# The Thermodynamic Change Laws of CO2-Coupled Fractured Rock
## 3 Results
### Mass Transfer Analysis  
When fracturing rock formations to create rock fracture voids through CO\({}_{2}\) fracturing fluids injected into the pipeline, the fracturing process results in increased seepage through the rock. This seepage affects conductive and convective heat transfer, causing spatial changes in CO\({}_{2}\) density. Figure 14a indicates that when the temperature is 320 K, the density of CO\({}_{2}\) is 200 kg/m\({}^{3}\), but when the temperature increases to 420 K, the corresponding density of CO\({}_{2}\) reduces to 105 kg/m\({}^{3}\). On the other hand, when the stress is 11.5 MPa, the CO\({}_{2}\) density is 105 kg/m\({}^{3}\), but when the stress increases to 18 MPa, the corresponding density increases to 205 kg/m\({}^{3}\). When the temperature and pressure of CO\({}_{2}\) exceed the critical values of 304 K and 8 MPa, its density exhibits a positive correlation with pressure, while Figure 14b indicates that the temperature exhibits a negligible impact on the density.  
The thermophysical properties of CO\({}_{2}\) change significantly near its critical point, which leads to rapid pressurization of CO\({}_{2}\) at the bottom of the wellbore. This accelerates the fracturing of the reservoir, intensifying the effects of rock seepage. Additionally, the thermal convective temperature gradient generated by liquid CO\({}_{2}\) contributes to the heat-fluid-solid-coupled heat-transfer effect within coal-rock fissures during seepage.  
When CO\({}_{2}\) is used as the fracturing medium to fracture the rock body, it intensifies the role of rock seepage, and the CO\({}_{2}\) medium exchanges heat with the rock mass. When the temperature and pressure of CO\({}_{2}\) exceed their critical values of 304 K and 7.38 MPa, the CO\({}_{2}\) transits into the supercritical state and exhibits low surface tension, weak intermolecular forces, and strong mobility. Consequently, CO\({}_{2}\) rapidly diffuses in the pores, and seepage contributes to heat transfer.  
Figure 14c shows that as the CO\({}_{2}\) temperature reaches 260 K, its viscosity is 0.10 \(\mu\)/Pa-s. When the temperature increases to 320 K, the CO\({}_{2}\) viscosity reduces to 0.06 \(\mu\)/Pa-s. On the other hand, the CO\({}_{2}\) viscosity is 0.08 \(\mu\)/Pa-s at the pressure of 18 MPa. As the pressure reduces to 11.5 MPa, the corresponding viscosity increases to 0.12 \(\mu\)/Pa-s. Figure 14d indicates that the viscosity exhibits a negative correlation with temperature, and the temperature is closely related to the flow rate. As a result, adjusting the flow rate can effectively increase the heat transfer coefficient while reducing the viscosity of the CO\({}_{2}\) flow.  
The viscosity and pressure contours reveal that the change in pressure and temperature significantly affects the viscosity. As the fracture length expands during fracturing, the temperature of liquid CO\({}_{2}\) in the fracture of the rock gradually increases through convective and conductive heat transfer. Consequently, CO\({}_{2}\) gradually transforms into a low-viscosity supercritical state within the coupled fractured rock fractures, thereby increasing the  
Figure 14: Thermal properties of supercritical CO\({}_{2}\) in the temperature range 240–440 K and pressure range 10–25 MPa. (**a**) Contours of density. (**b**) Density graphs. (**c**) Contours of viscosity. (**d**) Viscosity graphs.  
resistance to seepage of supercritical CO2 in the rock fractures. However, seepage is an effective parameter in heat-fluid-solid coupling. Therefore, it is of significant importance to analyze the flow rate variations to study heat-fluid-solid coupling.