Permeability is an important transport property of porous materials, and its accurate evaluation is relevant in studying applied tasks such as CO2 injection into reservoirs and investigating groundwater quality issues. This study examines the dependence of permeability on total and connected porosity, hydraulic tortuosity, specific surface area, and mean pore radius based on the data of 408 cubic sub-volumes extracted from heterogeneous and naturally fractured cylindrical carbonate samples before and after injection of HCl solutions into them. These parameters were computed using pore-scale modeling of fluid flow. It has been shown that permeability correlates well with porosity and mean pore radius with correlation coefficients of R2≈0.65-0.79 for heterogeneous samples. It was found that the presence of natural fractures significantly influenced the relationship between permeability and other parameters. The relationship between permeability k, tortuosity τ, and specific surface area S is described by power laws k~τ-α and k~S-β, with coefficients α and β substantially exceeding those in the Kozeny-Carman equation. It was also found that there is a parabolic relationship between connected and total porosities both before and after rock dissolution with R2≈0.96-0.99. This allowed for estimation of percolation threshold porosity that are in good agreement with the literature data.