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Title: Comparison of up-scaling methods in poroelasticity and its generalizations

Abstract

Four methods of up-scaling coupled equations at the microscale to equations valid at the mesoscale and/or macroscale for fluid-saturated and partially saturated porous media will be discussed, compared, and contrasted. The four methods are: (1) effective medium theory, (2) mixture theory, (3) two-scale and multiscale homogenization, and (4) volume averaging. All these methods have advantages for some applications and disadvantages for others. For example, effective medium theory, mixture theory, and homogenization methods can all give formulas for coefficients in the up-scaled equations, whereas volume averaging methods give the form of the up-scaled equations but generally must be supplemented with physical arguments and/or data in order to determine the coefficients. Homogenization theory requires a great deal of mathematical insight from the user in order to choose appropriate scalings for use in the resulting power-law expansions, while volume averaging requires more physical insight to motivate the steps needed to find coefficients. Homogenization often is performed on periodic models, while volume averaging does not require any assumption of periodicity and can therefore be related very directly to laboratory and/or field measurements. Validity of the homogenization process is often limited to specific ranges of frequency - in order to justify the scaling hypotheses thatmore » must be made - and therefore cannot be used easily over wide ranges of frequency. However, volume averaging methods can quite easily be used for wide band data analysis. So, we learn from these comparisons that a researcher in the theory of poroelasticity and its generalizations needs to be conversant with two or more of these methods to solve problems generally.« less

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
15013760
Report Number(s):
UCRL-PROC-201487
TRN: US200803%%755
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Conference
Resource Relation:
Conference: Presented at: ASCE Engineering Mechanics Conference, Newark, DE, United States, Jun 13 - Jun 16, 2004
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; DATA ANALYSIS; HOMOGENIZATION METHODS; MIXTURES; PERIODICITY

Citation Formats

Berryman, J G. Comparison of up-scaling methods in poroelasticity and its generalizations. United States: N. p., 2003. Web.
Berryman, J G. Comparison of up-scaling methods in poroelasticity and its generalizations. United States.
Berryman, J G. 2003. "Comparison of up-scaling methods in poroelasticity and its generalizations". United States. https://www.osti.gov/servlets/purl/15013760.
@article{osti_15013760,
title = {Comparison of up-scaling methods in poroelasticity and its generalizations},
author = {Berryman, J G},
abstractNote = {Four methods of up-scaling coupled equations at the microscale to equations valid at the mesoscale and/or macroscale for fluid-saturated and partially saturated porous media will be discussed, compared, and contrasted. The four methods are: (1) effective medium theory, (2) mixture theory, (3) two-scale and multiscale homogenization, and (4) volume averaging. All these methods have advantages for some applications and disadvantages for others. For example, effective medium theory, mixture theory, and homogenization methods can all give formulas for coefficients in the up-scaled equations, whereas volume averaging methods give the form of the up-scaled equations but generally must be supplemented with physical arguments and/or data in order to determine the coefficients. Homogenization theory requires a great deal of mathematical insight from the user in order to choose appropriate scalings for use in the resulting power-law expansions, while volume averaging requires more physical insight to motivate the steps needed to find coefficients. Homogenization often is performed on periodic models, while volume averaging does not require any assumption of periodicity and can therefore be related very directly to laboratory and/or field measurements. Validity of the homogenization process is often limited to specific ranges of frequency - in order to justify the scaling hypotheses that must be made - and therefore cannot be used easily over wide ranges of frequency. However, volume averaging methods can quite easily be used for wide band data analysis. So, we learn from these comparisons that a researcher in the theory of poroelasticity and its generalizations needs to be conversant with two or more of these methods to solve problems generally.},
doi = {},
url = {https://www.osti.gov/biblio/15013760}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Dec 13 00:00:00 EST 2003},
month = {Sat Dec 13 00:00:00 EST 2003}
}

Conference:
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