Drying of geological formations by supercritical gas injection and the associated precipitation of salts from the formation water may have serious consequences for upstream operations in terms of injectivity/productivity impairment. The potential effect on the formation permeability near the injection well is controversially discussed in literature with some studies finding a strong and others no impairment. In an earlier publication (Ott et al., 2014), we argue that this is related to the microscopic pore structure and capillary-driven brine transport therein, and that in well sorted sandstone reservoirs, permeability may be less affected than in dual- or multi-porosity systems. In the present paper, we investigate the consequences of dolomite-formation drying due to the injection of under-saturated supercritical CO2 into samples from a Middle-East dolomite formation. Compared to earlier reported results on sandstone, the experiments show a complex behavior with a much larger effect on permeability. A permeability reduction of up to three orders of magnitude has been found. This is explained by a simple numerical model on local capillary-driven flow of water from micro- to the macro-porous regions at low brine saturation where evaporation dominates desaturation. The model suggests salt precipitation in the CO2 conductive macropores, which impacts the effective CO2 permeability. The volumetric ratio of micro to macro porosity, the capillary pressure contrast and water salinity and saturation are identified as the controlling parameters.