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In this article, the renormalization process for the permeability and the attractive distribution of the renormalized permeability are investigated. It is known that the attractive distribution is log-normal for 2D case but it isn’t for 3D case. It is discovered that the renormalized permeability from infinite system is independent of the attractive distribution variance. Making use of this important property, numerical simulation is then performed to find the specific form of the attractive distribution. Based on the numerical results, it is shown that the attractive distribution is 1/3-normal in the 3D case.

The Attractive Distribution of the Renormalized Permeability in 3D Case