04924 0.03133
110.
1
2 3 4 5 6 7 8 9 10 11 12 13 13 15 16
17 18 19 20 a
~
x
~
___ o'
Wilson
5.7 11.6 7.8 4.2 6.9 2.6 7.5 2.1 6.7 11.5 3.4 4.4 24.8
5.6 11.2 6.6 4.2 6.9 2.5 6.9 2.1 6.7 11.6 3.4 4.3 24.8
equU
___
~ ~ ~ ( ~ 1N~' ~x ~i o)3 .~~ /~ . ~v
very close to unity; (2) cidoes not depend significantly on molecular size (uior qi);(3) cifor water is only exceptional. The proposed method yields almost the same size of immiscibility regions as those observed, and the estimation of the binary parameters as well as the prediction of the ternary tie lines were carried out with no problem. Acknowledgment The author would like to thank S. Endo for his help with calculations. Nomenclature ci = parameter of component i in eq 2, 3, and 4
gE = excess Gibbs energy of mixing gEcomb = gEms
excess Gibbs energy for an athermd mixture
= gE - gEcomb
N; = total number of molecules i in mixture = vapor pressure of pure component i, atm p , = vapor pressure of component i in mixture, atm R = gas constant r, = number of segments in molecule i T = absolute temperature, K L', = molar volume of i L ~ O = molar volume of key molecule z = coordination number x , = mole fraction of component i in liquid phase y = mole fraction of component in vapor phase Greek Letters y, = activity coefficient of component i in liquid phase A,, = Wilson-like parameter P,'O
Subscripts i, j , k , N = component
Literature Cited Abrams, D. S.; Prausnitz, J. M. AIChE J. 1975, 21, 116. Arm, H., et al. Heh. Chim. Acta 1967, 50, 1013. Arm, H.; Bankay, D. Helv. Chim. Acta 1968, 51, 1243. Grlswold, J.; Klecka, M. E. Ind. Eng. Chem. 1950, 42, 1250. Guggenheim, E. A. "Mixtures", Clarendon Press: Oxford, 1952. Hand, D. B. J . Phys. Chem. 1930, 34, 1980. Hiranuma, M. Ind. Eng. Chem. Fundam. 1974, 13, 219. Hiranuma, M. J . Chem. Eng. Jpn. 1975, 8 , 162. Kagaku Kogaku Kyokai,',"Bussei Jyosu" 1965, 3,205. Kagaku Kogaku Kyokai Bussei Jyosu" 1970, 8 , 112. Nlppon Kagaku Kai "Kagaku Blnran, Klsohen 11" 1966, 596. Palmer, D. A.; Smith, B. D. J . Chem. Eng. Data 1972, 17, 73. Renon, H.; Prausnitz, J. M. AIChE J . 1969, 15, 785. Sorensen, J. M., et al. Fiuid Phase Equlllb. 1979, 3,47. Sugi, H., et al. J. Chem. Eng. Jpn. 1976, 9 , 12. Sugi, H.; Katayama, T. J . Chem. Eng. Jpn. 1978, 1 1 , 167. Venkataratnam, et ai. Chem. Eng. Sci. 1957, 7 , 104.
Received for review August 8, 1979 Accepted September 8, 1980
Liquid-Phase Adsorption of Binary and Ternary Systems of n-Paraffins on LMS-5A Ram K. Gupta, Deepak Kunzru,' and Deoki N. Saraf Department of Chemical Engineering, Indian Institute of Technology, Kanpur-2080 16, India
Liquid-phase adsorption studies of binary and ternary systems of n-paraffins (C,-Cs)on LMSdA were conducted at 6, 18, 30, and 42 OC. Equilibrium adsorption was found to be essentially independent of temperature, for all the binary systems studied, except those containing pentane at 30 OC where a decrease in adsorption was observed. A two-parameter statistical model was developed to represent liquid-phase adsorption isotherms of n-paraffins on LMSdA. This model was then extended for adsorption in binary and ternary systems and has been validated against the experimental data. Predicted values were in good agreement with experimental observations for all the systems studied. The discrepancy was relatively higher for systems containing pentane at 30 OC.
Introduction The phenomenon of adsorption has been widely studied and considerable data are now available for pure component vapor phase adsorption of light hydrocarbons and other components on different zeolites. However, indus-
trial separation processes generally involve multicomponent adsorption, data for which are scanty. In any petroleum fraction there is a large number of combinations of hydrocarbons and it is, therefore, not possible experimentally to study all these systems. Hence for design of
0196-4313/81/1020-0028$01.00/00 1981 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 29
any adsorption process, a reliable method for predicting equilibrium adsorption data for mixtures from the isotherms of the pure components is essential. Very little information is available in the published literature on multicomponent liquid-phase adsorption of n-paraffins on molecular sieves. Sundstrom and Krautz (1968) have reported some data on the liquid-phase adsorption of binary systems of C7, Cl0, C12 and C14 nparaffins on LMS-5A. For all the systems studied, they found that the lower molecular weight paraffin was preferentially adsorbed and that the temperature had a negligible effect on the composition of adsorbate in equilibrium for a given liquid composition. Satterfield and Cheng (1972) studied the adsorption of a wide variety of liquid binary hydrocarbon systems on NaY zeolite. Satterfield and Smeets (1974) have reported the liquid-phase adsorption data for binary systems of n-octane with either n-decane, n-dodecane, or n-tetradecane on NaY zeolite. They found that the lower molecular weight paraffin was preferentially adsorbed. They suggested that the packing characteristics of the higher molecular weight paraffin, rather than its physicochemical characteristic, play a dominant role in the adsorption selectivity on a zeolite. In the present investigation, liquid-phase adsorption of the binary systems pentane-hexane, hexane-heptane, heptane-octane, pentane-heptane, and pentane-octane has been studied on the synthetic zeolite LMS-5A. The ternary systems studied were pentane-hexane-heptane, pentane-hexane-octane, and pentane-heptane-octane. Benzene was used as a diluent in all the measurements since its adsorbability on the zeolite used is negligible. The equilibrium adsorption for different hydrocarbon concentrations was measured at 6, 18, 30, and 42 "C. The experimental data were then used to validate a proposed model for liquid-phase multicomponent adsorption. Mathematical Model for Adsorption The conventional adsorption models are not applicable to zeolite adsorption because the basic assumptions from which the models are derived are generally not fulfilled (Barrer and Lee, 1968; Schirmer et al., 1967; Barrer and Davies, 1970). Other available approaches are potential theory and thermodynamic methods. The potential theory approach has been used by several investigators (Lewis et al., 1950; Malson et al., 1953; Grant and Manes, 1964) to predict adsorption equilibria for gas mixtures. The thermodynamic methods are those that are independent of any molecular theory of adsorption. Thermodynamic methods of estimating adsorption equilibria of gas mixtures include those of Arnold (1949), Lewis et al. (1950), Cook and Basamadjian (1965),Myers and Prausnitz (1965),and Kidnay and Myers (1966). The basic postulate, common to all these models, is that the adsorbed phase forms an ideal adsorbed solution, but the methods differ in their choice of standard states. However, only the method of Myers and Prausnitz (1965) is thermodynamically consistent and hence has been used extensively. The advantages and disadvantages of different methods described above have been reported by Sircar and Myers (1973). Ruthven (1971), using the principles of statistical thermodynamics, has proposed a pure-component vaporphase model and the extension of this model for binary systems has been presented by Ruthven and Loughlin (1972), Ruthven et al. (1973a,b),and Ruthven (1976). No attempt has been made so far to develop theoretical models for liquid-phase adsorption on molecular sieves. In this study, the vapor phase theory has been modified to predict equilibrium loadings in multicomponent liquid phase adsorption. In a closed vessel, partially filled with
liquid adsorbate, adsorption from the liquid phase will be the same as that from the vapor phase provided that this vapor is in equilibrium with the liquid. This follows from the fact that if two phases are in equilibrium with a third phase, then these are in equilibrium with each other as well. This implies that one can use a vapor-phase adsorption model to predict liquid phase adsorption by simply replacing the partial pressure of the component in terms of the vapor pressure and the mole fraction of the adsorbable component in the liquid phase. Assuming ideal behavior, the partial pressures can be obtained using Raoult's law. For a single adsorbable component in the liquid phase, the expression for the isotherm in vapor phase adsorption (Ruthven, 1971) can be modified using Raoult's law to yield the expression
c=
[
aPX
(aPX)"
+ ( a P X ) 2 ( 1 - 2p/v)2 + ... + ( m - l)!(1-
where m is the maximum number of molecules adsorbed per cavity and satisfies the constraint mp I V . The assumptions involved in the derivation of the above expression have been given by Ruthven (1971). Equation 1 gives the number of molecules adsorbed per cavity in terms of Henry's constant, a,effective molecular volume, p , the vapor pressure of the normal paraffin at adsorption temperature, P, and the equilibrium mole fraction of the normal paraffin in the liquid phase, X . The corresponding expression for the isotherm for two adsorbable componenttj in the liquid phase can be similarly obtained by extending the vapor phase adsorption model presented earlier (Ruthven et al., 1973b). The number of molecules of A adsorbed per cavity, CA, in a binary liquid mixture of A and B is given by eq 2 where the summations
are carried out over all values of i and j satisfying the constraints i + j 2 2 ipA
+j p , Iv
(3) (4)
Equation 2 along with constraints 3 and 4, with a similar equation for Cg, can be used to calculate the average number of molecules of A or B adsorbed per cavity. Values of a A , a,, P A , and @B can be obtained from the isotherms of pure components. The binary adsorption model was extended for ternary systems, and the expression for CA in a ternary mixture of A, B, and C is given in eq 5 with the constraints given in eq 6 and 7. Equation 5, with similar expression for
30
Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981
r CA =
1
+
1'pA
IPB
v
v
h%)i+j+h]
(5)
v Mol2 lraclion O t pentane
in liquid pnaw
Figure 1. Equilibrium curves for pentane-hexane system at different temperatures.
components B and C, can be used to calculate the average number of molecules adsorbed per cavity. Experimental Section The molecular sieves used were LMS-5A in the form of 1/16-in,pellets containing 20% inert clay binder. Benzene (AR grade E. Merk/B.D.H.) had a minimum purity of 99.0%. Benzene was used as a diluent. Owing to their size (6.8 A), benzene molecules were essentially excluded from the pores. Equilibrium loading of benzene on LMS-5A has been reported as 0.002 g / g of zeolite (Breck et al., 1956). The experiments were conducted in a Pyrex glass assembly which consisted of a 100-mL adsorption cell attached to a three-way vacuum stopcock. A weighed quantity of liquid paraffin and benzene mixture was then added under vacuum to the adsorption cell containing regenerated molecular sieves. The adsorption was conducted under isothermal conditions with constant shaking. Preliminary runs had indicated that equilibrium was reached in 24 h and, to ensure complete equilibrium, each run was continued for 48 h. The samples were analyzed by gasliquid chromatography on a 10 m long column of 20% bentone on Chromosorb W. Details of the experimental procedure have been reported elsewhere by Gupta et al. (1980). Results and Discussion Figures 1through 5 show the equilibrium curves for the various binary systems investigated. Temperature had a negligible effect on equilibrium loadings in hexaneheptane and heptane-octane systems as evidenced from Figures 2 and 3. Sundstrom and Krautz (1968) have also reported (for binary systems of higher paraffins) that temperature has a negligible effect on the composition of an adsorbate in eqilibrium with a given liquid composition. However, for pentane-hexane, pentane-heptane, and pentane-octane systems (Figures 1,4, and 5), the amount of pentane adsorbed at 30 "C decreased in comparison to the lower temperatures. For these systems, equilibrium curves for 6" and 18a coincide, but the 30 OC curve is distinct from the 6' and 18" curves. Since this temperature of 30 "C is close to the boiling point of pentane (36.1 " C ) , it is possible that the nature of the adsorbed pentane molecules is different compared to the lower temperatures resulting in lower adsorption. Determination of a and 8. The equation derived from the model for isotherms of pure component (eq 1)has two parameters, a and P. a can be calculated from the slope of the adsorption isotherm at very low concentrations. The nature of the experimental isotherms (Gupta et al., 1980) did not permit direct measurement of the slope because
c
01
c2
Mol2 IraCtiGn Of hemre in
03 iquia phase
Figure 2. Equilibrium curves for hexane-heptane system at different temperatures.
51
32
C3
q o e fiact1or a t neptone i n liquid Phase
Figure 3. Equilibrium curves for heptane-octane system at different temperatures.
of experimental limitations of finding equilibrium loadings at very low concentrations. It was also observed that, for the n-paraffins studied, eq 1 was very sensitive to P, the molecular volume of the adsorbate. The approximation of its value by van der Waals co-volume, as suggested by Dubinin and used by Ruthven and co-workers (1971,1972, 1973a,b), was found to be unsatisfactory for the systems investigated. Thus, a more accurate determination of the values of the parameters CY and 8 was required to predict the adsorption isotherms for the hydrocarbons studied. However, in the absence of better prediction procedures
Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 31 0
08-
A 0
Pentane Hexane HeDtane
07-
: 06-
8
$ 050
c_
E 04-
.. 0
c
0 6’C A tB’C
3m
v 2 01
P
I
I
I
01
02
03
Mole troction
01
I
pentane in liquid phase
Figure 4. Equilibrium curves for pentane-heptane system at different temperatures.
Equilibrium liquid p h o s e concentration moiesilifre
Figure 6. Comparison between predicted and experimental isotherms at 18 O C . Table I. Values of a and p at Different Temperatures paraffin
Figure 5. Equilibrium curves for pentane-octane system at different temperatures.
for a and 0, it was decided to obtain these using the experimental data. Thus, it has been implicitly assumed that our two-parameter model is valid for pure hydrocarbon adsorption. Experimental isotherms (Gupta et al., 1980) were matched with the model by a least-square minimization procedure, using the Blind Search Technique, to evaluate a and p. An objective function E was defined as
where n = number of data points, Cd = calculated value of molecules adsorbed per activity from eq 1,and Cexpt= experimental value of molecules adsorbed per cavity. E was then minimized over a wide range of values of parameters a and p to give a minimum value, Emin, of the objective function. n
The values of a and p corresponding to Ed,, were then taken to represent the best values of these parameters for a given paraffin at a fixed temperature. Figure 6 shows typical predicted adsorption isotherms using calculated values of a and B along with experimentally observed data points at 18 O C . Similar plots were obtained at other temperatures also. This should not be taken as a validation of the model because the prediction is not totally independent of experimental data; rather, it makes use of
C
a
P
Em,
n-pentane
6 18 30
4.50 3.96 1.86
94.50 116.55 129.50
0.0521 0.0487 0.0072
n-hexane
6 18 30 42 6 18 30 42 6 18 30 42
64.05 50.92 46.03 22.46 365.54 222.43 101.44 36.14
136.50 165.71 179.88 183.79 166.19 179.31 183.96 184.99
0.0121 0.0241 0.0465 0.0333 0.0227 0.0199 0.0488 0.0877
3079.89 824.36 485.90 247.75
181.92 187.41 215.00 225.10
0.0019 0.0002 0.0063 0.0207
n-heptane
Mole lractlan 01 pentane in liquid phase
komP,
n-octane
the latter to calculate the former. The comparison has been made merely to show that the two-parameter model is able to represent the experimental data fairly well. As will be seen later, the validation of the pure-component model comes from the fact that, for most of the systems studied, the predictions made using this model for binary and ternary systems match within 10% of the experimentally determined values. The values of a and p along with the minimum errors for all the paraffins studied at different temperatures are given in Table I. a decreased with increasing temperature, which implies that adsorption decreases with increasing temperature. It was also observed that a increased with molecular weight of the paraffin. As expected, the molecular volume of the adsorbate, p, increased with temperature and at a particular temperature increased with increasing molecular weight of the paraffin. Figure 7 is a van’t Hoff plot for the variation of a with temperature for all the hydrocarbons studied. The heats of adsorption calculated from the slopes of these plots were approximately equal to the latent heats of vaporization. For example, for n-octane, the heat of adsorption was found to be -9100 cal/mol, whereas the latent heat of vaporization for n-octane is 8230 cal/mol. Adsorption of Binary Systems. Equations 2 with similar expression for CB along with constraints 3 and 4 are used to predict values of CA and Cg, for all the binary systems studied, using appropriate values of a and p ob-
32 Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 Table 11. Comparison of Experimental and Predicted Values for Binary Systems a t 6 " C a equilib compn in liquid phase. mole fraction
molecules adsor bed / cavity
_ _ _ _ _ _ ~ . _ _
exptl
pred
% error
- .__.._______--__
run BPX-1 BPX-2 BPX-3 BPX-4 BXH-1 BXH-2 BXH-3 BXH-4 BHO-1 BHO-2 BHO-3 BHO-4 BPH-1 BPH-2 BPH-3 BPH-4 BPO-1 BPO-2 BPO-3 BPO-4
1
2
1
2
1
0.321 0.213 0.134 0.052 0.063 0.138 0.206 0.285 0.055 0.127 0.208 0.280 0.302 0.237 0.157 0.065 0.054 0.141 0.219 0.314
0.052 0.115 0.201 0.290 0.284 0.214 0.144 0.062 0.278 0.198 0.122 0.053 0.042 0.094 0.164 0.263 0.275 0.203 0.117 0.052
4.75 3.20 1.96 1.31 1.36 2.02 2.75 3.69 1.17 1.61 2.31 3.04 5.00 3.92 2.62 1.44 1.20 2.05 3.27 4.77
1.36 2.01 2.98 3.90 2.91 2.13 1.59
4.88 3.44 2.17 1.33 1.41 2.06 2.81 3.78 1.25 1.69 2.35 3.11 5.14 4.15 2.85 1.57 1.28 2.17 3.44 4.85
1.18 2.89 2.24 1.61 1.20 1.13 1.47 2.11 3.10 2.94 3.22 1.59 1.11
2
1
2
1.32 2.7 2.5 2.00 7.3 0.3 2.95 10.8 1.0 3.88 1.7 0.5 2.95 3.6 1.4 1.9 2.0 2.17 1.64 2.0 3.3 1.21 2.3 3.4 2.92 6.7 1.1 2.30 5.4 2.7 1.70 1.6 5.7 1.27 2.2 6.1 1.16 2.7 2.4 1.45 5.9 1.3 2.04 9.0 3.4 3.05 9.0 1.4 7.2 0.3 2.93 3.29 5.7 2.2 1.65 5.2 3.9 1 . 2 1 1.8 9.1
a Note: 1represents the lighter hydrocarbon in a given binary mixture and 2 represents the remaining component. BPX = Pentane-hexane; BXH = hexane-Heptane; BHO = Heptane-Octane; BPH = Pentane-Heptane; BPO -Pentane-Octane.
Table 111. Comparison of Experimental and Predicted Values for Binary Systems at 18 O c a ____ equilib compn molecules in liquid adsorbed/cavity phase, mole fraction exptl pred % error ____I_.___
_ _ _ _ __ __--
___ _____
run BPX-5 BPX-6 BPX-7 BPX-8 BXH-5 BXH-6 BXH-7 BXH-8 BHO-5 BHO-6 BHO-7 BHO-8 BPH-5 BPH-6 BPH-7 BPH-8 BPO-5 BPO-6 BPO-7 BPO-8 a
1
2
1
2
0.327 0.231 0.152 0.064 0.064 0.146 0.219 0.302 0.052 0.114 0.178 0.264 0.320 0.243 0.177 0.070 0.067 0.156 0.237 0.327
0.052 0.119 0.203 0.288 0.279 0.201 0.130 0.061 0.248 0.166 0.108 0.045 0.045 0.098 0.168 0.264 0.249 0.170 0.114 0.045
4.05 3.04 1.99 1.22 1.26 1.84 2.51 3.14 1.16 1.57 2.03 2.82 4.13 3.39 2.36 1.29 1.36 2.25 3.10 4.26
1.07 1.55 2.23 3.10 2.00 1.90 1.46 1.13 2.49 1.85 1.42 1.08 1.07 1.35 1.82 2.63 2.54
1
4.17 3.14 2.11 1.36 1.39 2.01 2.63 3.29 1.23 1.65 2.17 2.89 4.29 3.45 2.51 1.42 1.48 1.81 2.38 1.35 3.32 1.05 4.33
2
1
2
1.20 3.0 12.4 1.64 3.2 5.4 2.32 6.2 4.2 3.19 11.6 2.9 2.10 10.4 5.1 1.98 9.1 4.1 1.52 4.7 4.4 1.20 4.9 6.4 2.52 6.4 1.2 1.93 5.3 4.0 1.50 6.8 5.6 1.16 2.3 7.2 1.14 3.9 6.2 1.42 1.9 5.5 1.88 6.4 3.7 2.74 10.2 4.1 2.56 9.0 0.9 1.89 6.7 4.4 1.45 7.0 7.2 1.12 1.7 6.8
Note: Notations are same as used in Table 11.
tained for pure components. Tables 11-V give the results of all the systems at 6, 18, 30, and 42 "C, respectively. In general, errors are less than 10% for more than 123 of a total of 136 predictions made. At 6 "C, the maximum error of 10.8% is observed in the case of the pentane-hexane system, all others out of a total of 40 predictions showing less than 10% error. At 18 "C the maximum error of 12.4% is also observed for the pentane-hexane system. At
'
30
31
32
33
34
I T
133 O K -
h
~ 3 5 35
3-
Figure 7. van't Hoff plot of the variation of Henry's constant for different n-paraffins. Table IV. Comparison of Experimental and Predicted Values for Binary Systems at 30 " C a
run BPX-9 BPX-10 BPX-11 BPX-12 BXH-9 BXH-10 BXH-11 BXH-12 BHO-9 BHO-10 BHO-11 BHO-12 BPH-9 BPH-10 BPH-11 BPH-12 BPO-9 BPO-10 BPO-11 BPO-12 a
equilib compn molecules in liquid adsor bed/cavity phase. mole fraction exptl pred. 1 2 1 2 1 2 0.074 0.170 0.247 0.335 0.317 0.251 0.155 0.064 0.049 0.104 0.180 0.270 0.339 0.268 0.197 0.075 0.071 0.173 0.254 0.330
0.288 0.205 0.123 0.052 0.050 0.135 0.189 0.274 0.280 0.197 0.119 0.050 0.047 0.102 0.171 0.265 0.279 0.200 0.120 0.051
1.04 1.42 1.88 2.96 3.04 2.54 1.98 1.33 1.12 1.43 1.93 2.55 3.38 2.67 1.89 1.20 1.26 1.96 2.73 3.75
2.80 2.39 1.92 1.34 1.04 1.24 1.55 2.20 2.36
1.81 3.53 1.06 1.16 1.49 1.88 2.56 2.39 1.67 1.29 1.05
1.19 1.56 2.09 3.13 3.14 2.62 2.07 1.41 1.20 1.52 2.06 2.68 3.58 2.75 2.06 1.35 1.44 2.17 2.91 3.73
3.06 2.54 2.04 1.44 1.10 1.32 1.62 2.30 2.41 1.88 1.42 1.14 1.24 1.58 2.00 2.70 2.47 1.78 1.37 1.13
%error 1 14.4 9.9 10.9 5.6 3.1 3.1 4.2 6.2 7.1 6.4 6.5 5.2 6.2 2.8 8.8 12.5 13.8 10.5 6.6 0.4
2 9.3 6.7 6.0 7.6 6.0 5.9 4.5 4.4 2.2 3.8 5.1 7.1 7.1 5.9 6.1 5.2 3.2 6.2 6.4 7.4
Note: Notations are same as used in Table 11.
Table V. Comparison of Experimental and Predicted Values for Binary Systems at 42 "C equilib compn in lisuid phase. mole &action ._
niolecules adsor bedlcavity exptl pred
run
1
2
1
BXH-13 BXH-14 BXH-16 BXH-16 BHO-13 BHO-14 BHO-15 BHO-16
0.063 0.148 0.236 0.308 0.050 0.120 0.190 0.271
0.271 0.193 0.120 0.050 0.275 0.224 0.120 0.050
1.22 1.80 2.32 2.69 1.10 1.40 1.90 2.49
2 2.01 1.44 1.14 0.98 2.25 1.78 1.34 1.06
1 1.39 2.01 2.52 2.92 1.20 1.50 2.01 2.58
%error 2
1
2
2.13 13.5 5.7 1.53 11.4 5.8 1.24 8.7 7.8 1.08 8.2 9.2 2.35 8.8 4.3 1.86 6.6 4.1 1.41 5.5 5.2 1.14 4.1 7.1
30 "C this difference between predicted and experimental value increases to approximately 14% for systems having
Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 33 Table VI. ComDarison of ExDerimental and Predicted Values for Ternary Systems a t 6 "C" molecules adsorbed/cavity
equilib compn in liquid phase, mole fraction
exptl
% error
pred
run
1
2
3
1
2
3
1
2
3
1
2
PXH-1 PXH-2 PXH-3 PXH-4 PXO-1 PXO-2 PXO-3 PXO-4 PHO-1 PHO-2 PHO-3 PHO-4
0.235 0.082 0.053 0.134 0.207 0.082 0.052 0.1 24 0.223 0.082 0.017 0.055
0.047 0.174 0.139 0.087 0.046 0.149 0.132 0.088 0.056 0.086 0.162 0.130
0.083 0.089 0.165 0.141 0.045 0.045 0.086 0.088 0.050 0.086 0.045 0.075
3.29 1.45 1.20 1.99 3.49 1.67 1.35 2.11 3.60 1.66 1.32 1.35
1.26 2.46 2.02 1.61 1.27 2.50 2.26 1.64 1.16 1.44 2.17 1.83
1.29 1.30 1.72 1.60 1.15 1.14 1.47 1.44 1.19 1.62 1.23 1.51
3.68 1.66 1.32 2.27 3.62 1.76 1.44 2.22 3.75 1.80 1.45 1.46
1.32 2.60 2.15 1.66 1.37 2.59 2.31 1.74 1.23 1.53 2.31 1.91
1.31 1.33 1.76 1.61 1.24 1.25 1.54 1.50 1.25 1.70 1.32 1.57
11.9 14.1 9.9 14.0 3.7 5.6 7.0 5.1 4.2 8.5 9.7 8.3
4.6 5.5 6.7 3.0 8.5 3.4 2.3 6.0 5.7 5.9 6.5 4.2
3 1.6 2.3 2.4 1.0 7.6 9.6 5.0 4.1 5.2 4.5 7.7 3.7
a Note: 1 is the lightest hydrocarbon in a given ternary system and 3 is the heaviest hydrocarbon. PXH = Pentanehexane-Heptane; PXO = Pentane-hexane-Octane; PHO = Pentane-Heptane-Octane.
Table VII. Comparison of Experimental and Predicted Values for Ternary Systems at 1 8 'CU molecules adsorbed/cavity
equilib compn in liquid phase, mole fraction run PXH-5 PXH-6 PXH-7 PXH-8 PXO-5 PXO-6 PXO-7 PXO-8 PHO-5 PHO-6 PHO-7 PHO-8 Note:
exptl
pred
% error
1
2
3
1
2
3
1
2
3
1
2
3
0.114 0.119 0.216 0.129 0.045 0.221 0.114 0.056 0.101 0.216 0.063 0.166
0.051 0.123 0.121 0.168 0.04 8 0.073 0.144 0.153 0.042 0.044 0.103 0.099
0.165 0.108 0.028 0.029 0.170 0.023 0.040 0.089 0.143 0.025 0.092 0.03 6
1.66 1.62 1.74 1.85 1.22 3.15 1.80 1.21 1.70 3.42 1.33 2.47
1.17 1.60 1.54 2.04 1.23 1.31 2.04 2.07 1.09 1.11 1.58 1.46
1.86 1.37 0.99 0.98 1.96 1.03 1.07 1.29 1.73 1.01 1.38 1.06
1.80 1.79 2.85 1.96 1.33 3.29 1.89 1.34 1.86 3.60 1.51 2.62
1.27 1.72 1.63 2.17 1.34 1.41 2.09 2.19 1.21 1.21 1.67 1.54
1.90 1.46 1.09 1.11 2.10 1.08 1.15 1.36 1.83 1.10 1.50 1.15
8.4 10.3 3.9 5.8 9.1 4.3 4.9 10.2 9.3 5.2 13.4 6.2
8.3 7.0 5.8 6.2 8.7 7.2 2.2 5.8 10.5 8.6 5.6 5.0
2.1 6.2 10.4 12.1 7.0 4.7 7.4 5.4 5.6 8.3 8.7 8.0
Notations are same as used in Table VI.
Table VIII. Comparison of Experimental and Predicted Values for Ternary Systelils at 30 O c a molecules adsorbed/cavity
equilib compn in liquid phase, mole fraction run
1
PXH-9 PXH- 10 PXH-11 PXH- 1 2 PXH-13 PXH-14 PXH-15 PXH-16 PXO-9 PXO-10 PXO-11 PXO-12 PHO-9 PHO-10 PHO-11 PHO-12
" Note:
0.077 0.259 0.184 0.170 0.072 0.123 0.142 0.150 0.071 0.165 0.254 0.168 0.070 0.160 0.168 0.270
2 0.221 0.055 0.135 0.056 0.144 0.037 0.111 0.138 0.216 0.113 0.041 0.044 0.043 0.101 0.046 0.039
3 0.044 0.042 0.046 0.103 0.115 0.181 0.083 0.103 0.050 0.045 0.049 0.099 0.185 0.055 0.114 0.0 54
exptl
1 1.04 2.28 1.54 1.67 1.09 1.43 1.44 1.38 1.06 1.62 2.59 1.90 1.30 1.91 2.01 2.84
2 2.54 1.32 1.90 1.30 1.96 1.16 1.78 1.86 2.62 1.96 1.30 1.36 1.16 1.56 1.18 1.08
% error
pred 3 1.04 1.12
1.08 1.42 1.30 1.80 1.24 1.23 0.99 0.97 1.02 1.25 1.87 1.09 1.30 1.05
1 1.23 2.49 1.72 1.85 1.25 1.57 1.58 1.52 1.24 1.79 2.71 2.11 1.49 2.08 2.20 3.02
2 2.67 1.46 2.04 1.45 2.09 1.26 1.88 1.93 2.74 2.06 1.38 1.44 1.24 1.65 1.26 1.20
3 1.11 1.17 1.14 1.47 1.38 1.93 1.30 1.31 1.08 1.08 1.11 1.28 1.92 1.15 1.38 1.13
1
18.5 9.1 11.8
10.8 14.9 9.7 9.8 9.7 16.8 10.1 4.8 10.9 15.0 8.7 9.3 6.2
2 5.2 10.6 7.4 11.3 6.4 8.5 5.6 7.3 4.4 5.0 6.2 6.1 7.2 5.7 6.8 11.4
3 6.4 4.8 5.7 3.6 5.9 7.1 4.4 6.0 8.3 11.0 8.2 2.3 2.6 5.4 6.1 7.8
Notations are same as used in Table VI.
pentane as one of the components. This larger error for pentane at 30 O C may be due to the different nature of the adsorbed pentane molecules at this temperature, which is close to its boiling point. Adsorption of Ternary Systems. Equations 5 along with constraints 6 and 7 with similar expressions for CB and Cc are used to predict values of CA,CB,and Cc for all the ternary systems studied, using appropriate values of
a and 6 obtained for the pure components. Tables VI-VIII
give the results of all the ternary system studied at 6, 18, and 30 "C, respectively. Since pentane was present as one of the components in all these systems, temperatures higher than 30 OC were not studied. It has been observed that for about 85% of a total of 120 predictions made, errors are less than 10%. At 6 O C , maximum error is 14% and there are only two more predictions for which errors
Ind. Eng. Chem. Fundam. 1981, 20, 34-41
34
are greater than 10%. At 30 "C, errors increase up to 18.5%, and 25% of the predicted values are 10% higher than the experimentally observed values. This does not imply that the model is invalid for ternary systems. Many predicted values are probably higher because all of the ternary systems studied had pentane as one of the components; hence errors are greater at 30 " C . From the comparison between predicted and experimental values for binary and ternary systems, it seems that the maximum discrepancy occurs at 30 "C for systems having pentane as one component. The proposed model for liquid phase adsorption predicts the amount adsorbed with reasonable accuracy. In this model the sorbate-sorbate attraction term has been neglected, which might be appreciable near the boiling point of a component, and any modification to the theory should also take this into account. Nomenclature C = average number of molecules adsorbed per cavity Ccal = average number of molecuies adsorbed per cavity (calculated) Cexpt= average number of molecules adsorbed per cavity (experimental) E = sum of square of errors in eq 8 Emin= minimum value of E m = maximum number of molecules adsorbed in a cavity n = number of data points in an adsorption isotherm P = vapor pressure at adsorption temperature T = absolute temperature, K V = volume of the cavity (= 776 A' for LMS-5A) X = mole fraction in liquid phase
Greek Letters a = Henry's constant, (molecules)/(cavity)(torr) 0 = molecular volume, A3
Subscripts A = component A B = component B
C = component C Literature Cited Arnold, J. R. J. Am. Chem. SOC.1040, 77, 104. Barrer, R. M.; Davies, J. A. Roc. R. SOC.London, Ser. A 1070, 320, 289. Barrer, R. M., Lee, J. A. Surf. Sci. 1066, 72, 354. Breck, D. W.; Eversole, W. G.; Milton, R. M.; Reed, T. B.; Thomas, T. L. J. Am. Chem. Soc. 1056, 78, 5963. Cook, W. H.; Basmadjian, D. Can. J. Chem. Eng. 1065, 43. 78. Grant, R. J.; Manes, M. Ind. Eng. Chem. Fundam. 1064, 3, 221. Gupta, R . K.; Kunzru, D.; Saraf, D. N. J. Chem. Eng. Data 1060, 25, 14. Kdnay, A. J., Myers, A. L. AICM J. 1066, 72, 981. Lewis, W. K.; Gllliland, E. R.: Chertow. 6.: Cadwen, W. P. Ind. Ena. Chem. 1050, 42, 1319. Malson, F. D.; ARman, M.; Alberth, E. R. J. Phys. Chem. 1053, 57, 106. Myers, A. L.; Prausnltz, J. M. AICM J. 1065. 7 7 , 121. Ruthven, D. M. Nature(Phys. Scl.) 1071, 232, 70. Ruthven, D. M.; Loughlin, K. F. Trans. Faraday Soc. 1072, 68, 696. Ruthven, D. M.; Loughiin, K. F.; Derrah, R. I. Adv. Chem. Ser. 1073a, No. 127, 330. Ruthven, D. M.; Loughlin, K. F.; Holborow, K. A. Chem. Eng. Sci. 1073b, 28 701. Ruthven, D. M. AIChE J. 1076. 22, 753. Satterfield, C. N.; Cheng, C. S. AIChE J. 1072, 78, 720. Satterfield, C. N.; Smeets, J. K. AIChE J. 1074, 20, 818. Schirmer, W.; Fiedrich, G.; Grossman, A.; Stach, H. "Proceedings, First Conference on Molecular Slew Zeolltes", London, 1967. Sircar, S.; Myers, A. L. Chem. Eng. Sci. 1073, 28, 489. Sundstrom. D. W.; Krautz, F. G. J. Chem. Eng. Data 1068, 73,223.
Received for review August 14, 1979 Accepted August 12, 1980
Self-Poisoning in Single Catalyst Pellets Duong D. Do' and Ralph H. Welland' Department of Chemical Engineering, University of Queensiand, St. Lucia, Queenshnd, 4067 Australia
A combination of generalized two-timing with a novel application of finite Sturm-Liowille integral transforms is used to give a theoretical description of series and parallel self-poisoning in slab, cylindrical, and spherical catalyst pellets for first-order kinetics. The entire catalyst pellet is assumed available for reaction but with pore diffusion and external mass transfer resistance playing significant roles. Simple infinite series solutions for reactant concentration, activity, and intra-phase effectiveness factor, valid over the entire life of the catalyst, are obtained. Comparison with known numerical solutions shows excellent agreement over a wMe range of Thiele modulus.
Introduction Single catalyst particles with deactivation have been the subject of several studies in the past 15 years. The model equations were first solved numerically by Masamune and Smith (1966) for spherical particles with first-order chemical kinetics and first-order parallel and series deactivation mechanisms in the absence of external mass transfer resistance. They also obtained approximate shell-model solutions for particles with very large Thiele modulus. The shell model was reasonably accurate for parallel deactivation, but for the case of series deactivation
* Department of Chemical Engineering, Clarkson College of Technology, Potsdam, NY 13676. 'Department of Chemical Engineering,California Institute of Technology, Pasadena, CA 91125. 0196-4313/81/1020-0034$01,00/0
it deviated markedly from the exact numerical solution. This failure resulted from the fact that in the series case the poison (or product) concentration is never particularly high in any one region of the particle as it is for parallel deactivation. Later, Chu (1968) extended the work of Masamune and Smith to Langmuir-Hinshelwood kinetics. Nothing exceptional was found although one might expect that multiple solutions could exist for this type of kinetics, even under strictly isothermal conditions. The lack of multiplicity may be due to the assumption of small Thiele modulus. Chu found that the effectiveness factor was exponentially dependent on nondimensional time (scaled on the deactivation rate constant). Do and Weiland (1980a) have shown that such a result is only valid for small Thiele modulus. Khang and Levenspiel (1973) also repeated the work of Masamune and Smith (1966) for spherical catalyst pellets with first-order chemical kinetics 0 1981 American Chemical Society
