Top

Hydrogeology Journal

Published in:

01-04-2006 | Paper

Scale-dependent hydraulic conductivity in anisotropic media from dimensional cross-over

Author: A. G. Hunt

Published in: Hydrogeology Journal | Issue 4/2006

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A cross-over from 1D conduction to 3D conduction with increasing scale is shown to account for the kind of scale-dependent hydraulic conductivity sometimes observed in anisotropic systems. The cross-over is investigated in the context of the application of continuum percolation theory to a random fractal model. The dimensional cross-over is defined in terms of a comparison between the correlation length from percolation theory and the system dimensions.

previous article Geomechanical model for fracture deformation under hydraulic, mechanical and thermal loads

next article Estimation of land subsidence caused by loss of smectite-interlayer water in shallow aquifer systems

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Ambegaokar VN, Halperin BI, Langer JS (1971) Hopping conductivity in disordered systems. Phys Rev B 4:2612CrossRef

Banavar JR, Johnson DL (1987) Characteristic pore sizes and transport in porous media. Phys Rev B 35:7283–7286CrossRef

Bernabe Y, Bruderer C (1998) Effect of the variance of pore size distribution on the transport properties of heterogeneous networks. J Geophys Res 103:513 CrossRef

Bernabe Y, Bruderer-Weng C, Maineult A (2003) Permeability fluctuations in heterogeneous networks with different dimensionality and topology. J Geophys Res (in press)

Bittelli M, Campbell GS, Flury M (1999) Characterization of particle-size distribution in soils with a fragmentation model. Soil Sci Soc Am J 63:782–788CrossRef

Brace WF (1984) Permeability of crystalline rocks: new in situ measurements. J Geophy Res 89:4327–4330CrossRef

Bradbury KR, Muldoon MA (1990) Hydraulic conductivity determinations in unlithified glacial and fluvial materials. In: Nielson DM, Johnson AI (eds) Ground water and vadose zone monitoring, ASTM STP 1053, pp 138–151

Butler JJ, Healey JM (1998) Relationship between pumping-test and slug-test parameters: scale effect or artifact? Ground Water 36:305–313CrossRef

Chen G, Illman WA, Thompson DL, Vesselinov VV, Neuman SP (2000) Geostatistical, type curve and inverse analyses of pneumatic injection tests in unsaturated fractured tufs at the pache Leap Research Site near Superior Arizona. In: Faybishenko B et al. (eds) Dynamics of fluids in fractured rocks. Geophys Monogr 122, AGU, Washington, DC, pp 73–98

Davy P, Bour O, Darcel C, De Dreuzy J (2002) Permeability of 2D multi-scale fracture networks, Eos, Trans. AGU Abstract H71B-0822, 83(47)

Di Federico V, Neuman SP (1997) Scaling of random fields by means of truncated power variograms and associated spectra. Water Resour Res 33:1075–1085CrossRef

Di Federico V, Neuman SP (1998) Flow in multiscale log conductivity fields with truncated power variograms. Water Resour Res 34:975–987CrossRef

Di Federico V, Neuman SP, Tartakovsky DM (1999) Anisotropy, lacunarity, and upscaled conductivity and its autocovariance in multiscale random fields with truncated power variograms. Water Resour Res 35:2891–2908CrossRef

Friedman L, Pollak M (1981) The Hall effect in the variable-range hopping system. Philos Mag B44:487–507CrossRef

Friedman SP, Seaton NA (1998) Critical path analysis of the relationship between permeability and electrical conductivity of three-dimensional pore networks. Water Resour Res 34:1703CrossRef

Hunt AG (1998) Upscaling in subsurface transport using cluster statistics of percolation theory. Trans Por Med 30:177–198CrossRef

Hunt AG (2001a) Applications of percolation theory to porous media with distributed local conductances. Adv Water Resour 24:279–307CrossRef

Hunt AG (2001b) AC hopping conduction: perspective from percolation theory. Phi Mag B, 81:875–913

Hunt AG, Gee GW (2002a) Applications of critical path analysis to fractal porous media: Comparison with examples from the DOE Hanford Site. Adv Water Resour 25:129–146CrossRef

Hunt AG, Gee GW (2002b) Water-retention of fractal soil models using continuum percolation theory: tests of Hanford Site soils. Vadose Zone J 1:252–260CrossRef

Hunt AG (2003) Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity. Adv Water Resour 26:71–77CrossRef

Hyun Y, Neuman SP, Vesselinov VV, Illman WA, Tartakovsky DM, DiFederico V (2002) Theoretical interpretation of a pronounced permeability scale-effect in unsaturated fractured tuff. Water Resour Res (in press)

Ioannidis MA, Chatzis I (1993) The effect of spatial correlations on the accessibility characteristics of three-dimensional cubic networks as related to drainage displacements in porous media. Water Resour Res 27:1777CrossRef

Katz AJ, Thompson AH (1986) Quantitative prediction of permeability in porous rock. Phys Rev B34:79–81CrossRef

Kirkpatrick S (1973) Hopping conduction: experiment versus theory. In: Stuke J, Brenig W (eds) Proceedings of the Fifth Annual Conference on Amorphous and Liquid Semiconductors, Taylor & Francis, London, pp 103–107

Le Doussal P (1989) Permeability versus conductivity for porous media with wide distribution of pore sizes. Phys Rev B39:4816–4819CrossRef

Lee J-Y, Lee K-K (1999) Analysis of the quality of parameter estimates from repeated pumping and slug tests in a fractured porous aquifer system in Wonju, Korea. Ground Water 37:692–700CrossRef

Martinez-Landa L, Carrera J, Guimera J, Vasquez-Suñe E, Vives L, Meier P (2000) Methodology for the hydraulic characterization of a granitic block. In: Stauffer F, Kinzelbach W, Kovar K, Hoem E (eds) Calibration and reliability in groundwater modeling: coping with uncertainty, ModelCARE 99. IAHS Publication 265, IAHS Press, Wallingford, Oxfordshire, UK, pp 340–345

Matheron G (1967) Elements pur une theorie des milieux poreux [Elements of the theory of porous media] Masson, Paris

Moreno L, Tsang CF (1994) Flow channeling in strongly heterogeneous porous media: a numerical study. Water Resour Res 30:1421CrossRef

Paleologos EK, Neuman SP, Tartakovsky DM (1996) Effective hydraulic conductivity of bounded strongly heterogeneous porous media. Water Resour Res 32:1333–1341CrossRef

Pollak M (1972) A percolation treatment of dc hopping conduction. J Non-Cryst Solids 11:1–24CrossRef

Prakash S, Havlin S, Schwartz M, Stanley HE (1992) Structural and dynamical properties of long-range correlated percolation. Phys Rev B 46:R1724.

Raikh ME, Ruzin IP (1990) Size effect of the longitudinal hopping conduction of a narrow 2-dimensional channel. Phys Rev B 42:11203–11207CrossRef

Rieu M, Sposito G (1991) Fractal fragmentation, soil porosity, and soil water properties I. Theory. Soil Sci Soc Am J 55:1231CrossRef

Rovey II CW, Cherkauer DS (1995) Scale dependency of hydraulic conductivity measurements. Ground Water 33:769–780CrossRef

Sahimi M (1993) Flow phenomena in rocks—from continuum models to fractals, percolation, cellular automata, and simulated annealing. Rev Mod Phys 65:1393–1534CrossRef

Samper-Calvete FJ, Garcia-Vera MA (1998) Inverse modeling of groundwater flow in the semiarid evaporitic closed basin of Los Monegros, Spain. Hydrogeol J 6:33–49CrossRef

Sanchez-Villa X, Carrera J, Girardi JP (1996) Scale effects in transmissivity. J Hydrol 183:1–22CrossRef

Schad H, Teutsch G (1994) Effects of the investigation scale on pumping test results in heterogeneous porous aquifers. J Hydrol 159:61–77CrossRef

Schulze-Makuch D (1996) Ph.D. dissertation, Facies dependent scale behavior of hydraulic conductivity and longitudinal dispersivity in the carbonate aquifer of Southeastern Wisconsin, University of Wisconsin, Milwaukee

Schulze-Makuch D, Carlson DA, Cherkauer DS, Malik P (1999) Scale dependency of hydraulic conductivity in heterogeneous media. Ground Water 37:904–919CrossRef

Schulze-Makuch D, Cherkauer DS (1998) Variations in hydraulic conductivity with scale of measurement during aquifer tests in heterogeneous, porous, carbonate rocks. Hydrogeol J 6:204–215CrossRef

Seager CH, Pike GE (1974) Percolation and conductivity: a computer study. II. Phys Rev B10:1435–1446CrossRef

Shah CB, Yortsos YC (1996) The permeability of strongly disordered systems. Phys Fluids 8:280–282CrossRef

Shklovskii BI, Efros AL (1984) Electronic properties of doped semiconductors. Springer, Berlin Heidelberg New York

Shouse PJ, Ellsworth TR, Jobes JA (1994) Steady-state infiltration as a function of measurement scale. Soil Sci 157:129–136CrossRef

Stauffer D (1979) Scaling theory of percolation clusters. Phys Rep 54:1–74CrossRef

Stauffer D, Aharony A (1994) Introduction to percolation theory, 2nd edn. Taylor & Francis

Tartakovsky DM, Neuman SP (1998) Transient effective hydraulic conductivity under slowly and rapidly varying mean gradients in bounded three-dimensional random media. Water Resour Res 34:21–32CrossRef

Tidwell VC, Wilson JL (1997) Laboratory method for investigating permeability upscaling. Water Resour Res 33:1067–1616CrossRef

Tidwell VC, Wilson JL (2000) Heterogeneity, permeability patterns, and permeability upscaling: physical characterization of a block of Massillon sandstone exhibiting nested scales of heterogeneity. SPE Reserv Eval Engin 3:283–291

Vyssotsky VA, Gordon SB, Frisch HL, Hammersley JM (1961) Critical percolation probabilities (bond problem). Phys Rev 123:1566–1567CrossRef

Zhang D, Zhang R, Chen S, Soll WE (2000) Pore scale study of flow in porous media: scale dependency, REV, and statistical REV. Geophys Res Lett 27:1195–1198CrossRef

Zlotnik VA Zurbuchen BR Ptak T, Teutsch G (2000) Support volume and scale effect in hydraulic conductivity: experimental aspects. In: Zhang D, Winter CL (eds) Theory modeling, and field investigation in hydrogeology: a special volume in honor of Shlomo P. Neuman’s 60th birthday. Geol Soc Am Spec Pap 348, Boulder, Colorado, pp 191–213

Title: Scale-dependent hydraulic conductivity in anisotropic media from dimensional cross-over
Author: A. G. Hunt
Publication date: 01-04-2006
Publisher: Springer-Verlag
Published in: Hydrogeology Journal / Issue 4/2006
Print ISSN: 1431-2174
Electronic ISSN: 1435-0157
DOI: https://doi.org/10.1007/s10040-005-0453-6

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 4/2006

Occurrence of salt water above fresh water in dynamic equilibrium in a coastal groundwater flow system near De Panne, Belgium

Effects of fracture lineaments and in-situ rock stresses on groundwater flow in hard rocks: a case study from Sunnfjord, western Norway

Subsurface dams to harvest rainwater— a case study of the Swarnamukhi River basin, Southern India

Estimation of land subsidence caused by loss of smectite-interlayer water in shallow aquifer systems

Determination of specific yield using a water balance approach – case study of Torla Odha watershed in the Deccan Trap province, Maharastra State, India

Dynamics and interaction of organic carbon, turbidity and bacteria in a karst aquifer system