Electric power fractal dimension for characterizing shajara reservoirs of the shajara formation of the permo carboniferous unayzah group, saudi arabia

1. Professor 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
Acknowledgement Number/Paper ID: ICICSA – 1135

2. Electric power fractal dimension for characterizing
Shajara Reservoirs of the Shajara Formation of the
Permo-Carboniferous Unayzah Group, Saudi Arabia
Professor 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

3. The quality and assessment of a reservoir can be documented in details by
the application of electric power. This research aims to calculate fractal
dimension from the relationship among electric power, maximum electric
power 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 contaminating
the pores of sandstone samples in consideration. Two equations for
calculating the fractal dimensions have been employed. The first one
describes the functional relationship between wetting phase saturation,
electric power, maximum electric power 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 utilized. The first procedure was done by plotting the
logarithm of the ratio between electric power and maximum electric power
versus logarithm wetting phase saturation. The slope of the first procedure =
3- Df (fractal dimension).

4. The second procedure for obtaining the fractal dimension was
concluded 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
fabricated stratigraphic column and the attained 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 Electric Power Fractal Dimension
Unit, Middle Shajara Electric Power Fractal dimension Unit, and Upper
Shajara Electric Power Fractal Dimension Unit. The results show
similarity between electrical power 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
dimensions due to an increase in their connectivities. In our case, and
as conclusions the higher the fractal dimension, the higher the
heterogeneity, the higher the permeability, the better the reservoir
characteristics.

5. Biography
Professor: Khalid Elyas Mohamed Elameen Khidir is professor at king Saud
University. He did his postdoctoral research at King Saud University, College of
Engineering, Department of Petroleum and natural Gas Engineering, Al-
Amoudi Research Chair in Petroleum, enhanced oil recovery. He published
papers in sandstone reservoirs characterization, tight carbonate reservoirs
characterization, and in an enhanced oil recovery.

6. Al-Khidir et al 2010 Reservoirs Heterogeneity Characterization of
the Shajara Member: Permo-Carboniferous Unayzah Formation.
The 2nd Saudi meeting on Oil and Natural Gas Exploration and
production Technologies
King Fahad university of Petroleum and minerals Campus,
Dhahran, saudi Arabia December 18 - 20, 2010
http://saudiarabiaoilandgas.com/magazines/SAOG_ISSUE_17/saog
17.pdf
Al-khidir et al 2011 Bimodal pore size behavior of the Shajara
Formation Reservoirs of the Permo-Carboniferous Unayzah
Group, Saudi Arabia

7. Journal of petroleum exploration and Production technology
http://fac.ksu.edu.sa/sites/default/files/Bimodal_Shajara.pdf
Al-khidir et al 2012 Characterization of heterogeneity of the Shajara
reservoirs of the Shajara formation of the Permo-Carboniferous Unayzah
group.
Arabian Journal of Geoscienes
http://fac.ksu.edu.sa/sites/default/files/characterization_of_heterogeneity_
of_the_shajara_reservoirs_of_the_shajara_formation_of_the_permo-
carboniferous_unayzah_group.pdf
Al-Khidir et al Geoscience; New Findings Reported from King Saud
University Describe Advances in Geoscience Science Letter (Oct 25, 2013):
359.
http://search.proquest.com/docview/1442487929?accountid=44936

8. Al-Khidir et al 2013 Differential Capacity Fractal Dimension and
Water Saturation Fractal Dimension as Parameters for Reservoir
Characterization: Shajara Formation of the Permo-Carboniferous
Unayzah Group as a Case Study.
10th Meeting of the Saudi Society for Geoscience “Geosciences for
Sustainable Development” 15-17 April, 2013 King Fahad university
of petroleum and minerals Campus, Dhahran, Saudi Arabia.
https://www.scribd.com/document/139694517/Differential-
Capacity-Fractal-Dimension-and-Water-Saturation-Fractal-
Dimension-as-Parameter-for-Reservoir-Characterization-Shajara-
Formation-of-the

9. Al-Khidir 2015 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.
The Eleventh International Geological Conference 23 – 25 Rajab
1436 12 – 14 May 2015.
https://sciences.ksu.edu.sa/sites/sciences.ksu.edu.sa/files/imce_imag
es/program-geo.pdf

10. Al-Khidir 2017 Nuclear magnetic resonance relaxation time as a
diagnostic parameter for reservoir .
International Conference on Petrochemical Engineering July 10-
12, 2017 Dubai, UAE.
http://fac.ksu.edu.sa/sites/default/files/nuclear_magnetic_resonance
_relaxation_time_as_a_diagnostic_parameter_for_reservoir_chara
cterization.pdf
Al-Khidir 2017 Pressure Head Fractal Dimension for
Characterizing Shajara Reservoirs of the Shajara Formation of the
Permo-Carboniferous Unayzah Group, Saudi Arabia.
Archives of Petroleum Environmental Biotechnology
http://fac.ksu.edu.sa/sites/default/files/apeb-113.pdf

11. Al-khidir 2017 On the equality of resistivity fractal dimension and
geometric relaxation time fractal dimension of induced
polarization for characterizing Shajara Reservoirs of the Shajara
Formation of the Permo-Carboniferous Unayzah Group, Saudi
Arabia
International Meeting On petroleum engineering , Singapore November
7- 8, 2017
https://d2cax41o7ahm5l.cloudfront.net/mi/pdfs/petroleum-meeting-
2017-16001-tentative-program33276.pdf
http://fac.ksu.edu.sa/sites/default/files/khalid_al-khidir_al2017.pdf

12. Khalid Elyas Mohamed Elameen Alkhidir (2018)
Geometric Relaxation Time of Induced Polarization
Fractal Dimension For Characterizing Shajara
Reservoirs of The Shajara Formation of the Permo-
Carboniferous Unayzah Group, Saudi Arabia
SciFed Journal of Petroleum
http://fac.ksu.edu.sa/sites/default/files/geometric_r
elaxation_time_of_induced_polarization_fractal_dim
ension_for_characterizing_shajara_reservoirs_of_the
_shajara_formation_of_the_permo-
carboniferous_unayzah_group_saudi_arabia.pdf

13. Stratigraphic column of the type section of the Permo-carboniferous
Shajara Formation of the Unayzah Group, Wadi Shajara, Qusayba area,
al Qassim district, Saudi Arabia, N 26 52 17.4, E 43 36 18

14. Sample SJ1,Φ=29%,K=1680 mD, electric power fractal
dimension=2.7859 , capillary pressure fractal dimension=2.7859

15. Sample SJ2,Φ=35%,K=1955 mD, electric power fractal
dimension=2.7748 , capillary pressure fractal dimension=2.7748

16. Sample SJ3,Φ=34%,K=56 mD, electric power fractal
dimension=2.4379 , capillary pressure fractal dimension=2.4379

17. Sample SJ4,Φ=30%,K=176 md, electric power fractal
dimension=2.6843 , capillary pressure fractal dimension=2.6843

18. Sample SJ7,Φ=35%,K=1472 mD, electric power fractal
dimension=2.7683 , capillary pressure fractal dimension=2.7683

19. Sample SJ8,Φ=32%,K=1344 mD, electric power fractal
dimension=2.7752 , capillary pressure fractal dimension=2.7752

20. Sample SJ9,Φ=31%,K=1394 mD, electric power fractal
dimension=2.7786 , capillary pressure fractal dimension=2.7786

21. Sample SJ11,Φ=36%,K=1197 mD, electric power fractal
dimension=2.7586 , pressure fractal dimension=2.7586

22. Sample SJ12,Φ=28%,K=1440 mD, electric power fractal
dimension=2.7859 , capillary pressure fractal dimension=2.7859

23. Sample SJ13,Φ=25%,K=973 mD, electric power fractal
dimension=2.7872 , capillary pressure fractal dimension=2.7872

24. electric power fractal dimension versus capillary pressure
fractal dimension

25. Petrophysical model showing the three Shajara reservoirs with their electric
power fractal dimension and capillary pressure fractal dimension values
Reservoirs Φ% K md Electric
power
fractal
dimensiob
Capillary
pressure
fractal
dimension
Lower Shajara
Reservoir
29 1680 2.7859 2.7859
35 1955 2.7748 2.7748
34 56 2.4379 2.4379
30 176 2.6843 2.6843
Middle
Shajara
reservoir
35 1472 2.7683 2.7683
32 1344 2.7752 2.7752
31 1394 2.7786 2.7786
Upper
Shajara
Reservoir
36 1197 2.7586 2.7586
28 1440 2.7859 2.7859
25 973 2.7872 2.7872

26. Conclusion
• The sandstones of the Shajara Reservoirs of the Shajara
formation of the permo-Carboniferous Unayzah group
were divided here into three units based on electric
power fractal dimension.
• The Units from base to top are: Lower Shajara Electric
Power Fractal dimension Unit, Middle Shajara Electric
Power Fractal Dimension Unit, and Upper Shajara Electric
power Fractal Dimension Unit.
• These units were also proved by capillary pressure
fractal dimension.
• The fractal dimension was found to increase with
increasing grain size and permeability.

27. Thank you