Experimental Method

The experimental surface sorption amount can be a starting point for the calculation of absolute adsorption and adsorbed gas density. From Equations (24) and (25), we can obtain another expression of excess sorption:

$$G\_{cx} = (\rho\_{ad} - \rho\_{\mathcal{K}})v\_{ad}.\tag{83}$$

For high-pressure adsorption, bulk gas is more compressible than adsorbed gas and the excess sorption isotherm is mainly influenced by bulk gas EOS, where the adsorbed gas volume can be seen as a constant with increasing pressure. From this standpoint, the line segmen<sup>t</sup> after the inflection point on plot of excess sorption amount versus bulk gas density can be used for calculating the volume and density of adsorbed gas, as we can see from Figure 34. The density and volume of adsorbed gas after the maximum sorption amount can be speculated by the slope and intercept of line, according to Equation (83), where the absolute value of the slope is adsorbed gas volume and the intersection point of linear segmen<sup>t</sup> and *x*-axis is adsorbed gas density [80,104]. The calculated adsorbed gas density of methane is between 413.78 kg/m<sup>3</sup> and 433.41 kg/m3, which is in the range of liquid density at its boiling point ρ*b* = 422.36 kg/m3. The calculated adsorbed gas volume for methane is between 0.423 cm<sup>3</sup>/g and 0.467 cm<sup>3</sup>/g for 303 K < *T* < 333 K. Note that, due to data error and the di fference in data processing methods, there is a slight variation in the results between our calculation (see in Figure 35) and that of Moellmer et al. [80].

**Figure 34.** Excess sorption amount of methane in three di fferent temperatures and the line segmen<sup>t</sup> after inflection point of maximum [80].

**Figure 35.** The change in adsorbed gas density (**a**) and adsorbed gas volume (**b**) with temperature, calculated by an experimental method.

As we can see from Figure 35a, the adsorbed gas density of methane decreases as temperature increases, showing a similar tendency to the Ozawa prediction [75], but with a higher value. This may provide a way to modify the Ozawa model of Equation (82), as we have mentioned that constant values of ρ*b* and *Tb* for gases as well as the coefficient −0.0025 may not be suitable for methane sorption studies at high pressure. The calculated adsorbed gas volume of methane also shows a decreasing tendency with increasing temperature, as shown in Figure 35b, which corresponds to a decreasing amount adsorbed at increasing adsorption temperatures [80].

## **4. Concluding Remarks**

Due to the massive development of shale gas reservoirs in recent years, the understanding of shale formation characteristics and shale gas storage forms has become a research hotspot. Our increased understanding has helped to extend the application of the classical seepage theory to new fields, where nanoscale flow spaces, gas sorption behaviors, and real gas properties are taken into account. However, much disagreement and confusion on this subject still exist, so it requires comprehensive investigation in the future.

This review includes a summary, discussion, and comparison of shale formation characteristics, shale gas occurrence types, and property calculation methods of adsorbed gas and free gas, providing fundamental support to the deep understanding of shale gas reservoirs. (1) The typical mineral

composition and organic geochemical characteristics, as well as pore size distribution, of shale formations are given based on our measurements and analysis of samples from the Longmaxi Formation. We found that mesopores are the mainly developed pore types in the Longmaxi Shale Formation, with the gas-filled porosity of shale samples ranging from 1% to 7.5%, and permeability usually smaller than 0.1 mD. Three shale gas types are usually classified, free gas, adsorbed gas, and dissolved gas, where adsorbed gas and dissolved gas are often considered as one type due to the equilibrium state between them. Therefore, it is claimed that there are two gas types, free gas and adsorbed gas, in shale gas plays in some research. (2) Methane in shale gas reservoirs is in a supercritical state, so Gibbs excess sorption models and supercritical state sorption models are employed to capture the gas adsorption and desorption behaviors. Meanwhile, di fferent models considering not only the gas adsorption but also the absorption are introduced. Great discrepancies could occur if the supercritical state and Gibbs excess adsorption characteristics are ignored. Di fferent mechanisms of adsorption in micropores and macropores may explain the hysteresis between adsorption and desorption, rather than capillary condensation. (3) Di fferent methods of calculating gas properties, such gas free gas density, free gas viscosity, and adsorbed gas density considering high-pressure and high-temperature conditions, are summarized, with recommended approaches given after the comparison. From our review, we can see that the geological characteristics of shale formations are quite di fferent from those of conventional ones, and need further assessment using a high-resolution apparatus. Gas adsorption mechanisms are still not clear, although numerous models have been developed to account for this phenomenon. For example, current supercritical adsorption models based on the potential theory are modifications of a previous adsorption theory, which are dependent on empirical parameters and lack of a universal theoretical basis. Applicable multicomponent gas adsorption models considering high-pressure and high-temperature conditions and pore size distribution are in demand to describe gas behavior in shale gas reservoirs. They are a rough way to clarify adsorbed gas and dissolved as one type, since dissolved gas may play an important role in shale gas production. Therefore, current adsorption and absorption models should be improved, based on the practical relationship between adsorbed gas and dissolved gas under in situ conditions.

**Author Contributions:** Conceptualization, Y.Z. and L.Z.; methodology, B.Z. and B.S.; validation, B.S. and Y.Z.; formal analysis, B.Z. and B.S.; investigation, B.Z.; resources, L.Z..; writing—original draft preparation, B.Z., B.S. and Y.Z.; writing—review and editing, L.Z.; supervision, B.S. and L.Z.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (grant nos. 51874251 and 51704247) and the Science and Technology Cooperation Project of the CNPC-SWPU Innovation Alliance.

**Acknowledgments:** The authors would like to thank the reviewers and editors, whose critical comments were very helpful in preparing this article.

**Conflicts of Interest:** The authors declare no conflict of interest.
