Simulation of the flow of a viscous fluid with particles through porous medium cells

Abstract

A mathematical model for the dynamics of a viscous fluid with particles in a porous medium has been developed using the idea of representing the environment as a system of stationary particles, through which a viscous fluid with moving particles simulating a dispersed phase flows. The model takes into account the hydrodynamic interaction of all, both mobile and fixed, particles. For computer simulation of this type of the flow, a software package is proposed. Numerical calculations of the fluid flow in a porous medium were performed for two model structures, consisting of, respectively, 450 and 599 fixed particles of the effective size. Dimensions of the dispersed particles placed in the viscous fluid were 0.3 and 0.1 of the effective particle size. Analysis of the calculated values of the fluid flow rate and the rate of displacement of dispersed particles allowed us to determine the appropriate numerical values of these parameters in a real porous medium. It has been found that by changing the size of dispersed particles, one can affect the trajectory and velocity of particle motion within the porous structure not only quantitatively, but also qualitatively. Using as an example one of the model structures, we have obtained the result indicating that some threshold space is blocked by a mobile particle, which leads to the cessation of further movement of particles.