The experience of dealing with oil and gas wells shows that during their operation the significant contamination of the near-wellbore zone (NWZ) of the productive formation is observed. This causes a decrease in the well productivity due to the deterioration of the filtration properties of formations. Therefore, there is a need to assess the state of damaged formations in order to further develop recommendations for the well operation and to carry out measures for NWZ renewal. The conducted studies clarify the influence of the physical properties of a formation as well as the fluid in it on the filtration dynamics in a reservoir. In particular, mathematical modeling of filtration in a heterogeneous formation as an NWZ model is carried out. In the research, a model of nonsteady non-equilibrium filtration in a semi-infinite heterogeneous layer with harmonic disturbance at its boundary is constructed. This model consists of a linearized equation of the law of conservation of fluid mass in a porous medium and relaxation Darcy law, in which the permeability coefficients are power functions of the spatial coordinate. Using the method of separation of variables, a quasisteady solution of the boundary value problem is constructed, based on which the influence of the piezoconductivity anomaly and the rate of nonequilibrity on the filtration dynamics in the NWZ is determined. We also discuss the issue of using theoretical results in the development of technologies for testing of well systems and methods of processing NWZ with harmonic disturbances to increase the flow rate of wells.