Ind. Eng. Chem. Res. 1996, 35, 199-206
199
Adsorption Equilibria of Dimethylnaphthalene Isomers Renato Rota and Massimo Morbidelli* Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, via Mancinelli 7, 20131 Milano, Italy
Elisabetta Rombi, Roberto Monaci, Italo Ferino, and Vincenzo Solinas Dipartimento di Scienze Chimiche, Universita` di Cagliari, via Ospedale 72, 09124 Cagliari, Italy
Adsorption processes for separating mixtures of dimethylnaphthalene (DMN) isomers are of potential interest for the production of 2,6-DMN. In this work, the adsorption equilibria of liquid mixtures of DMN isomers on zeolites have been investigated experimentally. The separation factors between the various isomers have been found to depend strongly on the composition of the fluid phase. A suitable equilibrium model, based on the adsorbed solution theory, has been developed to describe the multicomponent adsorption equilibria in the entire range of interest. Its performance has been tested using binary and ternary equilibrium data. 1. Introduction Commercial sources of DMNs are the aromatic petroleum fraction of the appropriate boiling range and the coal liquefaction products. The main problem in recovering pure 2,6-DMN from such fractions is its separation from its isomers (Iwai et al., 1994). For this, selective adsorption is probably the most promising technique, particularly with respect to the separation of 2,6-DMN from 2,7-DMN and 1,5-DMN, which are the isomers most similar to 2,6-DMN in terms of physicochemical properties (Verduijin et al., 1989; Barder, 1989; Ootake et al., 1989). Other separation processes, such as extraction with suitable complexing agents or selective crystallization, are not effective in the separation between 2,6-DMN and 2,7-DMN. One of the key aspects in developing an adsorption separation process is the determination of the adsorption equilibria of the compounds to be separated (cf. Paludetto et al., 1987). In general, both mono- and multicomponent equilibria have to be studied. The aim is 2-fold: first, to identify a suitable couple adsorbent/ desorbent able to achieve the desired separation and, then, to develop multicomponent equilibrium models. The aim of this work is to analyze the adsorption equilibrium behavior of the mixture constituted by three isomers of dimethylnaphthalene, namely, 1,5-DMN, 2,6DMN, and 2,7-DMN, at ambient temperature and pressure. As these compounds are solid at ambient conditions, they have been dissolved in a solvent before contacting them with the adsorbent. 2. Experiments First, some preliminary experiments have been performed to identify the most suitable adsorbent for the desired separation. Several X and Y zeolites exchanged with different cations have been considered. Next, using the best adsorbent, several experimental runs have been carried out to fully characterize the monoand multicomponent adsorption equilibria. 2.1. Materials and Methods. The equilibrium behavior of 2,6-DMN, 2,7-DMN, and 1,5-DMN, both alone and mixed with each other, has been investigated through batch experiments. The solid (at ambient conditions) DMNs have been dissolved in n-octane. * FAX: (+)39 2 23993180. E-mail: MORBIDELLI@IPMCH2. POLIMI.IT.
0888-5885/96/2635-0199$12.00/0
Single-component (that is, one DMN dissolved in n-octane), binary, and ternary mixtures of known amount and composition have been prepared and contacted with a known amount of freshly regenerated adsorbent. Regeneration has been performed by calcination at 500 °C for 5 h. All the chemicals were commercial reagent grade. Equilibrium conditions, evidenced by the invariance of the liquid-phase composition, have been reached after about 5 h. However, all the runs have been carried out under stirring conditions for about 24 h at 25 °C and 1 atm. The composition of the liquid mixture has been measured by gas chromatography with a relative error equal of about 5%. Commercial powders of X and Y zeolites (i.e., Na13X with Si/Al ) 1.4 and LZY-52 with Si/Al ) 2.4 from Union Carbide), suitably exchanged with different cations as summarized in Table 1, have been used in all the experiments. The cation exchange has been carried out by treating 10 g of the commercial zeolite with 150 cm3 of a boiling aqueous solution of alkaline chloride (1 mol/ L) for 2 h. This procedure has been repeated five times before washing the sample. Finally, the zeolite has been dried at 100 °C for 3 h and calcinated at 500 °C for 12 h. 2.2. Screening of the Adsorbents. About 1.5 g of each of the adsorbents investigated have been contacted with equimolar (4 wt % of each isomer) binary mixtures of DMNs dissolved in n-octane. The final total concentration of DMNs in n-octane was equal to about 0.2 mol/ L. Higher concentrations cannot be achieved due to the low solubility of DMNs. The results of such experiments are summarized in Figure 1 in terms of separation factor values, Rij, defined as:
Rij )
θi/zi θj/zj
(1)
where zi is the solvent-free mole fraction in the liquid phase:
zi )
xi
Nc xi ∑i)1
)
xi xi ) xtot 1 - xs
(2)
Nc while θi ) Γi/∑i)1 Γi are the solvent-free mole fractions in the adsorbed phase. It is evident from Figure 1 that the Y zeolites perform generally better than the X zeolites, whose values of the separation factor range from 1 to 2. Among the Y zeolites, that exchanged with potassium shows values
© 1996 American Chemical Society
200
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996
Figure 1. Separation factor values for equimolar binary solutions on DMN on various zeolites (see Table 1): (A) 2,6-DMN/1,5-DMN; (B) 2,7-DMN/2,6-DMN; (C) 2,7-DMN/1,5-DMN. Table 1. Chemical Composition and Ionic Radius (Å) for the Various Zeolites Considered sample
chemical composition
ionic radius
LiNaX NaX KNaX RbNaX CsNaX LiNaY NaY KNaY RbNaY CsNaY
Li60Na20(AlO2)80(SiO2)112 Na80(AlO2)80(SiO2)112 K51Na29(AlO2)80(SiO2)112 Rb29Na51(AlO2)80(SiO2)112 Cs24Na56(AlO2)80(SiO2)112 Li31Na24(AlO2)55(SiO2)137 Na55(AlO2)55(SiO2)137 K47Na8(AlO2)55(SiO2)137 Rb23Na32(AlO2)55(SiO2)137 Cs18Na37(AlO2)55(SiO2)137
0.59 0.99 1.37 1.51 1.67 0.59 0.99 1.37 1.51 1.67
Figure 2. Total adsorbed amounts as a function of the cation radius: (A) X zeolite; (B) Y zeolite; (O) 2,6-DMN/1,5-DMN; (4) 2,7DMN/2,6-DMN; (0) 2,7-DMN/1,5-DMN.
of the separation factor for all binary mixtures at least double the others and increasing in the series R2,6-DMN/1,5DMN < R2,7-DMN/2,6-DMN < R2,7-DMN/1,5-DMN. Thus, all the following experiments have been carried out using Y zeolites exchanged with potassium. Some insights in the behavior of this system can be gained by considering the dipolar moments of the three isomers. These can be computed by optimizing the molecular geometry by AM1 parametrization (Rajzman and Francois, 1969) and determining the electronic charge via the CNDO/2 method (Stewart, 1974) as follows: µ1,5-DMN ) 6.1 × 10-4D, µ2,6-DMN ) 7.6 × 10-3D, µ2,7-DMN ) 2.9 × 10-2D. It appears that the difference between the dipolar moments of the two isomers increases in the same order as the separation factor values reported above. Figure 2 shows the total adsorbed amounts for the three binary mixtures of DMNs as functions of the
volume (i.e., r3) of the cations in the zeolite structure. Apart from the larger values found for the Y zeolites with respect to X zeolites, both of them show a similar trend; that is, the value of the total adsorbed amount decreases when increasing the volume of the cations. The only exception is the KNaX sample, whose adsorbed amount is much lower than the others. This could be due to the steric hindrance of the large K+ cations located in the supercages. Rb and Cs do not show this anomaly as their exchange has been definitely lower than that of K (see Table 1). 2.3. Single-Component and Multicomponent Equilibrium Data. Let us first consider the adsorption equilibria of single DMNs. Several experiments have been performed by contacting the adsorbent with solutions of DMN in n-octane at various concentrations. The data reported in Table 2 indicate that the amount of DMN adsorbed first increases with the concentration in the liquid phase and then reaches a maximum value where it remains constant. Several experiments have been performed with binary mixtures of DMNs in n-octane. The results are summarized in terms of the separation factor (eq 1) in Figure 3, while Figure 4 shows the experimental measurements
Table 2. Single-Component Equilibrium Data 1,5-DMN
2,6-DMN
2,7-DMN
C, mol/L
Γ, mg/g
C, mol/L
Γ, mg/g
C, mol/L
Γ, mg/g
3.800 × 10-3 6.500 × 10-3 1.010 × 10-2 1.010 × 10-2 1.510 × 10-2 2.170 × 10-2 3.180 × 10-2 3.380 × 10-2 3.730 × 10-2 7.070 × 10-2 7.160 × 10-2 1.006 × 10-1 1.245 × 10-1 1.815 × 10-1
7.060 × 101 8.930 × 101 1.141 × 102 8.700 × 101 1.234 × 102 8.995 × 101 1.328 × 102 1.345 × 102 1.511 × 102 1.623 × 102 1.646 × 102 1.700 × 102 1.740 × 102 1.709 × 102
1.010 × 10-2 1.010 × 10-2 1.340 × 10-2 1.410 × 10-2 3.190 × 10-2 4.410 × 10-2 4.750 × 10-2 8.210 × 10-2 1.013 × 10-1 1.176 × 10-1 1.557 × 10-1
7.370 × 101 7.720 × 101 9.306 × 101 9.480 × 101 1.132 × 102 1.314 × 102 1.631 × 102 1.432 × 102 1.644 × 102 1.612 × 102 1.518 × 102
7.000 × 10-4 1.500 × 10-3 6.000 × 10-3 9.500 × 10-3 9.700 × 10-3 4.090 × 10-2 8.530 × 10-2 9.450 × 10-2 1.296 × 10-1 1.414 × 10-1
1.043 × 102 1.195 × 102 1.327 × 102 1.381 × 102 1.330 × 102 1.477 × 102 1.409 × 102 1.474 × 102 1.499 × 102 1.450 × 102
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 201
Figure 3. Experimental (O) and computed values of the separation factors, Rij, as a function of the solvent free mole fraction in the liquid phase for three binary systems: (A) 2,6-DMN/1,5-DMN; (B) 2,7-DMN/2,6-DMN; (C) 2,7-DMN/1,5-DMN. Model parameters reported in Tables 4 and 5. (s) Nonideal model with Langmuir single-component isotherm; (- -) nonideal model with squared single-component isotherm; (‚‚‚) ideal multicomponent Langmuir model.
Figure 5. Values of the separation factors, Rij, for binary (4) and ternary (b) mixtures as a function of the solvent free mole fraction in the liquid phase. Table 3. Measured and Computed Values for Ternary Systems (1 ) 1,5-DMN, 2 ) 2,6-DMN) single-component isotherm Langmuir (eqs 19, 21, 24)
experimental
squared (eq 27)
ideal Langmuir (eq 28)
z1
z2
θ1
θ2
θ1
θ2
θ1
θ2
θ1
θ2
0.58 0.33 0.24 0.58
0.39 0.43 0.70 0.21
0.14 0.06 0.06 0.09
0.29 0.27 0.45 0.15
0.13 0.05 0.05 0.09
0.32 0.20 0.38 0.13
0.13 0.05 0.05 0.09
0.32 0.20 0.39 0.13
0.43 0.09 0.16 0.17
0.23 0.09 0.36 0.05
3. Equilibrium Model
Figure 4. Experimental (O) and computed values of the adsorbed mole fractions as a function of the solvent free mole fraction in the liquid phase for three binary systems: (A) 2,6-DMN/1,5-DMN; (B) 2,7-DMN/2,6-DMN; (C) 2,7-DMN/1,5-DMN. Model parameters reported in Tables 4 and 5. Legend as in Figure 3.
on x-θ diagrams. The most evident feature of these data is that the separation factor value strongly depends on the composition of the fluid phase. Variations larger than 1 order of magnitude have been found. Finally, a set of equilibrium data relative to ternary mixtures of DMNs has been obtained, as reported in Table 3 and Figure 5. It can be seen that the presence of the third DMN does not influence significantly the separation factor value between the other two. This is not obvious as the presence of a third compound can, in principle, either depress or enhance significantly the value of the separation factor between the other two compounds.
A detailed analysis of the thermodynamics of the adsorption equilibrium from liquid mixtures has been developed by Larionov and Myers (1971) for binary systems and by Minka and Myers (1973) for multicomponent mixtures. The treatment was developed in terms of surface excess, which reduces to the amount adsorbed in the case of strongly adsorbable solutes. Our aim is to first briefly review the general approach and then to introduce the modifications needed to analyze the specific system at hand. It should be noted that the model developed is similar to that presented by Radke and Prausnitz (1972) for the case of diluted liquid solutions. However, our method accounts also for the case of strongly adsorbable solutes, for which it is very difficult to investigate experimentally the low concentration region for each single solute with the accuracy required by the model of Radke and Prausnitz. 3.1. Adsorbed Solution Theory. The adsorbed solution theory (AST) involves the equalities between the fugacities in the fluid and adsorbed phase, the Gibbs adsorption isotherm, and the stoichiometric relation:
fiL ) fiA 1 RT
(3)
N
dφ ) dψ )
Γi d ln(fiA) ∑ i)1
(4)
N
θi ) 1 ∑ i)1
(5)
The classical approach (Larionov and Myers, 1971; Minka and Myers, 1973) defines the standard state as
202
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996
the pure adsorbate at the same temperature and free energy of immersion as that of the adsorbed solution. This leads to the following expression for the fugacity of the adsorbed phase:
fiA(T,ψ,θ) ) fi°A(T,ψ) γi°Aθi
(6)
The influence of the free energy of immersion on the fugacity of a pure compound is represented by the Gibbs adsorption isotherm:
dψ ) Γi° d ln(fi°A)
(7)
which can be integrated under the assumption of Γi° ≈ const from (T, ψ) to (T, ψi°). Thus, the phase equilibrium relation (3) can be cast in the form (note that the Poynting’s correction has been disregarded):
fi°L(T) γiLxi ) fi°A(T,ψi°) γi°Aθi exp
(
)
ψ - ψi° Γ i°
(8)
As ψi° represents the free energy of immersion of an adsorbed phase in equilibrium with the ith pure compound at the same temperature as the mixture, it follows that fi°L(T) ) fi°A(T,ψi°). Moreover, by selecting the first compound as the reference one and defining ∆ψ° ) ψ - ψ1° and ∆ψij° ) ψi° - ψj°, the relation above reduces to:
γiLxi ) γi°Aθi exp
(
)
∆ψ° - ∆ψi1° Γi°
∫xx)1)0(Γi d ln(γiLxi) + Γj d ln(γjLxj)) j
j
fiA(T,ψ,θ) ) fiqA(T,ψ) γiqAθi
(10)
The integral on the right-hand side can be evaluated numerically using appropriate equilibrium experimental data of the binary system at hand. Various other alternatives for computing this integral have been discussed by Minka and Myers (1973). Thus summarizing, the classical approach to the AST is represented by the 2N equations 5, 9, and 10 in the 2N unknowns θi, ∆ψi1° (i ) 2, ..., N), and ∆ψ°. It requires the knowledge of the adsorption loads of the pure compounds (Γi°), as well as of several binary equilibrium data, properly distributed over the entire composition range of the liquid phase, for each of the binary systems which can be formed among the involved N compounds. These last experimental data are required to evaluate both the free energy of immersion differences between the pure compounds, ∆ψij°, and to tune the parameters of the model needed to estimated the activity coefficients in the adsorbed phase, γi°A. 3.2. Strongly Adsorbable Solutes. The method discussed above cannot be applied directly to the system described in the previous section. This is because the three DMNs are solid at ambient conditions, and therefore the corresponding binary equilibrium data required by the AST cannot be measured. Thus, we used a different reference state for developing an appropriate model, based on the same foundations as the AST, which can be used for all the systems where such a difficulty arises. The basic idea is to approximate the behavior of the solvent as that of an inert compound; that is, do not develop adsorption equilibrium relations for the solvent. This can be done assuming that the amount of the
(11)
Nc Here θi ) Γi/∑i)1 Γi are the solvent-free mole fractions in the adsorbed phase. Note that, as the reference state is different, also the activity coefficients (γiqA) differ from those (γi°A) defined by eq 6. The relation between the two activity coefficients is discussed in Appendix A. The fugacity value at the standard state (fiqA) can be evaluated using the phase equilibrium relation:
fiqA(T,ψ) ) fiL(T,xq) ) fi°L(T) (γiLxi)q
(12)
Thus, substituting eqs 11 and 12, the equilibrium relation (3) leads to:
fi°L(T) γiLxi ) fi°L(T) (γiLxi)qγiqAθi
(9)
The terms ∆ψij° can be computed using eq 4 applied to the corresponding binary system:
∆ψij° )
solvent adsorbed is quite constant and that for each solute Γi/xi . Γs/xs. This is reasonable for very diluted solutions, such as those considered in this work. However, if we can neglect the adsorptivity of the solvent (strongly adsorbable solutes), the aforementioned assumptions are fulfilled since Γs ≈ 0. In this case, the most suitable standard state for the solutes, indicated by the superscript q, is the single solute dissolved in the solvent at the same temperature and free energy of immersion as the mixture. Accordingly, the fugacity of the ith component in the adsorbed phase is given by:
(13)
While fi°L(T) drops out from the equation above, the terms (γiLxi)q represent new unknowns. These can be evaluated by considering the Gibbs isotherm applied to the binaray system constituted by the ith DMN and the solvent:
ψ - ψs )
) (Γi d ln(γiLxi) + Γs d ln(γsLxs)) ∫(γ(γ xx))0 L q i i L i i
(14)
From the assumption that the solute concentration in the liquid phase is very small, it follows that γsL ≈ 1 and Γi/xi . Γs/xs, and then the second term in the integral above can be neglected leading to:
ψ - ψs ≈
) Γi° d ln(γiLxi) ∫(γ(γ xx))0 L q i i L i
i
(15)
Note that in the previous equation the superscript ° (which means pure compound) has been used to indicate the single component in a mixture with the solvent. Similarly, for the sake of brevity, in the following the terms pure component, binary mixture, and so forth will be used for mixture of single compound and solvent, mixture of two compounds and solvent, and so forth, as it is coherent with the assumption of inert solvent. The evaluation of the integral in eq 15 exhibits a major difficulty due to the high sensitivity to the value of the integrand function at low values of the integration variable (cf. Ricther et al., 1989). Several different approaches to the AST for multicomponent equilibria have been proposed to overcome this problem (Rota et al., 1993). One of these involves the modification of eq 15 by replacing the pure solvent with a mixture of arbitrary composition xi* as follows:
ψ - ψi* ) ∆ψ* - ∆ψi1* )
∫(γ(γ xx)*) Γi° d ln(γiLxi) L q i i L i
i
(16)
where ∆ψ* ) ψ - ψ1*, ∆ψij* ) ψi* - ψj*, and ψi* is the free energy of immersion of a mixture of the solvent and
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 203
the ith DMN with composition equal to xi*. By choosing the concentration value xi* sufficiently larger than zero, we can remove entirely the sensitivity mentioned above. This, of course, is obtained at the expense of the introduction of the new parameters ∆ψi1*. Thus summarizing, the equations of the modified model are the Nc relations (16) together with the Nc phase equilibrium relationships (13) and the stoichiometric constraint: Nc
θi ) 1 ∑ i)1
(17)
in the 2Nc + 1 unknowns θi, (γiLxi)q, and ∆ψ*. The application of this model requires the knowledge of the adsorption loads (Γi°) of the pure compounds mixed with the solvent as a function of the bulk phase composition, the free energy of immersion differences between the pure compounds at the reference composition, ∆ψi1*, and appropriate models for the evaluation of the activity coefficients both in the liquid and in the adsorbed phase. The collection of this information is a key aspect in the application of the equilibrium model. The activity coefficients in the liquid phase can be taken from independent sources, such as vapor-liquid equilibrium data, or a predictive group contribution method (cf. Tiegs et al., 1987). In any case we should assume at this stage given a suitable model for computing activity coefficients in the liquid phase. For the adsorption loads of the single components as a function of their composition in the liquid phase, Γi°(xi), we can only rely on ad hoc experimental data. Thus, single-component equilibrium data for each involved compound have to be collected and interpreted through some equation (adsorption isotherm) to be used in the evaluation of the integral in eq 16. The problem is more complicated for the activity coefficients in the adsorbed phase. The usual approach is to consider that the adsorbed phase is liquidlike and then to use an activity coefficients model originally developed for liquid phases. Several such models exist which allow one to estimate, based only on binary interaction parameters, the activity coefficients in multicomponent systems. Thus, we will use binary adsorption equilibrium data to adjust the parameters of the model adopted for describing the activity coefficients in the adsorbed phase. The same binary equilibrium data are also used for estimating the remaining parameters of the developed model, i.e., the free energy of immersion differences between the single components at the reference composition, ∆ψi1*, which are functions only of the temperature. As discussed by Rota et al. (1993) in the context of adsorption from the gaseous phase, we can regard the ∆ψi1* as adjustable parameters in fitting the binary equilibrium data. It should be noted that all the free energy of immersion differences between two single components, say i and j, can be deduced from the values of the differences between the same compounds and the first one, chosen as reference:
∆ψij* ) ∆ψi1* - ∆ψj1*
(18)
It follows that considering a ternary system (1-2-3), only two of such parameters (namely, ∆ψ21* and ∆ψ31*) have to be simultaneously tuned to the three binary mixtures equilibrium data. In conclusion, the developed model allows one to predict, based on single and binary equilibrium data, the adsorption behavior of multicomponent systems. We
now analyze in detail the application of this model to the system of DMN isomers illustrated above. In this particular case, due to the very low solubilities of DMNs, their mole fractions in the liquid phase never exceed x ) 0.02. Thus, we can expect that the corresponding activity coefficient values range in a narrow interval. Estimations made using the UNIFAC group contribution method (Tiegs et al., 1987) confirmed that the average variation of the activity coefficients in the entire composition range examined is less than 10%. Accordingly, in the following we assume γiL ≈ const. Moreover, introducing the solvent-free mole fractions in relations (13), (16), and (17), the following set of equations is obtained:
zi ) ziqγiqAθi ∆ψ* - ∆ψi1* )
∫zz* Γi° d ln(zi) q
i
i
(19) (20)
Nc
θi ) 1 ∑ i)1
(21)
in the 2Nc + 1 unknowns: θi, ziq, and ∆ψ*. This model (which does not represent a new theory, but just a special application of the AST on the basis of a different selection of the reference state) has been used to represent the adsorption equilibrium of the system under examination as discussed in the next section. 3.3. Parameter Estimation. The evaluation of the integral in the right-hand side of eq 20 requires the interpolation of the single-component experimental data through a suitable equation. Since the low concentration region is not involved in eq 20, we need to represent only the data in the high concentration region, which is indeed not very demanding. In particular, two adsorption isotherms have been used: the singlecomponent Langmuir isotherm
Γ i° )
Γi∞Kixi Γi∞Ki(xtotzi) ) 1 + Kixi 1 + Ki(xtotzi)
(22)
where xtot ) 1 - xs refers to a given multicomponent mixture, and the squared isotherm
Γi° ) Γi∞
(23)
The last isotherm is usually a good approximation of the behavior of a strongly adsorbable compound in a region sufficiently away from the low concentration region. The estimated values of the adjustable parameters of the two single-component isotherms are reported in Table 4. Note that the parameter values have been estimated using the linearized Langmuir isotherm, since this procedure is well suited when the high coverage region is of interest (Ruthven, 1984). The good agreement between experimental and computed values is shown in Figure 6. However, from the discussion above it follows that the values of the equilibrium constant, Ki, in Table 4 do not allow reliable estimate of Henry’s constants; i.e., the models above do not describe the adsorption equilibria in the region of very low concentration, which is not experimentally characterized. As mentioned in the previous section, we need now to introduce a suitable model for describing the activity coefficients in the adsorbed phase as a function of composition. Hildebrand’s model, originally developed for liquid mixtures in the context of the regular solution theory and then extended to adsorption equi-
204
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 Table 5. Parameter Values for the Three Binary Systems Estimated Using Two Single-Component Adsorption Isotherms: Langmuir and Squared single-component isotherm Langmuir (eqs 19, 21, and 24)
squared (eq 27)
∆ψji*, mmol/g Aji, mmol/g
system i-j 1,5-DMN/2,6-DMN 2,6-DMN/2,7-DMN 1,5-DMN/2,7-DMN
-2.54 -3.26 -5.80
-2.37 -2.30 -3.33
βji
Aji, mmol/g
10.34 27.44 283.73
-2.24 -2.65 -4.10
Table 6. Average Percentage Errors between Measured and Computed Values for Adsorbed Mole Fractions (Eθ) and Total Amount Adsorbed (EΓtot) single-component isotherm Langmuir (eqs 19, 21, and 24)
Figure 6. Experimental (O) and computed (s) values for the three single-component isotherms. Model parameters reported in Table 4. Table 4. Parameter Values of the Single-Component Langmuir Isotherm for the Three Isomers component
Γ∞, mmol/g
K
1,5-DMN 2,6-DMN 2,7-DMN
1.17 1.09 0.94
642 557 10210
libria (cf. Gamba et al., 1989), has been used. This model, which is briefly summarized in Appendix B, involves one adjustable parameter for each binary system, Aij, which can be estimated by comparison with binary experimental data. Using the Langmuir isotherm (22), the integral in the right-hand side of eq 20 can be evaluated as follows:
ziq )
(
(
) )
∆ψ* - ∆ψi1* 1 (1 + Kixi*) exp -1 Kixtot Γi∞
(24)
This relation, together with eqs 19 and 21, provides the multicomponent adsorption equilibrium model. A reference value of xi* ) 3.54 × 10-2, which is the average value of xtot in all the experimental runs, has been used for all the computations reported in this paper. This model involves five adjustable parameters which can be estimated using equilibrium data for three binary systems. By indicating with 1, 2, and 3 the 1,5-DMN, 2,6-DMN, and 2,7-DMN, respectively, the adjustable parameters are ∆ψ21*, ∆ψ31*, A21, A31, and A32 (note that ∆ψ32* ) ∆ψ31* - ∆ψ21*). These parameters have been estimated all together through a nonlinear fitting procedure involving the binary experimental data relative to all three binary systems. The sum of the squared differences between experimental and predicted values of both the adsorbed mole fractions and the total adsorbed load (suitably weighted by the inverse of the experimental values) was used as an objective function in the regression procedure. The total adsorbed amount has been computed as:
) Γtot
θi
Nc
1
Nc
∑ ∑ i)1Γ °(ψ) i)1
θi
)
i
(25)
Γi°(ziq)
While the estimated values of the parameters are reported in Table 5, a comparison between the values
squared ideal Langmuir (eq 27) (eq 28)
system
θ
Γtot
θ
Γtot
θ
Γtot
1,5-DMN/2,6-DMN 2,6-DMN/2,7-DMN 1,5-DMN/2,7-DMN 1,5-DMN/2,6-DMN/ 2,7-DMN
6 2 5 13
9 17 10 14
5 2 7 13
4 16 9 13
90 32 39 61
15 7 8 13
experimentally measured and those computed by the model is reported in Figures 3 and 4. The overall performance of the model is summarized in Table 6 in terms of percentage errors. The developed equilibrium model can be reduced to a closed analytical form when the squared isotherm (23) is used for representing the single-component behavior. In this case eq 20 leads to:
(
ziq ) zi* exp
)
∆ψ* - ∆ψi1* Γi∞
(26)
This relation, together with eqs 19 and 21, can be further simplified by assuming that all the saturation loads are equal. This assumption is quite reasonable for the case under examination, as can be seen from the values reported in Table 4. By combining eqs 19, 21, and 26 to eliminate ∆ψ* and recalling that the same value of zi* has been selected for all components, we obtain:
θi )
zi/γiqA
Nc zjβji/γjqA ∑j)1
(27)
where βji ) exp(∆ψji*/Γ h ∞). Note that a similar relation has been derived by Hulme et al. (1991) for the case of multicomponent mixtures with constant total adsorption loading and ideal behavior for the liquid phase. Also in this case we have five adjustable parameters involving three binary systems, namely, β21, β31, A21, A31, and A32 (β32 ) β31/β21). Using the same regression procedure as in the previous case, the values reported in Table 5 have been estimated. It is worth noting that the two sets of parameter values are quite similar. This confirms that in the range [xi*, xiq] the squared isotherm is a good approximation of the experimental behavior. Table 6 and Figures 3 and 4 summarize the performance of this model in fitting the experimental binary data. It is evident that the difference between the two models is so small that in some cases the two curves cannot be distinguished. 3.4. Comparison between Model Predictions and Experimental Data. The comparison between experimental data and model results discussed in the previous section can only prove the ability of the
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 205
proposed model to fit the experimental values, since all these have been used to tune the adjustable parameters of the model. We now proceed to assess the reliability of the model in predicting multicomponent equilibria by comparing the model predictions with a set of ternary experimental data. Note that these are true predictions, since no data concerning ternary systems (that is, mixtures involving three DMNs) have been used for tuning the model parameters. The obtained results are reported in Table 3, while in Table 6 the average percentage errors have been summarized. It can be seen that the obtained errors are of the same magnitude as those obtained in fitting the binary data. This is a good indication of the reliability of the proposed models. Finally, in order to evidence the role of nonidealities in the system under examination, it is convenient to compare its behavior with the results of the classical ideal multicomponent Langmuir model:
Γi )
Γi∞Kixi 1+
Nc Kjxj ∑j)1
Γi∞Ki(xtotzi) ) 1+
Nc Kj(xtotzj) ∑j)1
(28)
It is well-known that this simple model assumes that the saturation capacities of all components are the same and that the adsorbed solution is ideal. As a consequence, it predicts a constant separation factor. Since, as shown in Figure 3, the experimental separation factor is a strong function of composition, this model is not expected to reproduce the experimental findings. This is confirmed by the relatively large values of the average errors between model and experimental data reported in Table 6. It should be pointed out that not only the nonideality of the adsorbed phase is responsible for such a behavior but also the insufficient characterization of the low concentration region which leads to a poor estimation of Langmuir’s constant in eq 28. Completely wrong behaviors, such as that illustrated in Figure 4 for the 2,6-DMN/1,5-DMN mixture, cannot be explained only by activity coefficients. 4. Conclusions In view of developing a separation process for producing 2,6-DMN from a mixture of its isomers, the adsorption equilibria of these mixtures have been studied. As DMNs are solid at ambient temperature and pressure, solutions in n-octane have been considered. Through a screening involving various zeolites, the LZY-52 exchanged with potassium has been selected as the one exhibiting the larger separation factor. Various equilibrium data involving single, binary, and ternary mixtures of 1,5-DMN, 2,6-DMN, and 2,7-DMN in noctane have been collected at constant temperature (25 °C). The main evidence from such experiments is the very strong variation of the separation factor with the composition of the liquid phase. In this work it has been explained in terms of large nonidealities in the adsorbed phase by introducing activity coefficients. However, it should be mentioned that similar behaviors can also be explained in terms of surface heterogeneity of the adsorbent (Valenzuela et al., 1988). A multicomponent equilibrium model has been developed from the adsorbed solution theory to reproduce all the collected experimental data. This model can be applied, in general, to all cases where we have strongly adsorbable components dissolved in an inert solvent. The model contains the following adjustable parameters: (Nc(Nc - 1)/2) binary interaction parameters, Aij, appearing in Hildebrand’s model for the activity coefficients in the adsorbed phase (see Appendix B) and (Nc
- 1) parameters ∆ψi1* representing the differences between the free energy of immersion of the single components at the reference composition. In order to apply the model, we need the Nc single equilibrium isotherms and adsorption equilibrium data for the (Nc(Nc - 1)/2) binary systems which can be formed among the Nc involved components. It has been shown that, at least for the system under examination, the model can predict the behavior of the system involving more than two components. Also the strong variations of the separation factor with composition (by more than 1 order of magnitude) have been predicted correctly. Acknowledgment The financial support of CNR-Progetto Finalizzato Chimica Fine and that of Regione Autonoma della Sardegna are gratefully acknowledged. Moreover, the authors thank Prof. M. Monduzzi for the quantumchemical computations. Nomenclature Aij ) binary interaction parameters of Hildebrand’s model C ) fluid phase concentration, mol/L f ) fugacity, Pa K ) Langmuir’s constant N ) number of components Nc ) number of solutes, Nc ) N - 1 r ) cation radius, Å R ) ideal gas constant, J/mol K T ) temperature, K x ) fluid phase mole fraction Nc xtot ) ∑i)1 xi z ) solvent-free fluid phase mole fraction Greek Letters Rij ) separation factor γ ) activity coefficient Γ ) adsorbed amount, mol/g ∆ψ° ) ψ - ψ1°, mol/g ∆ψij° ) ψi° - ψj°, mol/g ∆ψ* ) ψ - ψ1*, mol/g ∆ψij* ) ψi* - ψj*, mol/g ) average percentage error θ ) adsorbed phase mole fraction, solvent-free adsorbed phase mole fraction µ ) dipolar moment, D φ ) free energy of immersion of adsorbent, J/g ψ ) -φ/RT, mol/g Subscripts i, j ) component s ) solvent tot ) total Superscripts A ) adsorbed phase E ) excess quantity L ) liquid phase ° ) pure component or related standard state q ) solution of a single component in the solvent or related standard state * ) reference composition ∞ ) saturation value - ) average value or given value
Appendix A In this appendix we develop the relation between the activity coefficients γi°A and γiqA based on different
206
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996
standard states and defined by eqs 6 and 11, respectively, for the particular case of strongly adsorbable solutes (Γs ≈ 0). For a given adsorbed phase composition, θh , the fugacity of the ith component is given by:
fiA(T,ψ,θh ) ) fiqA(T,ψ,θq)γiqA(θ h ) θh i ) fi°A(T,ψ) γi°A(θ h ) θh i (29) Let us now consider an adsorbed mixture of the ith component and the solvent with composition equal to θq. In this case the fugacity of the ith compound is given by:
fiqA(T,ψ,θq) ) fi°A(T,ψ) γi°A(θq) θiq
(30)
By substituting eq 30 in eq 29, it follows that:
γi°A(θh ) ) γiqA(θ h ) γi°A(θq) θiq
(31)
For strongly adsorbable solutes we expect that θi ≈ 1, and then the previous relation leads to: q
γiqA(θ h ) ≈ γi°A(θ h)
(32)
In this case, the activity coefficients evaluated using the two different standard states are equal. Appendix B Hildebrand’s model used for describing the dependence of the activity coefficients on the composition of the adsorbed phase is given by (Gamba et al., 1989):
ln γi )
∑j ∑k (Aji - 1/2Ajk)ΦjΦk
Φi )
θi/Γi°(xiq)
∑jθj/Γj°(xjq)
Ajk )
Ajk Γi°(xiq)
q)
(33)
(34)
(35)
Γi°(xi replaces the original molar density of the liquid, and the Ajk ()Akj; Ajj ) 0) are the binary adjustable parameters. Literature Cited Barder, T. J. U.S. Patent 4929726, 1989.
Gamba, G.; Rota, R.; Storti, G.; Carra`, S.; Morbidelli, M. Adsorbed Solution Theory for Multicomponent Adsorption Equilibria. AIChE J. 1989, 35, 959-966. Hulme, R.; Rosenweig, R. E.; Ruthven, D. M. Binary and Ternary Equilibria for C8 Aromatics on K-Y Faujasite. Ind. Eng. Chem. Res. 1991, 30, 752-760. Iwai, Y.; Uchida, H.; Mori, Y.; Higashi, H.; Matsuki, T.; Furuya, T.; Arai, Y.; Yamamoto, K.; Mito, Y. Separation of Isomeric Dimethylnaphthalene Mixture in Supercritical Carbon Dioxide by Using Zeolite. Ind. Eng. Chem. Res. 1994, 33, 2157-2160. Kipling, J. J. Adsorption from Solutions of Non-Electrolytes; Academic Press: New York, 1965. Larionov, O. G.; Myers, A. L. Thermodynamics of Adsorption for Non-Ideal Solutions of Non-Electrolytes. Chem. Eng. Sci. 1971, 26, 1025-1030. Minka, C.; Myers, A. L. Adsorption from Ternary Liquid Mixtures. AIChE J. 1973, 19, 453-459. Ootake, M.; Masuyama, T.; Nakanishi, A. Jpn. Patent 92112840, 1989. Paludetto, R.; Storti, G.; Gamba, G.; Carra`, S.; Morbidelli, M. On Multicomponent Adsorption Equilibria of Xylene Mixtures on Zeolites. Ind. Eng. Chem. Res. 1987, 26, 2250-2258. Radke, C. J.; Prausnitz, J. M. Thermodynamics of Multi-Solute Adsorption from Dilute Liquid Solutions. AIChE J. 1972, 18, 761-768. Rajzman, M.; Francois, P. QCPE 1969, 11. Richter, E.; Schutz, W.; Myers, A. L. Effect of Adsorption Equation on Prediction of Multicomponent Adsorption Equilibria by the Ideal Adsorbed Solution Theory. Chem. Eng. Sci. 1989, 44, 1609-1616. Rota, R.; Gamba, G.; Morbidelli, M. On the Use of the Adsorbed Solution Theory for Designing Adsorption Separation Units. Sep. Technol. 1993, 3, 230-237. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. Stewart, J. J. P. QCPE 1974, 455. Tiegs, D.; Gmehlig, J.; Rasmussen, P.; Fredenslund, A. Vaporliquid Equilibria by UNIFAC Group Contribution. 4 - Revision and Extension. Ind. Eng. Chem. Res. 1987, 26, 159-161. Valenzuela, D. P.; Myers, A. L.; Talu, O.; Zwiebel, I. Adsorption of Gas Mixtures: Effect of Energetic Heterogeneity. AIChE J. 1988, 34, 397-402. Verduijin, J. P.; Janssen, M.; Gruitjer, C. B. Eur. Pat. Appl. 323893, 1989.
Received for review November 4, 1994 Revised manuscript received August 2, 1995 Accepted September 1, 1995X IE940644D
X Abstract published in Advance ACS Abstracts, November 15, 1995.
