The contact wetting is one of the effective methods of studying the adsorption capacity of sorbents. The purpose of the work was to compare the experimentally obtained data on the adsorption capacity of shungite, obtained by the sessile drop method, and the results of modeling the behavior of liquid droplets on heterogeneous surfaces using the Boltzmann lattice method, and to show the suitability of the simplified version of the LBM method that we applied within the framework of a two-dimensional model for modeling complex cases of contact interaction between liquids and sorbent, when it cannot be carried out by the method of contact wetting. The adsorption properties of shungite with regard to the extraction of various impurities from water-alcohol solutions and the capability of the sorbent to recover were investigated by the method of contact wetting and analyzed by involving the data obtained by the methods of nitrogen adsorption, thermogravimetry and IR spectroscopy. It is shown that the adsorption properties of shungite are due to the presence on its surface of hydroxyl functional groups attached to carbon atoms in phenol or enol form, which give the surface hydrophilic characteristics. These groups play a key role in the adsorption of components from the liquid (aqueous) phase due to the formation of a hydrogen bond during the sorption of components from the liquid phase, and are restored after heating in the temperature range of 80–180 °C with the formation of carbon-containing gases and water. It has been found that silanol groups present in shungite do not participate in sorption. Compared to the original shungite sample, the sample after five cycles of adsorption is characterized by a noticeable effect of mass loss (1.8 %) in the temperature range of 80–180 °С. At the same time, the loss of mass is not significant at temperatures below 100 °С. This suggests that the sorbed substances are in the pores and not on the surface of shungite, and they begin to be removed only after heating above 100 °C. The LBM method was used to study fast-moving processes at the meso-level. A comparative analysis of the experimental data obtained by the method of contact wetting with the results of simulation by the Boltzmann lattice method within the framework of the two-dimensional model was carried out. 2D modeling by the LBM method turned out to be an effective means of studying capillary condensation in mesopores, anticipatory wetting of the solid phase, liquid penetration into a porous medium with different topologies, and the formation of anisotropic droplets and anisotropic bridges. The role of mesopores in the sorption process was analyzed by modeling the behavior of liquid droplets on heterogeneous surfaces and using data on the course of adsorption and capillary processes on the surface of a solid phase with different levels of porosity, roughness, and functional composition.