Özet:

The object of research is a numerical simulation of the process of two-dimensional two-phase filtration of viscoplastic oil and water, taking into account the gravitational forces, some properties of liquids, as well as relative phase permeabilities and capillary forces. As is known, the problems of multiphase filtration have specific features. Therefore, there is a need to develop difference schemes in adaptive grids that reduce the artificial viscosity and oscillation of the numerical solution. They also make it possible to obtain acceptable results with a small number of nodes in the computational grid. To take into account the singularities of the solution, a difference-iteration method is used in moving grids. Based on the computational experiment, the influence of the initial pressure gradient and gravity on the displacement process is investigated. Economical difference schemes that combine the advantages of explicit and implicit schemes are constructed and make it possible to reduce the two-dimensional problem to a chain of one-dimensional problems. A difference-iterative method is also proposed in moving grids for solving two-dimensional (axisymmetric) non-stationary filtration problems of anomalous liquids, by means of which an iterative process is constructed to find the distribution of water saturation. The carried out calculations to determine the influence of gravity on the displacement process have shown that at z=0, even at low productive-bed thicknesses, gravitational forces influence the displacement process. And over time this influence increases: if at the time t=0.08 on the circuit the difference of water saturation was 0.0077; at t=0.24–0.0122, then at t=1.04 it becomes equal to 0.0292. It is shown that when modeling the process without taking gravity into account it is expedient to simplify the geometry of the filtration region, i. e., to consider a plane-radial flow in view of the considerable simplicity of the calculations. The developed algorithms can be used for hydro-gas dynamic calculations related to the development and operation of oil fields containing anomalous oil. Author Biographies Sardar Yusub Gasimov, Azerbaijan State University of Oil and Industry, 20, Azadlig ave., Baku, Azerbaijan, AZ1010 PhD, Associate Professor Department of General and Applied Mathematics

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