## 2 Development of Geochemical Models  
Geochemical models enable the conceptualization of chemical reactions to be represented by mathematical equations, which can then be coded up as a geochemical modeling software tool. The first geochemical model was introduced by [PERSON] and [PERSON] in 1962 [15]. [PERSON] and [PERSON] established a chemical model of seawater based on the major ions present in seawater. In the 1980s, researchers studied water-rock interactions from the perspective of physical chemistry and further integrated solute transport, dispersion transport, chemical reactions and water-rock interface chemistry. A coupled model of solute transport was therefore developed. Over the last few decades, geochemical models have been developed rapidly in response to an increasing number of problems in geochemical and environmental science which require quantitative analysis and assessment. In research supporting nuclear waste disposal, geochemical models have become a crucial tool for the simulation of geochemical processes, including the formation and evolution of hydrochemical components in water-rock systems, and surface complexation between minerals and nuclides. Geochemical models can simulate many geochemical phenomena and processes, covering: (1) chemical species in water; (2) the saturation index (SI), which can be expressed as SI = log(IAP/Ksp), where IAP is the ionic activity product, and Ksp is the solubility product; (3) the mixing of more than two solutions, as well as the resulting aqueous species composition, Eh, pH, and SI; (4) dissolution (precipitation) caused by the interaction of organic and inorganic compounds; (5) reduced pressure or changes in water's chemical composition and SI caused by boiling or the addition of a gas; (6) the rates or kinetics of geochemical reactions; and (7) water-rock interactions. Simulations of water-rock interactions can be further divided into forward and inverse modeling. Forward modeling involves the simulation of possible dissolution-precipitation, adsorption-desorption and oxidation-reduction reactions, and the prediction of the chemical species involved in the dissolution or precipitation, as well as the mass being adsorbed or desorbed by the minerals. Inverse modeling involves the simulation of the aqueous species composition and Eh and pH values in water-rock interactions. As chemical effects are highly crucial in the closure of a high-level radioactive waste disposal site, a geochemical model can provide an effective means to calculate the formation and evolution of chemical species under long-term water-rock interactions in both the engineering and natural barriers of the repository. Such a model is usually based on the thermodynamic data of chemical reactions. The geochemical reaction is represented by mathematical equations, which can be written into a numerical model and solved using a mathematical algorithm for its compilation into computer code. The approach of the law of mass action requires the concentration of the master chemical component and thermodynamic data such as the equilibrium constant of the product species at the pressure and temperature of interest in the heterogeneous system. For the Gibbs energy minimization, a value of the standard Gibbs free energy of each chemical component is taken from the thermodynamic database and corrected to the pressure and temperature of interest, if necessary. Amongst the most widely used geochemical models in the approach of the law of mass action are SOLINEQ.88 [16], EQ3/6 [10; 17; 18; 19], MINEQL+ [20], MINTEQA2 [21], PHREEQC [22] and WATEQ4F [23]. The represented geochemical models for the approach of Gibbs energy minimization are GEM Selektor [24], Reaktoro [25; 26], ChemApp [27] and ChemSage/FactSage [28; 29].