SciFed Journal of Petroleum
Geometric Relaxation Time of Induced Polarization Fractal Dimension For Characterizing Shajara Reservoirs of The Shajara Formation of the PermoCarboniferous Unayzah Group, Saudi Arabia
Research Article
Received on: February 18, 2018
Accepted on: February 28, 2018
Published on: March 10, 2018
*Corresponding author:
Khalid Elyas Mohamed Elameen Alkhidir,
Department of Petroleum and Natural Gas Engineering, College of
Engineering, King Saud University, Saudi Arabia. Email: kalkhidir@ksu.
edu.sa; Tel: +966 11 4679118
Abstract
Sandstone samples were collected from the surface type section of the Shajara Formation of the PermoCarboniferous Unayzah Group for detailed reservoir characterisation. Capillary pressure experiment was performed to contact porosity and permeability was derived from the Data. Geometric relaxation time of induced polarization was calculated from the distribution of pores and the fractal dimension was proven from the relationship between water saturation and geometric relaxation time of induced polarization. In addition to field observation and obtained results of fractal dimension, the Shajara reservoirs of the Shajara Formation of the permoCarboniferous Unayzah Group were divided here into three fractal dimension units. The Units from base to top are: Lower Shajara Geometric Relaxation Time Fractal dimension Unit, Middle Shajara Geometric Relaxation Time Fractal Dimension Unit, and Upper Shajara Geometric Relaxation Time Fractal Dimension Unit. These units were also proved by arithmetic relaxation time of induced polarization fractal dimension. It was found that the geometric relaxation time fractal dimension is similar to the arithmetic relaxation time fractal dimension of induced polarization. It was also reported that the obtained fractal dimension speeds with increasing permeability and relaxation time due to an increase in pore connectivity
Keywords
Shajara Formation; Unayzah Group; Geometric Relaxation Time Fractal Dimension; Arithmetic Relaxation Time Fractal Dimension
FullText
Introduction
The phenomenon of electrical induced polarization (IP) in waterbearing 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 confrmed 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 colecole relaxation time and pore size.
Bimodal Pore Size behavior of the Shajara Formation reservoirs of the permocarboniferous Unayzah group was investigated by [7]. Subdivision of the Shajara reservoirs into three units based on thermodynamic fractal dimension approach and 3D 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 PermoCarboniferous 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, IPTg the geometric relaxation time of induced polarization, IPTgmax the maximum geometric relaxation time of induced polarization, and Df the fractal dimension.
Equation 1 can be proofed from
Where k the permeability in millidarcy,9.6 constant, IPTg geometric relaxation time of induced polarization in milliseconds; Φ the porosity; and 1.57 constant.
The maximum permeability can be scaled as
Divide equation 2 by equation 3
Equation 4 after simplifcation will become
Take the square root of equation 5

References
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6. André Revil, Pauline Kessouri, Carlos Torres Verdín (2014) Electrical conductivity, induced polarization, and permeability of the Fontainebleau sandstone. Geophysics 79: D301D318.
7. Al Khidir KE, Al Laboun A, Al Qurishi A, et al. (2011) Bimodal Pore Size behavior of the Shajara formation reservoirs of the PermoCarboniferous Unayzah group, Saudi Arabia. J Pet Explor Prod Technol 1: 19.
8. Al Khidir KE, Benzagouta M, Al Qurishi A, et al. (2013) Characterization of heterogeneity of the Shajara Reservoirs of the Shajara formation of the PermoCarboniferous Unayzah group. ARAB J GEOSCI 6: 39893995.
9. Geoscience (2013) New findings reported from King Saud. University describe advances in geoscience. Al Khidir et al. science letter 359.
10. Al Khidir KE, Benzagouta MS, AlQuraishi AA, et al. (2013) Differential capacity fractal dimension and water saturation fractal dimension as parameters for reservoir characterization: Shajara formation of the PermoCarboniferous Unayzah Group as a case study. 10th Meeting of the Saudi Society for Geoscience Geosciences for Sustainable Development KFUPM Campus. Dhahran. Saudi Arabia.
11. Al Khidir KE (2017) Pressure Head Fractal Dimension for Characterizing Shajara Reservoirs of the Shajara Formation of the PermoCarboniferous Unayzah Group, Saudi Arabia. Arch Pet Environ Biotechnol 2.