Transport in Porous Media

, Volume 30, Issue 1, pp 75–86 | Cite as

Non-Newtonian Flow in a Variable Aperture Fracture

  • Vittorio Di Federico


The transmissivity of a variable aperture fracture for flow of a non-Newtonian, purely viscous power-law fluid with behavior index n is studied. The natural logarithm of the fracture aperture is considered to be a two-dimensional, spatially homogeneous and correlated Gaussian random field. We derive an equivalent fracture aperture for three flow geometries: (1) flow perpendicular to aperture variation; (2) flow parallel to aperture variation; (3) flow in an isotropic aperture field. Under ergodicity, results are obtained for cases 1 and 2 by discretizing the fracture into elements of equal aperture and assuming that the resistances due to each aperture element are, respectively, in parallel and in series; for case 3, the equivalent aperture is derived as the geometric mean of cases 1 and 2. When n=1 all our expressions for the equivalent aperture reduce to those derived in the past for Newtonian flow and lognormal aperture distribution. As log-aperture variance increases, the equivalent aperture is found to increase for case 1, to decrease for case 2, and to be a function of flow behavior index n for case 3.

fracture aperture heterogeneity non-Newtonian power-law fluid groundwater transmissivity nonlinear seepage 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Vittorio Di Federico
    • 1
  1. 1.DISTART, Idraulica, Universit di BolognaBolognaItaly

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