Mathematical models of active acoustic impact on diffusion in reservoirs with oil hierarchic inclusions

The work is devoted to the study of the influence of turbulent fluid movement in a vertical well passing through a reservoir with oil hierarchical inclusions. The processes of development of oil and gas fields are associated with the movement of multiphase multicomponent media, which are characterized by noneqiulibrium and nonlinear rheological properties. The actual behavior of reservoir systems is determined by complexity of moving fluids rheology and the morphological structure of the porous medium, as well as the variety of interaction processes between the fluid and the porous medium. Taking these factors into account it is necessary for a meaningful description of filtration processes due to nonlinearity, noneqiulibrium and heterogeneity inherent in real systems. At the same time, new synergetic effects are revealed (loss of stability with the onset of oscillations, the formation of ordered structures). This allows us to propose new methods for monitoring and managing complex natural systems that are tuned to account for these phenomena. In this case, the reservoir system from which it is necessary to extract oil is a complex dynamic hierarchical system. An algorithm for mathematical modeling of the propagation of a longitudinal acoustic wave in a layered block medium with a plastic layer above a reservoir with different-scale oil hierarchical inclusions, taking into account the effect of fluid turbulence in the reservoir, has been developed. The iterative algorithm uses integro-differential equations, which was previously tested for solving direct problems of acoustic wave propagation in a layered-block medium with hierarchical inclusions. Turbulent motion in the well creates, due to a set of vortices of different scales, a set of additional frequencies to the main frequency of acoustic excitation of the reservoir medium, which sets in motion both large and smaller hierarchical inclusions. Energy transfer occurs from larger eddies to smaller ones, depending on the viscosity of the reservoir medium. This effect can be controlled to enhance oil recovery from the reservoir.