## 3 Results and Discussion
### Adsorption Characteristics' Evolution during Coal Structure Deformation
#### 3.1.2 Absolute Adsorption Curve  
As mentioned above, isotherms of four coal specimens exhibited an increase at first and then a decrease with increasing pressure, and showed a single peak curve rather than monotonous characteristics. That indicates that with increasing pressure, CO\({}_{2}\) gradually approaches a critical state and exhibits supercritical fluid quality, especially with pressure larger than 5 MPa. Therefore, the adsorption capacity measured by isothermal adsorption experiment is the excess adsorption capacity, also known as apparent adsorption capacity; the corresponding absolute adsorption capacity is the real adsorption capacity. According to the relationship between the excess adsorption capacity and the real adsorption capacity, as described in Equation (5) [16; 17], the difference between them is mainly attributed to the densities of the adsorbed phase and bulk gas phase. \[V_{ab}=V_{ex}/(1-\rho_{g}/\rho_{ad}) \tag{5}\]  
where \(V_{ab}\) and \(V_{ex}\) denotes absolute and excess adsorption capacity, respectively (m\({}^{3}\cdot\)t\({}^{-1}\)); and \(\rho_{ad}\) and \(\rho_{g}\) denote the density of the adsorption phase and gas phase, respectively (kg m\({}^{-3}\)). When supercritical CO\({}_{2}\) is in the adsorption phase, it is often regarded as the gas with ultimate compression, which his attributed to its non-liquefying property. The volume occupied by a CO\({}_{2}\) molecule is its intrinsic volume, and reduces the free space of the molecule, which is consistent with the meaning of volume correction term \(b\) in a van der Waals gas state equation. Therefore, the volume correction term \(b\) value given by Equation (6) [18] is employed to calculated the density of CO\({}_{2}\) adsorption phase, i.e., the ultimate compression density of CO\({}_{2}\) equal to 1028 kg\(\cdot\)cm\({}^{-3}\). The gas phase density of CO\({}_{2}\) is chosen according to values determined by U.S. National Institute of standards and Technology (NIST):  
\[\rho_{ad}=1/b\times M \tag{6}\]  
where \(\rho_{ad}\) denotes the density of adsorption phase (kg\(\cdot\)m\({}^{-3}\)) and \(M\) represents the gas molar mass (g\(\cdot\)mol\({}^{-1}\)). Therefore, according to Equations (5) and (6), the real adsorption capacity can be obtained using the apparent adsorption capacity under the same temperature and pressure conditions (Figure 5). Figure 4: Isotherms for excess adsorption of CO\({}_{2}\) on coal. Figure 5a shows that the absolute adsorption capacity of tectonically deformed coals presents similar evolution laws with excess adsorption capacity. An increase of pressure at first causes an increase, and then a decrease of the isotherm curve, which indicates type I isotherm characteristics. An increase of coal deformation degree induces a gradual increase in the absolute adsorption capacity. The maximum adsorption value shifts to the high pressure point. In order to compare and analyze the relationship between absolute adsorption capacity and excess adsorption capacity with pressure, the error between excess adsorption capacity and absolute adsorption capacity at each pressure point is calculated, as shown in Equation (7):  
\[\text{Error}=(V_{ex}-V_{ab})/V_{ex} \tag{7}\]  
The error analysis indicates that an increase of pressure causes the rapid increase in the error between excess adsorption and absolute adsorption shown in Figure 5b. Meanwhile, error curves of four specimens almost coincide, which indicates that the error has no relationship with the degree of coal deformation. It should be noted that although the adsorption phase is taken into account in the absolute adsorption correction, the downward trend of the adsorption curve has not been eliminated. According to this downward trend, if the pressure continues to increase, the adsorption capacity may be negative, as indicated by [PERSON] et al. (2019) and [PERSON] et al. (2019).