Analysis of the solid phase stress tensor in multiphase porous media

International Journal for Numerical and Analytical Methods in Geomechanics - Tập 31 Số 4 - Trang 541-581 - 2007
William G. Gray1, Bernhard A. Schrefler2
1Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, NC 27599‐7431, U.S.A.
2Dipartimento di Costruzioni e Trasporti Facolta’ di Ingegneria, Universita’ degli Studi di Padova, via F. Marzolo 9, 35131 Padova, Italy

Tóm tắt

AbstractConservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd.

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International Journal for Numerical and Analytical Methods in Geomechanics

Tập 31 Số 4

541-581

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