Modeling Multicomponent Ion Exchange Equilibrium Utilizing Hydrous

May 1, 1997 - Sandia National Laboratories, Albuquerque, New Mexico 87185. An equilibrium ... high selectivity for cesium (Anthony et al., 1993, 1994)...
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Ind. Eng. Chem. Res. 1997, 36, 2427-2434

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Modeling Multicomponent Ion Exchange Equilibrium Utilizing Hydrous Crystalline Silicotitanates by a Multiple Interactive Ion Exchange Site Model Z. Zheng and R. G. Anthony* Kinetics, Catalysis and Reaction Engineering Laboratory, Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122

J. E. Miller Sandia National Laboratories, Albuquerque, New Mexico 87185

An equilibrium multicomponent ion exchange model is presented for the ion exchange of group I metals by TAM-5, a hydrous crystalline silicotitanate. On the basis of the data from ion exchange and structure studies, the solid phase is represented as Na3X instead of the usual form of NaX. By using this solid phase representation, the solid can be considered as an ideal phase. A set of model ion exchange reactions is proposed for ion exchange between H+, Na+, K+, Rb+, and Cs+. The equilibrium constants for these reactions were estimated from experiments with simple ion exchange systems. Bromley’s model for activity coefficients of electrolytic solutions was used to account for liquid phase nonideality. Bromley’s model parameters for CsOH at high ionic strength and for NO2- and Al(OH)4- were estimated in order to apply the model for complex waste simulants. The equilibrium compositions and distribution coefficients of counterions were calculated for complex simulants typical of DOE wastes by solving the equilibrium equations for the model reactions and material balance equations. The predictions match the experimental results within 10% for all of these solutions. Introduction The hydrous crystalline silicotitanate, labeled TAM-5 (TAM-5 is currently marketed by UOP as IONSIV IE910 and IE-911 ion exchange powder and ion exchange granules, respectively.), developed by Texas A&M University, Sandia National Laboratory, and UOP has a high selectivity for cesium (Anthony et al., 1993, 1994). This material exhibits excellent chemical, thermal, and radioactive stability, which makes it an excellent material for removing radioactive cesium from radioactive wastes stored at many DOE (Department of Energy of the U.S.A.) sites, such as Hanford and Savannah River. Designing ion exchange equipment requires knowledge of the ion exchange performance represented by distribution coefficients, which usually are determined experimentally. Because a wide range of compositions will be encountered in processing the waste within a site and from different DOE sites, an extensive experimental program will be required. An equilibrium model which predicts the performance of the material is anticipated to reduce the experimental effort. Zheng et al. (1996) and Zheng (1996) conducted numerous experiments to characterize the ion exchange properties of TAM-5. Their results showed that the solid phase is ideal along the binary ion exchange isotherms of Cs+/Na+, Rb+/Na+, and K+/Na+ prior to the step changes in the isotherms. However, nonideal behavior is exhibited when considering the effect of pH and K+ on the Cs+ distribution coefficients. In this work, we will explore the modeling of multicomponent ion exchange by TAM-5. We will present a method to represent the solid phase using information from ion exchange experiments and structure studies * To whom correspondence should be addressed. Telephone: (409) 845-3370. Fax: (409) 862-3266. E-mail: rg-anthony@ tamu.edu. S0888-5885(96)00546-5 CCC: $14.00

so that we can treat the solid phase as an ideal phase. This procedure simplifies the solid phase description for multicomponent ion exchange. The objective is to develop a model which predicts the ion exchange performance of cesium and other cations in complex solutions. To achieve this objective, we will first discuss the conventional approach of the thermodynamic treatment of ion exchange systems. We will then discuss our approach that utilizes knowledge of the structure of the ion exchange material in the solid phase representation, and we will propose a set of ion exchange reactions for the competitive exchange between H+, Na+, K+, Rb+, and Cs+. Zheng et al.’s (1996) experimental data obtained by using simple solutions were used to estimate the equilibrium constants for these reactions. We will show that the solid phase can be considered ideal by using a suitable solid phase representation, and the equilibrium constants of our model reactions will be the rational selectivities. Bromley’s model for activity coefficients of aqueous electrolytic solutions is used to account for liquid phase nonideality. To apply Bromley’s model in complex solutions, parameters for CsOH at high ionic strength and for NO2- and Al(OH)4are estimated. Predictions of the ion exchange equilibrium for complex solutions were obtained by solving the equilibrium and material balance equations of the model reactions, together with Bromley’s model for liquid phase activity coefficients. Cesium distribution coefficients for five complex simulants were predicted. These predictions give an excellent match with the experimental data. Theory of Ion Exchange Thermodynamics Conventional Approach. Ion exchange is a stoichiometric process which can be represented for monovalent cations as follows: © 1997 American Chemical Society

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A+ + BX a AX + B+

(1)

where A and B are the counterions involved in ion exchange and X represents the framework of the solid phase. Therefore, A+ and B+ are the ions in the liquid phase, and AX and BX are the ions in the solid phase. The thermodynamic equilibrium constant is defined as follows:

aAXaB+

Keq )

(2)

aBXaA+

where Keq is the thermodynamic equilibrium constant, aAX and aBX are the activities in the solid phase, and aA+ and aB+ are the activities in the liquid phase. Activity can be calculated by multiplication of concentration and an activity coefficient; therefore, eq 2 can be further represented as follows:

Keq ) KCKγ

(3)

where

KC )

Kγ )

QAXCB+ QBXCA+

(4)

γAXγB+

(5)

γBXγA+

and QAX and QBX are the concentrations in the solid phase, CA+ and CB+ are the concentrations in the liquid phase, γAX and γBX are the activity coefficients in the solid phase, and γA+ and γB+ are the activity coefficients in the liquid phase, which is an aqueous electrolytic solution in most cases. Tabulated and model-estimated data are available for liquid phase activity coefficients (Lide, 1991; Robinson et al., 1970; Pitzer, 1991; Bromley, 1973; Zemaitis et al., 1986). The distribution coefficient of ion A+ is defined as the ratio of the equilibrium concentrations of A+ in the solid and liquid phases (Zheng et al., 1995, 1996). The heat of ion exchange, eq 1, is related to the thermodynamic equilibrium constant by the Van’t Hoff equation (Holland and Anthony, 1989) as follows:

(

)

∂ ln Keq ∂T

)

P

∆H° RT2

(6)

where T and P are the temperature and pressure, ∆H is the heat or enthalpy change of the ion exchange reaction, and R is the gas constant, which is 8.314 J/(mol K). A major difficulty in ion exchange thermodynamics is modeling solid phase activity coefficients. Gaines and Thomas (Gaines et al., 1953) derived a set of equations for binary ion exchange by using the Gibbs-Duhem equation for calculating solid phase activity coefficients and thermodynamic equilibrium constants by using an equilibrium isotherm. These equations for binary ion exchange between monovalent ions are as follows:

ln Keq )

∫01ln KR dEBX

(7)

∫0E

(8)

ln γA ) -EBX ln KR +

BX

ln KR dEBX

ln γB ) EAX ln KR -

∫E1

BX

ln KR dEBX

(9)

where KR is the rational selectivity, which is defined as the thermodynamic equilibrium constant without solid phase activity coefficients, and EAX and EBX are the equivalent fractions of AX and BX in the solid phase. Because equilibrium concentrations are measurable and liquid phase activity coefficients can be obtained from published data or model estimation, the KR’s along an isotherm are known once the isotherm is measured. Gaines and Thomas’ equations allow us to calculate the thermodynamic equilibrium constants and solid phase activity coefficients from isotherm data. However, these equations do not provide the ability to predict the solid phase activity coefficients. To describe the nonideal behavior of the solid phase, many models have been proposed. Most of the models represent the solid phase nonideality in terms of a solid phase excess Gibbs energy. Solid phase activity coefficients can then be calculated from the excess Gibbs energy. Model parameters can be estimated from the experimental values of the solid phase activity coefficients by using Gaines and Thomas’s equations and isotherm measurement data. Most of the proposed solid phase excess Gibbs energy models are similar to nonideal liquid models (Grant et al., 1993). However, the causes of nonideality of the solid phase can differ significantly for different ion exchange materials; for example, ion exchange with organic resins is quite different from ion exchange with zeolites. Dyer (1991) pointed out that some apparent binary ion exchange systems with zeolites could be in fact ternary systems due to hydrolysis. Therefore, studying solid phase nonideal behavior requires understanding the ion exchange mechanism for particular ions with a particular ion exchange material. For structured inorganic ion exchange materials like zeolites, the knowledge of the structure of those materials is often a necessity. Barrer et al. (1959) studied the silver/sodium ion exchange with Linde Sieve 4A, and they concluded that the deviation from ideal behavior can be easily modeled by recognizing there were two kinds of ion exchange sites in the solid; both of them are ideal, and they were involved simultaneously in ion exchange. We observed similar behavior for TAM-5 (Zheng et al., 1996; Zheng, 1996). Although knowledge of the structure of an ion exchange material has been known to be very important to understand the solid phase in an ion exchange system, this information has been used only to justify the solid phase activity coefficient models. The structure information has not been used in the representation of ion exchange reactions. New Approach: Multiple Interactive Ion Exchange Site Model. Structured ion exchange materials have their particular molecular forms which are often represented by unit cells. If a material contains exchangeable B ions, the solid phase representation is not necessarily BX, as shown in eq 1, and a stoichiometric number can be included in that solid phase formula. If there are two B ions in one unit cell, the solid phase formula should be B2X. These two B ions can be located at different positions in a unit cell; therefore, a more appropriate representation could be BXIXIIB, where XI and XII represent two different positions in the framework. The exchange of the B ion at XI may affect the ion exchange properties of the B ion at XII and vice versa. Therefore, instead of writing the ion exchange reaction as eq 1, we should write the

Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2429

ion exchange reaction as follows if the B ion at XI is the first ion being exchanged:

A+ + BXIXIIB a AXIXIIB + B+

(10)

A+ + AXIXIIB a AXIXIIA + B+

(11)

Equations 10 and 11 can have different equilibrium constants. Sites XI and XII may even have a different selectivity sequence for different ions. For example, B at XI may be more favorably exchanged with H+ while B at XII may be more favorable to Na+. Therefore, for a mixture with H+ and Na+ exchange with BXIXIIB, the solid phase could be HXIXIINa. Interactions can exist between different unit cells; therefore, an ion exchange unit can be a combination of several unit cells. If ion exchange can be represented by the interaction among three unit cells and each unit cell can be represented by BXIXIIB, an ion exchange unit will be (BXIXIIB)3 or B3(XIXII)3B3. Model for Multicomponent Ion Exchange with Hydrous Crystalline Silicotitanates Zheng et al. (1996) and Zheng (1996) investigated the ion exchange properties of TAM-5 and found step changes in binary ion exchange isotherms of Cs+/Na+, Rb+/Na+, and K+/Na+ systems. Prior to the step changes, the solid phase was found to be ideal along the isotherms. The apparent ion exchange capacities prior to the step changes were measured to be 0.58 mequiv/g for cesium, 1.18 mequiv/g for rubidium, and 1.2 mequiv/g for potassium. Considering the errors in the experiments, the apparent capacities of rubidium and potassium are the same, and they are approximately double the capacity for cesium. Titration curves indicated multiple ion exchange sites with different acidic strengths existed in the solid, and the solid could be easily hydrolyzed by dissociation of water; i.e., hydrogen ions from water were ion exchanged with NaX, increasing the pH of the solution. Non ideal behavior was observed in competitive exchanges. The effects of liquid pH, i.e. H+, on distribution coefficients, suggested that partial hydrolysis of the material can improve the distribution coefficients of Cs+ instead of directly competing for the ion exchange sites with Cs+. The effects of potassium on cesium distribution coefficients showed that cesium distribution coefficients approached a small but constant value when potassium was added. However, adding rubidium caused a significant decrease in the cesium distribution coefficients when the rubidium concentration was high. By combining these ion exchange properties with the information from structure studies, we suggest that an ion exchange unit of TAM-5 can be represented by Na3X as the solid, since TAM-5, as synthesized, is initially loaded with sodium. The subscript 3 is the stoichiometric number, and when TAM-5 is partially exchanged with H+, there appears to be no framework difference between HNa2X, NaHNaX, or Na2HX. The H+ exchange along a titration curve with increasing acidity is represented as follows:

H+ + Na3X a HNa2X + Na+

(12)

H+ + HNa3X a H2NaX + Na+

(13)

H+ + H2NaX a H3X + Na+

(14)

Only one of the three sodium cations can be exchanged by cesium, and Na3X, HNa2X, and H2NaX can all exchange the sodium with cesium; therefore, the ion exchange of Cs+ with TAM-5 together with the effect of pH on Cs+ is represented as follows:

Cs+ + Na3X a Na2CsX + Na+

(15)

Cs+ + HNa2X a HNaCsX + Na+

(16)

Cs+ + H2NaX a H2CsX + Na+

(17)

Two of the three sodium cations can be exchanged by potassium, and the ion exchange of K+ together with the effect of pH on K+ is represented as follows:

K+ + Na3X a KNa2X + Na+

(18)

K+ + KNa2X a K2NaX + Na+

(19)

K+ + HNa2X a HKNaX + Na+

(20)

K+ + HKNaX a HK2X + Na+

(21)

K+ + H2NaX a H2KX + Na+

(22)

Ion exchange of Rb+ can be represented in the same way as that of K+ as follows:

Rb+ + Na3X a Na2RbX + Na+

(23)

Rb+ + Na2RbX a NaRb2X + Na+

(24)

Rb+ + HNa2X a HNaRbX + Na+

(25)

Rb+ + HNaRbX a HRb2X + Na+

(26)

Rb+ + H2NaX a H2RbX + Na+

(27)

One cesium cation can be loaded into the solid with potassium as follows:

Cs+ + KNa2X a KNaCsX + Na+

(28)

Cs+ + K2NaX a K2CsX + Na+

(29)

Rb+ and Cs+ are mutually exclusive; i.e., they cannot coexist in an ion exchange unit. This explains the direct competitive effect of Rb+ on Cs+ exchange (Zheng et al., 1996). Indirect competition caused by H+ and K+ (Zheng et al., 1996) is represented by eqs 16, 17, 28, and 29, in which H+ or K+ replaces part of the Na+ in the solid and still leaves some Na+ for cesium exchange. Because H+ is a smaller cation than Na+, more space is available for cesium after the solid is partially hydrolyzed. Because K+ is a larger cation than Na+, less space is available for cesium after the solid is partially loaded with K+. These comments explain the improvement in cesium distribution coefficients in the partially hydrolyzed solid and the decrease of cesium distribution coefficients in the solid partially loaded with K+. Equations similar to eqs 28 and 29 can be written for rubidium.

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Equations 12-29 are linearly independent. By using these equations, the solid phase can be assumed to be an ideal phase provided that step changes do not occur. For an ideal solid phase the equilibrium constants are equal to the rational selectivities. The equilibrium constants of these equations were determined by using well defined simple solutions (Zheng et al., 1996; Zheng, 1996). Estimation of the Equilibrium Constants, the Heat of the Model Reactions, and the Liquid Phase Activity Coefficients Estimation of the Liquid Phase Activity Coefficients. Aqueous electrolytic solutions, the most common liquid phase in an ion exchange system, are highly nonideal. Estimation of the activity coefficients is very important. While tabulated data are available for simple solutions (Lide, 1991; Robinson et al., 1970), utilization of models for estimating activity coefficients is necessary for complex solutions. Many models for estimating activity coefficients in electrolytic solutions have been proposed (Horvath, 1985; Zemaitis et al., 1986). Bromley’s and Pitzer’s models are considered to be among the best. Because the experimental data that were used to develop the models for the activity coefficients of CsNO3 and CsOH were obtained by using solutions with low ionic strengths, the model parameters apply only for solutions in the low ionic strength range. Zheng et al. (1996) measured the effect of pH on cesium distribution coefficients in solutions with high concentrations of Na+, NO3-, and OH-. They found that the effect of pH on cesium distribution coefficients in the basic solutions could be explained by the change of the ratio of the liquid phase activity coefficients of sodium to cesium. Bromley’s model was used to estimate the activity coefficients. However, when using activity coefficient models for cesium with the parameters determined by using solutions with low ionic strength, large deviations from the experimental data and the predictions occurred in some instances. If the solid phase is truly ideal and hydrolysis does not occur in the basic solutions, then the effect of pH on cesium distribution coefficients can provide data to estimate the activity coefficients and parameters for activity coefficient models of CsNO3 and CsOH at high concentrations. We chose Bromley’s model in this work because our final objective is to predict the equilibrium distribution coefficients of cesium in complex solutions. Pitzer’s model does not supply sufficient parameters for cesium electrolytes; however, Bromley assigned two parameters, B and δ, for individual cations or anions, and the parameter (combined parameter) for any cation and anion combination can be calculated from these parameters for each cation or anion. After comparing Bromley’s model with experimental data and considering our objective, we decided to use Bromley’s combined parameters except for NaOH, CsOH, and CsNO3, where Bromley’s single electrolyte parameters were applied, and the single electrolyte parameters for CsOH and CsNO3 were re-examined by using Zheng et al.’s experimental data on the effect of pH on cesium distribution coefficients. The results showed that the single electrolyte parameter for CsOH needed to be adjusted to 0.086 (original value is 0.1299), but no adjustment was required for the parameter of CsNO3.

Table 1. Equilibrium Constants for Model Equations model eq no.

equilibrium constants at 25 °C

heat of the reactions (J/mol)

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

7.7 × 108 6.1 × 107 7.4 4.4 × 104 3.3 × 105 1.5 × 106 9.7 × 101 1.8 × 101 2.9 × 102 7.5 × 101 9.1 × 101 1.4 × 103 2.8 × 102 1.2 × 104 1.1 × 104 1.3 × 104 1.9 × 104 1.5 × 104

-1.49 × 105 -1.48 × 105 2.64 × 104 -2.18 × 104 1.46 × 104 N/A -2.66 × 104 -7.52 × 103 7.79 × 103 6.91 × 103 N/A -2.62 × 104 -9.95 × 103 1.29 × 104 1.09 × 104 N/A -1.57 × 104 -1.93 × 104

Determination of the Equilibrium Constants. Zheng et al.’s (1996) experimental results were used to estimate the equilibrium constants of eqs 12-29. Bromley’s model with the modified parameter for CsOH was used for the estimation of the activity coefficients in the liquid phase. Equilibrium constants for eqs 1214 were first estimated by using the titration curves. Once equilibrium constants of eqs 12-14 had been determined, we could calculate the ratio of Na3X, HNa2X, H2NaX, and H3X in the solutions with different pH values and Na+ concentrations. For example, we found that the solid was completely in the form of Na3X in the solutions with 5.1 M NaNO3 and 0.6 M NaOH, HNa2X appeared in the solution with 5.7 M NaNO3 solution, and H2NaX was in the solid when we mixed H form TAM-5 in a neutral solution with 5.7 M NaNO3. Therefore, the equilibrium constant of eq 15 was then estimated by using the binary ion exchange isotherm proposed by Zheng et al. (1995) and the isotherm data in the solution with 5.1 M NaNO3 and 0.6 M NaOH. The resulting equilibrium constant for eq 16 is 4.4 × 104, which is the same as the rational selectivity obtained by Zheng et al. (1995) by using Polzer’s (1992) method with a Langmuir isotherm equation. The equilibrium constants of eqs 16 and 17 were estimated by using the cesium isotherm data in 5.7 N NaNO3 solution and a couple of points from the experimental data of the effect of pH on cesium distribution coefficients. Equilibrium constants for eqs 28 and 29 were estimated by using the experimental results of the effect of potassium on cesium distribution coefficients in simple solutions. Equilibrium constants for other reactions can be estimated in a similar way from the experimental data in simple solutions. The results are listed in Table 1. Figures 1 through 7 are scatter plots that illustrate the goodness of fit of the binary and ternary data used in determining the equilibrium constants. Determination of the Heats of Ion Exchange for the Model Ion Exchange Reactions. The heat of the ion exchange reaction in eq 6 can be considered constant if the temperature range is not very wide. Equation 6 can be integrated by using a reference temperature as follows:

ln Keq ) ln Kref -

(

)

1 ∆H° 1 R T Tref

(30)

where Tref is the reference temperature and Kref is the equilibrium constant at the reference temperature.

Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2431

Figure 1. Comparison of the calculated pH with the measured data from the titration experiments.

Figure 2. Comparison of the calculated cesium distribution coefficients with the measured data.

Holland and Anthony (1989) suggested the use of an intermediate temperature of the experimental conditions as the reference temperature in the estimation of the activation energy for reaction kinetics. This method was also used here for the estimation of the heat of the ion exchange reactions. The results are listed in Table 1. Zheng et al. (1996) present data on the effect of temperature on the distribution coefficients for basic and neutral solutions. Predictions of Cesium Distribution Coefficients in Complex Simulants and Discussion Cesium distribution coefficients were calculated for four types of complex simulants, NCAW, DSSF, 101AW, and ORNL. The compositions of NCAW 5 M Na, DSSF 7 M Na, 101AW 5 M Na, and two ORNL simulants are listed in Table 2. Other NCAW, DSSF, or 101AW simulants were dilutions of NCAW 5 M Na, DSSF 7 M Na, and 101AW 5 M Na simulants. Bromley’s Parameters for NO2- and Al(OH)4-. From Table 2, we can see that NO2- and Al(OH)4- are

Figure 3. Comparison of the calculated rubidium distribution coefficients with the measured data.

Figure 4. Comparison of the calculated potassium distribution coefficients with the measured data.

two major anions in these complex simulants. However, Bromley’s parameters for these anions are not available. To ensure better estimation of the distribution coefficients, Bromley’s parameters for NO2- were estimated by using Pitzer’s model in the following manner: Pitzer’s model gives parameters for NaNO2, KNO2, RbNO2, and CsNO2. Therefore, we used Pitzer’s model to calculate the activity coefficients for pure NaNO2, KNO2, RbNO2, and CsNO2 solutions at different ionic strengths and then estimated Bromley’s parameter from these results. These parameters are listed in Table 3 together with the new value for CsNO3. The parameters B and δ for Al(OH)4- were estimated by using the experimental data obtained to determine the effect of potassium on cesium distribution coefficients in DSSF 5 M Na simulants published by Zheng et al. (1996). This method was chosen because the equilibrium constants for the potassium reactions were determined by using simple simulants. Therefore, deviations from the experimental data in DSSF were

2432 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997

Figure 5. Comparison of the calculated cesium distribution coefficients with the measured data of the potassium effect on cesium ion exchange in simple solutions.

Figure 7. Comparison of the calculated cesium distribution coefficients for the estimation of Bromley’s parameters, B and δ, for Al(OH)4- with the measured data of the effect of K+ on cesium distribution coefficient in DSSF 5 M Na+ solution. Table 2. Compositions of NACW 5 M Na, DSSF 7 M Na, 101AW 5 M Na, and ORNL Simulants ORNL NCAW 5 M Na Na+ (M) K+ (M) Rb+ (M) Cs+ (M)

Figure 6. Comparison of the calculated rubidium distribution coefficients with the measured data of the potassium effect on rubidium ion exchange.

attributed to the lack of activity coefficients for Al(OH)4-. The results are listed in Table 3. Predictions for Cesium Distribution Coefficients. Model eqs 12-29, together with mass, charge, and site balances, can be solved by the Newton-Raphson method with Bromley’s model estimation for liquid phase activity coefficients to calculate the distribution coefficients of cesium. The predictions for NCAW simulants are presented in Figure 8. The experimental data were reported by Bray et al. (1993). Zheng et al. (1995) predicted the distribution coefficients of cesium in these solutions by using Polzer’s method. Their prediction was good in NCAW 1 M Na solution but failed in NCAW 3 M Na and 5 M Na solutions, where the effect of K+ was strong. However, the predictions presented in Figure 8 matched the experimental results very well in all solutions. The predictions for 101AW simulants are presented in Figure 9. The experimental results were reported

Li+ (M) Ca2+ (M) Zn2+ (M) OH- (M) NO3- (M) NO2- (M) F- (M) Cl- (M) SO42- (M) CO32- (M) PO43- (M) Al(OH)4- (M) AlO2- (M)

DSSF 7 M Na

101AW 5 M Na

5.0 7.0 5.0 0.12 0.945 0.475 5.0 × 10-5 not not not constant constant constant

1.68 1.69 0.43 0.089 0.15 0.23 0.43

1.75 3.52 1.51 0.10 0.008 0.147 0.014 0.721

2.17 1.49 0.875 0.043 0.065 0.0108 0.14 0.0175 0.497

NGLLLW

supernate

1.62

4.52 0.24

8.7 × 106 0.025

5.2 × 107

0.335 0.061

0.0001 0.001 0.22 4.157

0.059

0.1

0.587

0.1401 0.005

0.0117

Table 3. Bromley’s Parameter single electrolyte parameter Bij CsOH CsNO2 NO2Al(OH)4-

individual ion parameters B δ

0.086 -0.005 0.015 0.04

-0.0019 -0.2

by Brown et al. (1995). The predictions for ORNL simulants are presented in Figure 10. The experimental results were reported by Egan (1993). The predictions for DSSF simulants are presented in Figure 11, and the experimental data were collected at Sandia National Laboratories. Figures 8-11 show that the predictions match the experimental data very well for these complex simulants. The differences between prediction and experimental data are within 10%. The fact that none of the data reported in these figures were used to determine the equilibrium constants and the excellent predictions of the data enhances the validity of the model equations.

Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2433

Figure 11. Predictions for cesium distribution coefficients in DSSF simulants. Figure 8. Predictions for cesium distribution coefficients in NCAW simulants. Experimental data were reported by Bray et al. (1993) at Pacific Northwest National Laboratory.

representation, the solid phase can be considered as an ideal solid, and the rational selectivities are the same as the equilibrium constants. These equilibrium constants were estimated from experimental data obtained by using well-defined simple solutions. A set of model reactions were proposed for multicomponent ion exchange of group I metals by TAM-5. By using Bromley’s model for activity coefficients of electrolytic solutions, these model equations produce good predictions for the equilibrium compositions and cesium distribution coefficients in highly complex solutions. New values for Bromley’s parameters are also presented. Acknowledgment

Figure 9. Predictions for cesium distribution coefficients in 101AW simulants. Experimental data were reported by Brown et al. (1995) at Pacific Northwest National Laboratory.

This work was performed at Texas A&M University and Sandia National Laboratories. The work at Texas A&M was funded by Sandia National Laboratories under Texas A&M Research Foundation contract number RF8880, and Sandia National Laboratories is supported by the U.S. Department of Energy under contract number DE-AC04-94AL85000. Literature Cited

Figure 10. Predictions for cesium distribution coefficients in ORNL simulants. Experimental data were reported by Egan (1993) at Oak Ridge National Laboratory.

Conclusion By using data obtained from ion exchange experiments in simple solutions and data obtained from knowledge of the structure of TAM-5, an equilibrium model was proposed, which represents the solid phase as Na3X instead of NaX. By using this solid phase

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Received for review September 6, 1996 Revised manuscript received March 25, 1997 Accepted March 26, 1997X IE960546N

X Abstract published in Advance ACS Abstracts, May 1, 1997.