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Title: A stochastic multiscale framework for modeling flow through random heterogeneous porous media

Abstract

Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.

Authors:
 [1]
  1. Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States)
Publication Date:
OSTI Identifier:
21167747
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 228; Journal Issue: 2; Other Information: DOI: 10.1016/j.jcp.2008.10.006; PII: S0021-9991(08)00532-9; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; FINITE ELEMENT METHOD; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; PERMEABILITY; POROUS MATERIALS; RADIOACTIVE WASTE DISPOSAL; RANDOMNESS; SIMULATION; STOCHASTIC PROCESSES; VARIATIONAL METHODS

Citation Formats

Ganapathysubramanian, B, and Zabaras, N. A stochastic multiscale framework for modeling flow through random heterogeneous porous media. United States: N. p., 2009. Web. doi:10.1016/j.jcp.2008.10.006.
Ganapathysubramanian, B, & Zabaras, N. A stochastic multiscale framework for modeling flow through random heterogeneous porous media. United States. https://doi.org/10.1016/j.jcp.2008.10.006
Ganapathysubramanian, B, and Zabaras, N. Sun . "A stochastic multiscale framework for modeling flow through random heterogeneous porous media". United States. https://doi.org/10.1016/j.jcp.2008.10.006.
@article{osti_21167747,
title = {A stochastic multiscale framework for modeling flow through random heterogeneous porous media},
author = {Ganapathysubramanian, B and Zabaras, N.},
abstractNote = {Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.},
doi = {10.1016/j.jcp.2008.10.006},
url = {https://www.osti.gov/biblio/21167747}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 2,
volume = 228,
place = {United States},
year = {2009},
month = {2}
}