10
Ind. Eng. Chem. Fundam. 1983,
inating part) in elongational flows. The next logical step forward is to investigate the stability of extending viscoelastic films. To do this, one is immediately faced with a bewildering collection of constitutive equations. The recent review of Denn (1980) on the mechanics and stability of viscoelastic fibers would provide a convenient starting point for this development. Conclusion The linear stability theory predicts the onset of instability in the casting of power-law liquid films. The critical extension ratio increases with the power-law index. However, this stability enhancement is less marked than for fiber spinning. For n < 1.2 the perturbed film shows thickness oscillation but remains uniform across its width. For n > 1.2 instability manifests itself as waves travelling across the width of the film. Nomenclature A = dimensionless wave number, a1 = rate of strain tensor = extension ratio, h(O)/h(l) f = applied tension per unit film width h = film thickness H = dimensionless film thickness, h/ho I1 = second invariant of rate of strain tensor k = consistency, material constant 1 = distance between die exit and chill roll n = power-law index, material constant p = isotropic pressure q = volumetric flow rate per unit film width t = time T = dimensionless time, tuo/l t,,, t, t,,, t,, = components of stress tensor u = velocity component in the stretch direction U = dimensionless u, u/uo u = velocity component normal to film V = dimensionless u, vho/2uol w = velocity component across film width W = dimensionless w , w / u o
x =
22, 10-16
coordinate in the stretch direction
X = dimensionless x , x / l
Y = coordinate
to film
=
k 1~
Y , 2y/ho
~
'
width ~
~
~
l
Greek Letters
~~
a = disturbance wave number @ = dimensionless group, f P / (2"+'kquo"-') 6;, = Kronecker delta p w
= Newtonian viscosity = disturbance frequency
wr = real part of frequency wi = imaginary part of frequency D, = dimensionless w,, w,l/uo
Di = dimensionless ai, wil/uo
Subscripts 0 = condition at die exit Superscripts
_ -- steady-state variables
2
*
= disturbance quantities = d/dX
Literature Cited Agrawal, P. K., et al. Trans. SOC.Rheol. 1977, 21, 355-379. Chang, J. C.; Denn, M. M.; Geyllng, F. T. Ind. Eng. Chem. Fundam. 1981, 20, 147-149. Denn, M. M. Ann. Rev. FIuUMech. 1980, 12, 365-387. Donnelly, G. J.; Weinberger, C. B. Ind. Eng. Chem. Fundam. 1975, 1 4 , 334-337. Geider, D. Ind. Eng. Chem. Fundem. 1971, 10, 534-535. Pearson. J. R. A,; Matovlch, M. A. Ind. Eng. Chem. Fundam. 1969, 8 , 605-609. Petrie, C. J. S. "Elongational Flows"; Pltman: London, 1979. Shah, Y. T.; Pearson J. R. A. Ind. Eng. Chem. Fundam. 1974, 13, 134-138. Yeow. Y. L. J . Fluid Mech. 1974, 66, 613-622.
Received f o r review August 11, 1981 Revised manuscript received August 26, 1982 Accepted September 23, 1982
Improved Preparative Liquid Chromatography: The Moving Feed Point Method Roger S. YcGary' and Phllllp C. Wankat School of Chemical Engineering, Purdue University, West Lafayette, Indiana 4 7907
A moving feed point, high performance liquid chromatograph was developed using a series of short columns followed by a longer development column. Separations of naphthalene, anthracene, and pyrene with Polyclar AT as the statlonary phase were performed wRh 2-propanol as the mobile phase. Comparisons with the conventional stationary feed system showed that for long feed pulses the moving feed technlque had an average decrease of 50% of component bandwidth at the optimum feed velocity. Resolutions for binary separations were increased by an average of 50% at the optimum feed velocity. At the same resolution the feed capacity was increased by up to 300%. Similar improvements were shown for ternary separations. A linear local equilibrium model including dispersion was used successfully to predict the experimental results.
tions. Some of the reasons for this are discussed by Broughton et al. (1970). The usual form of elution chromatography is thermodynamicallyinefficient. As a result, Universal Oil Products developed a simulated countercurrent adsorption (Sorbex) which is much more efficient and has been a commercial success (Broughtonet al., 1970;
Although liquid chromatography was used by Shearon and Gee (1949) for industrial scale separation, it has not become a standard unit operation for industrial separaCaltex Petroleum Corporation, New York, NY. 0196-4313/83/1022-0010$01.50/0
0
1983 American Chemical Society
~
~
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983 11
01 ~
__
-I
_
_
_
FEED RESERVOIR
~ 5.0 CH COLUMNS
30.4 CM COLUMN
-
1 U-V OETECTOR
@
I
r;, --& . I\ - STRIP-CHRRT -___ RECORDER
SOLVENT PUMP
L
J
COLLECTION VESSEL SOLVENT RESERVOIR
Figure 1. Schematic of apparatus.
deRosset et al., 1976; Neuzil et al., 1980). Although the simulated countercurrent system is thermodynamically more efficient, it is limited to doing a binary separation and is much more complex than elution chromatography. Wankat (1977a) proposed a hybrid system which retains characteristics of both elution chromatography and the simulated countercurrent system. During the feed pulse the feed position was move continuously up into the column at a velocity that lies between the two solute velocities. Solvent was continuously fed into the bottom of the column. Elution development with solvent was used when the feed pulse was over. This method reduces irreversible mixing of solutes near the feed point. Wankat (1977b) extended the method to two-dimensional separations. The proposed method is general and could also be applied to gas chromatography. In actual practice a segmented column with feed ports at distinct locations would probably be used. Wankat and Ortiz (1982) studied this scheme for gel permeation chromatography. They found improved resolution, narrower bands, and higher feed throughputs. In this paper a similar method is used for high performance liquid chromatography (HPLC).The arrangement of the column is shown in Figure 1. Solvents flows continuously into the first of a series of small columns. In Figure 1the feed pulse is broken into five equal parts and fed sequentially into the five feed ports. The average feed velocity can thus be varied at will. After the feed pulse, the solutes are eluted with pure solvent. Near the feed point, operation is similar to the simulated countercurrent system. Near the product end of the column the system is similar to a normal preparative chromatograph. Multicomponent systems can be separated with a higher thermodynamic efficiency than in an elution chromatograph. The moving feed point system is intermediate in efficiency and complexity between the normal preparative chromatograph and the simulated countercurrent system.
Theory The advantages of using a moving feed can be demonstrated with the local equilibrium model. This model (see Sherwood et al., 1975) has been applied to the moving feed point system by Wankat (1977a, 1977b) and Wankat and Ortiz (1982). By neglecting dispersion, the equations can be solved by the method of characteristics. For the con-
Figure 2. Characteristic solution for a stationary feed system; models the naphthalene-anthracene separation; N is naphthalene; A is anthracene. r % j PI
'.O@
10'.00
20.m
Tr 30.oD
Y0.W
60.00
TIME I H I N l
60.00
7O.m
Q'.W
I
.m
Figure 3. Characteristicsolution for a moving feed system using five columns; models the naphthalene-anthracene separation ukav) = 1.0 cm/min; N is naphthalene and A is anthracene.
ventional stationary feed system the characteristic solution can be obtained (Sherwood et al., 1975; Wankat, 1977a) using the following boundary condition
c = co
(0 < t I tf, z = 0)
(1)
The solution is that concentration is constant along characteristic lines. With linear equilibria, q = kc, the slopes of the characteristic lines on a z vs. t plot are U 'BOlUk
=
1
1-C
+ --p& E
This solution is shown in Figure 2. In Figure 2 the first pulse of feed is input for 25 min (tF) and then is followed with pure solvent for 15 min. The outlet concentrations can be determined at z = L. This model predicts that the outlet concentration will be a square wave going from zero to the feed concentration and back to zero. As shown in Figure 2, the two solutes overlap considerably at the outlet for this set of operating conditions. For a step-wise moving feed system the characteristic solution can be obtained using a series of pulse inputs c = co (0 < t Itl, z = 0; tl < t It z , z = 2,; t* < t It 3 , z = 2 2 ; t 3 < t It 4 , ~= 2 3 ; t 4 < t It f , z = 24) (3)
Since the problem is linear, the solution can be obtained by superposition. Characteristic lines have the slope given
12
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983
in eq 2. This solution is shown in Figure 3. In Figure 3 the first feed pulse is again input for a total of 25 min. However, now the feed pulse is broken into five equal parts and input at z = 0,5,10,15,20, and 25 cm for 5 min each. The horizontal lines in Figure 3 represent these feed locations. The second feed pulse is started at 20 min and is input in the same way. This feed pulse is outlined only in Figure 3. The outlet concentrations can be determined at z = L. Note that naphthalene and anthracene from the first pulse are completely separated from each other while this was not the case in Figure 2. Also, the bandwidths of the N and A peaks in Figure 3 are considerably less than those in Figure 2. The time to input the second pulse was arbitrarily chosen so that the leading edge of the naphthalene peak would just touch the trailing edge of the anthracene peak. Thus the separation of A and N from different feed pulses should be the same in Figures 2 and 3. Comparing Figures 2 and 3, we see that the second feed pulse is input much sooner with the moving feed method. In fact, the moving feed system shown in Figure 3 always has feed input somewhere in the system and part of the time has feed input simultaneouslyat two different feed locations. Thus much more feed throughput is possible with the moving feed system at the same resolution. The reasons for the improved separation can be determined by comparing Figures 2 and 3. In both figures the region labeled N + A contains both components. These regions are caused by continual mixing of naphthalene and anthracene which were fed at different times. That is, the characteristic lines for N and A cross. The moving feed system is arranged so that the distance a component must travel to exit these mixed regions is shorter. A second important reason for improved performance is that the last A characteristic is input much earlier in the moving feed system. In Figure 2 the last A characteristic for the first pulse enters at 25 min while in Figure 3 it enters at 5 min. Thus solute A must exit 20 min earlier in the moving feed system. This allows the operator to input the next pulse 20 min earlier and greatly increases the throughput. Because dispersive effects cannot be neglected in reality, the local equilibrium model should be solved with the second-orderdispersive terms included. This solution was obtained for linear isotherms by Lapidus and Amundson (1950) and an approximate solution was reported for columns of sufficient length by Lightfoot et al. (1962). This latter solution for breakthrough is cA x A = - = -
1
+ erf [PeZ1/2(V- V)/2(VV)'/'I}
(1
(4)
CAO
where V = tuSt is the elution volume, V = Szt(1 + k? is a measure of bed capacity, and Pe, = ZU/(DAM + E m )is the Peclet number. The Peclet number is related to the number of plates Pe, = 2N = 2z/(HETP)
(5)
Since the system is linear, the solution for the moving feed system can be obtained by superposition. Let the general form of the breakthrough curve solution be XA
= x(z,v)
(6)
For a pulse of feed the solution can be represented as (Lightfoot et al., 1962) XA
= X ( Z , v ) - X(z,V - V")
(7)
A similar elution curve will result from the introduction of feed at each of the feed points in a moving feed system.
Table I. Experimental Conditions feed concn, c f a
component
.____
naphthalene anthracene pyrene
1.0 X lo-' mol/mL 1.0 X 10.' mol/mL 1.0 X lo-' mol/mL
solvent solvent flow rate feed flow rate estimated porosity, E overall HETP temperature U V wavelength
2-propanol, 99+% 0.72 mL/min -0.05 mL/min 0.37 0.30 c m 25 ' C a 254 n m for single solutes 254 and 280 nm for multisolute runs
component velocity, u , 1.15 cm/min 0.85 cm/min 0.62 cmimin
-
port
remaining bed length, cm
--_--_I_-______-~_------
1 2 3 4 5
50.4 45.4 40.4 35.4 30.4
a In 2-propanol. Fluctuations in temperature are within a few degrees which does not change column conditions appreciably.
The elution curves resulting from the individual feed pulses can be summed to give a single equation representing the elution curve resulting from using a moving feed. X A = [X(L,v) - x ( L , v - v")] [ x ( L - z , v - v") X ( L - z , v - 2V")] [ X ( L- 22, v - 2VO)- X(L - 22, V - 3Vo)] [ X ( L- z3,V - 3V") - X(L - z3,V 4Vo)] + [X(L - t4,V - 4V") - X(L - z ~ , V - 5Vo)] (8)
+
+
+
When the linear dispersion model is used, X is given by eq 4. Equation 8 can be easily solved by computer using parameters determined by the experimental conditions. Experimental Section The experimental equipment used was shown in Figure 1. The adsorbent bed is split up into five columns with four of the columns 5 cm long and the last 30.4 cm in length. The columns were 3/8-in.0.d. stainless steel tubes equipped with Swagelok zero-dead-volume end fittings with 2-pm stainless steel frits; 1/16-in.stainless steel tees connected the columns. A Cheminert 6-way automatic rotary valve controlled by a Chrontrol DL timer was used to change the location of the feed point. A Milton Roy minipump was used for the solvent pump, and a Rainin H.P. pump was used for the feed pump. The feed was introduced into each of the five feed ports for 1/6 of the total feed pulse. Thus the average feed velocity is inversely proportional to the total feed time. The columns were packed with 80-100 mesh polyvinylpyrollidone (Polyclar AT) using a modified slurry packing technique (McGary, 1981). The chemical systems studied were chosen from Goldstein (1976). Solutions of naphthalene, anthracene, and pyrene were separated using 2-propanol as the solvent. A Perkin-Elmer on-line UV spectrophotometer was used to record the chromatograms. The experimental conditions are summarized in Table I. The HETP was determined from pulse experiments with the conventional operating mode (e.g., see Snyder and Kirkland, 1974). The results are presented as reduced concentration vs. time. The reduced concentration was defined as c/co, where c is the measured concentration in the product and
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983 13
f2 EXPERINENTRL DRTR .___ MODEL WITHOUT
DISPERSION
- MODEL WITH DISPERSI3N
2.0004
9.m
Table 11. Percent Increase in the Amount of Feed Separated per Hour at a Specified Resolution Using a Moving Feed (Experimental Data) naphthaleneanthracene
-
naphthalenepyrene
anthracenepyrene
%
%
%
reso- increase reso- increase reso- increase lution in m t / h lution in amt/h lution in amt/h 0.5 0.6 0.7 0.8
107 160 219 302
0.9
1.0 1.1 1.2 1.3 1.4 1.44
90 96 109 120
0.6 0.7 0.8 0.84
125 162 200 206
131 129 121
co is the concentration of solute actually entering the column (after mixing with solvent). This definition of co satisfies eq 3. Because of the definition, the reduced concentration will be 1.0 after a normal breakthrough pattern is completed. In a moving feed system the reduced concentration can be greater than 1.0 since solutes fed at different times can overlap as shown in Figure 3.
Results Comparisons between theory and experiment for one pulse of a single solute are shown in Figure 4 for the stationary feed and in Figure 5 for the moving feed. The Peclet number was determined from the stationary feed experiment. The local equilibrium model without dispersion correctly predicts when the peak maximum exits, but'it does not show any dispersion. The local equilibrium model with dispersion gives a good fit of the experimental data. Comparison of these figures shows that the moving feed pulse is narrower and the naphthalene is more concentrated. Figures 6 and 7 show example chromatograms for the stationary and moving feed systems for the separation of ternary mixtures. Details of the experiments are given in Table 11. The moving feed system again has less dilution, narrower bands, and all three solutes exit earlier. The dashed line is the shape of the concentration trace resulting when a single wavelength is used on the W recorder. Our experimental results showed that for these dilute feed solutions the multicomponent separation results can be obtained by superposition of the single component chromatograms shown as the solid lines (McGary, 1981). Thus most of the experiments were done with single components and superposition was used to predict binary and ternary results.
1.0
Figure 5. Comparison of local equilibrium models for a moving feed system for a 25-min total feed time of naphthalene.
A wide range of experiments was performed for overall feed pulses up to 50 min. The experimental results were compared to the prediction of the dispersion model. Figures 8 and 9 show the bandwidth as a function of total feed time. The moving feed system gives shorter bandwidths than the stationary feed system for long feed pulses and goes through a minimum in the region where the feed velocity is the same as the component velocity. (The feed velocity is inversely proportional to the total feed times.) At the optimum feed velocity for each component the bandwidth is approximately 50% smaller than for the stationary feed case. The minimum bandwidth is predicted by both theories, but it is easiest to see from the local equilibrium model without dispersion. If the feed velocity were increased in Figure 3 until the feed velocity equaled the naphthalene velocity, all of the horizontal feed lines would be enclosed by the same pair of naphthalene characteristic lines. This gives a minimum bandwidth. As the feed velocity is increased further the bandwidth will again increase. Resolution was determined using the standard definition (Snyder and Kirkland, 1974)
where tR2 and tR1are the component retention times and t, and t, are the component bandwidths. Figures 10 and 11 show the resolution in binary separations as a fraction of the total feed time. The moving feed system shows increased resolution compared to the stationary feed system for longer feed pulses. A t the optimum feed velocity (optimum total feed time in these experiments) the resolution is significantly higher (50 to 95%) than the
14
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983
7-~
3-600
3.m
B NRPHTHHLENE A RNMRCENE 3 PYRENE
-!
Figure 6. Experimental chromatogram for a stationary feed system; 25-min feed pulse. NRPHMALENE ANTHRRCENE E PYRENE
I
A
3.m
i
2.m
j
p
Figure 7. Experimental chromatogram for a moving feed system; 25-min total feed time.
corresponding stationary feed experiments. Improved resolution occurs because of less mixing and is illustrated in Figure 3. As a measure of capacity the amount of feed that can be separated per hour using repeated injections was determined. The next feed pulse will be injected so that the same resolution between peaks will be obtained. Figures 12 and 13 show the resolution as a fraction of the amount of feed separated per hour. In Figure 13, feed times greater than 60 min mean that feed would be injected simultaneously a t the different points. These results were obtained by superimposing single peaks obtained with single-component runs. Comparison of Figures 12 and 13 shows that higher resolutions can be obtained with the stationary feed system but only at very low throughputs. A t higher feed throughputs the moving feed system can be significantly better. This comparison is shown in Table
11. If a resolution greater than 0.8 was desired for the naphthalene-anthracene separation, a longer final column could be used. When ternary mixtures are separated, the resolutions between all peaks will not be equal. For the system used here the solutes will exit in the order naphthalene, anthracene, and pyrene. The resolution between anthracene and pyrene will be better than the resolution between naphthalene and anthracene. The next feed pulse was timed so that the resolution between pyrene (from the first pulse) and naphthalene (from the second pulse) was the same as the anthracene-pyrene resolution (from the same pulse). Figure 14 shows the results. The experimental data shown (again obtained by superposition of single pulses) and the high resolution model results are for the anthracene-pyrene resolution while the low resolution model results are the naphthalene-anthracene resolution. Ex-
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983
-.-
I-.--
,
Q NRPHTHRLENE
A
b NRPHTHRLENE-RNTHRRCENE
RNTHRRCENE
A WPHTWILENE-PYRENE
LII PYRENE
60.00-
ANTHRACENE-PYRENE
- HdDEL
60.00-
f,
5 40.00-
3
1.333-
+ 3
I8
El
J (0 0
x
&
0 30.00-
z U a
20 .oo
15
-
10.00-
1.000-
.667
-
.333
-
WA CI
0
D 0
.00
Figure 8. Bandwidth vs. total feed time for stationary feed system. 70.00
Figure 10. Resolution w. total feed time for stationary feed system; binary pairs.
I 0
NRPHTHRLENE
A
RNTHRRCENE
0 NRPHTHRLENE-RNTHRRCENE A NRPHTHRLENE-PYRENE
MODEL
tII
2.000
-5
{
1. e 7
RNTHRRCENE-PYRENE MODEL
5 YO.00-
-+
I I-
n
m
x
z
1.333-
3
30.00-
_I
v) D
U
&
a
-
1.a00
20.00-
.ea7 10.00
.DO
i 1
.oo
.333 I
10.00
I
T%?L
I
I
JYi7
F E E ~ ~ Mi E
-
-
I
60.00
60.00
Figure 9. Bandwidth vs. total feed time for moving feed system.
perimental data for the low resolution (naphthalene-anthracene) separation were obtained but are not shown. Figures 12 to 14 and Table I1 show that for large amounts of feed the moving feed system can provide either significantly higher resolution at the same feed throughput, or higher feed throughput at the same resolution. Discussion and Conclusions The experimental results show that the moving feed technique offers improved separation and flexibility over the conventional stationary feed for preparative separations. Components can be separated faster and with less dilution by using a moving feed. Up to a 300% increase in feed throughput was observed. The increase is largest for the two solutes which are most difficult to separate (naphthalene-anthracene). The separation can be controlled by adjusting the average feed velocity, Uf-d. For example, the resolution of two adjacent components in a chromatogramcan be improved by choosing a feed velocity
.oo Figure 11. Resolution vs. total feed time for a moving feed system; binary pairs.
in between the two component velocities. By choosing a feed velocity equal to the velocity of a single component, the moving feed technique could be used to detect a trace component since there will be very little dilution. For dilute systems the moving feed system can be effectively modeled using the local equilibrium model including dispersion. Because of the close agreement between theory and experiment (shown in Figures 4 and 5), the dispersion model can be used quantitatively to predict the results of a moving feed separation. Commercial applications of moving feed HPLC would probably use concentrated feed solutions which are outside the linear equilibrium range used in this study. Thus the dispersion model employed here will not be applicable and superposition will not be valid. However, we still expect that the moving feed system will allow much higher
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983
16
0
NRF'HTHRLENE-FWTHRRCENE
A
NRPHMRLWE-PYRWE
aration costs will be reduced. In a commercial application one would be interested in the yield/purity curve which determines how much of a pulse can be cut from the effluent at a given purity. Unfortunately, for the complex moving feed system a simple relationship does not appear to exist between this curve and the resolution. However, we do expect that yield will be higher at a given purity when resolution is higher. For very large scale operations a simulated countercurrent operation is most efficient and probably will be most economical. For very small laboratory systems the simplicity of the stationary feed system (normal operation) will probably make it the choice. The moving feed technique will probably be most effectively used for intermediate sized operations.
0 RNTMRCENE-PYRENE MODEL
I
I
Acknowledgment
Figure 12. Resolution vs. amount of feed separated per hour for a stationary feed system; binary pairs. 2.W
0
A
p.m,
T
1
-
NRPHTHRLEM-RNTHRRCENE NWHTWENE-PYAENE ANTHRACENE-PYRENE
I I
MOOEL
I
1.867-3
Discussions with Pedro Ortiz were most helpful. This research was partially supported by NSF Grant ENG7721069. Paper presented a t AIChE National Meeting, Orlando, FL, March 1981. Nomenclature c = fluid concentration, mol/mL co = feed concentration after injection into column, mol/mL k = distribution coefficient k' (1 - t/t)k L = length of column, cm N = number of equilibrium stages in column Pe, = zv/(DAM Ep) = Peclet number
+
q = solid concentration, mol/g of adsorbent R, = resolution, eq 8 S = cross-sectional area of column, cm2
.-
I
.w
101.00
Ho$;.TMniN W'.OO
d.wRHDuNf.&
~
70.02
ad.00
Figure 13. Resolution vs. amount of feed separated per hour for moving feed system; binary pairs. 1
.m 1
0
S T A T I W R Y FE€D EWERI)(E)(TR CfilR
LII
WING FEED MPUIIWTRL DRTR
_-
W O E L FWI HIM RmUTIN IDOEL FW L b l RE%lLUICN
t = time, min tl, t2,t3,t4 = feed time for columns 1-4 for a step-wise moving feed system, min tf = total feed time, min tR1,tR2= retention time for components 1 and 2, min t,,, tpi2 = bandwidth for components 1 and 2, min u = interstitial fluid velocity, cm/min V = volume of solution fed into the column, mL = volume of feed pulse, mL V = Sze(1 + k ) = measure of bed capacity, mL x A = cA/cO = reduced concentration X = general form of breakthrough solution z = axial distance, cm zl, z2, 23, z4 = length of feed column segments, cm t = void fraction pB = bulk density of solid, g/mL
Literature Cited Broughton, D. 8.; Neuzll, R. W.; Pharls, J. M.; Breasley, C. S. Chem. f n g . Prm. 1870. -~ 66(91. ,, 70. deRos&tt, A. J.; Neuzll, R. W.; Korous, D. J. Ind. Eng. Chem. Process Des. Dev. 1976, 15, 261. Goldstein, G. J . Chromatogr. 1876, 129, 61. Lapldus, L.; Amundson, N. R. J . phys. Chem. 1950, 56, 984. Lightfoot, E. N.; Sanchez-Palm, R. J.; Edwards, D. 0. I n H. M. Schoen, Ed. "New Chemical Engineering Separation Techniques"; Interscience, New York. 1962; p 125. McGary, R. S. M.S. Thesis, Purdue Unlverslty. 1981. Neuzll, R. W.; Rosback, D. H.; Jensen, R. H.; Teague, J. R.; DeRossett, A. J. CHEMTECH 1980, 10, 498. Shearon, W. H.; Gee, 0. F. Ind. Eng. Chem. 1848. 42, 218. Sherwood, T. K.; Plgford. R. L.; Wlike, C. R. "MassTransfer"; McGraw-Hill, New York, 1975; Chapter 10. Snyder, L. R.; Kirkland, J. J., "Introduction to Modern Liquid ChromatoaraDhv": Wllev-Interscience. New York. 1974; D 35. Wankat, P. Cy I&: Eng. Chem. Fundam. 1977a, 16, 468.' Wankat, P. C. Sep. Sci. 1977b, 12, 553. Wankat, P. C.; Ortiz, P. M. I d . Eng. Chem. Process D e s . D e v . 1882, 21, 416.
--.
m
.
"
.
AdIlUNT
OF FEED/HIlUR
Figure 14. Resolution vs. amount of feed separated per hour for ternary system (see text for details).
throughputs with equal resolution when compared to the stationary feed case. Thus for the same amount of feed a smaller system with less adsorbent and less solvent will be required. Since less solvent is used, downstream sep-
Received f o r review August 26, 1981 Accepted August 21, 1982
