NON-ISOTHERMAL FILTRATION OF MULTILAYER OIL RESERVOIR BEDS: AVERAGED TWO-DIMENSIONAL MODELS FOR EXPONENTIAL PROBABILITY LAW IN COLD FLOODING
In problems of hydrodynamics, two-phase filtration models averaged over the thickness of the reservoir are often used, which, on the one hand, make it possible to lower the order of the original problem, and on the other hand, make high-quality hydrodynamic calculations. Note that the transition to lower dimensional models is a standard method for solving problems of continuum mechanics. In this case, the three-dimensional flow is considered as a vertical averaged two-dimensional flow using the averaged (modified) functions of the coefficients of the original system. Moreover, the modified relative phase permeabilities are used in models of reduced dimension instead of the initial relative phase permeabilities. However, the question of reducing the dimension of the problem is quite relevant, especially when studying layered heterogeneous oil beds. In this work, non-isothermal filtration of a ten-layer oil reservoir is studied on averaged two-dimensional models with an exponential probability law, to which the absolute permeability function obeys within the formation vertical. At the same time multilayer formations are considered in which the absolute permeability function is set to be heterogeneous both vertically and horizontally. During the development of heterogeneous multilayer formations, the reliability of the transition from a three-dimensional system of differential equations to averaged models of lower dimension has been investigated and a comparison has been made with reference models. A computational experiment was carried out during cool water flooding, the obtained numerical solutions are analyzed and a comparison is made of averaged two-dimensional solutions and reference numerical solutions for some of the main indicators of oil reservoir development. Based on the results of the computational experiment, graphs of the amount of oil produced were plotted for all considered models for quadratic and cubic functions of laboratory relative phase permeabilities. A computational experiment was also used to verify the proposed averaged models of non-isothermal oil displacement by cold water. Positive results have been obtained for a ten-layer heterogeneous reservoir, which can be recommended for use in various hydrodynamic calculations.