Skip to main content
SpringerLink
Log in
Book cover

Gas Transport in Porous Media pp 201–212Cite as

Scaling Issues in Porous and Fractured Media

  • Chapter

Part of the book series: Theory and Applications of Transport in Porous Media ((TATP,volume 20))

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ababou, R., D. McLaughlin, L.W. Gelhar, and A.F.G. Thompson, Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media, Transport in Porous Media, 4, 549–565, 1989.

    Article  Google Scholar 

  • Bachu, S. and D. Cuthiell, Effects of core-scale heterogeneity on steady state and transient fluid flow in porous media: Numerical analysis, Water Resour. Res., 26(5), 863–874, 1990.

    Article  Google Scholar 

  • Bakr, A.A., L.W. Gelhar, A.L. Gutjahr, and J.R. MacMillan, Stochastic analyses of spatial variability in subsurface flows, 1, Comparison of one- and three-dimensional flows, Water Resour. Res., 14(2), 263–272, 1978.

    Google Scholar 

  • Barton, C.C. and E. Larson, Fractal geometry of two-dimensional fracture networks at Yucca Mountain, Southwest Nevada, paper presented at the International Symposium on Fundamentals of Rock Joints, Swedish National Group of the International Society of Rock Mechanics, Bjorkliden, Sweden, September, 1985.

    Google Scholar 

  • Burrough, P.A., Multiscale sources of spatial variation in soil. I. The application of fractal concepts to nested levels of soil variation, Journal of Soil Science, 34, 577–597, 1983.

    Article  Google Scholar 

  • Chao, H.C., H. Rajaram, and T. Illangasekare, Intermediate-scale experiments and numerical simulations of transport under radial flow in a two-dimensional heterogeneous porous medium, Water Resour. Res., 36(10), 2869–2884, 2000.

    Article  Google Scholar 

  • Dagan, G., Time-dependent macrodispersion of solute transport in anisotropic heterogeneous aquifers, Water Resour. Res., 24(9), 1491–1500, 1988.

    Google Scholar 

  • Dagan, G., Solute transport in heterogeneous porous formations, J. Fluid Mech., 145, 151–177, 1984.

    Article  MATH  Google Scholar 

  • Desbarats, A.J., Spatial averaging of transmissivity in heterogeneous fields with flow toward a well, Water Resour. Res., 28(3), 757–767, 1992a.

    Article  Google Scholar 

  • Desbarats, A.J., Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media, Math. Geol., 24(3), 249–267, 1992b.

    Article  Google Scholar 

  • Desbarats, A.J., Numerical estimation of effective permeability in sand-shale formations, Water Resour. Res., 23(2), 273–286, 1987.

    Google Scholar 

  • Deutsch, C.V., Calculating effective absolute permeability in sandstone/shale sequences, SPE Form. Eval., 4(3), 343–348, 1989.

    MathSciNet  Google Scholar 

  • Eggleston, J. and S. Rojstaczer, Identification of large-scale hydraulic conductivity trends and the influence of trends on contaminant transport, Water Resour. Res., 34(9), 2155–2168, 1998.

    Article  Google Scholar 

  • Fogg, G.E., Groundwater flow and sand body interconnectedness in a thick, multiple-aquifer system, Water Resour. Res., 22(5), 679–694, 1986.

    Google Scholar 

  • Freyberg, D.L., A natural gradient experiment on solute transport in a sand aquifer, 2, Spatial moments and the advection and dispersion of nonreactive tracers, Water Resour. Res., 22(13), 2031–2046, 1986.

    Google Scholar 

  • Garabedian, S.P., Large-scale dispersive transport in aquifers: Field experiments and reactive transport theory, Ph.D. thesis, Dept. Civil Eng., Massachusetts Inst. Techn., Cambridge, Massachusetts, 290 pp., 1987.

    Google Scholar 

  • Gelhar, L.W., and C.L. Axness, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19(1), 161–180, 1983.

    Google Scholar 

  • Gelhar, L.W., C. Welty, and K.R. Rehfeldt, A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28(7), 1955–1974, 1992.

    Article  Google Scholar 

  • Gelhar, L.W., Stochastic Subsurface Hydrology, Prentice Hall, Englewood Cliffs, New Jersey, p. 390, 1993.

    Google Scholar 

  • Gomez-Hernandez, J.J. and A.G. Journel, Stochastic characterization of grid-block permeabilities, Stanford Center for Reservoir Forecasting, Reprt 7, Stanford, CA, p. 21 1994.

    Google Scholar 

  • Gutjahr, A.L., L.W. Gelhar, A.A. Bakr, and J.R. Macmillan, Stochastic analysis of spatial variability in subsurface flows, 2. Evaluation and application, Water Resour. Res., 14(5), 953–960, 1978.

    Google Scholar 

  • Haggerty, R., S.W. Fleming, L.C. Meigs, and S.A. McKenna, Tracer tests in a fractured dolomite 2. Analysis of mass transfer in single-well injection-withdrawal tests, Water Resour. Res., 37(5), 1129–1143, 2001.

    Article  Google Scholar 

  • Henriette, A., C.G. Jacquin, and P.M. Adler, The effective permeability of heterogeneous porous media, PCH PhysicoChemical Hydrodynamics, 11(1), 61–80, 1989.

    Google Scholar 

  • Hess, K.M., S.H. Wolf, M.A. Celia, and S.P. Garabedian, Macrodispersion and spatial variability of hydraulic conductivity in a sand and gravel aquifer, Cape Cod, Massachusetts, EPA/600/M-91/005, Environmental Research Brief, Environmental Protection Agency, Ada, OK, 1991.

    Google Scholar 

  • Hewett, T.A., Fractal distributions of reservoir heterogeneity and their influence on fluid transport, paper SPE 15386 presented at the 1986 Annual Technical Conference and Exhibition, New Orleans, La., 5–8 Oct, 1986.

    Google Scholar 

  • Indelman, P. and B. Abramovich, Nonlocal properties of nonuniform averaged flows in heterogeneous media, Water Resour. Res., 30(12), 3385–3393, 1994.

    Article  Google Scholar 

  • Journel, A.G., C.V. Deutsch, and A.J. Desbarats, Power Averaging for Block Effective Permeability, SPE 15128, in Proceeding of the 56th Annual California Regional Meeting of the Society of Petroleum Engineers, Oakland, 329–334, 1986.

    Google Scholar 

  • Katz, A.J. and A.H. Thompson, Fractal sandstone pores: Implications for conductivity and pore formation, Physical Review Letters, 54, 1325–1328, 1985.

    Article  Google Scholar 

  • Koltermann C.E. and S.M. Gorelick, Heterogeneity in sedimentary deposits: A review of structure-imitating, process-imitating, and descriptive approaches, Water Resour. Res., 32(9), 2617–2658, 1996.

    Article  Google Scholar 

  • Kossack, C.A., J.O. Aasen, and S.T. Opdal, Scaling up heterogeneities with pseudofunctions, SPEFE, 226–232, 1990.

    Google Scholar 

  • Lasseter, T.J., J.R. Waggoner, and L.W. Lake, Reservoir heterogeneities and their influence on ultimate recovery, in Reservoir Characterization, ed. by L.W. Lake and H.B. Carroll, Jr., Academic Press, New York, 545–560, 1986.

    Google Scholar 

  • Liu, H.H. and F.J. Molz, Multifractal analyses of hydraulic conductivity distributions, Water Resour. Res., 33(11), 2483–2488, 1997.

    Article  Google Scholar 

  • Matheron, G., Elements pour une theorie des milieux poreux, 166 pp., Maisson et Cie, Paris, 1967.

    Google Scholar 

  • Moltyaner, G.L. and R.W.D. Killey, Twin Lake tracer tests: Longitudinal dispersion, Water Resour. Res., 24(10), 1613–1627, 1988a.

    Google Scholar 

  • Moltyaner, G.L. and R.W.D. Killey, Twin Lake tracer tests: Transverse dispersion, Water Resour. Res., 24(10), 1628–1637, 1988b.

    Google Scholar 

  • Neuman, S. P., Generalized scaling of permeabilities: Validation and effect of support scale, Geophys. Res. Lett., 21(5), 349–353, 1994.

    Article  MathSciNet  Google Scholar 

  • Neuman, S.P., Universal scaling of hydraulic conductivities and dispersivities in geologic media, Water Resour. Res., 26(8), 1749–1758, 1990.

    Article  MathSciNet  Google Scholar 

  • Neuman, S.P. and Y.-K. Zhang, A quasi-linear theory of non-Fickian and Fickian subsurface dispersion, 1, Theoretical analysis with application to isotropic media, Water Resour. Res., 26(5), 887–902, 1990.

    Article  Google Scholar 

  • Parker, J.C., and K.A. Albrecht, Sample volume effects on solute transport predictions, Water Resour. Res., 23(12), 2293–2301, 1987.

    Google Scholar 

  • Spoval, B., M. Rosso, and J.F. Bouyet, The Fractal nature of a Diffusing front and the relation to percolation, Journal of Physics Letters, 46, L149-L156, 1985.

    Google Scholar 

  • Sudicky, E.A., A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process, Water Resour. Res., 22(13), 2069–2081, 1986.

    Article  Google Scholar 

  • Tidwell, V.C. and J.L. Wilson, Laboratory method for investigating permeability upscaling, Water Resour. Res., 33(7), 1607–1616, 1997.

    Article  Google Scholar 

  • Tidwell, V.C. and J.L. Wilson, Permeability upscaling measured on a block of Berea Sandstone: Results and interpretation, Math. Geol., 31(7), 749–769, 1999a.

    Article  Google Scholar 

  • Tidwell, V.C., and J.L. Wilson, Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution, Water Resour. Res., 35(11), 3375–3387, 1999b.

    Article  Google Scholar 

  • Tidwell, V.C. and J.L. Wilson, Heterogeneity, permeability patterns, and permeability upscaling: Physical characterization of a block of Massillon Sandstone exhibiting nested scales of heterogeneity, SPE Reservoir Eval. & Eng., 3(4), 283–291, 2000.

    Google Scholar 

  • Tidwell, V.C., A.L. Gutjahr, and J.L. Wilson, What does an instrument measure? Empirical spatial weighting functions calculated from permeability data sets measured on multiple sample supports, Water Resour. Res., 35(1), 43–54, 1999.

    Article  Google Scholar 

  • Warren, J.E. and H.S. Price, Flow in heterogeneous porous media, SPE J., 1, 153–169, 1961.

    Google Scholar 

  • Wheatcraft, S.W. and S.W. Tyler, An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry, Water Resour. Res., 24(4), 566–578, 1988.

    Google Scholar 

  • Zheng, C. and J.J. Jiao, Numerical simulation of tracer tests in a heterogeneous aquifer, J. Environ, Eng., 124(6), 510–516, 1998.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sandia National Laboratories, P. O. Box 5800, MS 0735, Albuquerque, NM, 87185, USA

    Vincent C. Tidwell

Authors
  1. Vincent C. Tidwell
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Sandia National Laboratories, P. O. Box 5800, Albuquerque, NM, 87185, USA

    Clifford K. Ho  & Stephen W. Webb  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this chapter

Cite this chapter

Tidwell, V.C. (2006). Scaling Issues in Porous and Fractured Media. In: Ho, C.K., Webb, S.W. (eds) Gas Transport in Porous Media. Theory and Applications of Transport in Porous Media, vol 20. Springer, Dordrecht . https://doi.org/10.1007/1-4020-3962-X_11

Download citation

  • DOI: https://doi.org/10.1007/1-4020-3962-X_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-3961-4

  • Online ISBN: 978-1-4020-3962-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation