## 5 Different Activity Coefficient Equations in Geochemical Models
### Comparison of the Activity Coefficients between the Models  
This study considered various concentration levels in a solution (Ca2+, HCO3-, Cl-, K+, Mg2+, Na+, SO42-, Fe3+ and PO43- were considered to be the major ions) in order to investigate the differences in the activity coefficient calculation performance between the four models (i.e., PHREEQC, MINEQL+, MINTEQA2 and EQ3/6).  
The considered cases were as follows:  
(1) The activity coefficient of a species calculated using the Davies equation in the four models.  
(2) The activity coefficient of a species calculated using the modified Debye-Huckel equation in EQ3/6 and PHREEQC.  
(3) The activity coefficient of a species calculated using the Pitzer equation in EQ3/6.  
(4) Considering the effect of temperature on the activity coefficient, the activity coefficient of a species calculated using the modified Debye-Huckel and Davies equations at 10 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, 60 \({}^{\circ}\)C and 90 \({}^{\circ}\)C.  
Calculation Results  
The results showed that if the ionic strength (I) of a solution was \(<\)0.0001 m, the activity coefficients of any species corrected using the Davies or modified Debye-Huckel equations for different charge numbers of ions (Z) were mostly greater than 0.95 (Table 10). It should be noted that except for Fe3+ ions with Z = 3, which are slightly less than 0.95, all other ions meet this threshold value (I \(<\) 0.0001 mol/kgw). The results suggest that the activity coefficient correction is small and can be neglected at such a low concentration level.  
Figure 10: The activity coefficients calculated by the Davies equation using the same thermodynamic database of the four models.  
When I was <0.5 mol/kgw, the activity coefficient variation calculated using the Davies equation was <3%; as I increased from 0.5 to 0.9 mol/kgw, the maximum variation in the activity coefficient increased to about 10% (Figure 11). Therefore, the Davies equation is suitable for solutions with an ionic strength of <0.5 mol/kgw. Moreover, the activity coefficients of high-charge species calculated using the Davies or modified Debye-Huckel equations were more sensitive than those of low-charge species. Comparing the activity coefficients calculated using the Davies and modified Debye-Huckel equations through PHREEQC and EQ3/6 revealed that if I was <0.5 mol/kgw, the activity coefficient differences were <5%; if I was >0.5 mol/kgw, the activity coefficient differences increased slowly (Figure 12). According to the theory of activity coefficient, the Davies equation can be suitable for solutions with I < 0.5 mol/kgw, and the modified Debye-Huckel equation can be suitable for solutions with I between 0.3 and 1 mol/kgw. If I was <0.5 mol/kgw, the differences in activity coefficients calculated using the Pitzer, Davies and modified Debye-Huckel equations through EQ3/6 were <8%. When I was >0.5 mol/kgw, the differences increased gradually (Figure 13). Notably, the Pitzer equation described the activity coefficient satisfactorily for solutions with high ionic strength (Figure 14). As the temperature increased from 10 \({}^{\circ}\)C to 90 \({}^{\circ}\)C, the activity coefficients calculated by the PHREEQC model using the Davies and modified Debye-Huckel equations decreased. Moreover, if I was <0.5 mol/kgw, the activity coefficients calculated using the Davies and modified Debye-Huckel equations were similar (Figure 15), suggesting that the Davies equation is applicable for conditions involving moderate temperature variations. The activity coefficient decreased with the increase of temperature from 10 \({}^{\circ}\)C to 90 \({}^{\circ}\)C for the modified Debye-Huckel equation, as calculated from EQ3/6 (Figure 16).