Applied Physics and Mathematics Annotation << Back AN ASYMPTOTIC SOLUTION TO THE PROBLEM OF THE MOVEMENT OF THE TRACER MARK IN A FORMATION WITH A HYDRAULIC FRACTURING CRACK A.I. FILIPPOV, M.A. ZELENOVA, A.YA. DAVLETBAEV, R.R. GAREEV The problem of the evolution of the tracer concentration during the flow of the indicator liquid in the formation in which hydraulic fracturing was carried out, taking into account convective and diffusive mass transfer, as well as the chemical activity of the substance, is solved. Based on the asymptotic method, an analytical solution of the problem is constructed for the case of an arbitrary transverse velocity distribution in a hydraulic fracturing crack in the main asymptotic approximation. The expressions obtained make it possible to analyze the contribution of various physical processes to the formation of concentration fields during the movement of a rectangular tracer mark during liquid injection. The necessity of using new natural dimensionless criteria for the study of convective diffusion processes in the reservoir is substantiated. It is shown that the main criterion determining the evolution of a rectangular label is convective diffusion processes, the contribution of which is determined by the number Ma. To account for the contribution of decay processes, it is necessary to use an additional Fi criterion. The developed mathematical model opens up new prospects for the study of the physical and geometric parameters of the crack, as well as the development of methods for interpreting the results of tracer studies. Keywords: tracer mark, hydraulic fracturing crack, convective diffusion, asymptotic method, concentration field. DOI: 10.25791/pfim.06.2024.1315 Pp. 26-34.