In this paper, experimental and computational approaches are used to study multiphase flows. In the first method, filtration experiments are carried out using microfluidics technology. Microfluidic chips were made from polydimethylsiloxane using soft lithography. To give the desired surface properties, the inner walls of the channels were treated with a hydrophobic or hydrophilic coating. Injection of liquids was carried out using a syringe pump at a constant flow rate. To measure the pressure difference at the inlet and outlet of the microchip, we used the method of measuring changes in gas volume. For numerical modeling, the most modern model of the Boltzmann lattice equations, adapted for two-phase flows of incompressible immiscible liquids, is used. The effects that occur at the phase boundary are described using the color field gradient model. Experimental studies have shown the possibility of studying the processes of liquid displacement from the microchannel system in a microfluidic chip simulating a porous medium. The dynamics of the displacement of liquids (water and oil) from a system of microchannels with different hydrodynamic drag cardinally depends on the angle of wettability of its walls. In the case of microchannels with hydrophilic walls, a complete displacement of oil by water occurs almost simultaneously from both channels. When water is displaced by oil from channels with a hydrophilic and hydrophobic coating, it is required to create an increased flow rate of the displacing liquid through microchannels. In this case, at the junction of the microchannels, before leaving the chip, emulsion droplets of "water in oil" will form. In the case of oil displacement by water from microchannels with a hydrophobic coating, complete removal of oil from the channel with high resistance did not occur. This is due to the fact that the viscosity of the oil is 30 times higher than the viscosity of water. The paper shows a successful comparison of the results of numerical modeling and experimental research in a two-phase flow in a pore doublet. Demonstrated examples of the developed program code are shown: the formation of emulsions at high flow rates, the motion of a drop under the influence of mass force; flow in digital microtomographic image; displacement of viscous oil from the pore medium.