## 3 Results and Discussion
### Permeability Behavior of CO\({}_{2}\) under Steady-State Conditions
The permeability of the siltstone was then calculated using the traditional Darcy equation for gas (see Equation (4)), and Figure 11 shows the calculated permeability values for each injection pressure. When the whole sample is filled with gaseous CO\({}_{2}\), the siltstone's permeability increases with increasing injection pressure, regardless of confinement. For example, increasing the injection pressure from 3 to 6 MPa causes the sample permeability to increase from 0.00457 mD to 0.00654 mD and 0.00264 mD to 0.00439 mD at 10 MPa and 40 MPa confining pressures, respectively. This permeability increment may be related to the effective stress effect. Increasing the injection pressure expands the rock pore throats, even opening some new flow paths for CO\({}_{2}\), which contributes to the reduced tortuosity for CO\({}_{2}\) movement along the sample. This trend of permeability increase appears to change with the phase transition, which occurs in CO\({}_{2}\) after around 6 MPa and continues, and permeability first slowly reduces with increasing injection pressure up to around 10 MPa (from 0.00654 mD to 0.00601 mD and 0.00439 mD to 0.00413 mD at 10 MPa and 40 MPa confining pressures). After that permeability is surprisingly subjected to a sudden increment. This permeability reduction is due to fact that after 6 MPa at 22 \({}^{\circ}\)C, CO\({}_{2}\) transfers into the liquid state from the gaseous state. As a result, the presence of liquid CO\({}_{2}\) in the siltstone sample (at the upstream side) causes this opposite permeability trend. The lower permeability for liquid CO\({}_{2}\) compared to gaseous CO\({}_{2}\) in the siltstone sample is due to the slip-flow effect. The reduction of permeability for liquid CO\({}_{2}\) compared with gaseous CO\({}_{2}\) is related to the slip-flow effect, as gas molecules with higher compressibility and lower viscosity have greater potential to slip through narrow pore throats [(36; 41)]. In addition, liquid CO\({}_{2}\) with higher viscosity meets much higher resistance than gaseous CO\({}_{2}\), and very tiny pore throats are impenetrable for liquid CO\({}_{2}\). Although the permeability at higher injection pressures is much lower than that for the gaseous state, the leak-off rate may be much higher than that for gaseous CO\({}_{2}\) because of its greater density. Importantly, this shows the calculation of permeability based on [PERSON]'s equation for gas is not accurate for the prediction of the permeability of samples under these two-phase CO\({}_{2}\) conditions (liquid at upstream and gas at downstream). Further, there is a sharp rise in viscosity when the CO\({}_{2}\) transfers into the liquid state at 6 MPa from 18.19 uPa\(\cdot\)s to 66.15 uPa\(\cdot\)s, and the use of the traditional [PERSON]'s equation with mean viscosity in the gaseous state causes some errors, because the basic assumption of [PERSON]'s equation for gas, that viscosity is nearly independent on the pressure variation, is no longer applicable when both liquid and gas co-occur in the sample. This is further highlighted by the sudden permeability  
Figure 11: Relationship between permeability of siltstone under different injection pressures (traditional method). increment after 12 MPa, caused by the abrupt change of the mean viscosity after 12 MPa (see Figure 12), and it is likely that the greater portion of liquid CO\({}_{2}\) in the sample at greater pressure significantly increases this error. This is confirmed by Table 2, which shows that when the injection pressure is greater than 6 MPa, liquid CO\({}_{2}\) is present in the sample, and the proportion is around 25% of the whole sample at 7 MPa injection pressure and around 80% at 16 MPa injection pressure. This suggests that the higher the injection pressure, the greater the proportion of liquid CO\({}_{2}\) in the sample for liquid CO\({}_{2}\) injection.