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Effect of dry density on Sr-90 diffusion in a compacted Ca-bentonite for a backfill of radioactive waste repository

Effect of dry density on Sr-90 diffusion in a compacted Ca-bentonite for a backfill of radioactive waste repository

Pergamon 0306449(9s)oos7-7 Am. Nucl. Energy Vol. 23, No. 9, pp. 121-138, 1996 Copyright 8 1996 Elsevier Science Ltd Printedin Great Britain. All rig...

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Pergamon

0306449(9s)oos7-7

Am. Nucl. Energy Vol. 23, No. 9, pp. 121-138, 1996 Copyright 8 1996 Elsevier Science Ltd Printedin Great Britain. All rights reserved 0306-4549/96 $15.00+0.00

EFFECT OF DRY DENSITY ON Sr-90 DIFFUSION IN A COMPACTED Ca-BENTONITE FOR A BACKFILL OF RADIOACTIVE WASTE REPOSITORY JAE OWAN LEE’, WON JIN CHO’, PIL SO0 HAHN’ and KUN JAI LEE’ ‘Korea Atomic Energy Research Institute, Taejon 305-600, Korea *Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea (Received 2 7 May 1995) Abstract-The transport of radionuclides in compacted bentonite is dominated by the diffusion process. The dry density is an important factor in the diffusion of radionuclides through the compacted bentonite. Through-diffusion tests were performed to investigate the effect of dry density on Q-90 diffusion. In the diffusion tests the sample used was a bentonite taken from the southeastern area of Korea and the experimental solution was synthetic groundwater spiked with a tracer of Sr-90 (as ?SrClJ. The dry density was adjusted in the range of I.&l.7 Mglm’. The distribution coefficient of Sr-90 in the compacted bentonite was much lower than that obtained by a batch test. The formation factor and porosity of the compacted bentonite were decreased with increasing dry density. The apparent and effective diffusion coefficients of Sr-90 were in the range of 1.41 x lo-“-1.20x 10-‘2m*/s, 1.81 x lo-“-1.11 x lo-“m%, respectively, and decreased with increasing dry density of compacted bentonite. It was found for Sr-90 that the higher the dry density increases, the more significant the surface diffusion, as compared with the pore diffusion. The results obtained will lx used as basic data for the safety assessment of a repository.

1. INTRODUCIlON

The major functions of backfill in a repository are to inhibit the intrusion of groundwater and to retard the release of radionuclides from radioactive waste to the surrounding environment. Bentonite, a natural clay, is widely favored as a backfill material, because it has very low hydraulic conductivity and relatively high sorption capacity. When the bentonitic clay is used for the backfill, the hydraulic conductivity is generally below lo-” m/s and the principal transport mechanism of radionuclides is known to be diffusion process (Gillham and Cherry, 1982; Lever, 1986). Understanding the characteristics of diffusion in compacted bentonite is, therefore, of essence in the assessment of radionuclide release through the backfill of a repository. Many experiments for the diffusion of radionuclide in compacted bentonite showed different diffusion behaviors depending on radionuclide, bentonite, groundwater, and system conditions (Eriksen et al., 1981; Eriksen and Jacobsson, 1981; Torstenfelt et al., 1982; Pusch et al., 1982; Neretnieks, 1982; Muurinen et al., 1983; Muurinen, 1989; Oscarson et al., 1992; Cho et al., 1993). Of these factors the dry density of compacted bentonite was of much interest as a system factor for the backfill of a repository since it affected pore structure and pore water chemistry and thus the radionuclide diffusion. Miyahara et al. (1991), Sato et al. (1992), Conca et al. (1991), Hoh et al. (1992), and Kim et al. (1993) carried out diffusion tests to investigate the effect of dry density on radionuclide diffusion. In their tests the diffusion coefficients had a wide range and the effect of dry density on radionuclide diffusion was explained in various manners. However, the phenomena required more systematic explanation, and moreover, little has been reported about such information on the diffusion of cationic radionuclide through a domestic bentonite available in Korea. In this connection, the present paper measured the diffusion coefficients of Sr-90 in a domestic bentonite with various dry densities using through-diffusion test and also discussed the effect of dry density on geometry factor, distribution coefficient, and the diffusion mechanism of Sr-90 in compacted domestic bentonite. 727

Jae Chvan Lee et al.

728

2. THRORETICAL

2. I. Dlffmion

BACKGROUND

coefficient

Diffusion is a process by which a matter is transported from one part of a system to another by random molecular motion. The mathematical description of diffusion is based on the Fick’s I and II laws of diffusion, which are expressed as follows: t= - DOVC

(1)

g=-V+=DOV%

(2)

where P is the diffusive tlux, C the concentration, DO the diffusion coefficient, and t the time. The above equations are applied to a homogeneous and isotropic medium such as free water. However, the Fick’s I and II laws of diffusion should be modified for a porous medium, because there are several interactions between solid and liquid phases. If the transport of a matter through the porous medium is controlled by diffusion, equations (1) and (2) are modified as fir,= - D,Vc $=

(3)

-V$,=D,V2~

(4)

where Fr, is the diffusive flux based on the cross sectional area of porous medium, c the average concentration of a diffusant over the solid and the liquid phases, and D, the apparent diffusion coefficient (Bear, 1972). In equations (3) and (4), the D, is not simply a molecular diffusion coefficient but denotes an apparent diffusion coefficient in the porous medium. The apparent diffusion coefficient is generally a function of many factors such as molecular diffusion, pore geometry, surface diffusion and physicochemical processes including adsorption, ion-exchange, and precipitation. It may therefore be defined in several forms depending upon factors taken into account for diffusion modelling. For sorbing radionuclides the apparent diffusion coefficient has been expressed as follows (Lever, 1986, 1989). When there is only pore diffusion, D, is defined:

where Dp is the pore diffusion coefficient, E the porosity of the porous medium, pd the dry density, and K,, the distribution coefficient in sorption. The so-called effective diffusion coefficient 0. is expressed: D,=D&

(6)

If surface diffusion by which radionuclides sorbed are migrated along the surface of a medium is considered, equations (5) and (6) are respectively given as D

=D&+ D&xd =

B

&+pd&

Dps

DA&

(7)

&+Pd&+&+Pd&

D, = Dpe + D&j&

where D, is the surface diffusion coefficient. On the other hand, when there is no sorption like anionic radionuclides as

(8)

(&=O),

simple forms are given

D,=D,=D$

(9)

D,=D&=D&

(10)

where DO is a molecular diffusion coefficient in free water and f cf=S/~p is a formation factor of the porous medium. The 6 and T in the formation factor are tortuosity and constrictivity, respectively.

Effect of dry density on Sr-90 diffusion

Tracer solution

129

SGW

~ -

x-direction

I

I

0

L

Fig. 1. Schematic representation of radionuclide migration in the through-diffusion method.

2.2. Through-diffusion model Several experimental techniques have been used for the measurement of the diffusion coefficients in compacted bentonite: through-diffusion, in-diffusion, back-to-back diffusion, and reservoir-depletion method (Lever, 1986, 1989). This study employed a through-diffusion method to determine the diffusion coefficients of Sr-90 in a domestic bentonite. A compacted bentonite saturated with groundwater is sandwiched between two reservoirs. Initially, one of the reservoirs contains tracer, whereas the other and the bentonite plug are free of tracer. The tracer diffuses from the high concentration reservoir through the compacted bentonite into the other reservoir where the concentration is measured. The concentration gradient from the reservoir initially containing tracer to the other reservoir is maintained during a test period. Figure 1 represents a schematic configuration of radionuclide transport in a through-diffusion method. If a compacted layer of bentonite are homogeneous and isotropic and the transport of radionuclide occurs only in the x-direction, equation (4) is expressed in a simplified form

(11) The following initial and boundary through-diffusion method

conditions

are given to describe the experimental

C(x, 0) = 0, qo,

O
constraints

of the

(12)

t) = c,

(13)

C(L, t) <
(14)

where c,, is an initial radionuclide concentration at the interface between tracer-containing reservoir and bentonite plug, and L the overall length of the bentonite plug. The solution of equation (1 l), subject to the initial and boundary conditions from equation (12) to equation (14), was given by Helfferich (1962) and Eriksen (1981) as

730

Jae Owan Lee ef al.

Fig. 2. Typical breakthrough curve of radionuclide in the through-diffusion method.

The total amount, Q of radionuclide accumulated obtained by integrating the flux at x = L with time:

in the solution at the far side of the bentonite plug, is

(16) Defining CO= (E+ (1 - a)p$,& = a& where COrepresents the initial concentration equation (16) can be expressed as

of spiked reservoir, the

(17)

where a is referred to as capacity factor which is defined as a =E + (1 -~)p,&= E+ P& for a sorbing radionuclide (Lever, 1989). A typical breakthrough curve of equation (17) is shown in Fig. 2. Initially, there is a transient period during which the concentration builds up at the plug, and then there is a stage of steady-state diffusion during which the amount of radionuclide transported through the plug is given by an asymptotic solution Q _=!T!&_~

GJ

L

as the diffusion time approaches to an infinite. Using the equations from (5) to (8), the relationship DJa is obtained, where a is the same as in equation (17). Thus, equation (18) becomes

e=D,t_aL C,,A

L

6’

of D,=

(19)

From equation (18), the apparent diffusion coefficient 0. can be obtained by using the intercept t,, (timelag) on the time-axis, i.e. by setting the left-hand side of equation (18) equal to zero:

Effect of dry density on Sr-90 diffusion

731

K

0.3( .

MontmorlllonIte

*

Feldsplr

I

Zeolite

C

Cdstobalite

+

Quartz

28

Fig. 3. X-ray diffraction pattern of a domestic bentonite used in the diffusion tests. Table 1. Chemical composition of a domestic bentonite from the southeastern area of Korea Component

Content (wt %) 53.20 22.05 a.31 0.32 2.63 I .98 0.96 1.36 0.11

SiOz 40, Fez03 Fe0 CaO MgO %O Na,O MnO IG-Loss

D”‘G

L2

The effective diffusion coefficient D, is obtained from the slope, S of steady-state diffusion in equation (19) as follows: De = SL.

(21)

3. EXPERIMENT

3.1. Material The domestic bentonite used was sampled from the southeastern area of Korea. The bentonite was airdried and passed through a 200 mesh of ASTM standard sieves. As shown in the result of X-ray diffraction analysis (Fig. 3), the bentonite contains mainly montmorillonite and small amounts of feldspar, quartz, and zeolite. The chemical composition of the bentonite is summarized in Table 1: about 53% Si02, 22% AlzOs,

Jae @van Lee et al.

132

Table 2. Elemental composition of synthetic groundwater used in tk diiusion tests Concentration (ppm)

Component Na

8.3

K Mg Ca

13

Cl so, ND, F

ND 5.0 8.6 0.62 0.19

::;

HCO,

tpH=7.0*0.5.

Connictor

.

Fig. 4. Experimental apparatus for the through-diffusion

test.

8% Fe203, and minor amounts of FeG, CaO, MgG, K,O, Na*O, and MnO. The weight percent of calcium was about 2 times higher than that of sodium, and the cation exchange capacity was 70.9 meq/lOO g.

3.2. Radionuclides and solution Sr-90 was chosen as a tracer in the form of SrC12. A synthetic ground water (SGW) was used to saturate bentonite. The elemental composition and pH of the synthetic groundwater are shown in Table 2. Tracer solutions were prepared by adding a small aliquot of Sr-90 to synthetic groundwater. The initial activity of Sr-90 was 1 Ci/m3. 3.3. Through-diffusion test The diffusion behavior of Sr-90 in a domestic bentonite was investigated using through-diffusion tests. Figure 4 shows an apparatus used in the through-diffusion test. As shown in the figure, it consists of three parts, a source reservoir, a collection reservoir, and a cylindrical diffusion cell made of stainless steel with 4 x IO-* m i.d. and 7 x 10m3m height. Experimental procedure is as follows. The air-dried bentonite was compacted in the diffusion cells to the target dry density of 1.0, 1.2, 1.4, and 1.7 Mg/m3 by a hydraulic press. The diffusion cells were placed in a housing and the bentonite was allowed to be saturated with SGW for 6 weeks. Nowak (1984) reported that this period was sufficient to saturate the bentonite. After the saturation period, a solution of SGW spiked with Sr-90 was passed over one end of the bentonite plug and an unspiked SGW was circulated through the other end. The flow rate of the unspiked solution was such that the activity of Sr-90 would be very close to zero at the outflow end of the plug. The collection reservoir was monitored every two or three days by a liquid scintillation counter. The activity in the source reservoir was also closely

Effect of dry density on Sr-90 diiusion

733

1.6 r 1.4 l

1.0 Mg/m3

1.2 -

0

1.2 Mglm3

I.0 -

A 1.4 Mg/m3 v 1.7 Mg/m3

. .

.o a

lo

G u” 0.8 -

.o

A A

A S

. . . 0.6 -

l

=a

-

l .

-

A .

. .

*

.;&/

Time (day) Fig. 5. Breakthrough curves of Sr-90 in compacted bentonite with various dry densities.

Table 3. Diiusion properties of Sr-90 in compacted bentonite with various dry densities Contribution by pore diffusion [in equation (5)J Pd (Mdm’)

1.0 1.2 1.4 1.7

E

(-)

0.63 0.56 0.48 0.37

D, x 10”

0. x 10’9

0.x 10”

(m’h)

(m’/s)

(m’/s)

2.81 2.61 2.14 1.41

1.41 I .32 I .28 1.20

1.81

1.75 1.51 1.11

(I&)

12.2 10.6 8.1 5.2

D, x IO” (m*/s)

3.13 23.5 42.2 66.3

Contribution by surface ditTiJ.sion[from equation (7)]

DIE EfPd&

1.38 x 1.10x 8.75 x 5.63 x

lo-” lo-” lo-” lo-”

s E+Pd&

2.98 x 2.25 x 4.05 x 6.37 x

lo-” 10-1’ IO-” IO-”

t 0. represent apparent diiusion wdhients dctcrmined from the breakthrough curve of through-diffusion test. t A?.,are calculated from tbe relationship of a = &ID, = E + x;P,.

monitored to maintain a constant concentration. When it approached about 90% of the starting activity, Sr90 was added to bring its activity up to that of the original solution. The test was ended several days after the steady-state was reached. During the test temperature was maintained at about 20°C. 4. RRSUMS AND DISCUSSION

4.1. Diffusion of Sr-90 in compacted bentonite with various dry densities Through-diffusion tests were performed to investigate the characteristics of Sr-90 diffusion in compacted bentonite. Figure 5 represents the breakthrough curves for the dry densities of 1.0, 1.2, 1.4, and 1.7 g/cm’ and the resulting diffusion coefficients are listed in Table 3. The diffusion coefficients were calculated using equation (20) and (21). For the dry densities of 1.0, 1.2, 1.4, and 1.7 g/cm’, the apparent diffusion coefficients were 1.41 x lo-“, 1.32 x lo-‘*, 1.28 x lo-‘*, and 1.20 x lo-‘*mYs, respectively, and theeffectivediffusion coefficientswere 1.81 x lo-“, 1.75 x lo-“, 1.51 x lo-“, and 1.11 x lo-” m’ls, respectively. The apparent diffusion coefficients were about one order of magnitude lower than the effective diffusion coefficients.

134

Jae Owan Lee et al.

.

t

I 1.0

I

I

I

I

1.2

1.4

1.6

1.8

Dry density Fig. 6. Apparent

diffusion coefficients

(Mg/m3)

and effective diffusion coefficients

of S-90

as a function of dry density.

8000

6000 “M c “, kj=

4000

2000

0

4

2

Solution-to-clay Fig. 7. Distribution

coefficients of S-90

6

[l/kg]

as a function of solution-to-clay

ratio.

The effect of dry density on D, and D, was plotted in Fig. 6. Both D, and D, decreased with increasing dry density as shown in the figure. This may be explained by the change of various factors, sorption distribution coefficient, pore geometry factor, and surface diffusion coefficient etc. 4.2. Effect of dry density on the sorption of Sr-90 onto a compacted bentonite The dry density of clay may affect pore water chemistry and thus the sorption of Sr-90 on compacted bentonite. To investigate this effect, sorption tests were performed for the solution-to-bentonite ratio in the range between 1 and 5 cm’/g. Figure 7 represents the distribution coefficients of Sr-90 as a function of the solution-to-bentonite ratio.

Effect of dry density on Sr-90 diffusion

735

Table 4. Formation factors for compacted bentonite with various dry densities (iodide throughdiiusioo test)

0.C= 4)

dk

( x lo-”

1.0

m*/s)

(%

1.52 7.12 5.80 3.80

1.2 1.4 1.7

0.042 0.039 0.032 0.02 I

tf= D,JD,, where DO= 1.79 x lo-’ m*/s for iodide.

0.050

0.65 0.60

0.040 8 ;; E .g z g 2

0.55

0.035

x

.z 0.50

0.030

b

2

a 0.025

0.45

0.020

0.40

0.015 0.35 0.010

I

I

1.0

1.2

I

I

1.4

1.6

I 1.8

Dry density Fig. 8. Formation factors and porosities of compacted bentonite with various dry densities.

As shown in this figure, the distribution coefficients for the solution-to-bentonite ratio below 5 cm’lg decreased with increasing bentonite content, that is, decreasing the solution-to-bentonite ratio. This indicates that an increase in bentonite content increases the ionic strength of pore water which leads to ion competition and thus decreases the distribution coefficient of Sr-90 onto bentonite. The batch sorption tests are, however, not available under the condition of solution-to-bentonite ratio used in the present through-diffusion test. When the bentonite is compacted to 1.0, 1.2, 1.4, and 1.7 g/cm’ of dry density, the solution-to-bentonite ratios correspond to 0.63, 0.46, 0.34, and 0.22cm3/g, respectively. In order to calculate the distribution coefficients under these conditions, the relationship of a = DADa = E+ &pd was employed. The & values calculated were 12.2, 10.6, 8.1, and 5.2 l/kg, respectively, which were much lower than that for the solution-to-bentonite ratio of lOcm’/g which was a typical condition for the measurement of & by batch experiment. This may reduce the retardation of Sr-90 by the bentonite and thus give an increase in the diffusion coefficient. 4.3. Effect of dry density on the sttwcture of compacted bentonite The dry density may also have influence on pore structure. The pore structure is characterized by formation factor and porosity. The formation factor is calculated from equation (9) by carrying out through-diffusion tests with a tracer of I-125 (Na”‘I). The I-125 was little sorbed on the domestic bentonite so that its distribution coefficient was regarded as nearly zero (Lee et al., 1994). In Table 4, the formation factors were in the range of 0.021-0.042. The porosities were calculated by the relationship of E= 1- pd/pp and were 0.63, 0.56, 0.48, and 0.37 for the dry densities of 1.0, 1.2, 1.4 and 1.7 g/cm’, respectively. As indicated in Table 3 and Fig. 8, an increase in dry density resulted in the decrease of the formation

136

Jae Owan Lee et al.

factor and porosity, which limited the Sr-90 diffusion. The pore diffusion coefficients of Sr-90 calculated were in the range of 1.41 x lo-” to 2.81 x lo-” m/s2, where the Q, for Sr-90 was 6.7 x lo-” (Li and Gregory, 1974). 4.4. Surface diffusion as an additional diffusion mechanism The apparent diffusion coefficients were compared with those predicted from a pore diffusion model which was given by equation (5). Table 3 indicates that the pore diffusion model did not adequately describe the transport of Sr-90 in compacted bentonite at higher dry densities. Several investigators (Cussler, 1984; Jahnke and Badke, 1987; Low, 1958; Mokady and Low, 1966) have considered surface diffusion as an additional diffusion mechanism in order to investigate the discrepancy between experimental and theoretical results. Cationic radionuclides sorbed on the surface of bentonitic clay are potentially of the nature of hop from one point to a nearby one by electrical potential gradient and lastly held at the position of minimum potential. Surface diffusion refers to such a diffusion mechanism. Literatures (Berry and Bond, 1992; Oscarson, 1994) reported that the surface diffusion occurred within the electrical double layer next to clay surface and was important especially for cationic radionuclides sorbed via ion exchange, i.e. an electrostatic sorption which proceeded due to the action of attractive coulombic forces and was largely rapid and reversible reaction. Weakly sorbing cations such as S?, Ca’+, M&+ formed the ion exchange (Berry and Bond, 1992; Berry et al., 1987, 1988; Park et al., 1994). Lee et al. (1995) also showed in his desorption test that most of Sr-90 were sorbed by the ion exchange. This probably suggests that the Sr-90 is allowed to diffuse along the pore surface of compacted bentonite. Surface diffusion coefficients were determined using equation (7). The values calculated were in the range of 3.1 x lo-l4 to 6.6 x lo-“m2/s and increased with increasing dry density (Table 3). The increase in D, may be explained by the change of sorbed ion interaction. The interaction among sorbed ions depends upon the number of interaction sites present on clay per unit volume, a hopping distance between two neighboring sites, and the mobility of sorbed ions. Lai and Mortland (1961) explained the influence of clay concentration on ion diffusion on the basis that an increase in clay concentration would increase the number of interaction sites and thereby the number of interactions which sorbed ions make in a given distance. Similar interpretation can be applied for an increase of interaction number with varying dry density. An increase of dry density gives a closer proximity of clay particles to one another and consequently a shorter hopping distance of sorbed ions which causes a lowering of the energy barrier for diffusion. This may lead to the enhancement of the diiusion of Sr-90 along the surface of clay. In Gast’s study (1966), clay concentration affected ion mobility. Increasing clay concentration increased the amount of exchangeable ions in pore water, which resulted in a significant change of ion mobility in clay as Lopez-Gonzales and Jenny’s contact exchange concept (1959) would apply to the movement of ions along charged surfaces. The increase of exchangeable ions with varying dry density is also likely to be a cause of increasing the surface diffusion. In Fig. 9, a comparison was made for the relative contributions of pore diffusion and surface diffusion to the overall diffusion of Sr-90 through compacted bentonite. The portion of surface diffusion was calculated using the relationship of Dg&/(e + pa&) in equation (7). The surface diffusion was observed to get comparable in significance to the pore diffusion with increasing the dry density of compacted bentonite. That is, it is expected that the higher the dry density is, the more significant the surface diffusion is as an additional diffusion mechanism.

5. CONCLUSION

Batch sorption tests and through-diffusion tests were carried out to investigate the characteristics of Sr-90 diffusion in the compacted bentonite. The conclusions obtained are as follows. The distribution coefficients of Sr-90 under diffusion test conditions were believed to be much lower than that for a batch sorption test with the solution-to-bentonite ratio of 10 g/cm3. The formation factor and porosity decreased with increasing dry density. The apparent diffusion coefficients and the effective diffusion coefficients were in the range of 1.41 x 10-‘2-1.20 x lo-12m2/s and 1.81 x lo-“-1.11 x lo-” m2/s, respectively. The diffusion coefficients decreased with respect to the dry density. The trend could be explained in terms of the change of formation factor, porosity, distribution coefficient, and surface diffusion coefficient. An increase in the dry density decreased the formation factor and porosity and thus the diffusion of Sr-90. The influence of a decrease in

Effect of dry density on Sr-90 diffusion

‘;; CT

731

1.40E-012

g g ‘5 z G

1.20E-012

2.00&012

3 ‘tl 2 -a 9

8.00E-013

2 ‘;: 1 5

6.00E-013

e z : !z ._ s .$ 2

l.OOE-012 1.50&012

D.

l.OOE-012

/”

5.OOE-013

.

4.00E-013

2.00E-0 13

8

‘/

l

/

/

O.OOE+OOO

1.o

1.2

1.0

Surface diffusion

I 1.2

I 1.6

1.4

I 1.8

Dry density [Mg/m3]

I

I

I

I

I

I

I

I

I

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Dry density

Fig. 9. Contribution

*/,

OBOE-000

AX

[Mg/m3]

of pore diffusion and surface diffusion to overall diffusion of Sr-90 through compacted bentonite with various dry densities.

& with increasing dry density reduced the retardation of Sr-90 by bentonitic clay. The surface diffusion of Sr-90 gradually increased in its significance with increasing the dry density as compared with pore diffusion. Acknowledgement-The

present study was supported by the Fund for Radioactive Waste Management of Korea. REFERENCES

Bear J. (1972) Dynamics of FluirLFin Porous Media. American Elsevier, New York. Berry J. A. and Bond K. A. (1992) Radiochim. Acta 58/59,329. Berry J. A., Bourke P. J., Green A. and Littleboy A. K. (1987) UKAEA Report AERE-R 12844. Berry J. A., Bourke P. J., Green A. and Littleboy A. K. (1989) UKAEA Report AERE-R 12978. Cho W. J., Oscarson D. W. and Hahn P. S. (1993) Appl. Cluy Sci. 8,283. Conca J. L., Ashida T. and Sato H. (1991) Proc. of the Second Annual Int. Conf of the High Level Radioactive Wmte Management, Vol. 2, pp. 1382-1389. Cussler E. L. (1984) Diffurion, Mass Transfer in Fluid Systems. Cambridge Univ. Press. Eriksen T. E. and Jacobsson A. (1981) KBS TR 81-12. Eriksen T. E. et al. (1981) KBS 81-06. Gast R. G. (1966) Soil Sci. Sot. Amer. Proc. Vol. 30. Gillham R. W. and Cherry J. A. (1982) Geol. Sot. Amer, pp. 3142. Helfferich F. (1962) ZonExchange, Chap. 8, p. 352. McGraw Hill, New York. Hoh Y. C., Peng J. Y. and Hsia Y. S. (1992) J. Nucl. Sci Technol. 29, 131. Jahnke F. M. and Badke C. J. (1987) In Coupled Processes Associated with Nuclear Waste Repositories, pp. 287-297. Academic Press. Kim H. T., Suk T. W. and Park S. H. (1993) Wuste Mgmt 13, 303. Lai T. M. and Mortland M. M. (1961) Soil Sci. Sot. Proc. 353. Lee J. O., Cho W. J., Hahn P. S. and Park H. H. (1994) J. Korea Nucl. Sot. 26,285. Lee J. 0. et al. (1995) J. Korean Nucl. Sot. (Submitted). Lever D. A. (1986) Harwell Report AERE-R-12321. Lever D. A. (1989) SKB TR 89-24. Li Y. H. and Gregory S. (1974) Geochim. Cosmochim. Acta 38, 703.

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Lopez-Gonzales J. and Jenny H. (1959) J. CON. Sci. 14, 533. Low P. F. (1958) Soil. Sci. Sot. Proc., pp, 395-398. Miyahara K., Ashida T., Kohara Y., Yusa Y. and Sasaki N. (1991) Radiochim. Acta 52153,293. Mdkady R. S. and Low P. F. (1966) Soil Sci. Sot. Amer. Proc. Vol. 30, pp. 438442. Muurinen A. (1989) Mat. Res. Sot. Svmu. Proc. Vol. 127. Muurinen A. et al. ‘(1983) Sci. Basis k&l. Waste Mgmt 6, 777. Muurinen A., Rantanen R., Ovaskinen R. and Heinonen 0. J. (1983) Sci. Basis Nucl. Waste Mgm?. VI. Neretnieks I. (1982) KBS TR 82-27. Nowak E. J. (1984) Sci. Basis Nucl. Waste Mgmr VII (edited by G. L. McVay), Materials Research Society Symposium Proceedings, Vol. 26, Elsevier Sci. Publishing Co., New York, pp. 59-68. Oscarson D. W. (1994) Surface Diffusion: Is It an Important Transport Mechanism in Compacted Clays?, in draft for AECL Publication, Canada. Oscarson D. W., Hume H. B., Sawatsky N. G. and Cheung S. C. H. (1992) Soil Sci. Sot. Amer. J. 56. Park C. K. et al. (1994) J. Korean Nucl. Sot. 26, 461. Pusch R., Eriksen T. E. and Jacobsson A. (1982) Sci. Basis Nucl. Waste Mgmt V, p. 649. Sato H., Ashida T., Kohara Y., Yui M. and Sasaki N. (1992) J. Nucl. Sci. Technol. 29, 873. Torstenfelt B., Andersoson A., Kipatsi H., Allard B. and Olofsson U. (1982) Sci. Basis Nucl. Waste Mgmt IV