This document describes a study analyzing fractal dimensions derived from seismoelectric transfer functions and capillary pressure measurements in sandstone samples from the Shajara reservoirs of the Permo-Carboniferous Shajara Formation in Saudi Arabia. Fractal dimensions were calculated using two methods and found to be similar. Based on the fractal dimension values, the reservoirs were divided into three units - Lower, Middle, and Upper Shajara. Fractal dimension increased with grain size and permeability, suggesting it can characterize reservoir properties. The units defined by fractal dimension were supported by capillary pressure fractal dimensions.

1. World Congress On Petrochemistry
and Chemical Engineering June 28-
30, 2018 | Dubai, UAE

2. Seismo electric transfer function fractal
dimension for characterizing Shajara reservoirs
of the Permo-Carboniferous Shajara
Formation, Saudi Arabia
Professor: Khalid Elyas Mohamed Elameen AlKhidir
Department of petroleum and Natural Gas
Engineering, College of Engineering, King Saud
University, Saudi Arabia
Kalkhidir@ksu.edu.sa

3. Abstract The quality of a reservoir can be described in details by the
application of seismo electric transfer function fractal dimension. The
objective of this research is to calculate fractal dimension from the
relationship among seismo electric transfer fuction, maximum seismo
electric transfer function 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 techniques. Two equations for calculating the fractal
dimensions have been employed. The first one describes the functional
relationship between wetting phase saturation, seismo electric transfer
function, maximum seismo electric transfer function 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 developed.
The first procedure was done by plotting the logarithm of the ratio
between seismo electric transfer function and maximum seismo electric
transfer function 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
completed 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 acquired values of the fractal
dimension, the sandstones of the Shajara reservoirs of the Permo-
Carboniferous Shajara Formation were divided here into three units.
The gained units from bottom to top are: Lower Shajara Seismo
Electric Transfer Function Fractal Dimension Unit, Middle Shajara
Seismo Electric Tranfser Function Fractal dimension Unit, and Upper
Shajara Seismo Electric Transfer Function Fractal Dimension Unit. The
results show similarity between seismo electric transfer tunction 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 dimension due to an increase in their connectivity and
seismo electric transfer function. In our case, and as conclusions the
higher the fractal dimension, the higher the permeability, the better the
shajara reservoir characteristics.

5. Biography
Professor: Khalid Elyas Mohamed Elameen AlKhidir 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_heterog
eneity_of_the_shajara_reservoirs_of_the_shajara_formation_of_th
e_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. 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, 2018, 2:1, 1-
6.
http://fac.ksu.edu.sa/sites/default/files/geometric_relaxation_time_o
f_induced_polarization_fractal_dimension_for_characterizing_shajara
_reservoirs_of_the_shajara_formation_of_the_permo-
carboniferous_unayzah_group_saudi_arabia.pdf
Khalid Elyas Mohamed Elameen Alkhidir. Geometric relaxation time of
induced polarization fractal dimension for characterizing Shajara
Reservoirs of the Shajara formation of the Permo-Carboniferous
Unayzah Group-Permo. International Journal of Petrochemistry and
Research. 2018, 2 (1): 105-108.
http://fac.ksu.edu.sa/sites/default/files/geometric_relaxation_time_o
f_induced_polarization_fractal_dimension_for_characterizing_shajara
_reservoirs_of_the_shajara_formation_of_the_permo-.pdf

13. Prof. Khalid Elyas Mohamed Elameen AlKhidir. Arithmetic
relaxation time of induced polarization fractal dimension for
characterizing Shajara Reservoirs of the Shajara Formation.
Nanoscience and Nanotechnology. 2018, 1 (1): 1-8.
http://fac.ksu.edu.sa/sites/default/files/arithmetic_relaxation
_time_of_induced_polarization_fractal_dimension_for_charact
erizing_shajara_reservoirs_of_the_shajara_formation.pdf
Khalid Elyas Mohamed Elameen Alkhidir. Electric Potential
Energy Fractal Dimension for Characterizing Permo-
carboniferous Shajara Formation. Expert Opinion on
Environmental Biology. 2018, 7(2).
http://fac.ksu.edu.sa/sites/default/files/electric_potential_ene
rgy_fractal_dimension_for_characterizing_permo-
carboniferous_shajara_formation.pdf

14. Professor Khalid Elyas Mohamed Elameen AlKhidir. Seismo Electric
Field Fractal Dimension for Characterizing Shajara Reservoirs of the
Permo-Carboniferous Shajara Formation, Saudi Arabia. Petroleum &
Petrochemical Engineering Journal. 2018, 2(3): 1-7.
http://fac.ksu.edu.sa/sites/default/files/seismo_electric_field_fracta
l_dimension_for_characterizing_shajara_reservoirs_of_the_permo-
carboniferous_shajara_formation_saudi_arabia_1.pdf
Khalid Elyas Mohamed Elameen Alkhidir. Electro Kinetic Fractal
Dimension for Characterizing Shajara Reservoirs of the Permo-
Carboniferous Shajara Formation, Saudi Arabia. Archives of Oil and
Gas Research.2018, 2018 (1): 1-7.
http://fac.ksu.edu.sa/sites/default/files/electro_kinetic_fractal_dim
ension_for_characterizing_shajara_reservoirs_of_the_permo-
carboniferous_shajara_formation_saudi_arabia.pdf

15. Khalid Elyas Mohamed Elameen AlKhidir. Seismo electric field
fractal dimension for characterizing Shajara reservoirs of the
Permo-Carboniferous Shajara Formation, Saudi Arabia. Academia
Journal of Environmental Science. , 2018 6(5): 113-1200.
https://fac.ksu.edu.sa/sites/default/files/seismo_electric_field_f
ractal_dimension_for_characterizing_shajara_reservoirs_of_the
_permo-carboniferous_shajara_formation_saudi_arabia.pdf
Khalid Elyas Mohamed Elameen Alkhidir. Resistivity Fractal
Dimension for Characterizing Shajara Reservoirs of the Permo-
Carboniferous Shajara Formation Saudi Arabia. Recent Advances
in Petrochemical Science. 2018 5(2):1-6.
http://fac.ksu.edu.sa/sites/default/files/resistivity_fractal_dim
ension_for_characterizing_shajara_reservoirs_of_the_permo-
carboniferous_shajara_formation_saudi_arabia.pdf

16. Stratigraphic column of the type section of the Permo-carboniferous
Shajara Formation, Saudi Arabia, N 26 52 17.4, E 43 36 18

17. Sample SJ1,Φ=29%,K=1680 mD, Seismo electric transfer function
fractal dimension=2.7859 , capillary pressure fractal
dimension=2.7859

18. Sample SJ2,Φ=35%,K=1955 mD, Seismo electric transfer function
fractal dimension=2.7748 , capillary pressure fractal 2.7748
dimension=2.7748

19. Sample SJ3,Φ=34%,K=56 mD, Seismo electric transfer function fractal
dimension=2.4379 , capillary pressure fractal dimension=2.4379

20. Sample SJ4,Φ=30%,K=176 md, Seismo electric transfer function fractal
dimension=2.6843 , capillary pressure fractal dimension=2.6843

21. Sample SJ7,Φ=35%,K=1472 mD, Seismo electric transfer function
fractal dimension=2.7683 , capillary pressure fractal
dimension=2.7683

22. Sample SJ8,Φ=32%,K=1344 mD, Seismo electric transfer function
fractal dimension=2.7752 , capillary pressure fractal dimension=2.7752

23. Sample SJ9,Φ=31%,K=1394 mD, Seismo electric transfer function fractal
dimension=2.7786 , capillary pressure fractal dimension=2.7786

24. Sample SJ11,Φ=36%,K=1197 mD, Seismo electric transfer function
fractal dimension=2.7586 , pressure fractal dimension=2.7586

25. Sample SJ12,Φ=28%,K=1440 mD, Seismo electric transfer function
fractal dimension=2.7859 , capillary pressure fractal
dimension=2.7859

26. Sample SJ13,Φ=25%,K=973 mD, Seismo electric transfer function fractal
dimension=2.7872 , capillary pressure fractal dimension=2.7872

27. electric power fractal dimension versus capillary pressure
fractal dimension

28. Petrophysical model showing the three Shajara reservoirs with seismo
electric transfer function fractal dimension and capillary pressure fractal
dimension values
Reservoirs Φ% K md Seismo electric transfer
function 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

29. 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 seismo electric
transfer function fractal dimension.
 The Units from base to top are: Lower Shajara seismo
electric transfer function Fractal dimension Unit, Middle
Shajara seismo electric transfer function r Fractal
Dimension Unit, and Upper Shajara seismo electric transfer
function 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.

30. Thank you