MODELING OF ROCK PERMEABILITY ANISOTROPY THROUGH FRACTAL ANALYSIS OF THIN SECTIONS

It is recognized for a long time that most of natural rocks are anisotropic. Unfortunately, physical parameters of rocks that govern permeability anisotropy have not been found or clearly understood yet. Deep investigation of Kozeny Carman equation, developing a new permeability equation, and innovations in core analysis are needed to solve the problem. The pupose of this study are finding a new permeability equation including physical parameters that govern permeability anisotropy, and developing a method to determine the parameters. A number of rock samples are taken. Each rock sample was cut into a cube to allow permeability measurement in three directions from one rock sample. One thin section was made for each side of cube to allow thin section analysis in three directions. Fractal characteristics (pore dimension, and surface dimension) of each thin section were calculated by box counting techniques, and the results were used to estimate rock physical parameters that govern permeability (tortuosity, mean hydraulic diameter, shape factor, and non active porosity constant) in three directions. According to the methodology of approach, this study used a number of relatively consolidated and non fractured sandstone samples that relatively meet the fractal object conditions. Iweenty rock samples use in this study gave rational tortuosity values between 1.42 and 2.26, and shape factor values between 1.57 and 1.83. This paper shows encouraging results in which the new permeability equation gave calculated permeability values close to the measured ones. This study also reveals that the physical parameters that govern permeability anisotropy can be determined by fractal analysis of thin sections.

The potential contributions of this study are: a new method for estimation of permeability in three directions, innovation in measurement of three direction permeability, and awareness to the purpose of fractal analysis of thin sections.