## 2 Materials and Methods
### Calculation Method of Dissolution Evaluation Parameters  
To quantitatively reflect the dissolution process and characteristics, the following four parameters are involved: rock dissolution amount per unit area, dissolution rate, chemical dissolution rate, and the relative change rate of fracture aperture. The formulas are as follows:  
(1) Dissolution amount per unit area  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Different pH Groups**} & \multicolumn{3}{c}{**Different Fracture Aperture Groups**} \\ \hline
**Rock** & **Fracture** & **pH** & **Rock** & **Fracture** & **pH** \\
**Specimen ID** & **Aperture [mm]** & **pH** & **Specimen ID** & **Aperture [mm]** & **pH** \\ \hline HY07 & 0.5–0.2 & 4 & HY10 & 0.7–0.1 & 2 \\ HY08 & 0.5–0.1 & 3 & HY11 & 0.2–0.1 & 2 \\ HY09 & 0.6–0.1 & 2 & HY12 & 0.05–0.01 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Dynamic dissolution experimental conditions.  
Dissolution amount per unit area refers to the mass or volume of rock lost due to dissolution per unit area. It is an important indicator that reflects the dissolution speed and intensity of rock specimens under experimental conditions [43], expressed as follows:  
\[K=\frac{m_{0}-m_{1}}{S} \tag{1}\]  
where \(K\) is the dissolution amount per unit area [g/cm\({}^{2}\)], \(m_{0}\) shows the mass of the rock specimen before dissolution [g], \(m_{1}\) refers the mass of the rock specimen after dissolution [g], and \(S\) is the surface area of the rock specimen [cm\({}^{2}\)].  
(2) Dissolution rate  
The dissolution of rocks by acid is characterized by the amount of rock that can be dissolved by the acid solution, which is expressed as the dissolution rate. Under different pH conditions, the dissolution rates of different lithologies vary. Through this static and dynamic dissolution experiment, we can understand the size of the dissolution rate of phosphogypsum leachate on carbonate rock, as well as analyze the dissolution capacity of phosphogypsum leachate on carbonate rock. The dissolution rate is one of the methods to quantitatively evaluate the characteristics of this dissolution reaction:  
\[R_{c}=\frac{W_{1}-W_{2}}{W_{1}}\times 100\% \tag{2}\]  
where \(W_{1}\) shows the mass of the drying specimen before the experiment [g], and \(W_{2}\) is the mass of the drying specimen after the experiment [g].  
(3) The chemical dissolution rate  
The chemical dissolution rate \(R\) serves as a quantitative indicator of the solubility strength of carbonate rocks [44], and is given by the following:  
\[R=\frac{2.5X+3.5Y}{t} \tag{3}\]  
where \(R\) shows the chemical dissolution rate of the main minerals in carbonate rocks [mg/(s\(\cdot\)L)], \(X\) gives the content of Ca\({}^{2+}\) in the dissolution solution [mg/L], \(Y\) shows the content of Mg\({}^{2+}\) in the dissolution solution [mg/L], \(t\) is the time of dissolution action [s]. For ease of subsequent calculations and plotting, this study converts the unit of \(R\) to mg/(d\(\cdot\)L) (where 1 d = 86,400 s).  
(4) The relative change rate of fracture aperture  
Figure 2: Dynamic dissolution experimental setup, comprising an adjustable peristaltic pump, pressure gauge, homemade acrylic cylindrical mold, and silicone tubing.  
The relative change rate of fracture aperture can be used to express the relative change degree of rock specimen fracture aperture before and after the experiment, which is a dimensionless parameter:  
\[\varepsilon_{b}=\frac{b_{1}-b_{0}}{b_{0}}\times 100\% \tag{4}\]  
where \(\varepsilon_{b}\) is relative change rate of fracture aperture; \(b_{0}\) shows the initial average fracture aperture [mm], \(b_{1}\) is the measured average aperture at the end of the reaction [mm].