Sorption and desorption of Sr onto a rough single fractured granite

Journal of Contaminant Hydrology xxx (xxxx) xxxx

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Sorption and desorption of Sr onto a rough single fractured granite Jianzheng Zang , Jinlong Wang, Xiaoyuan Han, Haibo Yao, Baofeng Fu, Jian Zhao, Bo Li, Jie Chen ⁎

Northwest Institute of Nuclear Technology, Xi'an City, Shaanxi Province 710024, China

ARTICLE INFO

ABSTRACT

Keywords: Sorption Desorption SR Single fracture Roughness angle

To investigate the migration behavior of Sr (strontium) in granite, a rough-walled single fracture of granite was prepared with the self-built rock splitting apparatus. Surface roughness angle and hydraulic aperture of the fracture were measured by 3D laser scanning and fluid flow experiment, respectively. The sorption and desorption breakthrough experiments of Sr in the single fracture were conducted at different flow rates and initial concentrates of Sr, and the important transport parameters were derived by fitting the BTCs and DPCs. The results suggested that the sorption of Sr onto the fracture surface was a linear and reversible ion-exchange process, unaffected by the variation of flow rate and initial concentrate of Sr.

1. Introduction Granite is the first choice as the host rock media of a radioactive waste repository for many countries (EPRI, 2010). Attributed to its low permeability, an intact granite can effectively restrict the flow of underground water and retard the migration of radionuclides. However, over a very long geological period the structure of granite mass can be disturbed as the result of the exogenic and endogenic geological processes, which generates many fractures with different geometrical morphologies. The fractures can become the main passages for seepage of underground water and transport of radionuclides. Therefore, for reliably assessing the safety of a repository, it is indispensable to take into account the migration behavior of radionuclides in granite fractures (Konzuk and Kueper, 2004; Huang et al., 2015). A single fracture is the basic unit of fracture networks. The experimental studies on the hydraulic behavior and radionuclide migration mechanism in a rough single fracture are the foundation stone for constructing a realistic model of radionuclides transportation in a jointed rock matrix (Konzuk and Kueper, 2004). Since water flow is the main driving force for nuclide migration, the study of flow in a single fracture is an important prerequisite for understanding nuclide migration behavior. In the past, considerable attentions have been paid to the fluid flow through a single fracture between two perfectly smooth parallel joint walls, in which the flow is generally assumed to be laminar and can be characterized by the cubic low (Bear, 1972; Witherspoon et al., 1980). Nevertheless, lots of studies have found that the flow through a real fracture may not be laminar on account of its rough surface and variable aperture (Ji et al., 2008; Luo et al., 2016). ⁎

Hence, it is essential to investigate the possible seepage behavior of flow in a rough single fracture with particular aperture before focusing on the migration of radionuclide. Another important topic is the migration of radionuclides in a single fracture. 90Sr is one of important fission products of radioactive wastes and spent fuels. For the reason of long half-life (29a) and high poisonous of 90Sr, once the soil or water is contaminated by 90Sr, the safety of environment will be exposed to danger for decades (Serne et al., 1996). In practice, non-radioactive 88Sr is usually selected as the experimental substitute of 90Sr for sake of safety. Moreover, the chemical sorption properties of stable 88Sr are the same with that of 90Sr (Li et al., 2011; Yu et al., 2015). For the moment, most studies have focused on the migration of 90Sr and stable 88Sr in the soil and crushed granite (Torstenfelt et al., 1982; Park and Hahn, 1999; Li et al., 2011; Palágyi et al., 2015; Wissocq et al., 2018), few studies (Hadermann and Heer, 1996; Vandergraaf et al., 1996; Vandergraaf et al., 1997; Hoehn et al., 1998; Vilks and Baik, 2001; Albarran et al., 2011) have concentrated on the dynamic sorption of the 85Sr in a single fracture filled with or without colloids at a certain flow rate. However, it is still lack enough knowledge about the sorption mechanism of Sr in a single fracture. The goal of this work is to analyze the seepage behavior of flow in a rough single fracture with particular aperture, and more importantly, investigate the sorption and desorption behavior of Sr in a rough single fracture. The probable sorption mechanism of Sr in the single fracture will be discussed in this paper.

Corresponding author. E-mail address: [email protected] (J. Zang).

https://doi.org/10.1016/j.jconhyd.2019.103558 Received 18 March 2019; Received in revised form 24 August 2019; Accepted 29 September 2019 0169-7722/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Jianzheng Zang, et al., Journal of Contaminant Hydrology, https://doi.org/10.1016/j.jconhyd.2019.103558

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Recently, He and his co-workers (He et al., 2016) have put forward the roughness angle to parameterize fracture surface roughness. Meanwhile, their studies proved that the well-known cubic law modified by the roughness angle αm could describe the steady flow through a single rough fracture better than the law modified by JRC. Hence, the roughness angle was chosen as the key parameter for the characterization of fracture surface. The roughness angle can be calculated by (He et al., 2016):

tan

m

=

1 L

((z i + 1

z i )/(x i + 1

x i )) 2

1/2

(1)

where L is the profile length, xi and zi represent the coordinates of the mth fracture surface profile, for example the A-B line in Fig. 3. However, due to the fractal characterization of surface topography (Guerrero et al., 2002), there will be different surface profiles along the x or y coordinate according to the sampling scale, and each profile may have particular roughness parameter. As a result, it is unreliable to characterize the surface roughness with one certain profile. On the other hand, only the surface profile along the flow path will have more remarkable influence on the seepage in the single fracture. Therefore, 49 surface profiles (P1~P49) along the flow path were extracted at 0.1 mm sampling spacing in the fracture wide direction, and the roughness angle αm of each profile was calculated by using Eq. (1) as shown in Table 1. The average roughness angle (effective inclination angle) αe of the fracture surface is 15.2°, which could be obtained by applying the follow equation:

Fig. 1. The apparatus developed for producing a single fracture (based on a Brazilian technique).

2. Materials and methods

e

2.1. Fracture generation

=

1 49

m

(2)

4. The fluid flow test in the single fracture

Grainte core was collected at the northwest area of China, the dimensions of which are 100 mm in length and 50 mm in diameter. X-ray diffractometer (XRD: Philips, MPD) was employed to identify the main minerals constituting the granite, and it was found that the granite sample was mainly composed of quartz (31.7%), albite (30.4%), microcline (26.4%), biotite (7.2%) and chlorite (4.3%). The cation exchange capacity (CEC) was determined to be 9.3 ± 0.2 meq/100 g (Chen et al., 2013). To create a ‘single fracture’ in the rock core sample, an apparatus (Fig. 1) made up of high carbon (1.20% C by weight) steel was developed to produce a single fracture (based on a Brazilian technique). The preparation process of a single fracture is in accordance with the procedure mentioned by (Singh et al., 2015). The rock core was then separated into two cylindrical halves by means of splitting. Subsequently, both cylindrical halves were joined together by means of epoxy resin generating ‘single fracture’.

The fluid flow characteristic of the single fracture was determined with the help of a self-built experiment apparatus, the schematic diagram of which was depicted in Fig. 3, and its operating principle was similar to that of flexible wall permeameter (Zhou et al., 2013). A confining pressure of 1 MPa was applied to the cell filled with compressed air to push the membrane in contact with the specimen side tightly, and deionized water was used to saturate the specimen wherein the specimen was exposed to water under an applied positive pressure of 150 kPa. Fluid flow tests were then conducted on the specimen at different positive pressure. The flow rate under particular hydraulic gradient was measured by weighing the volume of effluent water collected at every 10 min (i. e., gravimetrically). Each measurement under particular hydraulic gradient will be carried out three times in parallel to ensure the reliability of measurements. 5. The sorption and desorption breakthrough experiment of Sr

3. Roughness measurement of the fracture surfaces

The column experiments were carried out to survey the sorption and desorption of Sr in the single fracture. Influent solutions with two different initial concentrations of Sr (C0=3.0 × 10−5and 7.0 × 10−5g/ mL, respectively) were prepared by dissolution SrCl2 salt (Sigma Aldrich) into deionized water, which were injected into the influent pipe through three-way valve to provide the steady nuclide source for the migration study. In each column experiment, the fluid rate was changed by varying the hydraulic gradient so as to examine its effect on the migration behavior of Sr. In the dynamic sorption experiment, the influent solution was injected to the single fracture granite at certain constant flux, until the maximum concentration of Sr in effluents was reached; In the desorption experiment, the deionized water was introduced to displace Sr adsorbed onto the fracture surface at the constant flux until the concentration of Sr in effluents was approached to zero. The flow rate under particular hydraulic gradient was measured by weighing the volume of effluents, which is continually collected by using a fraction

Roughness measurement can be performed by employing a 3D laser profile scanner. The laser beam is adopted to capture the texture of the fracture surface or the topography of the surfaces. In the present work, roughness measurements were performed on both the fracture surfaces at 0.04 mm point spacing before being affixed together, which was done by employing the Creaform 3D laser profile absolute arm scanner, the data obtained from the scanner were handled to generate the 3D topography of the fracture surfaces as the way described by (Singh et al., 2015). Fig. 2 presents the 3D surface profile of the fracture surfaces of the sample. A typical surface profile, section A-B was taken at the center of the sample whole along the length of generated 3D surface roughness profile as displayed in dotted line in Fig. 2. In order to parameterize the fracture surface roughness, a number of parameters have been proposed, e.g., Joint Roughness Coefficient (JRC), asperity slope Z2, and fractal dimension (Luo et al., 2016). 2

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Fig. 2. 3D surface topography of the fracture surfaces (all dimensions are in mm).

Fig. 3. Schematic diagram of the experimental setup.

collector at constant sampling time. The concentrations of Sr in effluents were determined by ICP-AES (Leeman PSFO 2.0) and the concentration was expressed as a relative concentration C/C0, where C is the concentration in the effluent. Six BTCs (sorption breakthrough curves) and four DPCs (displacement curves) were obtained as a C/C0 vs. nPV (the number of pore volumes of liquid phase) plots. On the other hand, in order to evaluate the influence of initial concentration of Sr on its sorption behavior, the BTCs and DPCs were also determined under two different initial concentrations of 3.0 × 10−5 and 7.0 × 10−5 g/ mL.

Table 1 The calculated roughness angle αm (unit:°) of 49 surface profiles (P1~P49) along the flow path. P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

10.6 P11 15.8 P21 17.3 P31 13.9 P41 14.6

11.8 P12 16.7 P22 17.4 P32 13.8 P42 17.8

12.1 P13 16.8 P23 16.4 P33 14.5 P43 18.0

12.9 P14 15.9 P24 14.4 P34 15.3 P44 18.0

12.9 P15 16.1 P25 12.3 P35 15.2 P45 16.2

14.0 P16 17.1 P26 13.2 P36 14.9 P46 15.4

15.1 P17 17.0 P27 14.7 P37 14.1 P47 15.7

15.7 P18 17.2 P28 12.3 P38 12.9 P48 15.8

16.7 P19 18.0 P29 14.8 P39 13.3 P49 14.5

16.5 P20 18.9 P30 14.2 P40 13.7 – –

6. Theory model for transport experiments The governing equation describing the one dimension transport of 3

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nuclide in the fracture is based on (Albarran et al., 2011; Shahkarami et al., 2015; Zhu et al., 2016):

C C + t R x

DL 2C R x2

2 D eR

C =0 y

Table 2 Parameters of the seepage experiment of the single fracture.

(3)

where C and C' are the solute concentrations in the fracture and rock matrix respectively, DL is the longitudinal dispersion coefficient, υ is the fluid velocity under laminar flow condition, x is the distance in the direction of the flow field, y is the distance in the direction perpendicular to the fracture, t is time, D' is the effective diffusion coefficient in the rock matrix, θ is the rock porosity, e the hydraulic fracture aperture, R is the retardation factor, R = 1 + [Kf/(e/2)], Kf is the surface distribution coefficient. Due to the crystalline rocks' low permeability, the diffusion of nuclide through the matrix is so weak that the sorption of nuclide into the matrix at short time scales can be neglected. Hence, the transport of nuclide in the fractures is assumed to be the crucial process for evaluating the migration tendency of nuclide in the site. The initial [C= 0 at x=0 and t0 = 0, and Ct = C0 at x=L] and boundary [(C(0, t),x (0, L)] conditions yield the following equations describing the sorption BTCs and the desorption DPCs obtained for CrelS and CrelD, respectively.

Crels =

C (x , t ) 1 R = erfc C0 2 2

nPV R nPV Pe

(4)

Since the sorption and desorption breakthrough curves are theoretically mirror-symmetrical for a reversible adsorption process (Palágyi et al., 2015), the desorption DPCs function can be expressed as.

CrelD =

C (x , t ) =1 C0

1 R erfc 2 2

q(cm/s)

Re

e(cm)

400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 90 80 70 60 50 40 30 3.7

0.313 0.298 0.288 0.274 0.261 0.251 0.230 0.213 0.198 0.179 0.161 0.146 0.131 0.107 0.094 0.073 0.059 0.056 0.043 0.036 0.028 0.020 0.016 0.005

6.26 5.96 5.75 5.45 5.22 5.02 4.59 4.26 3.96 3.58 3.22 2.92 2.61 2.13 1.89 1.46 1.18 1.13 0.857 0.730 0.557 0.403 0.314 0.094

0.0253 0.0254 0.0255 0.0256 0.0257 0.0259 0.0258 0.0257 0.0258 0.0257 0.0256 0.0257 0.0257 0.0251 0.0254 0.0248 0.0239 0.0245 0.0234 0.0233 0.0226 0.0219 0.0222 0.0298

Re =

ql µA

(6)

where ρ is the fluid density, l is the characteristic dimension of the flow system, q is the volumetric flow rate, A is the flow area, μ is the dynamic viscosity of the fluid. For flow between two parallel plates, with w > > e (w is width of the fracture joint, e is hydraulic fracture aperture) l = e, and thus:

nPV R nPV Pe

J

(5)

In Eqs. (4) and (5) it means: S and D are indexes for sorption and desorption, respectively; nPV = ∑ V/PV, where PV is one pore volume and ∑V is the total volume of the liquid phase at the outlet from the column; Pe is the Peclet number, Pe = (υ ⋅ L/DL).

Re =

q µw

(7)

The obtained Reynolds values show low Re < 7 as presented in Table 1, which implies that the fluid flow in these cases is laminar as suggested by (Singh et al., 2015) and can be described by the cubic law (Ji et al., 2008). Besides, seeing that the variable groundwater velocities in rock fractures are 0.0012–0.0382 cm/s estimated by (Novakowski et al., 2006) and the open fracture apertures in granite are 0.3–3 mm (Widestrand et al., 2007), the Reynolds values will be Re < 1 (according to Eq. (7)), thereby it is reliable to apply the cubic law in seepage analysis of field site. Taking account to the effect of surface roughness on fluid low, He et al. (2016) proposed that the cubic law can be modified as follows:

7. Results and discussion 7.1. Seepage analysis of the single fracture The fluid rates are positively related to the variation of hydraulic gradient as demonstrated in Fig. 4. The Reynolds number provides an indication of flow regime (laminar or non-laminar) based on the geometry of the flowing system and the properties of the fluid (Ranjith, 2010). It can be expressed as:

q = cos4

e

ge 3 J 12

(8)

where αe is the average roughness angle of the fracture surface, g is the acceleration due to gravity, ν is the kinematic viscosity of the fluid J is the hydraulic gradient. The value of e could be calculated by using Eq. (8) as displayed in Table 2, and the average hydraulic aperture ē is 0.025 cm. 7.2. Migration of Sr in the single fracture Fig. 5 shows the BTCs of Sr at flow rates of 0.0013, 0.0444 and 0.2113 cm/s and the DPCs of Sr at flow rates of 0.0039, 0.0675 and 0.1145 cm/s when its initial concentration is 7.0 × 10−5 g/mL. The BTCs and DPCs were then fitted by using Eqs. (4) and (5), respectively, and their fittings (the blue lines shown in Fig. 5) present a nice match with the experimental data. The transport parameters for BTCs and DPCs at different flow rates derived by the fitting were summarized in Table 3. It can be concluded that the sorption of Sr onto the fracture

Fig. 4. The variation of q with J for the single fracture. 4

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Fig. 5. The BTCs of Sr (C0=7.0 × 10‐5 g/mL) at flow rates of 0.0013 (a), 0.0444 (b) and 0.2113(c) cm/s and the DPCs of Sr at flow rates of 0.0039 (d), 0.0675 (e) and 0.1145 (f) cm/s.

variation of Sr. This result is consistent with the viewpoint stated by (Torstenfelt et al., 1982; Pot and Genty, 2005). It can be safely inferred that the sorption of Sr onto granite fracture surface is linear. Consequently, its sorption distribution coefficient will be a constant and unaffected by the initial concentration change of Sr. There are two main types of adsorption sites on the granite (Jin et al., 2016): one is the negative surface-charge sites derived from isomorphous substitution, i. e., cation ion-exchange sites. This kind of adsorption sites can adsorb cations due to electrostatic interactions, and its sorption capacity will be affected by ion type and ionic strength; The other is surface hydroxyl groups (e. g., ≡Si ‐ OH and ≡Al ‐ OH) formed by the surface hydration reaction between granite surface and water. These sites can adsorb both anions and cations, and the sorption capacity was controlled by the protonation and deprotonation process of hydroxyl functional groups. Using batch techniques, Torstenfelt et al. (1982) found that the sorption of Sr on rock and minerals could qualitatively be correlated to the cation-exchange capacity of the solid sorbent. Moreover, the static sorption and desorption (sequential chemical extraction) experiments of Sr onto a Bulguksa granite were carried out by (Park and Hahn, 1999), and it was observed that Sr showed almost linear and reversible ion-exchange sorption behavior. Recently, employing the Generalised Composite approach (Davis et al., 2004; Tertre et al., 2008), Chen et al. (2013) performed numerical analysis of the sorption data obtained by (Park and Hahn, 1999), and they proposed that ion-exchange process was the main sorption mechanism of Sr onto the granite. Based on the analyses above, it can be safely concluded that the sorption of Sr onto the granite surface is dominated by rapid ion-exchange process, and under dynamic condition, this sorption behavior is linear and reversible. Furthermore, specific surface area, the ratio of the fracture surface area to the volume of mobile water in the fracture, has found to be the main factor that affects the sorption of Sr onto the fracture in neutral environment (Torstenfelt et al., 1982; Wels et al., 1996). Consequently, the sorption of Sr is governed by surface site capacities of the facture (Wissocq et al., 2018) and will not be affected by the variation of flow rate.

Table 3 The important transport parameters for BTCs and DPCs of Sr (C0=7.0 × 10‐5 g/ mL) at different flow rates. υs (cm/s)

DLs (cm/s2)

Rs

Kfs (cm)

υd (cm/s)

DLd (cm/s2)

Rd

Kfd (cm)

0.2113 0.1508 0.0444 0.0188 0.0029 0.0013

0.1227 0.0725 0.0136 0.0060 0.0012 0.0006

5.4 4.5 5.2 4.6 3.8 4.4

0.055 0.044 0.053 0.045 0.033 0.043

0.1145 0.0675 0.0150 0.0039 – –

0.1812 0.0558 0.099 0.0026 – –

2.7 3.4 3.8 3.4 – –

0.021 0.030 0.035 0.030 – –

Table 4 The important transport parameters for BTC and DPCs of Sr (C0=3.0 × 10‐5 g/ mL). υs (cm/s)

DLs (cm/s2)

Rs

Kfs (cm)

υd (cm/s)

DLd (cm/s2)

Rd

Kfd (cm)

0.0232

0.0061

5.8

0.53

0.0185

0.0104

4.6

0.045

surface is weak according to its low sorption distribution coefficient Kfs. Meanwhile, the adsorbed Sr can be completely desorbed from the surface as depicted in Fig. 5, which revealed that the sorption of Sr in these cases is reversible (Kfd < Kfs). Considering the sorption of Sr onto the granite is reversible and the sorption capacity quite small, the existence of fractures will significantly increase the risk of Sr leakage into biosphere. On the other hand, although the flow rates have been widely changed from 0.0013 to 0.2113 cm/s, the sorption distribution coefficients of Sr are inclined to be constant (approximately equal to 0.045 cm) as displayed in Table 3, which means the flow rates almost have no effect on the sorption of Sr. Table 4 displays the important transport parameters for BTCs and DPCs at initial concentrations of 3.0 × 10−5 g/mL. In this case, the value of sorption distribution coefficient Kf is quite close to that of BTCs at initial concentration of 7.0 × 10−5 g/mL, which means that the sorption of Sr may not be influenced by the initial concentration 5

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8. Conclusions

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