Modeling Cesium Ion Exchange on Fixed-Bed Columns of Crystalline

Texas A&M University, College Station, Texas 77843-3122 ... Best-fit diffusion coefficients from column simulations were compared with previously repo...
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Modeling Cesium Ion Exchange on Fixed-Bed Columns of Crystalline Silicotitanate Granules I. M. Latheef, M. E. Huckman, and R. G. Anthony* Kinetics, Catalysis, and Reaction Engineering Laboratory, Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122

A mathematical model is presented to simulate Cs exchange in fixed-bed columns of a novel crystalline silicotitanate (CST) material, UOP IONSIV IE-911. A local equilibrium is assumed between the macropores and the solid crystals for the particle material balance. Axial dispersed flow and film mass-transfer resistance are incorporated into the column model. Cs equilibrium isotherms and diffusion coefficients were measured experimentally, and dispersion and film masstransfer coefficients were estimated from correlations. Cs exchange column experiments were conducted in 5-5.7 M Na solutions and simulated using the proposed model. Best-fit diffusion coefficients from column simulations were compared with previously reported batch values of Gu et al. and Huckman. Cs diffusion coefficients for the column were between 2.5 and 5.0 × 10-11 m2/s for 5-5.7 M Na solutions. The effect of the isotherm shape on the Cs diffusion coefficient was investigated. The proposed model provides good fits to experimental data and may be utilized in designing commercial-scale units. Introduction A legacy of the Cold War has been the millions of gallons of radioactive waste currently stored at DOE (U.S. Department of Energy) facilities throughout the nation. In recent years, much research has focused on developing materials and technologies for the remediation of these wastes. Anthony et al.3 reported the synthesis of a crystalline silicotitanate, labeled TAM5, which proved to be a selective ion-exchange material for removing the radioactive Cs and Sr from these waste.4-7 Several studies have been conducted to determine the equilibrium behavior of the material8-10 and its diffusion characteristics.1,2 The industrial application of UOP IONSIV IE-911, the commercial, engineered form of TAM-5, is proposed to be in a continuous-flow arrangement through a series of fixed-bed columns. The objective of this study will be to present a mathematical model which will simulate the performance of the IE911 granules in a fixed-bed column. Model simulations will be compared with laboratory column data. The diffusion coefficients determined from previous batch diffusion studies1,2 will be compared with those from the current column modeling work. The DOE waste compositions vary, but typically Cs concentrations are in the parts per million (ppm) range. At very low concentrations, the equilibrium is usually assumed to be linear. A comparison of simulations using the linear and Langmuir isotherms will be presented, and the effect of the isotherm shape on the diffusion coefficient will be presented. Furthermore, the current work will evaluate the proposed model as a potential design tool for developing commercial ion-exchange units for the UOP IONSIV IE-911 granules. Modeling Equations An ion-exchange or adsorption process can be described as a series of steps, each of which must be properly accounted for to accurately model the overall process. The phenomena to be considered in an ion-

exchange process are as follows: (1) diffusion of an ion from the bulk fluid to the particle surface, (2) diffusion across the thin liquid film which forms around the particle, and (3) diffusion through a network of pores to reach an ion-exchange site. Often, the reaction rate at the ion-exchange site is assumed to be fast compared to mass-transfer rates.11 Thus, the reaction rate is considered to be instantaneous in kinetic studies. For fixed-bed columns, one must also account for hydrodynamic effects within the bulk fluid. Hence, to model the ion-exchange process in a fixed bed, it is important to understand the ion-exchange kinetics, which govern the diffusion of the ionic species within the particle, as well as the hydrodynamic effects within the column. The IE-911 granules are a composite material manufactured by combining the TAM-5 crystals with a binder material. Hence, the granule consists of two distinct phases: a crystal phase with micropores within the crystals and a pore phase with macropores between the crystals. Such a particle is classified as having a bidisperse pore structure. Extensive work has been published regarding the modeling of such particles, and summaries can be found in Gu et al.,1 Ruthven,12 Robinson et al.,13 DePaoli and Perona,14 and Huckman et al.15 The most realistic model for bidisperse particles would be a heterogeneous model, also known as a macromicro model. This model accounts for diffusion in the macropores between the crystal particles followed by diffusion into the micropores within the crystals. This model may account for multiple diffusion mechanisms within the macropores of the particle. Thus, oftentimes, surface and/or pore diffusivities for diffusion within the macropores are required along with a solid-phase diffusivity for diffusion in the micropores. The heterogeneous model may be described by eqs 1 and 2, which incorporates macropore diffusion in series with micropore diffusion. It should be noted that eq 2 written for the solid phase assumes the solid to be a homogeneous crystal particle. Hence, this equation assumes

10.1021/ie990748u CCC: $19.00 © 2000 American Chemical Society Published on Web 03/21/2000

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that only solid-phase diffusion is occurring within the crystal.

P

∂CPi 3 1 ∂ + (1 - P) JSi |s)RC ) - 2 ∂t RC r ∂r 2

[r Ji] ≡ particle balance (1) ∂q 1 ∂ ) - 2 [s2JSi ] ≡ crystal balance ∂t s ∂s

(2)

where CPi is the pore liquid concentration of i, P is the pellet porosity, RC is the crystal radius, and superscript S refers to the solid or crystal phase. For eq 1, the mass flux, Ji, into the particle can occur via surface and/or pore diffusion in parallel. If micropore diffusion is considered to occur in series with the macropore diffusion, then eq 2 describes the flux, JSi , into the micropores of the crystals. Thus, the heterogeneous or macro-micro model describes diffusion into a bidisperse particle as an initial flux into the macropores followed by diffusion into the micropores of the crystals by applying the two material balance equations (1) and (2). Although the heterogeneous model physically describes the diffusion within the bidisperse particle more accurately, often either the micropore or macropore resistances will dominate, justifying the use of simpler models. The particle material balance used in this study considers two phases in the particle, a pore liquid assumed to be in equilibrium with the solid, resulting in the two-phase homogeneous model:

[

]

∂qi ∂CPi 1 ∂ P + (1 - P) ) - 2 [r2Ji] ∂t ∂CPi r ∂r

(3)

where qi is the solid concentration of i. The boundary conditions are as follows:

∂CPi )0 ∂r

at (t, r ) 0) for all x

Ji|r)RP ) kf[Ci - CPi|r)RP]

(4)

at (t, r ) RP) for all x (5)

where Ci is the bulk fluid concentration of i, kf is the film mass-transfer coefficient, RP is the pellet radius, and x refers to the distance along the axial direction of the column. Equation 5 states that the flux of component i at the particle surface is equivalent to the flux of i across the thin film around the particle. The equilibrium is described by an isotherm equation, such as the Langmuir isotherm. This model accounts for concentration changes in the pore liquid and the solid phase through a single particle material balance. The diffusive flux may account for multiple parallel diffusion mechanisms (e.g., surface and/or pore diffusion) within the pores of the solid. However, diffusion resistance in the micropores is considered negligible with this model. Thus, cations entering the pores diffuse through the solid and form an instantaneous equilibrium between the solid and the pore liquid. Equations 1-3 describe the particle material balances typically used to model bidisperse pellets. The flux term, Ji, may account for both pore and surface diffusion. Gu et al.1 and Huckman et al.16 have considered surface diffusion to be negligible for the IE-911 granules and have shown that Fick’s law satisfactorily describes the

diffusive flux term, Ji, for this material. Thus, Fick’s law (eq 6) will be used as the constitutive equation to describe intraparticle diffusion for this study.

Ji ) -De

dCi dr

(6)

where De is the effective intraparticle diffusion coefficient. The effective diffusivity is defined in Froment and Bischoff17 as follows:

De ) (P/τ)Dm

(7)

where τ is the particle tortuosity and Dm is the molecular diffusivity. The ionic diffusivity at infinite dilution for Cs was reported as 2.06 × 10-9 m2/s.18 Gu et al.1 and Huckman et al.2,15,16 have indicated that the two-phase homogeneous model is sufficient for predicting the behavior of the IE-911 granules for most cases. Furthermore, dimensionless parameters developed by Huckman,2 Helfferich,11 Ruckenstein et al.,19 and Ruthven and Loughlin20 provide criteria for considering micropore or crystal-phase diffusional resistance negligible. The parameter presented by Huckman2 shown in eq 8 applies for nonlinear isotherms.

DeRC2 C0 NCr ) 3(1 - P) DSRP2 F(C0) P

(8)

where DS is the crystal-phase diffusivity and F(C0) is the evaluation of the equilibrium isotherm function F(C) at the initial concentration, C ) C0. When the crystal resistance parameter, NCr, is much greater than 1, the solid-phase resistance to diffusion controls. However, if NCr is much less than 1 (i.e., NCr e 0.001), the pore liquid resistance to diffusion controls. The batch kinetic studies provide valuable information for use in column models. The batch diffusion studies help determine the appropriate particle material balance for the material of interest. Theoretically, the diffusion coefficients from a batch reactor should be equivalent to diffusion coefficients determined for a fixed-bed column. This concept may be understood by recognizing that diffusion of a cation within the pore network of a granule is independent of the reactor type (i.e., fixed-bed column or stirred-tank reactor). Modeling fixed beds of bidisperse solids requires applying the differential particle balances (eqs 1 and 2 or eq 3) in addition to a bulk-phase material balance (eq 9) which further complicates the calculations.

( )

∂Ci ∂2Ci ∂Ci 3 1 - B kf[Ci - CPi|r)RP] ) -νi + DL 2 ∂t ∂x R B ∂x P (9) where Ci is the bulk fluid concentration, νi is the interstitial velocity, DL is the axial dispersion coefficient, and B is the bed porosity. Equation 9 accounts for film mass-transfer resistance by using a film mass-transfer coefficient (kf) and axial dispersion characterized by a dispersion coefficient (DL). The boundary conditions are given by Danckwerts21 as shown in eqs 10 and 11.

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|

∂Ci ∂x

x)0

)

νi (C 0 - Ci|x)0) DL i

|

∂Ci ∂x

)0

(10) (11)

x)L

where Ci0 is the feed concentration and L is the length of the reactor. The initial conditions for the system are as follows:

CPi ) Ci ) 0 at (t ) 0, r) and x * 1, Ci ) Ci0 at x ) 1 (12) The two-phase homogeneous model has been shown to successfully model adsorption in packed beds of zeolite particles22 as well as in complex soils and activated carbon.23,24 In this study, the two-phase homogeneous particle balance (eq 3) will be combined with the bulk-fluid material balance (eq 9) to model ion exchange in packed beds of the IE-911 granules. The determination of the model parameters will be presented in the following section. Determination of Model Parameters From study of the modeling equations (eqs 3 and 9), it is apparent that four parameters are required to complete the model: (1) the equilibrium isotherm, (2) the effective diffusivity, (3) the axial dispersion coefficient, and (4) the film mass-transfer coefficient. The equilibrium isotherm and diffusion coefficients were determined from batch experiments. The axial dispersion and film mass-transfer coefficient were estimated using correlations from the literature. Also, the model requires the physical parameters describing the IE-911 granules and the laboratory column. Physical Properties of CST Granules. Experiments were conducted with UOP IONSIV IE-911 granules or UOP IONSIV IE-910, the commercial form of the TAM-5 powder. The batches used in this study were IE-911-01 (lot 999096810001), IE-911-94 (a preliminary form labeled 7398-94), and IE-910-EF (an engineered form prepared at Texas A&M University). All samples were treated in 2 M NaOH to prepare the Na form of the material. BET analysis was conducted using a Micromeretics Digisorb 2600 and Micromeretics ASAP 2000. The physical parameters of these granules are shown in Table 1. Simulated Waste Solutions. The typical solutions at the DOE waste sites are highly alkaline and contain high concentrations of Na+. These waste solutions contain numerous other ions, and the composition varies by location. For experimental purposes, simulated waste solutions were prepared to mimic the composition of real waste. The standard waste simulated solution (SS) used was a 5.1 M NaNO3 and 0.6 M NaOH mixture. A second solution used was the standard solution modified by adding 0.5 M KNO3 (SSK) to incorporate the competitive effect of K+. These simplified compositions were based on previous studies conducted at Sandia National Laboratories. Also, a more complex solution labeled DSSF5 was used. The DSSF5 composition is based on real tank waste located at the Hanford, WA, waste storage site. These solutions were used for the column, batch kinetic, and equilibrium experiments. The composition for the DSSF5 solution is listed in Table 2. To

Table 1. Physical Parameters of IE-911 and IE-910-EF Granules parameter

IE-911-01

IE-911-94

IE-910-EF

pellet diameter, dp (µm) pellet porosity, P pellet density, FP (g/cm3) solid density, FS (g/cm3) BET pore volume (cm3/g) BET surface area (m2/g)

380 0.24 2.0 2.6 0.12 37.0

400 0.23 2.0 2.6 0.11 21.1

340 0.22 2.0 2.6

Table 2. Composition for DSSF5 Simulated Waste Solution ionic species

concentration (M)

ionic species

concentration (M)

Na+ K+ OHNO3NO2-

5.0 0.675 1.25 2.515 1.08

Al(OH)4CO32SO42PO33Cl-

0.515 0.105 0.006 0.01 0.073

these solutions was added CsNO3 to obtain different concentrations of Cs+. Equilibrium Studies. The objective of the equilibrium studies was to determine a functional relationship between the solid loading of a Cs to its equilibrium liquid concentration. To determine the equilibrium isotherm, batch experiments were conducted in 20-mL vials or 125-mL plastic bottles. A 0.05-0.10-g sample of IE-911 granules was contacted with a waste simulant solution of known initial Cs concentration and shaken gently on a platform or wrist shaker for 72 h. The equilibration period was determined based on previous experiments.2,10 The liquid supernatant was then separated from the solid pellets using a 0.2-µm Nalgene syringe filter. The final liquid concentration was measured by flame atomic absorption using a Varian SpectrAA-30 spectrophotometer. The corresponding solid concentration, q, was calculated from the initial and final liquid concentrations (Cinitial and Cfinal), the volume of liquid (V), and the mass of IE-911 granules (M) as shown in the following equation:

V q ) (Cinitial - Cfinal) M

(13)

A series of these experiments varying the initial cation concentration or the solid-to-liquid ratio provided equilibrium data over a broad concentration range. The data were then fit with the Langmuir isotherm (eq 14) to provide a mathematical relationship between the solid loading (q) and the liquid concentration (C). The bestfit parameters from the isotherm were the input parameters for the mathematical column model.

q)

qtKC 1 + KC

(14)

where qt and K are the Langmuir isotherm parameters. The equilibrium data were also compared to predictions from the previously developed ZAM (Zhen, Anthony, and Miller) equilibrium model.10 This equilibrium model was developed using TAM-5 powder, but column experiments were conducted using the engineered form, IE-911. In Figures 1 and 2, experimentally measured isotherms for the IE-911 granules are compared with model predictions from the ZAM model for the SS and SSK solutions. In all cases, the model predicts the granular data well, especially at low Cs levels. For most cases, the model overpredicts the equilibrium loading at the high concentrations, except for the IE-911-94 case

Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000 1359 Table 4. Cs Effective Diffusion Coefficients for IE-911-01 and IE-910-EF Granules Reported from Previous Batch Kinetic Studies

Figure 1. Cs equilibrium isotherm for IE-911-01 in SS. The Langmuir fit to experimental data (qt ) 67.27 ( 1.56 mg/g; K ) 1.58 ( 0.10 m3/mol) and the ZAM equilibrium model prediction are also shown.

solution

IE-911 batch

best fit De (m2/s)

source

SS SSK DSSF5

IE-911-01 IE-911-01 IE-910-EF

(3.0 ( 1.0) × 10-11 (4.0 ( 1.0) × 10-11 (2.0 ( 1.0) × 10-11

Huckman2 Huckman2 Gu et al.1

in Table 4 were determined from fitting the two-phase homogeneous model to batch kinetic data. Axial Dispersion and Film Mass-Transfer Resistance. Residence time distribution studies were conducted to estimate axial dispersion in the laboratory column.25,26 The Suzuki and Smith27 correlation (eq 15) provided the best estimates of the experimentally measured values.

DL u ) 0.44 + 0.83 Dm Dm

(15)

where Dm is the molecular diffusivity in cm2/s and u is the superficial velocity in cm/s. The film mass-transfer coefficient was estimated for the laboratory columns using the following equation:

kf )

2.62(Dmu)0.5 ap(dp)1.5

(16)

where ap is the external surface area of the particles per packed volume.28 Results and Discussion Figure 2. Cs equilibrium isotherms for IE-911-94 granules in SS and SSK. Langmuir isotherm fits to the data are shown as solid lines, and the ZAM model predictions are shown as dashed lines. Best-fit Langmuir parameters for SS were qt ) 91.9 ( 2.7 mg/g and K ) 1.5 ( 0.2 m3/mol, and those for SSK were qt ) 78.4 ( 3.8 mg/g and K ) 0.6 ( 0.1 m3/mol. This figure shows the competitive effect of K on Cs uptake. Table 3. Best-Fit Cs Isotherm Parameters for IE-911 Granules qt qt simulant granules (mg/g of solid) (mmol/g of solid) SS SS SSK DSSF5a

911-94 911-01 911-94

91.9 ( 2.7 67.3 ( 1.6 78.4 ( 3.8 77.0

0.69 ( 0.02 0.55 ( 0.01 0.59 ( 0.03 0.58

K (m3/mol) 1.54 ( 0.16 1.58 ( 0.10 0.57 ( 0.07 1.77

a Isotherm parameters determined from fitting data generated from the ZAM equilibrium model.

in SS. Thus, the ZAM equilibrium model accurately estimates the behavior of the IE-911 granules up to Cs levels of 150 ppm for the solutions used in this study. For the DSSF5 solution, the ZAM model was shown to accurately predict experimental data.10 Thus, the model was used to generate equilibrium data which were fit with the Langmuir isotherm. Figures 1 and 2 also show Langmuir fits to experimental data in SS and SSK. Table 3 shows the best-fit Cs isotherm parameters for these solutions. Diffusion Coefficient. A primary objective of this study was to compare the previously reported batch diffusion coefficients1,2 with those determined from the column experiments of the present study. Table 4 lists the best-fit Cs effective diffusion coefficients previously reported for the IE-911 granules in the various solutions used in this investigation. Note that the results shown

Column experiments were conducted using the IE911 batches shown in Table 1 for the SS, SSK, and DSSF5 solutions. Table 5 summarizes the column experimental conditions. The model simulations presented in this study were conducted by fitting the effective diffusion coefficient to the experimental column data by minimizing the errors between the data and the model simulation. Although the axial dispersion and film mass-transfer coefficients may be considered adjustable parameters, previous studies by Huckman et al.15 and Latheef26 have shown that both parameters do not contribute significantly to the shape of the breakthrough curves. Latheef26 considered model simulations with the film mass-transfer coefficient adjusted by 2 orders of magnitude and even neglecting film resistance altogether. All of these simulations essentially overlay each other, indicating the minimal effect of film resistance on the breakthrough curve. Consequently, the effective diffusion coefficient is the critical parameter in determining the shape of the breakthrough curves for IE-911 granules and thus it was the adjustable parameter in the present study. Numerical Methods. The experiments shown in Table 5 were simulated using the two-phase homogeneous column model. This model requires the simultaneous solution of eqs 3-6 and 9-11. These equations were solved numerically using orthogonal collocation on finite elements (OCFE). The OCFE method divides the solution domain into a specified number of finite elements. Then orthogonal collocation is applied within each element. This procedure increases the number of grid points in the solution domain without increasing the order of the trial function.29 When OCFE is implemented for the system of PDEs described above, the

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Table 5. Summary of Column Experimental Conditions expt 8 9 10 12 13 19 1 SNL-1a a

IE-911 batch simulant feed Cs (ppm) bed length (cm) bed vol (mL) bed density (g/mL) sup vel (cm/min) space vel (h-1) 911-94 911-94 911-01 911-01 911-01 911-01 910-EF 910-EF

SS SSK SS SS SS SS DSSF5 DSSF5

50 50 50 50 50 50 40 9.5

31.75 31.75 31.75 31.75 31.75 6.0 15.8 15

30.0 30.0 30.0 30.0 30.0 5.70 14.7 12

1.08 1.03 1.00 1.00 0.98 1.00 0.99 1.05

1.81 1.76 1.98 3.39 4.87 3.17 0.95 0.25

3.6 3.4 3.8 6.5 9.2 31.3 3.7 3

SNL-1 is a column experiment conducted at Sandia National Laboratories.

Figure 3. Simulation of Cs breakthrough data for IE-911-01 granules in SS from expts 10, 12, 13, and 19. The model simulations are a simultaneous best fit to the four experiments using De ) 4.5 × 10-11 m2/s.

system of equations reduces to a system of algebraic differential equations (ADEs). Petzold30 developed a computer code called DASSL to solve such systems of ADEs numerically. DASSL employs a backward differentiation scheme to advance the solution in the time domain.31 In the x direction (i.e., along the length of the column), OCFE was implemented using Jacobi polynomials to approximate the bulk fluid concentration profile within each element. To maintain continuity of the solution, the first derivatives at the boundary of each element were set equal. In the r direction (i.e., within the particle), the simple orthogonal collocation method was used with Legendre polynomials to approximate the particle concentration profile at each collocation point. Similar numerical techniques have been used previously to solve comparable systems of PDEs as described by Madras et al.23 and Thibaud-Erkey et al.24 for modeling adsorption on soil and Yu and Wang32 to model adsorption and ion exchange. Experimental Breakthrough Curves and Model Simulations. Several experiments (expts 10, 12, 13, and 19) were conducted using the IE-911-01 granules in SS. Although these experiments were all conducted at different flow rates (superficial velocities from 2 to 4.9 cm/min), the Cs effective intraparticle diffusion coefficient should be constant because the diffusion parameter is an intrinsic property of the ion-exchange particle and independent of flow rate or column size. These four experiments were fitted simultaneously using the two-phase homogeneous column model to determine a best-fit Cs diffusion coefficient. Figure 3 shows the experimental data along with the simulations for the best fit De ) 4.5 × 10-11 m2/s. The figure shows that this value provides an excellent match to the data sets. Huckman2 reported a Cs diffusion coefficient of 3.0

Figure 4. Cs breakthrough curves for IE-911-94 in SS and SSK with model simulations from the two-phase homogeneous column model. The best-fit diffusion coefficient for expt 8 was De ) 5.0 × 10-11 m2/s, and that for expt 9 was De ) 4.0 × 10-11 m2/s.

× 10-11 m2/s in the batch. If an error estimate of 30%, which is reasonable for such measurements, is assumed for these values, then there is considerable overlap between these diffusion coefficients. Experiments were also conducted using IE-911-94 in SS and SSK for expts 8 and 9, respectively. Figure 2 shows the experimentally measured isotherms for IE911-94 granules in these simulants. The Cs breakthrough curves for these column runs are shown in Figure 4 along with the two-phase homogeneous column model fits to the data. The best-fit diffusivities for these runs are De ) 5.0 × 10-11 m2/s for expt 8 and De ) 4.0 × 10-11 m2/s for expt 9. Huckman2 reported values of 3.0 × 10-11 m2/s for SS and 4.0 × 10-11 m2/s for SSK for the IE-911-01 granules. For SSK, the batch and column results are in excellent agreement. For SS, the column value is higher than the batch value, but again a 30% assumed error in the measurements would lead to slight overlap of the values. Figure 5 shows the difference between the batch diffusivity and best-fit values for model simulations of expt 8. The batch value of 3.0 × 10-11 m2/s for SS was much less than the bestfit diffusivity of 5.0 × 10-11 m2/s for expt 8. Clearly, the lower diffusivity value predicts early breakthrough for this experiment. Overall, these experiments demonstrate the difficulty in accurately measuring the Cs diffusivity and that an average value would probably be sufficient for modeling and design purposes. Huckman2 reported crystal resistance parameter (NCr) values between 0.009 and 0.039 for Cs exchange on IE-911 granules in the SS and SSK solutions. The results presented here indicate that for NCr values even as high as 0.04 the two-phase homogeneous column model can be used to predict IE-911 performance in fixed beds with good accuracy. Effect of the Isotherm Shape on the Diffusion Coefficient. The equilibrium experiments indicated

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Figure 5. Cs breakthrough curves for expt 8 (IE-911-94 in SS) with model simulations from the two-phase homogeneous column model. The best-fit diffusion coefficient for expt 8 was De ) 5.0 × 10-11 m2/s, and the batch diffusivity from Huckman2 was De ) 3.0 × 10-11 m2/s.

Figure 6. Langmuir and linear isotherms for DSSF5 simulant from the ZAM equilibrium model. The linear isotherm at Kd ) 930 mL/g was determined for 9.5 ppm Cs, and that at Kd ) 670 mL/g was determined for 40 ppm Cs. The Langmuir and linear isotherms coincide up to about 10 ppm Cs.

that IE-911 granules follow the Langmuir isotherm. Oftentimes the Cs concentration in the DOE wastes is low (e20 ppm) and a linear isotherm (eq 17) may be appropriate.

q ) KdC

(17)

where Kd is the distribution coefficient. Column experiments were conducted at 9.5 and 40 ppm for the IE910-EF granules in the DSSF5 solution. Model simulations were conducted using both the linear and Langmuir isotherms to determine the effect of the isotherm on the diffusion coefficient. Figure 6 shows the Langmuir isotherm determined from the ZAM equilibrium model along with linear isotherms at 9.5 and 40 ppm. It is clear that at the lower concentration the linear and Langmuir isotherms coincide. However, at 40 ppm Cs the two isotherms differ and the question is what affect does this difference have on the Cs diffusion coefficient for the two-phase homogeneous model. A column experiment was conducted at Sandia National Laboratories (SNL-1) using the IE-910-EF granules in DSSF5 with 9.5 ppm Cs in the feed. Figure 7 shows the experimental data along with the model simulations for the Sandia experiment. Simulations were conducted using the Langmuir isotherm and a linear isotherm with Kd ) 930 mL/g. Both simulations

Figure 7. Cs breakthrough curve for Sandia experiment (SNL1) using the IE-910-EF granules in DSSF5 with 9.5 ppm Cs. Model simulations were conducted using the two-phase homogeneous column model with linear (Kd ) 930 mL/g) and Langmuir isotherms with De ) 4.0 × 10-11 m2/s for both.

Figure 8. Expt 1 Cs breakthrough curve for IE-910-EF in DSSF5. Model simulations are shown using the linear isotherm (Kd ) 670 mL/g) with De ) 4.0 × 10-11 m2/s and using the Langmuir isotherm with De ) 2.5 × 10-11 m2/s.

overlay each other at a best-fit diffusion coefficient of De ) 4.0 × 10-11 m2/s. Thus, at the very low concentrations when the Langmuir and linear isotherms coincide, the linear isotherm simplification appears appropriate and both isotherms yield similar diffusion coefficients. Figure 8 shows column experimental results and model simulations for expt 1, which was also conducted using the IE-910-EF granules in DSSF5 with 40 ppm Cs in the feed. From Figure 6 it was clear that at 40 ppm the linear and Langmuir isotherm differed; however, the effect this difference would have on model simulations was not clear. Figure 8 shows that the simulations using the linear and Langmuir isotherms overlay each other; however, the best-fit diffusion coefficient determined from the linear isotherm simulation (De ) 4.0 × 10-11 m2/s) was greater than that determined when using the Langmuir isotherm (De ) 2.5 × 10-11 m2/s). Note that Gu et al.1 reported a diffusion coefficient of 2.0 ( 1.0 × 10-11 m2/s for the IE-910-EF granules in DSSF5. It appears that the diffusion coefficients determined from linear isotherm simulations were consistent at 9.5 and 40 ppm Cs, and these values were higher than previously reported estimates. For the Langmuir isotherm simulations, the diffusion coefficient at the higher feed level (i.e., 40 ppm) was lower than the corresponding value determined from the linear isotherm, but this value was more in line with previously reported diffusivities for DSSF5. Hence, when making the linear isotherm simplification, one must

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recognize that higher diffusion coefficients may be estimated than diffusivity values estimated using the Langmuir isotherm. This trend is more apparent at higher concentration levels. The obvious reason for the difference in the diffusivities appears to be the area between the Langmuir and linear isotherms at the higher Cs levels. Additional studies at higher and intermediate concentrations may provide more insight into this phenomenon. Conclusions The column experiments and simulations indicated that the two-phase homogeneous column model provides excellent fits to the data for the SS, SSK, and DSSF5 solutions. For the column, it appears that at 5-5.7 M Na the two-phase homogeneous particle balance may be substituted for the more rigorous macro-micro model. Gu et al.1 and Huckman2 have shown from batch experiments that two-phase homogeneous particle balance is sufficient for modeling the IE-911 granules. Hence, the proposed model appears to provide accurate simulations of IE-911 column performance for use as a design tool for high Na-level wastes. The effective diffusivity for Cs was estimated from the column runs to be between 4 and 5.0 × 10-11 m2/s for SS, 4.0 × 10-11 m2/s for SSK, and between 2.5 and 4.0 × 10-11 m2/s for DSSF5. These compare to previous batch estimates of (3.0 ( 1.0) × 10-11 m2/s for SS, (4.0 ( 1.0) × 10-11 m2/s for SSK, and (2.0 ( 1.0) × 10-11 m2/s for DSSF5. The batch values are consistently less than the column results. Thus, column designs based on batch diffusion coefficients would be conservative (i.e., they would predict early breakthrough of Cs). Note that higher diffusion coefficients would result in sharper breakthrough curves with the breakthrough point moving to the right (i.e., toward increased column volumes). Model simulations using the Langmuir and linear isotherms were compared to determine the effect of the isotherm shape on the Cs diffusion coefficient. At low concentrations, both isotherms provided identical results as expected. At higher concentrations, the linear isotherm required a higher diffusion coefficient to yield a simulation similar to the Langmuir isotherm. This result provides a better understanding of how to relate diffusivity values determined using different isotherm estimates. The ZAM equilibrium model previously had been shown to accurately predict TAM-5 powder data.10 Experimental results in this work have indicated that the ZAM model may also be used to predict equilibrium for the IE-911 granules, the engineered form of TAM5, especially at low concentrations below 150 ppm Cs. Acknowledgment The study was funded by the Department of Chemical Engineering, Texas A&M University, and Sandia National Laboratories under Texas A&M Research Foundation Contract RF8880. Sandia National Laboratories is supported by the U.S. Department of Energy under Contract DE-AC04-94AL85000. Nomenclature ap ) external surface area of the particles per packed volume C ) liquid-phase concentration

Cfinal ) final liquid-phase concentration Ci ) bulk liquid-phase concentration of i Cinitial ) initial liquid-phase concentration C0 ) feed concentration in the bulk liquid phase C0i ) feed concentration in bulk liquid phase of i CPi ) pore liquid concentration of i DL ) axial dispersion coefficient Dm ) molecular diffusivity De ) intraparticle diffusion coefficient DS ) intracrystalline diffusion coefficient dp ) particle diameter Ji ) liquid-phase diffusive flux of i JiS ) solid-phase diffusive flux of i K ) Langmuir isotherm constant Kd ) distribution coefficient kf ) film mass-transfer coefficient L ) length of reactor M ) mass of solid NCr ) crystal resistance parameter q ) solid-phase concentration qi ) solid-phase concentration of i qt ) maximum solid-phase concentration r ) radial direction to the center of the particle RC ) crystal radius RP ) particle radius s ) radial direction to the center of the crystal t ) time u ) superficial velocity V ) volume of liquid x ) spatial direction along the length of the column Greek Symbols B ) bed porosity P ) pellet porosity FP ) pellet density FS ) solid density τ ) particle tortuosity νi ) interstitial velocity

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Received for review October 15, 1999 Revised manuscript received February 1, 2000 Accepted February 2, 2000 IE990748U