Ind. Eng. Chem. Fundam. 1983, 22, 172-176
172
Nomenclature A = surface area of a W/O emulsion droplet, cm2 A , = surface mea of all emulsified aqueous droplets in a W/O emulsion drop, cm2 C, = concentration of phenol in the outer aqueous phase, g/cm3. Coi = initial concentration of phenol in the outer aqueous phase, g/cm3 CI = concentration of phenol in the organic liquid membrane phase for Ri < r 5 Ro, g/cm3 CII = concentration of phenol in the organic phase of the reacted inner core for ri 5 r 5 Ri, g/cm3 Do = diffusivity of phenol in the organic phase, cm2/s D , = diffusivity of phenol in the aqueous phase, cmz/s fa = frequency of the center of the aqueous droplets with radius, R,,, per unit volume of the W/O emulsion fal = frequency of the center of the aqueous droplets with radius, R,,, per unit volume of the W / O emulsion for 0 5 r 5 Ro - R,, HLB = hydrophile-lipophile balance k = mass transfer coefficient between the outer aqueous phase and the organic liquid membrane phase, cm/s m = distribution coefficient of phenol between the aqueous and the organic phases MN = molecular weight of NaOH M , = molecular weight of phenol R = radius of an emulsion drop, cm r = radius, cm Ri = initial radius of the unreacted inner core, cm ri = radius of the unreacted inner core, cm R, = radius of the W/O emulsion drop, cm R, = radius of the emulsified aqueous droplet, cm R,,, Rrb, R,, = radius of the emulsified aqueous droplets, respectively, cm R- = radius of the inner core of an emulsion drop, cm t = time, s V , = total volume of the W / O emulsion, cm3 V , = total volume of the aqueous phenol solution, cm3 VI = dimensionless concentration of phenol, rCI/RoCoi VI, = dimensionless concentration of phenol, rCII/RoCoi W = dimensionless concentration of phenol, Co/Coi W , = concentration of NaOH in the inner aqueous phase, g/cm3
W/O = water-in-oil W/O/W = water-in-oil-in-water x = dimensionless radius, r / R o xi = dimensionless radius of the unreacted inner core, r i / R o y, y' = distances from the surface of W/O emulsion drop, cm Greek Letters 6 = boundary layer thickness of the concentration at the surface of W/O emulsion drop, cm 4 = volume fraction of the aqueous phase in the W / O emulsion drop &, $b, & = volume fractions of the aqueous phase by droplets of radius, R,,, Reb,and R,,, respectively 4al = volume fraction of the aqueous phase by droplets of radius, R,,, for 0 5 r 5 Ro - 2R,, 41= volume fraction of the aqueous phase in a W/O emulsion drop for 0 < r < Ri T , = dimensionless time, Dnt/Rn2
Registry No. NaOH, 1310-73-2; C6H,0H, 108-95-2.
Literature Cited Alessi, P.; Kikic, I.; Canepa, B.; Costa, P Sep. Sci. Techno/. 1978, 13, 613. Becher, P. "Emulsions: Theory and Practice", 2nd ed.; Reinhold Publishing Co.: New York, 1966. Boyadzhiev, L.; Sapundzhiev, T.; Bozenshek, E. Sep. Sci. 1977, 12, 541. Cahn, R. P.; Li, N. N. Sep. Sci. 1974, 9 , 565. Carnahan, B.; Luther, H. A,; Wilkes, J. 0 . "Applied Numerical Methods"; Wiley: New York, 1969; pp 446, 451. Casamatta, G.; Chavarie, C.; Angelino, H. AIChE J . 1978, 2 4 , 945. Crank, J . "The Mathematics of Diffusion"; 2nd ed.; Clarendon Press: Oxford, 1975; pp 144, 286. Cussler, E. L.; Evans, D. F. Sep. Purif. Methods 1974, 3 , 339. Ihm, S.K.; Kim, K. S.; Choi, S. J. J . Korean Inst. Chem. Eng. 1981, 19, 217. Li, N. N. AIChE J . 1971a, 1 7 , 459. Li, N. N. Ind. Eng. Chem. Process Des. Dev. 1971b, 10, 215. Li, N. N.; Shrier, A. L. In "Recent Developments In Separation Science", Li. N. N., Ed.; Chemical Rubber Co.: Cleveland, 1972; Vol I, p 163. Matulevicius, E. S.;Li, N. N. Sep. fur;f. Methods 1975, 4 , 73. Reid, R. C.; Prausnitz, J. M.; Sherwood. T. K. "The Properties of Gases and Liquid"; McGraw-Hill: New York, 1977; p 567. Shah, N. D.; Owens, R. C. Ind. Eng. Chem, Prod. Res, Dev. 1972, 1 1 , 58.
Received f o r review November 30, 1981 Revised manuscript received December 21, 1982 Accepted January 19, 1983
Continuous Multicomponent Parametric Pumping Wu Xlang-Zhlt and Phillip C. Wankat' School of Chemical Engineering, Purdue University, West Lafayette, Indiana 4 7907
A new parametric pumping method which will fractionate two noninteracting solutes is developed. Cyclic steady-state experimental results for separating pyrene from acenaphthylene in 2-propanol are reported. Results from a short column disagreed qualitatively with the local equilibrium theory. A reverse separation was observed. I n a longer column results were in qualitative agreement with the same theory. A staged equilibrium model was in good agreement with single-component separation data from both long and short columns. With two solutes present, however, agreement was only qualitative because the acenaphthylene is more strongly adsorbed when pyrene is also present.
Introduction Parametric pumping systems have been extensively studied Over t h e past dozen yews a n d has been reviewed t Department of Chemical Engineering, Beijing Institute of Chemical Technology, Beijing, China.
0196-4313/83/1022-0172$01.50/0
by Sweed (1971), Rice (1976), Chen (1979), a n d Wankat (1981). Most of the articles on Parametric Pumping have been concerned with either removing a single solute from a nonsorbed material or separating two ions by ion-exchange parametric pumping. Separation of noncompeting solutes a n d of competing solutes or ions is quite different. I n the former system the 0 1983 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 22, No. 2, 1983 Feed,
173
Top Product
CF
I
F
a
b
C
d
I
Figure 1. Basic cycle for direct mode fractionation.
Bottom Product
total amount of material sorbed at any time is variable and depends upon temperature (or other thermodynamic cyclic variables employed) and concentration of the solutes in the system. In the ion-exchange systems electroneutrality must be satisfied and all sites must be covered. If the sorption of one ion is decreased as the temperature or pH is increased, then the sorption of the other ion must be increased. This coupling makes multi-ion separations much easier than multisolute separations where the solutes are not coupled. Multicomponent separations of nonionic systems by parametric pumping have not been extensively studied. Butts et al. (1972) used the local equilibrium model theoretically to consider a batch separation of multicomponent mixtures. They varied the operating parameters of the pump so that species could be removed one at a time. No experiments were reported. Ahmed (1974), Chen et al. (1974), and Shaffer and Hamrin (1975) separated multisolute mixtures. One solute was obtained in one reservoir (dissolved in nonadsorbed solvent) while all the solutes and solvent appeared in the other reservoir. In this paper a new parametric pumping method for fractionation of noncompeting solutes is presented. The local equilibrium model first developed by Pigford et al. (1969) is used qualitatively to explain the process. Then experimental results for the separativ of pyrene and acenaphthylene are presented and compared to staged model predictions. Operating Techniques The basic operating technique for separation of two noninteracting solutes in a direct mode thermal parametric pump is shown in Figure 1. During part a of the cycle, fresh feed is input to the column at a temperature T, or TI. During part b the downflow continues from the top reservoir reflux at an intermediate temperature TI, and a separation of solutes is obtained within the column. During part c, the low-temperature section at T,slows down the upward movement of A while the high-temperature section at T H makes solute B move faster. Upward flow is continued during portion d of the cycle, but at cold temperature, T, This portion of the cycle produces solvent free of solute A for reflux during the next cycle. Part of the fluid withdrawn during part b is taken as the bottom product which contains solute A concentrated in the nonadsorbed solvent. The remainder of this fluid is sent to a reservoir and refluxed to the column during parts c and d. Either mixed or unmixed reservoirs can be used. Sim-
Figure 2. Characteristic solution from local equilibrium model for segmented direct mode system.
ilarly, part of the fluid exiting during part c is withdrawn as a top product consisting of solute B concentrated in solvent. The remainder of the fluid exiting during parts c and d is sent to the top reservoir for later reflux to the column. In our case the equilibrium constants of the two solutes (pyrene, B, and acenaphthylene, A) are more different at the low temperature T, than at the other temperatures, TI and TH. During part a of the cycle, the column is set at T, so that A and B move farther apart. This makes separation easier during the rest of the cycle. At temperature TI we desire solute A to have a wave velocity considerably higher than that of solute B. T H should be chosen so that the B wave velocity is greater than the A velocity at T,.Thus B will rapidly elute from the column. This will allow the removal of B from the column while A remains in the lower section of the column where the temperature is low. The cold temperature, T,, must be chosen so that sufficient liquid for reflux can be obtained at the top of the column, but the reflux liquid should not contain solute A. This temperature must be low enough that solute A is fairly strongly adsorbed. The success of this operating cycle depends upon proper choice of the temperature levels and proper timing. Solute B must not break through during parts a and b of the cycle, and solute A must not break through during parts c and d. Some A and B may remain in the column at all times. The location, X, where the column jacket changes temperature must be selected so that all the B exits from the top of the column and none of the A does. Inequality constraints for cycle times and X have been developed but will not be presented here. The repeating steady-state solution using the local equilibrium model (Pigford et al., 1969; Rice, 1976; Wankat, 1981) for this direct mode scheme is shown in Figure 2. The solute wave velocities shown by slopes of straight lines in Figure 2 are easily calculated from the local equilibrium theory V UCi = 1+
(: g)
The predicted separation is shown in Figure 2. In our experiments pyrene was more strongly adsorbed and
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Ind. Eng. Chem. Fundam., Vol. 22, No.
2, 1983
should concentrate in the top product. If solute B has a higher heat of adsorption than A then solute B’s adsorption isotherm will be more temperature sensitive. In this case a segmented jacket may not be required. The entire column would be a t the high temperature during step C. We did not observe this behavior, but this separation scheme would probably work to separate toluene from aniline in the system toluene-anilinen-heptane on silica gel (see Chen et al., 1974). The basic scheme shown in Figure 1 can also be adapted to the recuperative mode of operation. Two columns connected in series would be used. During step c a heat exchanger would be placed between the sections labeled T, and TH.The local equilibrium solution for the recuperative mode is easily developed, but it will not be shown here. All our experiments and calculations were done with the apparatus shown in Figure 1. The discrete-flow, discrete-transfer, staged model developed by Wankat (1973) for batch parametric pumping was adapted to the system shown in Figure 1. The number of “equilibrium stages” is an adjustable parameter in the staged model. Experimental Section Polyclar AT (GAF), a commercial cross-linked polyvinylpolypyrollidone, was used as the adsorbent. A range of particle sizes was isolated by dry sieving. Soluble material was extracted by boiling in 10% HC1 for 10 min, and residual fines were removed by repeated washing and decantation in water. Then the particles were washed with 2-propanol in a filtration funnel. The particles were packed in the column by simple sedimentation by use of a column packing reservoir and then were compacted by pumping 2-propanol through the column. The product concentrations were determined off-line with a PerkinElmer double-beam spectrophotometer at wavelengths of 230 and 272 nm. Equilibrium constants were determined from breakthrough experiments for each solute. Feed concentration was 1.52 to 1.54 X lo* g/mL of pyrene or acenaphthylene in 2-propanol. Our results follow the equations
K,, = 0.0402 exp
( (
KACE= 0.2021 exp
) )
2.767 X lo3 RT
1.462 X lo3 RT
(2) (3)
where R = 1.98 (cal/deg mol) and T i s in K. Our results disagree with those of Goldstein (1976), obtained with pulse tests. The time distributions predicted by the characteristic method with our data are in agreement with the experiments for the parametric pump. The first experimental parametric pump was 27 cm long and was packed with 20 to 40 mesh particles. Syringe pumps were used for feed and reflux. The preliminary experiments showed that both anthracene and pyrene concentrated in the bottom although the local equilibrium model predicted that pyrene should be in the top. The staged model with less than 27 stages agreed qualitatively with the data. Thus, for short columns the local equilibrium model is qualitatively wrong. The apparatus was redesigned and high-pressure Milton-Roy minipumps were used for feed and reflux. Water circulation was controlled by solenoid valves and a cam timer. Since this column was 54 cm long and was packed with 80 to 100-mesh particles, there should be significantly more stages. Solutes separated were pyrene and acenaphthylene. Details of the column and operating conditions are in Table I.
Table I. Operating Conditions for Parametric Pumping Experiments; Base Case: Runs 1,2 , 3 length of column cm 54 top section/bottom section 211 size of particles, mesh 80-1 00 operating temperarure, “ F 38, 100,150 flow rate, mL/min 0.88 period of one cycle, min 96 time distribution, min: downflow, Tc and TI 4, 45 upflow segmented col 37 upflow a t T , 10 bottom product taken off at 4 to 6 rnin for run 4 1 4 to 1 6 top product taken off at 71 to 73 rnin (22 to 24 rnin in upflow) for run 4 26 to 28 rnin in upflow waiting period when 8 min temperature was changed total time for cycle 126 rnin /
,
. O ’ . Y
I
2k
12 1.10.
OF
3k
$8
0
CYCLES
Figure 3. Pyrene product concentrations vs. number of cycles: (X) bottom product; (m) top product; run no. 1. Curves are from staged theory with 45 stages. See Table I for experimental conditions.
Results A total of six parametric pumping experiments were done with the longer column, both with a single solute (pyrene or acenaphthylene) and with two solutes (pyrene and acenaphthylene). The results, including the theoretical predictions from the staged model, are given in Figures 3 through 6 to illustrate various aspects of the separation. Experimental results were obtained both for start-up and after the repeating steady state had been reached (usually the error *4%). The repeating steady state was usually reached after 50 to 60 cycles, starting with a clean column. The start-up results for pyrene as the only solute are shown in Figure 3 while the acenaphthylene start-up is shown in Figure 4. The slower moving pyrene concentrates in the top product while the faster acenaphthylene concentrates in the bottom. In the usual parametric pumping system both solutes would concentrate in the same reservoir. The solid lines are the predictions of the staged model with 45 and 27 stages for pyrene and acenaphthylene, respectively. The predictions appear to be quite satisfactory. The large difference in number of stages implies that there is considerably more dispersion of acenaphthylene. The measured separation factors are given in Table I1 for all runs.
Ind. Eng. Chem. Fundam., Vol. 22, No. 2, 1983 175
* L 1.6
1
LL V \
CI V
OF CYCLES Figure 4. Acenaphthylene product concentrations vs. number of cycles: ( X ) bottom product; (m) top product; run no. 2. Curves are from staged theory with 27 stages. See Table I for experimental conditions. NO.
1'.6
1.2
to
'
10
I 59
40
.30
20
TIME ( M I N , ) Figure 5. Pyrene concentrations exiting from top and bottom of column at repeating steady state. Top product is plotted with time beginning at start of upflow: (X) bottom product; (m) top product; run no. 1. Curves are from staged theory with 45 stages. See Table I for experimental conditions.
Table 11. Experimental Separation Factorsa run no.
1 acenaphthylene pyrene a
and inside the particles. The theoretical calculation predicted that the concentration profile changed discontinuously, but the experimental results show a continuous change. Agreement between theory and experiment for acenaphthylene was somewhat worse than that for pyrene. Once we were able to concentrate single components in the desired reservoir, the obvious next step was to separate mixtures of the two solutes. The time course of this separation is shown in Figure 6. As expected, pyrene concentrated in the top and acenaphthylene in the bottom. Until cycle 60 this experiment was exactly the same as in Figures 3 and 4. The pyrene experimental results in Figure 6 are quite similar to those in Figure 3, but acenaphthylene showed less separation than in Figure 4. .Thus, even at the very low feed concentrations employed, 1.52 X lo+ g/ mL, the pyrene appeared to affect the acenaphthylene. In fact, the acenaphthylene results shown in Figure 6 were consistent with the hypothesis that acenaphthylene was more strongly adsorbed when pyrene was present. This cooperative adsorption is unusual and is quite different from the usual case of competitive adsorption. Separate breakthrough experiments agreed with this hypothesis. The pyrene theoretical curves shown in Figure 6 are exactly the same as those in Figure 3. The acenaphthylene theoretical curves utilize the K values appropriate for the pyrene feed concentration and show less separation than in Figure 5. The fit between theory and experiment for acenaphthylene is not nearly as good as in Figure 5. This is not surprising since a single pyrene Concentration, the feed concentration, was used to adjust the acenaphthylene K values. ~ ~To study the effect of the product withdrawal time these times were changed at cycle 60 and the run (now run no. 4)was continued as shown in Figure 6. Acenaphthylene separation increased and pyrene separation decreased. Thus the designer has some control over the separation and can optimize for one component. Two additional runs were made with a fluid velocity times that used in previous runs. In run no. 5 the relative timing was the same as in run no. 3. That is, all times in Table I1 were multiplied by 5 / 8 . In run no. 6 the relative timing was the same as in run no. 4. The separation factors
-
.4
.o
NO. OF CYCLES Figure 6. Product concentrationsvs. number of cycles: (X) pyrene bottom product; (m) pyrene top products; (+) acenaphthylene bottom product; (A)acenaphthylene top product. Run 3 up to cycle no. 60. Run no. 4 after cycle 60. Curves are from staged theory. See Table I for experimental conditions.
2.92
2
3
2.51 1.57 3.17
4
5
6
2.08 2.38
1.67 2.94
1.98 2.36
Separation factors: a~~~ = C B ~ J C Tamr ~ ~ ;= C
T
~
CBot.
Figure 5 shows the concentration-time profiles for pyrene for the last cycle (repeating steady-state). The material exiting at the top has been superimposed on the bottom concentration by restarting the clock at the start of upflow. The calculated profiles do not match the experimental profiles as well as in Figures 3 and 4, but there is rough agreement. One of the reasons for the lack of fit might be the resistance to heat transfer inside the column
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Ind. Eng. Chem. Fundam., Vol. 22, No. 2, 1983
are shown in Table 11. The factors for runs 3 and 5 are quite similar, as are those for runs 4 and 6. Thus in this operating range fluid velocity does not greatly affect the separation. Runs 5 and 6 have the advantage of reaching the repeating steady state much faster since the cycles are shorter. Discussion Several novel aspects have been illustrated. First, we developed a new parametric pumping scheme for continuous fractionation of adsorbed, noninteracting solutes. None of the schemes in the literature can do this. Our scheme should also work for concentrated solutions. With larger shifts in equilibrium much higher separation factors should result. Second, our experimental runs were long-term runs reaching the steady cyclic state. With 126 min per cycle and 50 to 60 cycles, each run took a week. These runs illustrate that the parametric pump can run for long periods. Third, we found that the local-equilibrium theory was qualitatively incorrect in the short column. Both the staged model and the experimental results showed separations for pyrene which were the inverse of those predicted by the local equilibrium model. This reinforces warnings in the literature that the local equilibrium model must be used with discretion. Fourth, our data allow for a direct comparison with cycling zone adsorption. Foo et al. (1980) used a multiple-zone cycling zone adsorber to separate pyrene, anthracene, and acenaphthylene in 2-propanol on Polyclar AT. The separations they obtained were much sharper and at higher throughputs. Thus cycling zone adsorption was a better method for separation of these solutes. For different separations this conclusion might change. Finally, the observed c o o p e r a t i v e adsorption was unexpected. The increase in K values of acenaphthylene when pyrene is present (cooperative adsorption) may be due to acenaphthylene preferentially adsorbing on pyrene which has been already adsorbed. Although we have not proved this hypothesis, it is consistent with the data and the structure of the molecules. Acknowledgment This research was partially supported by NSF Grant number CPE-8006903. Discussions with Roger McGary were very helpful.
Nomenclature A = faster moving solute B = slower moving solute C = fluid concentration K = q / c , linear equilibrium constant L = length of column q = amount of solute adsorbed R = gas constant t = time T = temperature UCi= solute velocity, eq 1 V = interstitial fluid velocity X = location of jacket segment z = axial distance Greek Symbols a = separation factor, defined 6 = porosity
in Table I1
Subscripts C = cold
H = high or hot I = intermediate i = solute species Registry No. Pyrene, 129-00-0;acenaphthylene, 208-96-8.
Literature Cited Ahmed, 2. M. Paper F2-2,AIChE-GVC Joint Meeting, Vol. I V of Preprints, Munich, Germany, Sept 17-22, 1974. Butts, T. J.; Gupta, R.; Sweed, N. H. Chem. Eng. Sci. 1972,27,855. Chen, H. T. ”Parametrlc Pumping”, I n “Handbook of Separation Techniques for Chemical Engineers”; Schweltzer, P. A., Ed.; McGraw-Hill: New York, 1979;Sect. 1.15. Chen, H. T.; Lin, W. W.; Stokes, J. D.; Fabisiak, W. R. AIChEJ. 1974, 20,
306. Foo, S.C.; Bergsman, K. H.; Wankat, P. C. Ind. Eng. Chem. Fundam. 1960. 79, 86. Goldstein, G. J . Chromatug. 1976, 729, 61. Plgford, R. L.; Baker, B.; Blum, D. E. Ind. Eng. Chem. Fundem. 196P, 8 ,
144. Rice, R. G. Sep. Purif. Methods 1976, 5 , 139. Shaffer, A. G.; Hamrin, C. E. AIChE J . 1975,27, 782. Sweed, N. H. I n “Progress in Separation and Purification”, Perry, E. S.; Van Oss, C. J., Ed.; Vol. 4,WUey-Interscience: New York, 1971;pp 171-240. Wankat, P. C. I n d . Eng. Chem. Fundam. 1973, 72, 372. Wankat, P. C. “Cycllc Separation Techniques”, I n “Proceedings of NATO AS1 Conference on Percolatlon Process, Theory and Appllcatlons”, Rodrlgues, A. E.; Tondeur, D., Ed.; Sijthoff and Noordhoff: Alphen aan den Rijn, Netherlands, 1981;pp 443-516.
Receiued for reuiew December 11, 1981 Reuised manuscript receiued November 4, 1982 Accepted January 19, 1983
