I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY,
October 1955 I
CD
= equivalent concentration of electrolyte taken up
CR d
= =
F
=
K1 K* Ka = I ~ ~ c ,
=
K O
= =
KR K?"
+z, y,
= = E
=
by resin, equivalents per milliliter of resin resin capacity, equivalents per milliliter of resin fractionallength of solid component of conductance element 1 as shown in Figure 6 formation resistivity factor; a dimensionless parameter descriptive of the geometry of the conducting interstitial solution network contributions of conductance elements 1, 2, and 3, respectively (Figure 6), t o specific conductance of porous plug, mho cm. -l equivalent conductance of potassium and chloride ions in resin, respectively, mho sq. em. eq.-l specific conductance of porous plug, mho cm.-' specific conductance of solidl mho em.-' specific cohductance of interstitial saturating solution, mho cm. porosity of porous plug dimensionless geometrical parameters descriptive of conductance components of model (Figure 6), as defined in Equation 1 LITERATURE CITED
G* E's Trans' Am' Inst Mining
Met* Engrs'p 146* j4 (1942). (2) Bauman, W. C., Anderson, R. E., and Wheaton, R. AI., Ann. Rev. Phys. Chem., 3, 109 (1952). (l)
2193
(3) Duncan, J. F., Proc. Roy. SOC.(London), A214, 344 (1952). (4) Gregor, H. P., J. Am. Chem. Soc., 70, 1293 (1948). (5) Gregor, H. P., and Gottlieb, M.H., Ibid., 75,3539 (1953). (6) Gregor, H. P., Gutoff, F . , and Bregman, J. I., J . Colloid Sei., 6,245 (1951). (7) Heymann, E., and O'Donnell, I. J., Ibid., 4, 395 (1949). (8) Patnode, H. W., and Wyllie, M. R. J., Trans. Ana. Inst. M i n i n g Met. Engrs., 189,47 (1950). (9) Perkins, F. M., Brannon, H. R., and Winsauer, W. O., J . Petroleum Technol., 6, 29 (1954). (10) Schofield, R. K., and Dakshinamurti, C., Discussions Faraday SOC., 3, 56 (1948). (11) Slawinski, A., J. chim. phys., 23, 710 (1926). (12) Spiegler, K. S., J . Electrochem. Soc., 100, 303C (1953). (13) Spiegler, K. S., and Coryell, C. D., Science, 113, 546 (1951). (14) Stamm, A. J., Physics, 1, 116 (1931). (15) Walters, W. R., Weiser, D. W., and Marek, L. J., IND.ENG. CHEM., 47,61 (1955). (16) Winsauer, W. O., and Y'cCardell, W. M., Trans. Am. Inst. M i n i n g Met. Engrs., 198,129 (1953). (17) Wyllie, M. R. J., and Gregory, A. R., Ibid., 198, 103 (1953). (18) Wyllie, M. R. J,, and Southwick, P. F., J. Petroleum Technol., 6 , 44 (1954). (19) Wyllie, M. R. J., and Spangler, M. B., Bull. Am. Assoc. Petroleum Geol., 36,359 (1952). RECEIVED for review Kovember 26, 1954.
ACCEPTED
April I:,
1955.
Rates of Ion Exchange in the System
Sodium-Potassium-Dowex 50 A. D. SUJATA', J. T. BANCHERO, AND R. R. WHITE D e p a r t m e n t of Chemical a n d Metallurgical Engineering, University of Michigan, A n n Arbor, M i c h .
THE
ion exchange process is carried out b y passing solution through a fixed bed of ion exchange material. As the solution passes through the bed, some of its ions are exchanged for ions of a different species from the resin. For each ion entering the resin, the resin must give up one of its ions, as expressed by the equation
A++BR=AR+B+ h s this is a reversible reaction, it can go in either direction, depending on the concentrations of the reactants and products. When a n ion exchange unit is first placed on stream, i t will deplete the solution of most of its A + ions. As the bed becomes partially saturated, more of the A + escapes capture, and the concentration of A + in the effluent increases. Later the bed becomes saturated. No exchange occurs, and the Concentration of A + in the effluent is the same as in the feed t o the bed. The concentration history of the bed effluent is given by a breakthrough curve such as shown in Figure 1. The shape of a break-through curve depends on inany things: the feed concentration, the exchange capacity and dimensions of the bed, t h e diameter of the exchanger particles, the rate of liquid flow, and the temperature of the system. These variables t h a t control the rate of ion exchange were studied for the sodium chloride-potassium chloride-Dowex 50 system. The range of experimental variables studied is summarized in Table I. APPROACH
Two methods of approach can be used t o relate the rate of ion exchange t o the variables mentioned. T h e first assumes a reac1
Present address, C. F. Braun and Co., Alhambra, Calif.
tion mechanism, translates the assumed mechanism to an integral equation describing bed performance, and fits the derived equation t o the experimental data. The second method takes the experimental data, and extracts from them the rates of ion exchange. First (Integral) Method. A material balance, written on a differential basis, is derived t o express the distribution of the exchanging ion among the feed, effluent, holdup-the quantity of liquid retained in the bed-and the resin. The mechanics of the transfer process are postulated and stated as a rate e uation. The material %dance and the rate equation, with suitable boundary conditions, are solved t o give an equation representing a family of break-through curves. The derived equation is fitted t o the experimental breakthrough curves t o evaluate the arbitrary constants. These constants determine the particular equation t h a t represents the experimental curve. The constants determined in the fitting process are correlated in terms of the variables.
Table I.
Range of Experimental Variables Investigated
Feed concentration. 0.134N KC1 or NaCl Temperature. ca. 25' C. Column diameter. 2.54 om. Flow Rate, Resin Diameter (Na Form), Mm. Bed Equivalence, Meq. Ml./Min.
+
Exchange reaction. 0.715 0.428 0,236
KC1 N a R = KR 81-628 81-324 81-275
Exchange Reaction. 0.715 0.236
NaCl KR 81-628 81-278
+
=
+ NaCl
NaR
0.1-8.4 0.1-4.2 0.1-2.1
+ KC1 0.1-1.2
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Such a procedure, if successful, permits correlation over a wide range of conditions with a minimum of experimental data. But this method has its faults. Many assumptions are involved] t h e most important of which is the postulated exchange mechanism. Even if the correct mechanism were assumed, the resulting system of differential equations is usually too complex to be solved by analytical methods. Further approximations are made, and the equations are reduced t o a form that can be solved. It is always difficult t o distinguish between the effect of the assumptions made in solving the equations and the applicability of the postulated mechanism.
Vol. 47, No. 10
by Kunin and Myers (11)for strong sulfonic exchangers. These results and the average diameters of the particles in the wet sodium and wet potassium form are given in Table 11. Swelling. The diameter of Dowex 50 spheres depends on the ion associated with the resin and the strength of the solution surrounding it. To define the swelling property of the resin, the particle diameter was measured in solutions containing sodium or potassium chloride at various strengths. The results are expressed as the ratio of the diameter in the specified media t o the diameter of NaR in water. The swelling data are presented in Table 11. Equilibrium. The equilibrium behavior of the exchanger in contact with solutions containing both sodium and potassium is important in describing the behavior of ion exchange columns. The equilibrium is represented by the equation
Values for the equilibrium constant, K , are shown in Table 111. These values are applicable for concentrations less than 0.134N. THE EXPERIMENT
Equipment. The ion exchange columns were constructed from Tenite tubing, 1 inch in inside diameter and l l / g inch in outside diameter] as shown in Figure 2. Two 200-mesh Monel screens were placed so as t o contain the resin within the column and t o provide support for the bed. The top screen supports a layer of 65/80-mesh glass beads. Other equipment was provided to pump, meter, and control the influent to the exchange columns (Figure 3). Solution was pumped from storage to a constant-head tank located 12 feet TIME
Figure 1. Typical break-through curve Second Method. A material balance is derived as in the first met hod. A large amount of experimental data is taken, and the rates of ion exchange are computed by differentiating the experimental data. The rates of ion exchange are correlated in terms of the variables. This method has a decided advantage over the first method. Fewer assumptions are made in its application, and the actual rate of ion exchange is measured. But this method requires voluminous experimental data t o establish correlation over even a small range of conditions. T h e first, or integral, method has been applied with some success by various investigators ( I , 4-6, IO). Application of the second, or differentiation method, has not been reported in the literature. The authors believed t h a t the integral method, with suitable modifications, would be successful in this program.
TOP E N D FITTING
IiII TIE
I
__
ROD
~
I/-RESIN
!
I SECTION!
I I I
I
!
I/ L
I
(I
, -POLYETHYLENE GASKET
MATERIALS USED
Preparation of Resin. The Dowex 50 resin as received was placed in shallow trays and air-dried t o facilitate screening. Three cuts were selected for the experiment-24/28, 35 48, and 85/80 Tyler mesh. Broken and split particles were separated by rolling the sized material down an inclined plane. Samples from each cut were used t o determine the equivalent weight of air-dried resin according to a modification of the procedure given
-
BOTTOM END FITTING ( L U C I T E I
‘
STOPCOCK
Figure 2. Table IT.
TENITE COLUMN
2 0 0 - MESH MONEL SCREEN
3
-
Experimental ion exchange column
Some Properties of Dowex 50 (Resin equivalence)
Mesh of Sir-Dried Resin 24/28 36/48 66/80 Swelling Solution Water, N a form 0.01N NaCl 0.1NNaCl 1N iVaC1
Actual Resin in Wet Na Form, Meq./Ml. 3.48 3.47 3.47
D s o i n / D ~farm * 1.000 1.000
0.988 0.984
Diameter of Wet Na Form Resin, Mm. 0.715 0.428 0.236
Solution Water, K form 0.01N KC1 0 . 1 N KC1 1.ONKC1
D a o d D N a form
0.983 0.983 0.981 0.967
Table 111. Values of Equilibrium Constant (17) System. Dowex 50-NaC1-KC1-water Concentrations. < O . 134N Ionic Fraction K + in Solution, Equilibrium Constant, c/co
KE+
0 0.25 0.50 0.75 1.00
1.80 1.70 1.54 1.46 1.43
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1955
2195
of the exchanging species in the effluent to the concentration of the exchanging species in the influent was calculated. This ratio, C / Q , corresponds to the fraction of the exchanging ion remaining in solution. The volume of solution passed by the bed, y, aws calculated from the flow rate-time product (milliliters) corrected for the voids volume in the bed. Plotting C/CO against $1 gives the break-through curve for the run.
r-----l TO DRAIN
I I
STOPCOCK
Table IV.
ROTAMETER
ION- EXCHANGE COLUMN
4
STOPCOCK VALVE
e/co
!I
0.0336 0.0604 0.0945 0.1475 0.213 0.286 0.371 0.458
207.9 258.8 308.5 359.0 408.8 359.4 509.8 559 .9
B
v
I
5 GAL. STORAGE JUG
MILTON ROY
PUMP
Figure 3.
Typical Experimental Data (13)
Run 1 Partiole diameter 0.715 mm. Flow rate, 0.827m l . / s e c . co, 0.1338N KC1 Column diameter, 2.54 em. Column height, 7.4cm. Total meq. in bed, 81 Temperature, 23" C.
A
Schematic diagram of experimental flow system
above the floor level. An overflow on the constant-head tank returned excess solution to storage. Solution passed from the tank through a rotameter and then to the exchange columns. The effluent and samples were collected a t the discharge end of the bed. Methods of Analysis. The concentrations of sodium and potassium in the solutions were determined with a Beckman Model DU spectrophotometer that was equipped with a Model 9600 flame photometer attachment. Standard solutions containing both sodium and potassium in definite known proportions and of the same total normality of the unknowns were run concurrently with the unknowns. The per cent transmittance of the standards and the unknowns was measured and recorded. As the concentrations of the standards and their respective transmittances were known, a plot of the logarithm of the per cent transmittance against the logarithm of the standards concentration was prepared. The per cent transmittance of the unknowns was imposed on this plot and the corresponding unknown concentration obtained. The technique described above avoids the effect of overlapping spectra (spectral interferences) caused by the presence of both sodium and potassium in the samples. Experimental Procedure. Two steps are used in the operation of an ion exchange bed: the conditioning of the bed for the exchange operation, and the actual operation of the bed. The resin bed was converted t o the desired ionic form and washed to remove excess ions. A regenerant solution of 1N sodium (or potassium) chloride was passed dropwise through the bed until it was entirely in the desired form. Approximately 100 times the total ion capacity of the bed was passed through the column as regenerant solution. This was considered more than adequate to convert the resin completely to the desired ionic form. Five gallons of distilled water per 100 meq. in the bed were used to wash the bed of regenerant. The following data were taken for each run: bed height, eolution temperature, flow rate, as indicated by the rotameter and measured by collecting the effluent over the entire run, voids volume in the bed, total solution normality, and sodium and potassium concentrations in the effluent throughout the operation of the bed. Calculated Data. From the sodium and potassium determination, and from the total normality, the ratio of the concentration
Typical experimental data are given in Table IV. Estimated experimental errors on the measured quantities are: flow rate ~k.57~~ cumulative volume passed by bed ( y ) 1 5 ml., and fractional nonremoval of exchanging ion 1170. Values for the total normality and total equivalence of the bed have an experimental error l e v than 1 0 . 5 % . 1.0
0.8
0.6
C
I
C. 0.4
0.2
0 0
3000
4000
Y
5000
6000
WLl
Figure 4. Experimental break- through curves of runs 36 and 37, showing reproducibility of data Check runs weie made t o ascertain the reproducibility of the experimental technique. A typical comparison of the breakthrough curves for runs 36 and 3 i is shown in Figure 4. The comparisons indicated that the experimental technique gave reproducible results. THEORY
Rate Equation. In a n ion exchange process three mechanisms may offer resistance to the over-all transfer rate: (1) liquidphase mass transfer, (2) resin-phase diffusion, and (3) chemical exchange or adsorption (or reaction). Thus, the kinetics of the process will be governed by either mass transfer or chemical exchange or a combination of both. Qualitatively reviewing previous results (1-4, 6, 8-10, l a ) , it seems probable that only liquid-phase mass transfer and resin-phase diffusion would have a significant effect on the transfer process. A rate function incorporating these mechanisms into an analytic expression has been derived by Baddour ( 1 ) . This result is (Equation 2):
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 10
Equation 6 or Equation 7 permits the evaluation of the rate constant, IC, from experimentally measured quantities. From the experimental results
where k, the rate coefficient, is taken as
C -,
co
21112,
g ~ and , K are known;
S1/2is obtained by differentiation of the break-through curve. These numerical quantities are substituted in Equation 7 and n value for u is assumed. Successive cut-and-try leads to a value of u that satisfies the slope equation. From the definition of ZL the value of k is computed. Equilibrium Behavior. The equilibrium break-through curve is a limit that can be approached in practice, and thus it is a measure of the ultimate performance of an ion exchange bed. For a favorable equilibrium, K > 1, the limiting curve is given by Walter (16).
The rate function is analogous to the expression of a second-order reversible chemical reaction. The assumptions made or implied in the derivation of this rate function are: The mechanisms that limit the transport of ions from the liquid phase into the exchan er are liquid-phase transfer by eddy or molecular diffusion, an8 resin-phase diffusion. The driving forces involved in the transfer are expressible in terms of concentrations. The anion in the resin does not influence the process. A linear concentration gradient exists in the liquid phase from the exchanger surface. A linear concentration gradient exists in the resin exchanger, and can be written in terms of the surface concentration of the exchanging ion and the concentration a t the center of the particle. Equilibrium exists a t the liquid-solid interface and can be represented by the equation
From the plot of Equations 8 in Figure 5, it is seen that the equilibrium curve is vertical; thus it has infinite slope. Nonequilibrium operation gives a break-through curve that has a finite slope. As equilibrium operation is approached, this slope approaches infinity. For an unfavorable equilibrium, I< < I, the limiting curve is given by (16).
Integral Equation. The rate equation is combined with a differential material balance, and solved. The solution, as derived by Thomas (15),gives the concentration history of any point in the bed as
c/co = 0
where u = flow modulus, dimensionless, and v = bed modulus, dimensionless.
Values for the function +(u,v) are not readily obtainable from the defining equations, but they can be approximated from the asymptotic expansion of +(u, v) developed by Onsanger (14). The asymptotic expansion is given here in a somewhat modified form ( 1 ) .
