ISSN:
1573-1634
Keywords:
Effective permeability
;
heterogeneous media
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Technology
Notes:
Abstract Steady flow of an incompressible fluid takes place in a porous formation of spatially variable hydraulic conductivityK. The latter is regarded as a lognormal stationary random space function and Y=ln(K/K G ), whereK G is the geometric mean ofK, is characterized by its variance σ2 and correlation scale I. Exact results are known for the effective conductivityK eff in one- and two-dimensional flows. In contrast, only a first-order term in a perturbation expansion in σ2 has been derived exactly for the three-dimensional flow. A conjecture has been made in the past onK eff for any σ2, but it was not yet proved exactly. This study derived the exact nonlinear correction, i.e. the termO(σ4) ofK eff, which is found to be the one resulting from the conjecture, strengthening the confidence in it. It is also shown that the self-consistent approximation leads to the exact results for one-dimensional and two-dimensional flows, but underestimates the nonlinear correction ofK eff for in the three-dimensional case.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00624462
