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Modeling of diffusion behavior of humic acid and Nd in the presence of humic acid in compacted bentonite
Physics and Chemistry of the Earth 65 (2013) 66–71
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Modeling of diffusion behavior of humic acid and Nd in the presence of humic acid in compacted bentonite Kazuki Iijima a,b,⇑, Seiichi Kurosawa c, Satoshi Kibe c, Minoru Tobita c, Yuji Ouchi c a
Waste Isolation Research Division, Japan Atomic Energy Agency, 4-33, Muramatsu, Tokai, Ibaraki 319-1194, Japan Waste Management Department, Nuclear Fuel Cycle Engineering Laboratories, Japan Atomic Energy Agency, 4-33, Muramatsu, Tokai, Ibaraki 319-1194, Japan c Inspection Development Company Ltd., 4-33, Muramatsu, Tokai, Ibaraki 319-1112, Japan b
a r t i c l e
i n f o
Article history: Available online 28 May 2013 Keywords: Humic acid Compacted bentonite Neodymium Diffusion Modeling
a b s t r a c t The diffusion behavior of HA and Nd in the presence of HA in compacted bentonite was investigated experimentally by means of the through-diffusion method. Breakthrough of HA is observed in 1 and 0.1 mol dm3 NaCl solution and is more significant with a lower dry density such as 1.2 Mg m3. The one dimensional diffusion model taking parallel complexation equilibrium into account was fitted to the experimentally obtained breakthrough curves and concentration profiles, and the diffusion parameters, such as effective diffusivity and rock capacity factor, were evaluated. The obtained effective diffusivity, around 1011 m2 s1, for HA and Nd–HA is comparable to the previously reported value. Using these parameters, predictive calculations were performed to evaluate the effect of HA concentration and sorption distribution coefficient. It is indicated that the effect of sorption distribution coefficient is significant only for a short period and that relatively low HA concentrations might bring higher diffused mass depending on the diffusion behavior of dominant species. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In the safety assessment of the geological disposal system of high level radioactive waste (HLW) planned in Japan, the radionuclides (RNs) in HLW are considered to be dissolved by groundwater and migrate through the buffer material and host rock by diffusion and/or advection, which is expected to be retarded by sorption onto minerals contained in the buffer material and host rock, and by diffusion into the host rock matrix (JNC, 2000). This migration behavior is affected not only by ligands complexing with RNs, but also by colloids which strongly interact with RNs (Avogadro and De Marsily, 1984; McCarthy and Zachara, 1989; Kersting et al., 1999; Miller et al., 2000; Geckeis et al., 2004). Humic acid (HA) is a natural organic matter and is ubiquitous in groundwater (Stevenson, 1994; Tipping, 2002). Since the complexation behavior of RNs with HA has been investigated for decades by a number of researchers using various experimental methods, it is well known that HA forms strong complexes with trivalent and tetravalent metal ions, such as lanthanides (Ln) and actinides (An) (Dearlove et al., 1991; Kim, 1991; Geckeis and Rabung, 2008). Some actinides, e.g. Np, Th, Pu, are considered to be dominant in the safety assessment of geological disposal (JNC, 2000). Therefore, evaluating the ⇑ Corresponding author at: Waste Isolation Research Division, Japan Atomic Energy Agency, 4-33, Muramatsu, Tokai, Ibaraki 319-1194, Japan. Tel.: +81 29 287 2193; fax: +81 29 282 9328. E-mail address: [email protected] (K. Iijima). 1474-7065/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pce.2013.05.009
effect of HA on the migration behavior of An(III) and An(IV) is unavoidable. Regarding Ln(III)- and An(III)-humic acid interaction, numerous investigations were carried out on complexation behavior (Kim et al., 1991, 1993, 1997; Takahashi et al., 1994; Czerwinski et al., 1996; Rao et al., 1994; Dong et al., 2001; Kubota et al., 2002; Wall et al., 2002; Wenming et al., 2002; Chang et al., 2006), spectroscopic characterization (Monsallier et al., 2003; Plaschke et al., 2004; Naber et al., 2006; Rabung and Geckeis, 2009), competition to sorption on solid phase (Ledin et al., 1994; Samadfam et al., 1998, 2000; Takahashi et al., 1998; Sakuragi et al., 2002; Darvanche et al., 2008; Tan et al., 2008), migration experiments in a rock column (Kim et al., 1994; Nagao et al., 1998; Schussler et al., 2001; Vilks and Baik, 2001; Artinger et al., 2002) and field observation (McCarthy et al., 1998; Novikov et al., 2006), while migration experiments in compacted bentonite are quite limited. One reason for this is that colloids are considered to be filtered by the fine structure of compacted bentonite and to hinder, rather than facilitate, RN migration. For example, diffusion behavior of colloidal particles through compacted bentonite was studied and it was shown that gold colloids with a mean size of 15 nm were filtered by compacted bentonite with dry density 1.8 Mg m3 (Kurosawa et al., 1997). However, some recent studies show that macromolecule organics can migrate through compacted bentonite. Wold and Eriksen (2003) studied the diffusion behavior of lignosulfonate colloids with molecular weight of 30 kD through
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compacted bentonite and obtained apparent diffusivities in the order of 1012 m2 s1, which was independent of ionic strength (0.1– 0.01 mol dm3) and dry density (0.6–1.8 Mg m3). Through diffusion experiments of Eu(III) and Co(II) in the compacted bentonite were also carried out in the presence of HA under the same ionic strength and dry density conditions (Wold and Eriksen, 2007). It was shown that HA diffused through compacted bentonite regardless of conditions and apparent diffusivities significantly increased for both Co(II) and Eu(III) when HA were present. Similar influence of HA was also reported for diffusion behavior of Nd(III) in compacted bentonite and the migration behavior of Nd(III) in the presence of HA was successfully described by the diffusion model taking Nd–HA complexation equilibrium into account (Iijima et al., 2009). On the other hand, Wang et al. (2004) reported that HA formed precipitation or complexation with Eu(III) at the surface of compacted bentonite and reduced the diffusion of Eu(III) in the compacted bentonite. Differences in behavior of the HA and RN–HA complex between these studies might be caused by the difference in molecular weight of the RN–HA complex. Thus, the influence of HA on the diffusion behavior of RNs in compacted bentonite should be investigated and evaluated quantitatively based on the model. In this study, the diffusion behavior of HA was investigated under various ionic strength and dry density conditions to evaluate diffusion parameters, such as diffusivity and the rock capacity factor, which were necessary for the diffusion model. Finally, long term diffusion behavior of RNs in compacted bentonite is discussed referring to diffusion parameters for Nd(III). 2. Experimental 2.1. Materials The bentonite used in this study was Kunigel V1Ò, supplied by Kunimine Industry Co. Ltd. This bentonite contains about 46–49 wt% of smectite, and trace minerals such as quartz, chalcedony, plagioclase, calcite, dolomite, analcime, and pyrite. Its detailed properties are given elsewhere (JNC, 2000). The commercial HA purchased by Aldrich Co. Ltd was purified based on the International Humic Substance Society Method. All other chemicals were reagent grade and used without purification. Doubly distilled water supplied by ADVANTEC CPW-200 was used to prepare all the solutions.
Fig. 1. Schematic drawing of diffusion cell.
Dried bentonite was compacted into the acrylic cell and sandwiched by solution cells. Firstly, both cells were filled with an appropriate concentration of NaCl solution and saturated for one month. The tracer cell solution was then replaced with the experimental solution, in which 500 mg dm3 HA and/or 1 106 mol dm3 Nd was added, according to the experimental conditions. The pH of the experimental solution was adjusted by HCl or NaOH to 8, which was kept within 7.7–8.2 during all of the experiments. The 5 mL aliquot of the sample cell solution was taken at regular intervals and replaced with the same volume of fresh NaCl solution. The concentration of the total organic carbon (TOC) of the samples was measured by a TOC analyzer (SHIMADZU TOC5000A) after dilution 6 times with 0.1 mol dm3 KH2PO4 and bubbling with N2 gas for at least 3 min to remove CO2. Other protocols and measurement results of absorbance, molecular weight distribution and Nd concentration were reported in detail in Iijima et al. (2009). 1–2 years later, post-diffusion extraction was carried out. The bentonite sample was sliced into thin, 0.2 mm thick pieces. Each slice was immersed in 5 mL of 1 mol dm3 NaCl solution and shaken for two weeks to extract HA and Nd (if added) from the bentonite. This suspension was centrifuged at 6000 rpm for 100 min and the supernatant was taken for TOC measurements. The distribution coefficient of HA to bentonite used to estimate the total concentration in the slice is 7.7 102 m3 kg1, referring to Iijima et al. (2009).
2.2. Diffusion experiments 2.3. Data analysis Experiments were carried out in the through-diffusion method under aerobic conditions. Experimental conditions are summarized in Table 1. Italic numbers in this table are used to indicate the corresponding experimental conditions under which each data were acquired. The schematic drawing of the diffusion cell was shown in Fig. 1.
One-dimensional diffusion of diffusant in the compacted bentonite can be described by Fick’s second law:
@C De @ 2 C ¼ @t a @x2
ð1Þ
Table 1 Experimental conditions for through-diffusion. Dry density (Mg m3), content of HA and Nd
1.2, HA, Nd 1.2, HA 1.2 (without HA, Nd) 1.4, HA 1.6, HA
NaCl concentration (mol dm3) 1.0
0.1
2056 2050 2000 4050 6050
2156
Italic numbers listed in this table and also used in the text show the corresponding experimental conditions.
2100
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K. Iijima et al. / Physics and Chemistry of the Earth 65 (2013) 66–71
where C is the concentration of diffusant in solution (mol m3), t is the diffusion time (s), De is the effective diffusivity (m2 s1), a is the rock capacity factor (–) and x is the distance (m). Assuming linear sorption, the rock capacity factor is described as:
a ¼ e þ qK d
ð2Þ
where e is the porosity (–), q is the dry density of bentonite (kg m3) and Kd is the sorption distribution coefficient (m3 kg1). In this study, the equilibrium among Nd, HA and Nd–HA complex in the process of diffusion is considered. The stability constant for the equilibrium: 3þ
Nd
þ HAðIIIÞ $ ½Nd—HAðIIIÞ
ð3Þ
can be described, for example based on the charge neutralization model (Kim and Czerwinski, 1996), as follows:
bNd—HA ¼
½Nd—HAðIIIÞ 3þ
½Nd f ½HAðIIIÞf
¼
C NdHA 3þ
½Nd f C HA PECLC 3
ð4Þ
where bNd–HA is the stability constant of Nd–HA complex (m3 mol1), [Nd–HA(III)] (replaced with CNd–HA), [Nd3+]f and [HA(III)]f are the concentrations of Nd–HA complex, free Nd3+ and free deprotonated HA, respectively (mol m3), CHA is the total concentration of free HA (g m3), PEC is the proton exchange capacity (eq g1) and LC is the loading capacity (–). Complexation reactions of Nd3+ with other ligands, Li, in the solution are given as: 3þ
Nd
zi
þ ni Li
i zi $ NdðLi Þ3n ni
i zi ½NdðLi Þ3n ni
3þ
ð6Þ
½Nd f ½Li i ni z
If the concentration of ligands is high enough to be considered constant, the total concentration of free Nd, CNd (mol m3), can be expressed as follows: 3þ
C Nd ¼ ½Nd f þ
X i zi ½NdðLi Þ3n ¼ ni
@C HA De;HA @ 2 C HA ¼ @t aHA @x2
ð13Þ
On the other hand, summing Eq. (11) for free Nd and Eq. (12) for the Nd–HA complex becomes:
@C Nd @C Nd—HA De;Nd @ 2 C Nd De;Nd—HA @ 2 C Nd—HA þ ¼ þ @t @t aNd @x2 aNd—HA @x2
ð14Þ
and using Eq. (10) we obtain:
ð1 þ K Nd—HA Þ
@C Nd De;Nd De;NdHA @ 2 C Nd—HA ¼ þ K Nd—HA @t aNd aNd—HA @x2
ð15Þ
In this study, Eqs. (13) and (15) were used for numerical calculation by the implicit method. Firstly, Eq. (13) was fitted to breakthrough curve and concentration profile data for HA. Secondly, after defining KNd–HA using HA concentration data obtained by the above numerical calculation, Eq. (15) was fitted to breakthrough curve for Nd. 3. Results and discussion 3.1. Diffusion experiments
ð5Þ
and the equilibrium constant Ki is defined as follows:
Ki ¼
experiment, CHA is usually sufficiently higher than the total concentration of Nd to ignore DNd–HA for HA. Then the equation for CHA is described as follows:
1þ
i
! X 3þ z K i ½Li i ni ½Nd f
ð7Þ
i
Breakthrough curves for HA based on the TOC measurements are shown in Figs. 2 and 3. Previously reported data for HA and Nd in 2056 are also indicated in Fig. 2. Observed TOC background measurements, even for blank experiments (2000 and 2100), are subtracted from each data point. Organics originally contained in the bentonite are considered to contribute this background. Although some data show scatter, the increasing trends with the elapse of time are clearly observed for all experiments. Concentration profiles obtained in the experiments shown in Fig. 2 are illustrated in 191 Fig. 4.
It is noticed that the CNd is not defined as Nd without any complexation (concretely Nd3+) but all Nd species except Nd–HA complex. Substituting Eq. (7) into Eq. (4) gives:
bNd—HA ¼ 1þ
C Nd—HA PC Nd zi n C HA PECLC 3 i
K i ½Li
ð8Þ
i
Since CHA can be considered constant, we define the equilibrium constant, KNd–HA, by the following equation:
K NdHA ¼ bNdHA
1þ
P
1 C HA PEC LC zi ni 3 K ½L i i i
ð9Þ
Then Eq. (8) becomes:
C Nd—HA ¼ K Nd—HA C Nd
ð10Þ
If three species diffuse with different diffusivity and sorption distribution coefficients, either association or dissociation of the Nd–HA complex is expected to occur to maintain equilibrium. Therefore, Eq. (1) is modified for each species as follows:
@C i De;i @ 2 C i ¼ þ DNd—HA @t ai @x2
ði ¼ Nd; HAÞ
ð11Þ
@C j De;j @ 2 C j ¼ DNd—HA @t aj @x2
ðj ¼ Nd—HAÞ
ð12Þ
where DNd–HA is the concentration of Nd–HA dissociated to free Nd and HA to keep equilibrium per unit time (mol m3 s1). In this
Fig. 2. Breakthrough curves for HA obtained in 4000. Those for HA and Nd in 2056 (Iijima et al., 2009) are also illustrated. Dashed and solid lines indicate fitting curves to each data.
K. Iijima et al. / Physics and Chemistry of the Earth 65 (2013) 66–71
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the diffusion equations. In other experiments, the breakthrough curves of which are shown in Fig. 3, the concentration of extracted HA is relatively low making it difficult to obtain a significant profile.
3.2. Data fitting
Fig. 3. Breakthrough curves of HA obtained in 2050, 6050 and 2156. Solid lines indicate fitting curves to each data.
These profiles can be divided into two regions with significantly different slopes. As reported by Iijima et al. (2009), the first region of the profile within 1 mm of the tracer cell with the steep slope is likely to correspond to a higher molecular weight fraction, while the second region farther than 1 mm with a gradual slope corresponds to a lower molecular weight fraction, which shows breakthrough. Only the data in this second region was fit using
Fig. 4. Concentration profiles for HA in compacted bentonite obtained in 4000. Those for HA and Nd in 2056 (Iijima et al., 2009) are also illustrated. Dashed and solid lines indicate fitting curves to each data.
The results of fitting Eqs. (13) and (15) to the breakthrough curves and concentration profiles are also illustrated in Figs. 2 and 4 as dashed lines for HA and solid lines for Nd, respectively. Input data for the calculation and obtained fitting parameters are listed in Table 2. It is noticed that total concentration in the tracer cell is not equal to the initially added concentration of HA or Nd, but the fractional concentration of HA or Nd which can diffuse through the bentonite specimen. Effective diffusivity and distribution coefficients evaluated for 4050 are slightly higher than those of 2056. Bentonite with higher dry density usually shows lower effective diffusivity due to lower porosity. Therefore, differences in parameters between 2056 and 4050 are likely to be within variation. The obtained effective diffusivity, an order of 1011 m2 s1, is comparable to the previously reported value (Wold and Eriksen, 2007). The equations were also fitted to the data shown in Fig. 3. Since it is difficult to fix three parameters in parallel with only breakthrough curves, the distribution coefficient is reasonably assumed to equal 2056 for 2050, and 0 for 2156 and 6050, respectively. In the case of 2156, which was carried out under lower ionic strength conditions, the total obtained concentration was significantly lower. It is considered that diffusible HA is limited to lower molecular weight fractions due to the electrostatic repulsive force that is in effect under lower ionic strength conditions.
3.3. Predictive calculation Preliminary predictive calculations were performed for the 0.7 m long bentonite, which was the same as the reference design of an engineered barrier for HLW disposal in Japan, by means of Eqs. (13) and (15) with the obtained diffusion parameters listed in Table 2. The concentration of HA was parameterized from 1.4 101 mol m3, corresponding to 100 mg dm3 with the HA used in this study, to 1.4 105 mol m3. The concentration of HA in the bentonite was assumed to be constant to simulate the reference scenario in which RN was expected to start migration after a duration sufficient for saturation. The case with Kd = 0 was also carried out to evaluate the effect of Kd. The results, plotted as total diffused mass per unit surface area, are shown in Fig. 5. Although the diffused mass in case of Kd = 0 is initially significantly higher than that of Kd – 0, they approach a similar curve with time. Therefore, the effect of Kd is significant if the radioactive half-life decay of a specific RN is relatively short. On the other hand, the effect of the concentration of HA attracts much interest. The higher the HA concentration, the higher the total diffused mass is, which is illustrated at the beginning. However, this tendency is reversed with time. The cause of this tendency is still under investigation, but the difference of diffusion behavior of dominant species seems the key point. In the higher HA case, RN dominantly exists as the RN-HA complex, which migrates with less retardation due to low Kd, but the diffusion flux at the steady state is relatively lower due to low De. Oppositely, in the lower HA case, the expected dominant species is free RN, which migrates with retardation due to high Kd, but the diffusion flux at the steady state is relatively high. Based on this result, it should be notice that relatively lower HA concentration might bring higher diffused mass depending on the conditions.
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Table 2 Input data for fitting, obtained fitting parameters and input data for predictive calculation.
a b
Run No.
2056
4050
2050
2156
6050
Prediction
Input data q (Mg m3) e (-) bNd–HA (103 m3 mol1)a
1.2 0.556 2.3
1.4 0.481 2.3
1.2 0.556 2.3
1.2 0.556 2.3
1.6 0.407 2.3
1.2 0.556 2.3
Diffusion parameters HA De (1011 m2 s1) Kd (102 m3 kg1) Nd–HA De (1012 m2 s1) Kd (103 m3 kg1) Nd De (1011 m2 s1) Kd (102 m3 kg1)
1.8 1.9 6.0 9.5 5.0 1.5
2.5 4.0 – – – –
2.0 1.9 – – – –
1.2 0 N.D.b N.D.b N.D.b N.D.b
6.0 0 – – – –
1.8 0, 1.9 6.0 0, 9.5 5.0 1.5
Total concentration in the tracer cell HA (mg dm3) Nd (109 mol dm3)
95 9.3
81
121
24 N.D.b
70
0.1–100 1.0
Based on Iijima et al. (2009). These parameters were not evaluated due to lower concentration of Nd than detection limit.
Fig. 5. Predictive calculation of total diffused mass by means of the Eqs. (8) and (10) with obtained diffusion parameters listed in Table 2.
4. Conclusion Diffusion behavior of HA and Nd in the presence of HA in compacted bentonite was investigated by means of the through-diffusion experiment method and modeled based on the one-dimensional diffusion model taking parallel complexation equilibrium into account. The model is fitted to the experimentally obtained breakthrough curves and concentration profiles and the diffusion parameters are evaluated as around 1011 m2 s1 for effective diffusivity of HA and Nd–HA, which is comparable to the previously reported value. The predictive calculations show that the effect of Kd is significant only for a short term diffusion and relatively lower HA concentrations might bring higher diffused mass depending on the conditions.
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Stevenson, F.J., 1994. Humus Chemistry: Genesis, Composition, Reactions, second ed. John Wiley & Sons, New York. Takahashi, Y., Minai, Y., Meguro, Y., Toyoda, S., Tominaga, T., 1994. Ionic strength and pH dependence of binding constants of Am(III)- and Eu(III)-humates. J. Radioanal. Nucl. Chem. Lett. 186, 129–141. Takahashi, Y., Minai, Y., Kimura, T., Tominaga, T., 1998. Adsorption of europium(III) and americium(III) on kaolinite and montmorillonite in the presence of humic acid. J. Radioanal. Nucl. Chem. 234, 277–282. Tan, X.L., Wang, X.K., Geckeis, H., Rabung, Th., 2008. Sorption of Eu(III) on humic acid or fulvic acid bound to hydrous alumina studied by SEM-EDS, XPS, TRLFS, and Batch techniques. Environ. Sci. Technol. 42, 6532. Tippin, E., 2002. Cation Binding by Humic Substances. Cambridge University Press, Cambridge. Vilks, P., Baik, M.H., 2001. Laboratory migration experiments with radionuclides and natural colloids in a granite fracture. J. Contam. Hydrol. 47, 197–210. Wall, N.A., Borkowski, M., Chen, J.F., Choppin, G.R., 2002. Complexation of americium with humic, fulvic and citric acids at high ionic strength. Radiochim. Acta 90, 563–568. Wang, X., Chen, Y., Wu, Y., 2004. Diffusion of Eu(III) in compacted bentonite – effect of pH, solution concentration and humic acid. Appl. Radiat. Isot. 60, 963–969. Wenming, D., Weijuan, L., Zuyi, T., 2002. Use of the ion exchange method for the determination of stability constants of trivalent metal complexes with humic and fulvic acids II. Tb3+, Yb3+ and Gd3+ complexes in weakly alkaline conditions. Appl. Radiat. Isot. 56, 967–974. Wold, S., Eriksen, T.E., 2003. Diffusion of lignosulfonate colloids in compacted bentonite. Appl. Clay Sci. 23, 43–50. Wold, S., Eriksen, T., 2007. Diffusion of humic colloids in compacted bentonite. Phys. Chem. Earth 32, 477–484.
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Physics and Chemistry of the Earth journal homepage: www.elsevier.com/locate/pce
Modeling of diffusion behavior of humic acid and Nd in the presence of humic acid in compacted bentonite Kazuki Iijima a,b,⇑, Seiichi Kurosawa c, Satoshi Kibe c, Minoru Tobita c, Yuji Ouchi c a
Waste Isolation Research Division, Japan Atomic Energy Agency, 4-33, Muramatsu, Tokai, Ibaraki 319-1194, Japan Waste Management Department, Nuclear Fuel Cycle Engineering Laboratories, Japan Atomic Energy Agency, 4-33, Muramatsu, Tokai, Ibaraki 319-1194, Japan c Inspection Development Company Ltd., 4-33, Muramatsu, Tokai, Ibaraki 319-1112, Japan b
a r t i c l e
i n f o
Article history: Available online 28 May 2013 Keywords: Humic acid Compacted bentonite Neodymium Diffusion Modeling
a b s t r a c t The diffusion behavior of HA and Nd in the presence of HA in compacted bentonite was investigated experimentally by means of the through-diffusion method. Breakthrough of HA is observed in 1 and 0.1 mol dm3 NaCl solution and is more significant with a lower dry density such as 1.2 Mg m3. The one dimensional diffusion model taking parallel complexation equilibrium into account was fitted to the experimentally obtained breakthrough curves and concentration profiles, and the diffusion parameters, such as effective diffusivity and rock capacity factor, were evaluated. The obtained effective diffusivity, around 1011 m2 s1, for HA and Nd–HA is comparable to the previously reported value. Using these parameters, predictive calculations were performed to evaluate the effect of HA concentration and sorption distribution coefficient. It is indicated that the effect of sorption distribution coefficient is significant only for a short period and that relatively low HA concentrations might bring higher diffused mass depending on the diffusion behavior of dominant species. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In the safety assessment of the geological disposal system of high level radioactive waste (HLW) planned in Japan, the radionuclides (RNs) in HLW are considered to be dissolved by groundwater and migrate through the buffer material and host rock by diffusion and/or advection, which is expected to be retarded by sorption onto minerals contained in the buffer material and host rock, and by diffusion into the host rock matrix (JNC, 2000). This migration behavior is affected not only by ligands complexing with RNs, but also by colloids which strongly interact with RNs (Avogadro and De Marsily, 1984; McCarthy and Zachara, 1989; Kersting et al., 1999; Miller et al., 2000; Geckeis et al., 2004). Humic acid (HA) is a natural organic matter and is ubiquitous in groundwater (Stevenson, 1994; Tipping, 2002). Since the complexation behavior of RNs with HA has been investigated for decades by a number of researchers using various experimental methods, it is well known that HA forms strong complexes with trivalent and tetravalent metal ions, such as lanthanides (Ln) and actinides (An) (Dearlove et al., 1991; Kim, 1991; Geckeis and Rabung, 2008). Some actinides, e.g. Np, Th, Pu, are considered to be dominant in the safety assessment of geological disposal (JNC, 2000). Therefore, evaluating the ⇑ Corresponding author at: Waste Isolation Research Division, Japan Atomic Energy Agency, 4-33, Muramatsu, Tokai, Ibaraki 319-1194, Japan. Tel.: +81 29 287 2193; fax: +81 29 282 9328. E-mail address: [email protected] (K. Iijima). 1474-7065/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pce.2013.05.009
effect of HA on the migration behavior of An(III) and An(IV) is unavoidable. Regarding Ln(III)- and An(III)-humic acid interaction, numerous investigations were carried out on complexation behavior (Kim et al., 1991, 1993, 1997; Takahashi et al., 1994; Czerwinski et al., 1996; Rao et al., 1994; Dong et al., 2001; Kubota et al., 2002; Wall et al., 2002; Wenming et al., 2002; Chang et al., 2006), spectroscopic characterization (Monsallier et al., 2003; Plaschke et al., 2004; Naber et al., 2006; Rabung and Geckeis, 2009), competition to sorption on solid phase (Ledin et al., 1994; Samadfam et al., 1998, 2000; Takahashi et al., 1998; Sakuragi et al., 2002; Darvanche et al., 2008; Tan et al., 2008), migration experiments in a rock column (Kim et al., 1994; Nagao et al., 1998; Schussler et al., 2001; Vilks and Baik, 2001; Artinger et al., 2002) and field observation (McCarthy et al., 1998; Novikov et al., 2006), while migration experiments in compacted bentonite are quite limited. One reason for this is that colloids are considered to be filtered by the fine structure of compacted bentonite and to hinder, rather than facilitate, RN migration. For example, diffusion behavior of colloidal particles through compacted bentonite was studied and it was shown that gold colloids with a mean size of 15 nm were filtered by compacted bentonite with dry density 1.8 Mg m3 (Kurosawa et al., 1997). However, some recent studies show that macromolecule organics can migrate through compacted bentonite. Wold and Eriksen (2003) studied the diffusion behavior of lignosulfonate colloids with molecular weight of 30 kD through
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compacted bentonite and obtained apparent diffusivities in the order of 1012 m2 s1, which was independent of ionic strength (0.1– 0.01 mol dm3) and dry density (0.6–1.8 Mg m3). Through diffusion experiments of Eu(III) and Co(II) in the compacted bentonite were also carried out in the presence of HA under the same ionic strength and dry density conditions (Wold and Eriksen, 2007). It was shown that HA diffused through compacted bentonite regardless of conditions and apparent diffusivities significantly increased for both Co(II) and Eu(III) when HA were present. Similar influence of HA was also reported for diffusion behavior of Nd(III) in compacted bentonite and the migration behavior of Nd(III) in the presence of HA was successfully described by the diffusion model taking Nd–HA complexation equilibrium into account (Iijima et al., 2009). On the other hand, Wang et al. (2004) reported that HA formed precipitation or complexation with Eu(III) at the surface of compacted bentonite and reduced the diffusion of Eu(III) in the compacted bentonite. Differences in behavior of the HA and RN–HA complex between these studies might be caused by the difference in molecular weight of the RN–HA complex. Thus, the influence of HA on the diffusion behavior of RNs in compacted bentonite should be investigated and evaluated quantitatively based on the model. In this study, the diffusion behavior of HA was investigated under various ionic strength and dry density conditions to evaluate diffusion parameters, such as diffusivity and the rock capacity factor, which were necessary for the diffusion model. Finally, long term diffusion behavior of RNs in compacted bentonite is discussed referring to diffusion parameters for Nd(III). 2. Experimental 2.1. Materials The bentonite used in this study was Kunigel V1Ò, supplied by Kunimine Industry Co. Ltd. This bentonite contains about 46–49 wt% of smectite, and trace minerals such as quartz, chalcedony, plagioclase, calcite, dolomite, analcime, and pyrite. Its detailed properties are given elsewhere (JNC, 2000). The commercial HA purchased by Aldrich Co. Ltd was purified based on the International Humic Substance Society Method. All other chemicals were reagent grade and used without purification. Doubly distilled water supplied by ADVANTEC CPW-200 was used to prepare all the solutions.
Fig. 1. Schematic drawing of diffusion cell.
Dried bentonite was compacted into the acrylic cell and sandwiched by solution cells. Firstly, both cells were filled with an appropriate concentration of NaCl solution and saturated for one month. The tracer cell solution was then replaced with the experimental solution, in which 500 mg dm3 HA and/or 1 106 mol dm3 Nd was added, according to the experimental conditions. The pH of the experimental solution was adjusted by HCl or NaOH to 8, which was kept within 7.7–8.2 during all of the experiments. The 5 mL aliquot of the sample cell solution was taken at regular intervals and replaced with the same volume of fresh NaCl solution. The concentration of the total organic carbon (TOC) of the samples was measured by a TOC analyzer (SHIMADZU TOC5000A) after dilution 6 times with 0.1 mol dm3 KH2PO4 and bubbling with N2 gas for at least 3 min to remove CO2. Other protocols and measurement results of absorbance, molecular weight distribution and Nd concentration were reported in detail in Iijima et al. (2009). 1–2 years later, post-diffusion extraction was carried out. The bentonite sample was sliced into thin, 0.2 mm thick pieces. Each slice was immersed in 5 mL of 1 mol dm3 NaCl solution and shaken for two weeks to extract HA and Nd (if added) from the bentonite. This suspension was centrifuged at 6000 rpm for 100 min and the supernatant was taken for TOC measurements. The distribution coefficient of HA to bentonite used to estimate the total concentration in the slice is 7.7 102 m3 kg1, referring to Iijima et al. (2009).
2.2. Diffusion experiments 2.3. Data analysis Experiments were carried out in the through-diffusion method under aerobic conditions. Experimental conditions are summarized in Table 1. Italic numbers in this table are used to indicate the corresponding experimental conditions under which each data were acquired. The schematic drawing of the diffusion cell was shown in Fig. 1.
One-dimensional diffusion of diffusant in the compacted bentonite can be described by Fick’s second law:
@C De @ 2 C ¼ @t a @x2
ð1Þ
Table 1 Experimental conditions for through-diffusion. Dry density (Mg m3), content of HA and Nd
1.2, HA, Nd 1.2, HA 1.2 (without HA, Nd) 1.4, HA 1.6, HA
NaCl concentration (mol dm3) 1.0
0.1
2056 2050 2000 4050 6050
2156
Italic numbers listed in this table and also used in the text show the corresponding experimental conditions.
2100
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K. Iijima et al. / Physics and Chemistry of the Earth 65 (2013) 66–71
where C is the concentration of diffusant in solution (mol m3), t is the diffusion time (s), De is the effective diffusivity (m2 s1), a is the rock capacity factor (–) and x is the distance (m). Assuming linear sorption, the rock capacity factor is described as:
a ¼ e þ qK d
ð2Þ
where e is the porosity (–), q is the dry density of bentonite (kg m3) and Kd is the sorption distribution coefficient (m3 kg1). In this study, the equilibrium among Nd, HA and Nd–HA complex in the process of diffusion is considered. The stability constant for the equilibrium: 3þ
Nd
þ HAðIIIÞ $ ½Nd—HAðIIIÞ
ð3Þ
can be described, for example based on the charge neutralization model (Kim and Czerwinski, 1996), as follows:
bNd—HA ¼
½Nd—HAðIIIÞ 3þ
½Nd f ½HAðIIIÞf
¼
C NdHA 3þ
½Nd f C HA PECLC 3
ð4Þ
where bNd–HA is the stability constant of Nd–HA complex (m3 mol1), [Nd–HA(III)] (replaced with CNd–HA), [Nd3+]f and [HA(III)]f are the concentrations of Nd–HA complex, free Nd3+ and free deprotonated HA, respectively (mol m3), CHA is the total concentration of free HA (g m3), PEC is the proton exchange capacity (eq g1) and LC is the loading capacity (–). Complexation reactions of Nd3+ with other ligands, Li, in the solution are given as: 3þ
Nd
zi
þ ni Li
i zi $ NdðLi Þ3n ni
i zi ½NdðLi Þ3n ni
3þ
ð6Þ
½Nd f ½Li i ni z
If the concentration of ligands is high enough to be considered constant, the total concentration of free Nd, CNd (mol m3), can be expressed as follows: 3þ
C Nd ¼ ½Nd f þ
X i zi ½NdðLi Þ3n ¼ ni
@C HA De;HA @ 2 C HA ¼ @t aHA @x2
ð13Þ
On the other hand, summing Eq. (11) for free Nd and Eq. (12) for the Nd–HA complex becomes:
@C Nd @C Nd—HA De;Nd @ 2 C Nd De;Nd—HA @ 2 C Nd—HA þ ¼ þ @t @t aNd @x2 aNd—HA @x2
ð14Þ
and using Eq. (10) we obtain:
ð1 þ K Nd—HA Þ
@C Nd De;Nd De;NdHA @ 2 C Nd—HA ¼ þ K Nd—HA @t aNd aNd—HA @x2
ð15Þ
In this study, Eqs. (13) and (15) were used for numerical calculation by the implicit method. Firstly, Eq. (13) was fitted to breakthrough curve and concentration profile data for HA. Secondly, after defining KNd–HA using HA concentration data obtained by the above numerical calculation, Eq. (15) was fitted to breakthrough curve for Nd. 3. Results and discussion 3.1. Diffusion experiments
ð5Þ
and the equilibrium constant Ki is defined as follows:
Ki ¼
experiment, CHA is usually sufficiently higher than the total concentration of Nd to ignore DNd–HA for HA. Then the equation for CHA is described as follows:
1þ
i
! X 3þ z K i ½Li i ni ½Nd f
ð7Þ
i
Breakthrough curves for HA based on the TOC measurements are shown in Figs. 2 and 3. Previously reported data for HA and Nd in 2056 are also indicated in Fig. 2. Observed TOC background measurements, even for blank experiments (2000 and 2100), are subtracted from each data point. Organics originally contained in the bentonite are considered to contribute this background. Although some data show scatter, the increasing trends with the elapse of time are clearly observed for all experiments. Concentration profiles obtained in the experiments shown in Fig. 2 are illustrated in 191 Fig. 4.
It is noticed that the CNd is not defined as Nd without any complexation (concretely Nd3+) but all Nd species except Nd–HA complex. Substituting Eq. (7) into Eq. (4) gives:
bNd—HA ¼ 1þ
C Nd—HA PC Nd zi n C HA PECLC 3 i
K i ½Li
ð8Þ
i
Since CHA can be considered constant, we define the equilibrium constant, KNd–HA, by the following equation:
K NdHA ¼ bNdHA
1þ
P
1 C HA PEC LC zi ni 3 K ½L i i i
ð9Þ
Then Eq. (8) becomes:
C Nd—HA ¼ K Nd—HA C Nd
ð10Þ
If three species diffuse with different diffusivity and sorption distribution coefficients, either association or dissociation of the Nd–HA complex is expected to occur to maintain equilibrium. Therefore, Eq. (1) is modified for each species as follows:
@C i De;i @ 2 C i ¼ þ DNd—HA @t ai @x2
ði ¼ Nd; HAÞ
ð11Þ
@C j De;j @ 2 C j ¼ DNd—HA @t aj @x2
ðj ¼ Nd—HAÞ
ð12Þ
where DNd–HA is the concentration of Nd–HA dissociated to free Nd and HA to keep equilibrium per unit time (mol m3 s1). In this
Fig. 2. Breakthrough curves for HA obtained in 4000. Those for HA and Nd in 2056 (Iijima et al., 2009) are also illustrated. Dashed and solid lines indicate fitting curves to each data.
K. Iijima et al. / Physics and Chemistry of the Earth 65 (2013) 66–71
69
the diffusion equations. In other experiments, the breakthrough curves of which are shown in Fig. 3, the concentration of extracted HA is relatively low making it difficult to obtain a significant profile.
3.2. Data fitting
Fig. 3. Breakthrough curves of HA obtained in 2050, 6050 and 2156. Solid lines indicate fitting curves to each data.
These profiles can be divided into two regions with significantly different slopes. As reported by Iijima et al. (2009), the first region of the profile within 1 mm of the tracer cell with the steep slope is likely to correspond to a higher molecular weight fraction, while the second region farther than 1 mm with a gradual slope corresponds to a lower molecular weight fraction, which shows breakthrough. Only the data in this second region was fit using
Fig. 4. Concentration profiles for HA in compacted bentonite obtained in 4000. Those for HA and Nd in 2056 (Iijima et al., 2009) are also illustrated. Dashed and solid lines indicate fitting curves to each data.
The results of fitting Eqs. (13) and (15) to the breakthrough curves and concentration profiles are also illustrated in Figs. 2 and 4 as dashed lines for HA and solid lines for Nd, respectively. Input data for the calculation and obtained fitting parameters are listed in Table 2. It is noticed that total concentration in the tracer cell is not equal to the initially added concentration of HA or Nd, but the fractional concentration of HA or Nd which can diffuse through the bentonite specimen. Effective diffusivity and distribution coefficients evaluated for 4050 are slightly higher than those of 2056. Bentonite with higher dry density usually shows lower effective diffusivity due to lower porosity. Therefore, differences in parameters between 2056 and 4050 are likely to be within variation. The obtained effective diffusivity, an order of 1011 m2 s1, is comparable to the previously reported value (Wold and Eriksen, 2007). The equations were also fitted to the data shown in Fig. 3. Since it is difficult to fix three parameters in parallel with only breakthrough curves, the distribution coefficient is reasonably assumed to equal 2056 for 2050, and 0 for 2156 and 6050, respectively. In the case of 2156, which was carried out under lower ionic strength conditions, the total obtained concentration was significantly lower. It is considered that diffusible HA is limited to lower molecular weight fractions due to the electrostatic repulsive force that is in effect under lower ionic strength conditions.
3.3. Predictive calculation Preliminary predictive calculations were performed for the 0.7 m long bentonite, which was the same as the reference design of an engineered barrier for HLW disposal in Japan, by means of Eqs. (13) and (15) with the obtained diffusion parameters listed in Table 2. The concentration of HA was parameterized from 1.4 101 mol m3, corresponding to 100 mg dm3 with the HA used in this study, to 1.4 105 mol m3. The concentration of HA in the bentonite was assumed to be constant to simulate the reference scenario in which RN was expected to start migration after a duration sufficient for saturation. The case with Kd = 0 was also carried out to evaluate the effect of Kd. The results, plotted as total diffused mass per unit surface area, are shown in Fig. 5. Although the diffused mass in case of Kd = 0 is initially significantly higher than that of Kd – 0, they approach a similar curve with time. Therefore, the effect of Kd is significant if the radioactive half-life decay of a specific RN is relatively short. On the other hand, the effect of the concentration of HA attracts much interest. The higher the HA concentration, the higher the total diffused mass is, which is illustrated at the beginning. However, this tendency is reversed with time. The cause of this tendency is still under investigation, but the difference of diffusion behavior of dominant species seems the key point. In the higher HA case, RN dominantly exists as the RN-HA complex, which migrates with less retardation due to low Kd, but the diffusion flux at the steady state is relatively lower due to low De. Oppositely, in the lower HA case, the expected dominant species is free RN, which migrates with retardation due to high Kd, but the diffusion flux at the steady state is relatively high. Based on this result, it should be notice that relatively lower HA concentration might bring higher diffused mass depending on the conditions.
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K. Iijima et al. / Physics and Chemistry of the Earth 65 (2013) 66–71
Table 2 Input data for fitting, obtained fitting parameters and input data for predictive calculation.
a b
Run No.
2056
4050
2050
2156
6050
Prediction
Input data q (Mg m3) e (-) bNd–HA (103 m3 mol1)a
1.2 0.556 2.3
1.4 0.481 2.3
1.2 0.556 2.3
1.2 0.556 2.3
1.6 0.407 2.3
1.2 0.556 2.3
Diffusion parameters HA De (1011 m2 s1) Kd (102 m3 kg1) Nd–HA De (1012 m2 s1) Kd (103 m3 kg1) Nd De (1011 m2 s1) Kd (102 m3 kg1)
1.8 1.9 6.0 9.5 5.0 1.5
2.5 4.0 – – – –
2.0 1.9 – – – –
1.2 0 N.D.b N.D.b N.D.b N.D.b
6.0 0 – – – –
1.8 0, 1.9 6.0 0, 9.5 5.0 1.5
Total concentration in the tracer cell HA (mg dm3) Nd (109 mol dm3)
95 9.3
81
121
24 N.D.b
70
0.1–100 1.0
Based on Iijima et al. (2009). These parameters were not evaluated due to lower concentration of Nd than detection limit.
Fig. 5. Predictive calculation of total diffused mass by means of the Eqs. (8) and (10) with obtained diffusion parameters listed in Table 2.
4. Conclusion Diffusion behavior of HA and Nd in the presence of HA in compacted bentonite was investigated by means of the through-diffusion experiment method and modeled based on the one-dimensional diffusion model taking parallel complexation equilibrium into account. The model is fitted to the experimentally obtained breakthrough curves and concentration profiles and the diffusion parameters are evaluated as around 1011 m2 s1 for effective diffusivity of HA and Nd–HA, which is comparable to the previously reported value. The predictive calculations show that the effect of Kd is significant only for a short term diffusion and relatively lower HA concentrations might bring higher diffused mass depending on the conditions.
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