## 3 Results and Discussion
### Permeability Behavior of CO\({}_{2}\) under Steady-State Conditions
This was then considered by recalculating the permeability for liquid CO\({}_{2}\) injection (>6 MPa) using the proposed method (see Equation (6)), which separates the gaseous and liquid section along the tested sample, and the results are shown in Figure 13. This proposed method divides the liquid and gaseous states of CO\({}_{2}\) in the sample to apply the corresponding Darcy equation for the gas and liquid portions, respectively. The newly-calculated permeability values corresponding to liquid CO\({}_{2}\) injections are much lower than those for the gaseous CO\({}_{2}\) section (see Figure 13). For example, when the injection pressure increases from 6 MPa to 7 MPa, the permeability drops sharply from 0.00564 mD to 0.00244 mD at a confinement of 20 MPa, and the sudden permeability reductions are around 63%, 57%, 39% and 52% under 10, 20, 30 and 40 MPa confinements, respectively. For the liquid CO\({}_{2}\), although there is a little fluctuation in permeability with injection pressure, its permeability increases slightly with the increase of injection pressure, due to the decrease of effective stress. Overall, the range of variation of apparent permeability for liquid CO\({}_{2}\) is much smaller than that for gaseous CO\({}_{2}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Injection Pressure (MPa)**} & \multicolumn{4}{c}{**Confining Pressure (MPa)**} \\ \cline{2-5}  & **10** & **20** & **30** & **40** \\ \hline
7 & 23.96 & 26.74 & 34.18 & 28.99 \\
8 & 40.16 & 41.67 & 47.47 & 45.56 \\
9 & 48.59 & 49.60 & 54.78 & 53.33 \\
10 & & 56.55 & 60.00 & 58.12 \\
12 & & 70.00 & 68.48 & 67.33 \\
14 & & 75.29 & 76.79 & 77.31 \\
16 & & 79.00 & 80.74 & 81.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proportion of liquid CO\({}_{2}\) length in sample calculated using Equation (5) (%). Figure 12: Relationship between CO\({}_{2}\) viscosity at different injection pressures. In addition to the injection pressure, reservoir depth or confining pressure also significantly affects the flow behavior in any reservoir [42; 43], because increased confining pressure causes shrinkage in the pore structure in the formation rock matrix. This was investigated for the tested siltstone and Figure 14 shows the observed axial deformation variation of the sample with increasing applied confining pressure. There is a non-linear relationship between axial deformation and confining pressure, and the increasing rate of axial deformation decreases with increasing confining pressure (see Figure 14), because most of the shrinkable pores have already shrunk with the increase of confinement. This shrunken pore structure under high confining pressures results in the reduction of flow paths for CO\({}_{2}\) movement, and the rock permeability therefore decreases with the increasing confinement. This is confirmed by Figure 15, which shows that CO\({}_{2}\) downstream flow rates decrease with increasing confining pressure. Figure 14: Vertical displacement at different confining pressures. Figure 13: Relationship between apparent permeability of siltstone under different injection pressures (proposed method).