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).

Determination, Modeling and Evaluation of Kinetics of 223Ra Sorption on Hydroxyapatite and Titanium Dioxide Nanoparticles

“…Recently, the attention was devoted to nanoparticles (NPs) because of their large specific surface area that leads to relatively fast either sorption or desorption kinetics and high sorption capacity. Especially, the pH dependent sorption properties, based on the protonation or deprotonation of surface sites [1,[6][7][8][9], enable the sorption of cationic or anionic species on studied nanoparticles by ion exchange and surface-complexation mechanism simultaneously [6,[8][9][10][11].…”

Surface Complexation Models of Pertechnetate on Biochar/Montmorillonite Composite—Batch and Dynamic Sorption Study

“…The characterizations (surface area determination by nitrogen adsorption (NOVA 1200e Surface Area & Pore Size Analyzer, Quantachrome Instruments, Boyton Beach, FL, USA), field emission scanning electron microscopy (TESCAN MIRA 3, Oxford Instruments, Abingdon, UK), and Fourier-transform infrared spectroscopy (VERTEX 70, Bruker UK Ltd., Durham, UK)) were performed for both prepared materials BC1 and BC2a and they were well characterized in our previous work [17]. In order to complete and improve their surface properties, the X-ray fluorescence (XRF) and potentiometric, acid-base titrations [22] were performed.…”

“…The modeling of titration curves is described in detail in [22,24]. It is assumed that there are two types of surface, functional groups, namely the so-called edge and layer sites.…”

“…In general, if CEM and IExM models are taken into account [22], reactions taking place on the surface of biochar can be described by Equations ( 1)-( 3):…”

“…During this, the parameters of Freundlich equilibrium isotherm, k f,s and n f,s , and Peclet number (P e ), were sought. The software Famulus 3.5 (Charles University, Prague, Czech Republic) [22,24] and in-house computer code PNLRPA12.fm were used. Fit criterion WSOS/DF is equal to 3.01 × 10 −1 (BC1) and 3.83 × 10 −2 (BC2a) and the condition is WSOS/DF ≤ 20.…”