## 3 Results and Discussion
### Permeability Behavior of CO\({}_{2}\) under Transient Conditions  
The complex gas/liquid permeability characteristics observed in the rock sample during liquid CO\({}_{2}\) injection indicate the importance of checking the different permeability characteristics of the tested siltstone under pure gas and liquid CO\({}_{2}\) movement using transient tests. Here, the permeability was calculated using Equations (7) and (8), considering the long time of injection under steady-state flow conditions, as longer time is expected under transient conditions, the transient test conditions used for the study are therefore down-sized (see Table 3). The downstream pressure development relevant to each injection under 20 MPa confining pressure is shown in Figure 18. Here, the time taken to reach the injection pressure value at downstream decreases with increasing injection pressure, exhibiting a weakened flow behavior at lower injection pressures through the rock sample. For example, at 20 MPa confining pressure, the time taken to  
Figure 16: The phase diagram of CO\({}_{2}\) (date were obtained from REFPROP Database [38]). Figure 17: Isentropic plots of pure CO\({}_{2}\) for different initial conditions (date were obtained from REFPROP Database [38]). reach injection pressure level at downstream pressure is around 11 h, 6.4 h and 2.6 h at 3 MPa, 9 MPa, and at 15 MPa injection pressure, respectively. This is mainly due to the accelerated advective flux, which creates a greater pushing force under the existing greater initial pressure gap between the injecting point and the rock matrix pore space. Figure 19 compares the time taken to achieve 5.5 MPa (CO\({}_{2}\) still in gaseous state) pressure at downstream under various injection (6-15 MPa) and confining (10-40 MPa) pressures. The time taken to reach the 5.5 MPa at 6 MPa injection pressure condition decreases by 57% with the increase of injection pressure to 9 MPa at 10 MPa confining pressure, and the time taken at 6 MPa injection pressure reduces by 75%, 78% and 83% with increased injection pressure to 15 MPa at 20, 30 and 40 MPa confinement, respectively (see Figure 19). When the injection pressure is 3 MPa and 6 MPa, a steady-state downstream pressure development over time up to the injection pressure can be seen (see Figure 18). Interestingly, this downstream pressure development changes after 6 MPa at greater injection pressures, and the downstream pressure development curves exhibit two steady-state conditions. In other words, in addition to the final steady-state condition (closer to the injection pressure value), an intermediate steady-state pressure development may be seen under high injection scenarios (\(\geq\)9 MPa). Importantly, for each high injection pressure (from 9 MPa to 15 MPa), the intermediate pressure development occurs when the downstream reaches 6 MPa (it converts from gas to liquid at this pressure), due to the quite different physical properties of CO\({}_{2}\) in its gas and liquid phases (see Figure 18). Increasing the downstream pressure beyond 6 MPa causes the phase transition of the CO\({}_{2}\) there, and therefore in the whole sample, from gas to the liquid state. The associated sudden increment in CO\({}_{2}\) density (increasing from 210 kg/m\({}^{3}\) in the gaseous state to 760 kg/m\({}^{3}\) in the liquid state) and the reduction in adiabatic compressibility (0.154 (1/MPa) in the gaseous state to 0.009 (1/MPa) in the liquid state) are due to the phase transition. For this liquidation process, a certain amount of CO\({}_{2}\) must be aggregated in the downstream, until which time the downstream pressure development occurs only at a slower rate, showing an almost steady-state condition closer to 6 MPa. This is because pressure development in the gaseous state requires a large gas volume in constant space, due to its high compressibility characteristics, and when it converts to the liquid state, the associated huge compressibility reduction and density enhancement cause much quicker pressure development.