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In this paper, a mathematical model of multiphase filtration in a deformable porous medium is presented. Based on the proposed model, the influence of the deformation of a porous medium on the filtration processes is studied. Numerical calculations are performed and the characteristics of the process are determined. This paper shows that an increase in the compressibility coefficient leads to a sharp decrease in porosity, absolute permeability and internal pressure of the medium near the well, and a decrease in the distance between wells leads to a sharp decrease in hydrodynamic parameters in the inter-well zone.

Mathematical simulation of the propagation mechanisms of combustion waves and heterogeneous detonation in sharply expanding pipes was performed using the equations of twodimensional axisymmetric unsteady motion of a reacting mixture of a gas and monofuel particles. The influence of the main determining parameters of the gas-particle mixture and the pipeline on the propagation of nonstationary detonation waves was studied. Dependences of the critical ratio of the pipe diameters of the composite pipeline on the relative mass content of monofuel particles of different sizes are given.

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