Exactly averaged stochastic equations for flow and transport in random media

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It is well known that exact averaging of the equations of flow and transport in random porous media are at present realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series are not well known. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms ... continued below

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Shvidler, Mark & Karasaki, Kenzi November 30, 2001.

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Description

It is well known that exact averaging of the equations of flow and transport in random porous media are at present realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series are not well known. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding some general forms of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2 ) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present some general forms of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure of non-local equations in a general case of stochastical ly homogeneous fields.

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OSTI as DE00799574

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  • International Groundwater Symposium: Bridging the Gap between Measurement and Modeling in Heterogeneous Media, Berkeley, CA (US), 03/25/2002--03/28/2002

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  • Report No.: LBNL--49529
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 799574
  • Archival Resource Key: ark:/67531/metadc741365

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  • November 30, 2001

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  • Oct. 19, 2015, 7:39 p.m.

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  • April 4, 2016, 3:14 p.m.

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Shvidler, Mark & Karasaki, Kenzi. Exactly averaged stochastic equations for flow and transport in random media, article, November 30, 2001; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc741365/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.