Summary
An excess adsorption amount obtained in experiments is always determined by mass balance with a void volume measured by helium (He) –expansion tests. However, He, with a small kinetic diameter, can penetrate into narrow pores in porous media that are inaccessible to adsorbate gases [e.g., methane (CH4)]. Thus, the actual accessible volume for a specific adsorbate is always overestimated by an He–based void volume; such overestimation directly leads to errors in the determination of excess isotherms in the laboratory, such as “negative isotherms” for gas adsorption at high pressures, which further affects an accurate description of total gas in place (GIP) for shale–gas reservoirs.
In this work, the mass balance for determining the adsorbed amount is rewritten, and two particular concepts, an “apparent excess adsorption” and an “actual excess adsorption,” are considered. Apparent adsorption is directly determined by an He–based volume, corresponding to the traditional treatment in experimental conditions, whereas actual adsorption is determined by an adsorbate–accessible volume, where pore–wall potential is always nonpositive (i.e., an attractive molecule/pore–wall interaction). Results show the following: The apparent excess isotherm determined by the He–based volume gradually becomes negative at high pressures, but the actual one determined by the adsorbate–accessible volume always remains positive.The negative adsorption phenomenon in the apparent excess isotherm is a result of the overestimation in the adsorbate–accessible volume, and a larger overestimation leads to an earlier appearance of this negative adsorption.The positive amount in the actual excess isotherm indicates that the adsorbed phase is always denser than the bulk gas because of the molecule/pore–wall attraction aiding the compression of the adsorbed molecules.
Practically, an overestimation in pore volume (PV) is only 3.74% for our studied sample, but it leads to an underestimation reaching up to 22.1% in the actual excess amount at geologic conditions (i.e., approximately 47 MPa and approximately 384 K). Such an overestimation in PV also underestimates the proportions of the adsorbed–gas amount to the free–gas amount and to the total GIP. Therefore, our present work underlines the importance of a void volume in the determination of adsorption isotherms; moreover, we establish a path for a more–accurate evaluation of gas storage in geologic shale reservoirs with high pressure.
Determination of the Volume Changes Induced by Ligand Binding to Hsp90 Using High Pressure Denaturation
