Skip to main content
SpringerLink
Log in

Tracer transport in a fractured chalk: X-ray CT characterization and digital-image-based (DIB) simulation

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

Abstract

A digital-image-based simulation methodology is applied to evaluate the influence of heterogeneous porosity on the evolution of tracer concentrations in imaged tracer tests. Maps of computed tomography (CT)-number are calibrated relative to average porosity, and then thresholded to define porosity maps. These data are then used to automate the distribution of parameters within a finite element representation of the geometry. The technique is applied to characterize the variability of the porosity, the hydraulic conductivity, and the diffusivity for an artificially fractured chalk core (30 × 5 cm). X-ray CT was used both to characterize the initial condition of the core, and then to concurrently monitor the transport of an NaI tracer within the fracture and into the surrounding matrix. The X-ray CT imaging is used to characterize the heterogeneous rock porosity, based on which the hydraulic conductivity, and diffusivity of the chalk were defined and were directly imported into our newly developed three-dimensional FEMLAB-based multiple physics simulator. Numerical simulations have confirmed the observed tracer transport behaviors: (1) The different tracer-penetration distances imaged in the matrix above and below the horizontal fracture are indicative of a greater tracer mass penetrating into the lower matrix; and (2) Transport in the matrix below the fracture was enhanced. The computer simulated tracer concentration distributions compare favorably with those monitored by X-ray CT.

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

Abbreviations

C :

Concentration in terms of mass fraction (dimensionless)

D :

Diffusion coefficient (m2/s)

f k (i,j ):

Discrete function to express the digital image in RGB color space, where k = 1, 2, and 3 (dimensionless)

g :

Gravity acceleration (vector) (m/s2)

H, S, I :

Hue, saturation and intensity for HSI color space of the digital image (dimensionless)

k :

Permeability (m2)

M,N :

Number of pixels in horizontal and vertical directions for a digital image (dimensionless)

P :

Fluid pressure (Pa)

R, G, B :

Red, green, and blue components for RGB color space of digital image (dimensionless)

S s :

The specific storativity of the porous medium (1/m)

t :

Time (s)

u l(u l i ):

Pore velocity vector of fluid (m/s)

ϕ:

Porosity (dimensionless)

μ l :

Liquid dynamic viscosity (Pa·s)

ρ l :

Liquid density (kg/m3)

References

  • Blair S.C. and Cook N.G.W. (1998). Analysis of compressive fracture in rock statistical techniques: Part I: a non-linear rule-based model. Int. J. Rock. Mech. Min. Sci., 35: 837–848

    Article  Google Scholar 

  • Carman P.C. (1938). Fluid flow through granular beds. J. Soc. Chem. Ind., 57: 225

    Google Scholar 

  • Chen S., Yue Z.Q. and Tham L.G. (2004). Digital image-based numerical modelling method for prediction of inhomogeneous rock failure. Int. J. Rock. Mech. Min. Sci., 41: 939–957

    Article  Google Scholar 

  • Chermant J.L. (2001). Why automatic image analysis? An introduction to this issue. Cement Concrete Comp. 23: 157–169

    Article  Google Scholar 

  • Daïan, J.-F., Fernandes, C.P., Philippi, P.C., Bellini da Cunha Neto, J.A.: 3D reconstitution of porous media from image processing data using a multiscale percolation system. J Petrol. Sci. Eng. 42, 15–28 (2004)

  • Diabira I., Castanier L.M. and Kovscek A.R. (2001). Porosity and permeability evolution accompanying hot fluid injection into diatomite. Petrol. Sci. Technol., 19(9–10): 1167–1185

    Article  Google Scholar 

  • Finsterle S., Fabryka-Martin J.T. and Wang J.S.Y. (2002). Migration of a water pulse through fractured porous media. J. Contam. Hydrol., 54: 37–57

    Article  Google Scholar 

  • Gonzalez, R.C., Woods, R.F.: Digital Image Processing. Addison Wesley, Reading, MA (1992)

  • Hadjigeorgiou J., Lemy F., Cote P. and Maldague X. (2003). An evaluation of image analysis algorithms for constructing discontinuity trace maps. Rock. Mech. Rock. Eng., 36(2): 163–179

    Article  Google Scholar 

  • Hirono T., Takahashi M. and Nakashima S. (2003). In situ visualization of fluid flow image within deformed rock by X-ray CT. Eng. Geol., 70: 37–46

    Article  Google Scholar 

  • Karacan C.O. and Mitchell G.D. (2003). Behavior and effect of different coal microlithotypes during gas transport for carbon dioxide sequestration into coal seams. Int. J. Coal. Geol., 53: 201–217

    Article  Google Scholar 

  • Koh, C.J., Dagenais, P.C., Larson, D.C., Murer, A.S.: Permeability damage in diatomite due to in-situ silica dissolution/precipitation. SPE 35394. In: Proceedings of The SPE/DOE 10th Symposium on improved Oil Recovery, Tulsa, OK, 21–24 April, (1996)

  • Kozeny J. (1927). Sitzungsber. Akad. Wiss. Wien. Math.-Naturwiss. Kl., 136: 271

    Google Scholar 

  • Montemagno C.D. and Pyrak-Nolte L.J. (1999). Fracture network versus single fractures: Measurement of fracture geometry with X-ray tomography. Phys. Chem. Earth. (A), 24(7): 575–579

    Article  Google Scholar 

  • Nakashima Y. (2000). The use of X-ray CT to measure diffusion coefficients of heavy ions in water-saturated porous media. Eng. Geol., 56: 11–17

    Article  Google Scholar 

  • Nakashima S. (1995). Diffusivity of ions in pore water as a quantitative basis for rock deformation rate estimates. Tectonophysics 245: 185–203

    Article  Google Scholar 

  • Nativ R., Adar E. and Becker A. (1999). A monitoring network for groundwater in fractured media. Ground Water 37: 38–47

    Article  Google Scholar 

  • Nguyen Q.P., Currie P.K., Zitha P.L.J.: Effect of cross-flow on foam-induced diversion in layered formations. Soc. Petrol. Eng. J. (2005)

  • Nguyen Q.P., Currie, P.K., Zitha, P.L.J.: Determination of Foam Induced Fluid Partitioning in Porous Media using X-ray Computed Tomography, SPE 80245, SPE International Symposium on Oilfield Chemistry. Houston, TX, USA, 5–8 February (2003)

  • Polak A., Grader A.S., Wallach R. and Nativ R. (2003). Tracer diffusion from a horizontal fracture into the surrounding matrix: measurement by computer tomography. J. Contam. Hydrol., 67: 95–112

    Article  Google Scholar 

  • Qi, X.Z., Zhao, J., Xiao, C.W., Liu, R.L.: A study on the quantitative processing methods of image data. In: Proceedings of SPE International Oil and Gas Conference and Exhibition. SPE 64626, pp. 7–11. Beijing, China (2000)

  • Santos L.O.E., Philippi P.C., Damiani M.C. and Fernandes C.P. (2002). Using three-dimensional reconstructed microstructures for predicting intrinsic permeability of reservoir rocks based on a Boolean lattice gas method. J. Petrol. Sci. Eng., 35: 109–124

    Article  Google Scholar 

  • Scavia F.R. (1999). Determination of contact areas in rock joints by X-ray computer tomography. Int. J. Rock. Mech. Min. Sci., 36: 883–890

    Article  Google Scholar 

  • Schembre J.M. and Kovscek A.R. (2003). A technique for measuring two-phase relative permeability in porous media via X-ray CT measurements. J. Petrol. Sci. Eng., 39: 159–174

    Article  Google Scholar 

  • Takano N., Zako M., Kubo F. and Kimura K. (2003). Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling. Int. J. Solids Struct., 40: 1225–1242

    Article  Google Scholar 

  • Tang C.A. (1997). Numerical simulation of progressive rock failure and associated seismicity. Int. J. Rock. Mech. Min. Sci., 34: 249–261

    Article  Google Scholar 

  • Tang C.A., Liu H., Lee P.K.K., Tsui Y. and Tham L.G. (2000). Numerical tests on micro–macro relationship of rock failure under uniaxial compression, part I: effect of heterogeneity. Int. J. Rock. Mech. Min. Sci., 37: 555–569

    Article  Google Scholar 

  • Tham L.G., Li L., Tsui Y. and Lee PKK. (2003). A replica method for observing microcracks on rock surface. Int. J. Rock. Mech. Min. Sci., 40: 785–794

    Article  Google Scholar 

  • Tidwell V.C., Meigs L.C., Christian-Frear T. and Boney C.M. (2000). Effects of spatially heterogeneity porosity on matrix diffusion as investigated by X-ray absorption imaging. J. Contam Hydrol., 42: 285–302

    Article  Google Scholar 

  • Vinegar, H.J., Wellington, S.L.: Tomographic imaging of three-phase flow experiments. Rev. Sci. Inst., 96–107 (1987)

  • Vukuturi, V.S., Lama, R.D., Saluja, S.S.: Handbook on Mechanics Properties of Rocks, vol. 1. Trans. Tech. Publications, Switzerland (1974)

  • Wildenschild D., Hopmans J.W., Vaz C.M.P., Rivers M.L., Rikard D. and Christensen B.S.B. (2002). Using X-ray computed tomography in hydrology: systems resolutions and limitations. J. Hydrol., 267: 285–297

    Article  Google Scholar 

  • Withjack, E.M., Durham, J.R.: Characterization and saturation determination of reservoir metagraywacke from the Geysers corehole SB-15-D (USA), using nuclear magnetic resonance spectrometry and X-ray computed tomography. Geothermics 30, 255–268 (2001)

    Google Scholar 

  • Yue Z.Q., Chen S. and Tham L.G. (2003). Finite element modeling of geomaterials using digital image processing. Comput. Geotech., 30: 375–397

    Article  Google Scholar 

  • Zhu W.C. and Tang C.A. (2004). Micromechanical model for simulating the fracture process of rock. Rock Mech. Rock. Eng., 37(1): 25–56

    Article  Google Scholar 

  • Zitha, P.L.J., Nguyen Q.P., Currie, P.K.: Effect of Flow Velocity and Rock Layering on Foam Flow: an X-ray Computed Tomography Study, SPE 80530, SPE Asia Pacific Oil and Gas Conference and Exhibition held in Jakarta, Indonesia, 15–17 April (2003)

Download references

Author information

Authors and Affiliations

  1. School of Oil and Gas Engineering, The University of Western Australia, WA, 6009, Crawley, Australia

    W. C. Zhu, J. Liu, J. C. Sheng & J. X. Liu

  2. Department of Energy and Geo-Environmental Engineering, Penn State University, University Park, USA

    D. Elsworth & A. Grader

  3. Department of Civil and Environmental Engineering, Technion, Israel Institute of Technology, Haifa, 32000, Israel

    A. Polak

Authors
  1. W. C. Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Elsworth
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Polak
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Grader
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. C. Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. J. X. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, W.C., Liu, J., Elsworth, D. et al. Tracer transport in a fractured chalk: X-ray CT characterization and digital-image-based (DIB) simulation. Transp Porous Med 70, 25–42 (2007). https://doi.org/10.1007/s11242-006-9080-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-006-9080-5

Keywords

Search

Navigation