## 6 Discussion  
Internal Consistency of TDBs for Supporting the Safety Assessments of Radioactive Waste Repositories  
There is no internal database for PHREEQC or any other geochemical model. The different geochemical models are shipped with different thermodynamic databases. Each database is derived from different data sets or historical collections of data and experiments that possibly focus on systems with different conditions (e.g., the ionic strength and the pH of a solution, the pressure state and the temperature range), and they include different elements, minerals and ionic species. The chemical thermodynamics databases collect the values of the selected formations (Gibbs energy, enthalpy, entropy and constant pressure heat capacity), reaction data (equilibrium constant, Gibbs energy, enthalpy and reaction entropy), their uncertainty intervals, and the species and reactions in the safety assessments of radioactive waste repositories [55; 56; 57]. In addition, the modification of the activity coefficient by ionic strength must follow the activity coefficient equation, such as the Pitzer, Davies, modified Debye-Huckel equations, and the specific ion interaction theory (SIT) model. Thermodynamic data are collected from different data sets or experimental data. The internal consistency of a thermodynamic database must account for at least six different requirements: (1) all of the data in the database must conform to the basic thermodynamic relations and their results; (2) all of the data must be derived from a set of reference values (such as the reference temperature and pressure, the thermodynamic properties of elements and other basic compounds, etc.) and constants (such as the gas constant and molecular weight, etc. ); (3) the standard state should be properly selected and suitable for all similar substances; (4) the appropriate mathematical model must be selected to fit all of the temperature and pressure data; (5) the appropriate aqueous chemical model must be selected to fit all of the aqueous solution data; and (6) all of the relevant experimental data and the data types must expressed and considered, and the conflicts and inconsistencies between the experimental measurements must be resolved [30; 31]. The thermodynamic databases supporting the safety assessment of repositories may be internally inconsistent because they usually come from two or more source databases. Generally, the consistency of their internal databases can be verified through the following procedures: [31]  
* Check for internal consistency 1. Formation data The standard Gibbs energy of formation (\(\Delta_{f}G_{X}^{0}\)), enthalpy of formation (\(\Delta_{f}H_{X}^{0}\)) and entropy (\(\Delta_{f}S_{X}^{0}\)) for the chemical compound \(X\) are in the standard condition (T = 298.15 K). The internal consistency of the formation data for the chemical compound \(X\) is checked with the Gibbs-Helmholtz equation: \[\Delta_{f}G_{X}^{0}=\Delta_{f}H_{X}^{0}-T\Delta_{f}S_{X}^{0}\] (15) \[\Delta_{f}S_{X}^{0}=S_{X}^{0}-\sum_{i}\alpha_{i}S_{i}^{0}+\
u_{X}\frac{S_{H_{2 (i)}}^{0}}{2}\] (16)  
\(\Delta_{f}S_{X}^{0}\). is the absolute entropy of the chemical compound \(X\) in the standard condition, \(\alpha_{i}\) is the stoichiometric coefficient of the component element \(i\) in the chemical compound, \(S_{i}^{0}\) is the absolute entropy of the element \(i\) divided by the stoichiometric coefficient of at standard condition, \(\
u_{X}\) is the charge of the chemical compound \(X\) in the standard condition, and \(S_{H2(g)}^{0}/2\) is the electron entropy by convention. For chemical compound \(X\), the standard Gibbs energy (\(\Delta_{f}G_{X}^{0}\)), enthalpy (\(\Delta_{f}H_{X}^{0}\)), and entropy (\(\Delta_{f}S_{X}^{0}\)) are calculated by Equation (16). All of these values must conform to Equation (15) in the standard condition. 2. Reaction dataThe relationship between the standard Gibbs energy and the equilibrium constant must conform to Equation (5) at T = 298.15 K.
* Check cross-consistency  
1.