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Numerical schemes for the Barenblatt model of non-equilibrium two-phase flow in porous media
Author(s):
Denise
Aregba-Driollet;
Gabriella
Bretti;
Roberto
Natalini
Journal:
Quart. Appl. Math.
66
(2008),
201-231.
MSC (2000):
Primary 65M06;
Secondary 76S05, 35L65
Posted:
February 8, 2008
MathSciNet review:
2416771
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Abstract:
We introduce some numerical approximations to a quasilinear problem proposed by G. I. Barenblatt to describe non-equilibrium two-phase fluid flows in permeable porous media, which apply to secondary oil recovery from natural reservoirs. Taking into account the theoretical results of global existence and uniqueness, we approximate the solutions by three numerical schemes, namely, the Diagonal First Order schemes (DFO and DFO2) and the Diagonal Second Order scheme (DSO). For DFO schemes convergence is proved. The schemes' behaviour is analysed and discussed through some numerical experiments.
References:
-
- 1.
- G. I. Barenblatt, Flow of two immiscible fluids in homogeneous porous medium (in Russian), Izv. AN SSSR, Mekh. Zhidk. i Gaza 5 (1971), 144-151.
- 2.
- G. I. Barenblatt, V. M. Entov and V. M. Ryzhik, Theory of fluid flows through natural rocks, Kluwer Academic Publishers, Dordrecht (1990).
- 3.
- G. I. Barenblatt, J. Garcia-Azorero, A. De Pablo and J. L. Vazquez, Mathematical Model of the Non-Equilibrium Water-Oil Displacement in Porous Strata, Applicable Analysis 65 (1997), 19-45. MR 1674579 (99j:76121)
- 4.
- G. I. Barenblatt, A. P. Vinnitchenko, Non equilibrium seepage of immiscible fluids (in Russian), Uspekhi Mekhaniki 3 (1980), 35-50.
- 5.
- S. E. Buckley, M. C. Leverett, Mechanism of fluid displacement in sands, Trans. AIME 142 (1942), 107-116.
- 6.
- M. Muskat and M. Meres, The flow of heterogeneous fluids, Physics, 7 (1936), 346-363.
- 7.
- R. Natalini, A. Tesei, On the Barenblatt model for non-equilibrium two phase flow in porous media, Arch. Rational Mech. Anal. 150 (1999), 349-367. MR 1741260 (2001b:76090)
- 8.
- D. W. Peaceman, Fundamentals of numerical reservoir simulation, Developments in Petroleum Science 6, ed. Elsevier, Amsterdam (1977).
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Additional Information:
Denise
Aregba-Driollet
Affiliation:
Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, 351 Cours de la Liberation, F-33405 Talence, France
Email:
aregba@math.u-bordeaux.fr
Gabriella
Bretti
Affiliation:
Department of Information Engineering and Applied Mathematics of the University of Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy, & Istituto per le Applicazioni del Calcolo ``M. Picone'', Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 - Roma, Italy
Email:
g.bretti@iac.cnr.it
Roberto
Natalini
Affiliation:
Istituto per le Applicazioni del Calcolo ``M. Picone'', Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 - Roma, Italy
Email:
r.natalini@iac.cnr.it
PII:
S0033-569X-08-01079-0
Keywords:
Scalar conservation laws,
two-phase flows,
non-equilibrium flows
Received by editor(s):
August 2, 2005
Posted:
February 8, 2008
Copyright of article:
Copyright
2008,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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