## 1 Introduction
Davies equation The Davies equation [9] is an empirical extension of the Debye-Huckel equation, which can be used to calculate the activity coefficients of electrolyte solutions at a relatively high concentration, as follows:  
\[-\log\gamma_{i}=AZ_{i}^{2}(\frac{\sqrt{1}}{1+\sqrt{1}}-bI) \tag{11}\]  
where \(b\) is an empirical parameter ranging from 0.1 to 0.4. In the EQ3/6 model, the constant \(b\) is assigned a fixed value of 0.2, the PHREEQC and MINTEQA2 are 0.3, and MINEQL+ is set to 0.24 [10]. The modified Debye-Huckel equation (D-H), also called the B-dot equation [11; 12], is an improvement over the Debye-Huckel equation, and is presented in (12). \[\text{K}=\frac{\text{a}_{\text{C}}^{\text{c}}\text{a}_{\text{D}}^{\text{d}}} {\text{a}_{\text{A}}^{\text{a}}\text{a}_{\text{B}}^{\text{a}}} \tag{2}\]0  
where \(\overset{*}{B}\) is a temperature-dependent ion-specific parameter, and \(a_{i}\) is the theoretical distance of the closest approach between ions and opposite charges, but in practice, it is an adjustable parameter. Considering the effect of short-range interactions between ions and hydration reactions, the Davies model and modified Debye-Huckel (B-dot) model derived using polynomials of ionic strength can predict activity coefficients more precisely than the Debye-Huckel model when the ionic strength increases (Figures 1 and 2). \[\text{K}=\frac{\text{a}_{\text{C}}^{\text{c}}\text{a}_{\text{D}}^{\text{d}}} {\text{a}_{\text{A}}^{\text{a}}\text{a}_{\text{B}}^{\text{a}}} \tag{2}\]1 Change in ionic strength vs. the activity coefficients of Ca\({}^{2+}\) determined using the Debye–Hückel, Davies and B-dot models. Comparisons of the activity coefficients for Ca\({}^{2+}\) and Cl\({}^{-}\) with ionic strength (CaCl\({}_{2}\) solution, \(a_{i}\) = 4.86 for Ca\({}^{2+}\), \(a_{i}\) = 3.71 for Cl\({}^{-}\)[13]) are shown in Figures 1 and 2, respectively. The figures demonstrate the substantial differences in the activity coefficients calculated for calcium and chloride based on the [PERSON], Davies and B-dot models. The predictions clearly show that different ions have different activity coefficients at the same ionic strength. 3. Pitzer equation  
The Pitzer Equation [14], developed for deriving the excess Gibbs free energy of electrolytic solutions, combines the Debye-Huckel equation with additional terms in the form of a virial equation, and it is widely used in geochemistry to model systems of mixed or single strong electrolytes at high concentrations, such as seawater. \[ \begin{split}&\ln\gamma_{\pm}=-|Z_{M}Z_{X}|f^{\gamma}\\ &+m\Big{(}\frac{2\
u_{M}\
u_{X}}{\
u_{M}+\
u_{X}}\Big{)}B_{MX}^{ \gamma}+m^{2}\times\frac{2(\
u_{M}\
u_{X})^{\frac{3}{2}}}{\
u_{M}+\
u_{X}}C_{MX }^{\gamma}\end{split}  \tag{13}\]  
where \(\gamma_{\pm}\) is the mean activity coefficient; \(\
u_{M}\) and \(\
u_{X}\) are the numbers of \(M\) and \(X\) ions in the formula, respectively; Z\({}_{M}\) and Z\({}_{X}\) are their respective charges in electronic units; and m is the molality. The other quantities are defined as follows:  
\[f^{\gamma}=-A_{\phi}\Bigg{[}\frac{\text{I}^{\frac{1}{2}}}{1+b\text{I}^{\frac{ 1}{2}}}+\frac{2\ln(1+b\text{I}^{\frac{1}{2}})}{b}\Bigg{]} \tag{14}\]  
where \(A_{\phi}\) is the Debye-Huckel coefficient for the osmotic function, \(B_{MX}^{\gamma}\) is the second virial coefficient, and \(C_{MX}^{\gamma}\) is the third virial coefficient. When a radioactive waste repository is in a brackish water area, the surrounding groundwater can have a high ionic strength. If the concentration of a high-salinity ground  
Figure 2: Change in ionic strength vs. activity coefficients of Cl\({}^{-}\) determined using the Debye–Hückel, Davies and B-dot models. water quality is obtained by laboratory analysis, it can be difficult to determine the real reaction concentration values of the groundwater quality due to the chemical interactions among all of the relevant ion species.