The influence of Fe(II) competition on the sorption and migration of Ni(II) in MX-80 bentonite

The results from batch sorption experiments on montmorillonite systems have demonstrated that bivalent transition metals compete with one another for sorption sites. For safety analysis studies of high level radioactive waste repositories with compacted bentonite near fields, the importance of competitive sorption on the migration of radionuclides needs to be evaluated. Under reducing conditions, the bentonite porewater chosen has a Fe(II) concentration of ∼5.3 × 10 −5 M through saturation with siderite. The purpose of this paper is to assess the influence of such high Fe(II) concentrations on the transport of Ni(II) through compacted bentonite, Ni(II) was chosen as an example of a bivalent transition metal. The one-dimensional calculations were carried out at different Ni(II) equilibrium concentrations at the boundary (Ni(II) EQBM ) with the reactive transport code MCOTAC incorporating the two site protolysis non electrostatic surface complexation/cation exchange sorption model, MCOTAC-sorb. At a Ni(II) EQBM level of 10 −7 M without Fe(II) competition, the reactive transport calculations using a constant K d approach and the MCOTAC-sorb calculation yielded the same breakthrough curves. At higher Ni(II) EQBM (10 −5 M), the model calculations with MCOTAC-sorb indicated a breakthrough which was shifted to later times by a factor of ∼5 compared with the use of the constant K d approach. When sorption competition was included in the calculations, the magnitude of the influence depended on the sorption characteristics of the two competing sorbates and their respective concentrations. At background Fe(II) concentrations of 5.3 × 10 −5 M, and a Ni(II) EQBM level of 10 −7 M, the Ni(II) breakthrough time was ∼15 times earlier than in the absence of competition. At such Fe(II) concentrations the Ni(II) breakthrough curves at all source concentrations less than 3.5 × 10 −5 M (fixed by the NiCO 3,S solubility limit) are the same i.e. Ni(II) exhibits linear (low) sorption. Competitive sorption effects can have significant influences on the transport of radionuclides through compacted bentonite i.e. reduce the migration rates. Since, for the case considered here, the Fe(II) concentration in the near field of a high-level radioactive waste repository may change in time and space, the transport of bivalent transition metal radionuclides can only be properly modelled using a multi-species reactive transport code which includes a sorption model. 1 Introduction In many radioactive waste repository concepts, compacted bentonite is proposed as a backfill surrounding the canisters containing vitrified high-level waste and spent fuel. Calculations have shown that a considerable number of radionuclides will have decayed to insignificant levels before having diffused through the bentonite thickness ( Nagra, 2002 ). However, these calculations were performed using the simple K d sorption concept. In an actual radioactive waste repository, many radionuclides, inactive metal contaminants and groundwater components will be present simultaneously in the aqueous phase at a range of concentrations which will vary during the temporal evolution of the repository system. An important aspect influencing the sorption of any dissolved radioactive metal under a given set of geochemical conditions is competition with other metals present. Currently, competitive sorption effects are not explicitly included in safety assessments, and are thus issues which need to be addressed. In some previous work Bradbury and Baeyens (2005a) investigated competitive sorption effects on Na- and Ca-montmorillonites using various combinations and concentrations of Co(II), Ni(II), Zn(II), Eu(III), Nd(III), Am(III), Th(IV) and U(VI). The experimental results were consistent with the observation that metals with similar chemistries (valence state, hydrolysis behaviour) compete with one another, but metals with dissimilar chemistries do not compete i.e. competition is selective. In compacted, high clay mineral content systems, such as bentonite, significant concentrations of Fe(II) may be present, from, for example, saturation with siderite, FeCO 3,S . Also, Fe(II) in solution arises from the anaerobic corrosion of steel canisters in the near-field of radioactive waste repositories. Furthermore, it is likely that Fe(II) concentrations will not be depleted to any significant extent by sorption/diffusion since they are maintained by the solubilities of Fe phases present and by the anaerobic corrosion products/secondary mineral formation at the canister/bentonite interface ( Milodowski et al., 2009 ). If it is assumed that the compacted bentonite porewater is saturated with siderite, then the total Fe(II) concentration is ∼5 × 10 −5 M (pH = 7.25, pCO 2 = 10 −2.2 bar). Such an Fe(II) equilibrium concentration represents a considerable sorption competition potential for radioactive transition metals entering the bentonite from the waste e.g. 59 Ni(II). However, it is unclear whether this is a significant effect, or not, as far as performance assessment is concerned. The reason for this is that there are no reliable batch sorption measurements for Fe(II) on montmorillonite, nor are there any isotherm measurements of Ni(II) on montmorillonite in the presence of a constant concentration of Fe(II). Furthermore, there are no reliable diffusion data for Ni(II) in compacted bentonite in the presence and absence of a well defined Fe(II) concentration. Thus, the potential impact of high aqueous Fe(II) concentrations in compacted bentonite systems on the migration of divalent radioactive transition metals is unknown. Nevertheless, an assessment of the potential effect is important in the safety analyses for radioactive waste repositories. This is not only an issue for compacted bentonite, but also for any argillaceous host rocks containing siderite e.g. Opalinus Clay, Callovo Oxfordian. Hence, the only approach possible at the moment is a modelling one. For the case study presented here, 59 Ni(II) (half-life ∼7.6 × 10 4 a) was selected. Its sorption properties on montmorillonite/bentonite have been well investigated ( Baeyens and Bradbury, 1997; Bradbury and Baeyens, 1997, 1999 ). However, no such data are available for Fe(II) and the required model data were obtained as described below. 2 The 2SPNE SC/CE sorption model: equations and parameters The sorption model used in this study on the influence of Fe(II) on the concentration dependent uptake of Ni(II) on MX-80 (Section 3 ), and later, on the transport of Ni(II) through compacted MX-80 bentonite (Section 6 ), is the two site protolysis non electrostatic surface complexation and cation exchange (2SPNE SC/CE) model. The details of this model have been described on numerous occasions e.g. Bradbury and Baeyens (1997, 2006) , and will not be repeated here. However, a few explanatory remarks are needed for completeness and understanding. The surfaces of montmorillonite clay minerals carry a permanent negative surface charge resulting from the isomorphous substitution of lattice cations by cations of a lower valency. This total permanent negative surface charge, known as the cation exchange capacity of the clay, is neutralised by the presence of an excess of electrostatically bound cations held close to the surface which can exchange with cations in solution. Cation exchange is characterised by a pH independent stoichiometric sorption which tends to become more important the lower the pH, the lower the background electrolyte concentration and the higher the sorbate concentration. Cation exchange is treated following the Gaines and Thomas (1953) convention. A further set of active sorption sites, “edge” or “broken bond” sites, are envisaged to be situated at the edges of clay platelets. They are perceived as being surface hydroxyl groups, ( SOH), which can protonate and deprotonate and interact with aqueous metal species to an extent which depends strongly on the pH. In order to describe the protonation/deprotonation behaviour of montmorillonite, a two site protolysis model ( S W1 OH, S W2 OH) is used. For the modelling of sorption edges and sorption isotherms, two site types are also required, a so called strong site, S S OH, and one of the sites used to describe the titration data, S W1 OH, called weak-sites-1. Titration and isotherm measurements were used to determine site capacity and protolysis parameters which were fixed in all of the modelling ( Bradbury and Baeyens, 1997, 1999 ). The model was developed without the need for electrostatic terms in the mass action relations used to define protolysis and surface complexation constants. In general the surface complexation reactions used can be written as: (1) SOH + Me 2 + ⇔ SOMe + + H + ( log K 0 ) (2) SOH + Me 2 + + H 2 O ⇔ SOMe ( OH ) 0 + 2 H + ( log K 1 ) (3) SOH + Me 2 + + 2 H 2 O ⇔ SOMe ( OH ) 2 - + 3 H + ( log K 2 ) where Me 2+ represents Ni 2+ or Fe 2+ . Nickel(II) and Fe(II) will speciate in the MX-80 porewater, and the assumption made is that only free cations and hydrolysed species are sorbing. All other species are treated as being non-sorbing. No reliable surface complexation constant data for the uptake of Fe(II) on montmorillonite could be found in the open literature. Consequently, the Linear Free Energy Relationships (LFERs) for the strong and weak sites in the 2SPNE SC/CE model ( Bradbury and Baeyens, 2005b ) were used to generate the required values . For simplicity and consistency the corresponding values for Ni(II) were also obtained in the same manner. (The Ni(II) surface complexation constants taken from the LFERs differ from those reported in Bradbury and Baeyens (2005b) . However, the Ni(II) sorption isotherms, calculated with each set of constants for MX-80 bentonite in the porewater given in Table 1 , are virtually the same.) The LFER between surface complexation constants ( S K x −1 ) – x indicates the number of protons involved in the reaction – and the corresponding hydrolysis constants ( OH K x ) used for montmorillonite are given in following equations, (4) Strong sites log S K x - 1 = 8.1 + ( 0.90 log OH K x ) (5) Weak sites log W K x - 1 = 6.2 + ( 0.98 log OH K x ) Table 2 summarises the surface complexation constants derived from the relationships given in Eqs. (4) and (5) for strong and weak sites for each metal. The hydrolysis constants used are given in Table 3 . For all other speciation calculations the Nagra/PSI Thermodynamic Data Base TDB-01/01 was used ( Hummel et al., 2002 ) which also includes data for Fe(II) taken from Nordstrom et al. (1990) . The surface complexation equations given above are written with charged surface species. For example, the mass action equation for the reaction given in Eq. (1) is written as: (6) K 0 = [ ≡ SOMe + ] · { H + } [ ≡ SOH ] · { Me 2 + } where […] represents concentrations and {…} activities. Because of the way surface and aqueous species are treated in the calculations, the above notation leads to a charged solution compensated by a charged surface i.e. overall charge neutrality. This is not an important issue when modelling sorption data from batch sorption experiments which have a very low solid to liquid ratio (∼1 g L −1 ). However, when dealing with transport calculations in compacted systems using the 2SPNE SC/CE sorption model at high solid to liquid ratios (100’s of g L −1 ), large (opposite) charges would develop at the surface and in the aqueous phase. Generally, reactive transport codes monitor charge and mass balances as checks on the calculations. In addition, the calculations would involve the transport of charged diffusion fronts. In order to avoid such unnecessary and unwanted complications, the surface complexation equations above were re-formulated to achieve charge-balanced surfaces and solutions e.g. Eqs. (1) and (6) are re-written as: (7) SOH + Me 2 + + 2 Cl - ⇔ SOMe - Cl 0 + H + + Cl - (8) K 0 = [ ≡ SOMe - Cl 0 ] · { H + } [ ≡ SOH] · { Me 2 + } · { Cl - } The surface charge was neutralised with either Na + or Cl − ions. (Charge balancing with NaCl is an assumption, and was made because of the high concentration of NaCl in the MX-80 bentonite porewater relative to other components, see Table 1 .) The surface complexation constants given in Table 2 were modified by the activity of either the Na + or the Cl − ions in the aqueous phase. In the cases where the surface complexes were neutral, no modifications were required The charge compensated surface complexation reactions together with the corresponding surface complexation constants for protolysis and Fe(II) and Ni(II) sorption onto strong and weak sites are summarised in Table 4 . (It should be noted that there are no differences between the sorption edges and isotherms calculated with the surface complexation data sets given in Tables 2 and 4 .) Cation exchange reactions and corresponding selectivity coefficients are taken from ( Bradbury and Baeyens, 1997, 2002 ) and are included throughout, but because of the nature of the MX-80 bentonite porewater (pH = 7.25, high ionic strength, see Table 1 ), they play essentially no role in the sorption of Fe(II) and Ni(II). The site capacities and cation exchange capacity for MX-80 bentonite are given in Table 5 , assuming that the montmorillonite content of MX-80 is 75 wt.% ( Müller-Von-Moos and Kahr, 1983 ). 3 Calculated Ni(II) sorption isotherms: competition with Fe(II) Ni(II) sorption isotherms on MX-80 were calculated in the absence and presence of different equilibrium concentrations of Fe(II) in the bentonite porewater, Table 1 , using the data given in Tables 3–5 . The results are displayed in Fig. 1 a and b as sorption isotherms, and as solid liquid distribution ratios versus Ni(II) equilibrium concentrations, respectively. The maximum Ni(II) and Fe(II) equilibrium concentrations considered were 3.5 × 10 −5 M and 5.3 × 10 −5 M, respectively, which correspond to the solubility limits of NiCO 3,S and siderite (FeCO 3,S ) respectively ( Berner, 2002 ). In order to illustrate the influence of lower Fe(II) concentrations, an equilibrium value of Fe(II) 6 × 10 −6 M was chosen for the purpose of the calculation. In the equilibrium Ni(II) concentration range considered, sorption is predominantly occurring on the strong sites. The decrease in Ni(II) sorption at increasing Fe(II) concentrations is due to the lower uptake on these sites caused by competition. As can be readily appreciated in Fig. 1 b, the concentration range over which the sorption is linear, increases with increasing Fe(II) concentrations, but at the same time the sorption values for Ni(II) decrease. This continues until virtually all of the strong sites are occupied by Fe(II), thus blocking Ni(II) sorption on these sites. The uptake on the weak sites is scarcely affected, even at the highest Fe(II) concentration, because of their much higher sorption site capacity ( Fig. 1 a). The net result is that the Ni(II) sorption becomes essentially constant over the whole concentration range at the highest Fe(II) concentrations ( Fig. 1 b). Thus, at the background Fe(II) level in the MX-80 system corresponding to saturation with siderite, Ni(II) mainly sorbs on the weak sites due to the competitive influence of Fe(II) on the strong sites, resulting in a linear sorption isotherm for Ni(II) with a sorption value of ∼30 L kg −1 i.e. ∼20 times lower than in the absence of Fe(II). Although this is a significant decrease, Ni(II) is nevertheless still effectively taken up by the bentonite. The aim in the following section is to show how calculations on the diffusive transport of Ni(II) through compacted bentonite are influenced by competition with Fe(II). 4 MCOTAC-sorb In order to calculate the influence of competitive sorption processes on the transport of radionuclides in compacted systems, a reactive transport code containing a sorption model is required. Therefore, the 2SPNE SC/CE model was incorporated into the “in house” reactive transport code MCOTAC ( M odular C oupling O f T ransport A nd C hemistry, Pfingsten, 1996, 2002, 2010 ), and together called MCOTAC-sorb. Briefly, the reactive transport code MCOTAC calculates the one- or two-dimensional advective–dispersive/diffusive transport of all species in solution coupled with simultaneous equilibrium calculations for chemical reactions in solution, on surfaces and with the mineral phases present. Kinetic mineral reactions can also be accommodated (see Pfingsten, 2010 ; and references therein). Sorption can be included via a simple K d , or in the case of MCOTAC-sorb, via a fully integrated, mechanistic sorption model in the chemical module. The Davies equation is used for ionic strength corrections. The flow, transport and chemical reaction modules are sequentially (iteratively) coupled in order to take mineral dissolution/precipitation reactions into account which can change porosity, hydraulic conductivity and diffusivity and thereby the flow and transport parameters for solutes. These parameters (porosity, hydraulic conductivity, diffusivity) are variable in space and time and can be modified either by exchange terms of the coupled modules, or externally by pre-defined functions or look-up tables. Diffusion/dispersion coefficients can be space and time dependent, as well as flow velocities and mineral distributions in the model domain. Regarding the calculations of Ni(II) diffusion in bentonite, the multi-species diffusion is described by a set of diffusion equations in one spatial dimension, one for each species i in solution (9) ∂ C i ∂ t = D p ∂ 2 C i ∂ x 2 - R i , i = 1 , 2 , … , n aqueous , where C i [M] is the concentration of species i , D p [m 2 s −1 ] is the pore diffusion coefficient, t [s] and x [m] are coordinates in time and space, and R i [mol m −3 s −1 ] denotes a source/sink term for species i . The code accounts for equilibrium reactions in solution or between the solution and species sorbed onto immobile mineral surfaces according to ( Jakob et al., 2009 ): (10) R i = ∑ j = 1 n sorbed ν i , j 1 - ε ε ρ ∂ S j ∂ t , i = 1 , 2 , … , n aqueous , where n aqueous and n sorbed denote the number of species in solution and sorbed, respectively, and ν i,j [−] are stoichiometric coefficients. A constant mean value for the diffusion coefficient for all ions in solution was assumed in order to maintain charge balance during transport calculations. Lichtner (1996) has discussed species dependent diffusion coefficients and concluded that even if species dependent diffusion coefficients are used (which have to be known for all species in solution, which is hardly possible because of the lack of data), a charge imbalance might be created. This is compensated by electrical forces inducing corrections to the diffusion coefficients of individual species in solution, and, as a consequence, a mean diffusion coefficient results which can then be used for all species in solution. Non mobile species such as the surface sorption sites ( Table 5 ) can be introduced. Here, the source/sink terms, R i , in Eq. (9) are defined by mass action equations, e.g. Eq. (8) , maintaining the surface sorption and ion exchange equilibria during a time step Δ t for the diffusion of solutes in the bentonite porewater including related mass balances. It should be noted that sorption can be presented by a single K d for Ni(II), where the K d is defined as (11) K d = [ Ni sorbed ] { Ni dissolved } where Ni sorbed is the quantity of Ni(II) on the solid phase in mol kg −1 and Ni dissolved is the equilibrium Ni(II) concentration in the aqueous phase in mol L −1 . In this case the number of diffusion equations (Eq. (9) ) is reduced to only one; for Ni dissolved . 5 Calculation conditions Transport calculations were performed in a MX-80 bentonite compacted to a dry density of 1400 kg m −3 and total porosity of ∼0.49 (the equivalent solid to liquid ratio is 2.84 kg L −1 ). The compacted bentonite is treated as a homogenous porous medium in which all species are assumed to diffuse at the same rate with D e equal to 2.7 × 10 −10 m 2 s −1 . All cation exchange and surface complexation sites ( Table 5 ), as determined in sorption experiments on dispersed systems, are assumed to be accessible. The equilibrium bentonite porewater used is given in Table 1 . In total 24 so called “basis species” and 65 complexes in solution and on surfaces were used for the reactive transport calculations together with five solids. Table 6 shows the thermodynamic data for the major Fe(II) and Ni(II) complexation reactions in solution taken into account in the reactive transport calculations. Table 7 gives the percentage distribution of major aqueous species of Ni(II) and Fe(II) in the MX-80 porewater. For Ni(II), an initial background concentration of 10 −10 M was chosen, which is low compared to the Ni(II) source concentrations at the boundary, but might be realistic in natural systems. (The choice of an extremely low initial Ni(II) concentration of 10 −20 M yielded no differences in the calculated Ni(II) breakthrough curves, except that the Ni(II) breakthrough starts at lower Ni(II) concentration levels.) Siderite (FeCO 3,S ) is present in MX-80, and saturation with this mineral is assumed to be maintained in the real system, yielding an equilibrium concentration of Fe(II) of 5.3 × 10 −5 M. Another Fe(II) concentration fixed at 6 × 10 −6 M was arbitrarily chosen to illustrate the influence of lower aqueous Fe(II) levels. Each of the chosen fixed Fe(II) concentrations was set to be in equilibrium with the cation exchange and surface complexation sites of the montmorillonite. The transport calculations through compacted bentonite were carried out for two Ni(II) concentrations at the bentonite boundary, 10 −7 M and 10 −5 M. The Ni(II) concentrations were chosen deliberately. For the 2SPNE SC/CE model, sorption at Ni(II) concentrations ⩽10 −7 M is occurring on the strong sites in a linear sorption region, whereas at concentrations ⩽10 −5 M, Ni(II) uptake is occurring in non linear and linear sorption regions. For the transport calculations carried out in the absence of Fe(II), and assuming constant K d , the sorption values were taken from the isotherm given in Fig. 1 i.e. 565 L kg −1 at a Ni(II) equilibrium concentration equal to 10 −7 M, and 132 L kg −1 at a Ni(II) equilibrium concentration of 10 −5 M. In all other calculations the 2SPNE SC/CE model sorption description was used with the parameters given in Tables 3–7 . The conditions for the Ni(II) transport calculations are summarised in Table 8 . For all aqueous species a “no flow” boundary condition was assumed ( Fig. 2 ), simulating a bentonite – canister interface from which radionuclides and/or canister material would enter the bentonite porewater. Also, the extent of the bentonite in the x -direction was assumed to be infinite, with a “free outflow” boundary condition. In order to set a chosen equilibrium Ni(II) concentration in the porewater in the first bentonite volume element as a boundary condition for the calculations, a fictitious solid phase, NiX, was defined. The solubility product of this fictitious phase could be altered in any particular calculation to give a defined Ni(II) concentration required at the boundary. This procedure maintained the overall charge balance in the solution, and the speciation of Ni(II) in the equilibrium bentonite porewater was not affected. The concentration of Ni(II) was chosen so that no precipitation occurred in the bentonite porewater. At each time step, NiX (with the stoichiometric composition Ni 2+ X 2− ) was released into the porewater of the first bentonite volume element at a level according to a pre-defined NiX solubility product. There, the NiX was equilibrated simultaneously with the aqueous solution, the cation exchange sites and the surface complexation sites from the previous time step. This process was repeated until the chosen Ni(II) equilibrium concentration in the porewater in the first bentonite volume element was reached. The process is illustrated in Fig. 2 , and leads to a “ramp type input”, shown in Fig. 3 , for the two selected Ni(II) equilibrium concentrations of 10 −7 and 10 −5 M. From now on these Ni(II) equilibrium concentrations at the boundary are referred to as “Ni(II) EQBM ”. This Ni(II) ramp-like concentration increase was necessary to achieve convergence during the initial Ni(II) diffusion phase. “Switching” Ni(II) instantaneously from a low background level to the chosen Ni(II) concentration caused convergence problems in the code since the whole set of species (in solution and on the surfaces) had to change by orders of magnitudes within one time step. (This is also not physically realistic.) An alternative boundary condition would have been to fix the Ni(II) concentration in a “large reservoir” of bentonite porewater at the boundary. However, this would have resulted in SO 4 2 - and CO 3 2 - gradients across the boundary inducing SO 4 2 - and CO 3 2 - diffusion causing calcite and gypsum precipitation in the bentonite. Mineral precipitation reactions would have been accompanied by porosity changes. Such additional unwanted complications in the Ni(II) diffusion and sorption competition analysis were avoided by the present approach. The same procedure was used in the reactive transport calculations for the K d -approach, where at each time step “Ni(II)” instead of “Ni 2+ X 2− ” was released into the porewater of the first bentonite volume element. It should be noted that the K d approach does not include any Ni speciation and, therefore, the loading procedure for the K d approach is up to a Ni(II) concentration of 10 −7 M or 10 −5 M. However, the form of the Ni(II) ramp was different for the K d and MCOTAC-sorb calculations at the higher fixed Ni(II) concentration ( Fig. 3 ) because of the non-linear uptake behaviour of Ni(II) on MX-80. The Ni(II) sorption in the latter calculations is stronger at lower Ni(II) concentrations than in the K d approach. The consequence was that the Ni(II) concentration was reached earlier in the K d approach. For a Ni(II) EQBM level of 10 −7 M, there was no difference because the sorption was linear under this condition i.e. the same for both approaches. Loading up to 10 −7 M Ni(II) takes longer than for loading up to 10 −5 M Ni(II) simply because the sorption in the former case is stronger (see Fig. 3 ). 6 Results and discussion A major goal in this report was to assess the potential influence of different background concentrations of Fe(II) on the transport of Ni(II) through compacted bentonite. A further aim was to compare the diffusion breakthrough curves using a constant K d approach with ones in which retardation was calculated with the MCOTAC-sorb reactive transport code. The breakthrough curves were calculated for Ni(II) in solution at 0.2 m and 0.8 m from the compacted bentonite surface in contact with a fixed value for Ni(II) EQBM . 6.1 Ni(II) diffusion without Fe(II) competition In Fig. 4 the breakthrough curves calculated using the K d approach and the MCOTAC-sorb code for a Ni(II) EQBM of 10 −7 M are compared. As can be seen, the breakthrough curves are essentially identical, as expected, since at such low Ni(II) concentrations the sorption calculated by the 2SPNE SC/CE model is linear i.e. equivalent to a constant K d . This is essentially a trivial result, but provides a check that the MCOTAC-sorb code is performing correctly. However, if the breakthrough curves for a Ni(II) EQBM of 10 −5 M are compared ( Fig. 5 ), clear differences between the two approaches become apparent. The calculated breakthrough using the K d -approach occurs about a factor of five times earlier than the one calculated with MCOTAC-sorb code. The reason for this is that in the K d approach the sorption value was chosen at Ni(II) EQBM of 10 −5 M, but the sorption of Ni(II) is non-linear ( Fig. 1 ). This implies that the sorption of Ni(II) in such a calculation is consistently underestimated at all concentrations less than 10 −5 M. This is clearly conservative. In the MCOTAC-sorb calculations, the non-linear Ni(II) sorption behaviour is included. The form of the breakthrough curves are different for the cases where linear and non-linear sorption are considered ( Fig. 5 ). The typical shape for K d is a “symmetric S-shape” breakthrough curve whereas for non-linear sorption it is an “asymmetric S-shape” with an initial low level but longer Ni(II) breakthrough. Between 10 and 40 a there is only a small increase in the Ni(II) concentration ( Fig. 5 ), whereas after 40 a the breakthrough becomes stronger and steeper. 6.2 Ni(II) diffusion with Fe(II) sorption competition Fig. 6 shows the influence of the sorption competition of Fe(II) at two equilibrium concentrations, 6 × 10 −6 and 5.3 × 10 −5 M, on the breakthrough curves for Ni(II) at 0.2 m and a Ni(II) EQBM level of 10 −7 M. These two breakthrough curves are compared with one in which Fe(II) competition was not included. A similar set of breakthrough curves calculated at a Ni(II) EQBM level of 10 −5 M is shown in Fig. 7 . The trends seen for the two Ni(II) EQBM concentrations are the same i.e. increasing equilibrium Fe(II) concentrations lead to decreasing breakthrough times and changes in the breakthrough curve profiles. Under siderite saturation conditions (Fe(II) = 5.3 × 10 −5 M), the Ni(II) breakthrough curves for Ni(II) EQBM levels of 10 −7 and 10 −5 M are ∼17 and 13 times earlier, respectively, than when Fe(II) competition is not included. The calculated behaviour of the Ni(II) breakthrough curves illustrated in Figs. 6 and 7 can be readily understood by referring to the sorption isotherms given in Fig. 1 . Here it is shown that the Ni(II) sorption isotherm without Fe(II) is non linear. As the Fe(II) equilibrium concentration is increased, the sorption competition to Ni(II) uptake increases and this results in lower Ni(II) sorption values and a change in the shape of the sorption isotherm. The competitive effect of Fe(II) is a highly non linear function of both Fe(II) and Ni(II) concentrations. The breakthrough curves from Figs. 6 and 7 for Ni(II) EQBM levels of 10 −7 M and 10 −5 M, and an Fe(II) equilibrium concentration of 5.3 × 10 −5 M, are normalised according to their Ni(II) EQBM levels and plotted together in Fig. 8 . The aim here is to illustrate the effect of Ni(II) EQBM levels on the breakthrough curves under realistic bentonite porewater conditions i.e. at saturation with siderite. The calculations clearly show that the breakthrough curves lie over one another i.e. there is no difference in the normalised breakthrough times and in the shapes of the curves over this entire Ni(II) concentration range. The interesting feature is that with increasing Fe(II) equilibrium concentrations, the concentration range over which Ni(II) exhibits linear (but lower) sorption is extended ( Fig. 1 ). This explains why the breakthrough curves in the Ni(II) EQBM range from 10 −7 to 10 −5 M are the same under siderite saturation conditions. In a final comparative exercise, Ni(II) breakthrough curves were calculated with MCOTAC-sorb for a Ni(II) EQBM level of 10 −5 M in a system with 5.3 × 10 −5 M Fe(II), and without Fe(II), at distances of 0.2 and 0.8 m into the bentonite ( Fig. 9 ). The latter value represents the thickness of the bentonite in the planned Swiss concept for a high level waste repository ( Nagra, 2002 ). The same spatial discretisation was used in all of the calculations which implies considerably longer computing times for the 0.8 m cases. Both pairs of breakthrough curves – no Fe, and Fe competition – at 0.2 and 0.8 m have similar individual shapes and the breakthrough times scaled approximately as the distance squared. Again, although this was expected, the results confirmed the consistency of the modelling. 7 Summary The MCOTAC-sorb code was used to calculate Ni(II) breakthrough curves within a bentonite column for a series of Ni(II) EQBM concentrations at the bentonite boundary. In a first stage, the breakthrough curves calculated using constant K d values for two Ni(II) EQBM levels of 10 −7 and 10 −5 M were compared with those obtained using the MCOTAC-sorb code. The breakthrough curves were identical for 10 −7 M Ni(II) EQBM , because at such trace concentrations the sorption model predicts linear sorption with the same value as the K d used. At a higher Ni(II) EQBM level (10 −5 M) the breakthrough calculated with MCOTAC-sorb was shifted to later times by a factor of ∼5 compared to the calculation with a K d value. The reason for this difference is that the MCOTAC-sorb calculation takes into account the non-linearity of the Ni(II) sorption on bentonite i.e. Ni(II) exhibits higher sorption values than the K d value chosen at all concentrations below 10 −5 M. In general, at trace Ni(II) concentrations, the K d and the MCOTAC-sorb calculations yield the same breakthrough curves, whereas at higher Ni(II) concentrations the calculations with the appropriate K d values are conservative. In a radioactive waste repository the conditions will be reducing, and the compacted bentonite porewater will contain significant Fe(II) concentrations corresponding to saturation with siderite. For the system considered here the equilibrium Fe(II) concentration is 5.3 × 10 −5 M. It is anticipated that Fe(II) will compete with Ni(II) for the available sorption sites resulting in a decrease in the migration times for Ni(II) through the bentonite compared with the K d approach usually used. The results of the calculations with MCOTAC-sorb showed that the influence of sorption competition under the conditions specified is significant. The breakthrough curves calculated for Ni(II) EQBM values of 10 −7 M and 10 −5 M exactly overlap, implying that the Ni(II) sorption behaviour at all Ni(II) EQBM values up to ∼3.5 10 −5 M (for NiCO 3,S as the solubility limiting Ni(II) solid phase) is linear. Under these circumstances it would be justified to use a single K d value for the sorption of Ni(II) across the whole possible Ni(II) concentration range. However, this K d value is much lower than any of the values measured in a normal Ni(II) isotherm determination in the absence of Fe(II). For example, the Ni(II) breakthrough time with Fe(II) competition occurs a factor of approximately 15 times earlier than in the case when a constant K d value corresponding to a Ni(II) equilibrium concentration of 10 −7 M is used. In this modelling study only Fe(II) competition was taken into account. 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