Experimental and modeling studies on sorption and diffusion of radium in bentonite

Journal of Contaminant Hydrology 47 Ž2001. 171–186 www.elsevier.comrlocaterjconhyd

Experimental and modeling studies on sorption and diffusion of radium in bentonite Y. Tachi ) , T. Shibutani, H. Sato, M. Yui Japan Nuclear Cycle DeÕelopment Institute (JNC), Tokai Works, 4-33 Muramatsu, Tokai, Ibaraki 319-1194, Japan Received 1 October 1999; received in revised form 24 February 2000; accepted 3 April 2000

Abstract The sorption and desorption behavior of radium on bentonite and purified smectite was investigated as a function of pH, ionic strength and liquid to solid ratio by batch experiments. The distribution coefficients Ž K d . were in the range of 10 2 to ) 10 4 ml gy1 and depended on ionic strength and pH. Most of sorbed Ra was desorbed by 1 M KCl. The results for purified smectite indicated that Ra sorption is dominated by ion exchange at layer sites of smectite, and surface complexation at edge sites may increase Ra sorption at higher pH region. Reaction parameters between Ra and smectite were determined based on an interaction model between smectite and groundwater. The reaction parameters were then used to explain the results of bentonite by considering dissolution and precipitation of minerals and soluble impurities. The dependencies of experimental K d values on pH, ionic strength and liquid to solid ratio were qualitatively explained by the model. The modeling result for bentonite indicated that sorption of Ra on bentonite is dominated by ion exchange with smectite. The observed pH dependency was caused by changes of Ca concentration arising from dissolution and precipitation of calcite. Diffusion behavior of Ra in bentonite was also investigated as a function of dry density and ionic strength. The apparent diffusion coefficients Ž Da . obtained in compacted bentonite were in the range of 1.1 = 10y11 to 2.2 = 10y12 m2 sy1 and decreased with increasing in dry density and ionic strength. The K d values obtained by measured effective diffusion coefficient Ž De . and modeled De were consistent with those by the sorption model in a deviation within one order of magnitude. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Sorption; Diffusion; Radium; Bentonite; Smectite; Models

)

Corresponding author. Tel.: q81-29-282-1111; fax: q81-28-287-3258. E-mail address: [email protected] ŽY. Tachi..

0169-7722r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 0 0 . 0 0 1 4 7 - 9

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1. Introduction The Japanese high-level radioactive waste ŽHLW. disposal concept is based on a multi-barrier system which consists of containers, buffer materials Žbentonite. and surrounding rocks. Radionuclides released from a HLW may be transported through pores in the bentonite and may be retarded by interacting with pore surfaces. Radionuclide transport in bentonite will be controlled by diffusion and sorption because groundwater movement in bentonite is sufficiently slow. Therefore, it is important to understand the sorption and diffusion behavior of radionuclides in bentonite. The sorption behavior of radionuclides is usually evaluated using the distribution coefficient Ž K d .. The distribution coefficients are usually acquired by batch sorption experiments due to experimental simplicity. The K d values obtained by the batch method are often used directly in the performance assessment. However, when we use K d values obtained by the batch method for the performance assessment, we should consider some problems. For one thing, K d values obtained by the batch method are valid only for conditions employed in the experiments because K d depends on chemical conditions such as pH, ionic strength. The K d values for the performance assessment should be selected from K d values that closely correspond to the expected condition in the repository. In addition, the batch experiments are usually conducted at relatively high liquid to solid ratios compared with compacted bentonite. The effect of compaction on the sorption properties of bentonite must be evaluated. As an alternative, the retardation behavior of radionuclides in compacted bentonite is evaluated by in-diffusion experiments. The K d values obtained by in-diffusion experiments, which may include sorption, molecular filtration and ion exclusion, are more realistic values than those obtained by batch sorption and have been used in the performance assessment in Japan ŽPNC, 1993; JNC, 1999.. However, the quality and amount of diffusion data is limited and it is difficult to obtain data under various conditions. Therefore, it is necessary to develop mechanistic sorption models and to investigate the applicability of the model to compacted bentonite. Several mechanistic sorption models Že.g., Baeyens and Bradbury, 1995. and diffusion models in compacted bentonite Že.g., Sato et al., 1995; Ochs et al., 1998. have been developed up to now. In this study, the sorption and diffusion behavior of radium in bentonite was investigated by batch sorption and in-diffusion experiments. Additional batch sorption experiments were also conducted for purified smectite and reaction parameters for Ra sorption on smectite were determined based on interaction on model between bentonite and groundwater ŽJNC, 1999.. This sorption model was then used to interpret sorption results on bentonite by additionally considering dissolution and precipitation of minerals and soluble impurities contained in bentonite. This sorption model was further used to explain retardation in compacted bentonite. 2. Experimental 2.1. Materials The bentonite used in the experiments is Kunigel V1w ŽKunimine Industries, Japan.. This is a crude sodium bentonite and a candidate buffer material in Japan. The purified

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173

Table 1 Characteristics of materials used in sorption and diffusion experiments Mineralogical composition (%) Smectite Quartzrchalcedony Feldspar Calcite Dolomite Zeolite Pyrite

Bentonite ŽKunigel V1w .

Purified smectite

46–49 38–39 2.7–5.5 2.1–2.6 2.0–3.8 3.0–3.5 0.5–0.7

)99 -1

CEC (meqr100 g) 60.1

110.2

Initial exchangeable cation (meqr100 g ZNa Z 2 Ca ZK Z 2 Mg

51.3 7.4 0.6 0.7

107 1.4 1 0.7

Soluble impurities (wt.%) CaCl 2 CaSO4

0.014 0.244

)a

a

Z represents ion exchange site of smectite Žbentonite..

smectite is obtained from Kunipia F w ŽKunimine Industries, Japan. containing over 95 wt.% of sodium smectite by the following procedure ŽSasaki et al., 1995.: The fraction of smectite particles less than 1 mm is separated from fine minerals such as quartz by a hydraulic elutriation technique. Then the fraction is washed with a mixed solution of acetic acid and sodium acetate to remove any remaining calcite. Na- and OH-type ion exchangers are mixed with the smectite suspension to convert the smectite to the sodium form and to remove excess soluble salt. The purified smectite is then separated from the resins by sieving and filtering and is dried at 608C. The mineralogical composition, cation exchange capacity ŽCEC., initial exchangeable cations and the contents of soluble impurities of bentonite and purified smectite are given in Table 1 ŽIto et al., 1993; Oda and Shibata, 1999.. 2.2. Sorptionr desorption experiment Sorption and desorption experiments of Ra on bentonite and purified smectite were carried out by a batch method in an argon glove box with an oxygen level less than 1 ppm at room temperature. All the solutions used in the experiments were degassed by bubbling with argon gas in a glove box. The samples were contacted with distilled water and 0.1 M NaCl solutions in Teflon w vessels. The liquid to solid ratios were 500 and 50 ml gy1 . The pH values of the solutions were adjusted to 7–11 with HCl and NaOH, and were periodically measured with a calibrated combined glass electrode. After pre-equi-

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libration for 30 days, a tracer solution of Ra prepared by diluting a 226 RaCl 2 solutions ŽAmersham. was added to the solutions. The initial concentration of Ra was 1.0 = 10 2 Bq mly1 Ž1.2 = 10y8 mol ly1 .. The vessels were shaken frequently and the pH was measured periodically and adjusted if necessary. After a reaction time of 20 and 40 days, a small amount of the solution was withdrawn from each sample and was filtered through 10,000 molecular weight cut off ŽMWCO. ultrafilters ŽUSY-1, Advantec.. The concentration of Ra in the filtrates was analyzed with a Ge semiconductor detector ŽLO-AX-51370-20-P, ORTEC.. The concentrations of Na and Ca were analyzed using inductively coupled plasma atomic emission spectroscopy ŽICP-AES. ŽOptima-3000, PERKIN ELMER.. Desorption experiments were conducted by adding KCl and HCl to the residual solution containing the solids. The residual solution was adjusted to 1 M KCl and was shaken frequently for 3 days. A small amount of the solution was withdrawn from each sample and was filtered through 10,000 MWCO ultrafilters. Then, the residual suspension was adjusted to 1 M HCl and aliquots were taken from each sample in the same way as the desorption process by KCl. The sorption and desorption experiments were performed in duplicate. In addition, a blank test without solid was carried out to monitor precipitation and sorption of Ra on vessel walls and filters. 2.3. Diffusion experiments Diffusion experiments of Ra in compacted bentonite were carried out by an in-diffusion method Že.g., Sato et al., 1992. under aerobic conditions at room temperature. The bentonite was dried at 1108C for more than 24 h and compacted in an acrylic diffusion column with a size of 20 mm in diameter and 20 mm in length. The diffusion columns are shown in Fig. 1. Dry densities of 1.4 and 1.8 Mg my3 were chosen. The compacted bentonite was immersed in distilled water for more than 10 days in order to be saturated

Fig. 1. Schematic view of diffusion apparatus.

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with water. Compacted bentonite with a density of 1.8 Mg my3 was also immersed in 3% NaCl solution. A small amount of a tracer solution with a Ra concentration of 5.0 = 10 3 Bq mly1 Ž6.0 = 10y7 mol ly1 . was put on one end of the saturated bentonite specimen and a second bentonite specimen was placed on this end. After a diffusion period of 7–20 days, the bentonite was cut into slices of 0.5 mm in thickness. Each slice was weighed before and after drying at 1108C for about 24 h to determine its thickness. Then each slice was immersed for 3 h in 2 ml of 1 M HNO 3 in order to extract Ra. Liquid scintillator Ž18 ml PICO-FLOUR40, PACKARD. was added to the solution, and then the concentration of Ra was analyzed by a liquid scintillation counter ŽTRI-CARB 2750TRrLL, PACKARD..

3. Results 3.1. Sorptionr desorption The distribution coefficient and the desorption ratio are determined using the following equations, Kd s

C b y Ct Ct

fd ŽKCl r HCl. s

=

L

Ž 1.

S Cd ŽKCl r HCl. y Ct C b y Ct

= 100

Ž 2.

where K d is the distribution coefficient Žml gy1 ., C b is the concentration of Ra in the blank solution Žmol ly1 ., Ct is the concentration of Ra in the solution in sorption equilibrium Žmol ly1 ., and LrS is the liquid to solid ratio Žml gy1 ., fd ŽKClrHCl. is the desorption ratio for 1 M KCl or 1 M HCl solutions Ž%., Cd ŽKClrHCl. is the concentration of Ra in the solution in desorption equilibrium Žmol ly1 .. The distribution coefficients and the desorption ratios of Ra for purified smectite and bentonite are presented in Tables 2 and 3, respectively. The concentrations of Na and Ca are also shown in Tables 2 and 3. The pH values in the test solutions became stable at the desired values of 7–11 in a pre-equilibration period of about a month and remained more or less constant after addition of Ra. It was not found that the K d values increased with time between 20 and 40 days. This result indicated that sorption reaction attained equilibrium within about 20 days. The K d values of Ra on purified smectite for distilled water at a liquid to solid ratio of 500 ml gy1 are greater than 1.9 = 10 4 ml gy1 because of the detection limit. Sorption on purified smectite in 0.1 M NaCl solution was much weaker, the K d values at both liquid to solid ratios of 500 and 50 mg gy1 were in the range of 4.0 = 10 2 to ) 1.5 = 10 3 ml gy1 . No significant difference in K d values between two liquid to solid ratios was observed. The K d values increased gradually with pH. The K d values on bentonite for distilled water at a liquid to solid ratio of 500 ml gy1 were in the range of 3.3 = 10 3 to ) 1.7 = 10 4 ml gy1 and increased with pH. For 0.1 M NaCl solution, sorption was much weaker than that for distilled water. The K d values were in the range

176

Initial solution

Liquidrsolid ratio Žml gy1 .

pH

Distribution coefficient, K d Žml gy1 . 20 days 40 days

Concentration of ions Žmol ly1 . Na Ca

Desorption ratio Ž%. 1 M KCl 1 M HCl

Distilled water

500

7 8 9 10 11

Ž1.7"0.4.=10 4 Ž1.6"0.3.=10 4 ) Ž1.9"0.4.=10 4 )1.9=10 4 )1.9=10 4

)1.9=10 4 )1.9=10 4 )1.9=10 4 )1.9=10 4 )1.9=10 4

7.6=10y4 6.8=10y4 2.9=10y4 3.8=10y4 1.1=10y3

2.5=10y6 1.5=10y6 1.5=10y6 1.0=10y6 1.0=10y6

)100 88"10 91"10 80"10 86"10

)100 99"11 91"10 91"10 95"11

0.1 M NaCl

500

7 8 9 10 11

Ž6.6"1.4.=10 2 Ž6.0"1.5.=10 2 Ž7.9"1.6.=10 2 Ž1.5"0.3.=10 3 Ž1.9"0.4.=10 3

Ž6.5"1.0.=10 2 Ž4.1"1.2.=10 2 Ž9.0"1.8.=10 2 Ž1.1"0.2.=10 3 Ž1.3"0.3.=10 3

1.1=10y1 1.1=10y1 1.1=10y1 1.1=10y1 1.1=10y1

1.0=10y5 1.1=10y5 1.1=10y5 1.0=10y5 1.7=10y5

72"22 61"28 92"18 91"15 96"14

92"22 96"33 )100 )100 )100

50

7 8 9 10 11

Ž4.1"0.7.=10 2 Ž4.0"0.8.=10 2 Ž7.4"1.0.=10 2 Ž6.4"1.0.=10 2 ) Ž1.5"0.2.=10 3

Ž4.3"0.8.=10 2 Ž6.9"1.0.=10 2 Ž6.8"1.0.=10 2 Ž1.3"0.2.=10 3 Ž1.4"0.2.=10 3

1.1=10y1 1.1=10y1 1.1=10y1 1.1=10y1 1.1=10y1

2.0=10y5 5.5=10y6 8.0=10y6 5.0=10y6 3.2=10y6

98"12 83"9 93"9 94"9 67"8

)100 96"9 94"9 )100 )100

Y. Tachi et al.r Journal of Contaminant Hydrology 47 (2001) 171–186

Table 2 Result of sorptionrdesorption experiment of Ra on purified smectite

Initial solution

Liquidrsolid ratio Žml gy1 .

pH

Distribution coefficient, K d Žml gy1 . 20 days 40 days

Concentration of ions Žmol ly1 . Na Ca

Desorption ratio Ž%. 1 M KCl 1 M HCl

Distilled water

500

7 8 9 10 11

Ž3.3"0.4.=10 3 Ž4.1"0.6.=10 3 Ž6.2"0.9.=10 3 Ž1.3"0.2.=10 4 Ž1.6"0.2.=10 4

Ž3.4"0.4.=10 3 Ž5.6"0.8.=10 3 Ž9.4"1.4.=10 3 ) Ž1.5"0.2.=10 4 )1.7=10 4

1.1=10y3 1.1=10y3 9.6=10y4 9.4=10y4 1.8=10y3

1.2=10y4 4.1=10y5 1.3=10y5 5.2=10y6 9.0=10y6

85"9 74"8 78"7 84"7 80"7

92"9 93"9 82"8 90"8 93"8

0.1 M NaCl

500

7 8 9 10 11

Ž3.4"1.0.=10 2 Ž7.5"1.5.=10 2 Ž7.3"1.4.=10 2 Ž1.0"0.2.=10 3 Ž9.5"1.8.=10 2

Ž8.3"1.6.=10 2 Ž5.9"1.2.=10 2 Ž6.1"1.4.=10 2 Ž7.1"1.4.=10 2 Ž6.4"1.4.=10 2

1.1=10y1 1.1=10y1 1.1=10y1 1.1=10y1 1.1=10y1

4.0=10y4 3.4=10y4 3.3=10y4 2.4=10y4 2.0=10y4

93"20 79"22 96"21 59"18 60"19

90"19 )100 93"24 65"18 97"22

50

7 8 9 10 11

Ž2.1"0.4.=10 2 Ž3.2"0.6.=10 2 Ž2.9"0.6.=10 2 Ž2.9"0.6.=10 2 Ž4.4"0.8.=10 2

Ž1.8"0.4.=10 2 Ž3.6"0.7.=10 2 Ž2.1"0.4.=10 2 Ž3.8"0.7.=10 2 Ž5.8"0.9.=10 2

1.1=10y1 1.1=10y1 1.1=10y1 1.1=10y1 1.2=10y1

1.1=10y3 7.5=10y4 4.9=10y4 3.1=10y4 2.1=10y4

74"11 98"12 98"13 92"11 96"11

94"13 96"11 )100 )100 )100

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Table 3 Result of sorptionrdesorption experiment of Ra on bentonite

177

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of 3.4 = 10 2 to 9.5 = 10 2 ml gy1 at a liquid to solid ratio of 500 ml gy1 and 1.8 = 10 2 to 5.8 = 10 2 ml gy1 at a liquid to solid ratio of 50 ml gy1 . The K d values increased slightly with increasing pH at a liquid to solid ratio of 50 ml gy1 . Sorption at a liquid to solid ratio of 500 ml gy1 was slightly higher than that at 50 ml gy1 . The concentrations of Na were almost constant in the pH range of 7–11 and were in the order of 10y4 to 10y3 mol ly1 for distilled water. On the other hand, the Ca concentrations varied in the order of 10y6 to 10y3 mol ly1 and decreased with increasing pH. The desorption ratios for purified smectite and bentonite were in the range of 60–100% in 1 M KCl and 80–100% in 1 M HCl. Little effect of pH and ionic strength on the desorption ratio was found for both solids. For most samples, the desorption ratios by KCl were more than 80%, this result indicated that Ra sorbed reversibly on purified smectite and bentonite. 3.2. Diffusion The concentration profiles obtained by the in-diffusion experiments showed a typical shape as shown in Fig. 2. A concentration profile obtained by the in-diffusion experiment is usually interpreted by the constant source model or the instantaneous planar source model Že.g., Sato et al., 1992.. Hence, the concentration profile of Ra was interpreted by the constant source model as the result of comparison with instantaneous planar source model. Radium may precipitate in porewater at the surface. In the constant source model, the solution of the one-dimensional Fick’s second law equation is based

Fig. 2. Examples of concentration profiles and fitting curves of Ra as a function of distance from source.

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179

Table 4 Result of diffusion experiment of Ra in bentonite Dry density ŽMg m3 .

Immersed solution

Diffusion period Ždays.

1.4

distilled water

7

1.8

distilled water

15

3% NaCl solution

20

Apparent diffusion coefficient, Da Žm2 s. Ž1.1"0.1.=10y11 Ž1.0"0.1.=10y1 1 Ž6.0"0.1.=10y1 2 Ž6.9"0.1.=10y1 2 Ž2.2"0.0.=10y1 2 Ž2.7"0.0.=10y1 2

on initial and boundary conditions as follows: initial condition: C Ž t, x . s 0, t s 0, x ) 0; boundary condition: C Ž t, x . s C0 , t ) 0, x s 0, the analytical solution is derived as follows ŽCrank, 1975.. C s C0 erfc

x

ž( / 2 Da t

Ž 3.

where C is the concentration of Ra in the bentonite Žkg my3 ., C0 is the constant concentration of Ra at the interface of the bentonite Žkg my3 ., x is the distance from source in the diffusing direction Žm., Da is the apparent diffusion coefficient Žm2 sy1 ., t is the diffusing period Žs.. Eq. Ž3. was fitted to the concentration profiles by using a non-linear least squares method. The fitted curves are shown in Fig. 2. The apparent diffusion coefficients obtained are presented in Table 4. The Da values obtained in bentonite saturated with distilled water were in the range of 1.1 = 10y1 1 to 6.0 = 10y1 2 m2 sy1 and decreased with increasing dry density of bentonite. The Da values obtained in bentonite saturated with a 3% NaCl solution were lower than those in bentonite saturated with distilled water by a factor of about 3. Based on the result of batch sorption, the retardation in compacted bentonite is estimated to decrease with increasing ionic strength. However, the result of in-diffusion experiments is not consistent with this estimation. 4. Modeling and discussions 4.1. Modeling approaches The interaction between bentonite and groundwater has been evaluated using a thermodynamic model considering ion exchange reactions and surface complexation and, dissolution and precipitation of minerals Že.g., Wieland et al., 1994.. Hence, model and parameters developed to porewater chemistry in bentonite for the performance assessment in Japan ŽJNC, 1999. are adapted for modeling of sorption. In this model, ion exchange and surface complexation reactions are modeled based on the equivalent fraction model developed by Gaines and Thomas Ž1953. and the generalized two-layer model developed by Dzombak and Morel Ž1990., respectively. The characteristics of ion exchange reactions on layer sites of smectite were determined from cation adsorption

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180

Table 5 Model parameters for interaction between smectite and solution Reaction Ion exchange reactions a ZNaqKq s ZKqNaq 2ZNaqCa2q s Z 2 Caq2Naq 2ZNaqMg 2q s Z 2 Mgq2Naq ZNaqHq s ZHqNaq 2ZNaqRa2q s Z 2 Raq2Naq Surface complexation reactions b Surf – sOH sSurf – sOy qHq Surf – sOHqHq sSurf – sOHq 2 Surf – sOHqRa2q sSurf – sORaq qHq 2q Surf – sOHqCa sSurf – sOCaq qHq Site density Žmol gy1 . Surface area Žm2 gy1 . a b

Parameters

References

0.42 0.69 0.67 1.88 1.33

JNC Ž1999. JNC Ž1999. JNC Ž1999. JNC Ž1999. this study

y7.92 5.67 y7.02 y6.82

JNC Ž1999. JNC Ž1999. this study this study

6.48=10y5 29

JNC Ž1999. JNC Ž1999.

Zy represents ion exchange site of smectite. Surf – sOH represents surface site of smectite.

isotherms obtained for purified smectite ŽOda and Shibata, 1999.. The characteristics of protonation and deprotonation reactions on edge sites of smectite were derived from acidrbase titration data obtained for purified smectite ŽShibutani et al., 1999.. The equilibrium constants of ion exchange and surface complexation reactions and other parameters are shown in Table 5. Minerals such as chalcedony, calcite and pyrite, and soluble impurities were also considered to be dissolved or precipitated. Computations are performed with geochemical code PHREEQC ŽParkhurst, 1995. using the JNC thermodynamic database ŽYui et al., 1999.. Reaction parameters between Ra and smectite were determined based on this model and were used to explain Ra sorption for bentonite. 4.2. Sorption mechanism and modeling Radium is expected to exist mainly as Ra2q in solution and to sorb on smectite via ion-exchange mechanism. This is supported by the fact that the distribution coefficient of Ra on smectite and bentonite depends on ionic strength and that most of sorbed Ra is desorbed by KCl. However, ion-exchange mechanism does not explain that K d for purified smectite increases clearly with increasing pH at higher pH region. There is a possibility that radium sorbs on edge sites of smectite by a surface complexation reaction. The concentration of Ca decreases with increasing pH. Potassium may also sorb on edge sites of smectite by surface complexation at higher pH. Reaction constants for ion exchange of Ra and surface complexation constants of Ra and Ca were derived by using results on purified smectite in 0.1 M NaCl solutions. Calculations were performed with the computer code FITEQL 2.0 ŽWestall, 1982.. Reaction constants obtained are shown in Table 5. The K d values calculated by the sorption model are shown in Fig. 3 as a function of pH together with experimental results. The K d values

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181

Fig. 3. Experimental results and model calculations for K d of Ra on purified smectite.

for distilled water were predicted to be greater than 10 5 ml gy1 . This figure shows that Ra sorption is dominated by ion exchange at layer sites of smectite, and surface complexation at edge sites may increase Ra sorption at higher pH region. This sorption model was then used to explain the results of bentonite by considering dissolution and precipitation of minerals; chalcedony, calcite and pyrite, and soluble impurities. Here, the contents of minerals and soluble impurities in bentonite are based on Table 1. K d values and Ca concentration calculated by the sorption model are shown in Fig. 4Ža. and Žb. as a function of pH together with experimental results. The dependencies of experimental K d values on pH, ionic strength and liquid to solid ratio are qualitatively explained by the model. The difference between pH dependencies of K d values at two liquid to solid ratios in 0.1 M NaCl solution are caused by the difference of change in Ca concentration. The K d values in 0.1 M NaCl were slightly higher than those calculated by the model and this result may be explained by the difference between experimental and calculated Ca concentrations. The discrepancy between experimental and predicted K d values in distilled water is relatively large and may be caused by other competing cations such as K, Mg, Fe. The modeling result for bentonite indicated that sorption of Ra on bentonite was dominated by ion exchange and that the pH dependency was caused by change of Ca concentration arising from dissolution and precipitation of calcite and soluble impurities. 4.3. Application of sorption model to compacted bentonite The sorption model was investigated for application to compacted bentonite via diffusion model which accounts for electro-chemical interaction between the smectite

182

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Fig. 4. Experimental results and model calculations for Ža. K d and Žb. Ca concentration in Ra sorption on bentonite.

Dry density ŽMg my3 .

Immersed solution

1.4 1.8

Constrictivity

De Žm2 sy1 .

K d Žml gy1 . From Da From sorption and De model

1.7

1.7=10y10

11

6.7

2.3

y10

1.0=10

6.7

1.2

5.3=10y11

Measured Da Žm2 sy1 .

De calculation Porosity Tortuosity

Distilled water

1.1=10y11

0.48

Distilled water

y1 2

6.5=10

0.33

3% NaCl

2.5=10y1 2

0.33

4.2

8.5 12

74 60 8.3

Y. Tachi et al.r Journal of Contaminant Hydrology 47 (2001) 171–186

Table 6 Parameters for diffusion model and comparison between K d obtained from diffusion and K d calculated by sorption model

183

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184

surface and aqueous chemical species based on the diffuse double layer theory as follows ŽSato et al., 1995; Ochs et al., 1998.: The apparent diffusion coefficient is related to the effective diffusion coefficient and K d by Eq. Ž4. ŽSkagius and Neretnieks, 1984., Da s

De

´ q r Kd

´ s

d

´ q r Kd t 2

D0

Ž 4.

where De is the effective diffusion coefficient Žm2 sy1 ., ´ is the porosity, r is the dry density of bentonite Žkg my3 ., d is the constrictivity, t 2 is the tortuosity and D 0 is the ionic diffusion coefficient in free water Žm2 sy1 .. The effective diffusion coefficient is calculated by the diffusion model and K d in compacted bentonite is obtained from De and Da by means of Eq. Ž4.. In the diffusion model, the constrictivity is expressed considering electro-chemical interaction between the smectite surface and aqueous chemical species based on the diffuse double layer theory. The tortuosity was calculated from the Da of tritiated water ŽSato et al., 1993.. The ionic diffusion coefficient in free water used in the calculation was 8.9 = 10y1 0 m2 sy1 ŽCSJ, 1975.. The diffusion model and parameters are described in detail by Sato et al. Ž1995. with the exception of porewater chemistry which is calculated by the model described in Section 4.1. The distribution coefficient is also calculated by the sorption model. Table 6 shows the parameters for calculation of De and comparison between K d values obtained from measured Da and calculated De and those obtained from the sorption model. The K d values obtained by measured Da and modeled De were consistent with those by the sorption model in a deviation within one order of magnitude. However, the impact of ionic strength on K d obtained from Da is not consistent with the impact derived from the sorption model. In some studies, it was found that De values for cations decreases with increasing dry density and ionic strength ŽSato et al., 1992, 1993; Muurinen et al., 1987; Eriksen and Jansson, 1996.. These dependencies were qualitatively explained by the diffusion model. Eriksen and Jansson Ž1996. have reported De values of Cs and Sr in bentonite ŽMX-80. saturated with two different synthetic groundwater that have ionic strengths of 0.018 and 0.218, respectively. They showed that an increase in ionic strength decreased De values by 50% for Cs and by one order of magnitude for Sr. This result was explained by surface diffusion by considering difference of solvation between Cs and Sr. Radium is considered to show a behavior similar to that of Sr. The Da values of Ra obtained in this study agreed very well with those of Sr obtained by Idemitsu et al. Ž1998. under the same condition. The impact of ionic strength on De of RarSr may be greater than that calculated by the diffusion model. Therefore, this may be the reason why the impact of ionic strength on K d obtained from Da is not consistent with that derived from the sorption model.

5. Conclusions The distribution coefficients of Ra on purified smectite and bentonite by batch experiments were in the range of 10 2 to ) 10 4 ml gy1 and depended on ionic strength

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and pH and most of sorbed Ra was desorbed by 1 M KCl. The modeling result for purified smectite indicated that Ra sorption is dominated by ion exchange, and surface complexation may increase Ra sorption at higher pH region. For bentonite, the dependencies of experimental K d values on pH, ionic strength and liquid to solid ratio were qualitatively explained by the model considering dissolution and precipitation of minerals and soluble impurities. The modeling result for bentonite indicated that sorption of Ra on bentonite was dominated by ion exchange with smectite and the pH dependency was caused by change of Ca concentration arising from dissolution and precipitation of calcite. The apparent diffusion coefficient of Ra in compacted bentonite by in-diffusion experiments were in the range of 1.1 = 10y1 1 to 2.2 = 10y1 2 m2 sy1 and decreased with increasing dry density and ionic strength. The K d values obtained by measured Da and modeled De were consistent with those by the sorption in a deviation model within one order of magnitude.

Acknowledgements The authors would like to thank Messrs. S. Ueta, H. Kato and T. Nakazawa of Mitsubishi Materials Corporation and Mr. S. Mukai of Nuclear Development Corporation for conducting the experiments and valuable discussions.

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