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Transport in Porous Media

, Volume 118, Issue 1, pp 99–117 | Cite as

Pore-Scale Characterization of Two-Phase Flow Using Integral Geometry

  • Zhishang Liu
  • Anna Herring
  • Christoph Arns
  • Steffen Berg
  • Ryan T. ArmstrongEmail author
Article

Abstract

The pore-scale morphological description of two-phase flow is fundamental to the understanding of relative permeability. In this effort, we visualize multiphase flow during core flooding experiments using X-ray microcomputed tomography. Resulting phase morphologies are quantified using Minkowski Functionals and relative permeability is measured using an image-based method where lattice Boltzmann simulations are conducted on connected phases from pore-scale images. A capillary drainage transform is also employed on the imaged rock structure, which provides reasonable results for image-based relative permeability measurements even though it provides pore-scale morphologies for the wetting phase that are not comparable to the experimental data. For the experimental data, there is a strong correlation between non-wetting phase Euler characteristic and relative permeability, whereas there is a weak correlation for the wetting phase topology. The relative permeability of some rock types is found to be more sensitive to topological changes than others, demonstrating the influence that phase connectivity has on two-phase flow. We demonstrate the influence that phase morphology has on relative permeability and provide insight into phase topological changes that occur during multiphase flow.

Keywords

Minkowski functionals Euler characteristic X-ray microcomputed tomography Capillary drainage transform Maximum inscribed spheres Relative permeability 

Notes

Acknowledgements

This research was undertaken with the assistance of resources provided at the NCI National Facility systems through the National Computational Merit Allocation Scheme. The Australian Government provided funding through an Australian Research Council (ARC) Discovery Project (DP160104995; RA, CHA) and an ARC Future Fellowship (FT120100216; CHA). We thank the anonymous reviewers for excellent comments that further strengthened this manuscript.

References

  1. Alpak, F.O., Lake, L.W., Embid, S.M.: In: SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers (1999)Google Scholar
  2. Armstrong, R.T., Berg, S.: Interfacial velocities and capillary pressure gradients during Haines jumps. Phys. Rev. E 88(4), 043010 (2013)CrossRefGoogle Scholar
  3. Armstrong, R.T., Evseev, N., Koroteev, D., Berg, S.: Modeling the velocity field during Haines jumps in porous media. Adv. Water Resour. 77, 57–68 (2015)CrossRefGoogle Scholar
  4. Armstrong, R.T., Georgiadis, A., Ott, H., Klemin, D., Berg, S.: Critical capillary number: desaturation studied with fast X-ray computed microtomography. Geophys. Res. Lett. 41(1), 55–60 (2014a)Google Scholar
  5. Armstrong, R.T., Ott, H., Georgiadis, A., Rücker, M., Schwing, A., Berg, S.: Subsecond pore-scale displacement processes and relaxation dynamics in multiphase flow. Water Resour. Res. 50(12), 9162–9176 (2014b)Google Scholar
  6. Armstrong, R.T., McClure, J.E., Berrill, M.A., Rücker, M., Schlüter, S., Berg, S.: Beyond Darcy’s law: the role of phase topology and ganglion dynamics for two-fluid flow. Phys. Rev. E 94(4), 043113 (2016)Google Scholar
  7. Armstrong, R.T., Porter, M.L., Wildenschild, D.: Linking pore-scale interfacial curvature to column-scale capillary pressure. Adv. Water Resour. 46, 55–62 (2012)CrossRefGoogle Scholar
  8. Arns, C., Bauget, F., Sakellariou, A., Senden, T., Sheppard, A., Sok, R., Ghous, A., Pinczewski, W., Knackstedt, M., Kelly, J., et al.: Digital core laboratory: petrophysical analysis from 3D imaging of reservoir core fragments. Petrophysics 46(04), 260–277 (2005a)Google Scholar
  9. Arns, C.H., Bauget, F., Limaye, A., Sakellariou, A., Senden, T., Sheppard, A., Sok, R.M., Pinczewski, V., Bakke, S., Berge, L.I., et al.: Pore scale characterization of carbonates using X-ray microtomography. SPE J. 10(04), 475–484 (2005b)Google Scholar
  10. Arns, C.H., Knackstedt, M.A., Martys, N.S.: Cross-property correlations and permeability estimation in sandstone. Phys. Rev. E 72(4), 046304 (2005c)Google Scholar
  11. Arns, C., Knackstedt, M., Mecke, K.: 3D structural analysis: sensitivity of Minkowski functionals. J. Microsc. 240(3), 181–196 (2010)CrossRefGoogle Scholar
  12. Arns, C.H., Knackstedt, M.A., Pinczewski, W.V., Mecke, K.R.: Euler–Poincaré characteristics of classes of disordered media. Phys. Rev. E 63(3), 031112 (2001)CrossRefGoogle Scholar
  13. Benesty, J., Chen, J., Huang, Y., Cohen, I.: Pearson correlation coefficient. In: Noise reduction in speech processing, pp. 1–4. Springer, Berlin Heidelberg (2009)Google Scholar
  14. Berg, S., Armstrong, R., Ott, H., Georgiadis, A., Klapp, S., Schwing, A., Neiteler, R., Brussee, N., Makurat, A., Leu, L., et al.: Multiphase flow in porous rock imaged under dynamic flow conditions with fast X-ray computed microtomography. Petrophysics 55(04), 304–312 (2014)Google Scholar
  15. Berg, S., Cense, A., Hofman, J., Smits, R.: Two-phase flow in porous media with slip boundary condition. Transp. Porous Media 74(3), 275–292 (2008)CrossRefGoogle Scholar
  16. Berg, S., Ott, H., Klapp, S.A., Schwing, A., Neiteler, R., Brussee, N., Makurat, A., Leu, L., Enzmann, F., Schwarz, J.O., et al.: Real-time 3D imaging of Haines jumps in porous media flow. Proc. Natl. Acad. Sci. 110(10), 3755–3759 (2013)CrossRefGoogle Scholar
  17. Berg, S., Rücker, M., Ott, H., Georgiadis, A., van der Linde, H., Enzmann, F., Kersten, M., Armstrong, R., de With, S., Becker, J., et al.: Connected pathway relative permeability from pore-scale imaging of imbibition. Adv. Water Resour. 90, 24–35 (2016)CrossRefGoogle Scholar
  18. Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)CrossRefGoogle Scholar
  19. Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media and their relation to drainage design. Trans. ASAE 7(1), 26–0028 (1964)CrossRefGoogle Scholar
  20. Carman, P.C.: Flow of Gases Through Porous Media. Academic Press, New York (1956)Google Scholar
  21. Corey, A.T.: The interrelation between gas and oil relative permeabilities. Prod. Mon. 19(1), 38–41 (1954)Google Scholar
  22. Cueto-Felgueroso, L., Juanes, R.: A discrete-domain description of multiphase flow in porous media: rugged energy landscapes and the origin of hysteresis. Geophys. Res. Lett. 43, 1615–1622 (2016)CrossRefGoogle Scholar
  23. Datta, S.S., Dupin, J.B., Weitz, D.A.: Fluid breakup during simultaneous two-phase flow through a three-dimensional porous medium. Phys. Fluids 26(6), 062004 (2014a)Google Scholar
  24. Datta, S.S., Ramakrishnan, T., Weitz, D.A.: Mobilization of a trapped non-wetting fluid from a three-dimensional porous medium. Phys. Fluids 26(2), 022002 (2014b)Google Scholar
  25. Dullien, F.A.: Porous Media: Fluid Transport and Pore Structure. Academic Press, San Diego (2012)Google Scholar
  26. Fulcher Jr., R.A., Ertekin, T., Stahl, C., et al.: Effect of capillary number and its constituents on two-phase relative permeability curves. J. Pet. Technol. 37(02), 249–260 (1985)CrossRefGoogle Scholar
  27. Herring, A.L., Andersson, L., Schlüter, S., Sheppard, A., Wildenschild, D.: Efficiently engineering pore-scale processes: the role of force dominance and topology during nonwetting phase trapping in porous media. Adv. Water Resour. 79, 91–102 (2015)CrossRefGoogle Scholar
  28. Herring, A.L., Harper, E.J., Andersson, L., Sheppard, A., Bay, B.K., Wildenschild, D.: Effect of fluid topology on residual nonwetting phase trapping: implications for geologic CO 2 sequestration. Adv. Water Resour. 62, 47–58 (2013)CrossRefGoogle Scholar
  29. Herring, A.L., Sheppard, A., Andersson, L., Wildenschild, D.: Impact of wettability alteration on 3D nonwetting phase trapping and transport. Int. J. Greenh. Gas Control 46, 175–186 (2016)CrossRefGoogle Scholar
  30. Hilpert, M., Miller, C.T.: Pore-morphology-based simulation of drainage in totally wetting porous media. Adv. Water Resour. 24(3), 243–255 (2001)CrossRefGoogle Scholar
  31. Hussain, F., Pinczewski, W.V., Cinar, Y., Arns, J.Y., Arns, C., Turner, M.: Computation of relative permeability from imaged fluid distributions at the pore scale. Transp. Porous Media 104(1), 91–107 (2014)CrossRefGoogle Scholar
  32. Joekar-Niasar, V., Hassanizadeh, S., Leijnse, A.: Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-network modeling. Transp. Porous Media 74(2), 201–219 (2008)CrossRefGoogle Scholar
  33. Khayrat, K., Jenny, P.: Subphase approach to model hysteretic two-phase flow in porous media. Transp. Porous Media 111(1), 1–25 (2016)CrossRefGoogle Scholar
  34. Lake, L.: Enhanced Oil Recovery. Prentice Hall Inc., Old Tappan (1989)Google Scholar
  35. Latham, S., Varslot, T., Sheppard, A., et al.: Image registration: enhancing and calibrating X-ray micro-CT imaging. In: Proceedings of the Society Core Analysts, Abu Dhabi, UAE (2008)Google Scholar
  36. Meakin, P., Tartakovsky, A.M.: Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev. Geophys. 47(3), RG3002 (2009)CrossRefGoogle Scholar
  37. Mecke, K., Arns, C.: Fluids in porous media: a morphometric approach. J. Phys. Condens. Matter 17(9), S503 (2005)CrossRefGoogle Scholar
  38. Porter, M.L., Schaap, M.G., Wildenschild, D.: Lattice-Boltzmann simulations of the capillary pressure-saturation-interfacial area relationship for porous media. Adv. Water Resour. 32(11), 1632–1640 (2009)CrossRefGoogle Scholar
  39. Robins, V., Saadatfar, M., Delgado-Friedrichs, O., Sheppard, A.P.: Percolating length scales from topological persistence analysis of micro-CT images of porous materials. Water Resour. Res. 52(1), 315–329 (2016)Google Scholar
  40. Rücker, M., Berg, S., Armstrong, R., Georgiadis, A., Ott, H., Schwing, A., Neiteler, R., Brussee, N., Makurat, A., Leu, L., et al.: From connected pathway flow to ganglion dynamics. Geophys. Res. Lett. 42(10), 3888–3894 (2015)CrossRefGoogle Scholar
  41. Schlüter, S., Berg, S., Rücker, M., Armstrong, R., Vogel, H.J., Hilfer, R., Wildenschild, D.: Pore-scale displace mechanisms as a source of hysteresis for two-phase flow in porous media. Water Resour. Res. 52(3), 2194–2205 (2016)Google Scholar
  42. Schlüter, S., Sheppard, A., Brown, K., Wildenschild, D.: Image processing of multiphase images obtained via X-ray microtomography: a review. Water Resour. Res. 50(4), 3615–3639 (2014)CrossRefGoogle Scholar
  43. Scholz, C., Wirner, F., Götz, J., Rüde, U., Schröder-Turk, G.E., Mecke, K., Bechinger, C.: Permeability of porous materials determined from the Euler characteristic. Phys. Rev. Lett. 109(26), 264504 (2012)CrossRefGoogle Scholar
  44. Sheppard, A.P., Sok, R.M., Averdunk, H.: Techniques for image enhancement and segmentation of tomographic images of porous materials. Phys. A Stat. Mech. Appl. 339(1), 145–151 (2004)CrossRefGoogle Scholar
  45. Shikhov, I., Arns, C.H.: Evaluation of capillary pressure methods via digital rock simulations. Transp. Porous Media 107(2), 623–640 (2015)CrossRefGoogle Scholar
  46. Silin, D., Patzek, T.: Pore space morphology analysis using maximal inscribed spheres. Phys. A Stat. Mech. Appl. 371(2), 336–360 (2006)CrossRefGoogle Scholar
  47. Steiger, J.H.: Tests for comparing elements of a correlation matrix. Psychol. Bull. 87(2), 245 (1980)CrossRefGoogle Scholar
  48. Törnqvist, L., Vartia, P., Vartia, Y.O.: How should relative changes be measured? Am. Stat. 39(1), 43–46 (1985)Google Scholar
  49. Vogel, H.J., Weller, U., Schlüter, S.: Quantification of soil structure based on Minkowski functions. Comput. Geosci. 36(10), 1236–1245 (2010)CrossRefGoogle Scholar
  50. Wildenschild, D., Sheppard, A.P.: X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems. Adv. Water Resour. 51(2013), 217–246 (2012)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.School of Petroleum EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Department of Applied Mathematics, Research School of Physics and EngineeringAustralian National UniversityCanberraAustralia
  3. 3.Shell Global Solutions International B.V.RijswijkThe Netherlands

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