396
I n d . Eng. Chem. Res. 1991,30, 396-402
Estimation of the Adsorbent Capacities from the Adsorption Isotherm of Binary Liquid Mixtures on Solids Emmanuel A. Dada and Leonard A. Wenzel* Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Methods available in the literature t o estimate the adsorbent capacity from the adsorption isotherm of binary liquid mixtures generally assume that the adsorptives are identical, that the adsorbed phase is monolayer, and t h a t the separation factor (or selectivity) of the system is constant. These assumptions limit the application and reliability of these methods. Based on the concept of the average molecular thickness of the adsorbed-phase layer, an a1ternative method is proposed that addresses the shortcomings of the existing methods. The substitution ratio, r12,which represents the molecular size differences in the adsorptives, is calculated within *5% of the experimental values, for the systems tested. The characteristics of the adsorbent selectivities are successfully modeled after some hyperbolic functions. Compared with the experimental results, the proposed method gives a reliable estimate of the adsorbent capacities.
Introduction One of the most important variables required in the design of adsorption processes for the separation and purification of liquid mixtures is the capacity of the adsorbent for a given component. As shown in the work of Price and Danner (1988), reliable estimates of the capacities of the adsorbents are essential for the prediction of multicomponent liquid adsorption equilibria from the adsorption isotherms of the constituent binaries. The capacity of the adsorbent (otherwise called surface-phase capacity) can be determined experimentally by measuring the amount of the vapor of the liquid component adsorbed at saturation by the adsorbent. On the other hand, the capacity of the adsorbent cannot be measured directly from the adsorption of binary liquid mixtures onto solids except for zeolitic adsorbents where one component can be adsorbed almost exclusively in the presence of the other component due to the “molecular sieve” action of the zeolite. Consequently, methods have been devised in the literature to calculate the surface-phase capacity of the adsorbent from the adsorption isotherm of a completely miscible binary liquid mixture onto a solid. These methods have been critically reviewed by Dabrowski et al. (1987). The basic underlying assumptions of most of these methods are that the components have identical molecular sizes and that the adsorbed phase is monolayer. However, industrial separation processes usually involve liquid mixtures consisting of molecules of widely different sizes, and for many systems, the monolayer concept may not meet the thermodynamic stability requirement of the adsorption system. These methods, therefore, do not give reliable estimates of the capacities of the adsorbents except for a few cases where the stringent assumptions are satisfied. In effect, these methods may be used where appropriate, to estimate the specific surface area, As, of the adsorbent which is closely related to the monolayer capacity of the adsorbent. Of particular interest is the popular Schay and Nagy, SN, graphical method which is based on the concept that the surface excess isotherms of some adsorption systems have a fairly long linear section (Schay, 1969). As claimed by the authors, extrapolated intercepts of such sections may be used, where appropriate, to estimate the monolayer capacity of the adsorbents. This method has been widely criticized in the literature as being thermodynamically inconsistent with the stability of the system (Dabrowski et al., 1987). Schay and Nagy (1972) also gave a critical discussion on the use of their method. 0888-5885/91/2630-0396$02.50/0
The methods based on expressing the adsorption isotherm equation in a linear form were proposed by Schiessler and Rowe, by Siskova and Erdos, and by Everett (Dabrowski et al., 1987). These methods assumed that the molecules are similar, that the adsorbed phase is monolayer, and that the separation factor, a12,of the adsorbent is constant. The methods are not applicable to the adsorption isotherms that have azeotropic points. Results from these methods have shown that there is not particular advantage of using any one of these methods over the other methods to calculate the capacity of an adsorbent. However, the most commonly used of these three methods is that of Everett. The Everett method has been generalized by Schay and Nagy (1972) by taking into account the molecular differences of the binary components. If component 1 is the preferentially adsorbed component, the generalized Everett, GE, method can be written as (Dabrowski et al., 1987)
where and (3) Equation 1 reduces to Everett’s equation when r12= 1. The constancy of the separation factor, a12,is based on the assumption that the bulk liquid and the adsorbed phases are ideal. Equation 1 also gives a linear absorption isotherm for many adsorption systems due to some compensatory factors that obscure the variation of the separation factor, a12(Everett, 1982; Schay and Nagy, 1972). Like the grahical method of Schay and Nagy (SN), the Everett (E), generalized Everett (GE), Siskova-Erdos (SE), and Schiessler-Rowe (SR) methods can only be used to estimate the capacity of the adsorbent when the surface coverage of the adsorbent is not far from being monolayer. Dabrowski and Jaroniec (Dabrowski et al., 1987) have proposed that the linear form of the Langmuir-Freundlich (LF) and Dubinin-Radushkevich (DR) equations generally used for describing the adsorption of nonideal bulk liquid solutions onto heterogeneous adsorbents can be applied to calculate the capacity of the adsorbent. For the ad0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 397 Table I. Essential Information about the Adsomtion Svstems Studied system code 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
binary liquid mixture component 1 component 2 carbon tetrachloride l,l,l-trichloroethane' tert-butyl chloride l,l,l-trichloroethane benzene ethylene dichloride benzene methyl acetate benzene ethanol n-butylamine benzene benzene methyl acetate benzene ethylene dichloride benzene methyl acetate benzene ethylene dichloride benzene chloroform ethylene dichloride methyl acetate benzene ethanol benzene ethanol benzene ethylene dichloride benzene 1-butanol cyclohexane benzene cyclohexane benzene ethyl acetate benzene cyclohexane ethyl acetate benzene 1,2-dichloroethane n-heptane 1,2-dichloroethane cyclohexane benzene n-heptane benzene ethanol benzene ethanol n-heptane 1,2-dichloroethane benzene cyclohexane benzene benzene dioxane cyclohexane dioxane cyclohexane benzene benzene ethanol cyclohexane benzene benzene ethanol
adsorbent charcoal charcoal charcoal charcoal charcoal charcoal silica gel titania gel boehmite boehmite boehmite boehmite boehmite y-alumina y-alumina gibbsite spheron act. carbon act. carbon act. carbon silica gel silica gel silica gel silica gel graphon graphon graphon silica gel silica gel silica gel Cab-0-Si1 Cab-0-Si1 Hi-Si1 Hi-Si1
type of isotherm IV I1 IV
IV IV I1 I1 I1 I1 I I
I1 I11 I11 I I1 I1 I1 I1 IV I1 I1 I1 I1 I I IV I1 I1 I1 I1 I1 I I1
ref" to system 1 1 1 1 1 1
2 2 3 3 3 3 3 3 3 3 1 4 4 4 5, 6 6, 7 5, 6 5, 6 8 8 9 10 10
10 11 11 11 11
system temp, "C 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 30 30 30 30 30 30 30 25 25 25 30 30 30 30 30 30 30
reP to activity coeff 1 1 1 1
12 1 1 1 1 1 12 12 12 1 12 12 4 4 4 12 12 4 12 12 12 12 4 12 12 4 12 4 12
References: (1) Blackburn et al., 1957; (2) Kipling and Peakall, 1957; (3) Kipling and Peakall, 1956; (4) Minka and Myers, 1973; (5) Sircar and Meyers, 1970; (6) Sircar and Myers, 1986; (7) Sircar, 1970; (8) Brown et al., 1975; (9) Everett and Podoll, 1980; (10) Suri and Ramakrishna, 1969; (11) Matayo and Wightman, 1973; (12) DECHEMA, 1980 and 1982.
sorption of binary liquid solutions, the DR equation is given as (-In
X!,t)'/'
= Ak
+ Ck In
(4)
= Ak
+ Ck In (2112
(5)
and the LF equation is
hl
(X!,,t/x$,$
where x!,t
= (n!,t/n9)
+ x:
(6)
and
(7) Equations 4 and 5 are based on the assumptions that the adsorbed phase is ideal and that the molecules are identical. Dabrowski and Jaroniec further suggested that the value of n: that gives the minimum standard deviation of the experimental points from the straight lines of eqs 4 and 5, respectively, is the surface-phase capacity of the adsorbent. As evidenced in Table 11, the values of the surface-phase capacities calculated from the DR eq 4 are markedly different from those values obtained from the LF eq 5 for the same adsorption systems. These methods did not give good estimates of the experimental capacities of the adsorbents. Thus the existing methods in the literature used to calculate the capacity of the adsorbent from the adsorption isotherm of completely miscible binary liquid mixtures are
inadequate due to the underlying assumptions they were based on: molecules are identical, the adsorbed phase is monolayer, and the separation factor, a12,is constant. The objective of this present work is to develop an alternative method that will address the shortcomings of the existing methods.
Theoretical Development In this work, we shall be concerned with only binary liquid mixtures of components 1 and 2. The experimentally determined variable for an adsorption system is the surface excess ni defined as n! = nyxp - x\) (8) The total material balance of the adsorbed and the bulk liquid phases gives no = ns n1
+
If we combined the material balance for component 1in the adsorbed and bulk liquid phases with the result of eq 9, eq 7 can be rewritten in terms of the adsorbed-phase properties as ny = nyx; - xi) (10) In general, an adsorbent may be porous or nonporous. For macroporous and nonporous adsorbents, the condition that the surface is completely covered gives, approximately (Everett, 1973) n ! ~ l+ n& = As (11) The capacity of the adsorbent will depend on the orien-
398 Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 Table 11. Estimated Adsorbent Capacities of Some of the Adsorption Systems Given in Table I" system codeb 1 2 3 4 0
6 i 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
experimental r,2 ml 0.98 1.09 1.15 1.17 1.57 1.00 1.00 0.96 1.12 1.08 1.12 1.08 1.44 1.67 1.05 1.27 1.13 1.27 1.11 1.51 1.01 1.66 1.28 1.64
2.88 2.88 3.91 3.98 5.34 3.39 3.21 0.88 1.53 1.48 1.53 1.53 1.40 0.95 0.81 1.49 0.45 5.48 5.48 4.95 3.96 3.96 3.91 3.91
this work r12 ml 0.97 1.10 1.17 1.12 1.53 0.90 1.12 1.1i 1.10 1.14 1.10 0.97 1.44 1.44 1.14 0.98 1.17 1.21 1.10 1.11 1.13 1.85 1.21 1.65
2.69 2.34 4.41 3.14 6.65 2.48 2.80 1.15 1.57 1.36 1.75 1.35 1.33 0.81 0.88 1.62 0.46 5.54 5.40 4.74 3.80 4.11 3.60 3.91
mle
mlc
LF
DR
I/F
12.82 3.64 2.32
1.48 17.49 2.03 4.73 3.55 2.42
I/F I/ F
I/F I/F
I/F
1.34
I/F I/F
1.35 0.79
1.33 0.76
I/F I/F
I/F
9.32 17.43
1.78
0.57 2.73 2.61 2.28
I/F
4.96
I/F
5.28
2.61
1.34 1.15 4.33 6.66 2.67
I/F
5.08 5.90 6.79
mld
E
GE
SR
SE
0.52 1.67 1.19 1.47 4.29 1.59 3.45 0.67 1.19 0.98 1.25 1.32 1.34 0.79 0.50 1.01 0.35 2.04 1.48 1.48 0.27 3.56 3.49 2.83
0.00 2.31 -0.20 4.20 -0.32 1.57 3.31 2.67 1.43 1.63 2.13 1.53 0.38 0.21 1.73 0.91 0.42 2.16 1.61 0.00 0.59 3.84 3.01 3.21
0.00 2.25 -0.24 5.41 -0.45 1.57 3.26 1.98 1.48 1.52 2.02 1.54 0.40 0.22 1.40 0.91 0.41 2.14 1.60 0.00 0.58 3.75 2.96 3.08
0.00 2.51 0.11 -0.33 0.17 1.56 2.61 2.21 1.37 1.73 2.62 1.36 0.57 0.33 2.95 0.87 0.36 1.96 1.62 0.01 0.88 3.69 2.73 2.90
0.01 2.38 -0.73 -1.50 -3.76 1.55 2.73 2.66 1.39 1.67 2.21 1.40 0.66 0.39 1.81 0.87 0.38 2.04 1.64 0.01 0.89 3.75 2.81 3.07
DR, Dubinin-Radushkevich; E, Everett; GE, generalized Everett; LF, Langmuir-Freundlich; SE, Siskova-Erdos; SR, Schiessler-Rowe; I/F, iterations failed to give minimum standard deviation. "rI2experimental" is from eq 2; "rI2this work" is from eq 15 or eq 21. m, in units of mmol/g. bThe same system code as used in Table I. 'From the method of Dabrowski and Jaroniec. dFrom the method of Schay and Nagy. e From methods based on the linearized adsorption isotherm. (I
tation, packing density, and nature of the molecules in the adsorbed phase as well as the thickness of the adsorbedphase layer. The real thickness of the adsorbed-phase layer is not precisely defined. Rusanov (1971) has suggested that it is only possible to consider the effective thickness of the adsorbed-phase layer. This value represents the zone where there is significant change in the local concentration profile. However, effective thickness cannot be determined easily from the adsorption isotherm of liquid mixtures. What can be estimated realistically from the adsorption isotherm is the average thickness t of the adsorbed-phase layer. For example, it is widely accepted that, in the adsorption of a binary liquid mixture of benzene and ethanol, ethanol molecules are oriented perpendicularly to the surface of the adsorbent (Day and Parfitt, 1967) and the benzene molecules are oriented in parallel to the surface of the adsorbent (Kipling, 1965). Therefore, a certain number of molecular layers of the ethanol molecules will not be accompanied by the same number of molecular layers of the benzene molecules in the adsorbed phase. However, the effective surface areas occupied by the single molecules of benzene and ethanol are not significantly affected by the number of the molecular layers in the adsorbed phase (Schay, 1969). It will therefore be appropriate to assign a realistic molecular surface area for the molecules that will be thermodynamically consistent with the experimental results. This will then enable a realistic average thickness, t , of the adsorbed-phase layer to be evaluated. A realistic molecular surface area, a?,can be obtained from the empirical correlation of McClellan and Harnsberger (1967) as - 6.16 X 6.02 a? = (12) 0.596 where at = 10-7 x 1.091 ( u j ) 2 / 3 ~ , 1 / 3 (13) Adopting the concept of average thickness, t , for the ad-
Table 111. Some Physical Properties of the Adsorptives at 25 "C comDonent. i uf. cm3/mol a?, mZ/mmol 246.1 benzene 89.07 281.8 105.02 bromobenzene 263.0 96.50 carbon tetrachloride 274.7 101.77 chlorobenzene 225.2 80.17 chloroform 288.4 108.04' cyclohexane 237.3 85.92 dioxane 170.4O 58.39 ethanol 265.9 97.79 ethyl acetate 215.9 76.33 ethylene dichloride 120.1 40.51 methanol 223.1 79.32 methyl acetate 251.7 91.51 1-butanol 268.5 98.97 n-butylamine 367.3 146.50 n-heptane 336.0 130.77 n-hexane 292.5 109.94 tert-butyl chloride 222.8 79.17 1,2-dichloroethane 270.0 99.63 1,1,1-trichloroethane For the adsorption of ethanol on nonporous adsorbent, generally use a: = 120 m2/mmol.
sorbed-phase layer, the capacity of the adsorbent, mi, for component i can reasonably be given as
Representative values of af and u: are given in Table 111. Therefore, r12defined by eq 2 can be estimated from the physical properties of the molecules using eq 14 as r I 2 = u$/aB
As representatively shown in Table 11, r12values calculated from eq 15 are within *5% of the experimental values of r12calculated from eq 2. This error is within the experimental uncertainty usually associated with surface excess data. From eqs 11 and 14 we have
Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 399
-xs+ - =x!!mi
m2
1 ns
where xS, = n;/n8
(17)
For microporous adsorbents where adsorption is by a pore-filling mechanism (Bering et al., 1966; Dabrowski et al., 1987), the equivalent of eq 11, which is more exact for microporous adsorbents, is
nyu, + n;u2 = Vs
(18)
Similarly, adopting the concept of average thickness, t , for the adsorbed-phase layer we have
Table IV. Equations Describing the Adsorbent Selectivities tvDe of isotherm S, a, I p(cosh Z - tanh Z), q = 0 I1 p(tanh Z) I11 Z(sinh 2 - tanh 2) sinh Z + sinh-’ x i IV
OSl2= f ( Z ) ,where Z = p ( i ) + q.
adsorbed component over component 2 by the adsorbent before attaining the azeotropic composition, then S12 will have the following general properties: for U-shaped isotherms (type I, 11, 111) O < x ’ , < l , O
