The project’s aim is to comprehend the hydrodynamic aspects of the oil extraction process. This process, in general, includes two stages: dissolution of oil and displacement of a solution from porous media. The focus of the project is, therefore, twofold: (i) to develop and verify a theoretical model for an evolving miscible displacement with an account of dynamic surface tension and mass diffusion, and (ii) to provide a model for the miscible displacement from the porous volume. Owing to complexity in modelling the evolution of the interface between inter-diffusing liquids, a detailed theoretical analysis of the hydrodynamics of dissolution process has not been provided thus far. The pore-level description of the solvent extraction process from the porous medium has not been undertaken either.The final goal of the project is to construct the dynamic 2D network model of oil dissolution from porous media. The throats of the network will be represented as the capillary tubes of square cross-section of random side-widths; as the pores will be the volumes connecting four tubes. We will develop the numerical code for the 2D and 3D resolution of solvent/solute flows within a single element of the network, and then, will combine the results into macroscopic network. The evolution of the miscible solvent/solute interface will be modelled within the phase-field approach. The developed theoretical model will be verified by a series of experiments designed so that to support the calculations, i.e. to investigate the dynamics of miscible displacement through a single capillary tube of square cross-section and through a network of tubes.The project will help to predict the rate of oil dissolution from porous media, and its dependence on time, injection flux, wetting conditions, etc. We will determine the physical conditions, the time, and volume of solvent required for efficient complete or partial solvent extraction or cleaning. The results will be valuable for modelling of the various industrial processes, including the vegetable solvent extraction, and enhanced oil recovery and enhanced aquifer remediation in which the miscible injection is used for oil displacement.