Transverse Relaxation Time Fractal Dimension of Nuclear Magnetic Resonance 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 transverse relaxation time of nuclear magnetic resonance fractal dimension. The objective of this research is to calculate fractal dimension from the relationship among transverse relaxation time of nuclear magnetic resonance, maximum transverse relaxation time of nuclear magnetic resonance 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, transverse relaxation time of nuclear magnetic resonance, maximum transverse relaxation time of nuclear magnetic resonance 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 transverse relaxation time of nuclear magnetic resonance and maximum transverse relaxation time of nuclear magnetic resonance 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 logarithm of capillary pressure versus the logarithm of wetting phase saturation. The slope of the second procedure = Df -3. The results show similarities between transverse relaxation time of nuclear magnetic resonance and capillary pressure fractal dimension.