In previous works we have obtained an expression for the effective electrical conductivity of a columnar model simulating porous silicon. We used the averaging volume method that has proven to be successful in treating fluid transport in porous media. With this method we can calculate the bulk and the surface contribution to an effective transport property. The axial component can be solved analytically, but in the xY plane the calculation can only be performed numerically. However there is a certain approximation called Chang's cell (valid for high porosities) where the transverse component is also analytical. The extension of our original approach to find the axial component of the effective dielectric function is relatively simple, but the transverse component calculation presents interesting features.