메뉴 건너뛰기




Volumn 53, Issue 5, 2002, Pages 713-746

Capillary instability in models for three-phase flow

Author keywords

Capillary pressure instability; Flow in porous media; Nonunique Riemann solution

Indexed keywords


EID: 0036026443     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-002-8180-5     Document Type: Article
Times cited : (33)

References (44)
  • 1
    • 0000467530 scopus 로고
    • Multiple viscous solutions for systems of conservation laws
    • A. Azevedo and D. Marchesin, Multiple viscous solutions for systems of conservation laws, Trans. Amer. Math. Soc. 347 (1995), 3061-3078.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 3061-3078
    • Azevedo, A.1    Marchesin, D.2
  • 2
    • 0030521408 scopus 로고    scopus 로고
    • Nonuniqueness of nonclassical solutions of Riemann problems
    • A. Azevedo and D. Marchesin and B. Plohr and K. Zumbrun, Nonuniqueness of nonclassical solutions of Riemann problems, Z. Angew. Math. Phys. 47 (1996), 977-998.
    • (1996) Z. Angew. Math. Phys. , vol.47 , pp. 977-998
    • Azevedo, A.1    Marchesin, D.2    Plohr, B.3    Zumbrun, K.4
  • 3
    • 0033238564 scopus 로고    scopus 로고
    • Bifurcation of nonclassical viscous shock profiles from the constant state
    • A. Azevedo and D. Marchesin and B. Plohr and K. Zumbrun, Bifurcation of nonclassical viscous shock profiles from the constant state, Commun. Math. Phys. 202 (1999), 267-290.
    • (1999) Commun. Math. Phys. , vol.202 , pp. 267-290
    • Azevedo, A.1    Marchesin, D.2    Plohr, B.3    Zumbrun, K.4
  • 5
    • 0022890421 scopus 로고
    • Conservation laws of mixed type describing three-phase flow in porous media
    • J. Bell, J. Trangenstein and G. Shubin, Conservation laws of mixed type describing three-phase flow in porous media, SIAM J. Appl. Math., 46 (1986), 1000-1017.
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 1000-1017
    • Bell, J.1    Trangenstein, J.2    Shubin, G.3
  • 6
    • 0011545461 scopus 로고    scopus 로고
    • Nonexistence of Riemann solutions for a model arising in petroleum engineering
    • submitted
    • S. Čanić, Nonexistence of Riemann solutions for a model arising in petroleum engineering, Nonlinear Anal. (1997), submitted.
    • (1997) Nonlinear Anal.
    • Čanić, S.1
  • 7
    • 0035343318 scopus 로고    scopus 로고
    • Nonexistence of Riemann solutions and Majda-Pego instability
    • S. Čanić and G. Peters, Nonexistence of Riemann solutions and Majda-Pego instability, J. Differential Equations 172 2001, 1-28.
    • (2001) J. Differential Equations , vol.172 , pp. 1-28
    • Čanić, S.1    Peters, G.2
  • 8
    • 0000187598 scopus 로고
    • Shock wave admissibility for quadratic conservation laws
    • S. Čanić and B. Plohr, Shock wave admissibility for quadratic conservation laws, J. Differential Equations 118 (1995), 293-335.
    • (1995) J. Differential Equations , vol.118 , pp. 293-335
    • Čanić, S.1    Plohr, B.2
  • 9
    • 0002813152 scopus 로고    scopus 로고
    • Erratum to "The role of limit cycles in the admissibility of shock waves"
    • S. Čanić and B. Plohr, Erratum to "The role of limit cycles in the admissibility of shock waves", Mat. Contemp., 15 (1998), 33-34.
    • (1998) Mat. Contemp. , vol.15 , pp. 33-34
    • Čanić, S.1    Plohr, B.2
  • 10
    • 0003535772 scopus 로고
    • Allyn and Bacon, Boston
    • J. Dugundji, Topology, Allyn and Bacon, Boston 1966.
    • (1966) Topology
    • Dugundji, J.1
  • 11
    • 0002036676 scopus 로고
    • Nilpotent singularities and abelian integrals
    • Springer-Verlag, New York-Heidelberg-Berlin
    • F. Dumortier, R. Roussarie, J. Sotomayor and H. Złotadek, Nilpotent Singularities and Abelian Integrals, Lect. Notes Math. 1480, Springer-Verlag, New York-Heidelberg-Berlin 1991.
    • (1991) Lect. Notes Math. , vol.1480
    • Dumortier, F.1    Roussarie, R.2    Sotomayor, J.3    Złotadek, H.4
  • 12
    • 0000162712 scopus 로고
    • Cubic Liénard equations with linear damping
    • 1990
    • F. Dumortier and C. Rousseau, Cubic Liénard equations with linear damping, Nonlinearity, 3 (1990), 1015-1039, 1990.
    • (1990) Nonlinearity , vol.3 , pp. 1015-1039
    • Dumortier, F.1    Rousseau, C.2
  • 13
    • 0001704897 scopus 로고
    • Features of three-component, three-phase displacement in porous media
    • A. Falls and W. Schulte, Features of three-component, three-phase displacement in porous media, SPE Reservoir Engrg. 7 (1992), 426-432.
    • (1992) SPE Reservoir Engrg. , vol.7 , pp. 426-432
    • Falls, A.1    Schulte, W.2
  • 14
    • 0001412944 scopus 로고
    • Theory of three-component, three-phase displacement in porous media
    • A. Falls and W. Schulte, Theory of three-Component, three-phase displacement in porous media, SPE Reservoir Engrg. 7 (1992), 377-384.
    • (1992) SPE Reservoir Engrg. , vol.7 , pp. 377-384
    • Falls, A.1    Schulte, W.2
  • 15
    • 0001237844 scopus 로고
    • Existence and asymptotic behavior of measure-valued solutions for three-phase flow in porous media
    • H. Frid, Existence and asymptotic behavior of measure-valued solutions for three-phase flow in porous media, J. Math. Anal. Appl. 196 (1995), 614-627.
    • (1995) J. Math. Anal. Appl. , vol.196 , pp. 614-627
    • Frid, H.1
  • 16
    • 0000704369 scopus 로고
    • Measure-valued solutions for multiphase flow in porous media: Existence and asymptotic steadiness of water flooding
    • H. Frid, Measure-valued solutions for multiphase flow in porous media: Existence and asymptotic steadiness of water flooding, Mat. Contemp. 8 (1995), 177-201.
    • (1995) Mat. Contemp. , vol.8 , pp. 177-201
    • Frid, H.1
  • 17
    • 21844506359 scopus 로고
    • Oscillation waves in Riemann problems inside elliptic regions for conservation laws of mixed type
    • H. Frid and I-S. Liu, Oscillation waves in Riemann problems inside elliptic regions for conservation laws of mixed type, Z. Angew. Math. Phys. 46 (1995), 913-931.
    • (1995) Z. Angew. Math. Phys. , vol.46 , pp. 913-931
    • Frid, H.1    Liu, I.-S.2
  • 18
    • 0031232695 scopus 로고    scopus 로고
    • Mathematical properties of three-phase flow equations
    • R.E. Guzmán and F.J. Fayers, Mathematical properties of three-phase flow equations, SPE J. 23 (1997), 291-300.
    • (1997) SPE J. , vol.23 , pp. 291-300
    • Guzmán, R.E.1    Fayers, F.J.2
  • 19
    • 0031237832 scopus 로고    scopus 로고
    • Solutions to the three-phase flow Buckley-Leverett problem
    • R.E. Guzmán and F.J. Fayers, Solutions to the three-phase flow Buckley-Leverett problem, SPE J. 2, 3 (1997), 301-311.
    • (1997) SPE J. , vol.2 , Issue.3 , pp. 301-311
    • Guzmán, R.E.1    Fayers, F.J.2
  • 20
    • 0001781738 scopus 로고
    • On the Riemann problem for a prototype of a mixed type conservation law, II
    • Current Progress in Hyperbolic Systems: Riemann Problems and Computations (Bowdoin, 1938), B. Lindquist, ed., American Mathematics Society, Providence, RI
    • H. Holden and L. Holden, On the Riemann problem for a prototype of a mixed type conservation law, II. In: Current Progress in Hyperbolic Systems: Riemann Problems and Computations (Bowdoin, 1938), B. Lindquist, ed., Contemporary Mathematics, 100, American Mathematics Society, Providence, RI 1989, pp. 331-367.
    • (1989) Contemporary Mathematics , vol.100 , pp. 331-367
    • Holden, H.1    Holden, L.2
  • 21
    • 0025447129 scopus 로고
    • On the strict hyperbolicity of the Buckley-Leverett equations for three-phase flow in a porous medium
    • L. Holden, On the strict hyperbolicity of the Buckley-Leverett equations for three-phase flow in a porous medium, SIAM J. Appl. Math. 50 (1990), 667-682.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 667-682
    • Holden, L.1
  • 22
    • 0001912072 scopus 로고
    • Differential geometry in the large
    • Springer-Verlag, New York-Heidelberg-Berlin
    • H. Hopf, Differential Geometry in the Large, Lect. Notes Math., 1000, Springer-Verlag, New York-Heidelberg-Berlin, 1946.
    • (1946) Lect. Notes Math. , vol.1000
    • Hopf, H.1
  • 24
  • 25
    • 0001217962 scopus 로고
    • Change of type in three-phase flow: A simple analogue
    • B. Keyfitz, Change of type in three-phase flow: A simple analogue, J. Differential Equations, 80 (1989), 280-305.
    • (1989) J. Differential Equations , vol.80 , pp. 280-305
    • Keyfitz, B.1
  • 26
    • 0001215466 scopus 로고
    • A criterion for certain wave structures in systems that change type
    • B. Keyfitz, A criterion for certain wave structures in systems that change type, Contemp. Math. 100 (1989), 203-213.
    • (1989) Contemp. Math. , vol.100 , pp. 203-213
    • Keyfitz, B.1
  • 27
    • 0001498415 scopus 로고
    • Admissibility conditions for shocks in conservation laws that change type
    • B. Keyfitz, Admissibility conditions for shocks in conservation laws that change type, SIAM J. Math. Anal. 22 (1991), 1284-1292.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1284-1292
    • Keyfitz, B.1
  • 28
    • 84966252907 scopus 로고
    • The multiplicity of eigenvalues
    • P. Lax, The multiplicity of eigenvalues, Bull. Amer. Math. Soc. 6 (1982), 213-214.
    • (1982) Bull. Amer. Math. Soc. , vol.6 , pp. 213-214
    • Lax, P.1
  • 29
    • 0000384032 scopus 로고
    • Steady flow of gas-oil-water mixtures through unconsolidated sands
    • M.C. Leverett and W.B. Lewis, Steady flow of gas-oil-water mixtures through unconsolidated sands, Trans. SPE of AIME 142 (1941), 107-116.
    • (1941) Trans. SPE of AIME , vol.142 , pp. 107-116
    • Leverett, M.C.1    Lewis, W.B.2
  • 30
    • 0002124586 scopus 로고
    • Stable viscosity matrices for system of conservation laws
    • A. Majda and R. Pego, Stable viscosity matrices for system of conservation laws, J. Differential Equations, 56 (1985), 229-262.
    • (1985) J. Differential Equations , vol.56 , pp. 229-262
    • Majda, A.1    Pego, R.2
  • 31
    • 0000536486 scopus 로고
    • Stable hyperbolic singularities for three-phase flow models in oil reservoir simulation
    • H. Medeiros, Stable hyperbolic singularities for three-phase flow models in oil reservoir simulation, Acta Applicandae Mathematicae, 28 (1992), 135-159.
    • (1992) Acta Applicandae Mathematicae , vol.28 , pp. 135-159
    • Medeiros, H.1
  • 32
    • 0011661640 scopus 로고
    • Line fields defined by eigenspaces of derivatives of maps from the plane to itself
    • Santiago de Compostela, Spain
    • C.F. Palmeira, Line fields defined by eigenspaces of derivatives of maps from the plane to itself, Proceedings of the VIth International Conference of Differential Geometry, Santiago de Compostela, Spain, 1988, pp. 177-205.
    • (1988) Proceedings of the VIth International Conference of Differential Geometry , pp. 177-205
    • Palmeira, C.F.1
  • 34
    • 0034195813 scopus 로고    scopus 로고
    • On the oscillatory solutions in hyperbolic conservation laws
    • G. Peters and S. Čanić, On the oscillatory solutions in hyperbolic conservation laws,Nonlinear Anal. Real World Applications i (2000), 287-314.
    • (2000) Nonlinear Anal. Real World Applications , vol.1 , pp. 287-314
    • Peters, G.1    Čanić, S.2
  • 37
    • 0001486653 scopus 로고
    • The Riemann problem for a class of conservation laws of mixed type
    • M. Shearer, The Riemann Problem for a class of conservation laws of mixed type, J. Differential Equations, 46 (1982), 426-443.
    • (1982) J. Differential Equations , vol.46 , pp. 426-443
    • Shearer, M.1
  • 38
    • 0000789270 scopus 로고
    • Loss of strict hyperbolicity of the Buckley-Leverett equations for three phase flow in a porous medium
    • Numerical Simulation in Oil Recovery, M. Wheeler, ed. Springer-Verlag, New York-Heidelberg-Berlin
    • M. Shearer, Loss of strict hyperbolicity of the Buckley-Leverett equations for three phase flow in a porous medium. In: Numerical Simulation in Oil Recovery, M. Wheeler, ed., IMA Volumes in Mathematics and its Applications, 11, Springer-Verlag, New York-Heidelberg-Berlin 1988, pp. 263-283.
    • (1988) IMA Volumes in Mathematics and its Applications , vol.11 , pp. 263-283
    • Shearer, M.1
  • 39
    • 0001643513 scopus 로고
    • Loss of real characteristics for models of three-phase flow in a porous medium
    • M. Shearer and J. Trangenstein, Loss of real characteristics for models of three-phase flow in a porous medium, Transport in Porous Media 4 (1989), 499-525.
    • (1989) Transport in Porous Media , vol.4 , pp. 499-525
    • Shearer, M.1    Trangenstein, J.2
  • 40
    • 0020500507 scopus 로고
    • Admissibility criteria for propagating phase boundaries in a van der Waals fluid
    • M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 81 (1983), 303-319.
    • (1983) Arch. Rational Mech. Anal. , vol.81 , pp. 303-319
    • Slemrod, M.1
  • 42
    • 0014738016 scopus 로고
    • Probability model for estimating three-phase relative permeability
    • H. Stone, Probability model for estimating three-phase relative permeability, J. Pert. Tech., 22 (1970), 214-218.
    • (1970) J. Pert. Tech. , vol.22 , pp. 214-218
    • Stone, H.1
  • 43
    • 0000966040 scopus 로고
    • Three-phase flow with gravity
    • Current Progress in Hyperbolic Systems: Riemann Problems and Computations (Bowdoin, 1988), B. Lindquist, ed., American Mathematics Society, Providence, RI
    • J. Trangenstein, Three-phase flow with gravity. In: Current Progress in Hyperbolic Systems: Riemann Problems and Computations (Bowdoin, 1988), B. Lindquist, ed., Contemporary Mathematics, 100, American Mathematics Society, Providence, RI 1989, pp. 147-159.
    • (1989) Contemporary Mathematics , vol.100 , pp. 147-159
    • Trangenstein, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.