# Study on the Wellbore Flow for Carbon Dioxide Fracturing
## 4 Results and Discussion
### Sensitivity Analyses on Controlling Factors for CO\({}_{2}\) Fracturing  
During CO\({}_{2}\) fracturing, the displacement, injection temperature, and pressure can be adjusted directly. The temperature and pressure distribution under different displacement have been analyzed in Section 4.1, so the influence of injection temperature and pressure on wellbore flow behavior of CO\({}_{2}\) will be discussed in this section. Geothermal gradient is usually within a certain limit in one block; for the Sudong block where the working well is located, the measured geothermal gradient is 2.7-3.2 K/100 m. Therefore, the effect of geothermal gradient on wellbore temperature and pressure distribution is also considered in this section. Figure 11 shows the influence of injection temperature on pressure and temperature distribution of CO\({}_{2}\) fracturing. As can be seen in Figure 11b, there is an overall rise in wellbore temperature with the increase of injection temperature, while the temperature gradient in the wellbore almost remains unchanged. In addition, the injection temperature is in negative correlation with wellbore pressure, which means the pressure gradient in the wellbore reduces as injection temperature rises, as demonstrated in Figure 11a. Figure 10: Viscosity profile in the wellbore. Figure 9: Density profile in the wellbore. As a whole, the supercritical well depth (i.e., the well depth for CO\({}_{2}\) reaching supercritical phase) decreases with the increase of injection temperature, and when injection temperature exceeds critical temperature (304.13 K), CO\({}_{2}\) maintains supercritical state in the wellbore. However, excess injection temperature brings enormous cost in wellbore pressure, hence, it needs to be seriously considered whether to raise the injection temperature during CO\({}_{2}\) fracturing. The effect of injection pressure on pressure and temperature distribution during CO\({}_{2}\) fracturing is shown in Figure 12. The increase of injection pressure would lead to a rise of the whole wellbore pressure and the pressure gradient remains unchanged according to Figure 12a. As exhibited in Figure 12b, the whole wellbore temperature reduces as injection pressure increases, but the change is very small. Moreover, it can be drawn from Figures 11 and 12 that the rising temperature has a greater impact on the wellbore flow behavior of CO\({}_{2}\) compared to the rising pressure. This is because the physical properties, especially density and viscosity, fluctuate sharply with a great temperature rise under the temperature-pressure condition of CO\({}_{2}\) fracturing. Figure 11: Effect of injection temperature: (**a**) CO\({}_{2}\) pressure profile; (**b**) CO\({}_{2}\) temperature profile. Figure 13 presents the influence of the geothermal gradient on the pressure and temperature distribution in the process of CO\({}_{2}\) flow in the wellbore. As can be seen in Figure 13, there is little impact of geothermal gradient on wellbore pressure. Although wellbore temperature increases with the increase of geothermal gradient, as shown in Figure 13, the increase is not obvious. The reason for this phenomenon is that higher displacement will weaken the heat exchange between the stratum and CO\({}_{2}\) in the wellbore, and the temperature increment caused by geothermal gradient needs to be accumulated with well depth, which makes the increase of fluid temperature in the wellbore insufficient to change the wellbore pressure. In general, the displacement and injection temperature have greater impact on CO\({}_{2}\) flow behavior and phase state than injection pressure under the temperature-pressure condition of CO\({}_{2}\) fracturing. Nevertheless, excess injection temperature has an adverse effect on wellbore pressure, so displacement is the key factor affecting CO\({}_{2}\) flow behavior in the wellbore during CO\({}_{2}\) fracturing. Moreover, the influence of thermal gradient on wellbore flow is not obvious within one block during CO\({}_{2}\) fracturing.