## 3 Results and Discussion
### Considering Thermodynamic Properties Variation of CO\({}_{2}\) Flow
If there was no heat exchange between CO\({}_{2}\) and the rock matrix in the ideal condition, the gaseous CO\({}_{2}\) flow was assumed to be at adiabatic condition and its entropy kept constant. Considering that the temperature of gaseous CO\({}_{2}\) at the liquefied interface was lower than room temperature and it is difficult to determine its accurate value when the injection pressure is higher than 6 MPa, only the injection cases, where the injection pressure is not higher than 6 MPa, are used to analyze the CO\({}_{2}\) thermodynamic property evolution along the sample. According to Figure 17, with the decrease of pore pressure, the temperature decreases sharply. For example, when the injection pressure equals 5 MPa, its temperature can decrease to liquefaction point at \(-40.12\)\({}^{\circ}\)C at 1 MPa. With the decrease of both temperature and pressure, the CO\({}_{2}\) level tends to be close to the triple point (\(-56.6\)\({}^{\circ}\)C and \(0.52\) MPa). With the further decrease of pore pressure down to the atmospheric pressure, much heat is obtained from the solidification process, and CO\({}_{2}\) can be transferred into solid phase. For the ideal steady-state tests, the flow rate and pore pressure along the sample tend to be equilibrate state and the temperature maintains a constant (\(dU=0\)). However, in the real experiments, the temperature variation can also lead to the adjustment of flow behavior. Therefore, the flow rate, pore pressure and fluid temperature gradually reach a steady state with time, where continuous and stable heat was transferred from outside to the CO\({}_{2}\) flow through siltstone matrix, which indicates that the real condition is between two ideals conditions which are under constant temperature (\(dU=0\)) and under adiabatic conditions (\(\delta Q=0\)), respectively. For the complex flow system, it is difficult to accurately assess the flow behavior evolution along the sample, because these variables are interdependent with each other. The heat exchange rate, which is dependent on the thermal conductivity of siltstone, is therefore crucial to the CO\({}_{2}\) flow behavior. If the heat exchange rate is much lower than that needed for high CO\({}_{2}\) flow rate under high injection pressure, the presence of drikold particles in sample matrix can greatly disturb the steady-state flow, because it can block the flow channels for gaseous CO\({}_{2}\) flow. The forming and disappearing of drikold partials is more likely responsible for the unsteady flow rate at downstream at injection pressure higher than 9 MPa. In conclusion, the temperature variation can influence the flow behavior to some extent. The longer length of liquid CO\({}_{2}\) along the sample than expected can greatly increase the flow rate due to its much higher density than gaseous CO\({}_{2}\). Furthermore, unlike the idea of gas at constant room temperature, where gas volume is inversely proportional to its pore pressure, there is a non-linear relationship between pore pressure and gas volume at adiabatic condition, which is presented by the polytropic process equation in Equation (10) [46]. The higher density along the sample than that predicted at room temperature can also lead to slightly higher flow rate at downstream. The temperature variation, due to the unique thermodynamic properties of CO\({}_{2}\), therefore can result in the inaccuracy of permeability calculation under steady-state conditions, and it highlights the necessity of permeability calculation under transient conditions, where the thermodynamic heat exchange is negligible because of much lower pressure variation and flow rate. \[PV^{\gamma}=P_{0}V_{0}^{\gamma}=C \tag{10}\]where, \(P\) is the gas pressure, \(V\) is the gas volume, \(\gamma\) is the heat capacity ratio (approximately equals to 1.3 for CO\({}_{2}\)) and \(C\) is constant.