Mathematical modeling and experimental study on water condensation in nanopores of calcium carbonate

Condensed water in nanopores of rocks is closely related to many hydrogeological and engineering geological issues. In arid areas, condensed water is an important resource to maintain local ecological balance. For the protection of stone carvings cultural relics, condensed water is one of the key factors to be considered. Condensed water in nanopores of shale has an important influence on the accumulation and flow of shale gas in the project of shale gas engineering. In global carbon cycle problems, condensed water affects the interaction between CO2 and carbonate rocks. This paper presents the mathematical relationship between the amount of condensed water and temperature, relative humidity, porosity and particle size. In this relationship, the adsorption water is calculated based on the disjoining pressure theory, and the role of capillary condensation is considered by Kelvin equation. The analytical results are compared with measured values of three parallel experiments on condensed water at four different relative humidity to verify the proposed mathematical expression. In the experiment, spherical particles of calcium carbonate with diameter of 500 nm were selected and processed into samples by tamping. The samples were placed in a constant temperature and humidity environment to condense water vapor in the pores. The samples were weighed periodically to determine the quality of the condensed water until the condensation process reached equilibrium.