1. Induced Polarization Relaxation Time Fractal Dimension Derived from Capillary pressure data for characterizing Shajara Reservoirs of the shajara Formation of the Permo-carboniferous Unayzah Group 11 International Geosciences of the Saudi Society of Geosciences,12-14 May, 2015 Corresponding author: K.E.Al-Khidir King Saud university, College of Engineering

2. Abstract
Geometric average relaxation time of induced polarization was derived from capillary pressure data to characterize the sandstones of the Shajara Reservoirs of the Shajara Formation of the Permo-Carboniferous Unayzah Group. The acquired values of the geometric time have been used to calculate the fractal dimension. Based on the obtained values of the fractal dimension as well as unconformity surfaces and mudstone separator, the Shajara reservoirs were divided here into three geometric time fractal units. The attained units from base to top are: Lower Shajara Geometric Time Fractal Dimension Unit, Middle Shajara Geometric Time Fractal Dimension Unit and Upper Shajara Geometric Time Fractal dimension Unit. The three Shajara reservoirs geometric time units have been also confirmed by arithmetic time fractal dimension.

3. It was found that, the flow capacity (permeability) of the sandstones of the Shajara reservoirs increases with increasing both geometric and arithmetic time fractal dimension. The relaxation time fractal dimension be successful not only in characterizing the flow capacity of the shajara reservoirs, but also can be related to their textural attributes mainly their grain size variability. Concerning the grain size variability, it was also reported that, the relaxation time accelerate with increasing grain size owing to possibility of having interconnected channels and decrease with pore throat size reduction reproduced by compaction.

4. Introduction
Al-Khidir et al 2010, Oil Gas Exploration production technology (OGEP) subdivied the Shajara into three reservois, lower , middle and upper.
Al-Khidir et al 2011, Journal of Petroleum exploration and production Technology, studied Bimodal Pore Size behavior of the shajara Formation reservoirs of the permo-carboniferous unayzah group.
Al-Khidir et al 2012, subdivided the shajara reservois of the Shajara Formation of the Permo-Carboniferous Unayzah Group into three fractal Dimension Units
The work published by Al-Khidir et al 2012 was cited as Geoscience; New Finding reported from King Saud university Describe advnaces in geoscience. Science Letter (Oct 25, 2013): 359

5. units: Lower Shajara Thermodynamic Fractal Dimension Unit , Middle Shajara Thermodynamic Fractal Dimension Unit, Upper Shajara Thermodynamic Fractal Dimension Unit. These units were confirmed by 3 D fractal model . Arabian Journal of geosciences.
Al-khidir et al 2013, subdived 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. The Three reservoirs units were confirmed by water saturation fractal dimension.

6. Aims
The aim of this work is to confirm the three reservois units of the shajara Formation of the permo-Carboniferous Unayzah Grouop using geometric and arithmetic relaxation time fractal dimension of induced polarization previously studied by Al-Khidir et al.

7. Stratigraphic section showing three geometic time fractal dimension units of the Shajara reservoirs

8. Porosity =29 Permeability=1680 Geometric Time Fractal Dimension=2.11

9. 1955 Porosity =35 Permeability= Geometric Time Fractal 2.10Dimension=

10. 56=Porosity =34 Permeability Geometric Time Fractal Time Dimension=2

11. 176Porosity =30 Permeability= Geometric Time Fractal 2.03Dimension=

12. 55=Porosity =31 Permeability Geometric Time Fractal Dimension=2.01

13. 1472Porosity =35 Permeability= Geometric Time Fractal Dimension=2.08

14. 1344=Porosity =32 Permeability Geometric Time Fractal Dimension=2.09

15. 1394=Porosity =31 Permeability Geometric Time Fractal Dimension=2.09

16. 1197Porosity =36 Permeability= Geometric Time Fractal Dimension=2.07

17. 1440=Porosity =28 Permeability Geometric Time Fractal Dimension=2.10

18. 973=Porosity =25 Permeability Geometric Time Fractal 2.09Dimension=

19. 1680=Porosity =29 Permeability Arithmetic Time Fractal 2.12Dimension=

20. 1955=Porosity =35 Permeability Arithmetic TimeFractal Dimension=2.11

21. 56Porosity =34 Permeability= Arithmetic Time Fractal Dimension=2.02

22. 176=Porosity =30 Permeability Arithmetic Time Fractal Dimension=2.03

23. 55=Porosity =31 Permeability Arithmetic Time Fractal Dimension=2.02

24. 1472=Porosity =35 Permeability Arithmetic Time Fractal 2.10Dimension=

25. 1344=Porosity =32 Permeability Arithmetic time Fractal 2.10Dimension=

26. 1394=Porosity =31 Permeability Arithmetic Time Fractal 2.11Dimension=

27. 1197=Porosity =36 Permeability Arithmetic Time Fractal 2.08Dimension=

28. 1440=Porosity =28 Permeability Arithmetic Time Fractal 2.12Dimension=

29. 973=Porosity =25 Permeability Arithmetic Time Fractal Dimension=2.11

30. Geometric Time fractal Dimension Versus Permeability

31. Arithmetic Time Fractal Dimension versus Permeability

32. Geometric Time Fractal Dimension Versus Arithmetic Time Fractal Dimension

33. Table 1: Results of Induced Polarization Geometric Time Fractal Dimension and Arithmetic Time Fractal Dimension

34. Conclusion
Based on induced polarization geometric time fractal dimension , the Shajara Formation of the permo-carboniferous UnayzahGruop were divided here into three reservoirs units.
The obtained reservoirs units from base to top are : Lower Shajara Induced polarization Geometric Time Fractal Dimension Unit,Middle Shajara Induced polarization Geometric Time Fractal Dimension Unit, Upper Shajara Induced Polarization Geometric Time Fractal Dimension Unit.

35. The obtained Shajara geometric time fractal dimension reservoir units were also confirmed by arithmetic time fractal dimension of induced polarization.
It was found that, the higher the geometric and arithmetic time fractal dimension, the higher the permeability leading to better shajara reservoir characteristics.
It was also reported that, the induced polarization geometric and arithmetic fractal dimension increases with increasing pore size and grain size owing to possibility of having interconnceted channels.

36. Diagenetic features such as compaction plays an important role in reducing geometric and arithmetic time fractal dimension due to reduction in pore connectivity.
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