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Upscaling conductivity and porosity in three-dimensional heterogeneous porous media

Chinese Science Bulletin 2004年第22期49卷 2415-2423页

作者： ZHANG Yong Hydrologic Science,University of California,Davis,CA 95616,usa desert research institute,2215 raggio parkway,reno,nv 89512,usa Hydrologic Science University of California Davis USA desert research institute Reno USA

An empirical formula is presented to upscale the conductivity of 3-dimensional heterogeneous porous me- dia, in which the distribution of local-scale conductivity is non-Gaussian with a high variance. The upscaled conductiv- ity is determined as a function of the volumetric proportion, the spatial connectivity and the statistical geometric length of high-permeable inclusions, and the arithmetic mean of con- ductivities of all hydrofacies. A systematic comparison to other traditional upscaling methods indicates that this em- pirical formula provides a better estimation of the equivalent conductivity. In the second part of this study, numerical ex- periments of solute migration reveal that porosity also needs to be upscaled to capture the transport of contaminants in a heterogeneous medium using an effective or upscaled homo- geneous medium. This is due to the tendency of contaminants to be preferrentially transported by 3-dimensional pathways composed of high-permeable materials in heterogeneous aquifer systems. The apparent difference between the actual transport velocity of contaminants and the upscaled velocity, based on the equivalent conductivity, forces upscaling of po- rosity. Further systematic analyses demonstrate that the up- scaled porosity follows a non-linear trend as the content of high-permeable sediments decreases. Resultant upscaled porosity, with values varying between 0.004 and 1.5, is be- yond the definition of the traditional porosity on the representative elementary volume (REV) scale. When the content of high-permeable materials is less than 30%, the upscaling of porosity is critical in the simulation of the contaminant transport in a heterogeneous medium using an upscaled, homogeneous counterpart.

关键词：标度方法传导率多孔性三维空间异类多孔介质多孔材料

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