1887
Volume 67 Number 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Pore structure heterogeneity is a critical parameter controlling mechanical, electrical and flow transport behaviour of rock. Multi‐fractal analysis method was used for a heterogeneity comparison of three‐dimensional rock samples with different lithology. Six real digital samples, containing three sandstones and three carbonates, were used. Based on the mercury injection capillary pressure test on these samples, we found that the carbonate samples are more heterogeneous than sandstones, but primary results of multi‐fractal behaviours for all samples were similar. We show that if multi‐fractal is used to evaluate and compare heterogeneity of different samples, one needs to follow some considerations such as (1) all samples must have the same size in pixel, (2) samples volume must be bigger than representative volume element, (3) multi‐fractal dimensions should be firstly normalized to a determined porosity value and (4) multi‐fractal results should be interpreted based on resolution of the imaging tool (effects of fine scale sub‐resolution pores are missed). Results revealed that using normalized fractal dimensions, the real samples were divided to less and high heterogeneous groups. Moreover, the study of scale effect also showed that porous structures of these samples are scale invariant in a wide range of scales (from one to eight times bigger).

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12681
2018-09-13
2024-04-20
Loading full text...

Full text loading...

References

  1. Al‐KhidirK.E., BenzagoutaM.S., Al‐QurishiA.A. and Al‐LabounA.A.2013. Characterization of heterogeneity of the Shajara reservoirs of the Shajara formation of the Permo‐Carboniferous Unayzah group. Arabian Journal of Geosciences6, 3989–3995.
    [Google Scholar]
  2. AlhashmiZ., BluntM.J. and BijeljicB.2016. The impact of pore structure heterogeneity, transport, and reaction conditions on fluid–fluid reaction rate studied on images of pore space. Transport in Porous Media115, 215–237.
    [Google Scholar]
  3. AlyafeiN., MckayT.J. and SollingT.I.2016. Characterization of petrophysical properties using pore‐network and lattice‐Boltzmann modelling: Choice of method and image sub‐volume size. Journal of Petroleum Science and Engineering145, 256–265.
    [Google Scholar]
  4. AlyafeiN., RaeiniA.Q., PalusznyA. and BluntM.J.2015. A sensitivity study of the effect of image resolution on predicted petrophysical properties. Transport in Porous Media110(1), 157–169.
    [Google Scholar]
  5. AndräH., CombaretN., DvorkinJ., GlattE., HanJ., KabelM.et al. 2013a. Digital rock physics benchmarks‐part I: imaging and segmentation. Computers and Geosciences50, 25–32.
    [Google Scholar]
  6. AndräH., CombaretN., DvorkinJ., GlattE., HanJ., KabelM.et al. 2013b. Digital rock physics benchmarks‐part II: computing effective properties. Computers and Geosciences50, 33–43.
    [Google Scholar]
  7. AndrewM., BijeljicB. and BluntM.J.2014. Pore‐scale imaging of trapped supercritical carbon dioxide in sandstones and carbonates. International Journal of Greenhouse Gas Control22, 1–14.
    [Google Scholar]
  8. BrenchleyP.J. and RawsonP.F.2006. The Geology of England and Wales. Geological Society of London.
    [Google Scholar]
  9. ChattopadhyayP.B. and VedantiN.2016. Fractal characters of porous media and flow analysis. In: Fractal Solutions for Understanding Complex Systems in Earth Sciences (eds V.P.Dimri), pp. 67–77, Springer International Publishing, Cham, Switzerland.
    [Google Scholar]
  10. ChhabraA.B., MeneveauC., JensenR.V. and SreenivasanK.R.1989. Direct determination of the f (α) singularity spectrum and its application to fully developed turbulence. Physical Review A40, 5284.
    [Google Scholar]
  11. CurtisM.E., SondergeldC.H., AmbroseR.J. and RaiC.S.2012. Microstructural investigation of gas shales in two and three dimensions using nanometer‐scale resolution imaging. AAPG Bulletin96, 665–677.
    [Google Scholar]
  12. DatheA., TarquisA.M. and PerrierE.2006. Multifractal analysis of the pore‐and solid‐phases in binary two‐dimensional images of natural porous structures. Geoderma134, 318–326.
    [Google Scholar]
  13. Dathe, A. and ThullnerM.2005. The relationship between fractal properties of solid matrix and pore space in porous media. Geoderma129, 279–290.
    [Google Scholar]
  14. DubelaarC.W. and NijlandT.G.2015. The Bentheim sandstone: geology, petrophysics, varieties and its use as dimension stone. Engineering Geology for Society and Territory8, 557–563.
    [Google Scholar]
  15. EderyY., GuadagniniA., ScherH. and BerkowitzB.2014. Origins of anomalous transport in heterogeneous media: structural and dynamic controls. Water Resources Research50, 1490–1505.
    [Google Scholar]
  16. FederJ.1988. Fractals. Springer Science & Business Media.
    [Google Scholar]
  17. HalseyT.C., JensenM.H., KadanoffL.P., ProcacciaI. and ShraimanB.I.1986. Fractal measures and their singularities: the characterization of strange sets. Physical Review A33, 1141.
    [Google Scholar]
  18. HamzehpourH., AsgariM. and SahimiM.2016Acoustic wave propagation in heterogeneous two‐dimensional fractured porous media. Physical Review E93, 63305.
    [Google Scholar]
  19. HansenJ.P. and SkjeltorpA.T.1988. Fractal pore space and rock permeability implications. Physical Review B38, 2635.
    [Google Scholar]
  20. JouiniM.S., VegaS., Al‐RatroutA. and Al‐RatroutA.2015. Numerical estimation of carbonate rock properties using multiscale images. Geophysical Prospecting63, 405–421.
    [Google Scholar]
  21. JouiniM.S., VegaS. and MokhtarE.A., 2011. Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates. Nonlinear Processes in Geophysics18, 941–953.
    [Google Scholar]
  22. KarimpouliS., KhoshlesanS., SaengerE.H. and KoochiH.H.2018. Application of alternative digital rock physics methods in a real case study: a challenge between clean and cemented samples. Geophysical Prospecting66, 767–783.
    [Google Scholar]
  23. Karimpouli, S. and Tahmasebi, P.2015. Conditional reconstruction: an alternative strategy in digital rock physics. Geophysics, 81(4), D465–D477.
    [Google Scholar]
  24. KarimpouliS. and TahmasebiP.2017. A hierarchical sampling for capturing permeability trend in rock physics. Transport in Porous Media116, 1057–1072.
    [Google Scholar]
  25. KarimpouliS., TahmasebiP., RamandiH.L., MostaghimiP. and SaadatfarM.2017. Stochastic modeling of coal fracture network by direct use of micro‐computed tomography images. International Journal of Coal Geology, 179, 153–163.
    [Google Scholar]
  26. Karimpouli, S., Tahmasebi, P. and Saenger, E.H., 2018. Estimating 3D elastic moduli of rock from 2D thin‐section images using differential effective medium theory. Geophysics, 83, MR211–MR219.
    [Google Scholar]
  27. KatzA.J. and ThompsonA.H.1985. Fractal sandstone pores: implications for conductivity and pore formation. Physical Review Letters54, 1325.
    [Google Scholar]
  28. KewenL.2004. Characterization of rock heterogeneity using fractal geometry. SPE International Thermal Operations and Heavy Oil Symposium and Western Regional Meeting, Bakersfield, CA. Society of Petroleum Engineers.
  29. KrohnC.E.1988. Fractal measurements of sandstones, shales, and carbonates. Journal of Geophysical Research: Solid Earth93, 3297–3305.
    [Google Scholar]
  30. LealL., BarbatoR., QuagliaA., PorrasJ.C. and LazardeH.2001. Bimodal behavior of mercury‐injection capillary pressure curve and its relationship to pore geometry, rock‐quality and production performance in a laminated and heterogeneous reservoir. SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina. Society of Petroleum Engineers.
  31. LiK. and HorneR.N.R.2003. Fractal characterization of the geysers rock. Proceedings of the GRC 2003 Annual Meeting, Iceland.
    [Google Scholar]
  32. MandelbrotB.B.1982. Multifractal measures, especially for the geophysicist. Pure and applied geophysics131, 5–42.
    [Google Scholar]
  33. NgwenyaB.T., Elphick, S.C. and ShimmieldG.B.1995. Reservoir sensitivity to water flooding: an experimental study of seawater injection in a North Sea reservoir analog. AAPG Bulletin79, 285–303.
    [Google Scholar]
  34. NorbisrathJ.H., EberliG.P., LaurichB., DesboisG., WegerR.J. and UraiJ.L.2015. Electrical and fluid flow properties of carbonate microporosity types from multiscale digital image analysis and mercury injection. AAPG Bulletin99, 2077–2098.
    [Google Scholar]
  35. OhJ., KimK.‐Y., HanW.S. and ParkE.2017. Transport of CO2 in heterogeneous porous media: spatio‐temporal variation of trapping mechanisms. International Journal of Greenhouse Gas Control57, 52–62.
    [Google Scholar]
  36. PiniR., KrevorS.C.M. and BensonS.M.2012. Capillary pressure and heterogeneity for the CO2/water system in sandstone rocks at reservoir conditions. Advances in Water Resources38, 48–59.
    [Google Scholar]
  37. PosadasA.N.D., GiménezD., QuirozR. and ProtzR.2003. Multifractal characterization of soil pore systems. Soil Science Society of America Journal67, 1361–1369.
    [Google Scholar]
  38. RadlinskiA.P.P., IoannidisM.A.A., HindeA.L.L., HainbuchnerM., Baron, M., RauchH. and KlineS.R.R.2004. Angstrom‐to‐millimeter characterization of sedimentary rock microstructure. Journal of Colloid and Interface Science274, 607–612.
    [Google Scholar]
  39. RhodesM.E., BijeljicB. and BluntM.J.2008. Pore‐to‐field simulation of single‐phase transport using continuous time random walks. Advances in Water Resources31, 1527–1539.
    [Google Scholar]
  40. SahimiM.2011. Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. John Wiley & Sons.
    [Google Scholar]
  41. SahimiM. and YortsosY.C.1990. Applications of fractal geometry to porous media: a review. Annual Fall Meeting of the Society of Petroleum Engineers, New Orleans, LA. Society of Petroleum Engineers.
    [Google Scholar]
  42. SantarelliF. and BrownE.1989. Failure of three sedimentary rocks in triaxial and hollow cylinder compression tests. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts26, 401–413.
    [Google Scholar]
  43. SaucierA. and MullerJ.1999. Textural analysis of disordered materials with multifractals. Physica A: Statistical Mechanics and its Applications267, 221–238.
    [Google Scholar]
  44. Simonsen, I., Hansen, A. and Nes, O.M.1998. Determination of the Hurst exponent by use of wavelet transforms. Physical Review E, 58, 2779.
    [Google Scholar]
  45. ShenP., LiK. and JiaF.1995. Quantitative description for the heterogeneity of pore structure by using mercury capillary pressure curves. International Meeting on Petroleum Engineering, Beijing, China. Society of Petroleum Engineers.
  46. SwansonB.F.1981. A simple correlation between permeabilities and mercury capillary pressures. Journal of Petroleum Technology33, 2498–2504.
    [Google Scholar]
  47. Tahmasebi, P.2017a. Structural adjustment for accurate conditioning in large‐scale subsurface systems. Advances in Water Resources, 101, 60–74.
    [Google Scholar]
  48. Tahmasebi, P.2017b. HYPPS: a hybrid geostatistical modeling algorithm for subsurface modeling. Water Resources Research, 53, 5980–5997.
    [Google Scholar]
  49. TahmasebiP.2018a. Accurate modeling and evaluation of microstructures in complex materials. Physical Review E, 97, 023307.
    [Google Scholar]
  50. TahmasebiP.2018b. Packing of discrete and irregular particles. Computers and Geotechnics, 100, 52–61.
    [Google Scholar]
  51. TahmasebiP.2018c. Nanoscale and multiresolution models for shale samples. Fuel, 217, 218–225.
    [Google Scholar]
  52. TahmasebiP., SahimiM. and AndradeJ.E.2017. Image‐based modeling of granular porous media. Geophysical Research Letters, 44, 4738–4746.
    [Google Scholar]
  53. TahmasebiP., SahimiM., KohanpurA.H. and ValocchiA.2016. Pore‐scale simulation of flow of CO2 and brine in reconstructed and actual 3D rock cores. Journal of Petroleum Science and Engineering155, 21–33.
    [Google Scholar]
  54. TarquisA.M.M., McInnesK.J.J., KeyJ.R.R., SaaA., GarcíaM.R.R., DíazM.C.C.et al. 2006. Multiscaling analysis in a structured clay soil using 2D images. Journal of Hydrology322, 236–246.
    [Google Scholar]
  55. ThomeerJ.H.M.1960. Introduction of a pore geometrical factor defined by the capillary pressure curve. Journal of Petroleum Technology12, 73–77.
    [Google Scholar]
  56. TurcotteD.D.L.1997. Fractals and Chaos in Geology and Geophysics. Cambridge University Press.
    [Google Scholar]
  57. WatsonJ.1911. British and Foreign Building Stones: A Descriptive Catalogue of the Specimens in the Sedgwick Museum. Cambridge University Press, Cambridge, UK.
    [Google Scholar]
  58. VegaS. and JouiniM.S.S.2015. 2D multifractal analysis and porosity scaling estimation in Lower Cretaceous carbonates. Geophysics80, D575–D586.
    [Google Scholar]
  59. VossR.F.1988. Fractals in nature: from characterization to simulation. The Science of Fractal Images (eds H.O.Peitgen and D.Saupe), pp. 21–70. Springer, New York, NY.
    [Google Scholar]
  60. XieS., ChengQ., LingQ., LiB., BaoZ. and FanP.2010. Fractal and multifractal analysis of carbonate pore‐scale digital images of petroleum reservoirs. Marine and Petroleum Geology27, 476–485.
    [Google Scholar]
  61. XinN., ChangchunZ., ZhenhuaL., XiaohongM. and XinghuaQ.2016. Numerical simulation of the electrical properties of shale gas reservoir rock based on digital core. Journal of Geophysics and Engineering13, 481.
    [Google Scholar]
  62. ZhangZ. and WellerA.2014. Fractal dimension of pore‐space geometry of an Eocene sandstone formation. Geophysics79, D377–D387.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12681
Loading
/content/journals/10.1111/1365-2478.12681
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): 3D Digital Images; 3D Multi‐fractal; Heterogeneity evaluation

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error