Two cation exchange models for direct and inverse modelling of solution major cation composition in equilibrium with illite surfaces

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Abstract

Na/K, Na/Ca and Na/Mg exchange isotherms were performed on the fine fraction (<2 μm) of Imt-2 illite samples at a total normality of about 0.005 mol/L in anionic chloride medium. The derived selectivity coefficients for Na/K, Na/Ca and Na/Mg were found to vary as a function of the exchanger composition and compared well with the data collected in the literature for similar experimental conditions. Two models were built to reproduce the data: the first was a multi(2)-site model with constant Gaines and Thomas selectivity coefficients; the second was a one-site model taking into account surface species activity coefficients. The results of the models were in rather good agreement with both our data and literature data. The multi-site model proved to be efficient in predicting the exchanger composition as a function of the Na/Ca/Mg/K concentrations in solution, whereas the one-site model proved to be a better approach to derive the Na/Ca/Mg/K concentrations in solution based on the knowledge of the exchanger composition and the total normality of the solution. The interest of this approach is illustrated by the need for major cation solute concentration predictions in compacted clay for the characterization of nuclear deep disposal host rock repositories.

Introduction

The objective of the present study was to provide an up-to-date cation exchange constant database for Na, K, Ca and Mg on illite surfaces. Cation exchange databases are easily found in chemical reaction databases provided with speciation calculation codes, such as PHREEQC2 (Parkhurst and Appelo, 1999). However, (i) these databases contain no or few references to published results and (ii) the tabulated selectivity coefficients should be considered for montmorillonite only.

Knowledge of reliable cation exchange selectivity coefficients for major cations on illite is of importance in the context of nuclear waste deep disposal studies in order to simulate the porewater solute composition. The exchanger composition provides information about the relative amount of Na+, K+, Ca2+ and Mg2+ in solution:NaX+K+KX+Na+KNa/K2NaX+Ca2+CaX2+2Na+KNa/Ca2NaX+Mg2+MgX2+2Na+KNa/Mgwhere X represents one mole of the exchanger. The exchanger composition, an easily measurable parameter in compacted clayey rocks, is then an “image” of the porewater major cation composition, which cannot be directly characterized by water extraction and concentration measurements due to the low water content of these rocks (Bradbury and Baeyens, 1998, Pearson et al., 2003, Gaucher et al., 2006). The following calculation shows how to obtain the Na+ concentration assuming that (i) the exchanger composition is known, (ii) the sum of the equivalent concentrations of Na+, K+, Ca2+ and Mg2+ is equal to the sum of the equivalent concentrations of Cl and SO42 (i.e. neglecting H+ and other minor cation contributions) and (iii) the exchange selectivity coefficients are known.

In the following, the Gaines and Thomas convention is used to express the equilibrium equation with the exchanger phase (e.g. Sposito, 1981). According to this convention, the activity of an exchanged species is equal to the equivalent fraction occupied by the cation on the exchanger phase, times an activity coefficient. This activity coefficient is here set equal to 1 for the analysis that follows (Eqs. (1), (2), (3), (4), (5), (6), (7), (8)).

Exchange reaction equilibria then lead to the following equations:KexNa/Mg={Na+}2{Mg2+}×EMgX2ENaX2KexNa/Ca={Na+}2{Ca2+}×ECaX2ENaX2KexNa/K={Na+}{K+}×EKXENaXwhere values in brackets are representative of species activities and Ei is representative of the equivalent fraction on the exchanger of surface species i. The concentrations of each solution species as a function of the Na+ concentration are then:[Mg2+]=γNa+2γMg2+×[Na+]2KexNa/Mg×EMgX2ENaX2[Ca2+]=γNa+2γCa2+×[Na+]2KexNa/Ca×ECaX2ENaX2[K+]=γNa+γK+[Na+]KexNa/K×EKXENaXwhere γi is the activity coefficient of the species i in solution. These coefficients can be obtained using Debye-Hückel, Davies or Pitzer equations.

By combining Eqs. (4), (5), (6) with the electroneutrality relationship:[Cl-]+2×[SO42]=2×[Ca2+]+2×[Mg2+]+[Na+]+[K+]where values in square brackets are concentrations, one obtains:2×γNa+2ENaX2×[Na+]2×EMgX2γMg2+×KexNa/Mg+ECaX2γCa2+×KexNa/Ca+[Na+]×1+γNa+γK+[Na+]KexNa/K×EKXENaX-[Cl-]-2×[SO42]=0Bicarbonate concentrations are neglected in the electroneutrality relationship, because they were found to represent a minor fraction (∼2%) of the anionic charge in the considered clayey systems (e.g. Gaucher et al., 2006, for a Callovian–Oxfordian formation with total normality about 0.05–0.1 mol/L, or Pearson et al., 2003 for an Opalinus Clay formation). Second order equations similar to Eq. (8) can be derived for K, Ca and Mg. One obtains five second order equations with 10 unknown parameters (the five concentrations and the associated activity coefficients). Debye-Hückel, Davies or Pitzer (for concentrated solutions) equations give five other independent equations for the activity coefficients. Hence, the mathematical system is fully constrained (10 unknowns with 10 independent equations) and the Na, K, Ca and Mg concentrations can be calculated, based on the exchanger composition and the Cl and SO42 concentrations (and possibly other anions that contribute significantly to the total anion equivalent concentration). However, a good precision on the selectivity coefficient value is needed to obtain reliable concentration values. The present work aims at obtaining these selectivity coefficients for Na, K, Ca and Mg on illite.

Data collected from the literature are widely used in the following work together with new exchange data obtained in our laboratories. Data from the literature always originated from exchange experiments where both the solution and the exchanger composition were measured. New exchange data were obtained in the framework of the French Nuclear Waste Management Agency (ANDRA) investigation program on the clayey formation surrounding the French Underground Laboratory (URL) in Bure (Meuse Haute-Marne, France).

Section snippets

Chemicals

All solutions and suspensions were prepared with Millipore Milli-Q 18 MΩ water. NaCl, KCl, MgCl2 and CaCl2 solutions were prepared from analytical grade salts.

Clay material preparation

IMt-2 clay sample material was obtained from the Source Clays Repository (http://www.clays.org/sourceclays/SourceClaysCCM.html). After saturating the suspension with NaCl (0.5 mol/L), it was successively treated with a H2O2/HNO3 mixture (pH ∼2) to remove carbonate and organic matter impurities, then with a mixture of sodium

Experimental results

The complete set of data obtained in this study and from the literature is given in the table of Electronic Annex 1. It can be seen from this table that the Kv values calculated for divalent–monovalent cation exchange on the basis of the data reported by Thellier and Sposito (Thellier and Sposito, 1988, Thellier and Sposito, 1989b) are different from the values reported by these authors by a factor 2, probably due to a misuse of equivalent/kg instead of mol/kg for divalent cations in Thellier’s

Multi-site modelling approach

A multi-site modelling approach for cation exchange processes on illite has been shown to be successful in predicting Cs+ sorption under various conditions of pH and ionic strength (e.g. Brouwer et al., 1983, Poinssot et al., 1999, Zachara et al., 2002, Liu et al., 2004) or to explain the variation in CEC measurements as a function of ionic strength with the 22Na isotope dilution technique (Baeyens and Bradbury, 2004).

A similar approach was therefore adopted here in order to fit both the

One-site modelling approach

The uncertainty on the concentration prediction capability of the two-site model presented above leads us to model the data in a different way: the changes in selectivity coefficient are interpreted here as a continuous change in surface species activity coefficient. The use of a one-site model for cation-exchange on illite represents a departure from the approach used in all recent studies. Although questionable from a theoretical point of view, it will be shown in the following that this

Application to natural and engineered systems

Natural systems with a clay fraction constituted only by illite are not common. Here, we consider the example of illite rich layers in the Callovian–Oxfordian formation for the calculation of exchanger selectivity coefficients towards Na, Ca, Mg and K. Data on exchanger composition and ionic strength were obtained from Gaucher et al. (Gaucher et al., 2004) and are given in Table 4. Selectivity coefficients in the Vanselow convention were calculated using the model described in this paper (Table

Conclusions

We have shown that our one-site model considering the ionic strength effect and variations in the surface species activity coefficients is efficient for the determination of water major cation composition for a wide range of exchanger compositions. For natural systems, this model still needs to be refined in order to consider the presence of smectite and illite/smectite rather than pure illite. Moreover, the compaction effect deserves further study as a similar effect of compaction is expected

Acknowledgments

This research was funded by the French National Radioactive Waste Management Agency (ANDRA) and the French Geological Survey (BRGM) in the framework of the BRGM-ANDRA scientific partnership (THERMOAR project under the coordination of Dr. E. Jacquot and Dr. E. Gaucher). H.G. acknowledges ANDRA for her Ph.D. financial support, under the supervision of Dr. N. Michau. Dr. C.A.J. Appelo, two anonymous reviewers and Pr. Sposito, Associate Editor, are gratefully acknowledged for their constructive

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