Transport in Porous Media

, Volume 104, Issue 2, pp 349–362 | Cite as

Quantifying the Representative Size in Porous Media

Article

Abstract

We present a new approach to quantify the representative quality of pore-scale samples of porous media. It is shown that the flow field uniformity serves as a reliable criterion to decide if the computed flow properties are representative at larger sample sizes. The proposed approach is computationally inexpensive and requires minimal effort to implement. We rely on the correlation matrix of flow field to quantify the representative quality of the computed flow properties at the pore scale. Using this approach, we have been able to study several pore-networks and a high-resolution image of a sandstone, and quickly answer if the computed flow properties from these pore-networks/images are representative of the actual media.

Keywords

Porous media Pore-scale modeling REV Network modeling  Direct pore-scale modeling 

Notes

Acknowledgments

This research was partly supported by the financial support from the Center for Frontiers of Subsurface Energy Security (CFSES) at The University of Texas at Austin under U.S. Department of Energy contract DE-SC0001114. Professor Martin J. Blunt from Imperial College and Hu Dong from iRock Technologies are gratefully thanked for sharing their network and micro-CT data with us.

References

  1. Al-Raoush, R., Papadopoulos, A.: Representative elementary volume analysis of porous media using X-ray computed tomography. Powder Technol. 200(1–2), 69–77 (2010)CrossRefGoogle Scholar
  2. Arbogast, T., Pencheva, G., Wheeler, M.F., Yotov, I.: A multiscale mortar mixed finite element method. Multiscale Model. Simul. 6(1), 319–346 (2007)CrossRefGoogle Scholar
  3. Arns, C.H., Knackstedt, M.A., Pinczewski, W.V., Garboczi, E.J.: Computation of linear elastic properties from microtomographic images: methodology and agreement between theory and experiment. Geophysics 67, 1396–1405 (2002)CrossRefGoogle Scholar
  4. Balhoff, M.T., Thomas, S.G., Wheeler, M.F.: Mortar coupling and upscaling of pore-scale models. Comput. Geosci. 12(1), 15–27 (2008)CrossRefGoogle Scholar
  5. Bear, J.: Dynamics of Fluids in Porous Media. Courier Dover, New York (1972)Google Scholar
  6. Bijeljic, B., Mostaghimi, P., Blunt, M.J.: Insights into non-fickian solute transport in carbonates. Water Resour. Res. 49, 2714–2728 (2013a)CrossRefGoogle Scholar
  7. Bijeljic, B., Raeini, A., Mostaghimi, P., Blunt, M.J.: Prediction of non-fickian solute transport in different classes of porous media using direct simulation on pore-scale images. Phys. Rev. E 87(1), 013, 011 (2013b)CrossRefGoogle Scholar
  8. Dagan, G.: Flow and Transport in Porous Formations. Springer, New York (1989)CrossRefGoogle Scholar
  9. Dong, H., Blunt, M.J.: Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E 80(3), 036, 307 (2009)CrossRefGoogle Scholar
  10. Fredrich, J.T., Menendez, B., Wong, T.F.: Imaging the pore structure of geomaterials. Science 268(5208), 276–279 (1995)CrossRefGoogle Scholar
  11. Fredrich, J.T., DiGiovanni, A.A., Noble, D.R.: Predicting macroscopic transport properties using microscopic image data. J. Geophys. Res. 11(B03), 201 (2006)Google Scholar
  12. Gelhar, L.W.: Stochastic Subsurface Hydrolog. Prentice Hall, Englewood Cliffs (1993)Google Scholar
  13. Joekar-Niasar, V., Hassanizadeh, S.M., Leijnse, A.: Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-scale network modeling. Transp. Porous Media 74, 201–219 (2008)CrossRefGoogle Scholar
  14. Klov. T., Oren, P.E., Stensen, J.A., Lerdahl, T.R., Berge, L.I., Bakke, S., Boassen, T., Virnovsky, G.: Pore-to-field scale modeling of wag. SPE 84549 (2003)Google Scholar
  15. Li, H., Pan, C., Miller, C.T.: Pore-scale investigation of viscous coupling effects for two-phase flow in porous media. Phys. Rev. E 72, 026, 705 (2005)CrossRefGoogle Scholar
  16. Lindquist, W.B., Venkatarangan, A.: Investigating 3d geometry of porous media from high resolution images. Phys. Chem. Earth 24, 639–644 (1999)Google Scholar
  17. Mostaghimi, P., Blunt, M.J., Bijeljic, B.: Computations of absolute permeability on micro-ct images. Math. Geosci. 45, 103–125 (2012)CrossRefGoogle Scholar
  18. Neuman, S.P.: Generalized scaling of permeabilities: validation and effect of support scale. Geophys. Res. Lett. 21, 349–352 (1994)CrossRefGoogle Scholar
  19. Norris, R.J., Lewis, J.J.M.: The geological modeling of effective permeability in complex heterolithic facies. SPE 22692, 359–374 (1991)Google Scholar
  20. Oren, P.E., Bakke, S., Arntzen, O.J.: Extending predictive capabilities to network models. SPE J. 3(4), 324–336 (1998)CrossRefGoogle Scholar
  21. Oren, P.E., Bakke, S., Held, R.: Direct pore-scale computation of material and transport properties for north sea reservoir rocks. Water Resour. Res. 43, W12S04 (2007)CrossRefGoogle Scholar
  22. Ovaysi, S.: Direct pore-level modeling of fluids flow in porous media. Ph.D. thesis, University of Wyoming (2010)Google Scholar
  23. Ovaysi, S., Piri, M.: Direct pore-level modeling of incompressible fluid flow in porous media. J. Comput. Phys. 229(19), 7456–7476 (2010)CrossRefGoogle Scholar
  24. Ovaysi, S., Piri, M.: Pore-scale modeling of dispersion in disordered porous media. J. Contam. Hydrol. 124(1–4), 68–81 (2011)CrossRefGoogle Scholar
  25. Ovaysi, S., Piri, M.: Multi-GPU acceleration of direct pore-scale modeling of fluid flow in natural porous media. Comput. Phys. Commun. 183(9), 1890–1898 (2012)CrossRefGoogle Scholar
  26. Ovaysi, S., Piri, M.: Pore-scale dissolution of \(\text{ CO }_2\)+\(\text{ SO }_2\) in deep saline aquifers. Int. J. Greenhouse Gas Control 15, 119–133 (2013)CrossRefGoogle Scholar
  27. Ovaysi, S., Piri, M.: Pore-space alteration induced by brine acidification in subsurface geologic formations. Water Resour. Res. 50, 1–13 (2014)CrossRefGoogle Scholar
  28. Patzek, T.W.: Verification of a complete pore network simulator of drainage and imbibition. SPE J. 6(2), 144–156 (2001)CrossRefGoogle Scholar
  29. Piri, M., Blunt, M.J.: Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. i. model description. Phys. Rev. E 71, 026, 301 (2005)CrossRefGoogle Scholar
  30. Prodanovic, M., Lindquist, W.B., Seright, R.S.: Porous structure and fluid partitioning in polyethylene cores from 3D X-ray microtomographic imaging. J. Colloid Interface Sci. 298(1), 282–297 (2006)CrossRefGoogle Scholar
  31. Ramstad, T., Idowu, N., Nardi, C., Oren, P.E.: Relative permeability calculations from two-phase flow simulations directly on digital images of porous media. Transp. Porous Media 94(2), 487–504 (2012)CrossRefGoogle Scholar
  32. Raoof, A., Hassanizadeh, S.M., Leijnse, A.: Upscaling transport of adsorbing solutes in porous media: pore-network modeling. Vadose Zone J. 9, 624–636 (2010)CrossRefGoogle Scholar
  33. Rustad, A.B., Theting, T.G., Held, R.J.: Pore scale estimation, up scaling and uncertainty modeling for multiphase properties. SPE 113005 (2008)Google Scholar
  34. Siena, M., Riva, M., Hyman, J.D., Winter, C.L., Guadagnini, A.: Relationship between pore size and velocity probability distributions in stochastically generated porous media. Phys. Rev. E 89(013), 018 (2014)Google Scholar
  35. Spanne, P., Thovert, J.F., Jacquin, C.J., Lindquist, W.B., Jones, K.W., Adler, P.M.: Synchrotron computed microtomography of porous media: topology and transports. Phys. Rev. Lett. 73(14), 2001–2004 (1994)CrossRefGoogle Scholar
  36. Valvatne, P.H., Piri, M., Blunt, M.J.: Predictive pore scale modeling of single and multiphase flow. Transp. Porous Media 58(1–2), 23–41 (2005)CrossRefGoogle Scholar
  37. Wildenschild, D., Sheppard, A.: X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems. Adv. Water Resour. 51, 217–246 (2013)CrossRefGoogle Scholar
  38. Zhang, D., Zhang, R., Chen, S., Soll, W.E.: Pore scale study of flow in porous media: scale dependency, rev, and statistical rev. Geophys. Res. Lett. 27(8), 1195–1198 (2000)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Saeed Ovaysi
    • 1
  • Mary F. Wheeler
    • 1
  • Matthew Balhoff
    • 2
  1. 1.Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA
  2. 2.Department of Petroleum and Geosystems EngineeringThe University of Texas at AustinAustinUSA

Personalised recommendations