On the spatial-temporal averaging method for modeling transport in porous media |
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| Authors: | Yeqi He Jonathan F Sykes |
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| Institution: | (1) Civil Engineering Department, University of Waterloo, N2L 3G1 Ontario, Canada |
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| Abstract: | The spatial-temporal averaging procedure is considered with a nonhomogeneous distribution of elementary domains in the spatial-temporal space and the probabilistic interpretation of the ST-averaging is also given. Several averaging theorems and corollaries about the averages of spatial and temporal derivatives are presented and rigorously proved which allow elementary domain to vary in space and time. The macroscopic transport equation in the most general condition and the simplified macroscopic equation under the special form of distributions are developed which may be reduced to the classical macroscopic transport equation as the spatial-temporal average degenerates into the volume average. |
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| Keywords: | averaging theorem heterogeneity macroscopic equation microscopic equation probabilistic average REV spatial average spatial-temporal average temporal average transport equation volume average |
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