# The Thermodynamic Change Laws of CO2-Coupled Fractured Rock
## 3 Results  
### Experimental Results Thermodynamics of CO\({}_{2}\)-Induced Rock Fracturing  
The results of the CO\({}_{2}\)-water-rock coupling seepage test demonstrate that the compressive strength and elastic modulus of samples subjected to immersion in water and coupled fracturing fluid with a CO\({}_{2}\) mass fraction of 8% exhibit varying degrees of reduction. Figure 4a indicates that the CW-8 sample exhibits a significantly weakened stress-strain diagram in comparison to the rock samples in other states. Figure 4b reveals that the compressive strength and elastic modulus of the rock samples exposed to CO\({}_{2}\)-coupled fracturing fluid decreased greatly compared with those of the natural samples and the water-soaked samples; the larger the CO\({}_{2}\) mass fraction, the more obvious the decrease in compressive strength and the elastic modulus. The observed interaction between CO\({}_{2}\), water, and rock weakens the rock's resistance to mechanical damage. Among the coupled fracturing fluids, CW-8 had the most pronounced weakening effect on the strength of the rock samples. The results of the seepage test and uniaxial test are consistent. Figure 4: Mechanical parameters of rock samples under different test conditions. (**a**) Stress–strain curves. (**b**) Variations in mechanical properties. Figure 3: Rock samples under different conditions. (**a**) Rock samples in different states. (**b**) Rock samples prepared for the seepage test. (**c**) Installation of seepage test specimens. Therefore, this article examines the influence of temperature, stress, and time on the tensile strength of sandstone exposed to CW-8 fracturing fluid. Table 2 and Figure 5a,b show that during CO2-water-rock coupling, the tensile strength of sandstone samples decreases at different temperatures when compared with the tensile strength of the natural rock sample F1. More specifically, the tensile strength was reduced by 2.63 MPa, 1.66 MPa, and 1.32 MPa, exhibiting a decrease of 57.19%, 36.17%, and 28.68% at 25 \({}^{\circ}\)C, 35 \({}^{\circ}\)C, and 45 \({}^{\circ}\)C, respectively. Figure 5a illustrates that CO2-water-rock coupling results in rock samples reaching their peak load in the shortest duration, which is shorter than that of the natural samples. Moreover, it is observed that as the temperature increases, the time required to reach the peak load becomes longer. This is especially more pronounced at a temperature of 25 \({}^{\circ}\)C, with the shortest time to reach the peak being 58.2 s. As shown in Figure 5b, under these conditions, the tensile strength of rock samples experiences the largest decline and as the temperature rises; the reduction in tensile strength diminishes, and it consistently remains lower than the tensile strength of natural rock samples. Accordingly, it is inferred that temperature affects the tensile strength of rock samples after CO2-water-rock coupling. The higher the temperature, the lower the viscosity of CO2-coupled fracturing fluid, and the higher the permeability coefficient. As the temperature rises, the coupled fracturing fluid exhibits greater wetting characteristics on rock samples, which reduces the strength of the rock mass. Additionally, the tensile strength exhibits a positive correlation with the temperature, which may be attributed to the lower solubility of CO2 in hot water. Consequently, the PH of CO2-coupled fracturing fluid increases and the acidity of the fluid weakens, thereby reducing the chemical damage to the rock mass. Based on the distribution of tensile strength shown in Figure 6, the correlation between temperature and tensile strength after CO2-water-rock coupling can be approximated using the following expression:  
\[y=-0.0031x^{2}+0.286x-3.2212. \tag{1}\]  
Equation (1) indicates that the tensile strength of the rock sample gradually increases with increasing temperature.