Fractal dimension of pore space in carbonate samples from Tushka area (Egypt)

To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure Pc and cumulative fraction Vc resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction Vc and relaxation time T2 show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area Spor derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of Spor. The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.