## 3 Results and Discussion
### Considering Thermodynamic Properties Variation of CO\({}_{2}\) Flow  
The results analysis and discussion in Section 3.1 are premised on the condition that the temperature of both sample and flow fluid was kept at room temperature invariably. While in reality, although the temperature recorded by the thermometer in the tri-axial cell kept constant, the temperature variation inside the sample during CO\({}_{2}\) expansion with the decrease of pressure along sample cannot be ignored. According to the first law of thermodynamics [44] (see Equation (9)), the volume work done by gas expansion is compensated by its internal energy and the heat transferred into the system. The heat exchange, due to the temperature difference between CO\({}_{2}\) flow and sample matrix, can reduce the rate of CO\({}_{2}\) internal energy decline. However, considering that much energy consumed for the fast CO\({}_{2}\) volume expansion and the low thermal conductivity of siltstone sample may fail to transmit enough energy to maintain the temperature of CO\({}_{2}\) flow at room temperature along the sample, the premise condition for permeability calculation under steady-state conditions that CO\({}_{2}\) flow along the sample maintained at room temperature is therefore questionable. \[dU+\delta W=\delta Q \tag{9}\]  
where, \(dU\) is the change in the internal energy of the system, \(\delta W\) is work done by the system and \(\delta Q\) the heat transferred to the system. The temperature variation of CO\({}_{2}\) flow is closely related to its flow rate, thermal conductivity of rock, CO\({}_{2}\) phase transition and so on. Higher flow rate and lower thermal conductivity of siltstone can promote temperature variation of CO\({}_{2}\) flow. In particular when liquid CO\({}_{2}\) evaporates into gaseous CO\({}_{2}\), the heat of vaporization can greatly decrease the temperature of both liquid and gaseous CO\({}_{2}\), because much energy is needed to do the volume work during the rapid volume expansion process. The standard enthalpy change of vaporization at liquefaction point (22 \({}^{\circ}\)C and 6 MPa) is 6.27 kJ/mol, and it is much higher than the heat capacity of gaseous and liquid CO\({}_{2}\) which are around 36.6 J/mol\({}^{\circ}\)C and 133.8 J/mol\({}^{\circ}\)C, respectively. In other words, if the heat exchange between the CO\({}_{2}\) flow and rock matrix was not considered and CO\({}_{2}\) flow was in an adiabatic condition (\(\delta Q\) = 0), 6.27 kJ is needed to evaporate each mole of CO\({}_{2}\), which can decrease the temperature of gaseous and liquid CO\({}_{2}\) by 171.3 \({}^{\circ}\)C and 46.9 \({}^{\circ}\)C, respectively. The standard enthalpy change of vaporization can increase to 12.22 kJ/mol at \(-\)20 \({}^{\circ}\)C and 2 MPa, which can absorb more heat from the surroundings. The evaporation of liquid  
Figure 15: Relationship between permeability of siltstone at different confining pressures. CO\({}_{2}\) can greatly decrease the temperature of adjacent liquid CO\({}_{2}\) and evaporated CO\({}_{2}\), and even solid carbon dioxide can be formed at the liquefied interface [45]. According to Figure 16, with the decrease of temperature of liquid CO\({}_{2}\), the pressure at evaporating point also decreases, which indicates the liquid CO\({}_{2}\) length in sample is longer than predicted and the higher density of liquid CO\({}_{2}\) can lead to much higher flow rate compared with that at constant room temperature. Due to much energy being consumed for the vaporization process when the injection pressure is higher than 6 MPa, the temperature of gaseous CO\({}_{2}\) at the liquefied interface will definitely be lower than the room temperature. Besides the temperature variation around the liquefied interface, the gaseous CO\({}_{2}\) volume expansion with the decrease of pore pressure can also decrease its temperature. Although the rate of gas volume expansion is much lower than that in the evaporation process, higher gaseous CO\({}_{2}\) flow rate can also absorb much energy.