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A study has been made of the problem on the process of formation of a zone of higher-than-average permeability with a moving boundary in an initially low-permeability porous medium (problem on hydraulic fracturing of a bed) in a three-dimensional formulation. A characteristic feature of the three-dimensional problem was the taking into account the existence of two zones (zone with a regular permeability and the destruction zone) in the porous medium, whose contact region was determined using the condition of mass balance on the moving boundary. Special features fundamental to the process of mass transfer in such filtration-inhomogeneous porous media have been revealed and analyzed.

The problem of the squeezing out of a solution from aggregates in a porous medium has been considered and investigated. A specific feature of the problem lies in taking account of the existence of two compaction zones in deforming aggregates of a porous medium. Features essential to mass transfer in a deformable aggregated porous medium have been determined and analyzed.