The purpose of this work is to study the features of the numerical solution of two-phase flow in fractured porous reservoirs during non-stationary flooding using the Discrete Fracture Network model. The dependence of the oil production dynamics on the duration of the water injection cycles, the parameters and the position of the fracture relative to the wells was investigated. The investigations were carried on a model in which there were one or more fracture with different lengths and orientations relative to the wells. The equations were solved using the control volume method on an irregular grid, which allows us to simulate fractures correctly. In this case the grid inside the fractures was rectangular. As a result of the performed research, it is shown that in the case of stationary waterflooding, the presence of fracturing in the reservoir leads to a rapid breakthrough of water to production wells and to a reduction in the oil recovery factor. Non-stationary waterflooding makes it possible to increase oil production. At the same time, a non-stationary cyclic waterflooding in a homogeneous reservoir does not lead to a significant increase in oil recovery. The degree of effectiveness of the cyclic waterflooding strongly depends on the permeability and on the orientation of the fractures relative to the wells. The presence of a strong effect from the non-stationary waterflooding of the reservoir may serve as one of the signs of the presence of fractures in the reservoir.
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