Review article

The problem of depth filtration, which is determined by the balance equation of suspended and deposited particles and the kinetic equation of sediment growth, has no exact analytical solution. The paper deals with solving of the problem using an equivalent differential equation, application of which leads to the solution of the system of integral equations. As a result of integrating these equations, a system of transcendental equations is obtained. Numerical solutions of the transcendental system of equations and the initial hyperbolic system of partial differential equations in the finite difference method are very close. The mathematical model is constructed taking into account the dependence of porosity and allowable flow on the sediment concentration.