2250
Ind. Eng. Chem. Res. 1987, 26, 2250-2258
Inoue, K.; Kobayashi, S.; Kushiyama, S.; Koinuma, Y.; Aizawa, R.; Shimizu, Y.; Egi, K. Prepr.-Jpn. Pet. Inst., 16th Anna. Meet., Sapporo 1973, 32. Kobayashi, S.; Kushiyama, S.; Inoue, K.; Aizawa, R.; Koinuma, Y.; Shimizu, Y.; Egi, K. Znd. Eng. Chem. Res. 1987, preceding paper in this issue. Newson, E. J. Prepr.-Am. Chem. SOC., Diu. Pet. Chem. 1970,15(4), A141. Plumail, J. C.; Jacquin, Y.; Toulhoat, H. In Proceedings of the Climax Fourth International Conference on Chemistry and Uses of Molybdenum, Golden, CO, Aug 1982 Barry, H. F., Mitchell, P. C. H., Eds.; Climax Molybdenum: Ann Arbor, MI, 1982; p 389.
Pollack, S. S.; Yen, T. F. Prep.-Am. Chem. SOC.,Diu. Pet. Chem. 1969, 14(3), B-118. Riley, K. L. Prepr.-Am. Chem. SOC.,Diu. Pet. Chem. 1978, 23(3), 1104. Diu. Colloid Shimura, M.; Shiroto, Y.; Takeuchi, C. Am. Chem. SOC., Surf. Chem., Las Vegas Meet., March 1982, 30. Wheeler, A,, In Aduances in Catalysis; Academic: New York, 1951; p 249.
Received for review August 14, 1986 Accepted June 29, 1987
On Multicomponent Adsorption Equilibria of Xylene Mixtures on Zeolites Renato Paludetto, Giuseppe Storti, Giuseppe Gamba, Sergio Carrk, and Massimo Morbidelli* Dipartimento d i Chimica Fisica Applicata, Politecnico d i Milano, 20133 Milano, Italy
Adsorption equilibria of two ternary systems involving m-xylene, p-xylene, and either toluene or isopropylbenzene on zeolite K-Y have been studied. Due to nonideal behavior of the adsorbed phase, m-and p-xylene selectivity is strongly dependent upon composition. In particular, it is found that the addition of a third component can either enhance or depress such selectivity values. Ternary experimental data are well predicted by the developed equilibrium model, whose parameters can be estimated based only on experimental data relative to pure and binary mixtures. Finally, the role of these nonidealities in the equilibrium behavior on the dynamics of adsorption separation columns is discussed. The separation of fraction C8is one of the most classical separation problems in the petrochemical industry. The core of the process is constituted by the final separation of m- and p-xylene isomers, which is most frequently performed by adsorption on zeolites. Such a separation process is based on the principle of displacement chromatography, thereby involving the introduction of an extra component, so-called desorbent, which improves the process efficiency by displacing the adsorbed components along the adsorber. The most widely adopted process operates in the liquid state and involves a simulated countercurrent adsorption unit equipped with a quite efficient rotatory valve (Broughton et al., 1970). Recently, the possibility of operating in the gaseous state has been investigated (Morbidelli et al., 1986a). It was found that, in general, operation in the gaseous state is more efficient than operation in the liquid state, mainly because of the drastic reduction of the noneffective holdup of the separation unit. In this case, a multiport switching unit is more adequate for simulating countercurrent operation. A detailed study of the behavior of once-through adsorbers, packed with zeolite Y exchanged with zeolite K and fed by mixtures of various aromatics, has been previously reported (Morbidelli et al., 1985a; Storti et al., 1985). The aim was to predict the column behavior with a suitable mathematical model, based on simple independent measurements of adsorption equilibria. In particular, the multicomponent Langmuir isotherm was adopted. The aim of this work is twofold. Firstly, we develop an efficient procedure for fully characterizing adsorption equilibria of multicomponent mixtures, in order to accurately predict the adborber behavior. With this respect, it is worth noticing that pure-component equilibrium measurements can be quite difficult in practice, particu0888-5885/87/2626-2250$01.50/0
larly for compounds exhibiting very high affinity for the adsorbent, as in the case of aromatics on zeolite Y. Thus, in order to reach the Henry region of the isotherm, it is necessary either to reach extremely low values of pressure and concentration or to extrapolate the data from rather different temperature values. Secondly, we investigate the accuracy of the multicomponent Langmuir isotherm for systems of the type under examination here. In fact, previous studies on adsorption of chloroaromatics on zeolite X, exchanged with Ca, have indicated a strong influence of selectivity on mixture composition (Morbidelli et al., 198613; Paludetto et al., 1987). This feature cannot be accounted for by the Langmuir model which intrinsically predicts composition-independent selectivity values.
Equilibrium Model The equilibrium model is developed along the lines of the classical thermodynamic approach, i.e., the Ideal Adsorbed Solution theory originally developed by Myers and Prausnitz (1965), introducing suitable modifications to account for nonideal behavior of the adsorbed phase. In the following we will assume that the adsorbent operates at saturation conditions. More precisely, i t is assumed that operating pressure values are so large that all pure-component isotherms have reached their asymptotic region, so that a pressure increase does not produce any further uptake from the gas phase. As mentioned above, this is certainly the case for most aromatic-zeolite systems at atmospheric conditions. But, even more important, this can be safely assumed for any system operating on the principle of displacement chromatography, since the displacement process is really effective when the adsorbent is at saturation. Recalling that most bulk adsorption separation processes are based on this principle, it is apparent that this assumption does not limit the generality of the developed procedure. 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2251 It should be mentioned that a similar treatment has been previously presented by Minka and Myers (1973) in the context of multicomponent adsorption of hydrocarbons in the liquid phase onto activated carbon. Since also in this case saturation conditions prevail, similar conclusions can be drawn. In general, equilibrium conditions are expressed by the equality of the chemical potentials of the generic component in the gaseous and in the adsorbed phase. Since pressure is low, ideal behavior can be assumed for the gaseous phase, thus leading to Pyi = p ? ( T , ~ ) x i y i
i = 1, N
(1)
where yi and x i are the mole fractions in gas and adsorbed phase, y i is the adsorbed-phase activity coefficient, and pp(T,T) is the adsorption equilibrium pressure for the pure component at temperature and spreading pressure identical with that of the multicomponent mixture. Its value may be computed for each component through the Gibbs isotherm: (A dT)/RT = ri d In pi (2) Integration of eq 2 from pi0 to P = 1 atm can be done analytically by assuming ri = rim constant with pressure, in accordance with the assumption discussed above: A(ai* - a ) / R T =
rimIn (P/pp)
(3)
Thus, if eq 3 is substituted in eq 1,the following expression for the adsorbed phase mole fraction is obtained: x i = (yi/yi) exp[-A(Ar - Ari*)/(rimRT)]
(4)
where the following N parameters have been introduced: AT = T - r1*and Ari* = ri*- xl* (so that Aal* = 0, 1 being any reference component). Actually, the number of independent parameters is N - 1, because the parameter relative to the mixture spreading pressure (AT) can be determined from the usual stoichiometric relationship applied to eq 1 as follows:
Exj = C(yj/yj)exp[-A(Aa - A T ~ * ) / ( ~ ~ ~ =R 1T ) ](5) I
i
Thus, for any given set of values of P, T, and yi, eq 4 and 5 can be solved with respect to the unknowns x i and AT. Note that because of the dependence of the activity coefficients on the adsorbed-phase composition, eq 4 and 5 constitute a nonlinear system of algebraic equations. The next step is the calculation of the actual amount of each component adsorbed on the solid. Since mole fractions are now known, it is readily seen that
ri = rtxi
(6)
where rt is the total amount adsorbed per unit mass of adsorbent. This can be estimated by assuming no change in the adsorbed surface upon mixing, through the relationship
rt = cJ r j = (cxj/rj-)-l I
(7)
A final point worth mentioning is the particular case where all components exhibit the same saturation conIn this case, eq 4 and 5 can be combined centration, rim. to eliminate AT, leading to xi = ~ i / [ ~ i C ( a i j ~ j / ~ j ) I J
(8)
where aii = exp[-A(xi* - T~*)/(I"RT)]. This is a rather simple expression, particularly useful for adsorption separation column simulations. Its accuracy can be significantly increased, so as to make this approach
adequate also in cases where pure components exhibit rather different rim values, by adopting the mentioned simplification only for computing mole fractions, not the absolute quantities adsorbed. That is, eq 8 is used for computing mole fractions, x i , while the adsorbed amount of each component ri is computed from eq 6 and 7, thus accounting for the different values of the saturation concentrations, rjm of each component. In the sequel, we will refer to this model as the one with equal saturation concentrations. Note also that in the case of ideal adsorbed phase (i.e., yi = l), eq 8 reduces to the classical multicomponent Langmuir isotherm
which at saturation conditions (i.e., CjKjpj >> 1) reduces to xi = Pi/EbijPj J
(10)
where pij = Kj/Ki. Before we proceed with the model parameter estimation, it is worth briefly commenting on the formalism adopted in the thermodynamic treatment reported above. When we deal with adsorbents such as zeolites, characterized by a porous structure rather than by an adsorption surface, concepts like adsorption surface A and spreading pressure ( T ) become meaningless. It would be physically more adequate to substitute their product (in fact A and T always appear in this form) with some energy of adsorption specific to the amount of adsorbent. However, this does not change the substance of the treatment, while keeping the previous notation makes it more similar to the traditional treatments. Thus, we keep such notation for the benefit of readability.
Parameter Estimation Let us now summarize the physical parameters appearing in the model and indicate for each of them a suitable estimation procedure, based either on simple laboratory experiments or on suitable theories. Note that because of the ultimate goal of this work, we cannot use data relative to breakthrough curves from the adsorption column. Three types of parameters are present in the model. (1) The first parameters are the N saturation concentrations, rim, which can be conveniently measured experimentally. By use of the experimental apparatus described in the next section, these quantities can be accurately measured if operated at atmospheric pressure. (2) The second parameters are the N parameters, AT,*. Since these are relative to pure-component behavior, in principle they could be estimated by fitting any multicomponent equilibrium data. (3) The third parameters are the N activity coefficients, yi, which are a function of the adsorbed-phasecomposition. In this case, we need to adopt a model equation based on some theory of Gibbs free-energy excess of the adsorbed phase. Several such models have been developed in the context of vapor-liquid equilibria, and it appears convenient at this stage to directly apply one of those to the adsorbed phase. In particular, we will use in the sequel Wilson and Hildebrand models. Both of these can describe activity coefficients in multicomponent mixtures based only on binary interaction parameters, through the application of suitable mixing rules. The detailed relationships for each such models are summarized in the Appendix. Note that the Hildebrand model contains less adjustable parameters than the Wilson model (Le., 1 and
2252 Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 -B A
A-
B
--
Figure 1. Schematic diagram of the experimental apparatus: (1) heaters, (2) eight-port pneumatic rotary valve, (3) condensers, (4) zeolite-packed bed.
2 for a binary mixture, respectively). It can be concluded that all the involved parameters can be estimated based on experimental measurements at atmospheric pressure, that is, with no need to investigate very low pressure values in order to enter the Henry region of pure-component adsorption isotherms. Thus, for any given multicomponent mixture, the following experimental information have to be collected in order to calibrate the equilibrium model: (1)pure-component equilibrium data for estimating rim; (2) binary mixture equilibrium data for estimating AT;* and the-parameters of the adopted activity coefficient model (one or two adjustable parameters, depending on whether the Hildebrand or Wilson model is used). All possible binary combinations among all mixture components have to be examined. The extension to multicomponent mixtures is then straightforward: riaand AT,* remain unchanged, since these are quantities relative to pure-component behavior, while the activity coefficients are computed through suitable mixing rules according to the relationships reported in the Appendix.
Experimental Apparatus Experimental equilibrium measurements were performed by means of the isothermal adsorption-desorption apparatus, operating a t atmospheric pressure, schematically represented in Figure 1. Two independent circuits, A and B, entirely enclosed in a thermostatic oven, can be switched to a little column (200 mm long, 5 mm i.d.1 containing a weighted amount (2-3 g) of dehydrated zeolite, by operating an eight-port pneumatic rotary valve, of the type usually employed in analytical gas chromatography for column switching. The experimental procedure is as follows. A liquid mixture of known composition of the components under examination is fed to the system and vaporized before reaching the rotary valve. The obtained vapor stream flows first through the circuit not containing the zeolite sample in order to remove any residual of the previous measurement. Then, it is fed to the zeolite column for a period of time until adsorption equilibrium is reached. At the same time, the other circuit is flushed with a stream of pure desorbent that, a t the desired time, can be switched to the zeolite column in order to desorb all the previously adsorbed components. The outlet stream is condensed, recovered, weighed, and analyzed for determining the values of the adsorbed amounts. Some preliminary runs performed on a typical mixture, where the outlet streams are continuously analyzed, are needed in order to determine the optimal time for equilibration and desorption. Typically, the adsorbed bed is saturated by ahout 0.5 g of mixtures, and this is achieved by feeding about 10 cm3of liquid mixtures a t a rate ranging from 0.3 to 0.5 cm3/min. This adsorbed amount can be fully re-
moved through 10-15 cm3 of liquid desorbent, fed to the column at the same rate as above. This produces an eluted liquid volume of about 15 cm3 (adsorbed mixtures plus desorbent); the average volume fraction of the components to be analyzed in the mixtures is about 5%. Note that such a low dilution is obtained due to the strong adsorptivity of the desorbent, which is comparable to that of the components of the examined mixture. The operation can be repeated for various binary and multicomponent mixtures: also single-componentmeasurements can be made in order to determine the value of the saturation amount when operating at atmospheric pressure (rim). Commercial Nay-type zeolite (1/16-in.pellets), which was exchanged with potassium ions as reported elsewhere (Santacesaria et al., 1985),has been used. Xylene isomers, toluene, and isopropylbenzene were reagent grade (Farmitalia Carlo Erba) and were purified and dehydrated on 5A and NaY zeolite a t ambient temperature prior to use. The analysis of the recovered solutions were conducted with a Model 4200 Carlo Erba Strumentazione gas chromatograph using a 5-m stainless steel column (4-mm i.d.) containing 5% diisodecylphthalate and 5% bentone 34 on Chromosorb W AW, operating at 100 "C with TCD and helium as carrier gas. Eluted peaks were integrated with the corrected area normalization method. The adsorbed amount of the ith component can be determined by means of the material balance rr = (xisWs/MB - VpgYi)/ wz where ri is the equilibrium adsorbed amount per unit weight of the ith component; xil and yi are the mole fractions in the recovered and feed mixtures, respectively; p g is the molar density of the gas phase; W, and W, are the weights of the recovered mixture and of the zeolite sample, respectively; M,is the molecular weight of the recovered solution, which is easily evaluated from molar composition; and V is the free volume of the circuit containing the zeolite sample, where vapor at feed composition is present. V is estimated from tubing size, taking into account the void fraction of the zeolite packed bed as well as the macroporosity of the zeolite pellet. Care must be taken in the preparation of the zeolite column and of the circuit in order to minimize such a free volume, which contains nonadsorbed components. The described experimental apparatus has been demonstrated to be very useful for collecting equilibrium data at various compositions and a t atmospheric pressure. It is simple to operate, fast, and provides quite accurate equilibrium data. Moreover, for the equilibrium proposed model, all the required parameters can be obtained through such equilibrium measurements, thus reducing the experimental efforts usually required for a complete description (i.e., including the Henry region) of the singlecomponent equilibrium isotherms. The accuracy in the experimental results is greatly influenced by the gas-chromatographic analysis of the recovered mixture. In fact, in order to achieve the complete removal of the adsorbed components, the desorbent is fed for a relatively long period of time, thus leading to dilute recovered solutions, which are more difficult to analyze. For this reason, it is very important to select a suitable desorbent for an efficient recovery of the adsorbed components. The most appropriate desorbent is the one whose adsorptivity is intermediate between those of the components under examination, because it allows easy adsorption of the feeding mixture and rapid desorption of the adsorbed phase. For the cases under examination, very good results were obtained by using isopropylbenzene for the system involving m-xylene, p-xylene, and toluene, while
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2253 Table I. S a t u r a t i o n Concentrations, rim, for P u r e Components component iO3ri",mol/g T,"C p-xylene 1.96 150 m-xylene 1.91 150 toluene 1.78 150 p-xylene 1.62 170 isopropylbenzene 1.57 170 m-xylene 1.55 170
--
^,20
E
-E
15
I
C
0
5 10 0
'? $ 0
05
4
0
0
0.2 OL 06 08 vapor phase mole fraction of p -xylene
1
Figure 2. Absorbed amount; ri as a function of vapor-phase mole fraction for the system p-xylene-m-xylene a t 150 O C : experimental model 2 (-). point (O),
0 02 04 06 08 1 vapor phase mole fractlon of p-xylene
Figure 5. Adsorbed amount; r, as a function of vapor-phase mole fraction for the system p-xylene-isopropylbenzene at 170 O C : exmodel 2 (-). perimental point (O),
0 02 04 06 08 1 vapor phase mole f r a c t i o n of p-xylene
Figure 3. Adsorbed amount; Ti as a function of vapor-phase mole fraction for the system p-xylene-toluene at 150 O C : experimental point (01,model 2 (--).
0 02 04 06 08 1 vapor phase mole fraction of p-xylene
2'51-----7
20
Figure 6. Adsorbed amount; r, as a function of vapor-phase mole fraction for the system p-xylene-m-xylene at 170 "C: experimental model 2 (-). point (O),
0 02 04 06 08 1 vapor phase mole fracticn ot m-xylene
Figure 4. Adsorbed amount; ri as a function of vapor-phase mole fraction for the system m-xylene-toluene a t 150 O C : experimental point (O), model 2 (-).
conversely toluene was used for the systems involving isopropylbenzene.
Experimental Results and Discussion Two ternary systems are examined in the following: m-xylene, p-xylene, toluene and m-xylene, p-xylene, isopropylbenzene, both on zeolite Y fully exchanged with zeolite K a t atmospheric pressure and a t 150 and 170 "C, respectively. These systems arise in the separation process of m- and p-xylene through displacement chromatography,
0
02 04 0 6 08 vapor phase mole fraction of lsopropylbenzene
1
Figure 7. Adsorbed amount; ri as a function of vapor-phase mole fraction for the system isopropylbenzene-m-xylene at 170 OC: exmodel 2 (-). perimental point (O),
using either toluene or isopropylbenzene as desorbent (Storti et al., 1985). According to the procedure outlined above, pure-component experiments have been performed in order to estimate the saturation concentration values, rim.The obtained values are summarized in Table I. Next, for each of the ternary systems under examination, three binary systems have been investigated. In Figures
2254 Ind.. Eng. Chem. Res., Vol. 26, No. 11, 1987 Table 11. Percentage Error (%e) and Standard Deviation 2
1
1-2 1-3 2-3 4-5 4-6 5-6 au
(0)"
of the Binary Data Regression with Models 1-5* model 3 4 5
70 e
U
%e
U
%e
U
%e
U
%e
U
6.22 11.00 5.66 4.92 3.34 7.47
3.95 7.90 5.32
1.24 3.02 3.80
1.32 4.01 4.66
1.53 2.87 3.47
1.50 4.35 4.69
1.25 3.04 3.81
1.32 4.01 4.67
5.50 1.88 6.87
3.39 0.37 3.57
4.63 0.41 4.54
3.41 0.34 3.57
4.87 0.43 4.85
3.39 0.36 3.56
4.63 0.41 4.55
1.57 2.90 3.45 3.41 0.35 3.55
1.52 4.37 4.69 4.87 0.44 4.86
*
= (standard deviation) IO5. (1) p-xylene, (2) m-xylene, (3) toluene, T = 150 " C ; (4) p-xylene, (5) isopropylbenzene, (6) m-xylene, T =
170 "C.
2-7 are shown the experimental data collected for each of them at constant temperature and pressure. In particular, the adsorbed-phase concentration values of each component (together with their sum, i.e., total loading) are reported as a function of the vapor-phase mole fraction. In order to assess their reliability, the experimental data can be checked for thermodynamic consistency as discussed by Sircar and Myers (1971). If the Gibbs isotherm is applied to a binary mixture, it follows that
The value of the integral on the right-hand side can be computed directly from the experimental data of each binary system. Considering the left-hand side, it readily appears that the sum of such values for each group of three binary systems should be equal to zero. It is found that the result of this summation is in both cases equal to about 1-3% of the average absolute value of the corresponding three terms. Thus, the obtained data can be regarded as thermodynamically consistent. Each of the binary systems has been interpreted with the equilibrium models described above. In particular, five models have been considered, and the obtained results are summarized in Table I1 in terms of average percentage error and standard deviation. The parameter values have been estimated through a standard nonlinear optimization routine using as objective function the average percentage error on the adsorbed-phase concentration values, ri. With reference to Table 11, we note that model 1 refers to the case where the adsorbed phase is ideal and the saturation concentrations of all pure components are equal (eq 10). In models 2 and 3, the first of these approximations is removed, i.e., eq 8 is used, while in models 4 and 5 these are both removed, i.e., eq 4 and 5 are used. Moreover, the activity coefficients have been estimated from Hildebrand equations in models 2 and 4,while Wilson relationships have been used in models 3 and 5. In both cases, the effect of spreading pressure on the activity coefficients have been neglected. It should be noted that the five models differ only in the evaluation of the adsorbed phase mole fractions, x i ; from these, the adsorbed amount, ri,is computed through eq 6 and 7 in all models, using the saturation concentration values rim reported in Table I. In comparing the performance of these models, it should be considered that they do not contain the same number of adjustable parameters. In particular, because of the different type of relationships adopted for the activity coefficients, model 1contains one adjustable parameter, models 2 and 4 contain two, and models 3 and 5 contain three. From the results shown in Table 11,it appears that model 1 is significantly less accurate then all the others. This indicates that nonidealities in the adsorbed phase play a significant role in adsorption equilibria. This ap-
'L
00
02
04
06
08
1
vapor phase mole f r a c t i o n of
I
Figure 8. Selectivity values as a function of vapor-phase mole fraction for the binary systems a t 150 "C. Legend: p-xylene (l), m-xylene (2), toluene (3); experimental point ( O ) , model 1 (---), model 2 (-),
0
02
OL
06
08
vapor phase mole fraction of
1 i
Figure 9. Selectivity values as a function of vapor-phase mole fraction for the binary systems at 170 "C. Legend: p-xylene (I), isopropylbenzene (21, m-xylene (3); experimental point ( O ) , model 1 (---), model 2 (-1.
pears more evident from the results shown in Figures 8 and 9, where the binary selectivity values between m- and p-xylene as predicted by models 1and 2 are compared with the corresponding experimental data. It is seen that the assumption of composition-independentselectivity implicit in model 1does not hold for the systems under examination. Moreover, by comparing the results of models 2 and 4 with those of models 3 and 5,respectively, we can conclude that using the Wilson model does not provide any better performance than using the Hildebrand model. Since the latter contains one less adjustable parameter, it is to be preferred. One more reason for such a choice is given by considerations regarding the internal coherence of the model. Namely, Hildebrand model is based on the assumption of regular mixture; that is, it attributes devia-
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2255 Table 111. Equilibrium Parameters, ui,(=A A.rrij/RT)and A;;, and Infinite Dilution Binary Activity Coefficients. T
. .
1-J
1-2 1-3 2-3 4-5 4-6 5-6
1 0 3 ~ ~ ~
-1.7402 -2.3483 -0.6081 -0.3226 -1.5630 -1.2404
1 0 3 ~ ~ ~ Yi-0.4435 0.7975 -0.7436 0.6843 -0.3024 0.8536 -0.2148 0.8758 -0.2002 0.8837 -0.4151 0.7677
;
~
~
Tim
0.7928 0.6585 0.8438 0.8721 0.8788 0.7650
in Table 111, are less than one, thus indicating negative deviations from ideality. This behavior is actually quite general for adsorption systems, and it is most likely due to energetic heterogeneity of the surface (Myers, 1983, 1986). It is worth mentioning that the parameters uI,reported in Table I11 are not independent of each other. In fact, because of the thermodynamic consistency discussed above, these have to satisfy the constraint
+
Legend as in Table 11.
tions from ideal behavior to enthalpic rather then to entropic factors. On this same assumption is also based eq 7, which represents the additivity rule for the mixture molar adsorbed surface. Thus, the Hildebrand model is recommended for computing activity coefficient- in the equilibrium model developed here. Finally, it may be noted that the results of models 2 and 4 are not significantly different (as it is true also for models 3 and 5). This conclusion is certainly not general, for it depends on the extent of the difference among the saturation concentrations of the pure components involved in the mixture. However, in the case under examination, where such difference is at most equal to about lo%, the two models are equivalent. Since model 2 is much simpler with respect to equilibrium calculations, it is the one to be recommended, and it will indeed be used throughout the rest of this work. A detailed comparison of the results of model 2 is shown in Figures 2-7, where the curves represent the values calculated through the model and the points are the experimental data. In Table I11 are reported the values of the parameters used in model 2, together with the calculated values of the infinite dilution activity coefficients for each binary system. These indicate once again the importance of the deviations from ideal behavior in the adsorbed phase. It is noticeable that all the activity coefficient values computed in this work, as it also appears from the data
3 4 5 6 7 8 9 10 11 12 13 14
0
(12)
where each of the three u values refers to one of the three binary systems which constitute one ternary system. This constraint has been automatically enforced in the parameter estimation procedure. In order now to verify the reliability of the developed equilibrium model, one set of ternary equilibrium data for each examined system has been produced. According to the above-mentioned procedure, the equilibrium model can be directly used to predict ternary equilibrium data without any further change in its parameters. For the comparison between experimental and predicted values of the adsorbed quantities of each component, rIis shown in Tables IV and V for the two examined systems, respectively. It appears that the average percentage errors are 3.32% and 1.99%, respectively. It should be noted that using the other models for predicting these data yields results that confirm the conclusion reached above. In particular, the ideal model 1is much less accurate (average percentage errors are 7.72% and 11.2% for the two systems, respectively), while the more complex models 3-5 do not provide significantly better results. In the last columns of Tables IV and V, the experimental values of p - and m-xylene selectivity have been reported. It appears that such values depend not only on composition but also on the type of components involved. In particular, it is seen that the presence of toluene increase m- and p-xylene selectivity, while the presence of isopropylbenzene has the opposite effect. This behavior is
Table IV. Comparison between Calculated and Experimental Values of (2)-Toluene (3) on Zeolite K-Y at 150 "C exptl x io3 run 1 2
+
~ 1 2 ~ 2 3 ~ 3 = 1
ri for the Ternary System g-Xylene (1)-m-Xylene calcd
X
lo3
Yl
YZ
y3
rl
r2
r3
rl
rz
r3
0.1795 0.3602 0.5406 0.7180 0.1601 0.3193 0.4758 0.6313 0.1210 0.1210 0.2424 0.3601 0.4797 0.4854
0.7215 0.5400 0.3592 0.1804 0.6399 0.4774 0.3271 0.1694 0.4803 0.4803 0.3601 0.2397 0.1205 0.1193
0.0990 0.0998 0.1002 0.1017 0.2001 0.2032 0.1971 0.1993 0.3986 0.3986 0.3975 0.4002 0.3998 0.3952
0.724 1.140 1.438 1.660 0.685 1.083 1.357 1.558 0.569 0.576 0.952 1.197 1.381 1.396
1.060 0.672 0.404 0.189 0.963 0.608 0.371 0.182 0.746 0.759 0.485 0.283 0.132 0.130
0.121 0.109 0.101 0.098 0.244 0.225 0.203 0.195 0.512 0.515 0.468 0.427 0.397 0.392
0.719 1.129 1.425 1.659 0.669 1.058 1.336 1.560 0.559 0.563 0.912 1.164 1.370 1.378
1.077 0.694 0.416 0.194 0.987 0.637 0.396 0.190 0.806 0.804 0.529 0.320 0.149 0.147
0.124 0.108 0.098 0.093 0.252 0.224 0.198 0.186 0.521 0.519 0.459 0.425 0.397 0.391
Table V. Comparison between Calculated and Experimental Values (1)-Isopropylbenzene (2)-m-Xylene (3) on Zeolite K-Y at 170 OC exptl x IO3 run Y, Y, Y, r, r, 1 0.1608 0.2000 0.424 0.6392 0.496 0.4797 0.433 2 0.3200 0.2003 0.727 3 0.4794 0.3198 0.395 0.2008 0.976 0.360 4 0.6396 0.2007 1.181 0.1597 0.4802 0.817 5 0.1207 0.3991 0.290 6 0.2428 0.3584 0.748 0.3988 0.526 0.2404 0.690 7 0.3610 0.3986 0.718 0.1217 8 0.4786 0.651 0.3997 0.887
of
exptl 2.7461 2.5420 2.3616 2.2004 2.8426 2.6634 2.5137 2.2983 3.0577 3.0115 2.9175 2.8160 2.6320 2.6290
&I2
r, for the Ternary System p-Xylene calcd X
lo3
rl
r,
r9
rQ
0.652 0.438 0.273 0.127 0.467 0.321 0.201 0.095
0.440 0.743 0.975 1.162 0.299 0.537 0.725 0.883
0.472 0.405 0.359 0.322 0.806 0.727 0.667 0.619
0.663 0.438 0.263 0.120 0.468 0.318 0.198 0.094
S , i l exutl 2.5839 2.4873 2.3803 2.3241 2.4742 2.4220 2.3797 2.3662
2256 Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987
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Figure 11. Breakthrough curves for the binary system m-xylene (0)-toluene (0).Calculated curves: model 1 (---), model 2 (-) (conditions as Figure 1 in Morbidelli et al. (1985a)).
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Figure 10. p-Xylene and m-xylene selectivity values as a function of their relative composition, for fixed mole fraction of the third component: toluene (-.-) or isopropylbenzene (- - -1.
best displayed by the calculated data shown in Figure 10, where the selectivity between p- and m-xylene is reported, as a function of the relative composition of the two isomers, for various fixed values of the third component (i.e., toluene or isopropylbenzene). This finding has very important consequences on the issue of optimal desorbent selection for the separation process as based on the principle of displacement chromatography. Namely, since the classical analysis by De Vault (19431, it has been concluded that the appropriate desorbent should exhibit an affinity to the solid intermediate between those of the components to be separated (Morbidelli et al., 1985b). This conclusion holds for systems where the selectivity between such components does not depend upon the type of desorbent used; otherwise, this factor should also be taken into account while selecting the best desorbent. For example, in our previous related work (Storti et al., 1985), where any composition effect was neglected since equilibria were described through a multicomponent Langmuir isotherm, it was concluded that isopropylbenzene is a better desorbent then toluene. This conclusion was based solely on the relative adsorptivity of the various components. Namely, isopropylbenzene adsorptivity is intermediate between those of m- and p-xylene, while that of toluene is the lowest. This conclusion could be reversed by a new compound, which may be not as good as a desorbent but has the ability of significantly enhancing m- and p-xylene selectivity. Indeed toluene goes in this direction, but most likely in this case, such effect is not sufficient to make it more convenient than isopropylbenzene.
Adsorption Separation Column Behavior Let us now investigate the effect of adsorption equilibria deviations from ideality on the behavior of fixed-bed separation columns. All the following experimental runs have been previously reported by Morbidelli et al. (1985a) and Storti et al. (1985). The mathematical model used for the simulation of column dynamics takes into account
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Figure 12. Breakthrough curves for the binary system p-xylene (.)-toluene (a). Calculated curves: model 1 (- - -1, model 2 (-) (conditions as Figure 2 in Morbidelli et al. (1985a)).
time ( m i d
Figure 13. Breakthrough curves for the ternary system m-xylene (O)-p-xylene (.)-toluene (0).Calculated curves: model 1 (- - -), model 2 (-) (conditions as Figure 3 in Morbidelli et al. (1985a)).
inter- and intraparticle mass-transfer resistances and axial dispersion and describes the adsorption equilibria through the multicomponent Langmuir isotherm. All details about the experimental procedure and the mathematical model are reported in the original works and thus will not be repeated here. In the following, the same model is used, but Langmuir isotherm is replaced with model 2 described above. For comparison, in all reported simulations, two cases will be shown: one using model 2 (solid curves) and the other using the ideal model 1 (dotted curves). Figures 11and 1 2 refer to binary systems. In the first, the column, previously saturated with pure m-xylene, is then eluted with pure toluene. In the second, p-xylene is eluted by toluene. Figure 13 represents the breakthrough curve of an equimolar mixture of m- and p-xylene from a column previously saturated with pure toluene, followed by the elution of the same mixture by a stream of pure toluene. Finally, Figure 14 represents the same sequence of operations, now using isopropylbenzene instead of toluene as desorbent. On the whole, the reported comparison shows that the equilibrium model accounting for nonideal effects provides a more accurate simulation of the column behavior. This is particularly evident in those regions of the eluted profiles exhibiting the greatest irregularities, as well as in the initial
Ind. Eng. Chem. Res., Vol. 26, No. 11, 1987 2257 10
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Figure 14. Breakthrough curves for the ternary system m-xylene (0)-p-xylene (0)-isopropylbenzene (m). Calculated curves: model 1 (- - -), model 2 (-) (conditions as Figure 5 in Storti et al. (1985)).
portion and final tail of the breakthrough curves. These are of great importance in separation processes, since they are responsible for the separated streams purity level.
Conclusion An adsorption equilibrium model has been developed which applies to multicomponent mixtures at temperature and pressure values such that the adsorbent reaches saturation conditions. This is a rather common situation, particularly in the case of adsorption separation processes based on displacement chromatography. An example of this is given by the two ternary mixtures investigated in this work, whose practical importance stems from the classical m- and p-xylene separation problem. All the model parameters have been estimated from pure or binary mixtures equilibrium data. The accuracy in predicting ternary equilibrium data is found to be comparable to that obtained in fitting the corresponding binary data. This confirms the validity of the model and particularly its capability of predicting multicomponent mixture behavior based only on binary data, that is, introducing only binary interaction parameters. This conclusion agrees with previous findings by Minka and Myers (1973) in the context of adsorption on activated carbon from liquid mixtures. The thermodynamic model described above is of direct practical use in the design of adsorption separation processes. It is known that the accurate description of multicomponent equilibria is the key factor for a successful simulation of the separation unit, whether this is a oncethrough column or a simulated countercurrent unit (Morbidelli et al., 1984). Now, when a new separation process is designed, the adsorbent and the desorbent must be carefully selected, depending upon the specific performance requirements and the type of separation unit employed. This can be readily accomplished, once the adsorption equilibrium behavior of the involved multicomponent mixture has been characterized, through suitable simulation models. It is worth noticing that a highly nonideal behavior has been found also for mixtures of apparently quite similar components, such as m- and p-xylene and toluene. Such nonidealities lead to selectivity values strongly dependent upon composition, which cannot be described through Langmuir-type adsorption isotherms. This also suggests that those analytical solutions based on the assumption of constant selectivity (mainly derived from equilibrium theory), which are often applied to the simulation of displacement chromatography processes, should actually be used with some care. A major consequence of such nonideal behavior of the adsorbed phase is that m- and p-xylene selectivity depends upon the type of third component added as a desorbent. Since this behavior can be expected to apply to other situations as well, it can be concluded that these factors
should be carefully considered when selecting the optimal desorbent for a given separation. This finding opens up the possibility of designing adsorption separation processes based on the addition of an extra component whose role is solely that of enhahcing selectivity between those components to be separated. Such a procedure would correspond to extractive distillation in the context of distillation-based separation techniques.
Nomenclature A = surface area of adsorbent, cm2/g A, = Hildebrand activity coefficient parameters K = Langmuir constant, atm-' N = number of mixture components P = pressure, atm pl = partial pressure, atm p:( T,a) = adsorption equilibrium pressure for the pure component at T and a identical with that of the multicomponent mixture, atm R = ideal gas constant, (atm cm3)/(molK) S , = selectivity, ( r , / y J / ( r 1 / y j ) T = temperature, K x = adsorbed-phase mole fraction y = vapor-phase mole fraction Greek Symbols aii = exp[-A(xi* - aj*)/(F'=RT)] @ij = Ki/Kj y = activity coefficient in adsorbed phase r = adsorbed amount, mol/g r" = loading capacity of the adsorbent, mol/g x = spreading pressure, atm cm xi* = spreading pressure of the pure component at pressure equal to P, atm cm ui1 = A(ri* - aj*)/RT Aij = Wilson activity coefficient parameters Superscript * = pure component Subscripts i, j = component t = total Appendix Two models have been used to calculate the activity coefficients in the adsorbed phase. The first, based on regular solution theory, is the Hildebrand model (c.f., Hildebrand et al., 1970):
where ai = ( x i / I ' i m ) / ( x j x j / l ? , m ) In . this application, rim replaces the original molar density of the liquid. Ai/s (=Aji; Aii = 0) are the adjustable parameters. In the case of a binary mixture, this model reduces to 1
In y1 = -AI2a2
(A2)
r i m
which involves only one adjustable parameter. The Wilson model for multicomponent mixtures yields
where Aii = 1 and Aij # Aji are adjustable parameters. In the case of a binary mixture, this reduces to In y, =
I n d . Eng. Chem. Res. 1987, 26, 2258-2263
2258
where two adjustable parameters appear. Ragistry No. 3-H3CC6H4CH3, 108-38-3; 4-H3CC6H4CH3, 106-42-3;CeH5CH3, 108-88-3;C~H~CH(CH~)Z, 98-82-8. Literature Cited Broughton, D. B.; Neuzil, P. W.; Pharis, J. M.; Brearly, C. S. Chem. Eng. Prog. 1970, 66, 70. De Vault, D. J. Am. Chem. SOC. 1943,65, 532. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van Nostrand Rheinhold: New York, 1970; pp 107-109. Minka, C.; Myers, A. L. AIChE J . 1973, 19, 453. Morbidelli, M.; Storti, G.; Carrl, S.; Niederjaufner, G.; Pontoglio, A. Chem. Eng. Sci. 1984, 39, 383. Morbidelli, M.; Santacesaria, E.; Storti, G.; Carri, S. Ind. Eng. Chem. Process Des. Dev. 1985a, 24, 83. Morbidelli, M.; Storti, G.; Carrl, S.; Niederjaufner, G.; Pontoglio, A. Chem. Eng. Sci. 1985b, 40, 1155. Morbidelli, M.; Storti, G.; C a d , S. Ind. Eng. Chem. Fundam. 1986a, 25, 89.
Morbidelli, M.; Paludetto, R.; Storti, G.; Carrl, S. "Adsorption from Chloroaromatic Vapor Mixtures on X Zeolites: Experimental Results and Interpretation of Equilibrium Data", paper presented at the Second International Conference on Fundamentals of Adsorption, Santa Barbara, CA, May 4-7, 198613. Myers, A. L. AIChE J . 1983,29, 691. Myers, A. L. "Molecular Thermodynamics of Adsorption of Gas and Liquids Mixtures", paper presented at the Second International Conference on Fundamentals of Adsorption, Santa Barbara, CA, May 4-7, 1986. Myers, A. L.; Prausnitz, J. M. AIChE J . 1965, 11, 121. Paludetto, R.; Gamba, G.; Storti, G.; Morbidelli, M. Chem. Eng. Sci. 1987, in press. Santacesaria, E.; Gelosa, D.; Danise, P.; Carri, S. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 78. Sircar, S.; Myers, A. L. AIChE J. 1971, 17, 186. Storti, G.; Santacesaria, E.; Morbidelli, M.; Carrl, S. Ind. Eng. Chem. Process Des. Dev. 1985,24, 89.
Received for review September 11, 1986 Revised manuscript received July 8, 1987 Accepted July 22, 1987
Experimental and Predicted Performance of Pulsatile Fluidic Pumps James G. Morgan* and William D. Holland Fuel Recycle Division, Oak Ridge National Laboratory,' Oak Ridge, Tennessee 37831
As part of the Consolidated Fuel Reprocessing Program (CFRP) a t the Oak Ridge National Laboratory (ORNL), top-loading and bottom-loading pulsatile fluidic pumps were tested for possible use in a nuclear fuel reprocessing facility. A procedure was developed to obtain a calibration curve for a particular pump. A predictive model based on the calibration curve was found to adequately predict pump performance over the design range of interest. The model takes into consideration system resistance, density and viscosity of the pumped fluid, and air motivation pressure. 1. Introduction Fluidic pumps have been under development for some time and have found application in nuclear fuel reprocessing operations, especially in the United Kingdom (Tippetts, 1978, 1979). Having no moving parts, these pumps are maintenance free and do not dilute or heat the pumped fluid as do steam jets. Air is not entrained in the fluid as it is in air lifts. The pumps might be used in nuclear reprocessing plants as product tank mixers, as transfer pumps in accountability tanks, and as supplier pumps to metering devices that feed contador banks. The flow requirements for these pumps vary from about 8 to 300 L/h. The purpose of this investigation was to demonstrate prototypic fluidic pump applications and to develop a model to predict pump performance under different conditions. 2. Fluidic P u m p Description
Two types of pulsatile fluidic pumps, top-loading and bottom-loading, were studied. Both types operate submerged in a tank of the liquid to be pumped with only a discharge line and an air line leading to the surroundings. The top-loading pump is easier to fabricate and is shown in Figure 1. At the beginning of the pump stroke, the chamber of the pump is full of liquid, and pressurized air is forced into the chamber through a three-way control valve. The liquid stream passes through the nozzle and 'Operated by Martin Marietta Energy Systems, Inc., for t h e
U S . Department of Energy. 0888-5885/87/2626-2258$01.50/0
is directed into the diffuser and up the discharge tube. The amount of liquid flowing into or out of the refill port depends on the resistance to flow in the discharge system. At the end of the pumping stroke, when the level of liquid in the chamber has fallen to the bottom of the discharge line, the air in'the chamber is exhausted to the atmosphere. The refill cycle begins with liquid entering the chamber through the r e f i port. A column of liquid in the discharge tube above the diffuser also falls back into the chamber when the air pressure is released. The top-loading pump used in these tests had a diameter of 6 in. and was 15 in. in height. A bottom-loading pump is shown in Figure 2. The pump and refill cycles are similar to the top-loading pump, except the pump chamber refills through a port located at the bottom. This type of design allows the host tank containing the pump to be almost completely emptied. A prototypic bottom-loading product tank pump was made of 4-in. schedule 40 pipe and was 4 f t in height. These dimensions allowed the pump to fit into a critically safe tank and also allowed a longer, more easily controlled pump time. A reverse-flow diverter (RFD) is a generic name for a device that redirects flow in one of its inlets. The design of the nozzle-diffusers used in this investigation was based on earlier work by Smith and Counce (1984a) who characterized flat-walled, venturi-like RFDs and later investigated &symmetric RFDs (198413). They found that the characteristic curves for RFDs were similar over a range of nozzle-diffuser throat diameters of 0.37-0.73 in. Nozzle-included angles ranged from 14' to 26', and diffuser angles ranged from 4' to 8'. The gap between the 0 1987 American Chemical Society
