Ind. Eng. Chem. Process Des. Dev. 1984, 23, 660-664
860
Mass Transfer In a Countercurrent Ion-Exchange Plate Column Andries P. van der Yeer, Harry M. Woerde, and Johannes A. Wessellngh' Delft University of Technology, Laboratory of Chemical Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
Experiments are described with a countercurrent ion-exchange plate column. It consists of a series of fluidized beds separated by horizontal perforated plates. Resin transport is effected by pulsations in the liquid stream. Calcium loaded resin was treated with copper nitrate and copper sulfate solutions. Mass-transfer coefficients for every plate were calculated from the experlments by the McCabe-Thiile method. A mass-transfer model based on particle and Ilquid film diffusion resistance to mass transfer was set up. This model describes the performance of the column rather well.
Introduction Fluidized ion-exchange columns are suitable for continuous exchange processes. Two advantages of the fluidized bed over the usual fmed bed operation are (1)the possibility of treating liquids containing suspended particles and (2) the possibility of combining the ion-exchange process with an irreversible reaction (precipitation). Both applications would cause fouling in a fixed bed, and also, according to Slater (1982), ion-exchange in countercurrent equipment requires a lower resin inventory than a fixed bed. In a fluidized bed, however, mixing of the resin can greatly reduce the separation performance. In this study we have split the column in compartments to suppress solid mixing. The resin is fluidized on a perforated plate. Pulsations in the liquid flow allow the resin to fall through the holes in a plate into a lower compartment. The pulsation time is short compared to the time between pulsations. In essence, the multistage fluidized bed used here is the same as the Cloete-Streat (1962) contactor and the USBM contactor (George et al., 1968). The cation exchange system R-Ca
+ Cu2+
R-Cu
+ Ca2+
was studied (R denotes the resin matrix). Copper nitrate and copper sulfate solutions were treated. In the latter case the formation of a calcium sulfate precipitate was expected to enhance the mass-transfer rate.
Theoretical Section Our system can be approximated as a steady-state countercurrent staged column. Theoretical analyses of such systems can be found in textbooks, such as Treybal that of (1980, Chapters 5 and 10). The experimental results can be presented in a McCabe-Thiele diagram. As the transfer of calcium ions is from the resin to the liquid, the operating line is above the equilibrium line in Figure 1.
At the inlet the liquid only contains copper ions. At the outlet it contains copper as well as calcium. The resin is in the calcium form when it enters a t the top of the column. Before liquid concentrations on the plates are determined the column is first allowed to attain a steady state. The compositions of the resin outlet and compositions on every plate can be calculated by using overall and local material balances (Figure 2) L(O)x(O) - L(N)x(N)= S(l)y(l) - S(N + l)y(N + 1) (1)
O196-4305/04/ 1123-0660$01.50/0
where L and S are liquid and resin flow rate, respectively, and x and y are Ca2+fractions of the liquid and the resin. The total ionic flow rates in both the liquid and the resin are constant throughout the column. We therefore may write
L(x(0)- x(N)) = SMl) - Y ( N + 1))
(3)
The residence time of the two phases in one compartment is not sufficient to equilibrate the concentrations. A stage efficiency for the resin or the liquid phase can be defined as the fractional approach to equilibrium in any stage. The Murphree stage efficiency for the resin phase in compartment N is given as
The liquid and the resin are assumed to be well mixed in a compartment, so the concentrations are the same everywhere on a stage. In this case the Murphree dispersed phase efficiency can be written in terms of the number of overall transfer units for the dispersed phase, Noy
where Noyis defined as K....A
(7)
KO,is the overall mass-transfer coefficient based on the r e m phase, A is the specific interfacial area per plate, and Qdis the resin volume flow. The specific interfacial area per plate is given by A =
6(1 - e)V(comp)
(8)
d3,2
where e is the void (liquid) fraction, V(comp) is the volume of the compartment, and d3,2is the Sauter particle diameter. The observed rate of exchange may be either controlled by liquid film, particle, or mixed particle-liquid film diffusion. Particle diffusion control appears if diffusion inside the particle is slow compared to diffusion through the unstirred liquid film around the particle. In this case we have a concentration gradient inside the particle. In contrast if the diffusion step in the unstirred film is slow, 0 1984 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 861 >
1
i
8
z n
I COLUMN RESIN.LOADING VESSEL 3 . R E S I N CONTAINER 4 . R E S I N COLLECTOR 5. PULSATION-UNIT 6 . RESIN INLET 7 . R E S I N OUTLET 8. PUMP 9. L I Q U I D INLET I 0 . L I Q U I D OUTLET 1l.COPPER SOLUTION CONTAINER 12.WATER CONTAINER 1 3 . T I M E SWITCH I4.COMPRESSED A I R VALVE I 5 . A I R VENT 1 6 . R E S I N TRANSPORT L I O U I D
2:
YCN+l> YCN>
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Y
*
I
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YC2>
8
Y
I-
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I 16
@
3 OR 5 MM
XC8> XC1> X
XCN>
CONCENTRATION I N
LIQUID PHASE,
X
Figure 1. McCabThiele diagram for a steady-statecountercurrent process, Murphree efficiency.
30 MM
Figure 3. Sketch of the experimental setup. I
I
1 I
I
:
I
I
1
I
: 1
1
I
u
z 0 0
u
! 1
!
~ c m ,x c m
DIMENSIONLESS LIOUID Ca CONC.
Figure 2. Overall and local mass balances for a staged column.
Figure 4. The equilibrium distribution of Ca2+between the resin and the liquid, total liquid concentration 0.155 kequiv m-3.
no concentration gradient in the particle exists. As we shall see, both particle and film diffusion limitations play a role in our experiments. Experimental Section The Column and the Resin. Two plexiglass columns are used. One (0.4 X 0.03 m i.d.) is fitted with 6 plates. The distance between the plates is 0.05 m and plate height is 0.01 m. The second column is twice as long and contains 12 plates, other dimensions being the same. Sets of plates with four holes of 3 and 5 mm diameter are available. The plates are held in the column by a rubber ring. Liquid samples can be drawn from every second plate. The liquid enters at the bottom of the column; it is fed through a rotameter by a high-speed gear pump. Prior to exchange experiments the column is filled with deionized water. Resin is initially added to the column from the bottom compartment and is distributed over the other compartments by a water flow, slightly less than used in the exchange experiment; see Figure 3. The largest ionexchange particles are about 0.8 mm, so they can pass the plate holes. Excess of resin is withdrawn with the liquid effluent. The resin is fluidized on the perforated plates by the liquid. Periodically the liquid flow reverses and resin is transported downwards. Resin leaving the bottom compartment is withdrawn from the column and its volumetric flow rate is carefully measured. Fresh resin is now fed to the top compartment using “dense phase” flow; a small water stream passing through a resin container carries resin into a dipping tube and up to the top of the column. The resin flow rate is adjusted manually to the resin leaving the column. The fractional resin transfer throughout all experiments is about 15% of the resin content in a compartment. Resin holdup and resin transport are stationary after several pulsations. After a
hydrodynamic steady state is achieved we switch over to deionized water to which either copper nitrate or copper sulfate is added. The movement of a float between two photoelectric cells was utilized for periodically reversing the direction of the flow. On opening an air vent the head of the liquid in the contactor causes the float to go up. Its velocity can be adjusted. If the float goes up with sufficient speed the liquid flow in the column reverses, and resin is transferred to a lower stage. When the float has passed the upper photocell a relay operates to close the air vent and to open a compressed air valve. This forces the float back to the lower photocell which closes the compressed air valve. The opening of the air vent is contkolled by a timer switch. The cycle time was kept at 15 s, and liquid flow was reverse during approximative one second. After each experiment the resin holdup in the column is carefully measured. We used a common cation exchanger, Bayer’s Lewatit S100. It consists of sulfonated polystyrene cross-linked with 8% divinylbenzene. The beads are very nearly spherical. The Sauter diameter of the resin batch used is 0.62 mm (the arithmetic diameter is 0.56 mm). The density of the wet resin in the calcium form is 1290 kg m-3, and the capacity per volume of wet settled resin was determined at 2.1 kequiv m-3. The equilibrium curve for the exchange system was measured by the column method (Helfferich, 1962). A packed bed of Lewatit SlOO in the Na-form is slowly eluted with a triple excess of deionized water to which copper nitrate and calcium nitrate mixtures are added with calcium fraction x. The total concentration of the solution is 0.155 kequiv m-3. The equilibrium composition on the resin is slowly eluted by a triple excess of a barium nitrate solution. The copper and calcium ratio in the effluent is
662
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 0 -1 \ O
W
Z
0
H
I-
0
6
CY
i-
z W 0
z 8
0
iY W
a a
0
DIMENSIONLESS L I O U I D CONCENTRATION
0
Figure 5. Typical result presented in a McCabe-Thiele diagram, experiment no. 1. COMPARTMENT NUMBER
Table I. Experimental Conditions for the Experiments Presented in the Figuresa UC9
Ud,
expt no.
mm
mm
s-'
S-1
1 2 3 4 5 6
3.44 5.30 5.54 5.82 1.66 1.79
0.248 0.118 0.170 0.179 0.165 0.158
E
0.532 0.587 0.587 0.584 0.481 0.487
plate hole Cu(NO,),, CuSO,, diam, kequiv kequiv mm m-3 m-3 3 5 5 5 3 3
Figure 6. Influence of the slope of the operating line: experiment no. 2: (QL c,)/(Qs c) = 1.84, experiment no. 3: (QL c,)/(Qs e) = 1.33. -1 \
0
rl-l
l2
0
cuso4
0.155 0.0858 0.0858 0.085
B
I-
Z
0.1558 0.151
All experiments performed a t room temperature (- 2 1 "C).
W 0
z
0.04
a
t
!Y
W
a
analyzed by atomic adsorption; y is the calcium fraction of the copper and calcium ions in the effluent. The solid line drawn through the points in Figure 4 represents the equilibrium relation
a
0 v -
0
0
2
4
6
COMPARTMENT NUMBER
Figure 7. Influence of the counterion: Cu(NO& experiment no. 3; CuSO,, experiment no. 4.
The solid line drawn through the points present eq 9 with K = 2.5. All experiments were performed at room temperature (about 21 "C).
Results of Mass-Transfer Experiments After a steady state is reached in the column, liquid samples are drawn from every second plate and the feed. Copper concentrations are determined spectrophotometrically. Compositions on the intermediate plates were obtained by interpolation. A typical result presented in a McCabe Thiele diagram is given in Figure 5. It can be constructed from the concentration data given in Figure 10 using the procedure given before. The average Murphree stage efficiency is 40%. It is not a constant over the column length. The experiments are very reproducible. In general the overall mass-transfer coefficients per tray decrease from the bottom to the top compartments. The scatter in the mass-transfer coefficients is considerable. Although the concentrations scatter less than 5%, this may lead to a 30% error in the calculated overall mass-transfer coefficients. This is due to the small concentration differences per plate. The experimental conditions for all experiments are given in Table I. Figure 6 shows the effect of increasing the resin flow rate. The slope of the operating line is decreased. Meanwhile, the liquid flow and the liquid inlet concentration are kept constant. This yields a better copper removal. In Figure 7 experiments with copper nitrate and copper sulfate solutions are compared. Liquid and resin flow rates are the same. The counterion does not seem to have any influence on the exchange rate. No
-1 \
0
W
l6
r 0
cuso4
H i4:
i Y
0.08
8,
W
u
z 0
0,
0
0.04 W
a a a 0
0 '
2
4
6
8 10 12
COMPARTMENT NUMBER
Figure 8. Influence of calcium sulfate precipitation on the exchange rate: Cu(NO.&, experiment no. 5; CuSO,, experiment no. 6.
precipitation of calcium sulfate occurred. From Perry (1973) diffusion coefficients of the copper ion in nitrate and sulfate solutions can be calculated. They differ 30%, being higher in nitrate solutions; this difference does not yield a higher transfer rate of copper from the liquid to the resin. An experiment in which calcium sulfate precipitation occurred starting from the 5th plate is given in Figure 8. From Table I1 and Figure 8 it is apparent that the calcium sulfate solution is supersaturated by a factor of 2 at this stage. In the same graph the result of a comparable experiment using copper nitrate is shown. The precipitation does not seem to affect the mass-transfer rate; the pre-
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 663 Table 11. Physical Properties of the System Used C 2.1 kequiv m-3 wet settled resin (w.s.r.)
K Dcu
m 2.5 (c, = 0.155 kequiv m - ) ) 3x m2 s-l
Dca
6 x l o - ” m 2 s-l
6
16 0 -. -1 \
0 W
7.2 x 10‘lo m 2 s-l 7.9 x m z s-l
Dcu Dc,
Solubility of Calcium in Copper Sulfate Solutions (Linke and Seidel, 1958) 0 M CuSO, 1.53 x kmol m - 3 1.46 x kmol m” 0.02 M CuSO, 0.05 M CuSO, 1.37 x kmol m - 3 0.09 M CuSO, 1.29 x kmol m-3 0.12 M CuSO, 1.28 x kmol m - 3 0 . I6
I
I
6
0.04
a a 0 0
0
EXPERIMENT
s
SIMULATION
I I I I I I I I I I I I I
‘0
2
6
4
8
10 12
COMPARTMENT NUMBER
Figure 10. Comparison of experimental and predicted performance; same conditions as for Figure 5.
\
W
0
TIME
REFERENCE E X P .
SECONDS
Figure.9. The interruption test; 0.250 kg of wet resin in the calcium form in 1200 mL of copper nitrate solution; initial copper nitrate concentration was 0.1504 kequiv m4; stirring 2.2, rev s-l, and particle diameter, 1.09 mm.
cipitate is washed out of the column by the liquid. Study of the particles leaving the column revealed they were clean, with no precipitate adhering to their surface. Variations in the liquid and the particle fluxes were not found, within the experimental error made, to have any influence on the overall transfer coefficient. To check whether film or particle diffusion was controlling, we performed an interruption test (Helfferich, 1962). We performed the test with the resin transferred to a stirred vessel in which a standard turbine impeller of the Rushton type with a vessel diameter of 140 mm was used (Nagata, 1975). During an exchange experiment the beads were removed and quickly separated from adhering solution. After a brief period they were reimmersed in their solution and the experiment continued. The experiment was compared to one under the same conditions, without interruption. See Figure 9. Simulation of the Experiments The interruption test shows that particle diffusion or mixed particle-liquid f i i diffusion controls the exchange rate. In the batch experiments the liquid film masstransfer coefficient will be about twice as high as for the experiment in the plate column due to better stirring. Another indication of the rate-controlling step is obtained from the Helfferich criterion (Helfferich, 1962)
where E denotes the resin capacity, c, is the total liquid concentration, Dd and D, are the diffusion coefficients of the ions involved in the resin and the liquid, respectively, 6 is the liquid film thickness, d is the particle diameter, and K is the equilibrium constant. Taking the values from Table I1 with the resin in its original calcium form, a value of H = 0.34 is found. For H much smaller than unity, particle diffusion control is predominant. If H is very
much greater than unity the control is by film diffusion. These considerations lead to the conclusion that the particle diffusion resistance is the larger one, but that the film resistance is not entirely negligible. Calculation of overall mass-transfer coefficients from the partial ones can be found in textbooks (Treybal, 1980). The overall mass-transfer coefficient can be written for not too strongly curved equilibrium lines as -1- - -l m
+-
kd
kc
where k d and kc are the mass-transfer coefficients for the resin and the liquid phase, respectively; m is the local slope of the equilibrium line in Figure 1. This is the “two resistance” approach developed by Lewis and Whitman (1924). Because k, is relatively unimportant and the flow conditions on the plate are not too well-defined, we have roughly modeled the mass transfer in the liquid phase by a constant film thickness of m
DC k, = - m s-l
10-5 Values of this order of magnitude can be obtained from the Snowdon and Turner (1967) relation for solid-liquid fluidized beds. In the experiments the extraction factor, E, varies throughout the column; ita value is close to unity, however. Biot numbers, Bi,for every plate are about 35. From Vorstman (1971) a value of Shd = 10 can be found for these conditions. Diffusion coefficients of the copper and calcium ion inside the ion-exchanger are taken from the literature (Slater, 1979). Since calcium and copper have a slightly different diffusion coefficient inside the resin, a Nernst-Planck (Helfferich, 1962) relation is used. With the model above, the performance of the column is calculated. A summary of the physical properties used in the calculations is given in Table 11. The calculation is compared with experiment in Figure 10. All experimenta could be simulated with the model above within 5%. So far only experiments on the Cloete Streat contactor have been simulated using models based on either liquid film (Gomez-Vaillard et al., 1981, treatment of a 0.036 N sodium hydroxide solution) or intraparticle diffusion controlled kinetics (Gomez-Vaillard and Kershenbaum, 1981, treatment of a 0.1 N sodium hydroxide solution). Our model shows a gradual shift from liquid film to intraparticle diffusion controlled kinetics on raising the concentration of the solution treated. This is simulated for the copper/calcium system in Figure 11. In this simulation, E/co is taken as an average value for m.
884
Ind. Eng. C b m . Process Des. Dev., Vol. 23, No. 4, 1984
Y
\
E
u 0 Y \
1
u 0
~
~
005
C,
0 1
015
0 2
keq~n‘~
Figure 11. Simulation to ahow the dependency of the ” s f e r resistance upon the total concentration of calcium and copper ions in solution.
Conclusions (1) In the exchange experiments, no effect on a performance could be seen on changing the liquid f “ copper nitrate to copper sulfate solution. (2) Calcium sulfate precipitation did not affect the mass-transfer rate. (3) Precipitate is washed out of the column by the liquid. (4) A varying mass-transfer coefficient over the column length was calculated from the experiments. (5) The mass-transfer model proposed accounts for this; it simulated the experiments very well. (6) From the model it follows that the mass-transfer resistance inside the particle gredominates. (7) Plate efficiencies increase with increasing residence time of the liquid. Nomenclature A = specific interfacial area per plate, m2 Bi = Biot number = k,d/2bd, c = liquid concentration, kmol m-a c* = liquid concentration at equilibrium, kmol m-3 E = resin capacity, kmol m-s d = arithmetic mean particle diameter, m d,,, = Sauter particle diameter, m 6 = liquid film thickness, m D, = diffusion coefficient in liquid phase, m2 s-l D d = diffusion coefficient in resin phase, m2 s-l E = extraction factor = (Qc/Qd)m
E m = Murphree plate efficiency for the resin phase e = liquid holdup H = value of the Helfferich criterion K = equilibrium constant KOy= overall mass-transfer coefficient based on the resin phase, m s-l k = partial mass-transfer coefficent, m 8-l L = liquid flow rate, mol s-l m = slope of the equilibrium line, dP/dc NOy= number of overall transfer units based on the resin phase Q = volume flow, m3 s-l S = resin flow rate, mol s-l Sh = Sherwood number u = superficial velocity, m s-l V(comp) = compartment volume, m3 x = dimensionless calcium liquid concentration y = dimensionless calcium resin concentration Subscripts c = continuous, liquid phase
d = dispersed, resin phase N = compartment number L = liquid phase od = overall dispersed phase o = inlet S = solid, resin phase Literature Cited Cloete, F. L. D.; Streat, M. BrMh Patent 1070 251, 1982. George, D. R.: Ross, J. R.; Rater, J. D. Mln. €ng. 1988, 1 , 73. (bmez-Vallard, R.; Kershenbaum, L. S.; Streat. M. Chem. Eng. S d . 1981,
36.308. Gomez-Vaiiard, R.; Kershenbaum, L. S. Chem. Eng. Sci. 1981, 36, 319. HeHferlch, F. ”Ion Exchange”; McGrawHIII; New York, 1982; Chapters 5 and 8. Lewis. W. K.; Whitman. W. 0. Ind. Eng. Chem. 1924, 16, 1215. Llnke, W. F.; Seidei, A. “Solubilltles of Inorganic and Metalorganlc Compounds’’, 4th ed.; D. Van Nostrand: Princeton, NJ, 1958. Nagata, S. “Mlxlng”; Kodansha Ltd.: Toyko; WUey: New York, 1975. p 253. Perry, R. H.; Chllton, C. H. “Chemical Englneers’ Handbook”, 4th ed.; McGraw HN: New Ywk, 1973. Slater. M. J. t$&m”ehrgy 1879, 4, 299. Siater, M. J. Tans. I. chem.E. 1982, 60, 54. Snowdon, C. B.; Tumer, J. C. R. “Proceedings of the International Symposium on Fluldlzation”, June 1987, Elndhoven, Netherlands Universw Press, Amsterdam, 1987; p 599. Treybal, R. E. “Mass-Transfer Operations”, 3rd ed.; McGraw-HIII: Auckiand, 1980 Chapters 5 and 10. Vorstman, M. A. G.; Thlben, H. A. C. "Proceedings of the InternationalSdvent Extraction Conference”, The Hague, Society of Chemical Industry: London, 1971; p 1071.
Received for review January 13, 1983 Revised manuscript received September 21, 1983 Accepted October 20,1983
