## 3 Results and Discussion
### Permeability Behavior of CO\({}_{2}\) under Transient Conditions
For example, at 20 MPa confinement, it equals  
Figure 21: Logarithmic decay of difference between upstream pressure and downstream pressure at 20 MPa confinement. Figure 20: Development of downstream pressure with time at 3 MPa injection pressure under 20 MPa confinement. 3.78 MPa at 3 MPa injection pressure and 3.61 MPa at 6 MPa injection pressure, with an average value of 3.70 MPa, which is consistent with the findings of [PERSON] and [PERSON] [41]. According to Equation (3), the permeability for gas CO\({}_{2}\) is 0.001265 mD at 1 MPa pore pressure and 0.002268 mD at 0.5 MPa pore pressure, respectively, which is much higher than the liquid permeability. Similar to the steady-state permeability tests, the confining pressure under transient conditions also plays an important role in permeability evolution. Higher confining pressures cause the natural micro-fractures or preferential flow paths to shrink, resulting in a significant permeability reduction. With the increase of confining pressure, the times taken for the equilibrium between upstream and downstream are increased and the pressure increase rate is decreased (see Figure 23). The tested siltstone permeability decreases with increasing confining pressure (see Figure 22). For example, under 9 MPa injection pressure conditions, increasing the confinement from 10 to 20 MPa, 10 to 30 MPa and 10 to 40 MPa causes the siltstone permeability to decrease by 24%, 31% and 37%, respectively. Figure 23: Measurement of downstream fluid pressure for CO\({}_{2}\) injection under 3 MPa injection pressure without phase transition and under 12 MPa injection pressure with phase transition (for the effect of confining pressure). Figure 22: Relationship between permeability of siltstone at different injection pressures. Now, if the steady-state and transient permeability values are compared (Figures 13 and 22), it appears that the permeability calculated under transient conditions is much lower than the steady-state permeability of the tested siltstone. The slip-flow effect is reduced with the downstream pressure development which occurs under the transient test conditions, and for steady-state conditions, the flow behavior of CO\({}_{2}\) is mainly dominant at low pore pressure around downstream, where a greater pressure gradient is needed for higher flow rates. Therefore, the slip-flow effect around downstream can result in higher permeability under steady-state conditions compared with transient conditions. More significantly, the temperature variation can greatly change the CO\({}_{2}\) flow behavior along the sample and tend to increase the flow rate, which is introduced in detail in Section 3.2. In the field, depending on the flow characteristics of the surrounding rock layers, the flow behavior can be partially steady-state/transient and the permeability behavior can change accordingly, particularly for the gaseous state of CO\({}_{2}\). For the fracturing process, the leak-off rate of injected CO\({}_{2}\) is more dependent on the flow behavior under transient conditions compared with steady-state conditions.