Comparison of Upscaling Methods in Poroelasticity and Its Generalizations
Publication: Journal of Engineering Mechanics
Volume 131, Issue 9
Abstract
Four methods of upscaling 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.
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Acknowledgments
Work performed under the auspices of the United States Department of EnergyDOE by the University of California Lawrence Livermore National Laboratory under Contract No. DOEW-7405-ENG-48 and supported specifically by the Geosciences Research Program of the DOE Office of Energy Research within the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.
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Published In
Journal of Engineering Mechanics
Volume 131 • Issue 9 • September 2005
Pages: 928 - 936
Copyright
© 2005 ASCE.
History
Received: Dec 18, 2003
Accepted: Jul 29, 2004
Published online: Sep 1, 2005
Published in print: Sep 2005
Notes
Note. Associate Editor: Alexander H.-D. Cheng
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