Advertisement

Pore-scale numerical modeling of coupled fluid flow and medium geometrical deformations in an unconsolidated porous medium

  • Behnam Nasrollahzadeh
  • Hossein Ali Akhlaghi AmiriEmail author
  • Siavash Ghabezloo
Regular Article
  • 8 Downloads

Abstract.

The interplay of fluid flow and medium grains' deformation/movement in unconsolidated porous media was numerically studied. The numerical simulations were done through coupling Cahn-Hilliard phase field and Navier-Stokes equations for fluid flow as well as stress-strain and Arbitrary Lagrangian/Eulerian mesh alteration equations for geomechanical effects, by the finite-element method. Single/two-phase flow through a real patterned micro-scale medium with/without grains' deformation and movements/rotation were studied. In single-phase models, the fluid velocity distribution was quite similar for the cases with rigid grains and that with only deformed grains. However, in an unconsolidated medium, the velocity magnitude and distribution were modified. The medium porosity had a linear trend with pressure, and was independent of the grains' movement/rotation. The models with deformed grains showed good agreement with Kozeny-Carman equation in permeability variation versus pressure. In the two-phase flow models, the velocity/displacement profiles, relative permeability end-points and capillary pressure were quantitatively compared in rigid and unconsolidated media versus medium wettability. The effect of the grains' deformation on the fluid distributions was negligible at low capillary numbers, especially in water-wet and neutral wetting conditions. However, the grains' movement/rotation considerably modified the flow regime at different grains' contact angles. At higher capillary numbers, the grains' deformation effect was more pronounced.

Notes

References

  1. 1.
    M. Muskat, The Flow of Homogeneous Fluids through Porous Media (McGraw-Hill, New York, 1982)Google Scholar
  2. 2.
    P. Lehmann, M. Berchtold, B. Ahrenholz, J. Tölke, A. Kaestner, M. Krafczyk, H. Flühler, H.R. Künsch, Adv. Water Resour. 9, 31 (2008)Google Scholar
  3. 3.
    C. Cottin, H. Bodiguel, A. Colin, Phys. Rev. E 4, 82 (2010)Google Scholar
  4. 4.
    B. Ahrenholz, J. Niessner, R. Helmig, M. Krafczyk, Water Resour. Res. 7, 47 (2011)Google Scholar
  5. 5.
    H.A. Akhlaghi Amiri, A.A. Hamouda, Int. J. Multiphase Flow 52, 22 (2013)Google Scholar
  6. 6.
    S. Berg, H. Ott, S.A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J.-O. Schwarz, M. Kersten, S. Irvine, M. Stampanoni, Proc. Natl. Acad. Sci. U.S.A. 10, 110 (2013)Google Scholar
  7. 7.
    H.A. Akhlaghi Amiri, A.A. Hamouda, Int. J. Multiphase Flow 61, 14 (2014)Google Scholar
  8. 8.
    K. Kitamura, F. Jiang, A.J. Valocchi, S. Chiyonobu, T. Tsuji, K.T. Christensen, JGR Solid Earth 119, 7564 (2014)ADSGoogle Scholar
  9. 9.
    A. Setiawan, T. Suekane, Y. Deguchi, K. Kusano, J. Flow Control, Meas. & Visual. 2, 25 (2014)Google Scholar
  10. 10.
    T. Tsuji, F. Jiang, K.T. Christensen, Adv. Water Resour. 95, 3 (2016)ADSGoogle Scholar
  11. 11.
    F. Basirat, Z. Yang, A. Niemi, Adv. Water Resour. 109, 181 (2017)ADSGoogle Scholar
  12. 12.
    M.R. Rokhforouz, H.A. Akhlaghi Amiri, Adv. Water Resour. 113, 260 (2018)ADSGoogle Scholar
  13. 13.
    V.H. Nguyen, A.P. Sheppard, M.A. Knackstedt, W. Val Pinczewski, J. Petrol. Sci. Eng. 1, 52 (2006)Google Scholar
  14. 14.
    R.I. Al-Raoush, Environ. Sci. Technol. 13, 43 (2009)Google Scholar
  15. 15.
    D. Wildenschild, R.T. Armstrong, A.L. Herring, I.M. Young, J. William Carey, Energy Proc. 4, 4945 (2011)Google Scholar
  16. 16.
    F. Jiang, T. Tsuji, C. Hu, Transp. Porous Media 1, 104 (2014)Google Scholar
  17. 17.
    J.G.I. Hellström, V. Frishfelds, T.S. Lundström, J. Fluid Mech. 664, 220 (2010)ADSMathSciNetGoogle Scholar
  18. 18.
    M. Prodanović, J.T. Holder, S.L. Bryant, Int. J. Oil, Gas Coal Technol. 2-3, 5 (2012)Google Scholar
  19. 19.
    D.R. Hewitt, J.S. Nijjer, M.G. Worster, J.A. Neufeld, Phys. Rev. E 2, 93 (2016)Google Scholar
  20. 20.
    A. Settari, D.A. Walters, SPE J. 6 (2001)  https://doi.org/10.2118/74142-PA Google Scholar
  21. 21.
    L.K. Thomas, L.Y. Chin, R.G. Pierson, J.E. Sylte, SPE J. 8 (2003)  https://doi.org/10.2118/87339-PA Google Scholar
  22. 22.
    R.H. Dean, X. Gai, C.M. Stone, S.E. Minkoff, SPE J. 11, 132 (2006)Google Scholar
  23. 23.
    J. Kim, H.A. Tchelepi, R. Juanes, SPE J. 18 (2013)  https://doi.org/10.2118/141268-PA Google Scholar
  24. 24.
    Q.J. Zhu, Y.F. He, Y. Yin, Mater. Res. Innov. 18, 22 (2014)Google Scholar
  25. 25.
    F.O. Alpak, SPE J. 20, 1366 (2015)Google Scholar
  26. 26.
    F. Doster, J.M. Nordbotten, in Proceedings of the SPE Reservoir Simulation Symposium, Texas, USA, 2015, Vol. 10 (2015)Google Scholar
  27. 27.
    A. Wilson, J. Petrol. Technol. (2015)  https://doi.org/10.2118/1115-0078-JPT Google Scholar
  28. 28.
    A. Gajo, F. Cecinato, B. Loret, Transp. Porous Med. 1, 116 (2017)Google Scholar
  29. 29.
    P. Samier, Proceedings of the SPE Reservoir Simulation Conference, Texas, USA, 2017, Vol. 7 (2017)Google Scholar
  30. 30.
    G.U. Grün, H. Wallner, H.J. Neugebauer, Geolog. Rund. 1, 78 (1989)Google Scholar
  31. 31.
    L. Xikui, Commun. Appl. Numer. Methods 2, 6 (1990)Google Scholar
  32. 32.
    L. Xikui, O.C. Zienkiewicz, Comp. Struct. 2, 45 (1992)Google Scholar
  33. 33.
    N.A. Rahman, R.W. Lewis, Comp. Geotech. 1, 24 (1999)Google Scholar
  34. 34.
    J.A. White, R.I. Borja, J.T. Fredrich, Acta Geotech. 4, 1 (2006)Google Scholar
  35. 35.
    J.A. White, R.I. Borja, in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, United States, 2009, Vol. 12 (2009)Google Scholar
  36. 36.
    H. Fatahi, M.M. Hossain, J. Petrol. Explor. Product. Technol. 2, 6 (2016)Google Scholar
  37. 37.
    D.F. Boutt, B.K. Cook, J.R. Williams, Int. J. Numer. Anal. Methods Geomech. 9, 35 (2011)Google Scholar
  38. 38.
    S. Bakhshian, M. Sahimi, Phys. Rev. E 4, 94 (2016)Google Scholar
  39. 39.
    Y. Pan, R.N. Horne, Transp. Porous Med. 1, 45 (2001)Google Scholar
  40. 40.
    Y. Pan, R.N. Horne, Transp. Porous Med. 2, 45 (2001)Google Scholar
  41. 41.
    J.W. Both, K. Kumar, J.M. Nordbotten, F.A. Radu, in Proceedings of the 6th Biot Conference on Poromechanics, Princeton, United States, 2017, Vol. 5 (2017)Google Scholar
  42. 42.
    J.L. Auriault, O. Lebaigue, G. Bonnet, Transp. Porous Med. 2, 4 (1989)Google Scholar
  43. 43.
    B. Ju, Y. Wu, T. Fan, J. Petrol. Sci. Eng. 3-4, 76 (2011)Google Scholar
  44. 44.
    A. Settari, F.M. Mourits, SPE J. (1998)  https://doi.org/10.2118/50939-PA Google Scholar
  45. 45.
    R.H. Dean, X. Gai, C.M. Stone, S.E. Minkoff, SPE J. 1, 11 (2006)Google Scholar
  46. 46.
    J. Zhao, T. Shan, Powder Technol. 239, 248 (2013)Google Scholar
  47. 47.
    L. Jin, M.D. Zoback, JGR Solid Earth 122, 7626 (2017)ADSGoogle Scholar
  48. 48.
    V.A. Torrealba, Z.T. Karpyn, H. Yoon, K.A. Klise, D. Crandall, Geofluids 1, 16 (2016)Google Scholar
  49. 49.
    Y. Kaneko, O. Sano, Phys. Fluids 3, 17 (2005)Google Scholar
  50. 50.
    J.I. Siddique, D.M. Anderson, A. Bondarev, Phys. Fluids 1, 21 (2009)Google Scholar
  51. 51.
    M. Chekired, V. Roubtsova, in Proceedings of the Geotechnical Special Publication, Canada, 2010, Vol. 2 (2010)Google Scholar
  52. 52.
    J.W. Cahn, J.E. Hilliard, J. Chem. Phys. 2, 28 (1958)Google Scholar
  53. 53.
    P. Yue, C. Zhou, J.J. Feng, C.F. Ollivier-Gooch, H.H. Hu, J. Comput. Phys. 1, 219 (2006)Google Scholar
  54. 54.
    C. Zhou, P. Yue, J.J. Feng, C.F. Ollivier-Gooch, H.H. Hu, J. Comput. Phys. 2, 229 (2010)Google Scholar
  55. 55.
    D. Jacqmin, J. Comput. Phys. 1, 155 (1999)MathSciNetGoogle Scholar
  56. 56.
    V. Badalassi, H. Ceniceros, S. Banerjee, J. Comput. Phys. 2, 190 (2003)Google Scholar
  57. 57.
    F. Fichot, P. Meekunnasombat, J. Belloni, F. Duval, A. Garcia, M. Quintard, Nucl. Eng. Design 15, 237 (2007)Google Scholar
  58. 58.
    A. Sommerfeld, Lectures on Theoretical Physics: Mechanics of Deformable Bodies (Academic Press, 1964)Google Scholar
  59. 59.
    R.O. Davis, A.P. Selvadurai, Plasticity and Geomechanics (Cambridge University Press, 2005)Google Scholar
  60. 60.
    R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena (Wiley, 2009)Google Scholar
  61. 61.
    COMSOL Multiphysics, User's Guide, Version 4.4. (Comsol Inc., 2013)Google Scholar
  62. 62.
    S. Liang, J.Y. Yin, S.F. Xue, J. Canad. Petrol. Technol. 4, 48 (2009)Google Scholar
  63. 63.
    T.J. Hughes, W.K. Liu, T.K. Zimmermann, Comp. Methods Appl. Mech. Eng. 3, 29 (1981)Google Scholar
  64. 64.
    T. Liu, Q. Li, C. Zhao, Sci. China Phys., Mech. Astron. 4, 56 (2013)Google Scholar
  65. 65.
    M. Rokhforouz, H. Akhlaghi Amiri, Phys. Fluids 6, 29 (2017)Google Scholar
  66. 66.
    A.A. Keller, M.J. Blunt, A.P.V. Roberts, Transp. Porous Med. 3, 26 (1997)Google Scholar
  67. 67.
    G.V. Chilingar, R. Main, A. Sinnokrot, J. Sedime. Res. 3, 33 (1963)Google Scholar
  68. 68.
    R. Lenormand, E. Touboul, C. Zarcone, J. Fluid Mech. 189, 165 (1988)ADSGoogle Scholar
  69. 69.
    C. Zhang, M. Oostrom, T.W. Wietsma, J.W. Grate, M.G. Warner, Energy Fuels 8, 25 (2011)Google Scholar
  70. 70.
    G. Løvoll, Y. Meheust, K.J. Måløy, E. Aker, J. Schmittbuhl, Energy 6, 30 (2005)Google Scholar
  71. 71.
    D. Loggia, Z. Bo, L. Xiaorong, G. Vasseur, Transp. Porous Med. 1, 80 (2009)Google Scholar
  72. 72.
    K.J. DeHoff, M. Oostrom, C. Zhang, J.W. Grate, Vadose Zone J. 4, 11 (2012)Google Scholar
  73. 73.
    J. Sharma, S.B. Inwood, A. Kovscek, SPE J. 04, 17 (2012)Google Scholar
  74. 74.
    Y. Teng, Y. Liu, L. Jiang, Y. Song, J. Zhao, Y. Zhang, D. Wang, Magn. Res. Imaging 7, 34 (2016)Google Scholar
  75. 75.
    L.P. Dake, Fundamentals of Reservoir Engineering (Elsevier New York, 1978)Google Scholar
  76. 76.
    S. Berg, H. Ott, S.A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J.-O. Schwarz, M. Kersten, S. Irvine, M. Stampanoni, Proc. Natl. Acad. Sci. U.S.A. 110, 3755 (2013)ADSGoogle Scholar
  77. 77.
    R.T. Armstrong, N. Evseev, D. Koroteev, S. Berg, Adv. Water Resour. 77, 57 (2015)ADSGoogle Scholar
  78. 78.
    M.R. Rokhforouz, H.A. Akhlaghi Amiri, Adv. Water Resour. 124, 84 (2019)ADSGoogle Scholar
  79. 79.
    M.R. Rokhforouz, H.A. Akhlaghi Amiri, Pore-level influence of wettability on counter-current spontaneous imbibition, in 79th EAGE Conference and Exhibition, Paris, France (2017)  https://doi.org/10.3997/2214-4609.201701510

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Chemical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Laboratoire NavierEcole des Ponts ParisTech, Ifsttar, CNRS UMRMarne-la-ValléeFrance

Personalised recommendations