Polarization Density Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation

The quality and assessment of a reservoir can be documented in details by the application of polarization density. This research aims to calculate fractal dimension from the relationship among polarization density, maximum polarization density and water saturation and to confirm it by the fractal dimension derived from the relationship among capillary pressure and water saturation. In this research, porosity was measured on real collected sandstone samples and permeability was calculated theoretically from capillary pressure profile measured by mercury intrusion techniques. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, polarization density, and maximum polarization density and fractal dimension. The second equation implies to the wetting phase saturation as a function of capillary pressure and the fractal dimension. Two procedures for obtaining the fractal dimension have been utilized. The first procedure was done by plotting the logarithm of the ratio between polarization density and maximum polarization density versus logarithm wetting phase saturation. The slope of the first procedure is positive = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was completed by plotting logarithm of capillary pressure versus the logarithm of wetting phase saturation. The slope of the second procedure is negative = Df -3. On the basis of the obtained results of the fabricated stratigraphic column and the attained values of the fractal dimension, the sandstones of the Shajara reservoirs of the Shajara Formation were divided here into three units. These units from bottom to top are: Lower Shajara polarization density Fractal Dimension Unit, Middle Shajara polarization density Fractal Dimension Unit, and Upper Shajara polarization density Fractal Dimension Unit. The three reservoir units were also confirmed by capillary pressure fractal dimension. It was found that the obtained fractal dimension increases with increasing grain size and permeability.

Keywords: Shajara Reservoirs; Shajara Formation; polarization density fractal dimension; capillary pressure fractal dimension.