## 1 Introduction  
A nuclear regulatory authority must provide a permit for the construction and operation of a repository for radioactive waste disposal. Therefore, a comprehensive multidisciplinary approach to safety assessment is required in order to determine whether the repository can safely dispose of radioactive nuclear waste. Currently, radioactive waste disposal often employs a multibarrier system composed of engineering barriers and natural barriers. The engineering barrier system includes the waste form, waste package, and concrete; furthermore, a buffer material is combined with backfill material to act as a physical and chemical barrier to retard the migration of radionuclides. The multibarrier system is designed for the isolation of radioactive waste from the biosphere. The evolution of repositories for geological disposal involves highly complicated coupling processes, including the mechanical stress change (M) of the repositories during excavation and construction, radionuclide decay heat (T) after the repository's closure, groundwater pressure (H) in the geological environment, and the interactions of various geochemical processes (C) among the groundwater chemical species, rock minerals and possibly released nuclides. The chemical field plays a crucial role after the disposal site's closure. Chemical changes occur because of near-field geochemical interactions caused by changes in temperature, the flow field and the stress field. Geochemical evolution affects the chemical composition of groundwater, waste form dissolution and nuclide release. These changes are considered nuclide migration problems in the performance safety assessment of repositories. Therefore, geochemical models are required during the assessment process to predict the concentrations and chemical speciation of radionuclides entering the environment through different events and processes. A geochemical model is used to describe the water-gas-rock interaction in the aquatic system. The activity calculation method in a geo-chemical model is based on the ion-association theory. When the ionic strength of an aqueous solution increases to a value between 0.5 and 1 mol/kgw, the geochemical model can obtain reliable results. However, when the ionic strength exceeds this limit, a geochemical model based on an ion-interaction theory (such as the Pitzer equation) must be invoked for accurate predictions. There are two kinds of numerical methods for thermodynamic equilibrium modeling that can be applied to the calculation of speciation in aqueous systems, namely (1) the Law of Mass Action and (2) the Gibbs Energy Minimization. In general, two methods can be used to calculate the species distribution from a thermodynamic database. The first method consists in solving a set of nonlinear equations generated by the system's mass balances and equilibrium constants. The second method involves determining the most thermodynamically stable state by minimizing the reaction's free energy (the lowest energy state). Both methods are based on establishing the mass balance and chemical equilibrium state of the system. The relationship between the equilibrium constants, free energy, and the related chemical reactions and thermodynamic parameters is described below [1]. The following mass-action law defines an equilibrium constant in a thermodynamic database of a geochemical model:  
\[\text{aA}+\text{bB}\rightleftharpoons c+\text{dD} \tag{1}\]  
\[\text{K}=\frac{\text{a}_{\text{C}}^{\text{c}}\text{a}_{\text{D}}^{\text{d}}} {\text{a}_{\text{A}}^{\text{a}}\text{a}_{\text{B}}^{\text{a}}} \tag{2}\]  
where a, b, c and d are the stoichiometric coefficients of the reactants A and B, and the products C and D, respectively, for the reaction (1). The terms \(\text{a}_{\text{A}}\), \(\text{a}_{\text{B}}\), \(\text{a}_{\text{C}}\) and \(\text{a}_{\text{D}}\) are the activities of A, B, C and D, respectively. K denotes the thermodynamic equilibrium constant.