The method of the density functional hydrodynamics (DFH) is used to model compositional gas-condensate systems in natural cores at pore-scale. In previous publications, it has been demonstrated by the authors that DFH covers many diverse multiphase pore-scale phenomena, including fluid transport in RCA and SCAL measurements and complex EOR processes. The pore-scale modeling of multiphase flow scenarios is performed by means of the direct hydrodynamic (DHD) simulator, which is a numerical implementation of the DFH. In the present work, we consider the problem of pore-scale numerical modeling of three-phase system: residual water, hydrocarbon gas and hydrocarbon liquid with phase transitions between the two latter phases. Such situations happen in case of gas-condensate or volatile oil deposits, in oil deposits with gas caps or in EOR methods with gas injection. The corresponding field development modeling by the conventional reservoir simulators rely on phase permeabilities and capillary pressures, which are provided by laboratory core analysis experiments. But the problem with gas-liquid hydrocarbon mixtures is that in laboratory procedures it may be difficult or even impossible to achieve full thermodynamic equilibrium between phases as it must be under the reservoir conditions of the initial reservoir state. However, reaching the said equilibrium is quite possible in numerical simulation. In this work, the gas-liquid mixture, after being injected into core sample, would slowly undergo the rearrangement of the phases and chemical components in pores converging to the minimum of the Helmholtz energy functional. This process is adequately described by DFH with consequent impact on phase permeabilities and capillary pressure. We give pore-scale numerical examples of the described phenomena in a micro-CT porous rock model for a realistic gas-condensate mixture with quantitative characterization of phase transition kinetic effects.