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Applicable Analysis
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Volume 98, 2019 - Issue 8
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Articles

Homogenization of Kondaurov’s non-equilibrium two-phase flow in double porosity media

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Pages 1429-1450 | Received 27 Jun 2017, Accepted 02 Jan 2018, Published online: 31 Jan 2018

References

  • Bottero S , Hassanizadeh SM , Kleingeld PJ , et al . Nonequilibrium capillarity effects in two-phase flow through porous media at different scales. Water Resour Res. 2011;47:1–11.
  • Joekar-Niasar V , Hassanizadeh SM . Effects of fluids properties on non-equilibrium capillary effects: dynamic pore-network modeling. Int J Mult Flow. 2011;37:198–214.
  • Barenblatt GI , Entov VM , Ryzhik VM . Flow of fluids through natural rocks. Dordrecht: Kluwer Academic; 1984.
  • Coussy O . Poromechanics. New York (NY): Wiley; 2004.
  • Barenblatt GI , Zheltov IP , KochinaI N . Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. Prikl Math Mekh. 1960;24:852–864.
  • Hornung U . Homogenization and porous media. New York (NY): Springer-Verlag; 1997.
  • Panfilov M . Macroscale models of flow through highly heterogeneous porous media. London: Kluwer Academic; 2000.
  • Bourgeat A , Luckhaus S , Mikelić A . Convergence of the homogenization process for a double-porosity model of immicible two-phase flow. SIAM J Math Anal. 1996;27:1520–1543.
  • Choquet C . Derivation of the double porosity model of a compressible miscible displacement in naturally fractured reservoirs. Appl Anal. 2004;83:477–499.
  • Yeh LM . Homogenization of two-phase flow in fractured media. Math Methods Appl Sci. 2006;16:1627–1651.
  • Amaziane B , Pankratov L . Homogenization of a model for water-gas flow through double-porosity media. Math Meth Appl Sci. 2016;39:425–451.
  • Bourgeat A , Panfilov M . Effective two-phase flow through highly heterogeneous porous media: capillary nonequilibrium effects. Comput Geosci. 1998;2:191–215.
  • Amaziane B , Milišić P , Panfilov M , et al . Generalized nonequilibrium capillary relations for two-phase flow through heterogeneous media. Phys Rev E. 2012;85:1–18.
  • Salimi H , Bruining J . Upscaling of fractured oil reservoirs using homogenization including non-equilibrium capillary pressure and relative permeability. Comput Geosci. 2012;16:367–389.
  • Konyukhov A , Pankratov L . Upscaling of an immiscible non-equilibrium two-phase flow in double porosity media. Appl Anal. 2016;95:2300–2322.
  • Konyukhov A , Pankratov L . New non-equilibrium matrix imbibition equation for double porosity model. C R Méc. 2016;334:510–520.
  • Voloshin AS . A general non-equilibrium matrix imbibition equation for the homogenized Kondaurov double porosity model. Proc MIPT. 2016;8:157–170. Russian.
  • Amaziane B , Panfilov M , Pankratov L . Homogenized model of two-phase flow with local non-equilibrium in double porosity media. Adv Math Phys. 2016;2016. Article ID: 3058710, 1–13 p.
  • Arbogast T , Douglas J , Hornung U . Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J Math Anal. 1990;21:823–836.
  • Bourgeat A , Mikelic A , Piatnitski A . Modèle de double porosité aléatoire. C R Acad Sci Paris Sér. 1998;327:99–104.
  • Bourgeat A , Goncharenko M , Panfilov M , et al . A general double porosity model. C R Acad Sci Paris Sér IIb. 1999;327:1245–1250.
  • Marchenko VA , Khruslov EY . Homogenization of partial differential equations. Boston: Birkhauser; 2006.
  • Sandrakov GV . Homogenization of parabolic equations with contrasting coefficients. Izv Math. 1999;63:1015–1061.
  • Arbogast T , Douglas J , Hornung U . Modeling of naturally fractured reservoirs by formal homogenization techniques. In: Dautray R , editor. Frontiers in pure and applied mathematics. Amsterdam: North-Holland; 1991.
  • Kazemi H . Pressure transient analysis of naturally fractured reservoirs. Trans AIME. 1960;256:451–461.
  • Raghavan R , Ozkan E . A method for computing unsteady flows in porous media, Chapman & Hall/CRC research notes in mathematics series. London: Longman Group; 1994.
  • Kondaurov VI . A non-equilibrium model of a porous medium saturated with immiscible fluids. J Appl Math Mech. 2009;73:88–102.
  • Bourgeat A , Chechkin GA , Piatnitski A . Singular double porosity model. Appl Anal. 2003;82:103–116.
  • Pankratov L , Rybalko V . Asymptotic analysis of a double porosity model with thin cracks. Sb Math. 2003;194:123–150.
  • Bakhvalov N , Panasenko G . Homogenisation: averaging processes in periodic media. Dordrecht: Kluwer Academic; 1989.
  • Cioranescu D , Paulin SJ . Homogenization of reticulated structures. New York (NY): Springer; 1999.
  • Amaziane B , Pankratov L , Rybalko V . On the homogenization of some double-porosity models with periodic thin structures. Appl Anal. 2009;88:1469–1492.
  • Arbogast T . A simplified dual-porosity model for two-phase flow. Comput Methods Water Res IX. 1992;2:419–426.
  • Jurak M , Pankratov L , Vrbaški A . A fully homogenized model for incompressible two-phase flow in double porosity media. Appl Anal. 2016;95:2280–2299.
  • Warren J , Root P . The behavior of naturally fractured reservoirs. Soc Petrol Eng J. 1963;3:245–255.
  • Konyukhov A , Tarakanov A . On two approaches in investigation of non-equilibrium effects of filtration in a porous medium. In: Proceedings of the Fifth Biot Conference on Poromechanics ASCE. Vienna; 2013. p. 2307–2316.
  • Chavent G , Jaffré J . Mathematical models and finite elements for reservoir simulation. Amsterdam: North-Holland; 1986.
  • Helmig R . Multiphase flow and transport processes in the subsurface. Berlin: Springer; 1997.
  • Sanchez-Palencia E . Non-homogeneous media and vibration theory. Berlin: Springer-Verlag; 1980.
  • Pankratov L , Konyukhov A , Voloshin A . Non-equilibrium two-phase flow in porous media: homogenization and numerical simulation. Saarbrucken: Lambert Academic; 2016.
  • Antontsev SN , Kazhikhov AV , Monakhov VN . Boundary value problems in mechanics of nonhomogeneous fluids. Amsterdam: North-Holland; 1990.
  • Allaire G . Homogenization and two-scale convergence. SIAM J Math Anal. 1992;28:1482–1518.
  • Abramowitz M , Stegun IA . Handbook of mathematical functions with formulas, graphs and mathematical tables. In: Abramowitz M , Stegun IA , editors. National bureau of standards applied mathematics series. Vol. 55. Washington (DC): United States Department of Commerce; 1964.
  • Bateman H , Erdelyi A . Tables of integral transforms. Vol. 1. New York (NY): McGraw Hill; 1954.

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