(3) Cation exchange

Through cation exchange, Ca2+ and Mg2+ in groundwater were replaced by Na<sup>+</sup> , which may affect the cation concentrations and hydrochemical facies [16]. The binary phase diagram of (Na<sup>+</sup> – Cl−) vs. (Ca2+ + Mg2+ – SO<sup>4</sup> <sup>2</sup><sup>−</sup> – HCO<sup>3</sup> −) can indicate whether cation exchange occurs [16] based solely on the milligram equivalent ratios, this method is simple and not explained in detail here. Chlor–alkali indices can reflect the direction of cation exchange analysis based on the two indices (CAI<sup>1</sup> and CAI2), and the equations were listed below [41].

$$\text{CAI}\_1 = \left[\text{Cl}^- - (\text{Na}^+ + \text{K}^+) \right] / \text{Cl}^- \tag{2}$$

$$\text{CAI}\_2 = \left[\text{Cl}^- - (\text{Na}^+ + \text{K}^+)\right] / (\text{SO}\_4^{2-} + \text{HCO}\_3^- + \text{CO}\_3^{2-} + \text{NO}\_3^-) \tag{3}$$

where the units of the ions involved in the equations are meq/L. When the values of both CAI<sup>1</sup> and CAI<sup>2</sup> were negative, the forward reaction of cation exchange occurred in groundwater; when the values of both CAI<sup>1</sup> and CAI<sup>2</sup> were positive, the backward reaction occurred in groundwater.

(4) Isotope values

The isotope concentration analyses are usually expressed as the sample deviations from the standard [42]. The calculated equation is shown below.

$$\delta = \frac{R\_{sample} - R\_{standard}}{R\_{sample}} \times 1000\,\%\,\tag{4}$$

where *R* is the isotope ratio, such as D/1H, <sup>18</sup>O/16O and <sup>15</sup>N/14N, the H and O isotopes take Vienna Standard mean ocean water (V–SMOW) as the reference standard, the N isotope takes the atmospheric N<sup>2</sup> as the reference standard; δ is the sample deviation from the standard, such as δD, δ <sup>18</sup>O and δ <sup>15</sup>N, and its unit is ‰.
