Abstract The first application of digital rock technology (digital core analysis) with direct hydrodynamic modeling based on density functional theory for the Achimov formation is described. The technology consists of imaging core samples by X-ray microtomography, construction of corresponding digital rock models of pore space geometry, and multiphase hydrodynamic simulation on a pore scale by the density functional method. Despite the extremely low permeability values (less than 1 μd), digital measurements of relative permeability curves were completed successfully for model oil and water in steady-state flow mode whereas laboratory measurements in steady-state flow regime were unfeasible for the studied samples. The required spatial resolution of the digital rock models for the studied samples was about 1 μm and higher. At the same time, for a reasonable selection of a representative sample, it is desirable to conduct a larger sample scan with a coarser resolution. For the first time in the industry, a direct two-phase relative permeability simulation was performed on a record-size model of 1300 × 1300 × 1500 voxels. Also, for the first time, two-phase filtration experiments were carried out on a core miniplugs in the permeability range of less than 1 μd.