Mathematical Modeling of the Flow of a Multiphase Heterogeneous Medium in a Permeable Tube

A mathematical model is proposed to describe the flow of a rheologically complex disperse medium in a permeable tube with consideration of the change in the concentration of suspended particles in the flow and the formation of a deposit layer on the tube wall. The model characterizes the filtration of a heterogeneous medium in permeable tubes and generally takes into account the hydraulic resistance of the wall and the deposit layer on it. An equation for the change in the concentration of the dispersed phase is derived. The results of numerically solving the equations of the proposed model are presented as the profiles of the velocity, pressure, concentration, and deposit thickness with allowance for the initial portion of the tube.