Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes of transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is $a/L$, being the ratio of the obstacle to system size. Distribution of the angle $alpha$ between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of $alpha$ is found to decay with the system size as $(a/L)^{d/2}$, where $d$ is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume.
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