Advertisement

Transport in Porous Media

, Volume 55, Issue 1, pp 21–46 | Cite as

Effect of Network Topology on Relative Permeability

  • Ji-Youn Arns
  • Vanessa Robins
  • Adrian P. Sheppard
  • Robert M. Sok
  • W. V. Pinczewski
  • Mark A. Knackstedt
Article

Abstract

We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res.105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.

two-phase flow relative permeability network models topology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arns, J. Y., Arns, C. H., Sheppard, A. P., Sok, R. M., Knackstedt, M. A. and Pinczewski, W.: 2003, Relative permeability from tomographic images; effect of correlated heterogeneity, J. Petrol. Sci. Eng. (in press).Google Scholar
  2. Bakke, S. and Øren, P.: 1997, 3-D pore-scale modelling of sandstones and flow simulations in the Pore Networks, SPE J. 2, 136–149.Google Scholar
  3. Blunt, M.: 1997, Effects of heterogeneity and wetting on relative permeability using pore level modeling, SPE J. 2, 449–465.Google Scholar
  4. Blunt, M., King, M. and Scher, H.: 1992, Simulation and theory of two-phase flow in porous media, Phys. Rev. A 46, 7680–7699.Google Scholar
  5. Blunt, M., King, M. J. and Zhout, D.: 1994, What determines residual oil saturation in three phase flow, in: Proceedings of the SPE/DOE 9th Symposium on Improved Oil Recovery, Tulsa, OK.Google Scholar
  6. Dunsmuir, J. H., Ferguson, S. R. and D'Amico, K. L.: 1991, Design and operation of an imaging X-ray detector for microtomography, IOP Conference Series 121, 257–261.Google Scholar
  7. Fatt, I.: 1956, The network model of porous media. I. Capillary pressure characteristics, Trans. AIME 207, 144.Google Scholar
  8. Flannery, B. P., Deckman, H. W., Roberge, W. G. and D'Amico, K. L.: 1987, Three-dimensional X-ray microtomography, Science 237, 1439–1444.Google Scholar
  9. Galam, S. and Mauger, A.: 1996, Universal formulas for percolation thresholds, Phys. Rev. E 53, 2177–2180.Google Scholar
  10. Heiba, A., Sahimi, M., Scriven, L. and Davis, H.: 1992, Percolation theory of two-phase relative permeability, SPE Reserv. Eng. 7, 123–132.Google Scholar
  11. Hewett, T. A.: 1986, Fractal distributions of reservoir heterogeneity and their influence of fluid transport, in: Proceedings of the 61st Annual Technical Conference and Exhibition of Society of Petroleum Engineers, New Orleans, LA.Google Scholar
  12. Ioannidis, M. A. and Chatzis, I.: 1993, A mixed percolation model of capillary hysteresis and entrapment in mercury porosimetry, Chem. Eng. Sci. 48, 951.Google Scholar
  13. Ioannidis, M. A. and Chatzis, I.: 2000, On the geometry and topology of 3D stochastic porous media, J. Colloid Interf. Sci. 229, 323–334.Google Scholar
  14. Ioannidis, M. A., Kwiecien, M. J., Chatzis, I., MacDonald, I. F. and Dullien, F. A. L.: 1997, Comprehensive pore structure characterization using 3D computer reconstruction and stochastic modeling, in: Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX.Google Scholar
  15. Jerauld, G., Scriven, L. and Davis, H.: 1984, Percolation and conduction on the 3D Voronoi and regular Networks: a second case study in topological order, J. Phys. C 17, 3429.Google Scholar
  16. Knackstedt, M. A., Sheppard, A. P. and Pinczewski W. V.: 1998, Simulation of mercury porosimetry on correlated grids: Evidence for extended correlated heterogeneity at the pore scale in rocks, Phys. Rev. E. Rapid Commun. 58, R6923–R6926.Google Scholar
  17. Knackstedt, M. A., Sheppard, A. P. and Sahimi, M.: 2001, Pore network modelling of two-phase flow in porous rocks: The effect of correlated heterogeneity, Adv. Water Resour. 24, 257–277.Google Scholar
  18. Larson, R., Scriven, L. E. and Davis, H. T.: 1977, Percolation theory of residual phases in porous media, Nature 268, 409–413.Google Scholar
  19. Larson, R., Scriven, L. E. and Davis, H. T.: 1991, Percolation theory of two-phase flow in porous media, Chem. Eng. Sci. 36, 57–73.Google Scholar
  20. Lee, T. C., Kashyap, R. L. and Chu, C.-N.: Building skeleton models via 3D medial surface/axis thinning algorithms', CVGIP: Graph. Mod. Im. Proc. 56, 462–478.Google Scholar
  21. Lerdahl, T. R., Øren, P. and Bakke, S.: A predictive network model for three-phase flow in porous media, in: Proceedings of the 2000 SPE/DOE Improved Oil Recovery Symposium, Tulsa, OK.Google Scholar
  22. Lindquist, B. and Venkatarangan, A.: 1999, Investigation 3D geometry of porous media from high resolution images, Phys. Chem. Earth 24, 87.Google Scholar
  23. Lindquist, B., Lee, S. M. and Coker, D.: 1996, Medial axis analysis of void structure in threedimensional tomographic images of porous media, J. Geophys. Res. 101B, 8297–8310.Google Scholar
  24. Lindquist, W. B., Venkatarangan, A., Dunsmuir, J. and Wong, T. F.: 2000, Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainbleau sandstones, J. Geophys. Res. 105B, 21508.Google Scholar
  25. Mathews, G. P., Moss, A. K. and Ridgway, C. J.: 1995, Effects of correlated networks on mercury intrusion simulations and permeabilities of sandstone and other porous media, Power Technol. 83, 61–77.Google Scholar
  26. O'Keefe, M. and Hyde, B. G.: Crystal Structures I: Patterns and symmetry, Mineralogical Society of America, Washington DC.Google Scholar
  27. Øren, P. and Bakke, S.: 2002a, Process-based reconstruction of sandstones and prediction of transport properties, Trans. Porous Med. 46, 311–343.Google Scholar
  28. Øren, P. and Bakke, S.: 2002b, Reconstruction of Berea Sandstone and pore-scale modeling of wettability effects, in: Proceedings of the 7th International Symposium on Reservoir Wettability, Freycinet, Tasmania.Google Scholar
  29. Øren, P. and Pinczewski, W.: 1991, The effect of film flow in the mobilization of waterflood residual oil by gas flooding, in: Proceedings of the 6th European Symposium on Improved Oil Recovery, Stavanger, Norway.Google Scholar
  30. Øren, P. and Pinczewski, W.: 1994, Effect of wettability and spreading on recovery of waterflood residual oil by immiscible gasflooding, SPE Formation Eval. 8, 149–156.Google Scholar
  31. Øren, P., Billiotte, J. and Pinczewski, W.: 1992, Mobilisation of waterflood residual oil by gas injection for water-wet conditions, SPE Formation Eval. 7, 70–78.Google Scholar
  32. Øren, P., Billiotte, J. and Pinczewski, W.: 1994, Pore scale network modelling of waterflood residual oil recovery by immiscible gas flooding, in: Proceedings of the SPE/DOE Ninth Symposium on Improved Oil Recovery, Tulsa, OK.Google Scholar
  33. Øren, P., Bakke, S. and Arntzen, O. J.: 1998, Extending predictive capabilities to network models, SPE J. 3, 324–336.Google Scholar
  34. Paterson, L.: 1998, Trapping thresholds in ordinary percolation, Phys. Rev. E 58, 7137–7140.Google Scholar
  35. Paterson, L., Knackstedt, M. A. and Sheppard, A. P.: 2002, Trapping thresholds in invasion percolation, Phys. Rev. E 66, 056122.Google Scholar
  36. Paterson, L., Painter, S., Knackstedt, M. and Pinczewski, W. V.: 1996a, Patterns of fluid flow in naturally heterogeneous rocks, Physica A 233, 619–628.Google Scholar
  37. Paterson, L., Painter, S., Zhang, X. and Pinczewski, W. V.: 1996b, Simulating residual saturation and relative permeability in heterogeneous formations, in: Proceedings of the 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado.Google Scholar
  38. Pathak, P., Davis, H. and Scriven, L.: 1982, Dependence of residual nonwetting liquid on pore topology, in: Proceedings of The 57th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineering of AIME, NewOrleans, LA.Google Scholar
  39. Pereira, G., Pinczewski, W., Chan, D., Paterson, L. and Øren, P.: 1996, Pore-scale network model for drainage dominated three-phase flow in porous media, Trans. Porous Med. 24, 167–201.Google Scholar
  40. Sahimi, M.: 1994, Applications of Percolation Theory, 1st edn., Taylor and Francis, London.Google Scholar
  41. Sok, R. M., Knackstedt, M. A., Sheppard, A. P., Pinczewski, W., Lindquist, W. B., Venkatarangan, A. and Paterson, L.: 2002, Direct and stochastic generation of network models from tomographic images; effect of topology on two phase flow properties, Trans. Porous Med. 46, 345–372.Google Scholar
  42. Spanne, P., Thovert, J., Jacquin, J., Lindquist, W. B., Jones, K. and Adler, P. M.: 1994, Synchotron computed microtomography of porous media: topology and transports, Phys. Rev. Lett. 73, 2001–2004.Google Scholar
  43. Stauffer, D. and Aharony, A.: 1994, Introduction to Percolation Theory, 2nd edn., Taylor and Francis, London.Google Scholar
  44. Suding, P. N. and Siff, R. M.: 1999, Site percolation thresholds for Archimedean lattices, Phys. Rev. E 60, 275–283.Google Scholar
  45. Thovert, J.-F., Salles, J. and Adler, P.: 1993, Computerised characterization of the geometry of real porous media: their description, analysis and interpretation, J. Microscopy 170, 65–79.Google Scholar
  46. Tsakiroglou, C. D. and Payatakes, A. C.: 1991, Effects of pore-size correlations on mercury porosimetry curves, J. Colloid Interf. Sci. 146, 479–494.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ji-Youn Arns
    • 1
  • Vanessa Robins
    • 2
  • Adrian P. Sheppard
    • 1
    • 2
  • Robert M. Sok
    • 1
    • 2
  • W. V. Pinczewski
    • 1
  • Mark A. Knackstedt
    • 1
    • 2
  1. 1.School of Petroleum EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Department of Applied Mathematics, Research School of Physical Sciences and EngineeringAustralian National UniversityCanberraAustralia

Personalised recommendations