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Title: Multiscale analysis and computation for flows in heterogeneous media

Abstract

Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence ofmore » uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics. Below, we present a brief overview of each of these contributions.« less

Authors:
 [1];  [2];  [3];  [3]
  1. Texas A & M Univ., College Station, TX (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  3. Stanford Univ., CA (United States)
Publication Date:
Research Org.:
Texas A & M Univ., College Station, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Contributing Org.:
California Institute of Technology, Stanford University
OSTI Identifier:
1282326
Report Number(s):
DE-TAMU-06ER25727
DOE Contract Number:
FG02-06ER25727
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; multiscale; computation; porous media

Citation Formats

Efendiev, Yalchin, Hou, T. Y., Durlofsky, L. J., and Tchelepi, H. Multiscale analysis and computation for flows in heterogeneous media. United States: N. p., 2016. Web. doi:10.2172/1282326.
Efendiev, Yalchin, Hou, T. Y., Durlofsky, L. J., & Tchelepi, H. Multiscale analysis and computation for flows in heterogeneous media. United States. doi:10.2172/1282326.
Efendiev, Yalchin, Hou, T. Y., Durlofsky, L. J., and Tchelepi, H. Thu . "Multiscale analysis and computation for flows in heterogeneous media". United States. doi:10.2172/1282326. https://www.osti.gov/servlets/purl/1282326.
@article{osti_1282326,
title = {Multiscale analysis and computation for flows in heterogeneous media},
author = {Efendiev, Yalchin and Hou, T. Y. and Durlofsky, L. J. and Tchelepi, H.},
abstractNote = {Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics. Below, we present a brief overview of each of these contributions.},
doi = {10.2172/1282326},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Aug 04 00:00:00 EDT 2016},
month = {Thu Aug 04 00:00:00 EDT 2016}
}

Technical Report:

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  • In this proposal, we have worked on Bayesian uncertainty quantification for predictions of fows in highly heterogeneous media. The research in this proposal is broad and includes: prior modeling for heterogeneous permeability fields; effective parametrization of heterogeneous spatial priors; efficient ensemble- level solution techniques; efficient multiscale approximation techniques; study of the regularity of complex posterior distribution and the error estimates due to parameter reduction; efficient sampling techniques; applications to multi-phase ow and transport. We list our publications below and describe some of our main research activities. Our multi-disciplinary team includes experts from the areas of multiscale modeling, multilevel solvers, Bayesianmore » statistics, spatial permeability modeling, and the application domain.« less
  • Multiscale modeling of stochastic systems, or uncertainty quantization of multiscale modeling is becoming an emerging research frontier, with rapidly growing engineering applications in nanotechnology, biotechnology, advanced materials, and geo-systems, etc. While tremendous efforts have been devoted to either stochastic methods or multiscale methods, little combined work had been done on integration of multiscale and stochastic methods, and there was no method formally available to tackle multiscale problems involving uncertainties. By developing an innovative Multiscale Stochastic Finite Element Method (MSFEM), this research has made a ground-breaking contribution to the emerging field of Multiscale Stochastic Modeling (MSM) (Fig 1). The theory ofmore » MSFEM basically decomposes a boundary value problem of random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering modeling practices where fine-scale microstructure is approximated by certain effective constitutive constants, which can be solved by using standard numerical solvers. The fast scale problem evaluates fluctuations of local quantities due to random microstructure, which is important for scale-coupling systems and particularly those involving failure mechanisms. The Green-function-based fast-scale solver developed in this research overcomes the curse-of-dimensionality commonly met in conventional approaches, by proposing a random field-based orthogonal expansion approach. The MSFEM formulated in this project paves the way to deliver the first computational tool/software on uncertainty quantification of multiscale systems. The applications of MSFEM on engineering problems will directly enhance our modeling capability on materials science (composite materials, nanostructures), geophysics (porous media, earthquake), biological systems (biological tissues, bones, protein folding). Continuous development of MSFEM will further contribute to the establishment of Multiscale Stochastic Modeling strategy, and thereby potentially to bring paradigm-shifting changes to simulation and modeling of complex systems cutting across multidisciplinary fields.« less
  • The Environmental Molecular Sciences Laboratory (EMSL), a scientific user facility managed by Pacific Northwest National Laboratory for the U.S. Department of Energy, Office of Biological and Environmental Research (BER), conducted a one-day workshop on August 26, 2014 on the topic of “Multiscale Computation: Needs and Opportunities for BER Science.” Twenty invited participants, from various computational disciplines within the BER program research areas, were charged with the following objectives; Identify BER-relevant models and their potential cross-scale linkages that could be exploited to better connect molecular-scale research to BER research at larger scales and; Identify critical science directions that will motivate EMSLmore » decisions regarding future computational (hardware and software) architectures.« less