Geodesic
Absolute permeability upscaling for super element model of petroleum reservoir
Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 89-102.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper presents a new method of local upscaling of absolute permeability for super element simulation of oil reservoir. Upscaling performed for each block of super element unstructured grid. To do this, the set of problems of steady state one phase flow solved on a fine computational grid with the initial scalar field of absolute permeability with various boundary conditions that reflect the specific variants of filtrational flow through the super element and take into account the presence or absence of boreholes in the coarse block. The resulting components of the effective permeability tensor in each super element found from the solution of the problem of minimizing the deviations of averaged on a detailed computational grid from approximated on a coarse super element grid normal flows through the super element faces. The results of using the method are demonstrated for reservoirs with periodic and non-periodic structure of absolute permeability field. The comparison with the traditional methods of local upscaling is performed.
Keywords: upscaling, absolute permeability, porous media, petroleum reservoir simulation, super element method. 
@article{MM_2017_29_6_a5,
     author = {A. B. Mazo and K. A. Potashev},
     title = {Absolute permeability upscaling for super element model of petroleum reservoir},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {89--102},
     publisher = {mathdoc},
     volume = {29},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_6_a5/}
}
TY  - JOUR
AU  - A. B. Mazo
AU  - K. A. Potashev
TI  - Absolute permeability upscaling for super element model of petroleum reservoir
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 89
EP  - 102
VL  - 29
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_6_a5/
LA  - ru
ID  - MM_2017_29_6_a5
ER  - 
%0 Journal Article
%A A. B. Mazo
%A K. A. Potashev
%T Absolute permeability upscaling for super element model of petroleum reservoir
%J Matematičeskoe modelirovanie
%D 2017
%P 89-102
%V 29
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_6_a5/
%G ru
%F MM_2017_29_6_a5
A. B. Mazo; K. A. Potashev. Absolute permeability upscaling for super element model of petroleum reservoir. Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 89-102. http://geodesic.mathdoc.fr/item/MM_2017_29_6_a5/

[1] A.B. Mazo, D.V. Bulygin, “Superelementy. Novyi podkhod k modelirovaniiu razrabotki neftianykh mestorozhdenii”, Neft. Gaz. Novatsii, 2011, no. 11, 6–8

[2] A.B. Mazo, K.A. Potashev, E.I. Kalinin, D.V. Bulygin, “Modelirovanie razrabotki neftianykh mesto-rozhdenii metodom superelementov”, Matematicheskoe modelirovanie, 25:8 (2013), 51–64

[3] D.V. Bulygin, A.B. Mazo, K.A. Potashev, E.I. Kalinin, “Geologo-tekhnicheskie aspekty superelementnoi filtratsionnoi modeli neftianykh mestorozhdenii”, Georesursy, 53:3 (2013), 31–35

[4] A. Mazo, K. Potashev, E. Kalinin, “Petroleum reservoir simulation using Super Element Method”, Procedia Earth and Planetary Science, 15, 2015, 482–487

[5] A.B. Mazo, K.A. Potashev, “Relative phase permeability upscaling for super element model of petroleum reservoirs”, Mathematical Models and Computer Simulations, 9:5 (2017)

[6] K.A. Potashev, “Apskeiling otnositelnykh fazovykh pronitsaemostei v nesoobshchaiushchemsia sloistom plaste”, Uchenye zapiski Kazanskogo universiteta. Fiziko-matematicheskie nauki, 156:2 (2014), 120–134

[7] A. Iu. Beliaev, Usrednenie v zadachakh teorii filtratsii, Nauka, M., 2004, 200 pp.

[8] N.S. Bakhvalov, “Osrednennye kharakteristiki tel s periodicheskoi strukturoi”, DAN SSSR, 218:5 (1974), 1046–1048

[9] A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic Analysis for Periodic Structures, Studies in Mathematics and Its Applications, 5, North-Holland Publ., 1978, 699 pp.

[10] A.L. Berdichevskii, “Ob effektivnoi teploprovodnosti tel s periodicheski raspolozhennymi vkliucheniiami”, DAN SSSR, 247:6 (1979), 1363–1367

[11] S.M. Kozlov, “Osrednenie differentsialnykh operatorov s pochti periodicheskimi koeffitsientami”, Mat. sbornik, 107:2 (1978), 199–217

[12] M.B. Panfilov, I.V. Panfilova, Osrednennye modeli filtratsionnykh protsessov s neodnorodnoi vnutrennei strukturoi, Nauka, M., 1996, 383 pp.

[13] X.H. Wu, Y. Efendiev, T.Y. Hou, “Analysis of upscaling absolute permeability”, Discrete And Continuous Dynamical Systems. Series B, 2:2 (2002), 185–204

[14] C.D. White, R.N. Horne, “Computing absolute transmissivity in the presence of fine scale heterogeneity”, Society of Petroleum Engineers J., 1987, 16011, 209–221

[15] L. Holden, B.F. Nielsen, “Global Upscaling of Permeability in Heterogeneous Reservoirs; The Output Least Squares (OLS) Method”, Transp. In Porous Media, 40 (2000), 115–143

[16] L.J. Durlofsky, “Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media”, Water Resour. Res., 27:5 (1991), 699–708

[17] L.G. Strakhovskaya, R.P. Fedorenko, “A version of the finite element method”, USSR Computational Mathematics and Mathematical Physics, 19:4 (1979), 162–173

[18] A. Kh. Pergament, V.A. Semiletov, P. Yu. Tomin, “On Some Multiscale Algorithms for Sector Modeling in Multiphase Flow in Porous Media”, Mathematical Models and Computer Simulations, 3:3 (2011), 365–374

[19] N.G. Nikitin, “Nelineinyi metod konechnykh obiemov dlia zadach dvukhfaznoi filtratsii”, Matematicheskoe modelirovanie, 22:11 (2010), 131–147

[20] K.A. Lurie, A.V. Cherkaev, “G-zamykanie mnozhestva anizotropno-provodiashchikh sred v sluchae dvukh izmerenii”, DAN SSSR, 259:2 (1981), 328–331

[21] F. Murat, L. Tartar, “Les Methodes de l'Homogeneisation: Theorie et Applications en Physique”, Coll. de la Dir. des Etudes et Recherches de Electr. De France, Paris, 1985, 319–370