A Solid Solution Model for Sorption of Radionuclides in Cement
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A Solid Solution Model for Sorption of Radionuclides in Cement Allan T. Emrén Dept. Nuclear Chemistry, Chalmers University of Technology SE-41296 Goteborg, Sweden E-mail: [email protected]
ABSTRACT Of these two main phases in cement, portlandite is rather compact while the gel phase has a very irregular morphology, probably fractal. This work essentially deals with sorption that takes place as absorption in the gel phase, but the same theory is applicable for any of the phases present in cement. It is also able to handle sorption in any combination of phases in the cement. A model for multi component solid mixtures has been developed, essentially following the Guggenheim excess free enthalpy approach. Measurement of Kd for one gel composition makes it possible to calculate Kd values during the entire process of cement degradation. The main limitation is that the concentration of the radionuclide has to be low enough for all higher terms in the series expansion to be negligible. The model is mostly valid for elements forming cations and it also requires the sorbed element to form a compound of reasonably low solubility with one of the anions in cement (hydroxide or silicate). Kd values for Ni in cement has been taken from the literature and used to illustrate the model. INTRODUCTION Cement consists of a considerable number of phases, the two most important of which are the gel phase and a phase that is almost pure portlandite, Ca(OH) 2. Both can be considered as solid solutions, which means that they are able to incorporate different elements into their structure. Of these two phases, portlandite is rather compact while the gel phase has a very irregular morphology, probably fractal. This suggests that sorption essentially takes place as absorption in the gel phase. In addition to the CSH gel and portlandite phases, smaller quantities of other phases containing mostly Ca, Al, Fe, Si and S are present. A cement model consisting of several phases has been developed elsewhere [1,2] and it has been found to give good agreement with leaching experiments[3]. THEORY To handle the sorption, one may start from the definition of Kd.
mr − n, s m V ( aqueous phase ) m( solid phase) Kd = = r − n, s mr−n ,aq mr −n ,aqm( solid phase) V (aqueous phase)
JJ9.3.1
(1)
where V and m denote volume and mass respectively. As will be seen below, Kd is approximately a constant when the total concentration of the radionuclide is small compared to that of other elements. If this is the case, the speciation of the radionuclide in the aqueous solution is independent of the concentration. We will now approximate the cement-radionuclide system as a solid solution (mixture) with three end members, CaH2SiO4, CaOH and R-nOn. Here, the radionuclide is denoted by R-n. From a thermodynamic point of view, the choice of end members is not critical. Practically, however, the behaviour of activity coefficients is more regular, the better the end members fit to the real situation. To find equilibrium properties, one has to calculate the free enthalpy
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