## 3 Results and Discussion
### Permeability Behavior of CO\({}_{2}\) under Transient Conditions
In other words, downstream pressure closer to 6 MPa means the sample has almost liquid CO\({}_{2}\) throughout and is continually sending out CO\({}_{2}\) to downstream, which therefore creates an almost steady pressure holding period until the downstream CO\({}_{2}\) converts to its liquid state. The duration of this downstream pressure holding is therefore dependent on the advective flux rate through the sample pore space, which is proportional to the pressure difference between the injection point and the holding pressure. In such situations, greater injection pressures create more accelerated advective flux, causing much shorter pressure holding periods. For example, the pressure holding times for 9, 12 and 15 MPa injection pressures are around 2.24 h, 1.05 h and 0.51 h, respectively. Interestingly, once the downstream begins to increase again after the phase transition, the pressure development at downstream initiates after the holding period, and the pressure development seems to be even greater than the pressure development rate experienced during primary pressure development (0 to 6 MPa), which confirms the superior dense and incompressible characteristics of liquid CO\({}_{2}\) compared with its gaseous state (see Figure 18). For example, CO\({}_{2}\) compressibility reduces from 0.255 (1/MPa) to 0.00457 (1/MPa) with increasing pressure from 3 MPa to 12 MPa, and the possible pressure increment upon the addition of 1% by volume of CO\({}_{2}\) is around 0.039 MPa and 2.19 MPa at 3 MPa and 12 MPa, respectively. This shows that, although there is a much slower flow rate in the liquid state, the CO\({}_{2}\) pressure can be significantly changed from an additional CO\({}_{2}\) drop, which guarantees a high injection pressure of CO\({}_{2}\) during the fracturing process. The permeability of the siltstone was then calculated using pulse-decay permeability measurement (Equations (7) and (8)), and Figure 20 shows the logarithmic decay of the difference in pressure between upstream and downstream at 3 MPa injection pressure and 20 MPa confinement. Here, in order to reduce the influence of pore pressure on the permeability calculation, only the tail end of the development of the downstream pressure is used, and for each injection condition, the start time of the pulse decay permeability measurement begins when the pressure difference between upstream and downstream drops to 0.2 MPa (see Figure 20). In this case, the pore pressure approximates the injection pressure. There is a linear relationship between the logarithms of the pressure difference between upstream and downstream with time, and the slope of the straight line is the decay exponent \(\alpha\) in Equation (7) (see Figure 21), and the permeability of the siltstone sample at different injection pressures can be calculated from Equation (8). The calculated permeability values for each injection pressure condition are shown in Figure 22, which shows that the permeability decreases from 0.00061 mD to 0.000433 mD with increasing injection pressure from 3 MPa to 6 MPa at 20 MPa confinement, due to the reducing slip flow with increasing pressure, and gaseous CO\({}_{2}\) with lower compressibility has high penetration capacity through pore throats. In the case of liquid CO\({}_{2}\) injection, when the injection pressure is 9 MPa, the permeability drops to the lowest point of around 0.000270 mD, recalling the conclusion that the permeability for liquid CO\({}_{2}\) is much lower than that for gaseous CO\({}_{2}\).under steady-state conditions. With further increase of injection pressure, the permeability starts to slightly increase up to 0.000295 mD at 15 MPa, which is mainly related to the reduced effective stress effect in rock pores. In this study, the permeability at 9 MPa injection pressure is regarded as the reference liquid permeability, because the slippage effect is almost absent, and the permeability fluctuation is small when CO\({}_{2}\) is in the fluid phase. The Klinkenberg parameter \(b\) can be calculated using Equation (3).