Exact Averaging of Stochastic Equations for Flow in Porous Media Metadata

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  • Main Title Exact Averaging of Stochastic Equations for Flow in Porous Media


  • Author: Karasaki, Kenzi
    Creator Type: Personal
  • Author: Shvidler, Mark
    Creator Type: Personal
  • Author: Karasaki, Kenzi
    Creator Type: Personal


  • Sponsor: Lawrence Berkeley National Laboratory. Earth Sciences Division.
    Contributor Type: Organization


  • Name: Lawrence Berkeley National Laboratory
    Place of Publication: Berkeley, California
    Additional Info: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (United States)


  • Creation: 2008-03-15


  • English


  • Content Description: It is well known that at present, exact averaging of the equations for flow and transport in random porous media have been proposed for limited special fields. Moreover, approximate averaging methods--for example, the convergence behavior and the accuracy of truncated perturbation series--are not well studied, and in addition, calculation of high-order perturbations is very complicated. These problems have for a long time stimulated attempts to find the answer to the question: Are there in existence some, exact, and sufficiently general forms of averaged equations? Here, we present an approach for finding the general exactly averaged system of basic equations for steady flow with sources in unbounded stochastically homogeneous fields. We do this by using (1) the existence and some general properties of Green's functions for the appropriate stochastic problem, and (2) some information about the random field of conductivity. This approach enables us to find the form of the averaged equations without directly solving the stochastic equations or using the usual assumption regarding any small parameters. In the common case of a stochastically homogeneous conductivity field we present the exactly averaged new basic nonlocal equation with a unique kernel-vector. We show that in the case of some type of global symmetry (isotropy, transversal isotropy, or orthotropy), we can for three-dimensional and two-dimensional flow in the same way derive the exact averaged nonlocal equations with a unique kernel-tensor. When global symmetry does not exist, the nonlocal equation with a kernel-tensor involves complications and leads to an ill-posed problem.


  • STI Subject Categories: 58
  • Keyword: Symmetry
  • STI Subject Categories: 54
  • Keyword: Isotropy
  • Keyword: Steady Flow
  • Keyword: Transport
  • Keyword: Accuracy
  • Keyword: Convergence


  • Journal Name: Transport in Porous Media; Journal Volume: 72; Journal Issue: 3; Related Information: Journal Publication Date: 2008


  • Name: Office of Scientific & Technical Information Technical Reports
    Code: OSTI


  • Name: UNT Libraries Government Documents Department
    Code: UNTGD

Resource Type

  • Article


  • Text


  • Report No.: LBNL-764E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 935420
  • Archival Resource Key: ark:/67531/metadc895182