Morphological decomposition of sandstone pore-space: fractal power-laws

Morphological decomposition procedure is applied to estimate fractal dimension of a pore-space, which is isolated from a sandstone microphotograph. The fractal dimensions that have been computed by considering various probing rules have precisely followed the universal power-law relationships proposed elsewhere. These results are derived by considering structuring elements such as octagon, square and rhombus that have been used to decompose the pore-space of sandstone image. The radii of the structuring elements are made to increase in a cyclic fashion. To perceive the decomposed pore image, a color-coding scheme is adapted, from which one can identify several sizes of these structuring elements that could be fit into this pore. This exercise facilitates testing of the relationship between the radius of the structuring elements that could be used to decompose the pore at different levels, and the number of decomposed shapes that could be fit into the pore while using the corresponding structuring element. From the number-radius relationship, the fractal dimensions of pore-space estimated, by considering these structuring elements, yield the values of 1.82, 1.76, and 1.79. These values are in conformity with the values arising from estimation of box dimension method, as well as the dimensions of the corresponding pore connectivity networks (PCNs)