Geodesic
Accounting the heterogeneous waterflooding of the near-well drainage area for coarse scale simulation of petroleum reservoir
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 1, pp. 116-129 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{UZKU_2017_159_1_a9,
     author = {K. A. Potashev and L. R. Abdrashitova},
     title = {Accounting the heterogeneous waterflooding of the near-well drainage area for coarse scale simulation of petroleum reservoir},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {116--129},
     year = {2017},
     volume = {159},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2017_159_1_a9/}
}
TY  - JOUR
AU  - K. A. Potashev
AU  - L. R. Abdrashitova
TI  - Accounting the heterogeneous waterflooding of the near-well drainage area for coarse scale simulation of petroleum reservoir
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2017
SP  - 116
EP  - 129
VL  - 159
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZKU_2017_159_1_a9/
LA  - ru
ID  - UZKU_2017_159_1_a9
ER  - 
%0 Journal Article
%A K. A. Potashev
%A L. R. Abdrashitova
%T Accounting the heterogeneous waterflooding of the near-well drainage area for coarse scale simulation of petroleum reservoir
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2017
%P 116-129
%V 159
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2017_159_1_a9/
%G ru
%F UZKU_2017_159_1_a9
K. A. Potashev; L. R. Abdrashitova. Accounting the heterogeneous waterflooding of the near-well drainage area for coarse scale simulation of petroleum reservoir. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 1, pp. 116-129. http://geodesic.mathdoc.fr/item/UZKU_2017_159_1_a9/

[1] Mazo A. B., Potashev K. A., Kalinin E. I., Bulygin D. V., “Oil reservoir simulation with the superelement method”, Mat. Model., 25:8 (2013), 51–64 (In Russian) | MR | Zbl

[2] Amaziane B., Bourgeat A., Koebbe J., “Numerical simulation and homogenization of two-phase flow in heterogeneous porous media”, Transp. Porous Media, 6:5 (1991), 519–547

[3] Christie M. A., “Upscaling for reservoir simulation”, J. Pet. Technol., 48:11 (1996), 1004–1010 | DOI

[4] Farmer C. L., “Upscaling: A review”, Int. J. Numer. Methods Fluids, 40:1–2 (2002), 63–78 | DOI | MR | Zbl

[5] Durlofsky L. J., “Coarse scale models of two phase flow in heterogeneous reservoirs: volume averaged equations and their relationship to existing upscaling techniques”, Comput. Geosci., 2:2 (1998), 73–92 | DOI | MR | Zbl

[6] Jacks H. H., Smith O. J. E., Mattax C. C., “The modelling of a three-dimensional reservoir with a two-dimensional reservoir simulator – the use of dynamic pseudo functions”, Soc. Pet. Eng. J., 13:3 (1973), 175–85 | DOI

[7] Gasda S. E., Celia M. A., “Upscaling relative permeabilities in a structured porous medium”, Adv. Water Res, 28:5 (2005), 493–506 | DOI

[8] Potashev K. A., “Upscaling of relative phase permeabilities in an isolated stratified reservoir”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 156, no. 2, 2014, 120–134 (In Russian) | MR | Zbl

[9] Mazo A. B., Potashev K. A., “Relative phase permeability upscaling for super element model of petroleum reservoirs”, Mat. Model., 29:3 (2017), 81–94 (In Russian)

[10] Barenblatt G. I., Entov V. M., Ryzhik V. M., The Motion of Fluids and Gases in Natural Strata, Nedra, Moscow, 1984, 211 pp. (In Russian)