Ind. Eng. Chem. Res. 1987, 26, 1906-1909
1906
Mixed-Bed Ion Exchange at Concentrations Approaching the Dissociation of Water. Temperature Effects Suhas V. D i v e k a r and G a r y L. F o u t c h " School of Chemical Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
C. Eugene Haub Process Engineering Department, Conoco, Ponca City, Oklahoma 74603
The mixed-bed ion-exchange model for ultralow concentrations described and discussed in previously published models has been expanded to include the effects of temperature on the resin selectivity coefficients, ionic diffusion coefficients, ionization constant for water, and viscosity of the bulk solution phase. Simulations show the relative significance of these terms on the overall model as a function of temperature. Changes in the ionization constant of water and the ionic diffusion coefficients are most significant and override changes in the resin selectivity coefficients. The change in solution viscosity gives a complex affect in combination with the ionic diffusion coefficients. This work generalizes a previous mixed-bed ion-exchange model (Haub and Foutch, 1986a,b) by introducing temperature effects on equilibria and the kinetics of ion exchange. The previous model was developed with parameters assigned their respective values at 25 "C. The current model expands the temperature operating range from 10 to 90 "C. Expressions for the temperature-dependent terms (resin selectivity coefficients, ionic diffusion coefficients, ionization constant for water, and viscosity of the bulk solution phase) were obtained from the literature. The model is capable of handling variations in the cation-to-anion resin ratio; differing cation- and anion-exchange rates, exchange capacities, and particle sizes; reversibility of exchange at low concentrations; neutralization reactions within the film and bulk-liquid phases; and effluent ion concentrations on the order of 1 ppb (1 X M).
(1953), Harris and Rice (1956), Myers and Boyd (1956), Kielland (19351, and Gaines and Thomas (1953). All these models are based on fundamental thermodynamics. Most are complex and present formidable problems in evaluating model parameters. The simplest and most widely used model is that of Gregor (1948, 1951), based on the Gibbs-Donnan equilibrium. This has been extensively studied and applied to several ion-exchange systems. The match between experimental and theoretical results using Gregor's model is good. Using the Debye-Huckel theory of electrolytes, Kraus and Raridon (1959) developed a method for expressing selectivity coefficients as a function of temperature. Kraus and Raridon showed that if heat capacity changes are assumed to be constant, the expression for the selectivity coefficient is log K = log Kt + C'log ( T / T , ) + C"(1 - T t / T ) (1)
Introducing Temperature Effects The mixed-bed ion-exchange model of Haub and Foutch (1986a,b) assumes uniform isothermal conditions of 25 "C throughout the bed. Typical industrial beds operate at higher temperatures. This work expands the range for the model from 10 to 90 "C. These temperature limits are fixed by the range of temperatures for which resin selectivity coefficients have been correlated. The improved model calculates all parameters at the isothermal operating temperature. The parameters affected by temperature are resin selectivity coefficients, ionic diffusion coefficients, ionization constant for water, and viscosity of the bulk solution phase. Selectivity Coefficient. In general, ion exchange is an exothermic process. Thus, high temperature adversely affects ion-exchange equilibria and, hence, the selectivity coefficient. The effect of temperature on some common ion-exchange processes has been presented by Bonner and Pruett (1959a,b). For example, the selectivity coefficient for the exchange of hydrogen to sodium on 16% DVB Dowex-50 resin decreases from 1.97 to 1.24 between 0 and 97.5 "C. Selectivity coefficients can be related to their controlling parameters by theoretical models developed by Gregor (1948, 19511, Lazare et al. (1956), Katchalsky and Lifson
where C', C", and K, are constants and subscript t refers to a reference temperature. By fitting experimental data to eq 1, Bonner and Pruett (1959a,b) determined parameters C', C", and K,. The deviations between observed and calculated values of the selectivity coefficient appear to be within the limits of experimental error (Kraus et al., 1960). Other methods of correlating the temperature dependency of selectivity coefficients have been reported; however, none are easy to use nor extensively studied. For practical purposes, Gregor's model and the Kraus-Raridon method provide convenient and powerful practical methods for determining the effect of temperature on equilibria. Selectivity of ion-exchange resins is enhanced by increasing the degree of cross-linking and by decreasing the solution concentration. Ions with higher valence, smaller (solvated) equivalent volume, and greater polarizability are preferred. The effect of the degree of cross-linking on the selectivity is illustrated by Myers and Boyd (1956). Each resin exhibits a unique behavior depending on the type of resin used (chemical groups in the resin, degree of cross-linking, and method of preparation), initial relative proportion of ions in the resin and bulk solution phase, chemical nature of counterions, other substances present in the solution phase (reacting or nonreacting ions), and temperature. To compare mixed-bed ion-exchange behavior at various temperatures, the following equations for the cation and the anion resin selectivity coefficients were
* Author to whom all correspondence should be
sent.
0888-588518712626-1906$01.50/0 8 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1907 incorporated in the Haub and Foutch model:
Kga = 1.1814 + 9.9836/T - 9.195/T2
P$p = 1.2031 + 6.1505/T
+ 6.2143/T2
(2) (3)
The equation for the cation-exchangeselectivity coefficient was developed by using experimental results reported on 16% DVB Dowex exchanger (Bonner and Smith, 1957). This resin has a selectivity coefficient of 1.55 a t 25 "C. Data on anion-exchange resins are scarce compared to cation-exchange resins. The Haub and Foutch model used a selectivity coefficient of 1.45 for the anion-exchangeresin a t 25 "C, which is typical for Type I1 anion-exchange resins. Equation 3 was generated by a symmetrical fit to eq 2 through the value of 1.45. Diffusion Coefficients. In an electrolyte solution, the solute is in the form of cations and anions. Because the size of the ions differ, their mobility through the solvent differs. Smaller ions diffuse faster than larger ions. However, both ionic species must also respond to an overall charge balance. The Nernst (1888) equation provides a simple and accurate method for predicting diffusion coefficients in electrolyte solutions by relating the diffusion coefficient to electrical conductivities:
at regularly spaced temperature intervals. These are represented within experimental error by a quadratic least-squares fit. The relation between the ionization constant and temperature has been derived as (Hmned and Robinson, 1940) R In KIP = - A / T + B - C T (12) The ionization constant for water is represented by -(log K,) = 4470.99/T - 6.0875 + 0.01706T (13)
Viscosity of the Bulk Solution. Calculations of liquid viscosities based on theoretical methods have not yet been developed. Empirical estimations from structure or other physical properties have been used. The viscosity of liquids decreases with temperature. Viscosity-temperature plots can be represented by the Andrade correlation over a wide range of temperatures from above the normal boiling point to near the freezing point: p1 =
Dp = (RT/F2)AP
(5)
Equation 5 provides a convenient method of relating temperature to the ionic diffusion coefficients. The conductance of electrolytes increases with temperature (Maron and Prutton, 1958). The variation of equivalent conductance with temperature can be represented by
A! = Aj5oc(1 + P ( t - 25))
(6)
The constant /3 is 0.022-0.025 for salts and 0.016-0.019 for acids. Typical variations of equivalent conductance with temperature at infinite dilution are presented by Robinson and Stokes (1955). Temperature and the equivalent conductance are correlated by least squares a t infinite dilution, the representative equations being
+ 5.52964T - 0.014445T' Ab, = 104.74113 + 3.807544T2 Aha = 23.00498 + 1.06416T + 0.0033196T2 A& = 39.6493 + 1.391767' + 0.0033196T' Ab
= 221.7134
(7) (8) (9) (10)
Combining eq 5 and 7-10 provides expressions to relate the effect of temperature on the diffusion coefficients of ions of the form
Di = (RT/F2)(Ai + BiT + CiT2)
(11)
Ionization Constant of Water. Many equations have been proposed to represent the temperature variations of the ionization constant, but the methods used to evaluate the constants in the equation impose severe restrictions on their applicability. The most accurate equations are empirical. Experimentally, cell potentials are measured
(14)
Several other empirical relations between viscosity and temperature have been suggested (Reid et al., 1977; Fabuss and Korosi, 1967). One form shown to be accurate at low temperatures is p1 =
The Nernst equation has been verified experimentally for dilute solutions. The diffusion coefficients of single ions in solution can be calculated (Robinson and Stokes, 1955) by using
A exp(B/T)
exp(B/(T
+ C))
(15)
For a number of associated liquids, Makhija and Stairs (1970) tabulated parameters for use in their equation of the form p1 =
exp(A'+B'/(T-T'))
(16)
Constants A', B', and T'are -1.5668, 230.298, and 146.797, respectively, for water between -10 and 160 "C. Extensive experimental viscosity-temperature data for sodium chloride solutions are now available. However, since the salt concentration in water entering mixed-bed ion-exchange columns is very low (10-7-10-8 M), the solution can be treated as pure water for calculating the viscosity.
Results and Discussion The selectivity coefficient and the solution viscosity decrease as temperature is increased. The ionization constant of water and the ionic diffusion coefficients increase with an increase in temperature. The relative contributions of these opposing effects are dependent on the current properties of the bed. Model simulations have been examined to observe the combined effect. The system parameters for these mixed-bed simulations are presented in paper 2 (Haub and Foutch, 1986b). Figure 1shows the effect of temperature on typical sodium concentration profiles after 6, 57, and 97 min, for a cation/ anion ratio of 1.5. The concentration profiles after 6 min show that higher temperature results in lower effluent concentrations, indicating that exchange is better at higher temperatures. The concentration profiles after 57 and 97 min have two zones. Closer to the column inlet, the higher temperature curves give higher solute concentrations. However, farther from the column inlet, the situation is reversed. Thus, near the column inlet, where the resin is approaching saturation, ion exchange is slightly impaired a t higher temperatures. However, the exchange for the remaining portion of the column, which determines the effluent concentration, is significantly enhanced at higher temperatures. A similar effect is observed for chloride. As temperature is increased, the selectivity coefficients steadily decline, whereas, the ionization constant of water and the ionic diffusion coefficients increase. The ionization
1908 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987
0
-
01:
1 -
-
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O
oooolo
/
'
10
20
'
'
30
0 00010
DISTANCE FROM COLUMN I N '
20
40
60
80
100
120
140
Figure 1. Variation of sodium concentration profiles with temperature after 6, 57, and 97 min for a cation/anion ratio of 1.5.
i
t///,
P
i
0.0001
0
20
40
, 60
80
1.2 100
120
140 0.0
TIME (MINUTES1
=
0.2
0.6 0.4
0.6
0.8
1.0
EOUIVALENT FRACTION OF CHLORIDE IN THE RESIN PHASE ( y c I l
Figure 2. Variation of sodium breakthrough curves with temperature for mixed-bed simulation having a cation/anion ratio of 1.5.
constant shows a 20-fold increase from 15 to 70 "C. The ionic diffusion Coefficients increase by a factor of 3 in this range. The other parameters change to a much smaller extent. Thus, the most pronounced effect due to a temperature change is in the ionization constant. At higher temperatures, both Ch and C, (the hydrogen and hydroxide ion concentrations) are increased due to the increase in the ionization constant of water. This results in a reduced concentration gradient for ion mass transfer out of the exchange resin. Thus, the flux for mass transfer of the hydrogen and hydroxide ions is controlled by two opposing factors. The diffusion coefficients tend to increase the flux but the increased bulk-phase concentrations tend to reduce the flux. If the latter effect is dominating, the mass transfer of the hydrogen and hydroxide is impaired. Since ion exchange is a stoichiometric process, this reduces the flux of the ions diffusing out of the resins. The breakthrough curves (Figures 2 and 3) for sodium and chloride exhibit identical trends. The curves are steeper at higher temperatures. The ratios of the effluent to feed solution concentrations differ by an order of magnitude between the temperature range of 15 and 55 "C through most of the run. Higher temperatures give a significantly smaller effluent to feed concentration ratio until the bottom layers of the resin bed approach saturation.
C[/C;,
Figure 4. Variation of exchange rate with progression of ion exchange.
Figure 4 shows the effect of temperature on the rate of exchange as a function of the equivalent fraction of chloride in the resin phase. This resin has a finite rate of exchange at equilibrium. An increase in temperature increases the exchange rate. Due to the significant decrease in the solution viscosity at higher temperatures, the mass-transfer coefficients are increased. The viscosity effect completely cancels the effect of decreased selectivity coefficients and reduced concentration differences. The nonionic mass-transfer coefficients are calculated by using Kataoka's (1976) and Carberry's (1960) methods. The ratio of electrolyte to nonelectrolyte mass-transfer coefficients, R,, increases with temperature at high ion loading as seen in Figure 5 . R, is strongly dependent on temperature only in the latter stages of resin loading. At low chloride concentrations in the resin phase, R, factors are higher at lower temperatures. As chloride in the resin increases, a crossover occurs where higher temperatures give higher R, values. Conclusions
The four temperature-dependent parameters (resin selectivity coefficients, ionic diffusion coefficients, ionization
Ind. Eng. Chem. Res., Vol. 26, No. 9,1987 1909 performance is a complex function of these variables. 4. Two distinct zones are seen in the concentration profiles and breakthrough curves. In one zone, higher temperature gives better results; in the other, the reverse effect is noticed. 5. The breakthrough limits a t exhaustion are only marginally affected by temperatures. However, the effect of temperature below resin capacity is strong. Thus, temperature is an important parameter in mixed-bed ion exchange, particularly so, because column operation is terminated and the resins subjected to regeneration well below exhaustion.
Acknowledgment This work was partially supported by NSF Grant RIT8610676. Registry No. Na, 7440-23-5.
Literature Cited 1.01
00
I
I
1
I
I
0.6 0.8 1.0 EQUIVALENT FRACTION OF CHLORIDE IN THE RESIN PHASE ( y c ~ )
0.2
0.4
Figure 5. Variation of Ri with progression of ion exchange for C& = 1.0 X lo6 M.
constant of water, and viscosity of the bulk solution phase) have opposing overall effects on ion-exchange phenomenon. The most important temperature-dependent factor is the ionization constant of water, which shows a 16-fold increase as temperature is increased from 10 to 60 "C. The ionic diffusion coefficients exhibit a 3-fold increase in this temperature range. The remaining two factors, resin selectivity coefficient and the solution viscosity, decrease with an increase in temperature. The resin selectivity coefficients are reduced by a factor of 1.5 and the viscosity by a factor of 3. Based on simulations a t several temperatures, it is possible to conclude the following: 1. The ionization constant of water and the ionic diffusion coefficients cause the most significant changes in the mixed-bed ion-exchange behavior with respect to temperature. 2. The decrease in resin selectivity coefficient with increase in temperature is overridden by the above two factors. 3. The effect of the decrease in solution viscosity with increased temperature on the mixed-bed behavior is difficult to interpret qualitatively. The solution viscosity has a direct influence on the mass-transfer coefficients and hence the R, factors. The resulting effect on the mixed-bed
Bonner, 0. D.; Pruett, R. R. J . Phys. Chem. 1959a,63(9), 1417. Bonner, 0. D.; Pruett, R. R. J . Phys. Chem. 195913, 63(9), 1420. Bonner, 0. D.; Smith, L. L. J . Phys. Chem. 1957, 61, 1614. Carberry, J. J. AZChE J. 1960,4, 460. Fabuss, B. M.; Korosi, A. US. Office Saline Water Research Development Program Report 249,1967; U S . Government Printing Office, Washington, D.C., p 50. Gaines, G. L., Jr.; Thomas, H. C. J . Chem. Phys. 1953, 21, 714. Gregor, H. P. J. Am. Chem. SOC.1948,70, 1293. Gregor, H. P. J . Am. Chem. SOC.1951, 73, 642. Harned, H. S.; Robinson, R. A. Trans. Faraday SOC.1940,36, 973. Harris, F. E.; Rice, S. A. J . Chem. Phys. 1956,24, 1258. Haub, C. E.; Foutch, G. L. Znd. Eng. Chem. Fundam. 1986a,25, 373-381. Haub, C. E.; Foutch, G. L. Znd. Eng. Chem. Fundam. 1986b,25, 381-385. Kataoka, T., et al. J . Chem. Eng. Jpn. 1976,9, 130. Katchalsky, A.; Lifson, S. J . Polym. Sci. 1953,ZZ, 409. Kielland, J. J. SOC.Chem. Znd. (London) 1935,56,232T. Kraus, K. A.; Raridon, R. J. J . Phys. Chem. 1959,63, 1901. Kraus, K. A.; Raridon, R. J.; Holcomb, D. L. J . Chromatogr. 1960, 3, 178-179. Lazare, L.; Sundheim, B. R.; Gregor, H. P. J . Phys. Chem. 1956,60, 641. Makhija, R. C.; Stairs, R. A. Can. J . Chem. 1970,48, 1214. Maron, S. H.; Prutton, C. F. Principles of Physical Chemistry; Macmillan: New York, 1958. Myers, G. E.; Boyd, G. E. J . Phys. Chem. 1956,60, 521. Nernst, W. 2.Phys. Chem. 1888,2, 613. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1955; p 440.
Received for review April 27, 1987 Accepted June 15, 1987
