Berlin 2005 – wissenschaftliches Programm

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AK: Akustik

AK 4: Physikalische Seismologie (Sitzungsorganisation: Sergei A. Shapiro, Berlin)

AK 4.1: Hauptvortrag

Montag, 7. März 2005, 10:15–11:00, TU EB222

UP-SCALING METHODS IN POROELASTICITY AND DOUBLE-POROSITY GEOMECHANICS — •James G. Berryman — University of California, Lawrence Livermore National Lab, P. O. Box 808 L-200, Livermore CA 94551-9900, USA

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. E.g. 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 scaling for use in the resulting power-law expansions, while volume averaging requires more physical insight to motivate the steps needed to find coefficients. Some new models of reservoirs based on random polycrystals of laminates together with rigorous methods of analyzing such systems will also be discussed.