## 2 Experimental Methodology
### Permeability Calculation  
In shale formations or tight formations with ultralow permeability, the flow behavior of gas is affected by the combination of stress effects and the flow regime effect. The flow regime effect cannot be ignored, in particular when the gas pressure is low and the pore throat is small, and the transport of gas is governed by a mixture of Darcy flow, which is caused by the pressure gradient, and Knudsen flow, which is caused by molecular collisions along the walls of the flow channels [35]. Therefore, it is necessary to distinguish the flow pattern of CO\({}_{2}\) in siltstone before calculating the permeability. The flow behavior of gas depends on the pore throat, temperature, pressure and the molecular diameter, and can be divided into different flow types at different scales, and the flow regimes can be distinguished by the dimensionless Knudsen number (see Equations (1) and (2)) [3]. According to [PERSON] et al. [3], when the Knudsen number is less than 0.01, the pore size is much higher than the mean free path of gas molecules, and the flow is mainly driven by pressure difference (Darcy flow); in contrast, when \(K_{n}>10\), the gas molecules move along the tiny pore throats by the collisions between gas molecules and between the pore wall and gas molecules, and the driving force is mainly caused by the concentration gradient instead of the pressure difference (Knudsen flow), and [PERSON]'s law is therefore no longer applicable. The flow is in slip flow regime when \(0.01<K_{n}<0.1\) and in transition flow regime when \(0.1<K_{n}<10\), which are mainly induced by Darcy flow and Knudsen flow, respectively [3; 35]. \[K_{n}=\frac{\lambda}{d_{p}} \tag{1}\]\[\lambda=\frac{k_{B}T}{\sqrt{2}\pi d_{m}^{2}P} \tag{2}\]  
where, \(K_{n}\) is the dimensionless Knudsen number, \(d_{p}\) is the diameter of the pore, \(\lambda\) is the mean free path of CO\({}_{2}\) molecules, \(k_{B}\) is the Boltzmann constant (=1.38 \(\times\) 10\({}^{-23}\) m\({}^{2}\)kgs\({}^{-2}\)K\({}^{-1}\)), \(T\) is the temperature (K), \(d_{m}\) is the CO\({}_{2}\) molecular diameter, and \(P\) is the gas pressure. With the increase of gas pressure, the molecular mean free path of CO\({}_{2}\) becomes smaller with higher gas density (see Figure 4), and the effect of Knudsen flow recedes with the increase of pressure (see Figure 5). For example, for a pore with a diameter of 300 nm, the Knudsen number is 0.0139 at a pressure of 2 MPa and the flow is in slip flow, while the Knudsen number is 0.0093 at pressure of 3 MPa and the flow is in Darcy flow. When the pressure is higher than 5 MPa, the mean free path is 1.67 nm, and pure Darcy flow can only happen in pores with diameters greater than 167 nm and slip flow in pores between 16.7-167 nm. According to the pore size measured by mercury intrusion testing, the median pore diameter of siltstone is around 625 nm where the flow mainly belongs to Darcy flow, while there are still many pores with a diameter around 10-300 nm where the slip flow effect also has an important role (see Figure 5), in particular when CO\({}_{2}\) is in the gaseous state. Due to the smaller molecular diameter and larger mean free path of CO\({}_{2}\) compared with CH\({}_{4}\), (see Figure 4), slippage effects are slightly greater for CO\({}_{2}\), and the apparent permeability for CO\({}_{2}\) is slightly higher than that of CH\({}_{4}\). The slip-flow effect was first discovered by [PERSON] [36], and the effect is expressed as Equation (3), which indicates that the slip-flow effect can greatly increase the permeability for gas if the pore radius and pore pressure are small. \[k_{g}=k_{l}(1+\frac{b}{P}) \tag{3}\]  
where, \(k_{g}\) is apparent the permeability for gas CO\({}_{2}\), \(k_{l}\) is the intrinsic permeability of tested siltstone which can be measured using liquid CO\({}_{2}\) or water, \(b\) is the Klinkenberg parameter and \(P\) is the pore pressure.