## 5 Different Activity Coefficient Equations in Geochemical Models
### Model Calibration  
According to the analysis by [PERSON] et al. [54], the simulation of different chemical models in the same conditions brings about different outcomes due to the different thermodynamic databases in the models. The thermodynamic database includes the equilibrium constant, heat constant and stoichiometry. In the database of the geochemical model, there are chemical species that are mathematically independent, which are generally called chemical components. The chemical components in the database of the geochemical model are the main cation and anion species of in-situ water quality data. We can select these chemical components as reactants in order to calibrate the model. Thus, in order to realize the effect of the database on the chemical equilibrium model, a test case with the same concentrations of all of the reactants from the in-situ water quality data was selected as the input of the four models (Table 8). The concentration and activity coefficients were calculated using the Davies equation with their respective thermodynamic databases (Table 9).  
The concentration of the reaction products (Table 3) and activity coefficients (Table 4) given by the four models demonstrate great differences.  
Figures 7 and 8 show the concentration and activity coefficient of the major reaction products calculated by the Davies equation using the built-in thermodynamic databases of the four models, respectively. The concentrations of the reaction products and activity coefficients obtained from the four models demonstrate great inter-model differences, especially for MINEQL+. The reason for this is that MINEQL+ produces precipitation species, such as dolomite and calcite, while the saturation index (SI) values calculated by the other three model systems show that precipitation reactions do not easily occur. In order to remove the difference caused by these databases on the activity coefficients, we took the \"phreeqc.dat\" database of PHREEQC as the standard in order to revise the databases MINTEQA2 and COM, and recalculated new concentration of products (Figure 9) and  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Davies** & **Modified Debye-Hückel** & **Pitzer** \\ \hline PHREEQC & v & v & v \\ MINEQL+ & v & & \\ MINTEQA2 & v & & \\ EQ3/6 & v & v & v \\ \hline \end{tabular}
\end{table}
Table 7: Options of activity coefficient equations incorporated with four models.  
activity coefficients (Figure 10). The results showed that only the concentrations of Na+, NaHCO3 and NaCO3- in the EQ3/6 model were different from those in the other models. The reason for these differences is that there are chemical reactions of NaCl and NaOH in the COM database. These reactions were not considered in the PHREEQC and MINTEQA2 databases. Thus, the results showed that the differences of the concentration and activity coefficient between the models decreased significantly (Figures 7-10) and assured us that the use of the same thermodynamic database can produce similar activity coefficients through the four models.  
At present, there is no thermodynamic database in any geochemical model that contains all of the chemical species and reaction types of the solutions and minerals that may react. Developers cannot guarantee the internal consistency of the TDB. Recent research has focused on the determination of the optimal TDBs and the internal consistency of the data (e.g., standard Gibbs free energy) [30; 31]. Thus, the main challenges and limitations of geochemical modeling would be to check the accuracy of the data in the future.  
Figure 8: The activity coefficient calculated by the Davies equation using the built-in thermodynamic database of the four models.  
Figure 9: The solution concentration calculated by the Davies equation using the same thermodynamic database of the four models.  
database, the consistency of the chemical thermodynamics data, and the thermodynamic data sensitivity of the simulation using the database.