Computers & Geosciences 49 (2012) 256–266

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Reactive transport model and apparent Kd of Ni in the near field of a HLWrepository in granite

Chuanhe Lu a,n, Javier Samper b, Jose Luis Cormenzana c, Hongyun Ma b, Luis Montenegro b,Miguel Angel Cunado c

a Lawrence Livermore National Laboratory, P.O. Box 808, L-223, Livermore, CA 94550, USAb Escuela Tecnica Superior de Ingenieros de Caminos, Canales y Puertos. Universidad de A Coruna, 15071 A Coruna, Spainc ENRESA, C Emilio Vargas 7, 28040 Madrid, Spain

a r t i c l e i n f o

Article history:

Received 26 September 2011

Received in revised form

31 May 2012

Accepted 4 June 2012Available online 12 June 2012

Keywords:

Apparent Kd

Nickel

Reactive transport model

CORE

Bentonite

Sorption

04/$ - see front matter Crown Copyright & 2

x.doi.org/10.1016/j.cageo.2012.06.003

esponding author. Tel.: þ1 925 4232307.

ail address:

nl.gov (C. Lu).

a b s t r a c t

Current performance assessment models for radionuclide migration through the near field of high-level

radioactive waste repositories often rely on the assumption of a constant Kd for sorption. The validity of

such assumption is evaluated here with a reactive transport model for Ni2þ in the near field of a

repository in granite. Model results show that Ni2þ sorbs mainly by surface complexation on weak

sorption sites. The apparent Kd of Ni2þ , Kda, depends on the concentration of dissolved Ni and pH and is

constant only when the concentration of dissolved Ni is smaller than 10�6 mol/L. The results of the

sensitivity runs show that Kda is sensitive to the water flux at the bentonite–granite interface, the

effective diffusion of the bentonite and the concentration of weak sorption sites of the bentonite. The

competition of other nuclides such as Csþ on Ni2þ sorption is not important. Corrosion products,

however, affect significantly the sorption of Ni2þ on the bentonite. The model with a constant Kd does

not reproduce the release rates of Ni2þ from the bentonite into the granite. A model with a variable Kd

which depends on the concentration of dissolved Ni2þ and pH may provide an acceptable surrogate of

the multicomponent reactive transport model for the conditions of the repository considered in our

model. Simulations using the Kd-approach were performed with GoldSim based on the interpolation in

the pH and concentration table, while the reactive transport model simulations were performed with

CORE2D which incorporates multisite surface complexation.

Crown Copyright & 2012 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Current performance assessment models for radionuclidemigration through the near field of a high-level radioactive waste(HLW) repository usually rely on simplifying assumptions such asthe use of a constant Kd for nuclide sorption and ‘‘the limitedsolubility’’ for nuclide precipitation (Bethke and Brady, 2000;USEPA, 1999). But the distribution of aqueous species dependsstrongly on the chemical conditions, especially pH and theconcentrations of complexing ligands such as carbonate ions(Curtis et al., 2006; Davis et al., 2004). Although the effects ofchanges in the chemical conditions on the solubility of radio-nuclides usually can be calculated in a straightforward manner,the consequences of variable chemical conditions on adsorptionand the choice of the appropriate Kd value are more complex(Curtis et al., 2004; Davis et al., 2004; Kohler et al., 1996; USEPA,1999). Testing the validity of the constant Kd has been limited by:

012 Published by Elsevier Ltd. All

(1) the lack of nuclide surface complexation and cation exchangedata and (2) the unavailability of computer codes which couldhandle simultaneously the migration, sorption and precipitationof radionuclides and the geochemical evolution of the near field.Laboratory experiments performed in recent years have providedsubstantial data and understanding on the mechanisms of nuclidesorption. Thermodynamic sorption models based on cationexchange (Bolt, 1982; Fletcher and Sposito, 1989; Gaines andThomas, 1953) and surface complexation mechanisms (Davis andKent, 1990; Hayes et al., 1991; Sposito, 1984; Stumm and Morgan,1981) provide the framework for evaluating and predicting thecontribution of sorption reactions to radionuclide migration.Instead of the Kd approach often used in performance assessmentstudies, the way begins to open to methods capable of calculatingsorption values specific to different geochemical scenarios.Accounting for competitive sorption in repository safety analysesalso becomes a possibility (Bradbury and Baeyens, 2005).

The structural components of the fuel assembly are made ofInconel (INC-718) and stainless steel (SS-304) which containnickel (ENRESA, 2001b). Nickel release will be controlled by thedegradation of these alloys under repository conditions. Although

rights reserved.

Fig. 1. Dimensions of an individual disposal cell and the sketch of the 1D

axisymmetric model (Samper et al., 2010).

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266 257

these alloys are very resistant to corrosion, usually a shortduration of 1000 years is assigned to them in safety assessmentexercises (ENRESA, 2001a). Nickel is a transition metal of thetenth group which is often found in the þ2 oxidation state inaqueous and solid states. The solubility of Ni can be controlledeither by NiCO3(s) or Ni(OH)2(s), depending on the pH of thesystem. Ni solubility is a matter of controversy. There arediscrepancies among the reported solubilities and the solid phasecontrolling Ni solubility. Reported solubility constants forNiCO3(s) range from 1.0�10�11.2 to 1.0�10�6.82 (Duro et al.,2006). Ni solubility decreases an order of magnitude when pHincreases from 6 to 7 while NiCO3(s) is the solid phase controllingNi solubility. The concentration of dissolved Ni2þ is the largest forpH o7:5 (Mattigod et al., 1997). Pfingsten et al. (2011) studiedthe influence of Fe2þ competition on the sorption and migrationof Ni2þ in MX-80 bentonite. They adopted a Ni2þ solubility of3.5�10�5 mol/L for pH¼7.25. The mobility and availability ofNi2þ in soils depend primarily on the sorption on clay silicates,manganese, iron, and aluminum oxides (Ticknor, 1994; Tilleret al., 1984; Trivedi and Axe, 2001). Ni2þ sorption on thebentonite may occur via cation exchange and surface complexa-tion (Lazarevic et al., 2010; Yang et al., 2009b). The sorption ofNi2þ is endothermic (Ijagbemi et al., 2010; Lazarevic et al., 2010;Zhang et al., 2010) and depends on pH, ionic strength, humic acid,temperature and the concentrations of other dissolved ions(Domenech and Duro, 2008; Fan et al., 2009; Hu et al., 2010;Yang et al., 2009b). Ni2þ sorption via surface complexation (SC) isstrongly nonlinear and depends nonlinearly on pH. Ni2þ sorptionincreases with pH regardless of temperature (Bhattacharyya andGupta, 2007; Boonfueng et al., 2006; Tertre et al., 2005; Zhanget al., 2010). Bradbury and Baeyens (1997a,b, 1999) found that theNi2þ sorption is constant and occurs only via cation exchange forpH o5. At high pH, on the other hand, SC is stronger and theeffect of ionic strength becomes less relevant (Boonfueng et al.,2006; Bradbury and Baeyens, 1997b). Ni2þ uptaken by SC occurson at least two types of pH-dependant sites. Ni2þ sorption at lowradionuclide concentrations is strong and linear and occurs on arelatively small number of sites with a high binding affinity.These are the so-called ‘‘strong sites’’. For intermediate concen-trations of Ni2þ the sorption is non-linear because sorption takesplace on a second set of sites which have a larger concentrationbut a weaker binding constant. These are the so-called ‘‘weaksites’’. For the conditions of a radioactive waste repository, thesorption of Ni2þ is governed by surface complexation on the edgesurface sites (Bradbury and Baeyens, 1997a,b, 1999, 2005;Ijagbemi et al., 2010; Lazarevic et al., 2010; Montavon et al.,2006; Yang et al., 2009a; Zhang et al., 2010). Here we report theposibility of using the Kd models for Ni2þ with a reactivetransport model considering multisite surface complexation. Thepaper starts by describing the conceptual and numerical models.Then, model results are presented for the base run and thesensitivity runs. Competition effects are then evaluated. Finally,the results of the constant and variable Kd models performed withGoldSim are compared to those of the reactive transport model.The paper ends with the main conclusions.

2. Conceptual and numerical models

2.1. Reference concept

The Spanish reference concept for a spent-fuel repository ingranite envisages the emplacement of carbon-steel canisters in500 m long horizontal drifts excavated at a depth of 500 m in agranite formation by tunnel boring. Canisters are disposed incylindrical disposal cells built with blocks of compacted bentonite

having a dry density of 1700 kg/m3 to achieve a final dry densityof 1600 kg/m3. The bentonite blocks are initially unsaturated witha gravimetric water content of 14%. The disposal drifts have adiameter of 2.4 m. The dimensions of an individual ‘‘cell’’ corre-sponding to a single canister are shown in Fig. 1 (ENRESA, 2005;Samper et al., 2010). The volume of voids of each canister isestimated to be 0.5 m3.

2.2. Conceptual model

Canister failure due to steel corrosion is estimated to occurafter several thousands of years. After canister failure, the canistercavity will fill with the bentonite pore water. Then, radionuclideswill be released into the water and later will diffuse into thebentonite buffer. The model in this paper simulates the geochem-ical evolution and radionuclide migration after the canister hasfailed so that water can fill all the voids within the canister.According to ENRESA (2005, 2006) the bentonite barrier willbecome fully water-saturated after less than 50 years for theSpanish reference concept. The thermal pulse will dissipate in 104

years (ENRESA, 2001a). The numerical simulation starts aftercanister failure and once the thermal pulse has gone. Therefore,calculations are performed by assuming isothermal (25 1C) andwater-saturated conditions. The model does not account for thecorrosion of the liner in Fig. 1.

Given the low hydraulic conductivity of the bentonite, diffu-sion is the dominant transport process in the bentonite which hasa porosity equal to 0.407 (ENRESA, 2006; Samper et al., 2008b).All dissolved chemical species are assumed to have the sameeffective diffusion of 4.07�10�11 m2/s which is the value used inthe BENIPA project (BENIPA, 2003). A flux of 0.06 L/year percanister is used for the boundary condition at the bentonite/granite interface as indicated in Fig. 1 (Samper et al., 2010).

The geochemical model considers the following geochemicalreactions: aqueous complexation, acid-base, redox, dissolution/precipitation of calcite, goethite, gypsum, magnetite, quartz andsiderite, cation exchange of Ca2þ , Mg2þ , Naþ , Kþ , Fe2þ and Ni2þ

and protonation/deprotonation by surface complexation. Thechemical system is defined in terms of the following primaryspecies: H2O, O2(aq), Hþ , Naþ , Kþ , Ca2þ , Mg2þ , Fe2þ , HCO3

� , Cl� ,Ni2þ , SO4

2� , Ni2þ and SiO2(aq). Pore waters in the canister and thebentonite are assumed to have initially the same chemicalcomposition (Samper et al., 2008a) which is controlled by mineraldissolution/precipitation at chemical equilibrium (calcite andquartz), proton SC and cation exchange. A discussion of the

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266258

chemical processes buffering the bentonite pore water chemistry ispresented by Zheng et al. (2010). The chemical composition of inflowwater coincides with that of the granite pore water. The chemicalcompositions of the initial and boundary pore waters are listed in

Table 1Initial chemical composition of the bentonite and boundary (granite) pore waters.

Chemical species Bentonite Boundary

pH 6.435 7.825

Eh (V) �0.059 �0.188

Ca2þ (mol/L) 3.101�10�2 1.522�10�4

Mg2þ (mol/L) 3.473�10�2 1.604�10�4

Naþ (mol/L) 1.841�10�1 4.350�10�3

Kþ (mol/L) 1.507�10�3 5.371�10�5

Fe2þ (mol/L) 6.583�10�5 1.791�10�8

Ni2þ (mol/L) 0 0

Cl� (mol/L) 2.756�10�1 3.949�10�4

HCO�3 (mol/L) 1.689�10�3 5.049�10�3

SO2�4 (mol/L) 2.049�10�2 1.561�10�5

SiO2(aq) (mol/L) 8.426�10�4 3.761�10�4

Table 2Equilibrium constants for aqueous complexes at 25 1C.

Aqueous complexes Log K

CaClþ3Ca2þþCl� 0.6956

CaCl2ðaqÞ3Ca2þþ2Cl� 0.6436

CaCO3ðaqÞþHþ3Ca2þþHCO�3 7.0017

CaHCOþ3 3Ca2þþHCO�3 �1.0467

CaH3SiOþ4 þHþ3Ca2þþ2H2OþSiO2ðaqÞ 8.7916

CaSO4ðaqÞ3Ca2þþSO2�

4�2.1111

CaOHþ þHþ3Ca2þþH2O 12.850

CO2ðaqÞþH2O3Hþ þHCO�3 �6.3447

CO2�3 þHþ3HCO�3 10.329

Fe3þþ0:5H2O3Fe2þ

þHþ þ0:25O2ðaqÞ �8.4900

FeClþ3Fe2þþCl� 0.1605

FeCO3ðaqÞþHþ3Fe2þþHCO�3 5.5988

FeHCOþ3 3Fe2þþHCO�3 �2.0500

FeSO4ðaqÞ3Fe2þþSO2�

4�2.2000

HClðaqÞ3Hþ þCl� 0.6700

HSO�4 3Hþ þSO2�4

�1.9791

HSiO�3 þHþ3H2OþSiO2ðaqÞ 9.9525

H6ðH2SiO4Þ2�4 þ2Hþ38H2Oþ4SiO2ðaqÞ 13.446

KClðaqÞ3Kþ þCl� 1.4946

KSO�4 3Kþ þSO2�4

�0.8796

MgClþ3Mg2þþCl� 0.1349

MgCO3ðaqÞþHþ3Mg2þþHCO�3 7.3499

MgHCOþ3 3Mg2þþHCO�3 �1.0357

MgH2SiO4ðaqÞþ2Hþ3Mg2þþ2H2OþSiO2ðaqÞ 17.482

MgH3SiOþ4 þHþ3Mg2þþ2H2OþSiO2ðaqÞ 8.5416

MgSO4ðaqÞ3Mg2þþSO2�

4�2.4117

NaClðaqÞ3Naþ þCl� 0.7770

NaCO�3 þHþ3Naþ þHCO�3 9.8144

NaHCO3ðaqÞ3Naþ þHCO�3 �0.1541

NaHSiO3ðaqÞþHþ3Naþ þH2OþSiO2ðaqÞ 8.3040

NaOHðaqÞþHþ3Naþ þH2O 14.180

NaSO�4 3Naþ þSO2�4

�0.8200

NiClþ3Ni2þþCl� 0.9962

NiOHþ þHþ3Ni2þþH2 O 11.535

NiðOHÞ2ðaqÞþ2Hþ3Ni2þþ2H2O 19.990

NiðOHÞ�3 þ3Hþ3Ni2þþ3H2O 30.985

Ni2OH3þþHþ32Ni2þ

þH2O 10.700

Ni4ðOHÞ4þ4 þ4Hþ34Ni2þþ4H2O 27.680

NiSO4ðaqÞ3Ni2þþSO2�

4�2.1257

OH�þHþ3H2O 13.995

Table 1. The concentrations of most of dissolved species in thebentonite are larger than those in the granite except for bicarbonate.Relevant aqueous complexes were identified from exploratory spe-ciation runs performed with EQ3/6 (Wolery, 1992). They are listed inTable 2. Aqueous complexes and minerals reactions are assumed tobe at local chemical equilibrium. The Gaines–Thomas convention isused for cation exchange (Gaines and Thomas, 1953). Surface com-plexation reactions are implemented with a triple-site model con-sidering three types of protolysis sites (Bradbury and Baeyens,1997a,b), strong sites ð � SOHÞ and two weak sites ð �W1OH and�W2OH). Chemical reactions and their equilibrium constants at25 1C for mineral dissolution/precipitation (Wolery, 1992) as well asselectivity coefficients for exchangeable cations (Bradbury andBaeyens, 2005; ENRESA, 2006; Missana et al., 1999; Samper et al.,2008a,c; Zheng and Samper, 2008) and protolysis constants forsurface complexation reactions (Bradbury and Baeyens, 2005;Fernandez et al., 2001; Samper et al., 2008a) are listed in Table 3.

The mass of Ni per canister is 20 kg. The results of exploratorymodel runs performed with Ni solubility controlled either byNiCO3(s) or Ni(OH)2(s) show that computed dissolved concentra-tions of Ni2þ are exceedingly large before 1000 years (see Fig. 2).The initial pH in the bentonite is 6.435 (Table 1). For this pH, Nisolubility should be at least an order of magnitude larger thanthat of bentonite at pH¼7.25. As an educated guess, we adopted aNi solubility of 10�3 mol/L for the ‘‘base run’’ by considering a‘‘dummy Ni mineral’’ in the canister. In the section of sensitivityanalysis we consider a Ni solubility limit of 10�5 mol/L which iscloser to that of Pfingsten et al. (2011).

The initial volume fractions of calcite and quartz in thebentonite are both equal to 0.01 (Samper et al., 2008a). Gypsum,magnetite, siderite and goethite are minerals which are notinitially present in the system, but are allowed to precipitate. The

Table 3Equilibrium constants for minerals, selectivity coefficients for cation exchange

reactions, and protolysis constants for surface complexation reactions for a triple-

site model at 25 1C.

Minerals Log K

CaCO3ðsÞþHþ3Ca2þþHCO�3 1.8487

CaSO4 � 2H2OðsÞ3Ca2þþSO2�

4 þ2H2O �4.4823

SiO2ðsÞ3SiO2ðaqÞ �3.9993

Fe3O4ðsÞþ6Hþ33Fe2þþ0:5O2ðaqÞþ3H2O �6.5076

FeOOHðsÞþ2Hþ3Fe2þþ0:25O2ðaqÞþ1:5H2O �7.9555

FeCO3ðsÞþHþ3Fe2þþHCO�3 �0.1920

NiðOHÞ2ðsÞþ2Hþ3Ni2þþ2H2O 12.7485

NiCO3ðsÞþHþ3Ni2þþHCO�3

�1.8170

Cation exchange KNa-cation

Naþ þK�X3Kþ þNa�X 0.138

Naþ þ0:5Ca�X230:5Ca2þþNa�X 0.292

Naþ þ0:5Mg�X230:5Mg2þþNa�X 0.288

Naþ þ0:5Fe�X230:5Fe2þþNa�X 0.500

Naþ þ0:5Ni�X230:5Ni2þþNa�X 0.519

Surface complexation Log Kint

� SOHþ2 3� SOHþHþ �4.5

� SO�þHþ3� SOH 7.9

� SONiþ þHþ3� SOHþNi2þ 0.6

� SONiOHþ2Hþ3� SOHþNi2þþH2O 10.0

� SONiðOHÞ�2 þ3Hþ3� SOHþNi2þþ2H2O 20.0

�W1OHþ2 3�W1OHþHþ �4.5

�W1O�þHþ3�W1OH 7.9

�W1ONiþ þHþ3�W1OHþNi2þ 3.3

�W2OHþ2 3�W2OHþHþ �6.0

�W2O�þHþ3�W2OH 10.5

Fig. 2. Time evolution of the concentration of dissolved Ni2þ in the canister for different hypotheses about the source of Ni in the canister.

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266 259

parameters of the SC model for Ni and surface protonation/depro-tonation are taken from Bradbury and Baeyens (2005). The totalconcentration of sorption sites in the bentonite is 0.3279 mol/L. TheSC site densities of � SOH, �W1OH and �W2OH are equal to2�10�6, 4�10�5 and 4�10�5 mol/g, respectively. The sorption ofNi occurs only on the � SOH and �W1OH sites. Only protons areallowed to sorb on the �W2OH sites. To maintain the consistencyof the sorption model, the cation exchange capacity, CEC, of thebentonite is equal to 87 meq/100 g which corresponds to the valuereported by Bradbury and Baeyens (2005). The CEC reported byBradbury and Baeyens (2005) is slightly smaller than the CEC of102 meq/100 g used by Samper et al. (2008a) which corresponds tothe FEBEX bentonite as reported by Fernandez et al. (2001). Themodel assumes that surface complexation reactions do not takeplace in the granitic rock.

The apparent distribution coefficient of Ni, Kda, is calculated

from the output results of the reactive transport model with thefollowing equation:

Kad ¼ ðYþWÞ=C ð1Þ

where Y is the concentration of total sorbed Ni2þ (mol/kg of soil)by surface complexation, W is the concentration of sorbed Ni2þ

by cation exchange (mol/kg of soil) and C is the total concentra-tion of dissolved Ni2þ (in mol/L) which includes the concentra-tion of free Ni2þ and those of all the Ni aqueous complexes.

2.3. Numerical model and computer codes

Calculations are performed for 1 Ma with a 1D axisymmetricfinite element grid. The radial distance, r, is measured from theaxis of the gallery. The canister is located at 0oro0:45 m. Thebentonite barrier extends from r¼0.45 to r¼1.2 m (see Fig. 1).The finite element grid has 167 elements and 168 nodes. An extraelement of 0.01 mm of thickness is added at the outer surface ofthe bentonite to simulate the ‘‘washing effect’’ of the granitegroundwater flow at the bentonite/granite boundary. This ele-ment serves as a dilution element. A large (small) water flowmimics a strong (weak) dilution. Solutes diffuse into this outer-most element and the equivalent groundwater flow is injectedand extracted from this element. The first 16 elements representthe canister voids up to a radius of 0.45 m and the remaining 151elements are in the bentonite up to a radius of 1.2 m.

Simulations using the Kd-approach are performed with Gold-Sim (Golder Associates, 2007) while the reactive transport modelsimulations are performed with CORE2D, a 2D Galerkin finiteelement multicomponent reactive transport code which solvesfor groundwater flow, and multicomponent reactive solute trans-port in saturated/unsaturated steady or transient groundwaterflow under general boundary conditions in 1, 2 or 3D axisym-metric conditions. It accounts for acid–base, redox, aqueouscomplexation, surface adsorption via SC, cation exchange, mineraldissolution/precipitation, and gas dissolution/ex-solution. Thecoupled transport and chemical equations are solved by thesequential iterative approach (Samper et al., 2003, 2009, 2011;Xu et al., 1999). Multiple sorption sites are implemented inCORE2DV5 by assuming that the mathematical formulation ofsorption reactions is the same for strong and weak sites (Samperet al., 2009; Lu, 2009). These sites differ only in their sitecapacities and associated acid/base constants. Numerical calcula-tions are performed in parallel for each type of site and later theyare combined together in the total mass conservation equation:

Tj ¼ cjþXNX

i ¼ 1

vxijxiþ

XNP

i ¼ 1

vpijpiþ

XNYS

k ¼ 1

XNkY

i ¼ 1

vyk

ij yki þwj j¼ 1;2, . . . ,NC

ð2Þ

where Tj is the total analytical concentration of the jth compo-nent, cj is the concentration of the jth primary species, NX is thenumber of secondary species, vij

x is the stoichiometric coefficientof the jth primary species on the ith secondary species, xi is theconcentration of the ith secondary species, NP is the number ofminerals, vp

ij is the stoichiometric coefficient of the jth primaryspecies on the ith mineral, pi is the concentration of the ithmineral, NYS is the number of the surface complexation sites, Nk

Y isthe number of surface complexes at the kth sorption site, vyk

ij isthe stoichiometric coefficient of the jth primary species in the ithsurface complex on the kth sorption site, yi

k is the concentration ofthe ith surface complex at the kth sorption site, and wj is theconcentration of the jth interlayer exchanged cation.

CORE2D has been widely used to model laboratory and in situexperiments within the context of HLW disposal (Samper et al.,2006; 2008b,c; Yllera et al., 2004), to evaluate the long-termgeochemical evolution of radioactive waste repositories in clay(Yang et al., 2008a,b) and granite (Yang et al., 2007)), to model the

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266260

transport of corrosion products and their geochemical interac-tions with the bentonite (Lu et al., 2011; Samper et al., 2008a) andto study the concrete degradation (Galındez et al., 2006).

3. Model results

3.1. Base run

The dissolved Ni diffuses into the bentonite. This makes theconcentrations of dissolved and sorbed Ni2þ in the bentonite toincrease. The computed concentration of dissolved Ni2þ near thecanister (r¼0.45 m) increase at a rate larger than that at thebentonite–granite interface (r¼1.2 m). The Ni solid source isexhausted when all the Ni in the canister is dissolved. After that,the concentration of dissolved Ni2þ in the bentonite decreases(see Fig. 3a). The concentration of sorbed Ni2þ also decreases alittle but remains almost constant at the rest time of the simulation(see Fig. 3b). Though the Ni2þ sorbed via surface complexationdecreases, the Ni2þ sorbed through cation exchange increasesbecause of the decreases of other cations are larger than that ofNi2þ . So the change of total sorbed Ni2þ concentration is not

Fig. 3. Time evolution of the concentrations of dissolved (a) and sorbed by surface c

Fig. 4. Time evolution of computed pH at

significant. Here, the concentration of sorbed Ni2þ is given in molesof sorbed Ni2þ per liter of pore water in the same way as it iscomputed in the reactive transport model. The curves of the timeevolution of the concentrations of dissolved and sorbed Ni2þ atdifferent places within the bentonite show differences for0oto6350 years. After 6350 years, there is no more Ni source inthe canister, and the dissolved Ni2þ concentration already reachesthe same value throughout the bentonite. Now the dilution at theboundary is the only factor affecting the Ni2þ transport in thebentonite. So the evolution of the concentrations of both sorbedand dissolved Ni2þ are the same throughout the bentonite.

When the Ni2þ front transports through the bentonite, Ni2þ issorbed by SC and protons are released from the surface com-plexes. This makes the pH decrease slightly for 103oto6� 103

years (see Fig. 4). The effect of Ni2þ sorption on pH lasts untilt¼6�103 years. Later, the pH increases due to the calcitedissolution, Ni2þ desorption and the out diffusion of protonsfrom the bentonite into the granite.

The initial Kda at repository conditions is around 350 L/kg. Later,

Kda decreases (Fig. 5) because the concentration of dissolved Ni2þ

increases at a rate larger than that of sorbed Ni2þ (see Fig. 3). Kda

reaches its minimum value at t¼6350 years. Later, Kda increases

omplexation and cation exchange (b) Ni2þ at several locations in the bentonite.

two radial locations in the bentonite.

Fig. 6. Apparent Kad versus the concentration of dissolved Ni2þ at several locations in the bentonite.

Fig. 5. Time evolution of Kad of Ni at several locations in the bentonite.

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266 261

because the concentration of dissolved Ni2þ decreases while thatof sorbed Ni2þ remains almost constant.

Fig. 6 shows the relationship between Kda and the concentra-

tion of dissolved Ni2þ at several radial locations. The Kda of Ni2þ is

nearly constant when the concentration of dissolved Ni2þ issmaller than 10�6 mol/L (AB part in Fig. 6). During the time inwhich the concentrations of dissolved and sorbed Ni2þ increase(0oto6350 years), the Kd

a of Ni2þ decreases because the con-centration of dissolved Ni2þ increases at a rate larger than that ofsorbed Ni2þ (part BC in Fig. 6). Later, the Kd

a of Ni2þ increasesbecause the concentration of dissolved Ni2þ decreases while thatof sorbed Ni2þ remains constant (part CD of the curve).

Fig. 7 shows the plot of Kda versus pH at several locations

within the bentonite. The plot of Kda versus pH shows S-shape

curves within the pH range of 6.3–6.5 which according toFigs. 4 and 5 correspond to to6� 103. During this stage, Kd

a

changes mostly due to changes in the concentration of dissolvedNi2þ . For t4104 years, both Kd

a and pH increase steadily (seeFigs. 4 and 5). Their values plot on a parabola of a mild curvature.Therefore, at early times Kd

a is controlled mainly by the concen-tration of dissolved Ni2þ . Later, both Kd

a and pH increase, the Kda

can be depicted as a function of pH.Fig. 8 shows where the Ni2þ is sorbed and how much it is

sorbed. Initially, when the concentration of dissolved Ni2þ issmall, Ni2þ is mainly sorbed at strong and weak sites. The strongsites get saturated very quickly and the concentration of sorbedNi2þ at strong sites remains constant. The concentration ofsorbed Ni2þ at weak sites increases with the concentration ofdissolved Ni2þ in the bentonite. Sorption at weak sites is the maincomponent of sorbed Ni2þ . After 6350 years, the concentration ofsorbed Ni2þ at weak sites decreases with that of the dissovledNi2þ . The concentration of exchanged Ni2þ also decreases a little,

Fig. 8. Time evolution of the concentrations of exchanged and sorbed Ni2þ at strong and weak sites at r¼0.5 m.

Table 4Parameters of the base run (BR) and the sensitivity runs (SR). De is the effective

diffusion of the bentonite.

Runs pH De (m2/s) Density of

weak sorption

sites 1 (mol/kg)

Water

flow

(L/year)

Ni

solubility

(mol/L)

BR Variable 4�10�11 0.04 0.06 10�3

SR1 Constant 4�10�11 0.04 0.06 10�3

SR2 Variable 4�10�12 0.04 0.06 10�3

SR3 Variable 4�10�11 0.02 0.06 10�3

SR4 Variable 4�10�11 0.06 0.06 10�3

SR5 Variable 4�10�11 0.04 0.6 10�3

SR6 Variable 4�10�11 0.04 1.2 10�3

SR7 Variable 4�10�11 0.04 0.06 10�5

Fig. 7. Apparent Kad versus pH at several locations in the bentonite.

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266262

but it increases again due to the decrease of the concentrations ofthe other dissolved cations. So totally the concentration of sorbedNi2þ almost keeps constant during the rest of simulation time.

3.2. Sensitivity analysis

Depending on the base run, sensitivity runs, SR, are performedto evaluate the changes in Kd

a caused by changes in the followingmodel parameters and boundary conditions: (1) the density ofsurface sorption sites; (2) the effective diffusion of the bentonite,De; (3) the boundary water flux; (4) the chemical conditions(variable or constant); and (5) the solubility limit of Ni. Theparameters and conditions of the base run, BR, and the sensitivityruns are listed in Table 4. The chemical composition of the granitepore water is set equal to the initial composition of the bentonitepore water in the run with constant chemical conditions. In thisway, the environmental chemical conditions remain constant inthe bentonite.

The computed Kda of Ni2þ in the bentonite for all the sensitivity

runs is shown in Fig. 9. The comparison of runs BR, SR3 and SR4shows that the change in the density of weak sorption sites alters

Fig. 9. Comparison of the apparent Kad of Ni2þ at r¼1.2 m for the base and sensitivity runs.

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266 263

the Kda by a constant factor after 2000 years. The reduction in Kd

a isretarded by a factor of 10 when the effective diffusion coefficientof the bentonite is decreased to 10 times smaller value (compareruns BR and SR2). The change in the boundary water flow affectsstrongly the Kd

a which starts to increase sooner for the largestgroundwater flow (compare runs BR, SR5 and SR6). Fixing the pHand the chemical conditions affects mostly the final part of the Kd

a

curve (compare runs BR and SR1). The reduction of the solubilitylimit leads to a nearly constant Kd

a which is equal to its initialvalue of 350 L/kg for to2� 105 years (compare runs BR and SR7).The effect of sorption sites, boundary water flow and Ni solubilitylimit on the Kd

a of Ni2þ occurs through the dissolved Ni2þ

concentration. The effect of pH is very clear in the run with fixedpH. It can be concluded that the Kd

a of Ni2þ is mainly controlled bythe dissolved Ni2þ concentration at the beginning part since thepH change is not significant, and controlled by both dissolvedNi2þ concentration and pH at the final part. So the Kd

a of Ni2þ canbe interpreted with the pH and dissolved Ni2þ concentration inour conceptual model. This will be introduced in the later part ofthis paper.

3.3. Competition effects

The simultaneous migration and sorption of Ni2þ and Csþ aresimulated by adding Csþ exchange according to the modelreported by Samper et al. (2010). The effect of Csþ on Ni2þ

sorption is not significant (not shown here) because Csþ sorbsmainly by cation exchange while Ni2þ sorbs mostly by SC.

The corrosion of the carbon-steel canister will affect thechemistry of bentonite porewater and the radionuclide migrationthrough the bentonite. So the corrosion products are consideredhere to check their effect on Ni2þ transport. The corrosion of thecanister is assumed to proceed kinetically with a corrosion rate of0:05 mm=year using the model of Samper et al. (2008a) andLu et al. (2011). The following Fe surface complexes are consid-ered: � SOFeþ , � SOFeOH, �W1OOFeþ . As an educated guess,the surface complexation parameters of Fe2þ were taken equal tothose of Ni2þ (see Bradbury and Baeyens, 2005). Canister corro-sion causes an increase in the concentration of dissolved Fe2þ inthe bentonite. Magnetite and siderite precipitate in the bentonite.The iron released by canister corrosion competes with Ni2þ forsorption sites and causes a decrease in Ni2þ sorption. Canister

corrosion leads to an increase in the pH of the bentonite becauseof the large consumption of proton. The overall effects of corro-sion products on the Kd

a of Ni2þ are: (1) a reduction of Kda at early

times (to104 years) due to the competition effect and (2) anincrease of Kd

a at late times (t4104 years) due to the largeincrease of pH caused by corrosion (Fig. 10).

3.4. Kd models

The results of Ni release from the near field computed with themulticomponent reactive transport model based on the thermo-dynamic sorption models (denoted here as base run) are com-pared with those obtained with simplified Kd models using theapparent Kd

a derived from the reactive transport model.The previous analyses show that the Kd

a depends on theconcentration of dissolved Ni, CNi (Fig. 6), and pH (Fig. 7). Sinceboth of the factors change with time, t, Kd

a also changes withtime. Kd

a can be factorized as Kad½CðtÞ,pHðtÞ�. To implement a

Kda into a classical Kd model, the general expression of Ka

d½CðtÞ,pHðtÞ� is approximated with a set of eight functions Ka

d½C�1,Ka

d½C�2, . . . and Kad½C�8 corresponding to the following pH values:

6.2, 6.4, 6.543, 6.6, 6.8, 7.2, 7.2 and 7.4. The jth Kd function, Kad½C�j,

corresponding to the jth pH value, pHj, is obtained by performinga RTM run with a fixed pH equal to pHj. The values of Ka

d½C�j forsome selected concentrations of dissolved Ni, CNi, are listed inTable 5. For a given pH, the values of Kd

a are the columns ofTable 5. The Kd

a decreases drastically when the concentration ofdissolved Ni increases. On the other hand, for a given concentra-tion of dissolved Ni, the values of Kd

a are the rows of Table 5.Clearly, Kd

a increases significantly when the pH increases. The Kda at

a given time t, Kad½C�t , is derived with the following sequence:

1.

Get the pH at time t computed with the base run (from Fig. 4):pH(t).

2.

Select the relevant pH interval corresponding to pH(t) from theeight selected pH values. Let pHi and pHiþ1 be the lower andupper values of the pH interval containing pH(t).

3.

Compute Kad½C�t from a linear interpolation of the functions

Kad½C�i and Ka

d½C�iþ1 corresponding to pHi and pHiþ1

Kad½C�t ¼ Ka

d½C�iþfKad½C�iþ1�Ka

d½C�ig½pHi�pHðtÞ�=ðpHiþ1�pHiÞ ð3Þ

Table 5Values of the apparent Kd

a (L/kg) as a function of the concentration of dissolved

Ni and pH obtained with the RTM from a set of runs with fixed pH.

Concentration of

dissolved Ni

(mol/L)

pH

6.2 6.4 6.543 6.6 6.8 7.0 7.2 7.4

1�10�18 171.0 271.0 375.0 426.0 659.0 1000.0 1500.0 2160.0

5�10�18 170.0 270.0 373.0 423.0 651.0 986.0 1460.0 2080.0

1�10�17 170.0 268.0 370.0 418.0 642.0 963.0 1410.0 1990.0

5�10�17 165.0 256.0 346.0 389.0 574.0 820.0 1130.0 1460.0

1�10�16 159.0 242.0 321.0 357.0 508.0 693.0 899.0 1110.0

5�10�16 124.0 169.0 206.0 220.0 272.0 323.0 372.0 419.0

1�10�15 97.6 125.0 148.0 152.0 178.0 205.0 233.0 266.0

5�10�15 39.6 46.2 52.6 53.6 63.3 76.4 93.8 116.0

1�10�14 25.3 29.7 34.3 35.8 44.4 56.0 71.0 89.7

5�10�14 10.9 14.2 17.3 18.7 24.3 31.2 38.6 45.9

1�10�13 8.6 11.3 13.7 14.7 18.6 22.7 26.7 30.1

Table 6Correction factors used to transform the Kd

a values in Table 5 into the Kd values of

the corrected variable-Kd model.

pH 6.2 6.4 6.543 6.6 6.8 7.0 7.2 7.4

Correction factor 1.00 1.00 1.00 1.67 1.87 2.18 2.18 2.29

Fig. 10. Time evolution of the apparent Kad of Ni2þ at r¼1.2 m for the base run and the run with corrosion products.

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266264

4.

Use the nonlinear isotherm Kad½C�t to calculate the Ni release

with the single-species Kd model implemented in GoldSim.This isotherm was obtained from the curve ABC in Fig. 6.

For given values of pH and the concentration of dissolved Ni2þ ,the Kd

a values obtained in the base run ðK1dÞ and in the run with a

fixed pH ðK2dÞ are different. Their ratio, K1

d=K2d , increases with pH.

It is equal to 1 for pHo6:543 and is larger than 2 at pH� 7:4.To take into account these differences, a pH dependant correctionfactor is used to transform the K2

d values in Table 5 into the K3d

values for the variable Kd model. The correction factors are listedin Table 6.

Calculations performed with Kd models assume that the 20 kgof nickel are released from the waste during 103 years at aconstant rate. Model comparison is made in terms of the rate ofNi released from the near field. The following three Kd modelswere tested:

1.

A constant-Kd model for Kd values of 10, 20 and 50 L/kg. 2. A variable-Kd

2 model using the values of Kd2 listed in Table 5.

This is the so-called uncorrected variable-Kd model.

3. A variable-Kd

3 model with the correction factors listed inTable 6. This is denoted as the corrected variable-Kd model.

Computed Ni2þ release rates with the constant-Kd model arecompared with those obtained from the base run in Fig. 11. Itshows clearly that the constant-Kd model does not reproduce theconcentrations computed with the RTM, especially at large times(t4104 years). The comparison of the variable-Kd models withthe base run shows that the variable-Kd models provide a goodapproximation of the Ni release rate computed with the base runfor t4104 years. The corrected variable-Kd model provides thebest solution. Therefore, while the constant-Kd model does notreproduce the Ni release, the variable-Kd model provides anacceptable surrogate for the base run.

There are some differences between both solutions at earlytimes which may be caused by the numerical dispersion errors ofthe base run solution which uses a sequential iterative approachto solve the coupled transport and chemical equations.

4. Summary and conclusions

A reactive transport model of Ni2þ in the near field of a HLWrepository in granite has been presented. In this model, Ni2þ issorbed by surface complexation and the protons are released fromthe surface complexes into solution, thus producing a small decreasein pH between 103 and 104 years. Later, pH increases due to calcitedissolution and the flux dilution at the boundary. Initially, theconcentration of dissolved Ni2þ is small and Ni2þ is mainly sorbedat strong sites which are saturated quickly. At larger Ni2þ concentra-tions, most of the Ni2þ sorbs at weak sites. When the sorbed Ni2þ onweak sites decreases with the dissolved Ni2þ concentration, the Ni2þ

sorbed through cation exchange increases because the decreases of

Fig. 11. Comparison of the Ni2þ release rate at the outer boundary computed with the base run of the reactive transport model and constant-Kd models for several Kd

values, the corrected and uncorrected variable Kd models.

C. Lu et al. / Computers & Geosciences 49 (2012) 256–266 265

other cations are larger for the reason of dilution. So totally, thesorbed Ni2þ keeps almost constant at the later time. The Kd

a of Ni2þ isnearly constant when the concentration of dissolved Ni2þ is smallerthan 10�6 mol/L. The initial Kd

a at repository conditions is around350 L/kg. Later, Kd

a decreases because the concentration of dissolvedNi2þ increases at a rate larger than that of sorbed Ni2þ . Kd

a reaches itsminimum value at t¼6350 years. Later, Kd

a increases because theconcentration of dissolved Ni2þ decreases while that of sorbed Ni2þ

remains almost constant.The corrosion products alter the pH of the bentonite pore water

significantly, and therefore affect significantly the sorption of Ni2þ inthe bentonite. The competition between corrosion products and Ni2þ

for sorption sites is less important than the effect on pH.The applicability of Kd models for Ni2þ has been compared with

the base reactive transport model run. Model results show that theapparent distribution coefficient of Ni2þ , Kd

a, depends on the concen-tration of dissolved Ni2þ and the pH of the bentonite pore water. TheKd

a of Ni2þ is nearly constant when the concentration of dissolvedNi2þ is o10�6 mol=L. A constant-Kd model does not reproduce therelease rates of Ni2þ from the bentonite into the granite.

The safety assessment of HLW repositories requires the eva-luation of prediction uncertainties. Such uncertainties are usuallyquantified with stochastic sensitivity methods which requireperforming a large number of model runs. Kd models are com-monly used for radionuclide sorption and migration through theengineered barrier because they are fast. The models based onthermodynamic sorption data provide a more sound representa-tion of radionuclide sorption and migration, but require a lot ofcomputing time. A model with a variable Kd which depends on pHand the concentration of dissolved Ni2þ provides a good surro-gate for the RTM for the conditions of the repository considered inour model.

In general, the apparent Kd of Ni is a nonlinear function ofphysical and chemical parameters and boundary conditions. Herewe accounted only for the two most relevant factors affecting theapparent Kd of Ni, i.e. pH and the concentration of dissolved Ni2þ .We claim that the changes in other parameters such as thediffusion coefficient and the water flux will affect the Kd mostlythrough the changes in the pH and the concentration of dissolvedNi2þ . Our study could be improved in the future by expressingthe apparent Kd in terms of a reduced number of factors using

high-dimensional model representation methods (Li et al., 2001).The model could also be improved by: (1) simulating thegeochemical evolution of the system during the bentonite resa-turation and the dissipation of the thermal pulse; (2) accountingfor surface diffusion and (3) considering the electric field thatdevelops when ions have different charges, diffusivities andconcentration.

Acknowledgments

This work was supported by ENRESA through the PAMINAProject (Contract # 78000125), the European Union through thePAMINA Project (FP6-036404) and the University of A Corunathrough a research scholarship awarded to the first author. Partialfunding was provided also by the Spanish Ministry of Science andTechnology (Project CGL2006-09080). We thank Lara Duro andCristina Domenech from AMPHOS XXI (Spain) for providingsupport on thermodynamic data and Wilfried Pfingsten from PSI(Switzerland) for fruitful discussions on reactive transport mod-eling of nuclide sorption for repository performance assessment.We are indebted to the anonymous reviewers who contributed tothe improvement of the paper with their reviews, comments andrecommendations.

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