Skip to main content
SpringerLink
Log in

Direct and Stochastic Generation of Network Models from Tomographic Images; Effect of Topology on Residual Saturations

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

We generate the network model equivalents of four samples of Fontainebleau sandstone obtained from the analysis of microtomographic images. We present the measured distributions of flow-relevant geometric and topological properties of the pore space. We generate via bond dilution from a regular lattice, stochastic network models with identical geometric (pore-size, throat-size) and topological (coordination number distribution) properties. We then simulate the two-phase flow properties directly on the network model and the stochastic equivalent for each sample. The simulations on the stochastic networks are found to provide a poor representation of the results on the direct network equivalents. We find that the description of the network topology is particularly crucial in accurately predicting the residual phase saturations. We also find it necessary to introduce into the stochastic network geometry both extended pore-pore correlations and local pore-throat correlations to obtain good agreement with flow properties on the rock-equivalent network.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bakke, S. and Oren P.: 1997, 3-D pore-scale modelling of sandstones and flow simulations in the Pore Networks,SPE J. 2, 136–149.

    Google Scholar 

  2. 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 

  3. Blunt, M., King, M. J. and Zhou, D.: 1994, What determines residual oil saturation in three-phase flow, In: SPE/DOE 9th Symp. on Improved Oil Recovery.

  4. Doyen, P.: 1988, Permeability, conductivity and pore geometry of sandstone, J. Geophys. Res. 93, 7729–7740.

    Google Scholar 

  5. Dullien, F.: 1992, Porous Media: Fluid Transport and Pore Structure; NY: Academic.

  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 conf. Series 121, 257–261.

    Google Scholar 

  7. 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 

  8. Galam, S. and Mauger, A.: 1994. J. Appl. Phys. 75, 5526–5531.

    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. and Sahimi M.: 1982, Scriven, L. & Davis, H., Percolation theory of two-phase relative permeability, SPE Paper 10015.

  11. Heiba, A.: 1983, Effect of Wettability on 2-phase relative permeabs & Capill. presence, SEP Paper 12172.

  12. Heiba, A., Sahimi, M., Scriven, L. and Davis, H.: 1992, Percolation theory of two-phase relative permeability, SPE Reserv. Engng bd7, 123–132.

    Google Scholar 

  13. Hewett, T.: 1986, Fractal distributions of reservior heterogeneity and their influence of fluid transport, Technical Report, SPE Paper 15836.

  14. Hilfer, R.: 1996, Transport and relaxation phenomena in porous media, Adv. Chem. Phys. XCII, 299–424.

    Google Scholar 

  15. 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 

  16. Ioannidis, M. A., Kwiecien, M. J., Chatzis I., MacDonald, I. F. and Dullien, F. A. L.: 1997, Comprehensive pore structure characterization using 3-D computer reconstruction and stochastic modelling, Technical report, SPE Paper 38713.

  17. Kamath, J., Xu, B. and Yortsos, Y. C.: 1998, Use of pore network models to interpret laboratory experiments on vugular rocks, J. Petroleum Sci. Engng. 20, 109–120.

    Google Scholar 

  18. Knackstedt, M. A., Marrink, S. J., Sheppard, A. P., Pinczewski W. V. and Sahimi, M.: 1999, Invasion percolation on correlated and elongated lattices: Implications to the interpretation of phase saturations in rock cores, Transport in Porous Media 44, 465–485.

    Google Scholar 

  19. Knackstedt, M. A., Sahimi, M. and Sheppard, A. P.: 2000a, Invasion percolation with long-range correlations: First-order phase transition and nonuniversal scaling properties, Phys. Rev. E. 61, 4920.

    Google Scholar 

  20. Knackstedt, M. A., Sheppard, A. P. and Pinczeswki, W. V.: 1998, Simulation of mercury porosi-metry on correlated grids: Evidence for extended correlated heterogeneity at the pore scale in rocks, Phys.Rev.E.RapidCommun. 58, R6923–R6926.

    Google Scholar 

  21. Knackstedt, M. A., Sheppard, A. P. and Sahimi, M.: 2000b, Pore network modelling of two-phase flow in porous rocks: The effect of correlated heterogeneity Adv. Water Resour. Volume 24, pp. 257–277 (2001).

    Google Scholar 

  22. Koplik, J., Lin, C. and Vermette, M.: 1984, Conductivity and permeability from microgeometry, J. Appl. Phys. 56, 3127–3132.

    Google Scholar 

  23. Larson, R., Scriven, L. E. and Davis, H. T.: 1977, Percolation theory of residual phase in porous media, Nature 268, 409–413.

    Google Scholar 

  24. 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 

  25. Lee, T. C., Kashyap, R. L. and Chu, C.-N.: 1994, Building skeleton models via 3-D medial surface/axis thinning algorithms, CVGIP: Grophic. Models Image Process. 56, 462–478.

    Google Scholar 

  26. Lin, C. and Cohen M. H.: 1982, Quantitative methods for microgeometric modelling, J. Appl. Phys. 53, 4152–4165.

    Google Scholar 

  27. Lindquist, B., Lee, S. M. and Coker D.: 1996, Medial axis analysis of void structure in three-dimensional tomographic images of porous media, J. Geophys. Res. 101B, 8297–3210.

    Google Scholar 

  28. Lindquist, B. and Venkatarangan, A.: 1999, Investigation 3-D geometry of porous media from high resolution images, Phys. Chem. Earth 24, 87.

    Google Scholar 

  29. 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 

  30. McDougall and Sorbie: 1993, The predictions of waterflood performance in mixed wet systems from pae-scale modelling & simulation, SPE Paper 25271.

  31. O'Keefe, M.: 1999a, Coordination sequences for lattices, preprint.

  32. O'Keefe, M.: 1999b, On the calculation, use and properties of coordination sequence, preprint.

  33. O'Keefe, M. and Hydes B. G.: 1996, Crystal Structures I: Patterns and symmetry. Washington D.C.: Mineralogical Society of America.

    Google Scholar 

  34. Oren, P., Bakke, S. and Arntzen, O. J.: 1998, Extending predictive capabilities of network models, SPE J. 3, 324–336.

    Google Scholar 

  35. Oren, P., Billiotte, J. and Pinczewski, W.: 1992, Mobilisation of waterflood residual oil by gas injection of water-wet conditions, SPE Formation Evaluation 7, 70–78.

    Google Scholar 

  36. Oren, P., Billiotte, J. and Pinczewski, W.: 1994, Pore scale network modelling of waterflood residual oil recovery by immiscible gas flooding, In: SPE Improved Oil Recovery Symposium, Houston, USA.

  37. Oren, P. and Pinczewski, W.: 1991, The effect of film flow in the mobilization of waterflood residual oil by gas flooding, In: 6th European IOR-Symposium, Houston, USA.

  38. Oren, P. and Pinczewski, W.: 1994, Effect of wettability and spreading on recovery of waterflood residual oil by immiscible gasflooding, SPE Form. Eval. 8, 149–156.

    Google Scholar 

  39. Paterson, L., Painter S., Knacksstedt, M. and Pinczewski, W. V.: 1996, Pattern of fluid flow in naturally heterogeneous rocks, Physica A 233, 619–628.

    Google Scholar 

  40. Paterson, L., Painter, S., Zhang, X. and Pinczewski, W. V.: 1997, Simulating residual saturation and relative permeability of heterogeneous formations, SPE 36523.

  41. Pereira, G., Pinczewski, W., Chan, D., Peterson, L. and Oren, P.: 1996, Pore-scale network model for drainage dominated three-phase flow in porous media, Transport in Porous Media 24, 167–201.

    Google Scholar 

  42. Sahimi, M.: 1993, Flow, dispersion, and displacement processes in porous media and fractured rocks: From continuum models to fractals, percolation, cellular automata and simulated annealing, Rev. Mod. Physics 65, 1393–1534.

    Google Scholar 

  43. Sahimi, M.: 1994, Applications of Percolation Theory, (Ist edn.) Taylor and Francis, London.

    Google Scholar 

  44. Sheppard, A. P. and Sok R. M.: 2000, Fast algorithm for trapping and searching in invasion percolation, Transport in Porous Media p. submitted.

  45. Spanne, P., Thovert J., Jacquin, J., Lindquist, W. B., Jones, K. and Coker, D.: 1994, Syncho-tron computed microtomography of porous media: topology and transports Phys. Rev. Lett 73, 2001–2004.

    Google Scholar 

  46. Stauffer, D. and Aharony A.: (1994), Introduction to Percolation Theory, (2nd edn.) Taylor and Francis, London.

    Google Scholar 

  47. Studing, P. N. and Ziff, R. M.: 1999, Site percolation thresholds for Archimedean latticed, Phys. Rev. E 60, 275–283.

    Google Scholar 

  48. 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 

  49. Wilkinson, D. and Willemsen, J.: 1983, Invasion percolation: a new form of percolation theory, J. Phys. A: Math, Gen. 16, 3365–3376.

    Google Scholar 

  50. Xu, B., Kamath, J., Yortsos, Y. C. and Lee, S. H.: 1999, Use of pore network models to simulate laboratory corefloods in a heterogeneous carbonate sample, SPE J 4, 179–186.

    Google Scholar 

  51. Zhao, H. Q. and MacDonald, I. F.: 1993, An unbiased and efficient producedure for 3-D connectivity measurement as applied to porous media, J. Microscopy 172, 157–162.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT, 0200, Australia

    Robert M. Sok, Mark A. Knackstedt, Adrian P. Sheppard, W.B. Lindquist & A. Venkatarangan

  2. Australian Petroleum Cooperative Research Centre, University of New South Wales, Sydney, NSW, 2052, Australia

    Robert M. Sok, Mark A. Knackstedt, Adrian P. Sheppard & W.V. Pinczewski

  3. CSIRO Division of Petroleum Resources, Australian Petroleum Cooperative Research Centre, PO Box 3000, Glen Waverly, VIC, 3150, Australia

    Lincoln Paterson

Authors
  1. Robert M. Sok
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark A. Knackstedt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adrian P. Sheppard
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W.V. Pinczewski
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. W.B. Lindquist
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. Venkatarangan
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Lincoln Paterson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark A. Knackstedt.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sok, R.M., Knackstedt, M.A., Sheppard, A.P. et al. Direct and Stochastic Generation of Network Models from Tomographic Images; Effect of Topology on Residual Saturations. Transport in Porous Media 46, 345–371 (2002). https://doi.org/10.1023/A:1015034924371

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015034924371

Search

Navigation