Consumption and diffusion of dissolved oxygen in sedimentary rocks

Journal of Contaminant Hydrology 193 (2016) 35–47

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Consumption and diffusion of dissolved oxygen in sedimentary rocks M. Manaka ⁎, M. Takeda Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8567, Japan

a r t i c l e

i n f o

Article history: Received 18 March 2016 Received in revised form 25 August 2016 Accepted 29 August 2016 Available online 31 August 2016 Keywords: Consumption Diffusion Dissolved oxygen Fe(II)-bearing mineral Sedimentary rock

a b s t r a c t Fe(II)-bearing minerals (e.g., biotite, chlorite, and pyrite) are a promising reducing agent for the consumption of atmospheric oxygen in repositories for the geological disposal of high-level radioactive waste. To estimate effective diffusion coefficients (De, in m2 s−1) for dissolved oxygen (DO) and the reaction rates for the oxidation of Fe(II)-bearing minerals in a repository environment, we conducted diffusion–chemical reaction experiments using intact rock samples of Mizunami sedimentary rock. In addition, we conducted batch experiments on the oxidation of crushed sedimentary rock by DO in a closed system. From the results of the diffusion–chemical reaction experiments, we estimated the values of De for DO to lie within the range 2.69 × 10−11 b De b 6.30 × 10−11. Values of the second-order rate constant (k, in L mol−1 s−1) were in the range −3.66 b log k b −2.83 (from batch experiments) and in the range −3.87 b log k b −2.22 (from diffusion–chemical reaction experiments). Many of these values are within the range of previously published rates for reaction between O2(aq) and Fe(II) surface complexes. The average value for the total concentration of reactive sites was about 10−4 mol m−2 from batch experiments. In contrast, the value of reactive sites estimated from the physical surface area was about 10−8 mol m−2, indicating that the reaction within intact rock is limited to the sites that originally existed with accessible porosity for O2(aq). This difference arises because the batch experiments used powdered samples, meaning that new sites which formed during milling were added to the original reaction sites. On the basis of these observations and interpretations, diffusion–chemical reaction experiments make it possible to determine the values of the kinetic parameter and diffusivity for an intact rock sample simultaneously. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Research into the geological disposal of high-level radioactive waste is currently being conducted in many countries. Understanding the transport of radionuclides is important when evaluating options for geological disposal. The transport of redox-sensitive radionuclides such as Np, Pu, Tc, and U, which are soluble and mobile under oxic conditions (e.g., Langmuir, 1997), needs to be considered at the construction and operational stages of a repository. Conditions in the deep underground are expected to be reducing (e.g., Iwatsuki and Yoshida, 1999; Sasamoto et al., 2004); however, underground conditions temporarily become oxic when atmospheric O2 is introduced during the construction and operation of the repository. After the repository is backfilled, O2 trapped in the underground dissolves into underground water. The dissolved O2 (DO) is consumed by the inorganic (mainly Fe(II)) and organic redox buffers (Puigdomenech et al., 2001) as it diffuses into the rock matrix around the repository. To understand the timeframe until rocks and groundwaters around the repository become anoxic again, the kinetics and diffusion parameters for DO need to be determined. Therefore, it is important to understand the interactions ⁎ Corresponding author. E-mail address: [email protected] (M. Manaka).

http://dx.doi.org/10.1016/j.jconhyd.2016.08.007 0169-7722/© 2016 Elsevier B.V. All rights reserved.

between reduced mineral phases and DO, as well as the diffusion of DO in the rock matrix. Mineral phases such as Fe(II)-bearing minerals (e.g., biotite, chlorite, and pyrite) are present in granitic rocks and sediments, and these are therefore candidate host rock formations for the geological disposal of radioactive waste. The most abundant redox-buffering mineral in a granitic rock is typically biotite (e.g., Ishihara and Terashima, 1977). Chlorite is commonly present in hydrothermal veins and fault gouges (e.g., Manaka et al., 2012). Pyrite is ubiquitous in granitic rocks and sedimentary rocks (e.g., Terashima and Ishihara, 1984; Tada et al., 1992). It is expected that DO trapped in the underground will be consumed by these reduced mineral phases. Many studies have been devoted to measure the oxidation rates of these minerals or rocks, including in the presence of water (e.g., White and Yee, 1985; White et al., 1985; Grenthe et al., 1992; Banwart et al., 1994; Rivas-Perez et al., 2003; Perez et al., 2005; Giménez et al., 2006; Manaka, 2009). However, most measurements have been performed on crushed rock rather than intact rock samples. The use of crushed rock raises the question as to whether the results are representative, such as whether: (i) there is a difference in the reactivity of the reaction sites between the crushed and intact rock samples or not; and (ii) new reaction sites are created by milling a rock sample. To our knowledge, few studies have determined DO consumption parameters using intact rock samples

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M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

(e.g., Pirhonen and Pitkänen, 1991; Trotignon et al., 2002). Pirhonen and Pitkänen (1991) determined the reducing ability (redox capacity) of crystalline rocks and minerals in an aqueous granite solution. Trotignon et al. (2002) performed continuous DO, pH, and Eh monitoring experiments using cores sampled in boreholes and discussed oxidizing perturbations in deep crystalline rocks. However, estimations of DO diffusivity along with DO consumption parameters from intact rock samples have yet to be made. This work deals with the difference in DO consumption rates between crushed and intact rock samples from the Mizunami underground rock laboratory. The DO consumption parameter and DO diffusivity in intact rock samples were estimated from reactive transport experiments. DO consumption parameters for crushed rocks were estimated using standard batch reaction methods. The difference between DO consumption parameters measured for crushed and intact samples is discussed and the results are compared with data from the literature. Given that DO diffusivities for saturated sedimentary rocks are not available from the literature, the measured data are compared with diffusivities of tritiated water (HTO). Finally, the dominant DOconsumers in the Mizunami sedimentary rocks are evaluated.

2. Materials and methods 2.1. Characterization and preparation of the sedimentary rock samples The Mizunami underground laboratory site is located in the city of Mizunami, Gifu Prefecture, in central Japan. Around the site, Pliocene to Pleistocene rocks of the Seto Group (12–1.5 Ma) unconformably overlie Miocene sedimentary rocks of the Mizunami Group (27– 15 Ma). The latter rocks, at depths of about 100–200 m, in turn unconformably overlie a basement of the Cretaceous Toki Granite (75 Ma; Sasao et al., 2006). The Mizunami Group is divided into the Toki Lignite-Bearing Formation, the Hongo Formation, and the Akeyo Formation, from bottom to top (Itoigawa, 1974). The upper part of the Mizunami Group (i.e., the Akeyo Formation) is composed of shallowmarine siltstone–sandstone alternations. In contrast, the middle and lower parts of the Mizunami Group (i.e., the Hongo Formation and the Toki Lignite-Bearing Formation, respectively) are composed of fluvial sediments. The sedimentary rock samples were collected from borehole MSB-2, at depths of approximately 34, 35, 95, and 125 m. The samples from depths of 34 and 35 m belong to the Akeyo Formation of the Mizunami Group, and the samples from 95 and 125 m belong to the Toki LigniteBearing Formation of the Mizunami Group. The samples were cored (diameter = 20 mm) parallel to the drill core axis. The cylindrical samples were then sliced to a thickness of about 3 mm. Before each run, the sliced coin-shaped samples were stored in distilled deionized water in a refrigerator to remove salt formed by evaporation at the sample surface during storage. The samples were then stored in a test solution in the refrigerator to prevent oxidation. The remains of the drilled cores were crushed and air-dried. Part of the air-dried sample remained in a massive state for determination of the physical characteristics of the sedimentary rock, and the other was powdered using a fully automatic pulverizer (HP-MS, Herzog). The powdered samples were stored in a desiccator containing an oxygen scavenger to prevent oxidation until the experiments were performed. The porosities, bulk dry densities, and pore areas of the sedimentary rocks were measured by the mercury intrusion method (Autopore IV9520, Micromeritics) using the massive remains of the drilled cores from which the samples were taken. The specific surface areas of the rock powders were measured with a Shimadzu TriStar 3000 analyzer using the BET method (Brunauer et al., 1938). Measurement of triplicate samples indicated a precision of better than 2.7%. A confidence level of 95% was adopted for the analyses. Table 1 summarizes these results.

The bulk-rock powders were analyzed with an X-ray powder diffractometer (MultiFlex, Rigaku) using monochromatic CuKα radiation operated at 40 kV and 40 mA, from 2° to 65°. The step size was 0.02° and the scan speed was 1° min−1. The clay fractions (b 2 μm) of the sedimentary rocks were extracted using a conventional sedimentation method according to Stokes' Law. Clay identification and procedures were based on those reported by Wada (1966) and Shirozu (1988). For oriented aggregate mounts of the clay fraction of samples, clay mineral identification was confirmed by diagnosing the extent of d-spacing expansion and/or contraction, which is indicative of certain clay minerals during subsequent treatments. These treatments included air drying, ethylene glycol treatment, potassium saturation, and glycerol treatment after magnesium saturation. XRD patterns for clay fractions of samples were obtained with a Rigaku MultiFlex instrument operated at 40 kV and 40 mA from 2° to 20°, to determine the d-spacings in each sample. The step size was 0.02° and the scan speed was 0.5° min−1. Supplementary data files present the XRD patterns (Figs. A1 and A2) for the bulk-rocks and clay fractions of samples at each depth. These features are summarized in Table 2 and are consistent with the mineralogy reported by Iwatsuki et al. (1995). Focusing on the Fe(II)-bearing minerals associated with consumption of DO in the rocks, it is evident that smectite decreases with depth and hornblende is present at depths of N95 m. Furthermore, gypsum is present in samples at depths of b 35 m. Weight loss on ignition (LOI) was determined for each rock powder by means of whole-rock analysis. After determining LOI, the samples were analyzed for major elements at Activation Laboratories, Canada, using inductively coupled plasma–optical emission spectrometry (ICP–OES), apart from Fe(II), which was determined by titration. For the ICP–OES analysis, a Li metaborate/tetraborate fusion technique was used. Analytical errors were b0.01% (FeO is b0.1%). The compositions of the sedimentary rock samples are listed in Table 3. In general, the oxides SiO2, Al2O3, and LOI are dominant, and the sum of these oxides accounts for N 80% of the samples. Variations in the contents of FeO, Fe2O3, and CaO were greater than those of the other oxides. FeO contents decreased from 3.2 wt.% (at 32.90–33.00 m) to 1.2 wt.% (at 125.00–125.13 m), but Fe2O3 contents increased from 1.7 to 3.2 wt.% over the same interval. The CaO contents varied among samples, but this variation was unrelated to depth. Total sulfur and pyrite-sulfur contents in the rock powders were analyzed by the combustion–infrared absorptiometric method (e.g., Kakegawa et al., 1999). The powders were treated with 6 M HCl to remove most of the sulfate minerals. The residues were dried to form an acid-insoluble matter that is composed mainly of pyrite. The sulfate-sulfur content was calculated by subtracting the pyrite-sulfur content from the total sulfur content. The variation in the total sulfur content was greater than that in the oxides. Total sulfur content decreased upward. The highest abundance of pyrite was 0.60 wt.% at 34.90–35.00 m, and the abundances at 32.90–33.00 m, 95.50–95.63 m, and 125.00–125.13 m were 0.37, 0.36, and 0.047 wt.%, respectively. Sulfate–sulfur was documented at 32.90– 33.00 m and 34.90–35.00 m, which is consistent with the presence of gypsum indicated in the XRD analyses for these samples. The total Fe(II) surface site concentrations at the start of the experiment (ST), calculated independently using data from FeO titration, BET, and fusion ICP analyses of bulk-rock samples, are listed in Table 4. Perez et al. (2005) and Davis and Kent (1990) recommended a value of 2.31 sites per nm2 when estimating surface sites in coin-shaped materials. Fe(II) surface site concentrations are calculated using this quantity and the measured data for Fe2 + concentration and surface area for each sample. This calculation yields estimates for ST × solution volume (V)/ sample surface area (SA) in the region of 10−8 mol m−2. 2.2. DO consumption experiments on rock powder Experiments were conducted on rock powders in an air-saturated carbonate-buffered (ASCB) solution (initial pH ~ 9.4). Fig. 1 shows a

M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

37

Table 1 Summary of the properties of the studied sedimentary rocks. Rock sample

Akeyo Formation

Toki Lignite-Bearing Formation

Tuffaceous sandstone

Mercury intrusion method Block sample Porositya Bulk dry densitya Pore areaa BET method Powder sample Specific surface areaa Pippet method Clay (b2 μm) content a

Greywacke

32.90–33.00 m

34.90–35.00 m

95.50–95.63 m

125.00–125.13 m

(%) (g cm−3) (m2 g−1)

52.4 ± 5.9 1.14 ± 0.06 62.4 ± 7.0

55.6 ± 0.9 1.06 ± 0.06 41.6 ± 8.3

36.4 ± 2.7 1.65 ± 0.07 34.6 ± 10.3

33.7 ± 1.3 1.67 ± 0.03 10.7 ± 4.0

(m2 g−1)

81.8 ± 0.6

73.6 ± 0.8

74.7 ± 2.0

28.8 ± 0 0.3

(wt.%)

43.6

44.6

52.5

37.2

95% confidence level.

schematic diagram of the experimental apparatus based on Kamei and Ohmoto (2000). In each run, 0.05, 0.1, 0.2, or 0.5 g of powder was placed in the reaction vessel. The reaction vessel system consisted of a ~0.52 L acrylic vessel with a port for a DO probe and two ports for a solution inlet and an air-release outlet. After placing the DO electrode, the vessel was completely filled with the ASCB solution (i.e., [DO] = 2.53 × 10−4 mol L− 1 at 25 °C), sealed, and immersed in a water bath in a constant-temperature (25 °C) incubator. The air-saturated solution was prepared by bubbling air through a NaHCO3/Na2CO3 buffer solution for N 24 h using a small air pump. It was ensured that vapor was not present in the vessel before experiments because the partitioning of O2 between the liquid and vapor phases could cause complications in interpreting the measured DO values. After the vessel was stored in the incubator, simultaneous measurements of DO and temperature were made. The solution in the vessel was constantly stirred by a magnetic stirrer during the experiment. Temperature fluctuations were monitored during each run, which lasted up to 30 days, and were always within 0.2 °C for individual runs. We also ran several blank experiments where the entire experimental procedure was conducted in the same way as in the real experiments, but with a low DO concentration and no rock powder in the system. As a result, the DO concentrations were initially 2.94 × 10− 5 mol L− 1, 3.25 × 10− 5 mol L− 1 after 1 day, and 3.50 × 10−5 mol L−1 after 40 days. These blank experiments indicated little leakage.

Table 2 Mineral compositions of the studied sedimentary rocks by X-ray powder diffraction analysis. Rock sample

Akeyo Formation

Toki Lignite-Bearing Formation

Tuffaceous sandstone

Greywacke

32.90–33.00 m 34.90–35.00 m 95.50–95.63 m 125.00–125.13 m X-ray powder diffraction Bulk sample Quartz Plagioclase Hornblende Smectite Gypsum Clinoptiolite Clay-size fraction Quartz Plagioclase Kaolin mineral Smectite Clinoptiolite

− ++

− −

− −

− − −

+ ++ − −

−

−

+++ −

++ −

++ ++ − −

+++

+++: 2500-5000cps, ++: 500-2500cps, +: 250-500cps, −: b250cps.

− − − + ++

2.3. DO diffusion–consumption experiments on intact rock samples The electrochemical technique was applied to measure the effective diffusion coefficients of DO and the oxidation rates of reducing agents by DO in the sedimentary rocks. Full details of the experimental methods and computations used in the present study are given in Manaka et al. (2000), and are briefly reviewed here. Fig. 2 illustrates the experimental apparatus for measuring the diffusion and consumption of DO in the sedimentary rocks by the electrochemical technique. The working electrode (WE) is a Pt electrode mounted at the bottom of the experimental cell. The surface area of the working electrode is 3.14 cm2. The counter electrode (CE) is a Pt electrode at the top of the experimental cell. The saturated calomel electrode (SCE) is used as the reference electrode. The capacity of the experimental cell is about 15 mL. The inside of the diffusion cell was filled with the ASCB solution (initial pH ~9.3). The WE was cathodized at −400 mV using a potentiostat. The diffusion cell was kept at 25 °C during the experiments by using a temperature-controlled incubator. Each experiment was performed until the current density produced by the DO flux reached a steady state. In this technique, the effective diffusion coefficient of DO and the oxidation rates of reducing agents by DO in the sedimentary rock were determined by comparing the calculated value with the observed

Table 3 Whole-rock chemistry of the studied sedimentary rocks. Rock sample

Akeyo Formation

Toki Lignite-Bearing Formation

Tuffaceous sandstone

Greywacke

32.90–33.00 m 34.90–35.00 m 95.50–95.63 m 125.00–125.13 m Fusion ICP and FeO titration SiO2 (wt.%) 57.7 (wt.%) 0.6 TiO2 (wt.%) 14.5 Al2O3 FeO (wt.%) 3.2 (wt.%) 1.7 Fe2O3 MgO (wt.%) 2.3 CaO (wt.%) 3.2 (wt.%) 2.3 Na2O K2O (wt.%) 1.1 LOI* (wt.%) 11.6 Total 98.2

59.6 0.6 14.2 2.0 2.3 1.8 2.9 2.3 1.3 11.6 98.7

Combustion-infrared absorptiometric method Total S (wt.%) 0.56 1.06 Pyrite-S (wt.%) 0.20 0.32 a 0.74 Sulfate-S (wt.%) 0.36 Pyriteb (wt.%) 0.37 0.60 a b

Sulfate-S = Total S − Pyrite-S. Pyrite = Pyrite-S × 1.87.

52.3 1.0 17.6 1.4 5.0 4.1 4.5 2.5 1.4 11.0 100.6

57.5 0.9 18.8 1.2 3.2 1.6 3.5 3.3 1.9 7.8 99.7

0.17 0.19 – 0.36

0.041 0.025 0.016 0.047

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Table 4 Summary of the results and interpretation of DO consumption experiments performed on the powder samples of sedimentary rocks. Rock sample

Akeyo Formation

Toki Lignite-Bearing Formation

Tuffaceous sandstone

Greywacke

32.90–33.00 m Powder sample mass M (g) Solution volume V (L)

Initial solution (mg L−1) DOb (–) pHb (S m−1) ECb Final solution (mg L−1) DOb (–) pHb (S m−1) ECb + K (mg L−1) (mg L−1) Ca2+ (mg L−1) Mg2+ (mg L−1) SO2− 4 Estimated parameters ST × 104a (mol L−1) k × 104a (L mol−1 s−1) a b

95.50–95.63 m

125.00–125.13 m

0.0509

0.0993

0.2003

0.0506

0.1075

0.2003

0.1006

0.2007

0.5000

0.0497

0.1007

0.1997

0.526

0.529

0.528

0.526

0.526

0.529

0.529

0.526

0.529

0.526

0.529

0.528

Solution volume/total surface area (L m−2) 0.126 ± V/SAa

Fe(II) surface sites ST × 108 (mol L−1)

34.90–35.00 m

0.065 ±

0.032 ±

0.141 ±

0.066 ±

0.036 ±

0.070 ±

0.035 ±

0.014 ±

0.367 ±

0.182 ±

0.092 ±

0.001

0.001

0.0002

0.002

0.001

0.0004

0.002

0.001

0.0004

0.004

0.002

0.001

75

146

295

43

91

168

58

116

286

10

20

40

8.11 9.41 0.217

8.11 9.41 0.217

8.11 9.41 0.217

8.11 9.53 0.221

8.11 9.56 0.222

8.11 9.53 0.221

8.11 9.49 0.221

8.11 9.49 0.221

8.11 9.49 0.221

8.11 9.41 0.222

8.11 9.41 0.222

8.11 9.41 0.222

4.37 9.29 0.217 0.15 0.41 0.11 1.00

1.73 9.25 0.215 0.25 0.75 0.21 2.09

0.00 9.22 0.215 0.40 1.64 0.36 4.29

4.65 9.52 0.224 0.18 0.44 0.10 1.69

3.86 9.53 0.225 0.26 1.10 0.23 3.92

2.78 9.49 0.223 0.48 1.38 0.32 6.66

1.72 9.42 0.216 0.18 1.15 0.33 0.15

1.45 9.41 0.222 0.27 1.85 0.47 0.21

0.00 9.38 0.218 0.45 1.66 0.63 0.40

4.97 9.33 0.220 0.26 0.58 0.08 0.14

3.73 9.32 0.218 0.33 0.99 0.15 0.13

1.60 9.31 0.216 0.40 1.31 0.21 0.24

14 ± 5 2.18 ±

30 ± 17 2.46 ±

67 ± 189 2.60 ±

6 ± 0.7 5.35 ±

10 ± 2 3.82 ±

8 ± 0.6 14.6 ±

36 ± 23 3.22 ±

33 ± 51 2.53 ±

77 ± 492 2.28 ±

7±3 4.68 ±

11 ± 3 4.39 ±

18 ± 20 4.07 ±

0.97

1.67

7.86

0.97

0.85

2.82

2.39

4.43

15.5

2.41

1.38

5.83

95% confidence level. Measurements at 25 °C.

current density changes. The details of this calculation method are explained in the following section. 2.4. Analytical techniques The DO in the solutions was measured with a DO electrode (DKKTOA OE-270AA). Systematic error associated with this electrode was b0.02 mg L−1. The pH, electrical conductivity (EC), and temperature of the solutions at the beginning and end of the experiment were measured using two different electrodes (pH: DKK-TOA GST-2729C; EC: DKK-TOA CT-27112B). The pH electrode was calibrated using standard buffer solutions (pH = 6.86, 9.18, and 10.02 at 25 °C) before use. The EC meter was tested using deionized distilled water and 0.1 M KCl. The measurement precisions for pH, EC, and temperature were b 0.02 pH units, b0.5%, and b0.2 °C, respectively. After aliquots of the solution sample were removed for the pH and EC measurements, the residual sample (55 mL) was filtered through a 0.2 μm filter. The chemical compositions (K+, Mg2 +, Ca2 +, SO24 −) of the solution sample were analyzed using an ion chromatograph (Shimadzu). The measurement error of the ion chromatograph method was within ~5%. 3. Mathematical formulation 3.1. Kinetics of DO reduction by Fe(II)(aq)

Fig. 1. Schematic of the experimental set-up for the DO consumption experiments on the Mizunami sedimentary rocks.

The kinetics and mechanisms of electron-transfer reactions between Fe(II) species and DO are understood relatively well. The reduction of DO by ferrous silicates has been documented for basalt (White et al., 1985) and for individual ferrous silicates such as biotite, augite, and hornblende (White and Yee, 1985). A coupled heterogeneous redox

M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

39

Fig. 2. Schematic of the experimental set-up for the DO diffusion and consumption experiments on the Mizunami sedimentary rocks.

reaction involving the reduction of O2 to H2O can be described by the stoichiometric surface reaction

where C0 is the initial DO concentration in the system at t = 0. Substituting Eq. (4) into Eq. (3) gives.


 h i 1 1 1 1 Fe2þ ; Mzþ þ O2 þ Hþ → Fe3þ þ Mzþ þ H2 O; z 4 z 2

dC ¼ −k∙fST −4ðC 0 −C Þg∙C: dt

ð1Þ

where M is a cation of charge z, and [Fe2+, 1z Mzþ] and [Fe3+] refer to the structural Fe at the mineral surface that undergoes a reaction with aqueous species. White and Yee (1985) presented evidence indicating that reaction rates for the reduction of DO by structural Fe(II) are faster than those for the reduction of DO by Fe(II) in solution: 1 3 Fe2þ þ O2 þ H2 O→FeOOH þ 2Hþ : 4 2

ð2Þ

Wehrli (1990) reviewed redox reactions at mineral surfaces to interpret the oxidation rates of dissolved and adsorbed Fe(II) species, and developed a second-order rate law: dC ¼ −k½FeðIIÞS C; dt

ð3Þ

where C is the DO concentration (mol L−1) at time t (s), k is the secondorder rate constant (L mol−1 s−1), and [Fe(II)]S is the concentration (mol L−1) of unreacted Fe(II) sites on the mineral surface. In addition, the k values are associated with the standard potential of the redox couple for oxidation of dissolved and adsorbed Fe(II) species. Rivas-Perez et al. (2003) proposed that [Fe(II)]S is related to initial DO concentration (C0) in a closed system with respect to DO, as follows: ½ FeðIIÞS ¼ ST −4ðC 0 −C Þ;

ð4Þ

ð5Þ

Rivas-Perez et al. (2003) rearranged and integrated this expression as follows: C¼

4C 20 −ST ∙C 0 : 4C 0 −ST ∙ expðk∙t∙ðST −4C 0 ÞÞ

ð6Þ

Given a time series of DO concentration from a batch experiment in a closed system with respect to DO, Eq. (6) can determine the total concentrations of Fe(II) surface sites (ST) and the DO consumption rate constants (k) for sedimentary rocks. 3.2. Analytical model for DO diffusion–consumption experiments Dissolved oxygen is consumed by cathodic reduction at a Pt electrode attached to the intact rock, and measured using a potentiostatic technique. The consumption can be described as follows:

O2 þ2H2 O þ 4e− →4OH− :

ð7Þ

Eq. (7) shows that the consumption rate of DO in sedimentary rocks is reflected by a reduction in current through the Pt electrode. This principle was applied to measure the effective diffusion coefficients of DO and the oxidation rates of reducing agents by DO within the intact rock.

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The DO that diffuses out of the bottom surface of the sample is consumed by the Pt electrode in contact with the downstream surface, which has the boundary condition

diffusion–reaction and batch experiments, this study adopts non-linear least squares regression analysis using the following expression:

CðL; tÞ ¼ 0;

SðxÞ ¼

ð8Þ

where C is the concentration of DO (mol m ) in the pore water, L is the thickness of the sample (m), and t is time (s). The top surface of the sample is exposed to the ASCB solution during the experiments (Fig. 2) and can be described by the upstream boundary condition: Cð0; tÞ ¼ C 0 :

ð9Þ

Prior to the experiment, samples were kept in the ASCB water and then mounted in the diffusion cell. During setup, the samples were exposed to air for a short time. Because this exposure might have affected the DO distribution within the sample, we assumed that the initial DO concentrations within the sample would show a linear distribution of DO concentration: C 0 −C 0;d  x; Cðx; 0Þ ¼ C 0 − L

ð10Þ

where x is the distance (m) from the source of DO in the diffusion direction and C0,d is the initial concentration at the downstream surface of the sample. The DO transport through the sample can be described as 2

∂C ∂ C ¼ De  2 þ f ðC Þ; 0bxbL; ∂t ∂x

ð11Þ

0btb∞;

where ε is the porosity of the sedimentary rock sample and De is the effective diffusion coefficient of DO (m2 s−1). The term f(C) represents the consumption rate of DO due to oxidation of the Fe(II) species. Accordingly, Eq. (11) can be rewritten using Eq. (5) as follows: 2

ε

∂C ∂ C ¼ De  2 −k  ½ST −4  ðC 0 −C Þ  C; 0bxbL; ∂t ∂x

0btb∞:

ð12Þ

The problems defined by Eqs. (8)–(12) were numerically solved by the finite element method to obtain the temporal distribution of DO concentrations within the sample. In the diffusion–consumption experiments, the diffusive flux of DO is monitored as the current density by the Pt electrode at the downstream (bottom) end of the sample. The current density is related to the DO diffusive flux at the downstream end by the following expression: J d ¼ −De 

 ∂C  1 I ¼  ; ∂x x¼L n  F A

i

i¼1

−3

ε

2 M
 X Y ðt Þ−Y i ðt; pÞ

ð13Þ

where Jd is the diffusive flux of DO at the downstream end of the sample, I is the current (A), A is the surface area of the Pt electrode (m2), n is the number of electrons supplied by the reduction of 1 mole of O2 (i.e., n = 4 by Eq. (7)), and F is the Faraday constant (96,485C mol−1). In the interpretation of the experiments, the current densities I/A calculated by Eq. (13) using trial values of De and k are fitted against the current densities measured by the Pt electrode. The value of ST is given as the total concentration of Fe(II) sites in the intact rock sample. The partial derivative of C with respect to x in Eq. (13) is obtained by the numerical differentiation of C, which is obtained by solving the problem defined by Eqs. (8)–(12). 3.3. Interpretation of experimental data In the diffusion–consumption experiments, the measured quantity is the current density I/A, representing DO diffusive flux at the downstream end of the sample, whereas in the batch experiments it is the temporal variation in the DO concentration. In the interpretation of both the

wi

;

ð14Þ

where S is the sum of the squared weighted residuals between the measured and calculated data (Yi* and Yi, respectively), p is the vector of the parameters to be identified, wi is the standard deviation of the i-th measurement data, and M is the number of measured data. In diffusion–reaction experiments, the parameters to be identified are De and k. In the batch experiments, the parameters of interest are ST and k. 4. Results 4.1. Consumption of DO in sedimentary rocks Table 4 shows the results of the DO consumption experiments with rock powder. The changes in DO concentrations during the experiment are shown in Fig. 3. All the data show a significant decrease in DO concentration for each experiment. However, there are differences in the final concentrations between experiments. For each of the samples, the differences in concentration may result from differences in the mass of the powder sample reacted in each experiment; i.e., the greater the mass, the faster the consumption of DO. For example, in the experiments on samples from 32.90–33.00 m depth, DO concentrations range from less than detection limits to 1.37 × 10−4 mol L−1 (Fig. 3a). When samples from different collection depths are compared, the above relationship between the mass and final concentration is not satisfied; i.e., the differences are unlikely to result from the variable chemical compositions of the samples. Alternatively, the differences may result from differences in reactivity between experiments. The degree of reactivity relates to the content and composition of the reduced minerals, which vary with the mineralogy of the tested samples. For example, the final DO concentrations were 0.54 × 10−4 mol L− 1 at 95.50–95.63 m, 0.54 × 10− 4 mol L−1 at 32.90–33.00 m, 1.17 × 10−4 mol L− 1 at 125.00–125.13 m, and 1.45 × 10−4 mol L−1 at 34.90–35.00 m in experiments on 0.1 g of powder sample (Fig. 3). In the solution chemistry component of these experiments, the pH value was almost unchanged in the solutions because of carbonate buffer effects in the alkaline solution, and EC was also almost unchanged. The final SO24 − concentrations in each sample increased with an inconcentracrease in the mass of the powder sample reacted. The SO2− 4 tions were high in the 32.90–33.00 m and 34.90–35.00 m samples, and low in the 95.50–95.63 m and 125.00–125.13 m samples. Similarly, the final concentrations of the cations Mg2+, K+ and Ca2+ for each sample increased with an increase in the mass of the powder sample reacted. The Ca2+ concentrations were higher than the Mg2+ and K+ concentrations. The differences in the mineralogy of the samples made only a small contribution to the differences in cation concentrations. Based on the relationship between the final concentrations of K+, Ca2 +, and the mass of powder sample reacted, the cations Mg2+, and SO2− 4 and anions that formed during the experiment must have originated from mass transfer between the mineral phases present; i.e., SO2− 4 originated from the dissolution of sulfate minerals such as gypsum and/or from the oxidation of pyrite, Mg2+ originated from the dissolution of hornblende and/or smectite, K+ originated from the dissolution of plagioclase and/or smectite, and Ca2+ originated from the dissolution of sulfate minerals, plagioclase, clinoptiolite, and/or smectite. To determine the contributors to DO consumption in the experiments using powder samples, it is necessary to assess the DO consumption reactions involving Fe(II) minerals. First, we evaluate the DO consumption reaction of pyrite and Fe(II)-silicate minerals such as smectite in a powder sample. The rate of DO consumption by pyrite can be estimated from the relationship between consumed DO and

M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

0.0003

0.0003

32.90-33.00 m

-1

DO (mol L )

41

34.90-35.00 m

0.0002

0.0002 0.05g

0.05g 0.1g

0.1g 0.0001

0.2g

0.0001 0.2g

(a) 0

(b) 0

0

100 200 300 400 500 600 700 800

0.0003

0

100 200 300 400 500 600 700 800

0.0003

-1

DO (mol L )

95.50-95.63 m

125.00-125.13 m

0.0002

0.0002 0.05g 0.1g

0.1g 0.0001

0.2g

0.0001 0.2g 0.5g

(c) 0

(d) 0

0

100 200 300 400 500 600 700 800

0

100 200 300 400 500 600 700 800

Time (hours)

Time (hours)

Fig. 3. Temporal changes in DO concentration for samples taken from depths of (a) 32.90–33.00 m, (b) 34.90–35.00 m, (c) 95.50–95.63 m, and (d) 125.00–125.13 m. The points and curved lines represent measured data and fitted lines, respectively.

produced sulfate during the oxidation of the pyrite in the powder sample. The concentration of sulfate in the experimental solution is generally increased by the consumption of DO through the reaction FeS2 þ

15 3 ‐ O2 þ4 OH– →FeðOHÞ3ðamÞ þ2SO4 2 þ H2 O; 4 2

ð15Þ

If gypsum dissolution by reaction (16) is the dominant DO-consuming reaction, then the molar ratio of the increase in Ca2+ to the increase 2+ and SO2− in SO2− 4 increase is 1 and the changes in Ca 4 content should lie on the line in Fig. 5. Fig. 5 also shows the data obtained from the experimental solutions. The data for the 32.90–33.00 m powder samples 1.5 x 10

CaSO4  H2 O⇄Ca2þ þSO4 2− þH2 O;

ð16Þ

-4

FeS + 15/4 O + 7/2 H O 2

2

2

Fe(OH) + 2 SO 3

SO42- (mol L -1 )

where the ferric iron is quantitatively precipitated as amorphous Fe(OH)3(am); this assumption does not affect the coefficients in the pyrite oxidation reaction. If pyrite oxidation by reaction (15) is the dominant reaction, then the molar ratio of the decrease in consumed DO to the increase in produced SO24 − is 0.53 (8/15) and the changes in DO and sulfate contents should lie on the line in Fig. 4. For example, when 250 μM DO in an experimental solution reacts with pyrite, the changing DO content proceeds along the line and eventually becomes zero, and the concentration of sulfate is expected to increase to about 130 μM. Fig. 4 shows the relationship between sulfate and DO concentrations for the experimental solutions. The powder samples from 32.90– 33.00 m and 34.90–35.00 m showed an increase in sulfate concentration with a decrease in DO concentration during the experiment. These points fall below the line. In contrast, the powder samples from 95.50–95.63 m and 125.00–125.13 m show no increase in sulfate concentration. This result suggests that the DO decrease in this case is not simply due to the oxidation of pyrite; consequently, an alternative explanation is required. Thus, we assess the derivation of sulfate from gypsum in a powder sample. The concentration of sulfate is increased due to the dissolution of gypsum through the following reaction:

1 x 10

-4

5 x 10

-5

24

+4H

+

Oxidation of pyrite

0 0

1 x 10

-4

2 x 10

-4

-1

ΔDO (mol L ) Fig. 4. Relationship between dissolved oxygen (DO) content and SO2− content in the 4 in the experimental solution is produced experimental solutions. When the SO2− 4 mainly by reaction between pyrite and the experimental solution (by the reaction indicated on the figure), the DO–SO2− relationships should lie on the solid line. Solid 4 circles represent the samples from 32.90–33.00 m depth, solid squares the samples from 34.90–35.00 m depth, solid diamonds from 95.50–95.63 m depth, and open circles from 125.00–125.13 m depth.

42

M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

lie on the line, which suggests that the source of the sulfate in this case is gypsum. The final Ca2+ and SO2− 4 concentrations indicate that the gypsum in this sample has been completely dissolved. For the 34.90– 35.00 m samples, the analysis points lie above the line, which suggests that the source of sulfate is both the dissolution of gypsum and the oxidation of pyrite. Based on the relationship between the concentration of sulfate minerals in the powder sample (Table 3) and the sulfate concentration in the experimental solution (Table 4), the experimental data for the 34.90–35.00 m samples indicate 14%–36% DO consumption by pyrite oxidation. The 95.50–95.63 m and 125.00–125.13 m samples show an increase in Ca2+ with no increase in sulfate concentration, suggesting that the source of the Ca2+ is plagioclase, clinoptiolite, and/or smectite. Thus, these results indicate that the oxidation of pyrite was only a significant contributor to DO consumption for the 34.90– 35.00 m samples, and that the majority of DO consumption in the experiments was due to the oxidation of Fe(II)-bearing minerals such as smectite and/or hornblende. The fitted curves derived from Eq. (6) agree well with the measured DO concentrations shown in Fig. 3. However, the curves calculated for the experiments using a mass of 0.2 g and of 0.5 g tend to deviate from the data. The results of the parameter estimations for each experiment are summarized in Table 4. The values of ST range from 10−4 to 10−3 mol L−1. The values of k estimated from samples at a given collection depth are similar, but these differ between samples from different collection depths. In general, the values in the 95% confidence interval for the parameters of ST and k are larger than the ST and k values estimated. This can be explained by the interrelation between the ST and k parameters during the analytical solution of Eq. (6). The k values reported in the literature also have large values in the 95% confidence interval (Table A1).

samples with a thickness of 3.65, 3.25, and 3.05 mm are 60, 57, and 83 nA cm−2, respectively. The current densities at a steady state tend to decrease with the thickness of the sample. This implies that the amount of DO reaching the Pt electrode is decreased by increasing the consumption of DO due to an increase in diffusion paths through the sample. It should be noted that this comparison is only valid at a given collection depth, which may be due to differences in reactivity between samples. For example, the current densities at a steady state are different for samples from different collection depths. However, differences in samples from the same collection depth may be explained by heterogeneous samples; i.e., Fe(II)-bearing minerals are unevenly distributed in samples due to the thinly sliced coin-shaped samples, and the diffusivity is variable due to heterogeneous pore structure between samples. Fig. 6 shows the fitted curves derived from the numerical model defined by Eq. (13), which agree well with the measured current density. 150

50 Thickness = 3.25 mm

100 50 0 150

CaSO42H2O→Ca + SO

4

+ 2H O 2

(b)

Measured Fitted

50

Current density (nA/cm 2)

-4

2-

Measured Fitted

Thickness = 3.05 mm

100

The changes in current density with time in the coin-shaped samples are shown in Fig. 6. These current densities changed in the form of a breakthrough profile and reached constant values after about 7.2 × 104 s in all experiments. The current density at a steady state for each experiment is listed in Table 5. As an example, we discuss the current density changes in the samples from 32.90–33.00 m depth. The average values of the current densities at a steady state in the

2+

(a)

0 150

4.2. Diffusion and consumption of DO in sedimentary rocks

1 x 10

Measured Fitted

100

Thickness = 3.65 mm

(c)

0 200 Measured Fitted

150 100 50 Thickness = 3.45 mm

(d)

0 600 Measured Fitted

400

SO42- (mol L -1 )

200 Thickness = 3.65 mm

5 x 10

-5

(e)

0 150

Dissolution of gypsum

Measured Fitted

100 50 Thickness = 4.40 mm

(f)

0 800

0 0

5 x 10

-5

1 x 10

Thickness = 3.00 mm

Measured Fitted

-4

400

Ca2+ (mol L -1) Fig. 5. Relationship between Ca2+ content and SO2− content in the experimental 4 in the experimental solution is produced mainly by dissolution of solutions. If the SO2− 4 2+ gypsum (by the reaction indicated on the figure), the Ca –SO2− relationships should 4 lie on the solid line. Solid circles represent the samples from 32.90–33.00 m depth, solid squares the samples from 34.90–35.00 m depth, solid diamonds from 95.50–95.63 m depth, and open circles from 125.00–125.13 m depth.

(g)

0 0

2x10

4

4x10

4

6x10

4

8x10

4

1x10

5

Time (sec) Fig. 6. Temporal changes in current density in samples from depths of 32.90–33.00 m (a, b, c), 95.50–95.63 m (d, e), and 125.00–125.13 m (f, g).

M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

43

Table 5 Summary of the results and interpretation of DO diffusion and consumption experiments performed on the cored samples of sedimentary rocks. Rock sample

Akeyo Formation

Toki Lignite-Bearing Formation

Tuffaceous sandstone

Greywacke

32.90–33.00 m

95.50–95.63 m

125.00–125.13 m

Sliced core sample Thickness (mm)

3.25

3.05

3.65

3.45

3.65

4.40

3.00

Initial solution DOa pHa ECa

8.11 9.27 0.215

8.11 9.27 0.215

8.11 9.27 0.215

8.11 9.27 0.215

8.11 9.27 0.215

8.11 9.37 0.221

8.11 9.38 0.221

Current density at 24 h I/A (nA cm−2)

57

83

60

92

164

62

34

Solution volume/total pore areab V/SA × 105 (L m−2)

0.74 ± 0.12b

0.74 ± 0.12

0.74 ± 0.12

0.64 ± 0.20

0.64 ± 0.20

1.89 ± 0.71

1.89 ± 0.71

Fe(II) surface sites (mol L−1) ST × 104

12.9

12.9

12.9

6.36

6.36

1.95

1.95

2.69 ± 0.17 3.76 ± 1.03

3.04 ± 0.40 1.36 ± 2.02

4.72 ± 0.52 13.4 ± 3.79

3.91 ± 0.16 5.01 ± 1.58

6.30 ± 0.70 8.42 ± 6.23

3.43 ± 0.10 18.5 ± 3.57

4.01 ± 0.32 59.7 ± 12.4

(mg L−1) (–) (S m−1)

b

Estimated parameter De × 1011 (m2 s−1) (L mol−1 s−1) k × 104 a b

Measurements at 25 °C. 95% confidence level.

Table 5 summarizes the conditions and results of the parameter estimation for each experiment. The estimated values of De for the DO are approximately equal for all samples. The estimated values of k range from 10−4 to 10−3 L mol−1 s−1. In general, the values in the 95% confidence interval for the parameter De are less than the estimated De values. Most of the values in the 95% confidence interval for the parameter k are less than the estimated k values. In addition, the ratio of the value of the 95% confidence interval to the value of its parameter in the diffusion–consumption experiments using coin-shaped samples is less than that in the consumption experiments using powder samples. Moreover, we plan to conduct further studies to reduce the value of the 95% confidence interval. From preliminary analyses, we expect that this reduction may be made by increasing the length of the coin-shaped sample by about 10 times. That is, the longer the transient state, the smaller the value of the 95% confidence interval.

Nernst equation is E = E0 + 0.059 log[M+z](1/z). Assuming the same conditions from White and Yee (1985), the surface oxidation half-cell standard potentials are calculated to lie between +0.43 and +0.65 V. From the straight line in Fig. 7, it is possible to estimate the logarithm of the rate constants against the estimated potentials. The values of the logarithm of the rate constants range from −3.22 to +0.11 (Fig. 7). These values fall between those for adsorbed Fe(II)(aq) and those for Fe2+, suggesting that structural Fe(II) is less reactive than adsorbed Fe(II)(aq), but is more reactive than Fe2+. Fig. 8 compares the second-order rate constants for Fe(II) oxidation reactions for the present study and for previous work (Table A1). The rate constants were calculated using data from previously published DO consumption experiments (White and Yee, 1985; White et al., 1985), obtained using digitally scanned images of plots of DO

5. Discussion

8 Fe(OH)2+/Fe(OH)2

5.1. Comparison of rate constants for DO consumption in closed systems with respect to DO

4

log k

The results of this study suggest that Fe(II)-bearing minerals such as smectite and hornblende were the primary contributor to DO consumption in the experiments using powder samples. That is, DO is consumed by the heterogeneous redox reaction between Fe(II)-bearing minerals and DO. Thus, second-order rate constants for the oxidation of structural Fe(II) at the surface of minerals such as smectite can be compared with second-order rate constants for the oxidation of ferrous Fe species (as indicated by Rivas-Perez et al., 2003; Perez et al., 2005). A plot of the logarithm of these rate constants against the redox potentials produces a straight line (Fig. 7), suggesting that the reaction mechanism is an outer-sphere electron-transfer whereby the hydration shell of the Fe(II)(aq) species remains intact during the electron transfer (Wehrli, 1990). The redox couples involving Fe(II) surface complexes and the values of the associated redox potential are summarized in Table 6. Table 6 also includes the standard half-cell potential for structural Fe(II) on the surface of silicate minerals, as estimated by White and Yee (1985). However, the potential was recalculated because their equation (Eq. 11 in White and Yee, 1985) was incorrect—the Nernst equation from the half-cell was reported as [Fe+2, 1z Mþz ]silicate → [Fe+3]silicate + 1z Mþz + e−, whereas the correct

6

2

Fe(OH)2+/Fe(OH)+ +

(=FeO) Fe /(=FeO) Fe 2

0 ≡ Si-Fe3+ /≡ Si-Fe2+

-2 -4 -6

2

standard half-cell potential for strctural Fe(II) on the silicate mineral surface

0

0.2

0.4

0.6

3+

Fe /Fe

2+

0.8

0

E (V) Fig. 7. Relationship between the logarithm of rate constants for Fe(II)-oxygenation reactions occurring in solution and the standard redox potentials. The field held between by dotted lines represents the values of the logarithm of the rate constants for structural Fe(II) on the surface of silicate minerals. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

44

M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

Table 6 Standard half-cell potentials and second-order rate constants for the oxidation of aqueous Fe(II) species and Fe(II) species on mineral surfaces. Redox couple

O2/O− 2 3+

Fe /Fe2+ Fe(OH)2+/Fe(OH)+ Fe(OH)+ 2 /Fe(OH)2 (_FeO)2Fe+/(_FeO)2Fe \Fe2+ `Si\ \Fe3+/`Si\

E0

log k

(V)

(M−1 s−1)

–0.16 0.771 0.34 –0.02 0.4005 0.43–0.65

–5.1 1.4 6.9 0.7 –3.22 to +0.11

Referencea

1 2 2 3 4, 5 6

a References: (1) Sawyer and Valentine (1981); (2) calculated from Singer and Stumm (1970); (3) Millero et al. (1987); (4) estimated value for goethite from Tamura et al. (1976); (5) Perez et al. (2005); (6) estimated from White and Yee (1985).

concentrations against reaction time. We estimated k and ST for single Fe(II) silicate minerals and basalts according to Eq. (6). Where necessary, the cited rate constants were recalculated so as to be presented in consistent units of mass, solution volume, and time (i.e., L mol−1 s−1). The majority of the values for k fall within the range of k obtained from redox potentials for structural Fe(II) on the surface of silicate minerals estimated by White and Yee (1985). However, some of the constants estimated from the data of the present study and presented by Perez et al. (2005) are below this range. This may be explained by differences in Fe(II)-bearing minerals, such as smectite (this study) and biotite, augite, and hornblende (White and Yee, 1985). The minimum value of the data (Perez et al., 2005) is also lower than that for the Fe3+–Fe2+ redox couple (log k = −5.1). 5.2. Comparison of kinetic parameters estimated from experiments using powder and coin-shaped samples Our results show that many of the second-order rate constants for the oxidation of Fe(II)-bearing minerals (e.g., smectite) in experiments using powder samples fall within the range of the second-order rate constants for the oxidation of Fe(II)-silicate minerals estimated by White and Yee (1985). Therefore, the first step to applying the results

0 -1

5.3. Correlation between the De of DO and the De of HTO

log k

-2 -3 -4 -5

of the present study to the natural system is to investigate whether the k value obtained from the DO diffusion–consumption experiments using coin-shaped samples falls within the range of, or equals the k value obtained from the experiments using powder samples. When we compare the k value obtained from the DO diffusion–consumption experiments using coin-shaped samples with the k value obtained from the DO consumption experiments using powder samples, we find that (i) there is no difference in the reactivity of the reaction sites estimated from both experiments, and (ii) the number of reaction sites given in the diffusion–consumption experiments using coinshaped samples is less than that estimated from consumption experiments using powder samples. The discrepancy in the number of reaction sites arises because new reaction sites are created by milling in the consumption experiments using powder samples, whereas no new reaction sites are created in the diffusion–consumption experiments using the coin-shaped samples, and only the original sites along the water flow paths are present. The k values obtained from diffusion–consumption experiments using coin-shaped samples are within the range of the k values obtained from consumption experiments using powder samples. In addition, many of the k values obtained from the diffusion–consumption experiments using coin-shaped samples fall within the range estimated by White and Yee (1985; Fig. 10). We now focus on the kinetic parameter ST. To effectively compare the ST values obtained from consumption experiments using powder samples, we multiply the obtained values of ST by the ratio of the solution volume (V) to the sample surface area (SA). The average values of ST × V/SA (mol m− 2) for the 32.90–33.00 m, 34.90–35.00 m, 95.50– 95.63 m, and 125.00–125.13 m powder samples are 1.97 × 10−4, 0.62 × 10-–4, 1.59 × 10−4, and 2.04 × 10−4, respectively. The 95% confidence limits are 0.36 × 10−4, 0.62 × 10−4, 1.60 × 10−4, and 0.84 × 10−4, respectively. The given values of ST × V/SA (mol m−2) for the 32.90– 33.00 m, 95.50–95.63 m, and 125.00–125.13 m coin-shaped samples are 9.48 × 10−8, 4.06 × 10–8, and 3.67 × 10−8, respectively. These values are the Fe(II) surface site concentrations estimated from the physical surface area. In general, the values of ST × V/SA for the powder samples are greater than those for the coin-shaped samples. This suggests that the difference between the two sample forms relates to the difference in the number of reaction sites, where the reaction sites in the powder samples are both the original sites and the new sites that formed during milling. The average values from the experimental data with the powder samples give estimates of ST, with the majority of values around 10−4 mol m−2. Perez et al. (2005) suggested that this is because the Fe(II) sites within the bulk mineral phases (i.e., below the mineral surfaces probed by the BET-N2 analysis) are also contributing to the reduction of molecular O2. It is possible that these sites are in a damage zone that formed during milling.

White and Yee (1985) White et al. (1985) Rivas-Perez et al. (2003) Perez et al. (2005) This study (powder) This study (whole rock)

-6 -7 Fig. 8. Comparison of second-order rate constants in this study and from previous research.

Our results indicate that DO in the pore-water in sedimentary rocks is consumed by the oxidation of Fe(II)-minerals entering the rock matrix by diffusion. However, the diffusion behavior of DO in the porewater in rocks, and especially the De of DO, has not been adequately examined experimentally. Therefore, we include an investigation of the De of DO in this study. Because the diffusion coefficient (D0) of DO in free water (2.50 × 10−9 m2 s−1; Himmelblau, 1964; Wise and Houghton, 1966) is very similar to the D0 of HTO in free water (2.49 × 10−9 m2 s− 1; McCall and Douglass, 1965), we can compare the diffusion behavior of DO and HTO in pore-water in porous media. To confirm the relationship between the De of DO and the De of HTO in sedimentary rocks, similarities in the diffusion migration characteristics are emphasized. In most cases, only the overall porosity (ε) of the porous medium can be determined because the pore size distribution and tortuosity are unknown for sedimentary rocks. Therefore, the

M. Manaka, M. Takeda / Journal of Contaminant Hydrology 193 (2016) 35–47

relative diffusivity (De/D0) is commonly defined as an empirical function of ε alone: De =D0 ¼ εm ;

parameter from the changes in DO concentration in just one experiment and in the same single sample. As illustrated in Fig. 6, the analytical results in this study indicate that it is possible to estimate the values of these parameters from the changes in DO concentration in diffusion– consumption experiments. Therefore, it is possible to measure the values of kinetic parameters for geological media in a laboratory. Although this analytical method is useful when investigating the time evolution of DO concentration in geological porous media such as sedimentary rocks, it needs further investigation. For example, the oxidation rate of Fe(II)-silicate minerals decreases with time because an increase in leached components leads to an increase in the degree of saturation of pore water. Variation in the oxidation rate of Fe(II)-silicate minerals can strongly affect not only the change in porosity and permeability of rocks, and the resultant flow of pore water, but also the precipitation rate of secondary minerals. In addition, the oxidation rate of Fe(II)-silicate minerals differs with the reactivity of minerals. Differences in the oxidation rate can affect redox conditions in groundwater. Thus, further research is required to explain these phenomena.

ð17Þ

where m is an empirical exponent (e.g., Grathwohl, 1998). Fig. 9 shows the relationship between De/D0 and ε for DO and HTO in sedimentary rocks. The relative diffusivity of HTO varies with respect to porosity in sedimentary rocks and seems to depend on the sample locality. For example, the value of m is 3/2 in the granodiorite and altered granodiorite at Kamaishi, Japan (Sato, 1999), is about 3 in Opalinus Clays in the Benken area (Van Loon et al., 2003b, 2004b, 2005), and about 5/2 in Opalinus Clays at Mont Teri (Van Loon et al., 2003a, 2004a, 2004b, 2005; Wersin et al., 2004; Yllera et al., 2004; Soler et al., 2008; Samper et al., 2010). The reason for this result is not known at present. However, if we have a sample for which the relative diffusivity of water is known, we can multiply the diffusivity of water by a factor and use this value for geochemical modeling instead of the relative diffusivity of DO. The observations suggest that the value of the exponent m is similar among samples with similar pore structure, even if there is a small variation in porosity. In addition, we estimate that the relative diffusivity of HTO is larger than the relative diffusivity of DO in porous media.

6. Conclusions The effective diffusion coefficients (De) of dissolved oxygen (DO) and the value of kinetic parameters for the oxidation of Fe(II)-bearing minerals in the Mizunami sedimentary rocks were determined by diffusion–chemical reaction experiments using electrochemical techniques in an open system with respect to DO, and batch experiments in a closed system with respect to DO. During the experiments, the values of current density and DO of the experimental solutions were continuously monitored using electrodes. After the experiments, the cation and anion contents in the aliquot of solution extracted from the reaction

5.4. Areas for future study of the consumption and diffusion of DO in sedimentary rocks The consumption and diffusion of DO depend strongly on the physical character and mineralogy of the sedimentary rock. However, because consumption and diffusion of DO occur simultaneously in sedimentary rocks, it is difficult to determine the values of each kinetic

De / D0

10

45

0

10

-1

10

-2

10

-3

De/D0 = ε3/2 = ε2

10

-4

10

-5

10

-6

= ε5/2

= ε4 = ε3

= ε6

= ε5

Intact granodiorite (HTO) Altered granodiorite (HTO) Fracture fillings Tournemire argillite (HTO) Opalinus Clays (Mont Terri) (HTO) Opalinus Clays (Benken area) (HTO) Bure-mudrock (HTO) COx (HTO) Fucoid sandstone (HTO) This study (DO)

10

-2

10

-1

10

0

Porosity Fig. 9. Relationships between the relative diffusivities of DO and HTO, and the porosity of sedimentary rock. The effective diffusion coefficients of HTO in intact granodiorite, altered granodiorite, and fracture fillings are from Sato (1999); Tournemire argillite (Motellier et al., 2007); Opalinus Clays (Mont Terri) (Van Loon et al., 2003a, 2004a, 2004b, 2005; Wersin et al., 2004; Yllera et al., 2004; Soler et al., 2008; Samper et al., 2010); Opalinus Clays (Benken area) (Van Loon et al., 2003b, 2004a, 2005); Bure-mudrock (Melkior et al., 2004); Cox (García-Gutiérrez et al., 2008; Naves et al., 2010); Fucoid sandstone (Havlová and Vopálka, 2010). The effective diffusion coefficients of DO in the Mizunami sedimentary rocks are from this study.

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vessel were analyzed. The important observations and interpretations may be summarized as follows. 1) The results of the diffusion–chemical reaction experiments show that the values of De for DO were within the range 2.69 × 10−11 to 6.30 × 10−11 m2 s−1. 2) The results of the batch experiments show that values of the secondorder rate constant (k, in L mol–1 s− 1) were within the range − 3.66 b log k b −2.83. In contrast, the results of the diffusion–chemical reaction experiments show −3.87 b log k b −2.22. Many of these k values are within the range (−3.22 b log k b 0.11) of the previously published rates for reaction between O2(aq) and Fe(II) surface complexes. 3) The results of the batch experiments show that the average value for the total concentration of reactive sites (ST × V/SA) was about 10−4 mol m−2. In contrast, the value estimated from the physical surface area is ~ 10−8 mol m−2. This difference arises because the batch experiments used powder samples, and therefore new sites that formed during milling were added to the original reaction sites, resulting in an increase in reactive site concentration. Because the diffusion–chemical reaction experiments used intact rock samples, the reaction sites were only the sites that originally existed on water flow paths in the sample, and there was no change in reactive site concentration. in the batch ex4) The decrease in DO with increasing Ca2+ and SO2− 4 periments indicates that the oxidation of pyrite was not a significant contributor to DO consumption, except for the samples from 34.90– 35.00 m depth, and that the oxidation of Fe(II)-bearing minerals (e.g., smectite) was the major contributor to DO consumption in the experiments. 5) Although the D0 of DO is almost equal to the D0 of HTO in free water, the relative diffusivity (De/D0) of DO was less than the relative diffusivity of HTO in porous media. 6) It is possible to determine the values of diffusion and kinetic parameters for sedimentary rocks simultaneously. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.jconhyd.2016.08.007. Acknowledgements The primary part of this research project has been conducted as the regulatory supporting research funded by the Secretariat of the Nuclear Regulation Authority, Japan. The authors wish to thank Takashi Mizuno and JAEA for providing samples of Mizunami sedimentary rock. Finally, an anonymous reviewer and the journal editor are gratefully acknowledged for their constructive and valuable comments. References Banwart, S., Gustafsson, E., Laaksoharju, M., 1994. Large-scale intrusion of shallow water into a vertical fracture zone in crystalline bedrock: Initial hydrochemical perturbation during tunnel construction at the Äspö Hard Rock Laboratory, southeastern Sweden. Water Resour. Res. 30, 1747–1763. Brunauer, S., Emmett, P.H., Teller, E., 1938. Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309–319. Davis, J.A., Kent, D.B., 1990. Surface complexation modeling in aqueous geochemistry. In: Hochella, M., White, A.F. (Eds.), Reviews in Mineralogy, Mineral–Water Interface Geochemistry Vol. 23. Min. Soc. Am., pp. 177–248. García-Gutiérrez, M., Cormenzana, J.L., Missana, T., Mingarro, M., Alonso, U., Samper, J., Yang, Q., Yi, S., 2008. Diffusion experiments in Callovo-Oxfordian clay from the Meuse/Haute-Marne URL, France. Experimental setup and data analyses. Phys. Chem. Earth 33, S125–S130. Giménez, J., Rovira, M., Clarens, F., Casas, I., Duro, L., Grivé, M., Bruno, J., de Pablo, J., 2006. The use of a high-FeO olivine rock as a redox buffer in a nuclear waste repository. J. Contam. Hydrol. 83, 42–52. Grathwohl, P., 1998. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/ Desorption and Dissolution Kinetics. Kluwer Academic Publishing, Boston (224 pp). Grenthe, I., Stumm, W., Laaksuharju, M., Nilsson, A.-C., Wikberg, P., 1992. Redox potentials and redox reactions in deep groundwater systems. Chem. Geol. 98, 131–150.

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