Climate change has become the main concern for humankind over the last decade, the environmental consequence is linked to the increase in global average temperatures. It can be explained by the gradual increase in greenhouse gas emissions, such as carbon dioxide (CO2). Therefore, the society aims to become carbon-neutral by 2050. To achieve this target, one of the most promising solutions is Carbon Capture and Storage (CCS), which involves capturing CO2 from industrial sources or the atmosphere, underground injection, and ultimately storing CO2 in deep geological formations. The most favorable option includes saline aquifers, because of their high storage capacity potential. The realization of the CCS projects would require highly precise modeling tools, and an important task is a description of the geochemical and physical processes, which lead to the evaporation of the saline formation water due to the injection of dry supercritical CO2 into brine aquifers. This mechanism leads to an increase in salinity and salt precipitation, which mainly happens because of water vaporization inside the CO2-saturated (dry-out) region. Therefore, permeability and porosity are altered and injectivity impairment arises. It is vital to understand the parameters which enhance salt precipitation, patterns of precipitation, and the displacement process of brine by CO2. The study will use publicly available multiphysics frameworks DuMux and Moose to evaluate the displacement process of brine by CO2 at the near injection region (assuming partitioning phase equilibrium is already achieved). The flow is described by two-phase slightly miscible displacement with the domination of primary drainage. The final target is to analyze the role of different parameters in the salt precipitation process, considering different injection rates and evaluating the role of relative permeability and the stabilizing effect of capillary pressure by using extended Brooks-Corey and Van Genuchten models. The obtained results and observations were compared with the benchmark simulator TOUGH2, which is utilized as commercial software and can be considered a proven simulator. All simulators - Moose, DuMux, and TOUGH2 are using the same principle of local equilibrium assumption, therefore all of them showed an accumulation of salt near the core inlet consistently with more pronate precipitation under the capillary-driven backflow of brine.