Özet:

The manuscript is aimed at improving the mathematical model of oil production in a heterogeneous environment with the use of a thermal mode of displacement considering the action of capillary effect. We have constructed an algorithm to solve numerically the respective nonlinear boundary value problem on multiphase filtering by introducing the function of quasi-potential  and the respective, conjugated thereto, flow function . In this case, the quasi-potential is represented in the form  thereby having essentially simplified the overall strategy to split the algorithm for solving the original problem. Owing to the algorithm, which is based on the ideas of methods for quasiconformal mapping and staged registration of parameters, we have carried out calculations of the hydrodynamic grid, velocity fields, temperature, saturation, taking into consideration the impact of a capillary effect and when ignoring it. In particular, the charts of saturation fields demonstrate a difference in the ratio of percentage content of a displacing fluid up to 15 % at temperatures above 80 °C, which explains the effect of capillary forces. Instead, at temperatures from 50 °С to 70 °С the difference is not noticeable, though at 50 °С and below the results of flooding slightly differ (to 5 %) for the worse in terms of the actual representation of the process. In this case, it is believed that the dynamic viscosities of phases change with a change in temperature, the fluid movement is slow and occurs without phase transitions, while functions of relative phase permeabilities and capillary pressure are the known and unambiguous saturation functions.Numerical calculations of multiphase non-isothermal filtering in the symmetry element at a five-point system of flooding have been presented. In this case, it was found that taking into account the capillary effect makes it possible to not only predict the location of stagnant zones, but also to more accurately estimate the time when a displacing reagent breaks through in an operational well in order to effectively perform respective waterproofing operations. Author Biographies Olga Michuta, National University of Water and Environmental Engineering Soborna str., 11, Rivne, Ukraine, 33028 PhD Department of Applied Mathematics

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