Ind. Eng. Chem. Fundam. 1988, 25, 89-95
89
Comparison of Adsorption Separation Processes in the Liquid and Vapor Phase. Application to the Xylene Isomer Mixture Masslmo Morbldelll, Gluseppe Storti, and Serglo Carre Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Piazza Leonard0 da Vinci, 32, 20 133 Milano, Italy
Adsorption Separation processes based on displacement chromatography are widely used in industry to separate various mixtures of isomers with very low differences in the boiling point temperatures. The efficiency of such processes, operated in either the liquid or vapor phase, is analyzed in detail. I n particular, the separation of a mixture of m-xylene, p-xylene, and ethylbenzene by adsorption on zeolites is considered. I t Is concluded that operation in the vapor phase at 150-170 O C yields higher separation efficiencies than in the liquid phase at 57 O C . The inefficiency of the liquid-phase process is due to the increase of gas-to-solid mass transfer resistance, axial dispersion, and column holdup. The role of each of these factors is analyzed on a general basis through the use of a suitable mathematical model. The results provided useful suggestions for improving the efficiency of liquid-phase separation processes.
Introduction A classical separation problem in chemical engineering is the fractionation of the hydrocarbon mixture of isomers constituted by o-, m-, and p-xylene and ethylbenzene. Several industrial processes have been developed in the past, usually coupled with an isomerization process aimed to transform some or all of the other isomers into p-xylene, due to its superior industrial importance as a raw material. Usually o-xylene, and sometimes also ethylbenzene, are separated by distillation in the first stage of the process. The first separation processes were based on crystallization (cf. Kirk-Othmer, 1970) or solvent extraction using HFBF, (Davis, 1971; Herrin and Martell, 1971). At present, however, most processes are based on selective adsorption on molecular sieves. In particular, potassium-exchanged Y zeolite has been shown to be one of the most selective in the separation of the mixture m- and p-xylene (Milevsky and Berak, 1975; Broughton et al., 1970). Two main industrial processes have been proposed using adsorption of the liquid mixture on molecular sieves. The first one is the Parex process (Broughton, 1968; Broughton et al., 1970), developed by UOP, and is based on a quite complex and expensive rotary valve which allows simulation of a moving bed operation. The adsorbent moves periodically countercurrent to the liquid stream, while maintaining the adsorbent as a series of stationary beds. The second process has been developed by Asahi using a different type of zeolite and an appropriate desorbent fluid in order to improve the displacement chromatography effect in the separation (Seko et al., 1979). Both these processes refer to the selective adsorption of a liquid mixture of xylene isomers on zeolite, which we have extensively studied both theoretically and experimentally (Santacesaria et al., 1982a,b;Carrb et al., 1982). Recently, the possibility of performing the separation using the same adsorbent, but operating with the fluid mixture in the gaseous phase, has been considered (Carrb et al., 1983). A detailed analysis of the adsorption process in the gaseous phase for a mixture of o-, m-, and p-xylene and ethylbenzene on potassium-exchanged Y zeolite (Santacesaria et al., 1985; Morbidelli et al., 1985) has yielded the conclusion that such a process is quite effective and highly competitive with the one mentioned above operating in the liquid phase. A specific analysis has been developed in order to identify the most efficient desorbent (Storti et al., 1985). The aim of the present work is to compare the processes that operate in liquid and gaseous states, in order to define 0196-4313/86/1025-0089$01.50/0
their relative convenience in the development of a separation process for the xylene isomer mixture. This task is accomplished by using the mathematical model developed and tested by direct comparison with experimental data in the references mentioned above. This allows comparison under identical operating conditions, except the operating temperature, which is 57 "C in the liquid process and 150-170 "C in the gaseous. Both are operated at atmospheric pressure. It is worthwhile pointing out that the examined processes are based on displacement chromatography (cf. Berg, 1983), where the desorbent and the components of the mixture to be separated exhibit comparable affinity to the adsorbent. Thus, unlike elution chromatography, in displacement chromatography the desorbent fluid adsorbs on the solid, displacing the components previously adsorbed and pushing them toward the outlet. The choice of an efficient desorbent is a key factor in establishing the efficiency of the entire separation process (cf. Seko et al., 1979; Storti et al., 1985). In particular, it is known that the appropriate desorbent is one whose adsorptivity is intermediate between those of the two components to be separated. Since such a desorbent is not the same for the processes operating in liquid and gas states, two different appropriate desorbents need to be considered in a proper comparison. Besides the particular case of xylene isomer separation, the general question of operating adsorption units in liquid or gaseous states is of great importance in developing industrial separation processes and therefore deserves more detailed analysis. Since the above-mentioned model has been successfully employed in the simulation of separation units, not only for the xylene isomer mixture (both in liquid and gaseous states) but also for other mixtures (see the case of p - and o-chlorotoluene; Morbidelli et al., 1984), it provides the ideal tool for this analysis. In the last section the results of a general comparison between separation processes that operate in liquid and gas states are reported. These results can serve as a guide in the development of separation processes for any mixture. All comparisons are performed for operation of the adsorption unit in a periodic fashion; i.e., a sequence of pulses of the mixture to be separated is fed to the unit, each followed by a stream of the pure desorbent. The time interval between two subsequent pulses is such that the end of the rear boundary of the last eluted peak of each cycle is coincident with the beginning of the front boundary of the first eluted peak of the next cycle. Even 0 1986 American Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 25, No. 1, 1980
though we will refer for simplicity to a once-through operation, the final conclusions can be extended to any other periodically continuous operating mode of the adsorption unit which increases its efficiency, such as chromatography with recycle (Bailly and Tondeur, 1982), two-way chromatography (Bailly and Tondeur, 1981), and, at least on a qualitative basis, the countercurrent moving bed operation as simulated by the rotary value in the UOP Parex process.
Table I. Dimensionless Equations of t h e Adsorption
Model of the Separation Unit and Its Experimental Verification Since the comparison among the various examined separation processes is based on the results of a mathematical model, it is convenient to briefly discuss its main characteristics first. In general, a reliable model of an adsorption unit must account for several phenomena, such as inter- and intraphase mass and heat transfer resistances, axial dispersion, and multicomponent competitive adsorption equilibria. In particular, in the case of zeolites, characterized by a bidisperse porosity structure, the influence of internal diffusion resistances must be considered, both in macro- and micropores. Since the numerical solution of a transient model inclusive of the detailed simulation of each of such phenomena would be excessively complicated, a simplified model must be developed. Such a model has been successfully applied to the simulation of several separation processes, operated in both phases, and is described in detail by Santacesaria et al. (1982b) and Morbidelli et al. (1984, 1985). Therefore, only the main features of this model will be reported here. We refer to a heterogeneous model where the external fluid phase and the adsorbent particles are described separately, with the only connection due to interphase mass transport. External Fluid Phase. The flow in the tubular unit through the bed void fraction is described by a one-dimensional pseudocontinuousmodel, where radial gradients are neglected while axial dispersion is taken into account. The first assumption derives from the process isothermality, as will be discussed shortly, while the second is due to the need of simulating processes operating with sudden and frequent changes in the feedstream composition (Morbidelli et al., 1982). Adsorbent Particle. Three series resistances to mass transport are usually present in the zeolite particle: diffusion in the boundary layer surrounding the particle, in the macropores among the zeolite crystals, and in the micropores inside the crystals themselves. The last resistance has been found to be negligible in the cases under examination (Santacesaria et al., 1982b; Morbidelli et al., 1985). Therefore, the so-called pore diffusion model, which accounts only for the first two mass transfer resistances, is used. Applying the lumping procedure proposed by Glueckauf (1955), we can express such a model in terms of only average concentration values for the fluid mixture inside the particle macropores. The obtained lumped model has been shown (Morbidelli et al., 1982) to be approximately equivalent to the complete model, where the concentration profiles inside the particles are simulated in detail, in the description of the interphase mass transport, thus allowing great simplification of the numerical solution of the adsorption unit model. Equilibrium conditions between the fluid phase in the macropores and the one adsorbed on the solid are described by using a suitable multicomponent adsorption isotherm. In particular, the Langmuir model is employed since it requires only parameters relative to the pure
mass balance in the adsorbent particle:
Unit Model
mass balance in the external fluid phase : e p ayi ayi _ _ t-=--Et
ax
aT
- ~ aypi p -Et
a7
1 a2yi Pe ax2
Jm
- --(yi Et
- ypi)-
VaGe i
(0 < x < 1, t > 0)
adsorption equilibrium isotherm: NC
ei =
Kipypi/(l + I: Kjiypj) (0
< x < 1, t >
0)
j= 1
boundary conditions:
aYi
-ax= o
(x=l,t>O)
initial conditions :
yi = Yio(x);ypi = ypjo(x) ( 0 4 x 4 1, t = 0)
components' adsorption equilibria and it can well describe the competition among various components in multicomponent adsorption. Obviously, this is an approximate model and it does not imply adherence to the monolayer theory which cannot apply to synthetic zeolites (cf. Ruthven et al., 1973). All the relevant equations of the model have been s u m marized in Table I in dimensionless form, and the adopted symbols are explained in the Nomenclature section. The entire adsorption process is assumed to be isothermal. This is due to the high concentration of adsorbable components characteristic of displacement chromatography. In fact, in such a situation, when one molecule is adsorbed another one is desorbed, so that the thermal effects of the two processes closely balance each other. The parameters appearing in the model equations have all been evaluated by Santacesaria et al. (1982) ,and Morbidelli et al. (1985). In particular, the equilibrium parameters of the Langmuir model relative to the adsorption equilibrium of pure components have been evaluated through independent experiments and are reported in Table 11. Note that, due to the large values of the equilibrium constants, the denominator of the Langmuir multicomponent model can be approximated as NC
NC
both in liquid and gas states. As a consequence, only the selectivity values, ai, = Ki/K,! instead of the absolute values of K,, need to be considered in the adsorption model. The mass transfer and the axial dispersion coefficients have been estimated in the above-mentioned works by using suitable literature expressions, and they are dependent upon the particular operating conditions. The values of the relative dimensionless parameters J,, Pe, and u are summarized in Table I11 for the various examined situations. Note that in all cases we refer to an adsorption column with internal diameter equal to 2 cm, packed with Y zeolite pellets fully exchanged with potassium, whose
Ind. Eng. Chem. Fundam., Vol. 25, No. 1, 1986 01
Table 11. Adsorption Equilibrium Parameters Ki (cma/mol)and rmi(mol/g) liquid phase (57 "C) vapor phase (150 "C) component io-3~, 1o3rmi 104Ki 1 0 3 ~ ~ m-xylene p-xylene ethylbenzene toluene isopropylbenzene
4.2 24.0 12.0 8.0
1.75 1.75 1.75 1.75
1.32 3.97 2.77 1.01
2.17
Table 111. Numerical Values of the Model Parameters for Figures 1-3a figure run L, cm T, O C At,,, min 10-2Jm 1 1 1 2a 2b 2c 3 3 3 3 3 3 3
LT GT GI LT GT GI 1 2 3 4 5 6 7
1.43 1.43 1.43 1.43
vapor phase (170 OC) 104Ki 103r-, 0.98 1.34 2.62 1.34 1.69 1.34
50 50 50 200 150 150 50 50 50 50 50 50 50
57 150 170 57 150 170 170 170 57 57 57 170 57
m
m m
20 20 20 20 20 20 20 20 20 20
0.17 1.10 1.12 0.67 3.60 3.72
10-3~e 0.19 1.04 1.08 0.75 3.06 3.18
m
m
1.12 0.17 1.12 0.17 0.17 1.12
1.08 0.19 0.19 1.08 0.19 1.08
10-sV
4.31 x 1.05 1.03. 4.31 x 1.05 1.03 1.35 1.35 4.31 x 4.31 x 4.31 x 1.35 4.31 x
10-3
10-3
10-3 10-3 10-3 10-3
1.34
vF, cm/s 5.30 x 10-3 1.61 1.69 5.30 x 1.61 1.69 1.69 1.69 5.30 x 5.30 x 5.30 x 1.69 5.30 x
10-3
10-3
10-3 10-3
10-3
"Equilibrium parameters as in Table 11. Adsorbent bed Characteristics: pn = 1.42 g/cm3, c = 0.42, tp = 0.20, up = 46.15 cm-l, i.d. = 2 cm.
characteristics are reported in detail by Santacesaria et al. (1982a). The reliability of the model has been tested by direct comparison with experimental data for the xylene isomer mixture over a wide range of operating conditions, both in liquid (Santacesaria et al., 1982b; Carrh et al., 1982) and vapor phases (Morbidelli et al., 1985). The same model has also been tested by using a different mixture, consisting of p- and o-chlorotoluene (Morbidelli et al., 1984). The satisfactory results obtained in all cases guarantee the model's reliability.
Comparison of the Separation Processes Before proceeding with the quantitative comparison, it is worthwhile pointing out some peculiar features of the two processes. The liquid-phase one is characterized by low temperature, low rates of inter- and intraparticle mass transfer, and significant axial dispersion. This leads, with respect to the gas-phase process, to a decrease of the separation efficiency and to the broadening of the breakthrough curves. Another important observation concerns the fraction of the fluid mixture present in the unit which actually participates in the adsorption process. This is given by the ratio of the amount of mixture present in the zeolite micropores and the total amount present in the bed. Due to the large hydrostatic pressure, the adsorbed fluid in micropores in the adsorption force field is similar to a liquid in a highly compressed state, independently of the aggregation state of the external flowing fluid. It follows that the fraction of the mixture participating in the adsorption process is much larger in the vapor than in the liquid phase. This obviously favors the efficiency of the process in the vapor phase, not only in the competitive adsorption step of the two components to be separated but also in the desorption step of the process. Thus, the amount of desorbent required to completely regenerate the bed operating in the gas state is less than the corresponding quantity in the liquid state. The above-reported considerations can be fully reversed by the effect of the temperature increase on the main separation characteristics of the adsorbent: the loading capacity and the selectivity between the two components to be separated. About the loading capacity of the zeolite, since the fluid adsorbed in the micropores approaches a
liquidlike behavior, it is reasonable to expect a small temperature effect. On the other hand, selectivity can be strongly affected by temperature changes. However, the selectivity, as well as the direction of the selectivity variation, depends upon the particular mixture under examination, so that general conclusions cannot be drawn. In the limiting case where the selectivity of the adsorption process is uniquely due to entropic factors (i.e., the enthalpy of adsorption is identical for the two components), its value should be temperature independent. The Case of the Xylene Isomer Mixture. For the xylene isomers, the values of the adsorption constants, Ki, and the loading capacity, Fmi,are reported in Table I1 for both the liquid state at 57 "C and the gas state at 150 and 170 "C. It appears that while the values of Piis slightly affected by temperature, the selectivity values are significantly lower a t higher temperature. In particular, the selectivity between p- and m-xylene (cypm = Kp/Km)drops from 5.7 to 3.0, as the temperature goes from 57 to 150 "C. Thus summarizing, in the case of xylene isomers the kinetic. factors favor the separation in the gas state, while the thermodynamic factors favor the separation in the liquid state. A more detailed comparison is then necessary in order to quantitatively establish their relative convenience. Besides the xylene isomers (i.e., m- and p-xylene) and ethylbenzene, the adsorption constants for some other componentswhich have been used as desorbents have been reported in Table 11. It appears that, with respect to mand p-xylene, toluene is an appropriate desorbent at 57 "C, while it is a weak desorbent at higher temperature, since its adsorption constant is lower than that of both components to be separated. On the other hand, operating in the gas state, the appropriate desorbent is isopropylbenzene, which has been studied only at 170 "C. Therefore, in order to have a fair comparison between separation processes which operate in liquid and gas states, three different processes will be examined in the following: the first ("LT") is in the liquid state, and toluene is used as a desorbent; the others are both in the gas state, and toluene ("GT") or isopropylbenzene ("GI") is used as desorbent. A comparison among these processes would give information not only about the influence of the fluid state but also about the effect of the appropriate desorbent selection on the efficiency of the separation.
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Ind. Eng. Chem. Fundam., Vol. 25, No. 1, 1986 1,0,
1
- GT ----
--
GI
LT
in-xylene
m-xylene I
A,I
/
1
0
20
40
60 -Time
I
1
80
A.'
100 (min)
/
I
120
I
140
I 160
Figure 1. Comparison of the breakthrough curves obtained by using the LT, GT, and GI processes for m-xylene and p-xylene (1:l) mixture (numerical values of model parameters as in Tables I1 and 111).
-Time b
A first comparison among the three separation processes is shown in Figure 1, with reference to the breakthrough curves of a m- and p-xylene (1:l)mixture. Identical operating conditions, except for temperature, have been used for each process (including the feed molar flow rate and the column geometry, which lead to different superficial velocities depending on the fluid density). The numerical values of the model parameters have been reported in Tables I1 and 111. From Figure 1it appears that the curves obtained in the gas state are much steeper and require much less operating time for their complete development. In particular, if one compares the breakthrough curves relative to the GI and the LT processes, in which both the appropriate desorbents are used, it appears that the first is more efficient for two reasons: (i) The amount of pure m-xylene separated before the exit of p-xylene is larger for the GI than for the LT process. This clearly appears from Figure 1 recalling that, since identical molar flow rates are used and the superficial velocity along the column is almost constant, the area below the breakthrough curves of each component a t a given time is proportional to the amount of the component which left the column at that time. It appears that operating in the gas state overcomes the effect of the decreased selectivity value. (ii) The amount of pure m-xylene is obtained in a much shorter operating time. The larger breakthrough time for the LT process is due to the larger amount of fluid mixture retained in the bed void fraction, which does not participate in the adsorption process. It is also interesting to analyze the effect of the desorbent type by comparing the GT and GI breakthrough curves shown in Figure 1. It is apparent that the enrichment in m-xylene in the outlet mixture is much more pronounced for toluene as a desorbent rather than isopropylbenzene. This behavior is characteristic of weak desorbents (such as toluene in the case under examination), and it would be completely reversed in the desorption step of the separation process. A more significant quantitative comparison between the two processes is developed in the following. A pulse of the ternary mixture m-xylene, p-xylene, and ethylbenzene has been separated by using the three examined processes, following the procedure proposed by Seko et al. (1979). The length of the adsorption column is designed in each process so that the front end of the p-xylene elution curve barely touches the rear end of the m-xylene one at the column outlet. This leads to a 1.5m-long column for the GT and GI processes and to a 2m-long one for the LT process. Each effluent is divided into four fractions, as shown in Figure 2, where the elution curves for each process are reported. Fraction A contains
(min)
0.7
-Time
0.20
(min)
IC
@
J 1
I 300
400
600 -Time
71
lmin)
Figure 2. Elution curves of a m-xylene, p-xylene, and ethylbenzene (1:l:l) mixture for (a) process LT, (b) process GT, and (c) process GI (numerical values of model parameters as in Tables I1 and 111): A, m-xylene and desorbent; B, ethylbenzene, m-xylene, and desorbent; C, ethylbenzene, p-xylene, and desorbent; D, p-xylene and desorbent.
m-xylene and desorbent; fraction B, ethylbenzene, desorbent, and m-xylene; fraction C, ethylbenzene, desorbent, and p-xylene; and fraction D, only p-xylene and desorbent. The advantage of this procedure, which is made periodic by alternatively feeding the xylene mixture and the desorbent, is to completely separate m- and p-xylene. Each obtained fraction requires a further separation through suitable distillation columns in order to obtain the desired pure components. m-Xylene is then usually sent to the isomerization process due to its limited industrial interest. In order to compare the performances of the three examined processes quantitatively, it is useful to define some characteristic separation parameters which allow us to estimate their efficiency. In addition to the adsorption column length, which is proportional to the total zeolite amount immobilized, the following parameters are considered: elution time, t, (proportional to the total desor-
Ind. Eng. Chem. Fundam., Vol. 25, No. 1, 1986 93
Table IV. Comparison of the Performance of the Three Separation Processes Whose Eluted Peaks Are Shown in Figure 2 process LT
GT GI
t!,
mAt
min
%
390 176 91
37 87 60
PDI % 63 72 65
X A
XD
0.04 0.20 0.14
0.02 0.04 0.20
bent employed and to the reciprocal of the column productivity, i.e., of the number of pulses treated per unit time); the percentage of m-xylene (mA) and p-xylene ( p ~re) covered in fractions A and D, respectively (which represent the fractions of such components which are readily obtained through a low-cost distillation, since they need to be separated only from the desorbent and not from ethylbenzene); and the average composition of m-xylene (XA)and p-xylene (XD) in fractions A and D, respectively (proportional to the purification cost of fractions A and D from the included desorbent). The values of such parameters for each examined process are reported in Table IV. Note that in the case of an adsorption unit, operated in a periodic fashion, the true productivity is given by the ratio between the percentage of a pure component separated in one cycle (mA or p D ) and the duration of the cycle ( t e ) . It is apparent that the process in the liquid state is less convenient than those in the gas state. In fact, the LT process yields lower productivity values even though it uses an adsorption column longer than that of the GT and GI processes. Moreover, as expected, the GI process gives better performance than the GT process, particularly in the required desorbent amount, which is almost halved. Strictly speaking, these conclusions are limited to the case of K-Y zeolite with the liquid phase at 57 "C and the vapor phase at 150-170 "C. However, due to the large difference in efficiency between the two processes, it is reasonable to expect that the process in the vapor phase at higher temperature is, in general, more efficient than that in the liquid phase at a lower temperature. In fact, kinetic factors are slightly affected by the type of components, desorbent, and adsorbent used, while it has been shown that these factors play a major role in determining the process efficiency. The situation can be reversed only in the case where the selectivity drops quite significantly for increasing temperature values. However, it should be recalled that the selectivity drop by a factor of 2, while going from 57 to 150-170 "C, encountered in the case under examination, has not been sufficient to overcome the beneficial effect of the kinetic factors. This observation justifies the tendency of industrial processes in the liquid phase to operate at higher temperatures, even though this requires higher pressures and then higher operating costs. An example is given by the Parex process mentioned above, which cannot be examined in detail here since it uses different adsorbent and desorbent. The conditions of the above-reported comparison have been selected in order to fall in the range of values explored experimentally, where the model's results have been verified and its reliability is then not questionable. In the next section a more general and detailed analysis of the causes for the liquid-phase process inefficiency is developed,with the aim of suggesting technological means for their removal. The General Case. From inspection of the model equations reported in Table I, which apply to both processes operated in liquid and gas states, it is apparent that the difference between the two processes is confined to the values of three dimensionless parameters. These are the fluid-to-solid mass transfer parameter J,, corresponding
Table V. Effect of J,, Pe, and u on the Efficiency of Separation Processes Operated in the Liquid and Vapor Phase" run J, RB t,, min Pe v RA 1
-
m
v"
100.00
100.00
2
Cyr,
uV
80.85
3
2,
72.12 13.82
4 5 6
Jv,
7
Cry,
Pe' Pel Pel PeV Pel Pe'
2, 2,
40 56 142
v1
1.54
u1 uv
7.92 3.71 12.76
57.61
120 80
v1
38.20
41.75
70
u'
16.80 19.03
110
Model parameters as in Table 111.
to the number of transfer units (NTU), the Peclet number Pe, and the ratio of the moles of fluid adsorbed to the moles of fluid in the macroporosity and in the interparticle volume, v. In order to restrict the comparison to these quantities, we will assume in the following identical selectivities and loading capacities of the zeolite for the processes operated in liquid and gas states. A first insight into the problem can be obtained by considering the particular case where all diffusion and dispersion effects are negligible, Le., Pe = m and J, = m. In this case the first two equations of the model in Table I reduce to ayi
aei
-ax+ - = at o
(1)
where the new dimensionless variable has been introduced [=-
7 - x
v(1 - t)
(2)
This is the model which is usually adopted by the wellknown equilibrium theory (cf. Helfferich and Klein, 1970; Rhee et al., 1970, 1971). From eq 1and 2 it appears that the processes operated in liquid and gas states, which now differ only in the value of v, are actually coincident in the x-[ plane. Thus, in the absence of kinetic resistances, the parameter v only has the effect of changing the time scale. In other words, operating in the liquid state (smaller v value) only has the effect of delaying the breakthrough time, but separation and elution time of the outlet peaks remain unchanged. This does not affect the efficiency of the separation processes when these are operated in a periodic fashion, i.e., feeding a periodic sequence of pulses. Therefore, in order to neglect this initial time delay due to the column holdup, the following comparison is performed using the variable 5 instead of real dimensionless time 7. Let us now consider the case where a pulse of a binary mixture of A and B is fed to an adsorption unit followed by a stream of a pure desorbent D. The values of the dimensionless parameters J,, Pe, and v for the liquid and gas phase are those reported in Table 111, while identical selectivities and loading capacities are taken in both cases (aBA= 2.86; aDA = 1.90; r m A = rmB = rmD = 1.75 x mol/g). The elution peaks for the two processes are shown in Figure 3, together with the solution obtained from the equilibrium theory (i.e., eq 1,run 1). The characteristic separation parameters are reported in Table V in terms of the percentage of component A (B), where B (A) is absent, separated in one cycle, RA (RB),and the elution time, t,. As expected, it appears that the process operated in the gas state (run2) is much more efficient than the one in the liquid state (run 3). In order to understand the cause of this difference, runs 4-6 have been performed, where, taking the values of the liquid-phase process as a basis, each of the parameters J,,
94
Ind. Eng. Chem. Fundam., Vol. 25, No. 1, 1985
oqK 60
80
Id0
120
IiO Id0
180
2dO
-Jr-
Figure 4. Percentage of pure A recovered per cycle ( R A ) as a function of J , for the processes operated in liquid and gas states (Pe = a,other parameters as in Figure 3).
OF I
60
-Time
'
I
\
/ , \ , 0' : 20 40 'I06 I I 1 80 100 120 140
8'0 1 160
160 1 180
I
200
(min)
Figure 3. Eluted peaks of a binary mixture A-B with desorbent D (numerical values of model parameters as in Table 111; aBA= 2.86, (YDA = 1.90, r m A = rmB = r m D = 1.75 x mol/g): 1, equilibrium model; 2, vapor phase; 3, liquid phase; 4, liquid phase with high J,; 5, liquid phase with high Pe; 6, vapor phase with low Jm and Pe; 7 . liquid phase with high J , and Pe
Pe, and u have, in turn, been set equal to the values of the vapor-phase process. The obtained elution peaks are also shown in Figure 3. It appears that the difference in the value of the parameter v is by far the most responsible for the inefficiency of the liquid-phase process. On the other hand, gas-to-solid mass transfer resistance and axial dispersion seem to play a similar, although minor, role. Recalling that the effect of u on the separation efficiency is negligible in the absence of mass transfer resistance and axial dispersion, this last result suggests that the role of v depends upon the value of the other parameters J , and Pe. This is confirmed by the results of run 7 in Table V where all the parameters are those of the vapor-phase process, except for v. By comparison with the results of run 2, it is seen that the effect of the parameter u is now much less significant. This phenomenon can be made more clear by rewriting the first two model equations in Table I, introducing the new variable {, and assuming piston flow (i.e., Pe = m): -ayL + - =do, - - - - tp 1 d(y, - yPJ ax
at
Et
(3)
at
1J
-
-
From eq 4 it follows that, as J , 00, (yi - ypi) 0; thus, the right-hand side of eq 3 vanishes, and the model becomes independent of the holdup parameter u. This behavior appears more clearly from the results shown in Figure 4,where the percentage of pure A recovered per cycle, R A , is reported as a function of the gas-to-solid mass transfer parameter, J,, for the liquid and vapor phase. It appears that lower values of the holdup u have a detrimental effect on the separation efficiency, but its amount tends to vanish for increasing values of the gas-to-solid m, eq 3 mass transfer parameter J,. Note that as J , and 4 reduce to eq 1 (which is independent of Y) and the two curves in Figure 4 tend to the same asymptotic value O f RA. Numerical difficulties due to the steepness of the elution curves prevent the solution of the complete model at very large J m values.
-
Summary and Final Remarks The separation processes of a mixture of xylene isomers, operated in the liquid (57 "C) and gas state (150-170 " C ) at atmospheric pressure, have been compared. It is found that, when the same adsorbent and an appropriate desorbent is used in both cases, the process in the gas state is much more efficient due to the increased mass transfer rate, the decreased axial dispersion, and a much lower holdup. These effects completely overcome the large drop in selectivity, due to the temperature increase when going from the liquid to the vapor phase. A more general analysis has shown that, besides thermodynamic factors, the process efficiency depends upon gas-to-solid mass transfer (J,), axial dispersion (Pe), and ratio of moles adsorbed to moles not adsorbed ( u ) . The effect of u is quite significant when the values of J, and Pe are those of the liquid phase, while it vanishes as J, and Pe m. These findings suggest some important conclusions. In the first place, the process operated in the gas state is more efficient in general, unless selectivity undergoes an extraordinarily large drop while temperature increases. On the other hand, liquid-phase processes usually require less energy, so that it may be of interest to investigate the possibility of increasing their separation efficiency. Our results show that this goal can be pursued by simply increasing the values of J, and Pe; when this is done, the detrimental effect of v, which originally is the most significant, also vanishes. In practice, the value of Pe can be increased through suitable technological strategies intended to reduce axial dispersion in industrial units (cf. Seko et al., 1982) and the value of J, by increasing the gas-to-solid mass transfer rate. Since this rate is mainly controlled by diffusion in the macropores, its dependence upon temperature is given by the dependence of the molecular diffusion coefficient, which is approximately proportional to temperature. Therefore, J, can be increased by increasing temperature which, in the case of mixtures in the vapor phase, requires a pressure increase and a consequent increase of energy. Note that the value of the parameter u is established by the value of the liquid density. It cannot be appreciably decreased simply by changing the separation operating conditions. However, according to Figure 4,this is not necessary since once J, and Pe are large enough, the effect of v on the separation efficiency becomes negligible. On the other hand, the effect of u on the time scale of the peaks' breakthrough remains unchanged, but this has no effect on the efficiency of separation processes operated in a cyclic mode. Acknowledgment The financial support of the Italian Consiglio Nazionale delle Ricerche (Progetto Finalizzato Chimica Fine e Se-
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Ind. Eng. Chem. Fundam., Vol. 25, No. 1, 1986 95
condaria) is gratefully acknowledged. Nomenclature up = ratio of the external surface to the volume of the pellets, cm2/cm3 C = concentration in external fluid, mol/cm3 C, = concentration in macropores, mol/cm3 D = axial dispersion coefficient, cm2/s GI = process in gas state with isopropylbenzene EIB desorbent GT = process in gas state with toluene as desorbent J, = vapor-to-solid mass transfer parameter = ka&,/v k = global mass transfer coefficient, cm/s K = equilibrium ratio of adsorption, cm3/mol L = length of the column, cm LT = process in liquid state with toluene as desorbent mA = percentage of m-xylene recovered in fraction A (see Figure 2), % p D = percentage of p-xylene recovered in fraction D (see Figure 21, %
Pe = Peclet number = Lv/tD percentage of component A (B) separated in one cycle see Figure 3) t = time, s t, = duration of the cycle, min u- = superficial fluid velocity, cm/s XA = average mole fraction of m-xylene in fraction A (see Figure 2) XD = average mole fraction of p-xylene in fraction D (see Figure 2) x = z/L y = molar fraction = C / p z = axial length coordinate, cm Greek Letters selectivity between components i and j according to Langmuir model = K J K . r = concentration in adsorhed phase, mol/g rm= loading capacity of the adsorbent, mol/g Atp = pulse duration, min e = external void fraction ep = particle porosity et = total void fraction = (1 - €)ep + e
aij =
e = r/r-
v = ratio of moles adsorbed to moles in the macropores and in the interparticle voids = p,(l - ep)I"/Ptt
p = molar density, mol/cm3 ps 7
= effective density of solid, g/cm3
= dimensionless time = ut/etL = dimensionless variable = (7- x ) / [ v ( l - e)]
Subscripts i = component p = macroporosity
Superscripts F = feed 0 = initial condition 1 = liquid phase v = vapor phase
Registry No, m-Xylene, 108-38-3; p-xylene, 106-42-3; ethylbenzene, 100-41-4.
Literature Cited Bailly, M.; Tondeur, D. Chem. Eng. Sci. 1981, 36, 455. Ballly, M.; Tondeur, D. Chem. Eng. Sci. 1982, 37, 1199. Berg, E. W. "Physical and Chemical Methods of Separation"; McGraw-Hill: New York, 1983. Broughton, D. B. Chem. Eng. Prog. 1988, 64(8), 80. Broughton, D. B.; Neuzil, P. W.; Pharis, J. M.; Brearly, C. S. Chem. Eng. Prog. 1970, 66(9),70. Carri, S.; Santacesaria, E.; Morbidelli, M.; Storti, G.; Gelosa, D. Znd. Eng. Chem. Process Des. Dev. 1982, 2 1 , 451. C a r 6 S.; Santacesaria, E.; Morbldelli, M.; Di Fiore, L.; Codignola, F. U.S. Patent 436 034 7, 1983. Davis, J. C. Chem. Eng. [Znt. Ed.] 1971, 78, 77. Glueckauf, E. Trans. Faraday SOC. 1955, 51, 1540. Helfferich, F.; Klein, G. "Multicomponent Chromatography"; Marcel Dekker: New York, 1970. Herrin, G. R.; Martell, E. H. Chem. Eng. [ I n t . Ed.] 1971, 78, 319. Kirk-Othmer "Encyclopedia of Chemical Technology", 2nd. ed.; Interscience: New York, 1970 Vol. 22, p 487. Mllevsky, M.; Berak, J. M. Przem. Chem. 1975, 5 4 , 698. Morbidelli, M.; Servida, A.; Storti, G.; Carrl, S. Ind. Eng. Chem. Fundam. 1982, 21, 123. Morbldelli, M.; Stortl, 0.; Carri, 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. 1985, 2 4 , 63. Rhee, H.; Aris, R.; Amundson, N. R. Philos. Trans. R . SOC.London, A 1970, 267, 419. Rhee, H.; Aris, R.; Amundson, N. R. Philos. Trans. R . SOC.London, A 1971, 269, 107. Ruthven, D. M.; Loughlin, K. F.; Holborow, K. A. Chem. Eng. Sci. 1973, 28, 701. Santacesarla, E.; Morbidelli, M.; Danise, P.; Mercenari, M.; Carrl, S. Znd. Eng. Chem. Process Des. Dev. 1982a, 21, 440. Santacesaria, E.; Morbidelli, M.; Servida, A,; Storti, G.; Carrl, S. Ind. Eng. Chem. Process Des. Dev. 1982b, 21, 446. Santacesaria, E.; Gelosa, D.; Danise, P.; Car& S. Znd. Eng. Chem. Process Des. Dev. 1985, 24, 78. Seko, M.; Miyake, T.; Inada, K. Znd. Eng. Chem. Prod. Res. Dev. 1979, 18, 263. Seko, M.; Takenchi, H.; Inada, T. Ind. Eng. Chem. Prod. Res. Dev. 1982, 2 1 , 656. Storti, G.; Santacesaria, E.; Morbidelli, M.; Carrl, S. Znd. Eng. Chem. Process Des. Dev. 1985, 24, 89.
Received for review December 28, 1983 Revised manuscript received December 5, 1984 Accepted May 8, 1985
