K.A. Potashev*, L.R. Abdrashitova**
Kazan Federal University, Kazan, 420008 Russia
E-mail: *kpotashev@mail.ru, **ina.abdrashitova@yandex.ru
Received December 21, 2016
Abstract
A method for taking into account lateral flooding heterogeneity in the near-well area enclosed within a single coarse grid block containing the production well has been introduced. The algorithm has been designed for coarse-scale finite volume simulation of two-phase flow in the petroleum reservoir. It can significantly improve the accuracy of calculating the total well rate and water cut, as well as the average saturation in the near-wellbore grid block. The advantage of this method is that upscaled relative permeability functions can be modified functions derived from the simplified upscaling problem solutions that does not require significant computational cost assuming radial symmetry of the flow with a uniform waterflooding of the grid block. The efficiency of the method has been demonstrated by the example of the local problem for a single wellbore in the formation with inhomogeneous boundary conditions for the saturation and by the example of superelement simulation of the reservoir with the seven-spotted placement of wells with various flow rates.
Keywords: two-phase filtration, coarse-scale simulation, relative permeability, upscaling, rescaling, superelements, heterogeneous waterflooding
Acknowledgments. The study was supported by the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan (projects no. 15-41-02698 and 15-41-02699).
Figure Captions
Fig. 1. Matching of the coarse model grid and superelement grid.
Fig. 2. Relative permeability curves: 1 –RP, 2 –MRP at the well, 3 – MRP on the inner edges.
Fig. 3. The waterflooding curve of the well: 1 – detailed grid, 2 – coarse grid with RP, 3 – coarse grid with MRP.
Fig. 4. The scheme of spurious sectors in FV of the well.
Fig. 5. Comparison of the computation results for the detailed (1) and coarse grids without (2) and with account of (3) heterogeneous waterflooding.
Fig. 6. The dependence of closing error values on unwatered regionlength without account (1) and with account (2) of heterogenous waterflooding.
Fig. 7. A reservoir region with seven-spot flooding system: a) scheme of well layout and coarse grid solution; b) total waterflooding of well products on the detailed (1) and coarse grids without account (2) and with account of heterogenous waterflooding.
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For citation: Potashev K.A., Abdrashitova L.R. Accounting the heterogeneous waterflooding of the near-well drainage area for coarse scale simulation of petroleum reservoir. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 1, pp. 116–129. (In Russian)
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