Comparison of two up-scaling methods in poroelasticity and its generalizations
Two 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 are discussed, compared, and contrasted. The two methods are: (1) two-scale and multiscale homogenization, and (2) volume averaging. Both these methods have advantages for some applications and disadvantages for others. For example, homogenization methods can 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.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 15014045
- Report Number(s):
- UCRL-PROC-202969; TRN: US200803%%1015
- Resource Relation:
- Conference: Presented at: 17th ASCE Engineering Mechanics Conference, Newark, DE, United States, Jun 13 - Jun 16, 2004
- Country of Publication:
- United States
- Language:
- English
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