205
Ind. Eng. Chem. Fundam. 1982, 21, 205-214
Literature Cited Chang, T. S. et al. J . Phys. Rev. A 1977, 76, 446. Ferer, M. Phys. Rev. 6 1977, 76, 419. Grimths, R. 8. Phys. Rev. 1967, 158, 176. Kadanoff, L. P. Physics 1966, 2 , 263. LeyXoo, M.; Green, M. S. Phys. Rev. A 1977, 16. 2483. Meyer. C. A. et al. ”ASME Steam Tables”, 3rd ed; 1977. Nuttlng, P. G. Ind. Eng. Chem. 1930, 2 2 , 771. Osborne, N. S. et al. J . Res. Net/. Bur. Stend. 1937, 18, 389. Osborne. N. S. et al. Trans. A S M 1930. 52, 191. Sengers, J. M. H.; Greer. S. C. Int. J . Heat Mess Transfer 1971, 15. 1865. Sengers, J. M. H.; Sengers, J. V. Phys. Rev. A 1975, 72, 2622. Sengers, J. V.; Sengers, J. M. H. NASA Contract Report, 1977. Stell, G. Phys. Rev. Lett. 1974, 32, 286.
Vause, C.; Sak, J. Phys. Rev. A 1980. 21, 2099. Watson, K. M. Ind. Eng. Chem. 1943, 35, 398. Wagner, F. J. Phys. Rev. 6 1972, 5 , 4529. WMom, B. J . Chem. Phys. 1965, 4 3 , 3969. Wilson, K. 0.;Fisher, M. E. Phys. Rev. Lett. 1972, 28, 248.
Receiued for review March 11, 1981 Accepted February 8, 1982
G.S. wishes to acknowledge the support of this work by the Office of Basic Energy Sciences, U.S.Department of Energy. S.T.is also indebted to the National Science Foundation for his support
while pursuing this research.
Parametric Pumping with pH and Electric Field: Protein Separations Helen C. Holleln, Hslen-Chlh Ma, Chlng-Rong Huang,’ and Hung T. Chen‘ Department of ch8mical Engineering and Chemistry, New Jersey Institute of Technology, Newark, New Jersey 07702
A new parametric pumping process for the separation of protein mixtures has been developed, based on cyclic variation of pH and electric field. The model system used is human hemoglobin plus human serum albumin on CM Sepharose ion exchanger. Experimental results are presented. They indicate that the process is a useful method for splitting proteins from each other.
Introduction Parametric pumping is a separation process which involves reciprocating flow of a mixture to be separated through a fixed bed and simultaneous, synchronous cyclic variation of intensive variables, such as gas pressure, solution temperature, solution ionic strength, solution pH, electric field, etc. The intensive variables most often used to motivate parametric pumping have been temperature and prmure. Electric field or pH has been used less often. Parametric pumping via pH variation usually involves the so-called “recuperative mode” of operation of the process (Sabadell and Sweed, 1970; Shaffer and Hamrin, 1975). In this mode, various levels of pH are set in the streams entering either end of the parametric pumping column. As the entering streams penetrate the column, a pH change in the column occurs. This is opposed to the “direct mode”, in which the intensive variable is changed uniformly over the entire length of the column. Unlike pH, changes in the electric field as an intensive variable can be immediately and speedily applied to the parametric pumping system. Electrochemical parapumping has been shown to be a promising technique for desalination of water (Thompson and Bass, 1974; Oren and Soffer, 1978). Chen et al. (1977,1979,1981) have studied the separation of hemoglobin and albumin by one-column pH parametric pumping. The experimental data have shown that a pH-driven parapump is capable of yielding high separation factors. Also, Chen et al. (1980a,b) have indicated that the multicolumn parapump (columns packed alternately with cation and anion exchangers) has a much higher separation capability than the one-column unit. In thispaper, separation of protein mixtures is experimentally investigated by pH and electric field-driven parametric Deceased April 21, 1981. 0196-4313/82/1021-0205$01.25/0
pumping. Emphasis is placed on the problem of separating two proteins from each other.
Experimental Section The experimental apparatus is shown in Figure 1. An LKB 7900 Uniphor column electrophoresis system was modified for continuous operation by the addition of a second elution stopper. Minor modifications were made on the elution stopper and the filter in order to supply adequate support for the solid phase. The column (0.026 m i.d. and 0.15 m height) was packed with CM Sepharose, a cation exchanger. The system was maintained a t 278 K by circulation of cooling water through the jacket of the Uniphor column and the jackets of the Uniphor buffer chambers. The external buffer reservoirs (2 L volume) were kept at 288 K. Reciprocating flow through the system was obtained by use of a reversible peristaltic pump (manufactured by Pharmacia Fine Chemicals). A higher capacity peristaltic pump (manufactured by Bio-Rad laboratories) was used for buffer circulation. A Buchler 3-1500 power supply was used for a direct current source to maintain constant voltage across the column. The feed pump and the power supply were connected to a timer for precise control of reservoir displacements and feed volumes. Valves were placed on each inlet channel of the feed pump in order to introduce the reservoir liquids, to introduce the high or low-pH feeds, and to take product samples. Each product stream was analyzed at the end of every cycle using a Bausch and Lomb spectrophotometer. Hemoglobin concentration was determined by adsorbance at a wavelength of 403 pm and total protein was determined at a wavelength of 595 pm. Albumin concentration was then determined by difference. pH Parametric Pumping The first system to be considered (Figure 2) is a onecolumn parametric pump (Chen et al., 1979). Two pH 0 1982 American Chemical Society
206
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982
-.1
I
r
I
I I
I
I I I
I I
I
I
I
I I I
1
I I
I I I
I
I I
I I
I I
I I I I
I I
I I
Bottom
F: Feed
g 1$
TP
I
P2fied
Table I. Results from Parametric Pumping
I
wt % top product
BP
max possible
exptl
100
8 92
hemoglobin albumin
bottom product max possible 66.1
exptl 63 37
For the anion column, the solute A migrates from the high-pH end (PI)toward the low-pH end (P2);in the cation column, it moves in the opposite direction. Human hemoglobin and human serum albumin with isoelectric points I A = 6.7 and 1, = 4.7, respectively, were chosen as the model system. A cation exchanger (CM Sepharose) with PI = 8.5 and P2 = 6 was used, leading to the expectation that hemoglobin would be removed from the top product stream and concentrated in the other stream, while albumin concentrations remain unchanged (Figure 2). This is to say that the maximum albumin weight fraction in the top product stream is loo%, and the limit for hemoglobin in the bottom product stream is
3
3
6
9
Since we are concerned with low protein concentrations, the concentration ratio will be essentially identical with the weight percent ratio (i.e., y/yo = Y / Y o ) . Thus
Figure 2. Experimental results for pH parametric pumping (run 1).
levels (PIand P2, are chosen to bracket the isoelectric point of a desired protein in a mixture, i.e., P, < I A < Pz. Therefore, a parametric pump operating with PI and P, should be capable of removing that protein from one product fraction and enriching it in the other fraction. The column is packed with an ion exchanger (cation or anion).
[(WB)mlHb
=
[ ( Y B ) m/YOIHb[YO]Hb
-
(2)
[YO]AI + [ ( Y B ) /YOIHb[YOI Hb For this run [YO]Hb = [YOINand F B = FT,so the maximum poasible weight percent for hemoglobin in the bottom product should be [ ( w B ) - ] H b = 66.7%
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982 207 Feed: 0.01% Hb
As indicated in Figure 2, the separations listed in Table I were obtained. Note that higher separation could be obtained by using the multicolumn parapumping system described by Chen et al. (1980a, 1981).
Buffer: O.IOM NaH2P04 +O.IOM Na2HP04
+ vo
yo
yo
I
yo
6
-
!I
yo
~ 8 0 1 (5.60) 9Occ 90cc
/ /,
(4)
Ri = (velocity of center of mass of species i a t zero field)/(velocity of center of mass of species i at finite field) ( 5 ) When the net velocity in the axial direction is relatively large as compared with axial diffusion, eq 5 becomes
(6)
If the bulk velocity is too low, any increase in the protein separation due to the effect of the electric field will be canceled by dispersion from diffusion and convection. On the other hand, the electric field will become significant if the protein mobility and migration velocity are relatively high. The optimum placement of the electrodes in each stage of pH parametric pumping (Figure 2) depends on the relative magnitude and direction of the migration velocities of the two proteins at Pl and Pz. Protein B is negatively charged at both P1and P2 and can be enriched in the top streams by placing the cathode a t the top of the column throughout the process. At P2,protein A is adsorbed by the cation exchanger and the equilibrium concentration in the fluid phase is nearly zero (Chen et al., 1979). Under these conditions, no effect of the electric field on protein A is expected. Negatively charged protein A is present in
I
l
i
I
4 -
2 -
Note that for vo >> v,, the effect of the electric field becomes negligible, as shown in Figure 3. If the bulk volumetric velocity Qo is decreased, the relative contribution of the migration velocity increases (Figure 3). The retardation coefficient Ri as defined for protein separation by Shah et al. (1979) is a measure of the relative effectiveness of the electric field in a dynamic system.
Ri = VO/(VO + vei)
----
(p2=601 9Occ
,
=8.0)
yp
(3)
At p H s lower than the isoelectric point, the proteins carry a net positive charge and migrate toward the anode at velocity v,. When the electric field is applied in the axial direction in a flow system, the net velocity v, in the axial direction is the vector sum of the migration velocity and the bulk velocity. v, = v,
No 120Power vults::
(y
0;0;4:
No Sampler
Electropolarization Chromatography The protein separation achieved in the pH parametric pumping process can be improved by applying an electric field across the chromatographic column during some stages of the process. Net upward movement of protein B relative to protein A is instituted by positive/negative or on/off cycling of the electric field coupled with the cyclic variation of pH and flow direction. Breakthrough curves, simulating the various pH conditions existing during the process, were run in order to determine the most effective stages for application of the electric field and the optimum placement of the positive and negative electrodes relative to the flow direction in those stages. At operating pH's higher than their isoelectric points, proteins carry a net negative charge and migrate toward the cathod with a velocity v, which is directly proportional to the strength of the electric field E and the protein mobility p. The mobility is a complex function of pH, protein concentration, buffer composition, buffer ionic strength, molecular shape, and particle diameter. v, = pE
1.C. in the Column:Faad
I I
I
I
\
I
I
O L '
.' V I , cc
Figure 5. Effect of volumetric flow rate on electropolarization chromatography.
the column in stages I, IV, V, and VI, and net downward movement of protein A dictates placement of the cathode at the bottom of the column in these stages; this conflicts with the optimum electrode placement for protein B. Effects of electric field on various stages of parapumping are experimentally demonstrated in Figures 4 to 6. Note that for all runs, the buffer is a mixture of Tris-maleate and NaOH (0.05 M each). Feed includes 0.01% each of protein A (hemoglobin) and B (albumin). Also, Q = 0.5 cm3/min and voltage = 210 V. First, consider stages V and VI as shown in Figure 4. Both proteins are negatively charged and the entire stage is operated a t P1.If the cathode is placed at the bottom of the chromatographic column, movement of both proteins occurs in the direction of the cathode with a peak developing in this direction. Since (P1- ZB)> (P1 - ZA), protein B is more affected by the field, as evidenced by its more distinct peak (Figure 41, and by its greater migration velocity (Table 11). The protein split will be favored by placement of the cathode at the top of the column in stages V and VI. However, the effect of the electric field is not significant under these conditions, so no power is necessary for stages V or VI. Next, consider stages I1 and I11 which are operated at Pz.Protein A is positive and protein B is negative in these stages, so the cathode should be placed at the top of the column. The concentration of protein A in the liquid is
208
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982
Table 11. Migration Velocitiesa case b
-
volts
t p , min
MA,
cm3
-
MB, cm3
(MA
cm/ min
cm/ min
veA,
-
VeB,
8.3 + 0.019 +0.033 10.2 0 0 IC 210 7.7 -0.017 t 0.001 IVa 210 19.9 + 0.046 t0.015 IVb 0 31.1 0 0 IVC 210 40.0 -0.048 -0.023 VIa 0 0 2.5 0 0 VIb 210 120 5.2 + 0.003 t 0.010 Buffer: 0.05 M Tris-maleate t 0.05 M NaOH; feed: 0.01 wt % hemoglobin (A) t 0.01 wt % albumin (B); Q, = Q 0.5 cm3/min; V = 45 cm3;v, = t 0.167 cm/min. For case 1, based on Figure 5 with Ve = 67.5 cm3;for case IV, basej i n Figure 6; for case VI, based on Figure 4. Ia Ib
210
45.0 0 45.0 120 0 120
0
Exp Haemoglob#n(Ai
-
----
Albumin (61
CASE
m
I
06
-
CASE Io __
yo (P2.581
150cc
I5OCC
No Power
b
i I
34
IPz=SOl
YO
(P2.581 150 cc
YP
YO
CASE IC -
CASE I b -
YO
,!
o
CASE
;[=?
29.3 33.8 33.6 69.8 75.1 83.3 73.2 69.6
, I
0 8 -
21.0 23.6 25.9 89.1 106.2 123.3 15.7 14.8
0
-
so
30
I20
90
150
Ve. cc
Figure 5. Effect of electric field in stage I. 02-
IEb ___
CASE S L O
i
I
YP
CASE
y
YP
YP
CASE 'P
mc P'
E*p
CASE I p o
----
01
5
30
60
9c
123
Ve , c c Yo
Figure 4. Effect of electric field in stage VI.
nearly zero and will be little affected by the presence of a finite field. Since (P2- IB)< (PI- IB), the retardation coefficient for protein B will be even smaller than observed in the previous case, so the effect of a finite field in stages I1 or I11 is negligible. The relative migration velocities of proteins A and B in stages I and IV are dependent on position and time, because the pH is changed from P2 to PI and vice versa during these stages. The protein mobility and the resulting migration velocity are strong functions of pH. The average effect of the electric field over the PI to Pz pH range is shown for these stages in Figures 5 and 6. Based on the relative movement of hemoglobin (protein A) and albumin (protein B) in these breakthrough curves, a number of generalizations for the process can be made. In stage I, negatively charged protein A is leaving the bottom of the column while positively charged protein A is entering the top. A+ is immediately adsorbed by the cation exchanger, so the cathode should be placed at the bottom of the column to favor downward movement of A-. As seen in Figure 5, a peak develops for both A and B in the downstream direction, which is detrimental to the split
Buffer
( P , = 8 5 1 IP,:SOl 60cc
Yo
Buffer
(7.851 (Pp:601 60cc
Yo Buffer (P,-85)lPp=60) 60cc
'r
1
0
30
60
Figure 6. Effect of electric field in stage IV.
of A and B. Since the total protein A removed from the column, as seen from comparison of the area under the
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982 209 1x1
cm1
Bottom ProdYct
Feed
TOP
(It Downflow
Feed
An on/off cycling of electric field was used in the new process, with a high flow rate Qo in the zero-field stages and a low flow rate Qp coupled to a finite field in stage IV. A low flow rate is necessary in stage IV in order to make the electric field effective. The use of a high flow rate in the other stages minimizes cycle time and maximizes production rate (g of proteinlmin). At t = 0, the column is saturated with P1feed. The bottom reservoir (VB; VB > V) is filled with P1feed and the top reservoir (V + V,) is filled with Pz feed. Automatic titrators are used to maintain the pH’s at P1and Pz in the various reservoirs as shown in Figure 1. The durations for the various stages are t I =z t I I tv IV/Qo (7)
Figure 7. Schematic of the pH paarapump with electrical field (Mode 1).
hemoglobin curves in Figure 5, is approximately equal in all three cases at QotI equal to 67.5 cm3, no relative advantage is achieved for the two-component split by the placement of the cathode a t the bottom of the column. Electrical field is not needed for stage I. In stage IV, the liquid leaving the top of the column contains A+ at very low concentration and B- at feed concentration. The liquid entering the bottom of the column contains A- at enriched concentrations and B- at feed concentration. Placement of the cathode at the top of the column in this stage should move both protein A and protein B from the PIliquid forward, relative to the concentration wave a t zero field. The protein A which moves into the Pz liquid in the upper part of the column will stick to the gel and be desorbed in the trailing Pl liquid giving a sharp peak behing I A (Figure 6). Conversely, placement of the cathode at the bottom of the column will move both protein A and B downward relative to the mass flow at zero field. Note that the desorption wave for protein A is integrally related to the pH wave (Figure 6). For positive, negative, or zero fields, the desorption wave always falls immediately behind pH = Ik Also, the net mass movement due to the electric field is much greater for the adsorbed protein, hemoglobin in our case, as seen in Table I1 and Figure 6. This phenomenon was unexpected, but it is the key to enhanced separation from the electrice field effect. Process Description Based on the preceding discussion, a new separation process was developed as shown in Figure 7. The goal in this process is to maintain the separation of protein A achieved via pH parametric pumping while selectively removing protein B from the bottom product via addition of an electric field in certain stages of the pH parapumping process. This will enhance the purity of the bottom product stream and, thus, the overall separation. By comparing the migration velocities for protein A and B (Table 11),protein A has a higher velocity due to electric field in cases IVa and c. Also, the greatest difference between the centers of mass of proteins A and B occurs in case IVc. Thus, the electric field is only applied to stage IV of the new process, with the cathode at the bottom of the column. This holds back the hemoglobin desorption wave relative to the albumin wave. After one void volume of upward displacement, the hemoglobin wave is still in the bottom portion of the column and albumin-rich solution is in the top portion of the column (Figure 6). High-pH buffer is pumped into the bottom of the column in order to push the hemoglobin wave to the top of the column while pushing additional albumin into the top streams.
FB/Qo
(8)
t ~ v c= Fo/Qp
(9)
~III ~IVA=
~ I V A+
t ~ w=
~ I V B+
VI
hvc = (Qo/Q+)tr
J’T/Qo
Also note PT = FB
+ Fo
(10) (11)
(12)
PB= FT (13) One complete cycle contains six distinct stages as outlined below. Stage IV is divided into three paarts. (I) Downflow. The solution with pH = Pz from the top reservoir enters the top of the column, and at the same time the solution in the column flows from the bottom to the bottom reservoir. Total downflow equals 1.5V. (11) Circulation. Circulate the fluid between the column and top reservoir. This will ensure that the pH in the column will be brought to Pz, and that protein A will be adsorbed in the solid phase. As seen in Figure 5, at the end of stage I, the pH in the lower half of the column is above Ik It is crucial that this pH be corrected. (111) Bottom Feed. The feed with pH equal to Pz enters the bottom of the column, and the solution rich in protein B is pushed out from the top of the column as the top product. (IV) Upflow. The optimum volume for upflow was experimentally determined and was found to be 2.4V for the operating conditions considered. The cathode is placed at the bottom of the column in order to delay the movement of protein A relative to protein B. The field is maintained at constant voltage, and the bulk flow rate is reduced to Q In stage I S A , the solution from the bottom reservoir is pumped into the bottom of the column, and additional top product is taken. The total product volume for this stage is 0.9V. In stage IV B, the remainder of the solution from the bottom reservoir, to a total of 1.5V, is pumped into the column and part of the fluid in the column is pumped to the top reservoir. In stage IV C, the high pH buffer, with volume equal to 0.9V, is pumped into the bottom of the column in order to push the protein B rich solution, originally in the top of the column, to the top reservoir. This completes the displacement to the top reservoir. ( V ) Bottom Product. The bulk volumetric flow rate is returned to Q,,. A t the beginning of stage V, a strong concentration gradient exists across the column, with both proteins richer near the top of the column and the fluid in the bottom of the column close to the buffer concentration. Dead volume solution from the bottom reservoir is pumped into the top of the column, and the fluid in the
.
210
Ind. Eng. Chem. Fundam., Vol. 21, No. 3. 1982
Table 111. Experimental Parametersa run 1. 2. 3. 4.
pump without power mode 2, FB = FT mode 1, FB = FT mode 1, FB = ~ F T
volts
t,, min
tw, min
FB
FT
0 210 210 210
36 27 27 27
36 225 215 215
35 35 35 52.5
35 35 35 17.5
FO 0 45 40 40
vT
82.5 82.5 112.5 112.5
VB 60.0 60.0 90.0 90.0
a Buffer: 0.05 M Tris-maleate + 0.05 M NaOH; feed: 0.01 wt % hemoglobin ( A ) + 0.01 wt % albumin (B); Q o = 2.5 cm3/min;QP = 0.5 cm3/min; V = 45 cm3;QatV= 60 cm3.
Table IV. Experimental Results at Steady State top product
bottom product
[(S.F.)-Im
[(S.F.),],,
a, -
electropolarization chromatography run 1 (pump without power) run 2 (mode 2, FB = F T ) run 3 (mode 1, FB = FT) run 4 (mode 1, FB = 3FT)
83 92 87 92 92
17 8 13
8 8
column is pushed out of the bottom of the column and mixed in the holding tank. The bottom product is taken from tank, and the remainder of the solution in the tank is then returned to the bottom reservoir. (VI)Top Feed. The high pH feed, with a volume equal to PB(the bottom product volume taken during the previous stage) is pumped into the top of the column, and the fluid in the column is pushed to the bottom reservoir. One cycle is now completed and stage I of the second cycle begins. Results and Conclusions Three experimental runs (runs 2-4) via the new process were made. Experimental apparatus is shown in Figure 1, and operating conditions are listed in Table 111. Three modes of the pump operation were experimentally investigated: pH parapumping without electric power, mode 1, and mode 2. The mode 1 operation is identical with that previously discussed (Figure 7). The difference between mode 1 and mode 2 is in the operation of stages V and VI. For comparison purposes, an experiment was also made in the Uniphor apparatus on the separation of hemoglobin and albumin via electropolarization chromatography (EPC). The resulta are shown in Table IV. EPC has been used previously for the separation of mixtures of albumin and y-globulin (Chiang et al., 1979). As seen in Figure 8 and Table IV, the tr,p product is identical at steady state in runs 1, 3 and 4. The top product is less pure for run 2 because the total upflow (112.5 cm3) was too large, leading to a fractional breakthrough of the hemoglobin desorption wave to the top product. The new process is designed to improve the bottom product while maintainingthe top product purity, achieved via pH-parapumping. The maximum possible hemoglobin weight fraction in the bottom stream for pH parametric pumping (eq 1 and 2) is 66.7%, if FB = FT as in runs 1, 2, and 3; 80.0% if FB = 3FT as in run 4. Higher weight fractions of hemoglobin in the bottom product were obtained in all three runs with the new process (Figure 8 and Table IV). The top product in runs 3 and 4 is equal in purity to that obtained via pH parametric pumping, while the purity of the bottom product is equal to or better than that via EPC. The separation in the new process is, therefore, higher than the separation which can be reached by either pH parametric pumping or EPC. As shown in Figure 9C,a separation factor a, as high as 120 was obtained. The overall separation factor a, is
20
80
4.3
4.8
20
31 26 21 11
63 74 79 89
20 14 20 38
1.0 1.7 2.3 3.2
20 24 46 120
EXP
Run
Haemoglobin
1 Pump wlthout power
A
2 Mode2
0
3 Model
0 0
4ModeI I
,iTop
Albumin
FB
7 35 e 35
F,
5 35
8
35
35
0
525
175
Product
K
0.6
I
%\‘O \ ‘0
0‘
0
2
4
n
6
8
10
Figure 8. Experimental results.
defied as the product of the separation factors of proteins A and B.
As shown in Figure 9A, the separation factor for protein A is approximately doubled in run 4 as compared to runs 1 and 3. This result is expected from eq 1. The separation factor for protein B is 1.0 for pH parametric pumping (run
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982
Run Exp --
A Hoemoglobin
“1
‘1 ‘1
211
FB FT -
I
A
2
0
No Power 35 Mode 2 35
3 4
0
Mode I Mode I
35 35 35 35 52.5 17.5
A
B Albumin
0
1 0
1
I
2
4
n
I
I
I
6
8
IO
2
4
10
0
6
n
Figure 9. The separation factors vs. number of cycles.
1, Figure 9B)and is improved significantly for all three runs with power. For the new process, eq 2 is modified as follows
[ ?$] [ (:.)-], [ y0
FB = FT ~ 3 5 ,Fo = 4 0
Run
Hb [YOIHb
[ ( WB)mlHb =
[YOIAI
+
(YB’.]
9 & 825
2 I
60
m 1 1 2 . 5 9 0
5
2
225
60
6
2
225
15
7
2
I12 5
I5
491
LYOIHb Hb
(15)
Also,the concentration of protein B in the bottom product is less than its feed concentration, as determined from the mass balance at steady state
L-J
3
In order to minimize the concentration of albumin (Al) in the bottom product, one must operate the pump with [ (yT)m]M as close to as possible. This will maximize the weight fraction of hemoglobin (Hb) in the bottom product (eq 15),as well as, the S.F. for albumin (eq 14). Figures 9B,10,and 11 show the calculated separation factors for albumin. The calculated results compare reasonably well with the observed values in runs 2-4. These calculations are based on a stage-by-stage mass balance including the effect of the electric field in stage IV,as seen in the Appendix. The prediction on the hemoglobin separation can be found elsewhere (Chen et al., 1981). The 1981 pH parapumping model has been modified to include the effect of the electric field on the adsorbed protein (hemoglobin). This work will be presented in subsequent papers.
Exp
2 3
BP
8
r-]Al 2
2
/
e
m
Ve
2
-
-*
e
e
e 4
6
8
10
Figure 10. Effect of reservoir dead volumes on albumin separation (mode 2).
Figure 10 compares mode 1 and mode 2. The main difference between modes 1 and 2 is in the operation of stages V and VI. As seen from Figure 10,mode 1 has a better separation than mode 2, but mode 2 separation will approach mode 1 as the dead volume of the bottom res-
212
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982 V~=112.5, VB=90, Fg = 4 0 RUN
FB
-
350 525 52 5
350 175 52 5
1050 60 0
350 I0 0
__
FT
_.
3
4 8 9 IO
4-
AI
3 -
/ / 9 3
8
0
I
I
3
6
n
I
I
I
9
12
15
Figure 11. Effect of feed volumes on albumin separation (mode 1).
ervoir becomes small. This can be explained as follows. From the Appendix, for mode 1 [ ( Y B ) -1 AI =
(RBV- FO)[(YBR)~]AI 4- ( Q o h
- V)[(YBR)mlAl
v + (Qotv - v)
The external equations are solute material balances on the streams flowing to and from the column and the reservoirs. The internal equations describe the events occurring within the column, i.e., the adsorption/desorption of protein A (hemoglobin) and the electric field effects on both proteins A and B. Since the increased separation in the new process relative to pH parametric pumping is due to improved albumin separation, a mathematical analysis on the protein B separation was made in order to verify the trends observed in runs 2-4 (Table IV). The separation factor for protein B (albumin) is defined by eq 14 and is graphed in Figures 9B, 10, and 11. The calculations for [ ( Y T ) n ] N and [ ( Y B ) n ] N are shown below. The following assumptions were made: (1)plug flow; (2) negligible axial diffusion; (3) constant properties in the radial direction; (4) no interaction between solutes A and B; and (5) constant migration velocity v e B in stage IV. Given that FoIV, QOtI1 V, and Qotv I V, three regions of operation may be studied: region 1, F B IV and F T I V; region 2, F B > V and F T 5 V; region 3, F B > V and F T > V. All three regions are considered in this paper for mode 1, and region 1is considered for mode 2. The region F B IV and F T > V is not included, because the separation factors for both proteins are low when F B < F T . Region 1-Mode 1. The top and bottom product concentrations are calculated by following the albumin concentrations from stage-to-stage and repeating the calculations cycle-to-cycle. The initial conditions in stage I of the nth cycle are [(YTR)nlAl, [(YC,I)nlAl, and [(YBR*)nIAl, where [(YC,I)nlAl
(17)
=
(A-1)
[(YC,VI*)n-lIAl
For cycles n to m, with n > 1, these concentrations are calculated in the previous cycle. For the first cycle, Le.,
For mode 2
n = l [ ( Y T R ) ll AI = [ (YC,I) 11Al= [ (YBR* ) 11Al = [ (YBR) 11AI =
By comparing eq 17 and 18, if R B 2 1 and VB I Qotv - V [ ( Y B ) -lAl,model [ ( Y B )mlAl,mode:! (19) From eq 16 and 19 [ (YT) mlAl,model
[ (YT) mlAl,mode2
(20)
Therefore [ (S*F* ) mlAl,model [ (SmF*) m]Al,modeZ (21) The retardation coefficient R B for protein B is approximately 1.16 for our operating conditions. Maximum separation is calculated when albumin is not retained by the field, i.e., R B = 1.00. Figure 11shows the effect of F B and F T on the albumin separation. The separation increases with a decrease in F T ; for a given FT, the separation will increase as F B increases. Furthermore, an increase in F B / F T will increase the separation of hemoglobin and albumin, and thus, the overall separation factor a. Many versions of parametric pumps are conceivable. The pump examined here appears to be a very promising device for splitting mixtures of two or more protein components. Acknowledgment The National Science Foundation (CPE 79-10540) provided financial support for this research. Portions of this paper were presented at the 2nd World Congress of Chemical Engineering in Montreal, Canada, Oct 6, 1981. Appendix Two types of equations are needed in parapumping calculations: internal equations and external equations.
[YOIAI
(A-2)
In stage I, yTRremains the same. Stage I1 is a recycle stage and does not alter the albumin concentrations. The concentrations at the end of stage I and beginning of stage I11 are [(YC,III)nlAl
=
(A-3)
[(YTR)nlAI
QO~+ I
VB (A-4)
In stage 111, YTR and YBR are unchanged. At the end of stage I11 and beginning of stage IV, two concentration zones are present in the column. top zone: volume = ( V - FB)at [ ( Y C , I V ~ ) ~ ] A=I [ (YTR ) n1 A1 (A-5)
bottom zone: volume = F B at [(yc,Ivz)n]& =
[YO]Al
(A-6) Also, from mass balance and eq A-3 [(YT,III)nlAl
=
[(YTR)nlAI
(3-7)
where the total top product is a mixture from stages I11 and IVA. (A-8) [ ( Y T ) n l A l = (FB[(YT,III)nlAI + FO[(YT,IVA)n]Al)/PT In stage IV, YBR is constant. An electric field is placed across the column so that the fluid phase moves upward at vo, while protein B moves upward at vo + veB. The
Ind. Eng. Chem. Fundam., Vol. 21, No. 3, 1982 213
concentration of albumin in the fluid leaving the column in time At is g-mol of protein B (A-9) Yout = cm3 of fluid
1 PB. Equation A-23 holds for regions 1 , 2 , and 3 when
IQ ( t w A + tm),or for the operating conditions in Table I I f when R B I 1.5.
RBV
[(YB)nlAl
=
((RBV- FO)[(YBR)nlAl
(Qotv - V ) [ ( Y B R ) ~ I A ~ ) / Q O ~ V (A-23)
(A-10)
From eq 6 and A-10 Yout
=
1 -Ycolumn RB
(A-11)
By mass balance, if the concentration leaving the column is smaller, the volume containing the initial mass will be larger; i.e., it will take a longer time period to exit from the column at v,,. v o u t = RBVinitial (A-12) The top product in stage IVA is calculated from eq A-5, A-6, A-11, and A-12 as follows. If Fo I R B ( V - F B ) [(YT,IVA)nlAl
If FO
=
(l/RB)[(YTT)n]~
(A-13)
> R B ( V - FB)
[(YTJVA)nlAl
=
- FB))((l/RB)[(YTR)nlAIJ + (FORB(V- FB)H(~/RB) [YOIAI)]/To (A-14)
[(RB(V
The totaltop product concentration is calculated from eq A-7, A-8, A-13, and A-14. If Fo I R B ( V - F B )
A volume of bottom product P B is taken from the holding tank, and the remainder of the fluid is returned to the bottom reservoir. In stage VI, YTR is constant and at the end of stage VI =
[(YBR*)n+l]Al
( ( V B - Q o ~ v ) [ ( Y B R ) ~ I A+ I (Qotv P B ) [ ( Y B )nlAl F T [ (YBR)nlAl) V B
+
/
(A-24)
Two concentration zones are present in the column at the end of stage VI. From mass balance and eq A-22, the average vdue is =
[(YC,VI*)nlAl
(FTIYOIAl
+ (v - F T ) [ ( Y B R ) n l A l ) / V
(A-25)
This completes the nth cycle of operation. Substitution eq A-1, A-24, and A-24 into eq A-4 = (((v+V B - QOtV)[(YBR)nlAl + (Qotv -
[(YBR)n+llAl
+ FT[YoIA~)/(Qo~I + VB)) + (((80tI
FT)[(YB)nlAl
+
V)[(YTR)~+I~A~)/(QO~I
-
vd) (A-26)
The albumin separation factors for region 1-mode 1 can be calculated from eq 14, A-2, A-16 (or A-15), A-21 (or A-20), A-23, and A-26. Regions 2 and 3-Mode 1. I ~ F> BV, Le., regions 2 and 3, the calculations for the top product concentration are slightly changed. Equations A-5 to A-7 become [(YC,IV)nlAl = [YOIAl (A-27) [(YT,III)nlAl
=
(V[(YTR)nlAl
+ (FB - V)bOlAl)/FB
(A-28)
Equations A-13 and A-14 become [ (YT,IVA) n l Al = (
/RB)
[YO] Al
(A-29)
Thus, [ (YT),,]M can be calculated from eq A-8, A-28, and A-29. The resulting equation is identical with eq A-16. If F T > V, Le., region 3, the calculations for stage VI are slightly changed. Equations A-24 and A-25 become =
[(YBR*)n+lIAl
- Qo~v)I(YBR)~IAI+ (Qotv + (V[(YBR)nlAl + ( F T - V ) b O l A l ) / v B
((VB
PB)[(YB)nlAl)/VB
(A-30) [ (YC,VI* )nlA1 =
[YOIAl
(A-31)
Thus, [ (YBR)n+l]M can be calculated from eq A-1, A-4, A-30, and A-31. The resulting equation is identical with eq A-26. The albumin separation factors for regions 2 and 3-mode 1 are calculated from eq 14, A-2, A-16, A-21, A-23, and A-26. Mode 2. The operation of stages V and VI is changed. Equations A-22 and A-24 become [(YC,VI)nlAl
=
[(YBR*)n+llAl
((RBV-
=
FO)[(YBR)nlAl
+ VB[(YBR)nlAl)/(V + VB)
(A-32)
Equations A-23, A-25, and A-26 are changed as follows. Regions 1 and 2 ( F T 5 V) (A-33) [ ( Y B ) n l A l = [ (YBR* )n+llAl =
[(yC,VI*)nlAl
(FT[YOIAl
+ (v- F T ) [ ( Y B R * ) n + l l A l ) / V
(A-34)
[(YBR)n+llAl FTbOIAl
((v+
V B - FT)[(YBR*)n+llAl + ( Q o ~ I - V ) [ ( Y T R ) ~ + I ] A ~ / ( Q O ~ I+ VB)
=
(A-35)
Ind. Eng. Chem. Fundam. 1982, 21, 214-220
214
Region 3
(FT
[(YB)nlAI
> V) =
(V[(YBR*)n+llAl
[(YC,VI* )nlAI [(YBR)n+llN
=
+ =
(FT
- V)[YOlAl)/pB
[YOIAl
(A-36) (A-37)
-k ~ [ Y o I A -k I (Qoti V ) [ ( Y T R ) ~ + ~ ] A I ) / ( Q O-k~ I vd (A-38)
(VB[(YBR*)n+llA1
The albumin separation factors for regions 1 and 2-mode 2 are calculated from eq 14, A-2, A-16, A-21, A-32, A-33, and A-35. Equations A-15 and A-20 are also needed for region 1. The albumin separation factors for region 3mode 2 are calculated from eq 14, A-2, A-16, A-21, A-32, A-36, and A-38. Nomenclature A = effective cross sectional area of packed column, cm2 BR = bottom reservoir BP = bottom product E = strength of electric field, V/cm EPC = electropolarization chromatography F B = volume of bottom feed, cm3 F T = volume of top feed, cm3 Fo = feed volume with zero protein concentration, cm3 I A = isoelectric point of protein A IB = isoelectric point of protein B M A = total elution volume at the center of mass of protein A, cm3 M B = total elution volume at the center of mass of protein B, cm3 P, = high pH level Pz = low pH level P B = volume of bottom product, cm3 PT = volume of top product, cm3 Qo = high bulk displacement rate, cm3/min Q, = low bulk displacement rate, cm3/min Ri = retardation coefficient of component i S.F. = separation factor t = duration, min f = average duration of electric field, min +R = top reservoir TP = top product V = volume of fluid phase, cm3 V, = bottom reservoir dead volume, cm3 V T = top reservoir dead volume, cm3 v, = migration velocity, cm/min veA= migration velocity of protein A, cm/min
v,B = migration velocity of protein B, cm/min vo = bulk velocity, cm/min v, = net velocity in axial direction, cm/min W = weight fraction of the product = weight fraction of the bottom product YB = concentrationof solute in the bottom product, g-mol/cm3 YBR = concentration of solute in the bottom reservoir, gmol/cm3 yc = concentration of solute in the column (fluid phase), g-mol/cm3 yo = concentration of solute in the feed, g-mol/cm3 YT = concentration of solute in the top product, g-mol/cm3 y m = concentration of solute in the top reservoir, g-mol/cm3 Y = concentration of solute in the fluid phase, g/g Yo = concentration of solute in the feed, g/g ( ) = average value
w”,
Greek Letters = protein mobility, cm2/V-s a = overall separation factor for protein mixture
Subscripts A1 = albumin Hb = hemoglobin n = nth cycle of operation 0 = initial condition P = product m = steady-state condition Superscript * = intermediate concentration in nth cycle of operation
Literature Cited Chen, H. T.; Hsien, T. K.; Lee, H. C.; Hill, F. B. AIChE J . 1977, 23,695. Chen, H. T.; Wong, Y. W.; Wu, S. AIChE J . 1979, 25,320. Chen, H. T.; Yang, W. T.; Pancharoen, U.; Parisi, R. J. AIChEJ. 1980a, 26, 839. Chen, H. T.; Pancharoen, U.; Yang, W. T.; Kerobo, C. 0.; Parisi, R. J. Sep. Sci. Techno/. 1980b, 15, 1377. Chen, H. T.; Yang, W. T.; Wu, C. M.;Kerobo, C. 0.; Jajaiia. V. Sep. Sci. Techno/. 1981, 16, 43. Chiang, A. S.; Kmioten, E. H.; Langan, S. M.; Noble, P. T.; Reis, J. F. G.; Lightfoot, E. N. S e p . Sci. Technd. 1979, 14, 453. Oren, Y.; Soffer, A. J . Electrochem. Soc. 1978, 125,869. Sabadeli, J. E.; Sweed, N. H. Sep. Sci. 1970,5, 171. Shaffer, A. G.; Hamrin, C. E. AIChE J. 1975, 21, 782. Shah, A. B.; Reis, J. F. G.; Lightfoot, E. N.; Moore, R. E. Sep. Sci. Techno/. 1979, 14, 475. Thompson, D. W.; Bass, D. Can. J . Chem. Eng. 1974,52,345
Received for review May 4, 1981 Accepted January 18, 1982
Solids Suspension in Mixing Tanks KakuJlTojo’ and Kel Mlyanaml Department of Chemical Engineering, University of Osaka Prefecture, Sakai, Osaka 59 1, Japan
The dynamic characteristics of solids flow in slurry reactors with an axial flow agitator, a marine propeller or a vibrating disk, have been investigated both theoretlcaliy and experimentally. The dynamic and steady state solids concentration profiles have been well described by means of the axial sedimentation-dispersion model. The correlation equations for the model parameters have been also provided.
Introduction Slurries have been used in a number of industrial operations. Typical examples of these operations are hy0 196-43 13/82/ 102 1-02 1480 1.25/0
drogenation, coal liquefaction, washing crystals and leaching. In these slurry operations, the solids in the tank are required to be suspended completely throughout the 0 1982 American Chemical Society
