Development of a Carousel Ion-Exchange Process for Removal of

Ind. Eng. Chem. Res. 1997, 36, 2775-2788

2775

Development of a Carousel Ion-Exchange Process for Removal of Cesium-137 from Alkaline Nuclear Waste Michael V. Ernest, Jr., Jane P. Bibler,† Roger D. Whitley,‡ and N.-H. Linda Wang* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-1283

A systematic model-based approach is used for development of an efficient carousel ion-exchange process for the selective removal of radioactive 137Cs+ from alkaline nuclear waste solutions. Equilibrium data for two resorcinol-formaldehyde (R-F) cation-exchange resins are correlated by an empirical equation of the Freundlich-Langmuir type over cesium/sodium concentration ratios of 10-9 to 10-2 and sodium concentrations of 1 to 6 N. The standard deviations are 3.5 and 6.6%, respectively. The data cannot be accurately described by mass action equations. A detailed rate model, developed in this study for the periodic countercurrent multicolumn operation of carousel systems, is used with the equilibrium correlations to simulate cesium breakthrough curves from R-F resin columns. Results show that accuracy of the predicted breakthrough curves are directly related to the accuracy of the isotherm data and correlations. Cesium breakthrough position is generally predicted to within 5% or less for 10 of 13 runs over linear superficial velocities of 0.16 to 8.8 cm/min, column lengths of 3.14 to 118.5 cm, and particle radii of 145 to 200 µm. One run shows later breakthrough than predicted as a result of a low potassium concentration in the feed. Two other runs show early breakthroughs as a result of channeling in poorly packed columns of a carousel system. Despite the channeling, strong thermodynamic self-sharpening effects helped establish constant pattern waves in the downstream columns. A case study for a pilot-scale carousel unit shows that 100% utilization of cesium capacity and maximum throughput can be achieved while containing the mass transfer zone within the downstream columns. Since intraparticle diffusion controls spreading of the breakthrough curves, reducing the particle radius from 200 to 145 µm increases throughput by 40%. Introduction Approximately 100 million gallons of radioactive and hazardous waste, primarily produced by reprocessing fuels from nuclear reactors for weapon production (Bibler et al., 1990), have been stored in underground steel tanks across the U.S. at Department of Energy (DOE) sites, including Hanford and Savannah River (McGinnis et al., 1995). Since the tanks contain high levels of radiation and some are leaking (d'Entremont and Hobbs, 1992), technologies are under development for remediation of the wastes which is estimated to cost at least $100 billion (McGinnis et al., 1995). A primary focus of remediation is the removal of low concentrations (micromolar to millimolar) of soluble radionuclides, such as 137Cs and 90Sr, from alkaline supernates which are highly concentrated salt solutions (molar) containing primarily sodium nitrate (NaNO3), sodium nitrite (NaNO2), and sodium hydroxide (NaOH) (Ebra et al., 1982; Kaczvinsky et al., 1985, 1987; Bibler et al., 1990). Selective removal of these radionuclides is important for significantly reducing the volume of the borosilicate glass in which the radionuclides are immobilized. The glass will be sent for permanent geologic isolation (d'Entremont and Hobbs, 1992; Bibler et al., 1993). The decontaminated supernates will be processed into saltstone (grout), a low-cost, high-volume waste form (d'Entremont and Hobbs, 1992). * To whom correspondence should be addressed. E-mail: [email protected]. Telephone: (765) 494-4063. Fax: (765) 494-0805. † Westinghouse Savannah River Company, Savannah River Laboratory, Aiken, SC 29808. ‡ Air Products and Chemicals, Inc., 7201 Hamilton Blvd., Allentown, PA 18195-1501. S0888-5885(96)00729-4 CCC: $14.00

The Resorcinol-Formaldehyde Resin. A proposed separation technique utilizes columns packed with a resorcinol-formaldehyde (R-F) cation exchange resin developed at the Savannah River Laboratory (SRL) for the selective removal of 137Cs+ from the alkaline supernates (Bibler et al., 1990; Crawford et al., 1994; McGinnis et al., 1995). This resin, produced by the polycondensation reaction of resorcinol (C6H6O2) with formaldehyde (HCHO), was chosen because it shows high selectivity for cesium in high salt concentrations. It is relatively stable in the alkaline supernates (pH ) 11-14) and radiolytically stable (Crawford et al., 1994). The high selectivity has been attributed to the two weakly acidic hydroxyl groups on resorcinol, which ionize and become functional at high pH (Ebra et al., 1982; Samanta et al., 1992). Due to this weak acid nature, that is, the resin has strong preference for H+ (Samanta et al., 1995), it can be eluted using acid to remove all the loaded ions, producing a low volume, highly concentrated cesium waste stream (Ebra et al., 1982; Kaczvinsky et al., 1985; Bibler et al., 1990; Samanta et al., 1995). The Carousel Process. Alkaline supernates will be loaded to two or three R-F resin columns in series in a carousel design with an additional column ready to enter into operation when the lead column becomes saturated with cesium (Bibler et al., 1990; McGinnis et al., 1995). By carousel, we refer to periodic countercurrent multicolumn operation (Svedberg, 1976; Liapis and Rippin, 1979). Proper preconditioning of the columns prior to supernate loading is important to this process; typically done with concentrated sodium hydroxide. This helps minimize volume changes caused by swelling of the R-F resin in alkaline solutions, which can lead to poor hydrodynamics. Also, since many supernates contain aluminum ions (Al3+), precondition© 1997 American Chemical Society

2776 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Figure 1. Schematic of a conceptual carousel ion exchange process for removal of

ing prevents aluminum hydroxide (Al(OH)4-) from precipitating out of solution. A conceptual carousel design is illustrated in Figure 1 and is operated in the following manner. Supernate is loaded through the lead column (A) while the second (B) and third (C) columns, acting as guard columns, ensure that supernate does not go through the system untreated. When column A becomes saturated with cesium, supernate flow is switched to column B, which becomes the new lead column. Column C "moves" into the second position and a fourth column (D) into the third position. Meanwhile, two options are available to column A. The first option is to discharge the cesiumsaturated resin from the column directly to the glass melter in the vitrification process, where the R-F resin is incinerated in the melter and cesium is immobilized in the borosilicate glass product (Bibler et al., 1993). The second option involves elution of cesium from the resin in the column with acid (i.e., formic acid or nitric acid) and discharging the eluate to the vitrification process. Since acid elution causes the R-F resin to shrink considerably, the column must be regenerated with sodium hydroxide prior to the next loading of supernate. If column A can be eluted/regenerated or discharged/ repacked in a relatively short time, then a fourth column may not be necessary. The system is operated continuously in this cyclic manner, allowing resin capacity to be used to its fullest extent. As Figure 1 shows, an on-line (γ) detection and control system would be an integral part of the carousel process. Detection and control are necessary for two reasons: (1) to control column switching (and maximize column utilization) and (2) to ensure waste does not go untreated. For the former, the effluent stream from the lead column would be monitored for cesium breakthrough. At a given point during breakthrough, feed flow to the lead column would stop and switch to the next column. Column switching is dependent on the length of the mass transfer zone (MTZ). For the latter, the effluent streams from the second and third columns would also be monitored for cesium. If cesium is detected exiting from the second or third columns, then column switching should occur.

137Cs+

from alkaline supernates.

Optimization Issues in the Carousel Process. Two important results can be realized by carousel processes: increased throughput and improved column utilization. Increased throughput is achieved by virtue of the continuous infusion of feed solution during multicolumn operation. This is in contrast to single column operation where flow of feed solution must stop when breakthrough just begins. Column utilization is significantly better for carousel systems with two columns as opposed to single column systems; however, column utilization is only slightly better for carousel systems with more than two columns (Svedberg, 1976; Liapis and Rippin, 1979). In addition to the number of columns, the MTZ length is an important factor affecting column utilization in the carousel process. The MTZ is the region of changing concentration within the columns. There are many factors that can influence the MTZ length, including the following: linear superficial or interstitial velocity, particle size and shape, packing distribution, feed concentrations, density, and viscosity. Flow distributors and extracolumn piping can also make contributions to the MTZ. The MTZ length is of course not always constant. At the start of feeding, the dispersive forces tend to spread the concentration wave. However, the spread is opposed by thermodynamic self-sharpening forces for favorable isotherms. If the column is sufficiently long, the net result is the development of a constant pattern wave where the MTZ length is constant (Wankat, 1990; Helfferich and Carr, 1993). In the carousel process, if the breakthrough pattern is still developing from cycle to cycle, that is, a constant pattern has not been established, then the column switching rate or cycle time may vary since the MTZ is changing. Column utilization is a particularly important issue for R-F resin systems used to remove 137Cs+ from alkaline supernate. First of all, only a small fraction of resin capacity (5-10%) is actually utilized to bind cesium (Figure 2d), despite the high selectivity of the R-F resin for cesium. This is due in part to the overwhelming amount of sodium present in supernates. Secondly, the carousel system (equipment and resin) is relatively expensive. Therefore, maximum utilization

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2777

of cesium capacity is desired to minimize the amount of resin required, the equipment size, and consequently the treatment costs. Maximizing the throughput per column volume is also desired to minimize treatment costs, as well as the ability to elute and regenerate the R-F resin. Multiple supernate loadings of the resin means less resin is required overall to treat a given volume of waste. The current carousel design has three columns to process alkaline supernate with R-F resin (McGinnis et al., 1995). To achieve maximum utilization of cesium capacity (i.e., approximately the equilibrium value) in the lead column and to keep 137Cs+ within the system, the MTZ should be contained within the second column since the third column may be temporarily off-line for discharging/repacking or elution/ regeneration. Systematic Design Approach. A systematic approach is important for design of carousel systems treating alkaline supernates for a few reasons. (1) Supernate composition often varies from site to site and tank to tank. Hence, process design based solely on an empirical approach for each tank supernate would be costly, time consuming, and possibly hazardous. Scaling up to large-scale systems based on such empirical data is unreliable. (2) The dynamics of carousel ion-exchange systems are complex with many process and operating variables, as indicated in the previous section. The dynamics are strongly dependent on multicomponent ion-exchange competition and various mass-transfer mechanisms. (3) Since bench-scale experiments involving radioactive wastes are expensive and involve special facilities and trained personnel, only limited experimental data have been obtained to support scale up to large-scale systems. For these reasons, a model-based design approach is used in this study for process development of carousel processes. A rate model and associated computer simulation package developed previously for fixed-bed operations have been modified to include periodic switching of inlet (feed) and outlet (product) ports in the carousel process. The rate model and simulations after validation serve as the primary tool for design. In addition, mass action equations for ion exchange have been implemented into the model (Ernest et al., 1997). Analysis of existing multicomponent equilibrium data is then performed to develop isotherm equations for data correlation. These isotherm equations are then tested by comparing computer simulation predictions with existing bench-scale column breakthrough data. Intraparticle diffusivities are estimated from comparison of simulated breakthrough curves with the data. Next, carousel simulations are compared with existing benchscale carousel data. Lastly, the model is applied to maximize column utilization and throughput of an existing pilot-scale carousel unit. Theory

Figure 2. Equilibrium data of simulated supernate solutions and R-F resin: (a) Hanford and SRS data, (b) comparison of Hanford data (symbols) and predictions (lines generated using eqs 2 and 5), (c) comparison of SRS data (symbols) and predictions (lines generated using eqs 2 and 6), and (d) SRS data (symbol) and predictions (lines generated using eq 9). Refer to Table 2.

This section presents the expansion of VERSE-LC (VErsatile Reaction and SEparation simulator for Liquid Chromatography) to simulate the dynamic phenomena in multicolumn carousel systems. VERSE-LC is a fixed-bed rate model and associated computer simulation package that considers detailed mass-transfer mechanisms including axial dispersion, film diffusion, intraparticle pore diffusion, and intraparticle surface diffusion. Its capabilities and features have been documented in a number of papers (Berninger et al., 1991; Van Cott et al., 1991; Whitley et al., 1991a,b, 1993, 1994;


Kim et al., 1992; Jin et al., 1994; Koh et al., 1995; Ma et al., 1996; Ernest et al., 1997). As indicated earlier, the term carousel refers to the operation of a set of columns where solution flows sequentially through the columns. The feed point moves periodically in the same direction as fluid flow to create the appearance of periodic column movement countercurrent to the fluid flow. Since the mathematical equations describing carousel operations are essentially the same as for single column operations (Ma et al., 1996), they are not repeated here. However, flux continuity conditions in the bulk phase are enforced between columns:

(

)

∂Cb Eb ∂x

k-1

(

)

∂Cb ) Eb , ∂x k

k ) 2, 3, ..., Ncol (1)

where the left-hand-side and right-hand-side of eq 1 are the fluxes for the exit of column k - 1 and the entrance of column k, respectively, Eb is the axial dispersion coefficient, Cb is the mobile or bulk phase concentration, x is the dimensionless axial distance, and Ncol is the number of columns. Since all columns are assumed to be identical in terms of column dimensions, packing characteristics, and interstitial velocity, then each column should have the same axial dispersion coefficient. Therefore, the axial dispersion coefficients drop out of eq 1. Extracolumn dispersion effects between columns are ignored. Numerical Treatment of Carousel Systems. Numerically, column movement is accomplished by shifting the contents of the arrays, which hold concentration and derivative values for the set of columns, in the direction opposite to fluid flow. The segment of the arrays at the product end is reinitialized with the initial conditions of the columns which were present when the simulation began (i.e., complete regeneration) (Svedberg, 1976; Liapis and Rippin, 1979). The total number of axial elements divided by the number of elements shifted in a period should equal the number of columns. Effluent concentration histories for each column can be printed out if desired, as well as the solute distributions within the columns at a given time. The rest of the numerical procedure is the same as reported previously (Berninger et al., 1991; Ma et al., 1996). Column switching is done by one of two ways: through time-based control or through concentration-based control. For the former, the columns are moved at certain specified times. For the latter, the columns are moved when a specified component has reached a specified concentration at a specified position in the columns. This is a useful option for optimization, particularly when it is desired to determine the proper time increment for column switching (the cycle time) and maximizing column utilization. Key Parameters Needed for Simulations. Several input parameters are required to perform single column and carousel simulations. Isotherm parameters are needed for each component, which can be obtained from correlation of batch equilibrium data. Process parameters are needed such as column length (L), column diameter (D), volumetric flow rate (Q), particle radius (R), and inter- (b) and intraparticle (p) void fractions. The void fractions are obtained from experiment. Mass transfer parameters required include axial dispersion (Eb) and film mass-transfer (kf) coefficients, which are obtained from literature correlations. Brownian diffusivities (D∞) for each component are obtained from literature data or calculated by equations such as

the Wilke and Chang equation (Cussler, 1984). Intraparticle diffusivities (Dp) are estimated from comparison of simulation with breakthrough data. Experimental Section Preparation of the R-F Resin. R-F resin was prepared in gram quantities at SRL by condensing resorcinol (C6H6O2), which was dissolved in a potassium hydroxide (KOH) solution, with a 37% formaldehyde (HCHO) solution in a large Petri dish. The resorcinol/ KOH and resorcinol/formaldehyde mole ratios were 1:1.67 and 1:3.67, respectively. This is different from the general method of Pennington and Williams (1959) which uses NaOH solutions with phenolic compound/ NaOH and phenolic compound/formaldehyde mole ratios of 1:1.5 and 1:2.5, respectively. The resulting solution was cured overnight at 100 °C in a vented oven located in a hood. A minimum of 1 h appeared to be necessary to provide adequate cross-linking of the gel. Water and excess formaldehyde were then removed by filtration and allowed to air dry. When dry, the resin was mechanically ground and then sized using a series of sieves. The resulting resin particles were granular, irregular in shape, and generally had a particle size distribution of 30-60 mesh (250-550 µm). The resin has also been prepared in kilogram quantities by the Boulder Scientific Co. batch (BSC), using a similar procedure. Equilibrium Experiments. Batch equilibrium data were obtained for Hanford NCAW (Neutralized Current Acidic Waste) and Savannah River Site (SRS) simulated supernate solutions in contact with R-F resin. The resin was pretreated with 2 N NaOH for several hours, followed by removal of NaOH by filtration and washing with deionized water. The resin was air-dried before weighing. The Hanford and SRS simulated solutions represent similar supernate wastes; however, there are differences in the simulated solutions and the methods used to obtain the equilibrium data. 1. Hanford Supernates. Experiments with Hanford NCAW simulated supernates were performed at the Pacific Northwest Laboratory (PNL) in 1992 (Bray et al., 1992; Kurath et al., 1994). Simulated solutions were prepared by first making a stock solution with concentrations about 20% larger than those listed in Table 1 and without Cs+. The stock solution was diluted to the desired Na+ concentration, and Cs+ (and trace 137Cs+) was added after dilution. Initial cesium/sodium concentration ratios varied from 2 × 10-6 to 2 × 10-2. The resulting solutions were equilibrated with resin for 48 h on a constant temperature shaker table maintained at 25 °C. The resin used was from batch BSC-187 with a particle size distribution of 260-420 µm. Changes in 137Cs+ concentrations were analyzed by γ counting. The experimental conditions are summarized in Table 2. 2. SRS Supernates. Experiments with SRS simulated supernates were performed at SRL (Table 2). The SRS solutions contained NaNO3, NaOH, CsNO3, and trace 137Cs+. In these solutions, the total initial Na+ concentration was varied from 1 to 6 N. The hydroxide concentration was 1.5 N, except when the Na+ concentration was 1 N. Initial Cs+ concentrations varied from 4 × 10-8 to 10-2 N. The solutions were equilibrated with resin (prepared at SRL) for 16 hours at 23 °C. Changes in 137Cs+ concentrations were analyzed by γ counting. Column Breakthrough Experiments. 1. Hanford Supernate. Experiments with the Hanford NCAW

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2779 Table 1. Concentration (mol/L) of Electrolytes and Ions in Hanford and SRS Alkaline Supernates component

Hanford NCAW

SRS simulated

NaOH NaNO3 NaNO2 Na2CO3‚H2O Na2SO4 NaF Na2HPO4‚7H2O Al(NO3)3‚9H2O KNO3 CsNO3 RbNO3 Na+ Al3+ K+ Cs+ Rb+ OH- (total) OH- (free)a NO3NO2CO32SO42F-

3.40 0.26 0.43 0.23 0.15 0.09 0.025 0.43 0.12 5.0 × 10-4 5.0 × 10-4 4.99 0.43 0.12 5.0 × 10-4 5.0 × 10-5 3.40 1.68 1.67 0.43 0.23 0.15 0.09

2.90 1.20 0.71 0.20 0.17 0 0 0.38 0.015 2.4 × 10-4 0 5.55 0.38 0.015 2.4 × 10-4 0 2.90 1.38 2.36 0.71 0.20 0.17 0

SRS actual

4.90 9.7 × 10-3 2.4 × 10-4

2.60 0.97 0.04

a Four moles of hydroxide are associated with aluminum to keep it in solution as Al(OH)4-.

Table 2. Batch Equilibrium Experiments solutionsa

resin

R (µm)

T (°C)

equilibration time (h)

figure no.

Hanford SRS

BSC-187 SRL

170 200

25 23

48 16

2a,b 2a,c,d

a

See the Experimental Section for details.

supernate were performed at PNL in 1993 using 200 mL glass columns (2.54 cm i.d. × 39.5 cm) operated in series or individually (Kurath et al., 1994). The columns were equipped with water jackets connected to a constant temperature water bath. A 15 L feed tank and a pump were located upstream of the columns. All columns were prepared by filling with 2 N NaOH and then adding untreated K+ form R-F resin (BSC-187). A single column experiment used a newer batch of resin (BSC-210). The columns were flushed and tested with at least 3 column volumes (CV) of 2 N NaOH at flow rates required for a specific experiment, where 1 CV ) 200 mL. Flow rates ranged from 30 to 45 mL/min (9 to 13.5 CV/h). The simulated supernate (Table 1), spiked with trace 137Cs+, was loaded downflow to the columns which were maintained at 25 °C. A sampling valve was located at the bottom of each column where samples of column effluents were collected periodically. Samples were analyzed for 137Cs+ by γ counting. The experiments are summarized in Table 3. 2. SRS Supernates. Experiments with SRS supernates were performed at SRL in 1987 using different column sizes and configurations (Table 3) (Bibler and Wallace, 1987; Bibler et al., 1990). The columns were prepared with pretreated R-F resin (prepared at SRL)

and 2 N NaOH. One experiment used a 2 mL column (0.9 cm i.d. × 3.14 cm) with a simulated supernate feed spiked with trace 137Cs+ (Table 1). The simulated supernate was loaded downflow at 0.1 mL/min (3 CV/ h) to the column which was maintained at 25 °C. Effluent samples (6 mL) were collected, and every fifth sample was analyzed for 137Cs+ by γ counting. A second experiment used two 10 mL columns (2.54 cm i.d. × 1.98 cm) connected in series and 4 L of an actual supernate feed from SRS Tank 32 (Table 1). This experiment was carried out in a high-level cell to provide adequate shielding from high concentrations of 137Cs+. The columns had to be tilted sideways to place them into the cell. The actual supernate was loaded downflow at 0.67 mL/min (2 CV/h where 1 CV ) 10 mL). Effluent samples (22 mL) were collected at the bottom of the second column and analyzed for 137Cs+ by γ counting. Carousel Experiment. The carousel experiment was performed at PNL in 1989 using three 200 mL glass columns (2.54 cm i.d. × 39.5 cm) operated in a semicontinuous mode (Table 3) (Bibler et al., 1990; Kurath et al., 1994). A SRS simulated supernate feed, spiked with trace 137Cs+, was used (Table 1). The columns were equipped with water jackets connected to a constant temperature water bath. A 15 L feed tank and a pump were located upstream of the columns. Each column was initially prepared with 72 g of untreated K+ form R-F resin (BSC-187) and 2 N NaOH. Several cycles were performed, where one cycle was made up of supernate loading, washing, acid elution, and regeneration. The simulated supernate was loaded downflow at an average flow rate of 6.67 mL/min (2 CV/h where 1 CV ) 200 mL). At approximately 50% Cs+ breakthrough from the lead column, feed flow was stopped and the columns were washed with 3 CV of 2 N NaOH followed by 6 CV of water. The lead column was then detached and eluted with 24 to 28 CV of 1 N formic acid at 1.67 to 6.67 mL/min (0.5 to 2 CV/h). After elution, this lead column was reattached in the third position. Before the next loading of supernate, the columns were washed with 3 CV of 2 N NaOH to prevent aluminum precipitation. All cycles were maintained at 35 °C. Effluent samples (4 mL) were collected at the bottom of each column in 4 to 16 h intervals and were analyzed for 137Cs+ by γ counting. Results and Discussion Equilibrium Data and Correlation. 1. Hanford Supernates. Figure 2a shows the comparison of the equilibrium data collected for the Hanford and SRS simulated supernates. The data are plotted as the cesium batch distribution coefficient, Kd,Cs, versus the cesium to sodium equilibrium solution phase concentration ratio, CCs/CNa. Kd,Cs in units of mL/g represents the theoretical volume of feed solution that can be processed per mass of air-dried exchanger, and is computed by the ratio of the equilibrium solid phase concentration to the equilibrium solution phase concentration, C h Cs/CCs.

Table 3. Column Breakthrough Experiments feed

resin

R (µm)

Ncol

L (cm)

D (cm)

Q (mL/min)

T (°C)

figure no.

Hanford NCAW Hanford NCAW Hanford NCAW SRS simulated SRS actual SRS simulateda

BSC-187 BSC-187 BSC-210 SRL SRL BSC-187

170 170 145 200 200 200

3 3 1 1 2 3

39.5 39.5 39.5 3.14 1.98 39.5

2.54 2.54 2.54 0.9 2.54 2.54

30 45 43.3 0.10 0.67 6.67

25 25 25 25 25 35

3a 3b 3c 4, 5 4 6

a

Carousel experiment.


Both sets of data show qualitatively similar trends despite different experimental conditions (different resin and equilibration times, see Table 2). Kd,Cs decreases (or selectivity decreases) as the sodium concentration increases. For constant sodium concentration, Kd,Cs increases for decreasing CCs/CNa and approaches a constant value at low CCs/CNa. This constant selectivity region is due to near saturation of the resin with sodium. Note the sodium concentrations are assumed to be constant since they are several orders of magnitude greater than the cesium concentrations. In general, Figure 2a shows that high selectivity for Cs+ can be achieved with the R-F resin despite high sodium concentrations. Figure 2b shows the equilibrium data collected for the Hanford-simulated supernates and is plotted as λ versus CCs/CNa. λ is simply Kd,Cs multiplied by the packed bed density, Fb, and represents the theoretical number of column volumes (at 50% breakthrough) of a feed solution that can be loaded on a given fixed-bed of resin. The density of R-F resin beds in 2 N NaOH has been measured as 0.36 g dry/mL (Bibler et al., 1990). The following general relationship is presented here to correlate the equilibrium data in Figure 2b:

C h Cs k1(CCs/CNa)m λ ) Kd,CsFb ) F ) CCs b k + (C /C )m 2

Cs

(2)

Na

where k1, k2, and m are empirical constants. The constant m is negative. The general validity of eq 2 is checked by comparison of the upper and lower limits with the experimental data. That is, for high and low CCs/CNa, eq 2 reduces to eqs 3 and 4, respectively:

λ)

k1 (C /C )m k2 Cs Na λ ) k1

5.6% of the experimental values. One standard deviation for λ is 3.5%. 2. SRS Supernates. Equilibrium data collected for the SRS simulated supernates are plotted in Figure 2c. A lack of data exists over four decades of CCs/CNa, from about 4 × 10-9 to 3 × 10-5. The data could not be collected in this range without maintaining Na+ and OH- at consistent concentrations. A close examination of the low CCs/CNa data, the trace data, reveals that they do not follow the general trend of decreasing selectivity for increasing sodium concentration. This may be due to the inaccuracies associated with detecting trace concentrations. (The trace data in Figure 2c are more than a magnitude smaller than the trace data in Figure 2b.) Also, the 16 h equilibration time of the SRS experiments, which were 3 times shorter than the Hanford experiments, may have contributed. In other words, sufficient time was not given to overcome the small driving forces associated with trace concentrations. Despite these problems, an attempt was made to correlate the SRS data as was done for the Hanford data. The results of the correlation are also shown in Figure 2c where the lines were generated according to eqs 2 and 6:

(3) (4)

Equation 2 assumes that cesium and sodium are the primary exchanging ions. The effects of other competing ions, such as potassium, are considered secondary because of the high sodium concentrations present. In other words, cesium loading is primarily modulated by sodium. This is termed the pseudobinary approach. This is the simplest approach for equilibrium data correlation. However, the correlated constants are only valid for feed with a fixed composition. The General Curve Fit feature of the Kaleidagraph software package on the Macintosh computer was used for correlating the equilibrium data in Figure 2b according to eq 2. This software uses least squares for curve fitting. The λ values were weighted to obtain the best fit. Empirical constants were obtained for each sodium concentration. Each constant appears to be a function of the sodium concentration as given by eq 5 with their corresponding correlation coefficients (Rc): -0.9022 , Rc ) 0.9999 k1 ) 6035CNa

(5a)

k2 ) 3203 - 257CNa, Rc ) 0.9998

(5b)

m ) 0.0112CNa - 0.6734, Rc ) 0.9780

(5c)

Figure 2b shows the good agreement between the experimental data and the equilibrium curves generated by eqs 2 and 5, where the predictions are within 0.4 to

0.2349 , Rc ) 0.8730 k1 ) 2060CNa

(6a)

k2 ) 4001 - 710CNa, Rc ) 0.9942

(6b)

-0.0546 , Rc ) 0.9419 m ) 0.7924CNa

(6c)

The low correlation coefficient for eq 6a reflects the problems with the trace data. Predictions are within 0.1 to 13.4% of the experimental values. One standard deviation for λ is 6.6%. Note the differences between the values of the empirical constants obtained for the two sets of equilibrium data in Figures 2b and 2c. These differences are related to the different resins used and different equilibration times. An attempt was also made to take a more fundamental approach to equilibrium correlation by using mass action equations, which naturally describe ion exchange. This was done for the SRS equilibrium data since the simulated supernates only contained Cs+ and Na+. First, binary exchange between Cs+ and Na+ is assumed. This assumption (the pseudobinary approach) is made despite the fact that pretreated resin still contains potassium ions (Bibler et al., 1990). Second, ideal exchange is assumed such that all activity coefficients are unity. It is well known that concentrated sodium nitrate and sodium hydroxide solutions do not behave as ideal electrolyte solutions (Robinson and Stokes, 1959). However, ideal exchange is assumed since ultimately it is desired to simulate breakthrough data with the rate model using the ideal mass action equations (Ernest et al., 1997). Next, since binary exchange is assumed, the total solid phase capacity is taken as the sum of solid phase concentrations:

h Cs + C h Na C hT ) C

(7)

The total solid phase capacity of the R-F resin has been determined previously as 2.85 mequiv/g (1.026 mequiv/ mL) in 2 N NaOH (Bibler et al., 1990). Now, writing the mass action constant as:


KCsNa )

CNa C h Cs CNa C h Cs ) C h Na CCs (C hT - C h Cs) CCs

(8)

and then solving eq 8 for the cesium solid phase concentration gives:

C h Cs )

hT KCsNaC KCsNa + CNa/CCs

(9)

To test eq 9, the equilibrium data must first be placed in terms of cesium solid phase concentrations by multiplying each data point by its corresponding cesium solution phase concentration, resulting in Figure 2d. Also in Figure 2d are isotherm lines generated by eq 9 using mass action constants of different magnitude. The figure clearly shows that all the data cannot be represented by a single ideal mass action constant. For instance, for the SRS simulated supernate in Table 1 where CCs ) 2.4 × 10-4 N and CNa ) 5.6 N, the corresponding mass action constant is KCsNa ) 1065. The isotherm line for this mass action constant only crosses the data at one point corresponding to the cesium and sodium concentrations in the supernate. The importance of accurate isotherm representation is shown later in Figure 5. Column Breakthrough Data and Simulation. VERSE-LC computer simulations performed in this study are considered converged when increases in ne (number of axial elements), na (number of interior collocation points), np (number of particle collocation points), and decreases in atol (absolute tolerance), rtol (relative tolerance), ∆θ (integration time step) did not cause any change in the numerical solution; convergence was also checked by comparison of expected and predicted mass balances. Sufficient convergence was obtained when: ne ) 75+, na ) 4, np ) 3, atol ) 0.001 × Ce, rtol ) 0.1-0.01%, and ∆θ ) 0.1-1.0 bed volume. Simulations used the Chung and Wen (1968) correlation for estimation of axial dispersion coefficients and the Wilson and Geankoplis (1966) correlation for estimation of film mass-transfer coefficients, unless noted otherwise. Brownian diffusivities for cesium (D∞,Cs ) 1.236 × 10-3 cm2/min) and sodium (D∞,Na ) 7.98 × 10-4 cm2/min) in water at 25 °C were obtained from Cussler (1984). The inter- (p) and intraparticle (b) void fractions used in all simulations were 0.51 and 0.49, respectively. These values were estimated from a pore volume filling experiment for a R-F resin bed in 2 N NaOH. It is expected that these void fractions represent average values because of the shrinking and swelling characteristics of the R-F resin. 1. Hanford Supernate. Experimental cesium breakthrough data are presented in Figure 3 for loading of Hanford NCAW simulated supernate to columns packed with the BSC resin (refer to Tables 1 and 3). Since these data showed constant pattern behavior and were collected for different volumetric flow rates, column sizes, configurations, and particle sizes; this allowed us to test the possibility of using one consistent set of parameters in the simulations to model all these data. Note that the 1st column data of Figure 3b (Q ) 45 mL/min, BSC187, R ) 170 µm) is also presented in Figure 3c for comparison with the single column data obtained using a similar flow rate (Q ) 43.3 mL/min) and the newer batch of resin (BSC-210, R ) 145 µm). Introduction of the Hanford supernate to a column causes the sodium concentration to increase from 2 N (preconditioned) to 5 N. Since the latter sodium con-

Figure 3. Cs+ breakthrough for loading of Hanford NCAW simulated supernate to columns packed with R-F resin; comparison of experimental data (symbols) and simulated breakthrough curves (lines): (a) Q ) 30 mL/min, (b) Q ) 45 mL/min, and (c) Q ) 43.3 mL/min. Freundlich-Langmuir isotherm parameters for cesium calculated using eqs 5 and 12. Refer to Tables 1 and 3.

centration is 104 times greater than the cesium concentration in the supernate feed and the fact that the R-F resin is very selective for Cs+, it is expected that Na+ breakthrough occurs at or very near the void volume of a column. Therefore this means the sodium concentration is 5 N in a column throughout most of the supernate loading time. Consequently, breakthrough behavior of a supernate with fixed composition can be well predicted as a one component (Cs+) system, where the effects of Na+ are lumped into the isotherm parameters. A generalized Freundlich-Langmuir isotherm equation for multiple components can be expressed as:

C hi )

a,i aiCM i

(10)

Nc

βi +

bjCM ∑ j j)1

b,j

where a, Ma, β, b, and Mb are the isotherm parameters. This equation is a simpler form of an empirical combination of the Freundlich and Langmuir equations proposed by Fritz and Schleunder (1974). It is also similar to the equation presented by Tien (1993). Here, the number of components, Nc, is 1. Since eq 2 can be


rearranged into a Freundlich-Langmuir type of expression:

C h CsFb )

m+1 k1CCs m m k2CNa + CCs

(11)

and then comparison of eqs 10 and 11 gives eq 12:

aCs ) k1

(12a)

bCs ) 1

(12b)

Ma,Cs ) m + 1

(12c)

Mb,Cs ) m

(12d)

m βCs ) k2CNa

(12e)

The Freundlich-Langmuir isotherm was used for simulation of the breakthrough data in Figure 3. The isotherm parameters were calculated using eqs 5 and 12. In Figures 3a and 3b, there was one experimental breakthrough curve for each of the 200 mL columns in the series. These experimental breakthrough curves can be simulated by two different methods which give equivalent results. The first method consists of three separate single column simulations. The first simulation is specified for a 200 mL column, the second for a 400 mL column, and the third for a 600 mL column. The second method consists of a pseudocarousel simulation that is specified for a 600 mL column with three segments. The column shift is specified at a time after 100% breakthrough from the third segment. Simulated breakthrough curves are produced for each column. Results of simulations, based on the assumptions, methods, and parameters described above, are compared with the experimental data in Figure 3. The breakthrough position is generally well predicted by the simulated breakthrough curves. In Figure 3a, the predictions lead the data by an average of about 4%. This discrepancy is near the error of the equilibrium correlation. The general agreement between data and simulated breakthrough curves show three things. First, constant pattern breakthrough curves are established in long columns. This constant pattern development is due to the strong self-sharpening effects associated with high cesium selectivity. Second, column systems using R-F resin can be scaled with respect to volumetric flow rate (30-45 mL/min) or linear superficial velocity (5.92-8.88 cm/min), column length (39.5118.5 cm), and particle radius (145-170 µm). Lastly, the performance of the BSC resin is reproducible in terms of cesium capacity from batch to batch. For the simulated breakthrough curves in Figure 3, an intraparticle pore diffusivity, Dp,Cs, of 1.3 × 10-4 cm2/ min was consistently used to fit the experimental data and is essentially the pore diffusivity calculated from the Mackie and Meares correlation (1955). This value was estimated when either the Chung and Wen (1968) or the Gunn (1986) axial dispersion correlations were used, despite the Gunn correlation predicting a smaller axial dispersion coefficient (by 10-15%). More interestingly, when axial dispersion was neglected all together, no change in the simulated breakthrough curves were observed. Similarly, no change in the simulated curves were observed when the film diffusion rates were increased. These results indicate that axial dispersion

Figure 4. Cs+ breakthrough for loading of SRS simulated and actual supernate to columns packed with R-F resin; comparison of experimental data (symbols) and simulated breakthrough curves (lines). Freundlich-Langmuir isotherm parameters for cesium calculated using eqs 6 and 12. Refer to Tables 1 and 3.

and film diffusion are not important for the Hanford experiments. If they were important, then decreases of axial dispersion coefficients or increases of film masstransfer coefficients would result in sharper breakthrough curves. Instead, the results show that the columns were well packed and that intraparticle diffusion is the controlling mass-transfer mechanism. The latter is expected since the R-F resin has a relatively large particle size and a small pore size (∼10 Å); the latter is due to its gel properties. Intraparticle surface diffusion effects were not considered in the simulations because cesium loading is very low (∼10%) as a result of the high sodium concentration. At low loading, both pore and surface diffusion result in symmetric breakthrough curves. Surface diffusion effects are more pronounced in high affinity non-linear systems where breakthrough curves are asymmetric (Ma et al., 1996). For symmetric breakthrough curves, the pore diffusion model with an effective pore diffusivity can replace the more detailed parallel diffusion model to predict the breakthrough curves. The asymmetric breakthrough curves in Figure 3b suggest that incorporating surface diffusion effects may help better explain the data at high flow rate. However, more systematic data are needed to determine the surface and pore diffusivities independently (Ma et al., 1996). 2. SRS Supernates. Experimental cesium breakthrough data are presented in Figure 4 for loading of SRS simulated and actual supernates to columns packed with R-F resin prepared at SRL (refer to Tables 1 and 3). The data were simulated in the same fashion as the Hanford breakthrough data, but eqs 6 and 12 were used to calculate the Freundlich-Langmuir isotherm parameters. The intraparticle diffusivity estimated from the Hanford data was used in the simulations. The simulations results are shown in Figure 4. For the 2 mL (simulated supernate) system, the breakthrough position is predicted relatively well by the simulation, within 5%. This is within the error of the equilibrium correlation. However, both axial dispersion correlations predict breakthrough curves sharper than the data. The sharper predictions suggest that the column was not well packed. Notice that unlike the Hanford systems in Figure 3, in which both axial dispersion correlations predicted identical breakthrough curves, the Gunn correlation predicts a noticeably sharper breakthrough curve than compared to Chung


and Wen. Apparently, these results are related to the Reynolds number which is proportional to the linear superficial velocity. At low Reynolds numbers (0.37 for the Hanford systems), the two correlations predict coefficients of roughly the same magnitude. These experimental and simulation results suggest that small columns operated at low Reynolds numbers can result in inaccurate estimation of masstransfer parameters. The breakthrough data for the actual supernate in Figure 4 only reached 30% of the Cs+ feed concentration, because there was only a limited supply of feed available for the experiment. Since cesium breakthrough was only monitored at the end of the second 10 mL column, the system was simulated as a single 20 mL column. The simulated breakthrough curves lead the data by 15%. This large discrepancy is in part due to inaccuracies of the equilibrium data and correlation. More likely, this is due to a 35% lower potassium concentration in the actual supernate (Table 1). The effects of sodium were taken into account in the isotherm parameters, but since a binary approach was taken for equilibrium correlation, the effects of potassium were not considered. Conceivably, a lower potassium concentration would lead to increased cesium loading as observed. However, independent K+/Cs+ equilibrium data are needed to determine how cesium loading is affected by the potassium concentration in the feed. This will be addressed in a future study. In Figure 4, both axial correlations predict breakthrough curves much sharper than the data. A simulation (not shown) with a 15 min dispersed input has no effect on the breakthrough curves, indicating that extracolumn dispersion is not responsible. Instead a high axial dispersion coefficient is needed, which suggests that the spreading of the breakthrough data was caused by dispersion within the column. There are two possibilities to explain this. First, the packed columns had to be tilted sideways in order to place then into the high-level cell. This could have disturbed the packing, leading to large dispersion within the column and a high degree of spreading. A second possibility is the precipitation of aluminum hydroxide on the resin, since formation of white solids on the resin was observed. This precipitation is thought to be responsible for the poor breakthrough kinetics (Bibler and Wallace, 1987; Bibler et al., 1990). The mass action isotherm was then tested for its ability to simulate breakthrough for the 2 mL column. The initial condition of the column was set to 2 N Na+. Figure 5 shows the comparison of experimental data with the simulated breakthrough curves, where the average breakthrough position could be well predicted. With the Chung and Wen axial dispersion correlation in Figure 5a, no matter how large the value of the cesium intraparticle diffusivity was set to in the simulations (when Dp,Na ) D∞,Na ) 7.98 × 10-4 cm2/min), the predicted breakthrough curve is always more spread out than the data. With the Gunn axial dispersion correlation in Figure 5b, a large intraparticle diffusivity is needed to fit the data. Since the mass action correlation underestimates the cesium loading (Figure 2d) over the concentration range of the breakthrough, the predicted breakthrough curve is always more spread out than the data unless a unrealistically large pore diffusivity is

Figure 5. Cs+ breakthrough for loading of SRS-simulated supernate to the 2 mL column packed with R-F resin; comparison of experimental data (symbol) and simulated breakthrough curves (lines) using mass action isotherm, KCsNa ) 1065: predictions using (a) Chung and Wen (1968) axial dispersion correlation and (b) Gunn (1986) axial dispersion correlation. Dp,Na ) D∞,Na ) 7.98 × 10-4 cm2/min. Refer to Tables 1 and 3.

used to compensate for the underestimation of the thermodynamic self-sharpening effects. The failure of the mass action correlation in the model to adequately simulate the column data in Figure 5 demonstrates the importance of having accurate isotherms to be able to obtain reliable estimates of the mass-transfer parameters. 3. Carousel. Figure 6a shows the column sequence for cycles 1-4 of the carousel experiment, where the primes indicate columns that have been loaded with SRS-simulated supernate, washed with sodium hydroxide and water, eluted with formic acid, and regenerated with sodium hydroxide. In the experiment, the volumetric flow rate was observed to fluctuate during supernate loading of cycles 1-4. The flow rate history is shown in Figure 6b, where the time scale is the cumulative time for supernate loading, that is, it does not consider time for washing, elution, and regeneration. Experimental cesium breakthrough data for the lead column of cycles 1-4 and data of cycle 1-column B are shown in Figure 6c. The time scale is the same as in Figure 6b. The breakthrough data of cycles 1 and 2 (Figure 6c) indicate severe hydrodynamic disturbances such as channeling in poorly packed columns in the first two cycles, particularly in cycle 1 where breakthrough occurred almost immediately from column A. In cycle 2, the breakthrough curve from column B is less dispersed. By cycles 3 and 4, a constant pattern is established with sharp breakthrough curves. Although the data suggest the columns were poorly packed initially and became better packed from cycle to cycle,


Figure 6. Carousel experiment-loading of SRS simulated supernate to columns packed with R-F resin: (a) schematic of the column sequence from cycle to cycle, (b) flow rate history for supernate loading in cycles 1-4, (c) Cs+ breakthrough from the lead column; comparison of experimental data (symbols) and simulated breakthrough curves (line) for cycles 3 and 4, and (d) Cs+ breakthrough from the lead column; comparison of experimental data (symbols) and simulated breakthrough curves (line) for cycle 2. Freundlich-Langmuir isotherm parameters for cesium calculated using eqs 5 and 12, but aCs reduced by 12%. Eb ) 0.259 cm2/min (Chung and Wen) or 0.148 cm2/min (Gunn). Refer to Tables 1 and 3.

it is not evident from the data alone if channeling in column A of cycle 1 was solely responsible for the

dispersed breakthrough data of column B or if channeling existed in both columns A and B. To investigate this question with computer simulations, the proper equilibrium correlations must first be selected. The appropriate choice is the Hanford equilibrium correlations (eqs 2 and 5), even though the carousel experiment used SRS-simulated supernate. These correlations can be used since the SRS and Hanford NCAW supernates are similar (Table 1). But the main reason for choosing the Hanford correlations is because both the Hanford equilibrium and carousel experiments were performed with the BSC resin. As Figure 2a shows, the SRL and BSC resin perform qualitatively similar, but are different quantitatively. This is further supported by literature data (Bibler et al., 1990). Consequently, eqs 5 and 12 were used to calculate the Freundlich-Langmuir isotherm parameters for the carousel simulations. Again, the same intraparticle diffusivity (1.3 × 10-4 cm2/min) was used. The flow rate changes shown in Figure 6b were accounted for in the simulations by a series of linear changes. The first carousel simulation was performed to test the isotherm parameters and to determine the state of the columns of cycles 3 and 4; only these cycles were simulated. This was done by first using the breakthrough data from column B of cycles 1 and 2 as the simulated concentration input to column C just prior to the end time of cycle 2 (14772 min), since the effluent from column B fed directly to column C during cycles 1 and 2 (Figure 6a). At the end of cycle 2, column C moved into the lead position; thus, the ideal step change at 14772 min in Figure 6c. The resulting simulated breakthrough curves are also shown in Figure 6c, where a 12% reduction in the capacity (aCs) was required to fit the data. The reason for the capacity reduction is related to temperature, because the carousel experiment was performed at 35 °C, whereas the equilibrium experiments were performed at 25 °C. Some experimental evidence suggests that resin performance is very sensitive to temperature. For instance, Bray et al. (1992), who collected equilibrium data for Hanford NCAW simulated supernates and BSC resin at different temperatures, found for an initial sodium concentration of 5 N and an initial cesium/ sodium ratio of 2 × 10-4, that λ decreases from 363 at 10 °C to 292 at 25 °C to 218 at 40 °C. These are reductions of 20.4 and 25.3%, respectively. Decreases in selectivity with increasing temperatures, as illustrated here, are usually observed for ion exchange systems (Helfferich, 1962). Therefore, the reduced capacity in the simulations appears consistent and justified. As Figure 6c shows, the simulated breakthrough curves compare well with the data of cycles 3 and 4 in terms of spreading and the breakthrough concentration reached just prior to column switching. The results confirm that columns C and A′ were well packed and show that thermodynamic self-sharpening effects are so strong that the effects of the highly dispersed concentration input and flow rate changes were overcome, producing sharp constant pattern breakthrough curves. The agreement between cycle 4 data and simulation demonstrates the ability to elute and regenerate the R-F resin for multiple supernate loadings without any appreciable loss of cesium capacity. The second carousel simulation was performed to determine the state of column B of cycle 2; only cycle 2


was simulated. This was done by first using the breakthrough from column A of cycle 1 as the simulated concentration input to column B prior to the end time of cycle 1 (7632 min), since the effluent from column A fed directly to column B during cycle 1 (Figure 6a). At the end of cycle 1, column B moved into the lead position; thus, the ideal step change at 7632 min in Figure 6d. The resulting simulated breakthrough curves, using the same isotherm parameters as in Figure 6c, are also shown in Figure 6d. The curves generated using the axial dispersion correlations are sharper than the data, again showing that strong thermodynamic self-sharpening in well-packed columns can overcome the effects of highly dispersed concentration inputs. However, as Figure 6d illustrates, a high axial dispersion coefficient of 10 cm2/min was needed to fit the column B data, indicating it was still not well packed during cycle 2. The slight discrepancy in position between data and simulation could be caused by a loss of capacity associated with channeling in the real system. Also shown in Figure 6d is a simulated breakthrough curve for column A of cycle 1, which was generated by a single column simulation. The axial dispersion coefficient of 500 cm2/min illustrates the severity of channeling during cycle 1. This result in conjunction with the lower flow rates observed during part of cycles 1 and 2 (Figure 6b) confirms that the columns were poorly packed initially, but became better packed from cycle to cycle. Application of the Model for Design of a PilotScale Carousel Unit. To this point, we have correlated batch equilibrium data, established confidence in those correlations by simulating dynamic breakthrough data for bench-scale column systems, and estimated mass-transfer parameters for the column systems. Not only has it been demonstrated that the rate model is capable of simulating carousel operations, but it has been shown it can simulate column systems of different lengths, flow rates, and particle sizes. Thus, we can now apply the rate model to predict the performance of an existing pilot-scale carousel unit. The pilot-scale unit of interest is the skid-mounted ion exchange demonstration (SKID) carousel unit designed at SRS (McGinnis et al., 1995). This SKID unit has three columns, each with an empty volume of 829 L and an inner diameter of about 100 cm. It is assumed that each column can be well packed and completely filled with BSC resin, making each column length to be approximately 106 cm. A SRS supernate of the simulated type is chosen as the feed to the SKID unit for cesium removal at 25 °C. The main focus of this case study was to determine the maximum feed rate (throughput) that could be achieved while maximizing utilization in the lead column and containing the MTZ within the second column. Since intraparticle diffusion was determined to be the controlling mass transfer mechanism in the absence of channeling, different resin particle sizes (R ) 145-200 µm) were considered to examine their effect on throughput and cycle time. In the simulations, the MTZ was taken to be from 1% to 99% of the feed concentration. Therefore, column switching occurred when the cesium effluent concentration from the lead column reached 99% of its feed concentration. Equations 5 and 12 were used to calculate the FreundlichLangmuir isotherm parameters. A throughput of 2 CV/h (1 CV ) 829 L) of SRS feed, as in the carousel experiment, served as the starting

Figure 7. Simulated loading of SRS-simulated supernate at 2 CV/h to the SKID unit (three 100 cm i.d. × 106 cm columns) packed with R-F resin of different particle sizes: (a) Cs+ breakthrough curves from the lead column and (b) Cs+ concentration profiles in the columns just prior to column switching. Freundlich-Langmuir isotherm parameters for cesium calculated using eqs 5 and 12.

point for the SKID unit simulations (Figure 7). For each particle size, a constant pattern is established over all cycles as shown by the breakthrough curves from the lead column in Figure 7a. The first cycle has the longest cycle time since initially all columns are cesium-free. After the first cycle, the cycle time is the same from cycle to cycle because of the constant pattern behavior, but shorter than the first since the columns are partially saturated with cesium when moved into the lead position. Naturally at the same throughput, the effect of increasing particle size is to spread the breakthrough curves because of increasing mass-transfer resistance. This increases the cycle time of the first cycle. But after the first cycle, the cycle time is not affected by particle size because of the constant pattern behavior. For instance, the cycle time (8000 min) for 145 µm particles is the same as for 170 and 200 µm particles. For any cycle, the solution concentration profiles in the columns just prior to column switching shows that at the same throughput the MTZ length increases for increasing particle size as expected, but each MTZ length is much less than a column length (Figure 7b). Therefore, the throughput for each particle size can be increased until the MTZ is approximately equal to one column length. Figure 8a-c shows how the breakthrough pattern from the lead column appears when this condition is satisfied. The corresponding solution profiles in the columns just prior to column switching is shown in Figure 8d and is identical for each particle size. As would be expected, the highest throughput (and smallest cycle time) is achieved for the smallest particle size (145 µm) which is 40% greater than the maximum


Figure 8. Simulated loading of SRS simulated supernate at maximum throughput (where MTZ length equals one column length) to the SKID unit packed with R-F resin of different particle sizes: (a-c) Cs+ breakthrough curves from the lead column and (d) Cs+ concentration profiles in the columns just prior to column switching. Same isotherm parameters as Figure 7.

throughput achieved for the largest particle size (200 µm). Notice that the maximum throughput for each particle size is related to the reference throughput of 2 CV/h by Qmax ) Qref/xMTZ,ref. This simple relation results because of the constant pattern behavior in Figures 7a and 8a-c. Conclusions Batch equilibrium data for multicomponent alkaline supernates and R-F resin could be adequately represented by binary equilibrium between cesium and sodium. This was the pseudobinary approach where sodium was assumed to be primarily responsible for modulation of cesium loading. With this approach, an empirical equation of the Freundlich-Langmuir type was capable of correlating the equilibrium data over eight decades of cesium/sodium concentration ratios (10-9 to 10-2) and sodium concentrations of 1 to 6 N. The correlation results confirmed that R-F resin performance is dependent on whether the resin was prepared in the laboratory (SRL) or on a large scale by BSC. The equilibrium data could also be described by mass action equations; however, it was found that ideal mass action constants varied by orders of magnitude over the range of the data. When the mass action equilibrium representation is used in the rate model simulation,

thermodynamic self-sharpening effects are underestimated, resulting in large errors in the estimated intraparticle diffusivity. Therefore, ideal mass action is not an accurate representation of the ion exchange equilibrium. Breakthrough data for loading of supernates to columns packed with R-F resin could be simulated with the rate model using the Freundlich-Langmuir isotherm equation. The effects of sodium could lumped into the isotherm parameters since the sodium concentration is constant through most of the supernate loading time. Consequently, these were one-component (cesium) simulations. This works well as long as feed composition remains constant. In most cases, the breakthrough position was predicted to within 5% or less, within the accuracy of the equilibrium correlations. The simulations confirmed that constant pattern breakthrough curves are established and that column systems using the R-F resin can be scaled with respect to linear superficial velocity, column length, and particle size. Also, the BSC resin is reproducible from batch to batch in terms of cesium capacity. In the absence of channeling and other dispersive effects, intraparticle diffusion is the controlling mass-transfer mechanism, which is expected because of the large particle size and small pore size of the R-F resin. Reliable estimation of the intraparticle diffusivity was obtained for long column systems where constant patterns were established. The benchmark of the carousel experiment with the rate model showed some interesting results, including the sensitivity of R-F resin performance to temperature, where cesium selectivity decreases with increasing temperature. For this particular experiment, a 12% reduction in cesium capacity was needed in the simulations to model the carousel data. This is because the equilibrium correlation at 25 °C overestimated the capacity at 35 °C, the temperature of the carousel experiment. The simulations also showed that the first and second cycles of the experiment suffered from a high degree of dispersion, due to channeling in poorly packed columns. However, from cycle to cycle, the columns became better packed and a constant pattern was established by the third and fourth cycles. Strong thermodynamic self-sharpening effects, due to high cesium selectivity, helped this constant pattern development. Lastly, the rate model was applied to design of an existing pilot-scale carousel unit, assumed to have three well-packed columns. The key simulation results show that column utilization in the lead column and throughput can be maximized while still containing the mass transfer zone in the second column. Higher throughputs are achieved for smaller particle sizes, because of decreased mass-transfer resistance and the shorter mass transfer zone in small particle systems. The latter is perhaps the most important result of this study because of the enormous amount of supernates to be treated. The overall time required for remediation and consequently overall treatment costs can be significantly reduced by simply using smaller particle sizes. Acknowledgment This work was supported through the DOE Office of Technology Development through TTP No. SR 1-3-2002 in the Underground Storage Tank Integrated Demonstration Program, the Peterson Foundation Technology Transfer Initiative, NSF grant GER 9024174, and a Showalter grant. We acknowledge L. A. Bray and co-


workers at Pacific Northwest Laboratory for collection of the Hanford equilibrium data, Hanford column data, and the carousel data. We thank Dr. Z. Ma for his comments concerning the rate model. Nomenclature a ) Freundlich-Langmuir isotherm parameter (mequiv/ mL column volume) b ) Freundlich-Langmuir isotherm parameter C ) equilibrium solution phase concentration (N) C h ) equilibrium solid phase concentration (mequiv/g or mequiv/mL column volume) C h T ) total solid phase concentration or capacity (mequiv/g or mequiv/mL column volume) D ) inner column diameter (cm) Dp ) intraparticle pore diffusivity (cm2/min) D∞ ) Brownian diffusivity (cm2/min) Eb ) axial dispersion coefficient (cm2/min) k1 ) empirical constant k2 ) empirical constant KCsNa ) cesium-sodium mass action constant Kd,Cs ) cesium batch distribution coefficient (mL/g) kf ) film mass-transfer coefficient (cm/min) L ) length of one column (cm) m ) empirical constant Ma ) Freundlich-Langmuir isotherm parameter Mb ) Freundlich-Langmuir isotherm parameter Nc ) number of components Ncol ) number of columns Q ) volumetric flow rate (mL/min) or throughput (CV/h) R ) average particle radius (µm) t ) time (min) T ) temperature (°C) x ) dimensionless axial position Subscripts e ) maximum inlet concentration i, j ) component counters Greek Letters β ) Freundlich-Langmuir isotherm parameter b ) interparticle void fraction p ) intraparticle void fraction λ ) theoretical number of column volumes of feed solution that can be loaded on a fixed-bed of resin (mL solution/ mL column volume) Fb ) bed density (g/mL swollen column volume)

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Received for review November 15, 1996 Revised manuscript received April 5, 1997 Accepted April 9, 1997X IE960729+

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

Development of a Carousel Ion-Exchange Process for Removal of

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