Phreeqc interactive calculation
The saturation index with respect to calcite (SIc) can indicate that whether the precipitation of travertine may occur or not (Dilsiz, 2006). Minvielle et al. (2015) proposed that the saturation index with respect to calcite (SIc) is a significant parameter that can be used to study hydrochemistry of karst systems through calcium-carbonate equilibriums. The values of saturation index with respect to the anhydrite, aragonite, calcite, dolomite, gypsum and halite in the Heinitang hot springs are determined by Phreeqc Interactive 3.1.4 (Parkhurst and Appelo, 1999), and they are presented in Table 4.
Table 3 SI values with respect to minerals in the hot water samples.
The values of saturation index with respect to aragonite range from -0.41 to 0.99. The values of saturation index with respect to calcite range from -0.29 to 1.11. The values of saturation index with respect to dolomite range from -1.14 to 2.22. The SI values with respect to anhydrite and gypsum are similar and in the range from -4.1 to -3.6. The SI values with respect to halite are the lowest and in the range of -7.48 to -6.59 (Table 3). The SI values with respect to aragonite, calcite and dolomite have the similar tendency, which are positive in water samples S2*, S2, S3, S4* and S4. The solution is in a state of saturation. However, the SI values with respect to aragonite, calcite and dolomite are negative for the S1, S5 and S6 water samples that almost not deposit travertine (Fig. 8). The results show that the SI values with respect to aragonite, calcite and dolomite can be affected by similar factors, and they are significant for the precipitation of travertine.
Fig. 8. SI values with respect to the anhydrite, aragonite, calcite, dolomite, gypsum and halite in the Heinitang hot spring samples.
As shown in Figure 8, compared with water samples S2* and S4*, the SI values with respect to aragonite, calcite and dolomite decrease in water samples S2 and S4. The SI values with respect to aragonite and dolomite decrease from positive to negative. The SI values with respect to calcite decrease from 0.8 to 0.06 and from 1.11 to 0.1, respectively. This indicates that the saturation index with respect to aragonite, calcite and dolomite can decrease with the precipitation of travertine from the hot spring. This may be the reason why travertine stops growing near these vents.
The main compositions of travertine are aragonite and calcite, and their molecular formulas are both CaCO3 (Pentecost, 2005). Based on the analyses above, it is clear that the concentration of calcium has a significant effect on the deposition of travertine. However, the concentration of calcium only represents the total calcium content, the concentration of free calcium and ion pairs of calcium are still unknown. Therefore, we want to know whether the concentrations of ion pairs of calcium have a significant effect on the precipitation of travertine. The main compositions of calcium include Ca, CaHCO3+, CaCO30, CaSO40, CaOH+ and CaHSO4+ in the Heinitang hot spring. Shen et al. (1993) suggested that the total concentration of calcium can be calculated by:
mCa (O) = mCa +\(\mathrm{m}_{\mathrm{\text{CaHCO}}_{\mathrm{3}}^{\mathrm{+}}}\)+\(\mathrm{m}_{\mathrm{\text{CaCO}}_{\mathrm{3}}^{\mathrm{0}}}\)+\(\mathrm{m}_{\mathrm{\text{CaSO}}_{\mathrm{4}}^{\mathrm{0}}}\)+\(\mathrm{m}_{\mathrm{\text{CaOH}}^{\mathrm{+}}}\)+\(\mathrm{m}_{\mathrm{\text{CaHSO}}_{\mathrm{4}}^{\mathrm{+}}}\) (5)
where m represents molality, O refers to the total concentration.
The concentration of free calcium and ion pairs of calcium are calculated by Phreeqc Interactive 3.1.4 (Parkhurst and Appelo, 1999), and are listed in Table 4.
Table 4 Concentrations of the free calcium and ion pairs of calcium in the Heinitang hot spring.
As shown in Table 5, the concentration of free calcium (Ca) is the highest in the water samples, with the concentration from 1.89 to 2.52 mmol /L, and the concentrations of ion pair CaHCO3+ and CaCO30 range from 0.22 to 0.32 mmol /L and from 0.004 to 0.097 mmol /L, respectively. Ion pair concentrations of CaSO40, CaOH+ and CaHSO4+ are extremely low. The concentration of CaSO40 ranges from 4.69x10-4 to 1.13x10-3 mmol/L, the concentration of CaOH+, from 2.2x10-7 to 6.56x10-6 mmol/L, and the concentration of CaHSO4+, from 3x10-10 to 1.63x10-8 mmol/L. Therefore, the CaSO40, CaOH+ and CaHSO4+can be ignored, and only the free calcium (Ca), CaHCO3+ and CaCO30 are considered.
The concentrations of Ca and CaHCO3+in the water samples collected in 2013 were relatively low. The concentrations of free calcium and CaHCO3+ in the water samples collected in 2018 were relatively high, which were similar in all the water samples (S1, S2, S3, S4, S5 and S6) (Fig. 9a). However, the tendency of the CaCO30 content in the water samples is completely different from those of Ca and CaHCO3+.  The concentrations of CaCO30 in the water samples collected in 2013 were significantly higher than those in the water samples collected in 2018. In addition, the concentrations of CaCO30 in water samples S2, S3 and S4 were relatively high, the concentrations of CaCO30 were relatively low for water samples S1, S5 and S6 (Fig. 9b). As mentioned above, the size of travertine in 2018 was significantly larger than that in 2013 near the hot spring vents S2 and S4. Therefore, it is known that the concentration of CaCO30 decreases and the concentrations of Ca and CaHCO3+almost remain constant with the precipitation of travertine. This indicates that the deposition of travertine can be greatly affected by the concentration of CaCO30, while the concentrations of Ca and CaHCO3+ have little influence on the precipitation of travertine. The high concentration of CaCO30 in the hot spring may be more conducive to the deposition of travertine.
Fig. 9. Concentrations of free Ca, CaHCO3+ (a) and CaCO30 (b) of the Heinitang hot spring.
Figures 8 and 9 show that the higher the concentration of CaCO30, the higher the saturation index with respect to calcite (SIc), aragonite (SIa) and dolomite (SId) wound be. However, they are not linearly related, but have an exponential relationship (Fig.10). The curve of CaCO30-calcite, with a steep slope, is almost the same as CaCO30-aragonite except the intercept. The curve of CaCO30-dolomite is relatively flat with a higher intercept. The intercept represents the corresponding concentration of CaCO30 when the saturation index with respect to calcite (SIC), aragonite (SIA) and dolomite (SID) are 0 (the solution is in equilibrium with calcite, aragonite and dolomite). When the calcite, aragonite and dolomite in the solutions are in equilibrium, the corresponding concentrations of CaCO30 are 0.008 mmol/L,0.01 mmol/L and 0.012 mmol/L (Fig. 10), respectively. This indicates that with the increasing CaCO30 concentration in the Heinitang hot spring, calcite first reaches the dissolution equilibrium compared with dolomite and aragonite.
In addition, the concentrations of CaCO30 in water samples S2* and S4* collected in 2013 are higher than those of water samples S2 and S4 collected in 2018.  The saturation index with respect to dolomite, calcite and aragonite are positive and the value of saturation index with respect to dolomite is significantly higher than those of calcite and aragonite, which may deposit firstly. However, with the precipitation of dolomite, the concentrations of CaCO30 and the saturation index with respect to dolomite, calcite and aragonite wound decrease. Therefore, the values of saturation index with respect to dolomite and aragonite are negative in water samples S2 and S4. The value of saturation index with respect to calcite also decreases but is positive. The precipitation of active travertine consisting of calcite occurs in 2018. This indicates that the precipitation of travertine is affected by the deposition of CaCO30. The relationship between the concentration of CaCO30and the saturation index with respect to dolomite, calcite and aragonite can be used to simply identify the composition of travertine. When the concentration of CaCO30 is higher than 0.018 mmol/L, the travertine may consist of dolomite, calcite and aragonite, and the concentration of dolomite is higher than calcite and aragonite. When the CaCO30concentration is between 0.008 and 0.018 mmol/L, calcite is the main component of travertine. When the concentration of CaCO30 is lower than 0.008 mmol/L, the precipitation of travertine will hardly occur near the hot spring’s vents.
Fig. 10. Relationship between SIc, SIa, SId values and CaCO30 in the hot water samples.