## 4 Discussion
### Soaking Rule of Sandstone  
During the immersion experiment, the mass of the sample decreased by 0.15 g, resulting in a mass reduction percentage of 0.26%. The entire soaking process can be subdivided into three distinct stages: the dissolution stage, the precipitation stage and the secondary dissolution stage. The quality changes observed in each stage were meticulously calculated, yielding the following results: the increase during the January stage was \(-\)0.485%, the decrease during the February stage was \(-\)0.9%, the decrease during the March stage was \(-\)0.117% and the decrease during the April stage was \(-\)0.262%. Furthermore, data fitting was conducted to analyze the relationship between the mass increase of the sample throughout the soaking process and time. The specific results are illustrated in Figure 12, along with the corresponding fitting formula. \[\Delta m_{t}=0.38t-1.14t^{2}+0.57t^{3}-0.08t^{4} \tag{6}\]  
Figure 11: Photos of the cracks in specimens after triaxial compression failure under different immersion times. Figure 12: Increased mass and change rate curves of samples after soaking in different months. In the formula, \(\Delta m_{t}\) represents the mass increase of the rock sample under specific conditions, measured in grams (g). We conducted detailed measurements and analyses of the mass increase in rock samples, with a particular emphasis on behavior across different stages of corrosion. The samples were tested within the designated immersion time in a supercritical CO2 solution, where \(t\) denotes the immersion duration in months (m). Additionally, the R2 value of 0.9998 indicates an excellent fit for our data. By deriving the relationship over time, we established a connection between soaking time and the rate of mass increase. \[m_{t}^{\prime}=0.66t-2t^{2}+0.99t^{3}-0.13t^{4} \tag{7}\]  
\[m_{t}^{\prime}=\frac{m_{t}-m_{t_{0}}}{m_{t_{0}}} \tag{8}\]  
\[r_{t}=\frac{m_{t}^{\prime}}{t} \tag{9}\]  
Substituting Equation (8) into Equation (9), we get  
\[r_{t}=\frac{m_{t}-m_{t_{0}}}{m_{t_{0}}t} \tag{10}\]  
\[\Delta m_{t}=m_{t}-m_{t_{0}} \tag{11}\]  
Substituting Equation (10) into Equation (11), we get  
\[r_{t}=\frac{\Delta m_{t}}{m_{t_{0}}t} \tag{12}\]  
In the above description, \(m_{t_{0}}\) represents the mass of the sample in the unimmersed state, and \(m_{t}\) represents the mass of the sample at soaking time \(t\). At the same time, \(m_{t}^{\prime}\) refers to the mass increase rate of the sample measured at the soaking time \(t\), while \(r_{t}\) refers to the reaction rate of the sample at the same soaking time \(t\), and its unit is m\({}^{-1}\). \[r_{1t}=\frac{\Delta m_{1t}}{m_{1t_{0}}t} \tag{13}\]  
Figure 11:0  
Figure 11:1  
Figure 11:2  
Figure 11:3  
In this context, \(m_{1t_{0}}\) denotes the mass of Ca\({}^{2+}\) present in the sample prior to any soaking treatment, while \(\Delta m_{1t}\) indicates the mass increase of Ca\({}^{2+}\) in the sample following a soaking duration of \(t\). Furthermore, \(r_{1t}\) represents the reaction rate of Ca\({}^{2+}\) in the sample during the soaking period \(t\), and \(w_{1}\) signifies the mass proportion of Ca\({}^{2+}\) in the sample before soaking. Testing of the mineral components revealed that the calcium carbonate content in the sample before soaking was 5.47%. From this, it can be inferred that the Ca\({}^{2+}\) content in the sample is approximately 2.19%. Figure 11:4In this article, \(V\) denotes the volume of the soaking solution, which is approximately 8 L, and it is assumed that this volume remains constant throughout the experiment. Additionally, \(S_{0}\) represents the initial salinity of the soaking solution, valued at 128.13 milligrams per liter (mg/L). After a soaking duration of time \(t\), \(S_{t}\) indicates the salinity of the solution at that time, expressed in grams per liter (g/L).