Geometric Relaxation Time of Induced Polarization Fractal Dimension For Characterizing Shajara Reservoirs of The Shajara Formation of the Permo-Carboniferous Unayzah Group, Saudi Arabia

Introduction The phenomenon of electrical induced polarization (IP) in water-bearing sediments was reported by [1]. Laboratory study of induced polarization in sandstone rocks with varying salinity and shalyness was investigated by [2]. An increase of induced polarization effect with increasing permeability, increasing porosity, and decreasing shalyness was examined by [2]. An increase of permeability with increasing geometric and arithmetic induced polarization relaxation time and increasing porosity was confirmed by [3]. A new integrated model with relaxation time spectra, porosity and formation factor was proposed to predict permeability was recognized by [4]. Relationships between induced polarization relaxation time and hydraulic properties of sandstone was investigated by [5]. They reported a positive logarithmic relationship between the relaxation time and the pore throat diameter. They also observed an increase of permeability with increasing characteristic relaxation time. Electrical conductivity, induced polarization, and permeability of the Fontainebleau sandstone was studied by [6]. They reported a positive correlation between cole-cole relaxation time and pore size.


Introduction
The phenomenon of electrical induced polarization (IP) in water-bearing sediments was reported by [1]. Laboratory study of induced polarization in sandstone rocks with varying salinity and shalyness was investigated by [2]. An increase of induced polarization effect with increasing permeability, increasing porosity, and decreasing shalyness was examined by [2]. An increase of permeability with increasing geometric and arithmetic induced polarization relaxation time and increasing porosity was confirmed by [3].
A new integrated model with relaxation time spectra, porosity and formation factor was proposed to predict permeability was recognized by [4]. Relationships between induced polarization relaxation time and hydraulic properties of sandstone was investigated by [5]. They reported a positive logarithmic relationship between the relaxation time and the pore throat diameter. They also observed an increase of permeability with increasing characteristic relaxation time. Electrical conductivity, induced polarization, and permeability of the Fontainebleau sandstone was studied by [6]. They reported a positive correlation between cole-cole relaxation time and pore size.
Bimodal Pore Size behavior of the Shajara Formation reservoirs of the permo-carboniferous Unayzah group was investigated by [7]. Subdivision of the Shajara reservoirs into three units based on thermodynamic fractal dimension approach and 3-D fractal geometry model of mercury intrusion technique was reported by [8]. New Finding reported from King Saud University Describe advances in Geoscience was reported by [9]. Subdivision of the Shajara reservoirs into three units: Lower Shajara Differential Capacity Fractal Dimension Unit, Middle Shajara Differential Capacity Fractal Dimension Unit, Upper Shajara Differential Capacity Fractal Dimension Unit was described by [10]. Pressure head fractal dimension for characterizing Shajara Reservoirs of the Shajara Formation of the Permo-Carboniferous Unayzah Group, Saudi Arabia was studied by [11].

Method
The geometric relaxation time of induced polarization can be scaled as Where Sw the water saturation, IPTa the induced polarization relaxation time arithmetic , IPTamax the maximum induced polarization relaxation time arithmetic , and Df the fractal dimension. Porosity was measured on collected sandstone samples from the surface type section of the Shajara formation of the permo-carboniferous Unayzah Group. Permeability was calculated from the measured capillary pressure date.The objective of this paper is to calculate the geometric relaxation time and arithmetic relaxation time of induced polarization from the distribution of pores and to calculate the fractal dimension from the relaxation time.

Results and Discussion
Based on field observation the Shajara Reservoirs of the Shajara Formation of the Permo-Carboniferous Unayzah Group were divided into three units as described in figure1.These units from base to top are: Lower Shajara Reservoir, Middle Shajara reservoir, and Upper Shajara Reservoir.
Their acquired results of the geometric relaxation time fractal dimension and arithmetic relaxation time fractal dimension of induced polarization are displayed in table 1. Based on the attained results it was found that the geometric relaxation time fractal dimension is equal to the arithmetic relaxation time fractal dimension. The maximum value of the fractal dimension was found to be 2.7872 assigned to sample SJ13 from the Upper Shajara Reservoir as verify in Table 1. Whereas the minimum value of the fractal dimension was reported from sample SJ3 from the Lower Shajara reservoir as displayed in table1. The geometric relaxation time induced polarization fractal dimension and arithmetic relaxation time fractal dimension were observed to increase with increasing permeability as proofed in table1 owing to the possibility ( ) of having interconnected channels. The Lower Shajara reservoir was denoted by four sandstone samples out of six, label as SJ1, SJ2, SJ3 and SJ4 as confirmed in figure1. Their geometric fractal dimension and arithmetic time fractal dimension values are proofed in table 1. As we proceed from sample SJ2 to SJ3 a pronounced reduction in permeability due to compaction was reported from 1955 md to 56 md which reflects decrease in geometric and arithmetic relaxation time fractal dimension from 2.7748 to 2.4379 as specified in table 1. Again, an increase in grain size and permeability was recorded from sample SJ4 whose geometric fractal dimension and arithmetic fractal dimension was found to be 2.6843 as described in table 1. In contrast, the Middle Shajara reservoir which is separated from the Lower Shajara reservoir by an unconformity surface as shown in figure 1. It was designated by three samples out of four, namely SJ7, SJ8, and SJ9 as illustrated in figure 1. Their geometric relaxation time induced polarization fractal dimensions (IPTg) and arithmetic relaxation time fractal dimensions (IPTa) show similarities as delineated in Table 1.Their fractal dimensions are higher than those of samples SJ3 and SJ4 from the Lower Shajara Reservoir due to an increase in their permeability as explained in table 1.
On the other hand, the Upper Shajara reservoir is separated from the Middle Shajara reservoir by yellow green mudstone as revealed in figure 1. It is defined by three samples so called SJ11, SJ12, SJ13 as explained in table 1. Moreover, their geometric relaxation time fractal dimension and arithmetic relaxation time fractal dimension are also higher than those of sample SJ3 and SJ4 from the Lower Shajara Reservoir due to an increase in their permeability as clarified in table 1.