Extension of Kevin equation to CO2 adsorption in activated carbon


Carbon dioxide exhibit excellent physical and chemical properties that facilitate its separation from a mixture of different gases. Among the several available separation techniques, adsorption is widely used. This is due to its chemical properties that enables it to work well with solid surfaces.

Recently, the use of activated carbon in the separation of carbon dioxide from a mixture of gases has attracted significant attention of researchers. Condensation or liquefaction in the pores facilitates the physical adsorption of carbon dioxide. Therefore, with the pores size distribution of the activated carbon, it is easy to determine the adsorption capacity. This is based on the nonlocal density functional theory that assumes different sizes of the adsorbed pores at any adsorption condition. Unfortunately, it is difficult to determine the adsorption capacity due to the inexplicit relationship between the operating conditions and the adsorption capacity. The problem has however been effectively addressed by the Kelvin equation theory owing to its capability of directly correlating the operation conditions and the geometric characteristics of the pores. Unfortunately, the theory can only be applied effectively to a certain range of micropore diameter while it remains invalid for significantly small micropores diameters. To this end, the Kelvin equation has been modified to fit the desired application such as in the case of narrower pores.

Dr. Guojun Yin at Yantai University in collaboration with Professors Zhenyu Liu, Qingya Liu and Professor Weize Wu at Beijing University of Chemical Technology extended the Kelvin equation to investigate the adsorption behavior of carbon dioxide in three types of activated carbon in a dynamic adsorption unit at favorable conditions. They purposed to determine a general dimensionless parameters based on the pore size distribution to account for the physical parameter changes in the carbon dioxide micropores. This was done by measuring the adsorption capacity of the CO2 for the three activated carbon samples, fitting them to the pores and determining the critical pore diameter which would, in turn, be used to calculate the dimensionless parameters by Kelvin equation. Their work is published in the journal, Fuel Processing Technology.

The authors observed that the dimensionless parameters could be approximated by using the empirical equation because of it slight variation with the pore diameter and significantly variation with the temperature. Consequently, Kelvin equation was also useful for filling of pores up to 1 nm of a diameter which also supported the adsorption of CO2 in the activated carbon. It was necessary to determine the adsorption capacities of the three activated carbon samples at different temperatures. A critical pore diameter of 0.45 and 1.07 nm was obtained.

The research team successfully fitted the obtained data to the modified Kelvin equation through the dimensionless parameter. The parameters were important as they accounted for the deviations in the liquid density and surface tension of CO2 in micropores. According to the authors, the modified Kelvin equation is effective for describing CO2 adsorption data for a wide range of activated carbons. As such, the study will advance the design of CO2 adsorption processes based on activated carbons.


Yin, G., Liu, Q., Liu, Z., & Wu, W. (2018). Extension of Kelvin equation to CO2 adsorption in activated carbon. Fuel Processing Technology, 174, 118-122.

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