2013 1(12)

Back to table of content

   Short abstract



244 - 250





Click to get extended abstract

Download paper: [RU]





Potashev K.A.

Kazan (Volga Region) Federal University, Kazan, Russia


Potashev, K.A., (2013) Upscaling in super element models of two-phase flows, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(12), PP. 244 - 250.


upscaling; two-phase flow in porous media; relative phase permeability; oil reservoir simulation; super element method


The new super element approach to petroleum reservoir simulation has been developed by the authors. The suggested method is based on a numerical solution of 3D two-phase filtration flow equations on a coarse unstructured grid. Each grid cell represents a superlement which is bounded by a Voronoi cell around a well projection in a horizontal plane (hundreds of meters across) and by borders of geological pack (a collection of adjacent geological layers) in the vertical direction. In present work methods of upscaling of absolute and relative permeability of oil reservoir is presented. The suggested methods consider peculiarities of superelement structure and provide equivalence of resulted upscaled properties to an original geological formation. An upscaling of absolute permeability is carried out by considering each superelement separately. The given high-resolution scalar permeability field is evaluated into the permeability tensor as a result of numerical solution of local single phase filtration problem within each coarse 3D element. Average velocity and minimum dissipation energy principles are used to obtain tensor components. Upscaling of phase permeabilities consists of adjustment of relative permeabilities curves. With low variability of layers properties in a horizontal direction taken into account upscaling problem reduces to averaging of two-phase 2D flow in a vertical section of reservoir. Testing of presented method of relative permeability upscaling confirmed its appropriateness.


  1. Durlofsky, L.J. (2005), "Upscaling and gridding of fine scale geological models for flow simulation", Department of Petroleum Engineering, Stanford University, Stanford, CA 94305-22220 USA.

  2. Artus, V., Noetinger, B. (2004), "Upscaling Two-Phase Flow in Heterogeneous Reservoirs: Current Trends", Oil & Gas Science and Technology, Rev. IFP, Vol. 59, no. 2, pp. 185-195.

  3. Wu X.H., Efendiev Y., Hou T.Y. (2002) "Analysis of upscaling absolute permeability", Discrete And Continuous Dynamical Systems. Series B, Vol. 2, № 2, pp. 185-204.

  4. Dagan, G., Fiori, A., Jankovic, I. (2013), "Upscaling of flow in heterogeneous porous formations: Critical examination and issues of principle", Advances in Water Resources, Vol. 51, no. 1, pp. 67-85.

  5. Mazo, A.B., Potashev, K.A., Kalinin, E.I. and Bulygin, D.V. (2013), "Modeling the development of oil reservoirs by a method of super elements", Matematicheskoe modelirovanie, no. 8, pp. 83-87.

  6. Bulygin, D.V., Bulygin, V.Ya. (1996), Geologiya i imitatsiya razrabotki zalezhey nefti [Geology and development imitation of oil reservoirs], Nedra, Moscow, Russia.

  7. Nikitin, N.G. (2010), "Nonlinear finite volume method for problems of two-phase flow in porous media", Matematicheskoe modelirovanie, Vol. 22, no. 11, pp. 131147.

  8. Kanevskaya, R.D. (2003), Matematicheskoe modelirovanie protsessov razrabotki mestorozhdeniy uglevodorodov [Mathematical modeling of hydrocarbon deponents development processes], Institut kompiuternykh issledovaniy, MoscowIzhevsk, Russia.

  9. Plokhotnikov, S.P., Fatykhov, R.H. (2006), Matematicheskoe modelirovanie filtratsii v sloistykh plastakh [Mathematical modeling of flows in layered reservoirs], Kazanskiy tekhnologicheskiy universitet, Kazan, Russia.



© SPIC "Kappa", LLC 2009-2016