Seismo Electric Transfer Function Fractal Dimension for Characterizing Shajara Reservoirs Of The Permo-Carboniferous Shajara Formation, Saudi Arabia

The quality of a reservoir can be described in details by the application of seismo electric transfer function fractal dimension. The objective of this research is to calculate fractal dimension from the relationship among seismo electric transfer fuction, maximum seismo electric transfer function and wetting phase saturation and to confirm it by the fractal dimension derived from the relationship among capillary pressure and wetting phase 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, seismo electric transfer function, maximum seismo electric transfer function 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 developed. The first procedure was done by plotting the logarithm of the ratio between seismo electric transfer function and maximum seismo electric transfer function versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was completed by plotting the logarithm of capillary pressure versus the logarithm of wetting phase saturation. The slope of the second procedure = Df -3. On the basis of the obtained results of the constructed stratigraphic column and the acquired values of the fractal dimension, the sandstones of the Shajara reservoirs of the Shajara Formation were divided here into three units. The gained units from bottom to top are: Lower Shajara Seismo Electric Transfer Function Fractal Dimension Unit, Middle Shajara Seismo Electric Tranfser Function Fractal dimension Unit, and Upper Shajara Seismo Electric Transfer Function Fractal Dimension Unit. The results show similarity between seismo electric transfer tunction fractal dimension and capillary pressure fractal dimension. It was also noted that samples with wide range of pore radius were characterized by high values of fractal dimension due to an increase in their connectivity and seismo electric transfer function. In our case , and as conclusions the higher the fractal dimension, the higher the permeability, the better the shajara reservoir characteristics.