Mathematical Modeling of a Cs(I) – Sr(II) – Bentonite – Magnetite Sorption System, Simulating the Processes Taking Place in a Deep Geological Repository

Abstract

The derivation of mathematical models of systems consisting of Cs(I) or Sr(II) and of bentonite (B), magnetite (M) or their mixtures (B+M) are described. The paper deals especially with modeling of the protonation and sorption processes occurring on the functional groups of the solid phase, namely on so called edge sites and layer sites. The two types of sites have different properties and, as a result, three types of Surface Complexation Models (SCM) are used for edge sites, viz. two electrostatic SCMs: the Constant Capacitance Model (CCM) and the Diffusion Double Layer Model (DLM), and one without electrostatic correction: the Chemical Model (CEM). The processes taking place on the layer sites are described by means of the Ion Exchange Model (IExM). In the course of modeling, the speciation of the given metal in the liquid (aqueous) phase has to be taken into account. In principle, the model of protonation or sorption processes is based on the reactions occurring in the aqueous phase and on the surface of the solid phase, and comprises not only the equations of the equilibrium constants of the individual reactions, but also the mass and charge balance equations. The algorithm of the numerical solution is compatible with FAMULUS 3.5 (a Czech software product quite extensively used at Czech universities in the last decade, the bookcase codes of which are utilized).