Development and Testing of a Mathematical Model for Dynamic Network Simulation of the Oil Displacement Process

Multiphase flows in porous media are widespread in nature and various technologies. One of the most common examples of this kind of task is the task of recovering oil from the rock. This article describes a mathematical model of the flow of a two-phase (immiscible) liquid based on a new approach of network hydrodynamics for a highly branched microchannel medium (simulating a porous space in the rock). The coupling of the flow and pressure fields in the network is performed using a well-proven SIMPLE algorithm in CFD problems; this approach allows us to use effective approaches to modeling 3D tasks. Phase transfer over the network is carried out by an explicit method with an adaptive time step. The article presents the results of verification of the model, with analytical calculations and in comparison with the results of experimental studies. As an experiment, the displacement of oil from a microchip (Dolomite: 3200284) simulating a porous medium was simulated. The good qualitative and quantitative compliance with the results calculated and the results of the experiment show the correct functioning of the model.