Problem of upscaling the transport through highly heterogeneous media characterized by a period of heterogeneity ε, a ratio of global permeabilities ωK, and a ratio of the order of capillary forces ω c is studied. Upscaling corresponds to the limit transition when ε tends to zero at small ωK and large ω c . The limit of upscaling transition is shown to be not equivalent to simple homogenization, in case of the high heterogeneity. In this case more general notion as nonuniform homogenization becomes more constructive. The outline of general nonuniform homogenization method is developed, which leads to decomposition of initial heterogeneous medium on two continuous homogeneous media, in limit. The method is applied to the problem of the two-phase transport through dual-porosity media.A macroscopic model is constructed for one ratio between determining parameters. First, it allows to effective computing of macroscopic relative permeability tensors. Then, two macroscopic capillary pressure corresponding to each part of the medium result from upscaling procedure. One of them shows the non-equilibrium properties and is related to another one by kinetic equation, where relaxation time depends on saturation.
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- Upscaling Two-Phase Flow in Double Porosity Media: Nonuniform Homogenization
- Springer Netherlands
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