Electro kinetic fractal dimension for characterizing shajara reservoirs

1. 2nd World Congress & Expo on
Nanotechnology & Materials Science
June 25-27, 2018 | Dubai, UAE

2. Electro kinetic fractal dimension for
characterizing Shajara reservoirs of the
Shajara Formation, Saudi Arabia
Presenting Author*1 Prof. Khalid Elyas Mohamed Elameen Alkhidir
Department of Petroleum and Natural Gas
Engineering, Riyadh, King Saud University,
Saudi Arabia)
Presenting Author* (kalkhidir@ksu.edu.sa, khalidalkhidir@gmail.com
+966114679118)

3. Biographt
Prof. Khalid Elyas Mohamed Elameen Alkhidir is a researcher 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

4. Abstract
Electro kinetic parameters such as streaming potential coupling coefficient,
electro osmosis coupling coefficient, and their ratio play important role in the
determination of quality and assessment of a reservoir. This research aims to
calculate fractal dimension from the relationship among the ratio of streaming
potential to electro osmosis coupling coefficient, maximum streaming potential
to electro osmosis coupling coefficient ratio and wetting phase saturation and to
confirm it by the fractal dimension derived from the relationship among capillary
pressure and wetting phase saturation. The ratio of streaming potential to electro
osmosis coupling coefficient was determined from effective pore radius, fluid
viscosity, and fluid electric conductivity. The effective pore radius of the real
collected sandstone samples was calculated from packing constant and pore
radius determined from capillary pressure measured by mercury intrusion
technique which enables measurement of porosity and calculation of
permeability. Two equations for calculating the fractal dimensions have been
employed. The first one describes the functional relationship between wetting
phase saturation, ratio of streaming potential to electro osmosis coupling
coefficient, maximum streaming potential to electro osmosis coefficient ratio and
fractal dimension.

5. 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 streaming potential to electro
osmosis coupling coefficient divided by the logarithm of maximum value
describing the ratio between streaming potential and electro osmosis
coupling coefficient versus logarithm wetting phase saturation. The slope of
the first procedure = 3- Df (fractal dimension). The second procedure for
obtaining the fractal dimension was resolved 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
constructed 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 obtained units from bottom to top
are: Lower Shajara electro kinetic Fractal Dimension Unit, Middle Shajara
electro kinetic Fractal dimension Unit, and Upper Shajara electro kinetic
Fractal Dimension Unit. The results show similarity between electro kinetic
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 and
effective pore radius.

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. 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

13. Sample SJ1,Φ=29%,K=1680 mD, electro kinetic fractal
dimension=2.7859 , capillary pressure fractal dimension=2.7859

14. Sample SJ2,Φ=35%,K=1955 mD, electro kinetic fractal
dimension=2.7748 , capillary pressure fractal dimension=2.7748

15. Sample SJ3,Φ=34%,K=56 mD, electro kinetic fractal
dimension=2.4379 , capillary pressure fractal dimension=2.4379

16. Sample SJ4,Φ=30%,K=176 md, electro kinetic fractal
dimension=2.6843 , capillary pressure fractal dimension=2.6843

17. Sample SJ7,Φ=35%,K=1472 mD, electro kinetic fractal
dimension=2.7683 , capillary pressure fractal dimension=2.7683

18. Sample SJ8,Φ=32%,K=1344 mD, electro kinetic fractal
dimension=2.7752 , capillary pressure fractal dimension=2.7752

19. Sample SJ9,Φ=31%,K=1394 mD, electro kinetic fractal
dimension=2.7786 , capillary pressure fractal dimension=2.7786

20. Sample SJ11,Φ=36%,K=1197 mD, electro kinetic fractal
dimension=2.7586 , pressure fractal dimension=2.7586

21. Sample SJ12,Φ=28%,K=1440 mD, electro kinetic fractal
dimension=2.7859 , capillary pressure fractal dimension=2.7859

22. Sample SJ13,Φ=25%,K=973 mD, electro kinetic fractal
dimension=2.7872 , capillary pressure fractal dimension=2.7872

23. Electro kinetic fractal dimension versus capillary
pressure fractal dimension

24. Petrophysical model showing the three Shajara reservoirs with their electro
kinetic fractal dimension and capillary pressure fractal dimension values
Reservoirs Φ% K md Electro
kinetic
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

25. conclusions
The sandstones of the Shajara Reservoirs of the
Shajara formation of the permo-Carboniferous
Unayzah group were divided here into three
units based on electro kinetic fractal dimension.
 These Units from base to top are: Lower Shajara
electro kinetic Fractal dimension Unit, Middle
Shajara electro kinetic Fractal Dimension Unit,
and Upper Shajara electro kinetic Fractal
Dimension Unit.

26. 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