The fractal dimension of pores in sedimentary rocks and its influence on permeability

Perimeter-area power-law relationship of pores in five sedimentary rocks are estimated from scanning electron micrographs of thin sections. These relationships for the pores of four sandstones were found to lie between 1.43 and 1.49, while that of an Indiana limestone was found to be 1.67. We show how the perimeter-area power-law relationship of pores, along with a pore-size distribution, can be used to estimate the hydraulic permeability. A discussion is given of how the fractal dimension of the pore perimeter derived by Mandelbrot for islands whose boundaries are fractal: P = ϵDAD/2, where ϵ is some constant that depends on the length of the measuring grid size and D is the fractal dimension of the pore perimeter, influences permeability.