Mathematical Modeling of Suspension Flow in the System of Intersecting Fractures

Abstract— In this paper, mathematical modeling of the suspension flow in a complex system of fractures, when the main fracture is crossed by the secondary one, is carried out. The mathematical model of the process is constructed in the one-fluid approximation and includes the continuity equation for the suspension, the system of equations of suspension motion, and the mass conservation equation in the form of a convective—diffusion transfer equation for the volume concentration of particles. The solution to the problem in a 3D formulation is implemented in the OpenFOAM software package. The dynamics of the distribution of solid spherical particles in the network of fractures is studied depending on the ratio of the characteristic Reynolds numbers for the flow and particles, as well as on the ratio of the lengths of the main and secondary fractures.