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XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications

HYP 2016: Theory, Numerics and Applications of Hyperbolic Problems II pp 255–267Cite as

Mathematical Theory of Two-Phase Geochemical Flow with Chemical Species

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 237))

Abstract

In this work, we introduce a formalism for two-phase geochemical flow. Here, we admit that the chemical species flow in both phases. Moreover, we consider chemical interaction and chemical equilibrium laws for which it is possible to obtain algebraic relationships between the chemical species. In this work, we consider that we have only one free chemical species, i.e., by using equilibrium laws, we admit that all chemical species can be written as function of only one, which we denote as y. We present a formalism for this kind of flow, moreover, we obtain the eigenvalues, eigenvectors, and bifurcations structures. We also show the structure of integral and Hugoniot curves in the saturation versus chemical species plane.

This work was supported in part by: CNPq under Grants 402299/2012-4, 301564/2009-4, 470635/2012-6, FAPERJ under Grants E-26/111.416/2010, E-26/102.965/2011, E-26/110.658/2012, E-26/111.369/2012, E-26/110114.110/2013, ANP-731948/2010, PRH32-6000.0069459.11.4, CAPES Nuffic-024/2011, TUDelft, Section Petroleum Engineering.

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References

  1. C.A.J. Appelo, D. Postma, Geochemistry, Groundwater and Pollution (Taylor & Francis, 2005)

    Google Scholar 

  2. O. Dahl, T. Johansen, A. Tveito, R. Winther, Multicomponent chromatography in a two phase environment. SIAM J. Appl. Math. 52(1), 65–104 (1992)

    Article  MathSciNet  Google Scholar 

  3. F.G. Helfferich et al., Theory of multicomponent, multiphase displacement in porous media. Soc. Pet. Eng. J. 21(01), 51–62 (1981)

    Article  Google Scholar 

  4. G. Hirasaki et al., Ion exchange with clays in the presence of surfactant. Soc. Pet. Eng. J. 22(02), 181–192 (1982)

    Article  Google Scholar 

  5. E.L. Isaacson, J.B. Temple, Analysis of a singular hyperbolic system of conservation laws. J. Differ. Equ. 65(2), 250–268 (1986)

    Article  MathSciNet  Google Scholar 

  6. T. Johansen, A. Tveito, R. Winther, A riemann solver for a two-phase multicomponent process. SIAM J. Sci. Stat. Comput. 10(5), 846–879 (1989)

    Article  MathSciNet  Google Scholar 

  7. T. Johansen, R. Winther, The solution of the riemann problem for a hyperbolic system of conservation laws modeling polymer flooding. SIAM J. Math. Anal. 19(3), 541–566 (1988)

    Article  MathSciNet  Google Scholar 

  8. T. Johansen, R. Winther, The riemann problem for multicomponent polymer flooding. SIAM J. Math. Anal. 20(4), 908–929 (1989)

    Article  MathSciNet  Google Scholar 

  9. B.L. Keyfitz, H.C. Kranzer, A system of non-strictly hyperbolic conservation laws arising in elasticity theory. Arch. Ration. Mech. Anal. 72(3), 219–241 (1980)

    Article  Google Scholar 

  10. W. Lambert, D. Marchesin, The riemann problem for multiphase flows in porous media with mass transfer between phases. J. Hyperbolic Equ. 8(02), 149–156 (2009)

    MATH  Google Scholar 

  11. B.J. Merkel, B. Planer-Friedrich, D.K. Nordstrom, Groundwater Geochemistry (Springer, 2005)

    Google Scholar 

  12. D.L. Parkhurst, C. Appelo, Description of Input and Examples for PHREEQC Version Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations (US Geological Survey, Denver, 2013)

    Google Scholar 

  13. G. Pope, L. Lake, F. Helfferich et al., Cation exchange in chemical flooding: Part 1-basic theory without dispersion. Soc. Pet. Eng. J. 18(06), 418–434 (1978)

    Article  Google Scholar 

  14. A. Puime. INDEPENDÊNCIA ENTRE TERMODINÂMICA E HIDRODINÂMICA EM PROCESSOS DE RECUPERACÃO AVANCADA DE PETRÓLEO. PhD thesis, Universidade Estadual do Norte Fluminense, 2003

    Google Scholar 

  15. B. Temple, Global solution of the cauchy problem for a class of 2\(\times \) 2 nonstrictly hyperbolic conservation laws. Adv. Appl. Math. 3(3), 335–375 (1982)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. ICT - UNIFAL, Cidade Universitária, BR 267 Km 533, Rodovia José Aurélio Vilela, Poços de Caldas, MG, Brazil

    W. J. Lambert

  2. Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona, Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil

    A. C. Alvarez & D. Marchesin

  3. TU Delft, Civil Engineering and Geosciences, Stevinweg 1, 2628 CE, Delft, The Netherlands

    J. Bruining

Authors
  1. W. J. Lambert
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  2. A. C. Alvarez
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  3. D. Marchesin
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  4. J. Bruining
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Corresponding author

Correspondence to W. J. Lambert .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Lambert, W.J., Alvarez, A.C., Marchesin, D., Bruining, J. (2018). Mathematical Theory of Two-Phase Geochemical Flow with Chemical Species. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_20

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