Skip to main content

Chemical or Heat Convection-Diffusion Transport Through Highly Heterogeneous Porous Media

  • Chapter
Macroscale Models of Flow Through Highly Heterogeneous Porous Media

Part of the book series: Theory and Applications of Transport in Porous Media ((TATP,volume 16))

  • 282 Accesses

Abstract

The next step of the developed theory is related with the flow of miscible mixtures. The linear convection-diffusion equation written relatively to the concentration of a chemical component is a simplest model of mixture flow. In this chapter a more general model is studied when the field of convection transport velocity is not given and should be found as the solution of a parabolic equation for the velocity potential (the pressure).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allaire, G. (1992) Homogenization and two-scale convergence, SIAM J. Math. Anal, 23, no.6, pp. 1482–1518.

    Article  Google Scholar 

  2. Amaziane, B., Bourgeat A., Koebbe J.V. (1990) Proc. 2nd European Conf. Mathematics of Oil Recovery, Aries, France, Sept 11–14 , 1990, Ed.Technip, Paris, pp. 75–81.

    Google Scholar 

  3. Amirat, Y., Hamdache, K. and Ziani, A. Homogénéisation d’ équations hyperboliques du premier ordre: Application aux milieux poreux, Rapport I.N.R.I.A., no. 803.

    Google Scholar 

  4. Amirat, Y., Hamdache, K. and Ziani, A. (1989) Homogénéisation d’ équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux, Ann. Inst. H. Poincaré. Analyse non linéaire., 6, no. 5, pp. 397–417.

    Google Scholar 

  5. Amirat, Y., Hamdache, K. and Ziani, A. (1990) Comportemet limite de modèles d’ équations de convection-diffusion dégénérées, C. R. Acad. sei. Paris, Ser. A., 310, pp. 76–78.

    Google Scholar 

  6. Amirat, Y., Hamdache, K. and Ziani, A. (1990) Etude d’ une équation de transport à mémoire, C. R. Acad. sci. Paris, Ser. A., 311.

    Google Scholar 

  7. Amirat, Y., Hamdache, K. and Ziani, A. (1991) Kinetic formulation for a transport equation with memory, Commun. Partial Differ. Equations, 16, no. 8–9, pp. 1287–1311.

    Article  Google Scholar 

  8. 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, pp. 823–836.

    Article  Google Scholar 

  9. Arbogast T., Douglas J., Hornung U. Modelling of Naturally Fractured Reservoirs by Formal Homogenization Thechniques- In: “Frontiers in Pure and Applied Mathematics”, Ed. R. Dautray, Elsevier, Amsterdam, 1991, pp. 1–19.

    Google Scholar 

  10. Bakhvalov N., Panasenko G. Homogénéisation:Averaging Processes in Periodic Media - Kluwer, Dordrecht, 1989.

    Book  Google Scholar 

  11. Barenblatt G.I., Entov V.M., Ryjik V.M. Theory of Transient Liquide and Gas Flow Through Porous Media - Moscow, Nedra, 1972, 288 p. (translated in Kluwer, Dordrecht).

    Google Scholar 

  12. Barenblatt G.I., Zheltov Iu.P., Kochina I.N. Basic Concepts in The Theory of Seepage of Homogeneous Liquids in Fissured Rocks -PMM, 24, 1960, pp. 852–864.

    Google Scholar 

  13. Barker J.A. Block-Geometry Functions Characterizing Transport in Densely Fissured Media- J. Hydrol, 1985, 77, pp. 263–279.

    Article  Google Scholar 

  14. Barker J.A. Modelling the Effects of Matrix Diffusion on Transport in Densely Fissured Media- Mem. of 18th Congress of the Inter. Assoc, of Hydrogeol., Cambridge, 1985, pp. 250–269.

    Google Scholar 

  15. Bedrikovetski P.G., Istomin G.V., Kniazeva M.B. Miscible Displacement From The Fractured Porous Media - Izvstiya Academii Nauk SSSR, Ser. MJG, 1986, N6, pp. 100–110 (translated in: Fluid Mechanics, 1987).

    Google Scholar 

  16. Böhm M., Showalter R.E. Diffusion in Fissured Media- SIAM J. Math. Anal., 1985, 16, N 3, pp. 500–509.

    Article  Google Scholar 

  17. Bourgeat A. Homogenization Method Applied to the Behaviour of a Naturally Fissured Reservoir- Mathematical Method in Energy-Research, Ed. SIAM (K.J. Kross), 1984, pp. 181–193.

    Google Scholar 

  18. Bourgeat A. Homogenized Behaviour of Diphasic Flow in a Naturally Fissured Reservoir with Uniform Fractures - Comput. Methods in Applied Mechanics and Engineering, 1984, N 47, pp. 205–217.

    Google Scholar 

  19. Businov S.N., Umrihin I.D. Gydrodynamics Methods of Well and Field Investigations - Moscow, Nedra, 1973, 243 p. (in Russian).

    Google Scholar 

  20. Charlaix E., Hulin J.R, Plona T.J. Experimental Study of Tracer Dispersion in Sintered Glass Porous Materials of Variable Compaction - Phys. Fluids, 1987, 30, pp. 1690–1698.

    Article  Google Scholar 

  21. Coats K.H., Smith B.D. Dead-End Pore Volume and Dispersion in Porous Media - Trans. Soc. Pet. Eng., 1964, 231, N 3, pp. 73–84.

    Google Scholar 

  22. Deans H.A. A Mathematical Model For Dispersion in the Direction of Flow in Porous Media - Trans. Soc. Pet. Eng., 1963, v.288, pp. 49–52.

    Google Scholar 

  23. De Swaan A.O. Analytic Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing - SPE J., 1976, June, pp. 117–122.

    Google Scholar 

  24. Douglas J., Arbogast T. Dual Porosity Models for Flow in Naturally Fractured Reservoirs - In: “Dynamics of Fluids in Hierarchical Porous Media”, Ed. J.H. Cushman, Academic Press, 1990, pp. 177–220.

    Google Scholar 

  25. Duguid I.O., Lee P.C., Water Resour. Res., 13, N3, (1977), pp. 558–566.

    Article  Google Scholar 

  26. Egorov A.G., Pudovkin M.A., in: .Applied Problems of Math. Phys., Riga, Ed. Latvien State University, (1983), pp. 98–107 (in Russian).

    Google Scholar 

  27. Egorov A.G., Salamatin A.N., Teplophysika Vysokikh Temperatur, 22, N5, (1984), pp. 919–923 (in Russian).

    Google Scholar 

  28. Evans R.D., SPE J., 22, N5, (1982), pp. 669–680.

    Google Scholar 

  29. Hornung U., in -.Nonlinear Partial Differential Equations(P. File, R. Bates, Eds.), Springer-Verlag, Berlin/New York, (1988).

    Google Scholar 

  30. Hornung U., Jager W., in :Complex Chemical Reactions, Modelling and Simulation(P. Denflhard, W. Jager, Eds.), Springer - Verlag, Berlin/New York, (1987).

    Google Scholar 

  31. Hornung U., Showalter R.E., J. Math. Analysis and Applications, 147, Nl, (1990), pp. 69–80.

    Article  Google Scholar 

  32. Hornung U., Showalter R.E., Walkington N.J., J. Math. Analysis and Applications, 155, Nl, (1991), pp. 1–20.

    Google Scholar 

  33. Kazemi H., Seth Thomas G.W., SPE J., (1969), Dec, pp. 463–472.

    Google Scholar 

  34. Khruslov E.Ya., Averaged Model of Non Stationnary Flow through Fractured Porous Media, USSR, Ed. Acad. Sei. Ukraine, Preprint N50, (1988), 34p. (in Russian).

    Google Scholar 

  35. Khruslov E.Ya., Uspekhi Math. Nauk, 45, Nl(277), (1990), pp. 197–198 (in Russian).

    Google Scholar 

  36. Kutliarov V.S., J. PMTF, (1967), Nl, pp. 84–88 (in Russian).

    Google Scholar 

  37. Levy T., European J. of Mechanics. Ser. B : “Fluids”, 9, N4, (1990), pp. 309–327.

    Google Scholar 

  38. Nguetseng G., SIAM J. Math. Anal., 20, N3, (1989), pp. 608–628.

    Article  Google Scholar 

  39. Odeh A.S., SPE J., (1965), Janv., pp. 60–66.

    Google Scholar 

  40. Palatnik B.., Proc. 1th All Russian Congress on Theoretics and Applied Mechanics, Moscow, Aug. 15–21, (1991), p. 275 (in Russian).

    Google Scholar 

  41. Panasenko G.P. Averaging Fields in Composite Materials with High-Modulus Reinforcement- Vestnik MGU, Ser. 15, N 2,1983, pp. 20–27 (in Russian).

    Google Scholar 

  42. Panasenko G.P. Averaging of Processes in Highly Heterogeneous Structures - Dokladi AN SSSR, 298, 1988, pp. 76–79 (translated in: Soviet Phys. Dokl., 1988.)

    Google Scholar 

  43. Panasenko G.P., J. Vychislitelnoi Mathematiki i Mathematicheskoi Physiki, 30, N2, (1990), pp. 243–253 (translated on English)

    Google Scholar 

  44. Panfilov M., Proc. 6th All Russian Congress on Theoretical and Applied Mechanics, Tashkent, Sept. 24–30, (1986), pp. 503–504 (in Russian).

    Google Scholar 

  45. Panfilov M., Proc. 3rd Ukraine Conf. of Ukraine Acad. Sei. “Integral Equations in Applied Modelling”, Odessa, Nov. 1–16, (1989), part.2, pp. 102–103 (in Russian).

    Google Scholar 

  46. Panfilov M., Soviet Physics Dokl, 35(3), (1990), pp. 225–227.

    Google Scholar 

  47. Panfilov M.B., Proc. 2nd European Conference on the Mathematics of Oil Recovery, Aries, France, Sept. 11–14, 1990, Ed. Technip, (1990), pp. 347–350.

    Google Scholar 

  48. Panfilov M., Izvestiya Academii Nauk (Russia), Mekhanika Zhid-kosti i Gasa, N6, (1992), pp. 103–116; (translated in Fluid Dynamics, N3, (1993), pp. 112–120).

    Google Scholar 

  49. Panfilov M., CR. Acad. Sei. Paris, 318, Serie II, (1994), pp. 1437–1443.

    Google Scholar 

  50. Panfilov M., Homogenised Models of Convection-Diffusion transport in Periodic Network Media, Moscow, Ed. Oil h Gas Research Insti- tute, Russian Acad.Sci., preprint N26, (1995), 72p.

    Google Scholar 

  51. Panfilov M., Averaged Models of Convection-Diffusion Transfer Through Highly Heterogeneous Porous Media, in : Math. Modelling of Flow Through Porous Media, Proc. Int. Conf., World Scientific Pub., Singapore, pp. 276–300.

    Google Scholar 

  52. Panfilov, M. and Panfilova, I. (1996) Averaged models of flows with heterogeneous internal structure. Ed. Nauka, Moscow (in Russian).

    Google Scholar 

  53. Prues K., Narasimhan T.N., SPE J., (1985), Feb., pp. 14–26.

    Google Scholar 

  54. Showalter R.E., Walkington N.J., J. of Mathematical Analysis and Applications, 155, Nl, (1991), pp. 1–20.

    Article  Google Scholar 

  55. Volkov I.A., in :.Problems of Appl. Math. Geometr. Modelling, Leningrad, Ed. Ingenerno-Stroitelnogo Instituta, (1967), pp. 33–35 (in Russian).

    Google Scholar 

  56. Volkov I.A., in :Theor. and Experim. Research of Hydrocarbon Migration Laws, Leningrad, Ed. VNIIGRI, (1980), pp. 104–117 (in Russian).

    Google Scholar 

  57. Warren J.E., Root J., SPE J., 3, Sept., (1963), pp. 245–255.

    Google Scholar 

  58. Wu Y.-S., Prues K., SPE Res. Eng., 3, N1, (1988), pp. 327–336.

    Google Scholar 

  59. Teodorovich E.V., Fluid Dynamics, no. 4, (1994).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Panfilov, M. (2000). Chemical or Heat Convection-Diffusion Transport Through Highly Heterogeneous Porous Media. In: Macroscale Models of Flow Through Highly Heterogeneous Porous Media. Theory and Applications of Transport in Porous Media, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9582-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9582-7_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5401-2

  • Online ISBN: 978-94-015-9582-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics