Semi-analytical model for the interpretation of oil reservoir tracer test data: solution of a direct problem for low resistance channels

The article considers the problem of interpretation of tracer tests in oil reservoirs, into which a specific chemical substance - tracer - is injected via an injection well for flow monitoring and tracer concentration measurements in surrounding production wells. The testing data provide evidence of the existence of low resistance channels in the reservoirs, along which the tracer moves at velocities several orders of magnitude higher than in the reservoir. The nature and properties of these channels are unknown, and a semi-analytical model involving two small parameters is proposed to solve this problem. This makes it possible to construct two non-conjugate solutions: universal numerical and analytical. Such an approach allows us to solve both direct and inverse problems. The present article is devoted to solving the direct problem. The problem of pressure distribution in a rectangular reservoir pattern is solved in dimensionless coordinates and is universal, i.e., it does not depend on the size of the area and the pressure drop. This solution is approximated by power functions and is further used to determine the mass transfer between channel and reservoir. The problem of tracer slug propagation through the channel obeys the law of conservation of tracer mass and Darcy's law. Its solution is found by the methods of characteristics under the condition of smallness of the parameter reflecting the ratio of reservoir permeability to channel permeability. The results of the semi-analytical solution are compared with the numerical solutions previously obtained by other authors. The fundamental difference between these solutions is the presence of numerical diffusion when using the finite-difference method of solution, which leads to the «dissipation» of the trace slug edges.