Investigation of Colloid-facilitated Effects on the Transport of N-member Radionuclide Chains in the Fractured Medium

Transcription

1 Investigation o Colloid-acilitated Eects on the Transport o N-eber adionuclide Chains in the Fractured Mediu N.-C. Tien Cheical Engineering Division, Institute o Nuclear Energy esearch, No. 00, Wunhua d., Jiaan Village, Longtan Township, Taoyuan County 325 Taiwan,.O.C. C.-P. Jen Departent o Mechanical Engineering, National Chung Cheng University, No. 168, University d., Min-Hsiung, Chia Yi, 622 Taiwan,.O.C. ABSTACT A previous analytical odel or N-eber radionuclide decay chains has been extended to include the eect o radionuclide sorption with groundwater colloids. Site-speciic distribution coeicients were eployed in the nuclide decay chain to illustration the present odel. The colloid concentration was assued constant in tie and space owing to equilibriu between colloid generation and sedientation by cheical and/or physical perturbations. Furtherore, the diusion o colloids into the rock atrix was ignored because the diaeter o colloid is relatively large and colloids and racture suraces are like-charged. The results indicated that colloids could acilitate the transport o radionuclides and the large adsorbability o nuclides with colloids enlarged the eect o acceleration by colloids. The inluence o colloids on the radionuclide transport was expected to be crucial to the actinides with large adsorbability; however, the present results revealed that the low-adsorbing nuclides whose parent nuclides have large capability o sorption could be also acilitated signiicantly by colloids indirectly. Thereore, the role o colloids played in the transport o the radionuclides decay chain should be assessed careully in the radioactive waste disposal. The analytical ethod presented herein is helpul to veriy/validate urther coplex ar-ield odels. INTODUCTION Colloids are tiny particles in the size range 1 n to 1 µ which can reain suspended in water. Groundwater oten contains signiicance populations o natural colloids which can interact with pollutants and inluence their transport. Natural colloids as well as waste- and repository-derived colloids in radioactive waste disposal ay inluence nuclide transportation signiicantly. Laboratory experients[1] in ters o colloid-acilitated containant transport have conired that colloids can enhance the transport o cationic and anionic etals through ractured edia. Moreover, the unexpectedly rapid transport o plutoniu and aericiu at experiental sites ay be also attributed to colloid-acilitated transport[2]. In any countries, the processes o colloid oration and colloid transport are included in the eatures, events, and processes (FEPs list o their Perorance Assessent (PA progras or high-level waste/spent nuclear uel disposal. Although soe PAs have deerred the consideration o colloid-nuclide transport until detailed evaluations has been perored, other PAs, or instance, H-12 o Japan[3] and the Yucca Mountain Project o USA[4], have

2 considered the eects o the presence o colloids. The experiental results[3] indicated that the engineered barrier designed to have the practical density bentonite ore than 800 kg/ 3 had enough property to eliinate the colloid transport through the engineered barrier. However, ailure o the engineered barriers and bentonite buer to ilter colloids should be considered as an alternative scenario[5], especially according to the colloid and radionuclide retardation experients[6,7] recently carried out in situ at Grisel test site. In the past decades, the single radionuclide transport acilitated by colloids has attracted lots o researcher s attention[8-]. When a radionuclide is adsorbed onto the colloidal surace, it can not diuse into the rock atrix and be adsorbed in the atrix rock, since the sizes o colloids are conservatively assued to be larger than those o the rock atrix pores. Colloids ay ove along the groundwater, thereore, radionuclides attached to these colloidal suraces will be transported urther such that the concentration in the racture will be higher than that in the absence o colloids. Those studies did not address the signiicance o the colloids in the chain decay, however, the in-growth and decay o actinides are crucial or assessing their transport ability owing to the long hal-lie ties and radiotoxicity o actinides. Sun and Buscheck[11] reported an analytical odel or N-eber decay chains in a single racture in the absence o colloids. We previously developed a sei-analytical odel to access the co-transport o a two-eber decay chain radionuclides and groundwater colloids[12]. Currently, the role o colloids in acilitating the transport o radionuclides is not understood enough to eectively odel radionuclide transport. However, there is a growing body o evidence that suggested low-soluble and strong-absorbing radionuclides, such as actinides, could be accelerated by colloids[2,6]. This present study extends previous studies to investigate the eects o the presence o colloids on actinides decay chains transport. Parent and daughter radionuclides could peror copletely dierent retardation properties which are explicitly represented within this study. Thus, the present odel is useul to veriy coplex nuerical odels or ulti-species transport with dierent retardation actors and to understand the signiicances o colloids on the retardation properties o radionuclide decay chains. CONCEPTUAL MODEL The Far- Field (geosphere is a physical region representing the natural barrier in the concept o geological disposal o nuclear waste. In the concept o deep geological disposal o nuclear waste, the natural barrier is the geological aterial hosting the repository. In deterining the ediu type o the ar ield, any potential pathways ust be identiied. Usually tight orations are considered ideal candidates or hosting repositories. Due to various reasons such as stresses, deects, and heterogeneous, geological aterials are seldo perect. The ost coon deects are ractures. Most rock orations considered in geological disposal o nuclear waste contain ractures. Because ractures have greater void spaces than rock atrix, they are considered, in PA odeling, as the ast pathway o the geological ediu. adionuclide transport in ractured rock is characterized by advection and diusion/dispersion attenuated by sorption and atrix diusion. Apparently, these transport process ust be considered in the PA odeling. Approaches to odeling low and transport in racture systes are not unique. However, it is known that knowledge o various processes taking place in a single racture is undaental to iprove our understanding radionuclide transport in ractured subsurace orations[13]. Thereore, the case o a thin rigid racture slab in a saturated porous rock is considered herein. Several assuptions are ade regarding the properties o the groundwater colloids and the

3 syste[8-14]: 1. The racture is open and hence has unit porosity. 2. In the racture, groundwater lows in one direction. adionuclides in the aqueous phase, both dissolved and sorbed on the obile colloids, transport advectively and dispersed along the racture. 3. Transverse dispersion is eicient to ensure ixing o radionuclide concentrations across the racture slab in the direction perpendicular to low. 4. In the atrix, groundwater is at rest and radionuclide diusion only occurs in the direction perpendicular to the racture. 5. Considering radioactive in-growth and decay. 6. Colloidal particulates are obile in the racture. However, they cannot diuse into the rock atrix due to their large size. 7. The colloidal concentration is constant and unior along the racture. 8. Paraeters (porosity, groundwater/colloid velocity, sorption coeicients, diusion and dispersion coeicients, etc. are assued to be constant and unior. MATHEMATICAL MODEL Accordingly, the equation describing the ith decay chain radionuclide transport with colloids in the racture is[12,15,16]: 2 N,i N,i N,i N,i, i + v D a 2 θd = λi 1,i-1N,i 1 λi,in,i, t x x z z= b x0, bz0, t0 (Eq. 1 where, = 1+ Kdρδa + KdcC0, v = v + vckdcc0, D = D + DcKdcC0. Siilarly, the transport equation or the ith radionuclide in the atrix is: 2 N,i N,i, i D = λ 2 i 1,i 1N,i 1 λi,in,i t z x0, zb, t0 (Eq. 2 Sybols appearing in the above equations are deined as ollows: N is the aqueous concentration (kg/ 3, v is the groundwater/colloid velocity in the racture (/yr, /c D is the longitudinal dispersion coeicient o radionuclide/colloid in the racture ( 2 /yr, /c θ is the rock atrix porosity, D is the diusion coeicient o radionuclide in the rock atrix pores ( 2 /yr, λ is decay constant (1/yr, Kd is sorption (distribution coeicient or radionuclide on rock/colloid ( 3 /kg, /c ρ is bulk density o the rock (kg/ 3, is the atrix retardation coeicient deined as: Kd + ρ = 1, θ δ is sorption length or radionuclide on the racture surace (, b is the hal o the racture aperture (,

4 a is speciic low-wetted area o racture per unit low volue (1/, or sooth racture 1 surace: a =, b C 0 is the colloidal concentration in the racture (kg/ 3. Subscripts i and i-1 reer to the ith and (i-1th radionuclides, respectively, and subscripts and reer to the racture and rock atrix, respectively. As or the case o the single radionuclide transport in the absence o colloids, Eq. (1 could be reduced to the or siilar to that used in the literature 14 or odeling advective/dispersive radionuclide transport in a 1-D racture. Initial and boundary conditions or the transport equations, Eq. (1 coupled with Eq. (2 are given as: N, i( x = 0,t = N0, iδ( 0, (Eq. 3a N, i ( x =,t = 0, (Eq. 3b N, i ( x,t = 0 = 0, (Eq. 3c N, i( x,z = b,t = N, i( x,t, (Eq. 3d N, i ( x,z =,t = 0, (Eq. 3e N, i ( x,z b,t = 0 = 0, (Eq. 3 where N 0 is the initial concentration at the inlet o the racture, δ ( 0 is the delta unction, hence, it represents the pulse injection case at t = 0. Any other injection odel, e.g., tie series outputs ro near-ield odeling, can be analyzed using the principle o superposition. For the single-radionuclide odeling, the analytical solution o the transport equation, Eq. (1, subject to the conditions o Eqs. (3a- has been obtained and the total obile concentration o radionuclide, N T, in the racture can be given as : N T0 Y 2 α x Y N T = η exp αx ξ λt dξ. (Eq π 2 2 t T 4ξ 4T 2 x b v where, N T0 = N0( 1+ KdcC0, Y =, A =, T = t YA, α =, and ξ is 2 4ADξ θ( D 1 2 2D the integration paraeter. Sun and Buscheck[11] eployed a transored unction to decouple the in-growth and decay ters ro Eqs. (1 and (2. The transport syste o each radionuclide becae independent with an identical atheatical orat in the transored doain. The transored unction is deined as: i 1 i 1 K nλn N T, i = NT,i + NT, j. (Eq. 5 j= 1 n = j λn λi where, N is the analytical solution, with the or o Eq. (4, o the ith radionuclide in the T,i,n 1 transored doain and K n =. Thereore, the analytical solution o the ith total,n obile concentration o radionuclide in the presence o colloids could be expressed as: i 1 i 1 K nλn N T, i = NT,i NT, j (Eq. 6 j= 1 n = j λn λi

5 NUMEICAL ILLUSTATIONS The analytical solution o Eq. (4 can be integrated by Gauss-Legendre quadrature. Nuerical deonstrations will be conducted by eploying the paraeters listed in Table I. Colloidal velocity is assued equal to groundwater velocity and the value o colloidal dispersion coeicient is quoted ro Grindrod et al.[17]. The colloidal concentration in groundwater could range ro -4 (experiental data[18] to -1 (assued value[8] kg/ 3. Our previous study[12] illustrated that the eect o the presence o colloids becoes signiicant when the 4 colloidal concentration is greater than kg/ 3. Thus, the colloidal concentration used in 1 the present study is assued as kg/ 3, or a conservative point o view. However, the colloids coposition is not included in our present odeling. Table II suarized the sorption coeicients o several isotopes used in dierent PA progras. The sorption coeicients o H-12, Kristallin-I and SITE-94 are basically the sae order o agnitude; hence, the coeicients o H-12 are adopted or nuerical illustrations herein. The sorption coeicients o H-12 and hal-lie o radionuclides are listed in Table III. First o all, the results obtained by our analytical odel was copared with those solve by CYSTAL, which is a nuerical code or ar-ield radionuclide transport used in SKI s SITE-94 progra[24]. CYSTAL solves one-diensional radionuclide transport through ractured edia in the absence o colloids by ipleenting the nuerical inversion o Laplace transor. For the purpose o veriication, the analytical breakthrough curves at 0 or the our radionuclides are alost identical with those obtained by CYSTAL. Table I Transport paraeters used in the present work Paraeter Value Transport length ( 0 Sorption length, δ ( 0.05 Fracture aperture, 2b ( 3 5 Bulk density o the rock, ρ (kg/ ock atrix porosity, θ 0.02 Groundwater velocity in the racture, v (/yr 40 Longitudinal dispersion coeicient o nuclide, D ( 2 /yr 50 Diusion coeicient o nuclide in the rock atrix pores, D ( 2 /yr Colloidal velocity in the racture, v (/yr 40 c Longitudinal dispersion coeicient o colloid, D c ( 2 /yr 140 Colloidal concentration, C 0 (kg/ Initial concentration o the ith nuclide, N 0,i (kg/ 3 1

6 Table II Sorption coeicients o several isotopes or dierent PA progras. Kd ( 3 /kg Isotope H Kristallin-I 20 SITE TILA S U Th A Np a Table III Sorption coeicients and hal-lie o radionuclides (H-12 Nuclide Kd ( 3 /kg Hal-lie (yrs A Np U Th U U Th a The results obtained by the analytical solution and the nuerical results by CYSTAL or Neptuniu decay chain: A-241; Np-237; U-233; Th-229. The retardation actors or sorption on racture surace are all set to unity or all radionuclides in this case[25]. The analytical solutions not only agree well with the nuerical results, but also eliinate the phenoenon o oscillation, which is the inherent drawback while using nuerical inversion o Laplace transor. The analytical ethod is helpul to veriy/validate urther coplex ar-ield odels. Figure 1 depicts the breakthrough curves or the our nuclides in the Neptuniu decay chain based on the distribution coeicients or H-12[19], when the concentration o colloids is 0.1 kg/ 3. The distribution coeicients or radionuclides with colloids (Kd c ight be quite dierent than those with the atrix rock (Kd due to the discrepancy in sorption surace area and/or coposition. The nuclide-colloid sorption coeicients are then assued to be an order o agnitude greater than the nuclide-rock sorption coeicients[1] to elucidate the eect o adsorbability o nuclides with colloids in Figure 1. As shown in Figure 1, it indicates that radionuclides transported in the racture are greatly enhanced and accelerated by the presence o colloids. The peak concentrations o radionuclides when the colloids exist in the syste are approxiately one order o agnitude larger than those without colloids. The results herein show clearly that the transport o radionuclides in the racture is acilitated by the large sorption o nuclides with colloids. The large adsorbability o nuclides with colloids, which provide an

7 alternative obile carrier or nuclides, iplies the reinorceent o obility o radionuclides. In other words, increasing the sorption coeicients o radionuclides with colloids will increase the capability o colloids to adsorb radionuclides and enhance the eects o acceleration by colloids. As illustrating in Table II, the sorption coeicients o TILA-99[22] are extraordinarily saller than other data. Figure 2 illustrates the breakthrough curves with and without colloids or the our nuclides in the Neptuniu decay chain based on the distribution coeicients or TILA-99 or both Kd c and Kd c. This igure indicates that the inluence o colloids on the transport o radionuclides in the ractured edia is insigniicant because o their low adsorbability, even when the nuclide-colloid sorption coeicients are assued to be an order o agnitude greater than the nuclide-rock sorption coeicients; there is only slightly enhanceent on the transport o radionuclides. -3 Concentration (kg/ w/o colloid A241 w/o colloid Np237 w/o colloid U233 w/o colloid Th229 A241 (Kd c Np237 (Kd c U233 (Kd c Th229 (Kd c Tie (yrs Figure 1. The breakthrough curves o our nuclides in the Neptuniu decay chain at the distance o 0 away ro the radioactive source with/without colloids (the colloidal concentration is 0.1 kg/ 3 and Kd c.

8 -3 Concentration (kg/ w/o colloid A241 w/o colloid Np237 w/o colloid U233 w/o colloid Th229 A241 (Kd c Np237 (Kd c U233 (Kd c Th229 (Kd c A241 (Kd c Np237 (Kd c U233 (Kd c Th229 (Kd c Tie (yrs Figure 2. The breakthrough curves o our nuclides in the Neptuniu decay chain at the distance o 0 away ro the radioactive source with/without colloids (the colloidal concentration is 0.1 kg/ 3 based on the paraeters o TILA-99[22]. To urther investigate the eect o colloids or the dierent decay chain, the breakthrough curves or the our nuclides in the Uraniu decay chain based on the distribution coeicients or H-12[19] are plotted in Figure 3, or Kd c is set to be equal to Kd and Kd c is ten-old o Kd. The transport o radionuclides in the Uraniu decay chain is also slightly enhanced due to the existence o colloids when Kd c is equal to Kd. The enhanceent becoes signiicant while increasing the nuclide-colloid sorption. Moreover, Figure 4 shows the breakthrough curves or the our nuclides in the Uraniu decay chain based on the distribution coeicients or S-97[23] to investigate the eect o colloids on the transport o radionuclides in the Uraniu decay chain. The breakthrough curves o U-238, U-234 and Th-230 in the right hand side o Figure 4 are enhanced and accelerated by obile colloids because o the large sorption capability. There are two breakthrough curves o a-226 in the Uraniu decay chain: one is contributed by a-226 itsel; the other is iputed by the parent nuclide o Th-230. The breakthrough curve o a-226 in the let o the igure, which is contributed by a-226 itsel, shows that the transport o a236 is not acilitated by the colloids because o its low adsorbability ( /kg in Table II; even Kd c is ten ties the value o Kd. However, another breakthrough curve o a-226 decayed ro the parent nuclide o Th-230 in the right o the igure is signiicantly acilitated by colloids in the ractured edia. The transport o Th-230 is enhanced by colloids; thereore, this enhanceent acilitates the transport o a-226 indirectly. When Kd c is ten ties the value o

9 Kd, the eect o colloids on the transport becoes stronger. The nuclide o a-226 with low adsorbability is accelerated unexpectedly because o the sorption o its parent nuclide o Th-230 on colloids. The Th-230 nuclide is kidnapped by the colloids in the aqueous phase to keep its obility and decays into a-226 aterward, thus, the concentration o obile a-226 in the racture increases. The inluence o colloids on the radionuclide transport was expected to be crucial to the actinides with large adsorbability; however, the present results reveal that the low-adsorbing nuclides whose parent nuclides have large capability o sorption could be also acilitated signiicantly by colloids indirectly. This unexpected enhanceent o the transport o such nuclides, or instance a-226, indicates that the existence o colloids should be seriously treated in the transport o the radionuclide decay chain in the geologic syste. -4 Concentration (kg/ w/o colloid U238 w/o colloid U234 w/o colloid Th230 w/o colloid a226 U238 (Kd c U234 (Kd c Th230 (Kd c a226 (Kd c U238 (Kd c U234 (Kd c Th230 (Kd c a226 (Kd c Tie (yrs Figure 3. The breakthrough curves o our nuclides in the Uraniu decay chain at the distance o 0 away ro the radioactive source with/without colloids (the colloidal concentration is 0.1 kg/ 3.

10 Concentration (kg/ 3-2 w/o colloid U238 w/o colloid U234-3 w/o colloid Th230 w/o colloid a226 U238 (Kd c U234 (Kd c -4 Th230 (Kd c a226 (Kd c U238 (Kd c U234 (Kd c -5 Th230 (Kd c a226 (Kd c Tie (yrs Figure 4. The breakthrough curves o our nuclides in the Uraniu decay chain at the distance o 0 away ro the radioactive source with/without colloids (the colloidal concentration is 0.1 kg/ 3 based on the paraeters o S CONCLUSIONS This present study has extended previous studies to study the eects o colloids on actinides decay chains transport in the ractured edia. The site-speciic paraeters were eployed herein to deonstrate our odel. The results indicated that colloids could enhance and acilitate the transport o radionuclides. The large adsorbability o nuclides with colloids would enlarge the eect o acceleration by colloids. On the other hand, the acilitated transport by colloids is reduced while the decreasing adsorpability o nuclides with colloids. When the obile colloids exit in a non-negligible concentration and have the capability o adsorb nuclides stably in the geologic syste, colloids will be iportant or the transport o radionuclides 26. Furtherore, an unexpected enhanceent o the transport o the low-absorbing a-226 in the Uraniu decay chain under the paraeters o S-97 occurred in the presence o colloids due to the large adsorbability o its parent nuclide o Th-230. The obility o Th-230 is aintained by adsorbing on colloids and decays into a-226, thereore, the transport o a-226 contributed by the parent nuclide o Th-230 was enhanced indirectly. Consequently, the role o colloids played in the transport o the radionuclides decay chain should be assessed careully in the radioactive waste disposal.

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