1. The document analyzes fractal dimensions derived from electric potential gradient and capillary pressure measurements on sandstone samples from the Shajara Formation in Saudi Arabia.
2. Equations relating wetting phase saturation, electric potential gradient, maximum gradient, and fractal dimension were developed and used to calculate fractal dimension from log-log plots. Fractal dimension was also calculated from the relationship between capillary pressure and wetting phase saturation.
3. Results showed that the electric potential gradient fractal dimension was equal to the capillary pressure fractal dimension. Higher fractal dimensions correlated with higher permeability and were found in the Upper Shajara Reservoir units, indicating more heterogeneous and interconnected pore spaces.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Residence time distribution studies in flow through tubular electrochemical r...IJERD Editor
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
Capacitance-voltage Profiling Techniques for Characterization of Semiconduct...eeiej_journal
A new capacitance-voltage profiling technique of semiconductor junctions is proposed for characterisation of semiconductor materials and devices. The measurement technique is simple, non-destructive and it has a greater accuracy compared with the classical C-V method of J. Hilibrand and R. D. Gold, developed in 1960.
ANALYSIS OF SMALL-SIGNAL PARAMETERS OF 2-D MODFET WITH POLARIZATION EFFECTS F...VLSICS Design
An improved analytical two dimensional (2-D) model for AlGaN/GaN modulation doped field effect
transistor (MODFET) has been developed. The model is based on the solution of 2-D Poisson’s equation.
The model includes the spontaneous and piezoelectric polarization effects. The effects of field dependent
mobility, velocity saturation and parasitic resistances are included in the current voltage characteristics of
the developed two dimensional electron gas (2-DEG) model. The small-signal microwave parameters have
been evaluated to determine the output characteristics, device transconductance and cut-off frequency for
50 nm gate length. The peak transconductance of 165mS/mm and a cut-off frequency of 120 GHz have been
obtained. The results so obtained are in close agreement with experimental data, thereby proving the
validity of the model.
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
On the equality of electric power fractal dimension and capillary pressure fr...Khalid Al-Khidir
On the equality of electric power fractal dimension and capillary pressure fractal dimension for characterizing shajara reservoirs of the permo carboniferous shajara formation
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Residence time distribution studies in flow through tubular electrochemical r...IJERD Editor
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
Capacitance-voltage Profiling Techniques for Characterization of Semiconduct...eeiej_journal
A new capacitance-voltage profiling technique of semiconductor junctions is proposed for characterisation of semiconductor materials and devices. The measurement technique is simple, non-destructive and it has a greater accuracy compared with the classical C-V method of J. Hilibrand and R. D. Gold, developed in 1960.
ANALYSIS OF SMALL-SIGNAL PARAMETERS OF 2-D MODFET WITH POLARIZATION EFFECTS F...VLSICS Design
An improved analytical two dimensional (2-D) model for AlGaN/GaN modulation doped field effect
transistor (MODFET) has been developed. The model is based on the solution of 2-D Poisson’s equation.
The model includes the spontaneous and piezoelectric polarization effects. The effects of field dependent
mobility, velocity saturation and parasitic resistances are included in the current voltage characteristics of
the developed two dimensional electron gas (2-DEG) model. The small-signal microwave parameters have
been evaluated to determine the output characteristics, device transconductance and cut-off frequency for
50 nm gate length. The peak transconductance of 165mS/mm and a cut-off frequency of 120 GHz have been
obtained. The results so obtained are in close agreement with experimental data, thereby proving the
validity of the model.
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Similar to Electric potential gradient fractal dimension for characterizing shajara reservoirs of the permo carboniferous shajara formation, saudi arabia
On the equality of electric power fractal dimension and capillary pressure fr...Khalid Al-Khidir
On the equality of electric power fractal dimension and capillary pressure fractal dimension for characterizing shajara reservoirs of the permo carboniferous shajara formation
Transverse relaxation time fractal dimension of nuclear magnetic resonance fo...Khalid Al-Khidir
Transverse relaxation time fractal dimension of nuclear magnetic resonance for characterizing shajara reservoirs of the permo carboniferous shajara formation, saudi arabia
Analysis of Electric Circuit Model on Atmospheric Pressure Dielectric Barrier...AM Publications
Analysis of Electric Circuit Model on Atmospheric Pressure Dielectric Barrier Discharge (DBD) Plasma has been simulated using the Simulink-Matlab R2010a software. Plasma reactor being used as the basis to determine the parameters in the circuit is in the coaxial form made of pyrex glass with an iron rod as the active electrode and spiral copper wire as passive electrode. The reactor was filled with argon gas with the flow rate of 2 L/s. Simulation circuit model which was prepared based on a DBD equivalent circuit, operated in a voltage range of 1.0 kV to 6.0 kV for frequency of 10 kHz to 66 kHz. Electrical characterization was performed to describe the plasma discharge that occurs in the reactor. The datas of supply voltage and current, as well as voltage and current discharge, was used to determine the average power during one period. From the simulation was obtained an increase in supply and discharge currents with increasing of frequency at the same operating voltage. Discharge power has increased in a specific voltage and increased frequency. It is obtained the average discharge power for 5.5 kV of 11.28 W and 10.90 W at a frequency of 21 kHz and 24 kHz, respectively. The highest efficiency obtained from the simulation that achieved at voltage of 1 kV and frequency of 45.7 kHz is equal to 56.59%.
ELECTRICAL PROPERTIES OF NI0.4MG0.6FE2O4 SYNTHESIZED BY CONVENTIONAL SOLID-ST...IAEME Publication
Ni0.4Mg0.6Fe2O4 samples are prepared by conventional double sintering approach and sintered at 1300oC/ 2 h. These ferrites are characterized using X-ray diffractometer. The diffraction study reveals that the present compound shows perfect single phase cubic spinel structure. In addition, the behavior of distinct electrical properties such as dielectric constant (ε'), dielectric loss (ε") and ac-conductivity (σac) as a function frequency as well as temperature is analyzed using the LCR controller
Similar to Electric potential gradient fractal dimension for characterizing shajara reservoirs of the permo carboniferous shajara formation, saudi arabia (20)
On Similarity of Differential Capacity and Capillary Pressure FractalKhalid Al-Khidir
On Similarity of Differential Capacity and Capillary Pressure Fractal Dimensions for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Electric potential gradient fractal dimension for characterizing shajara reservoirs of the permo carboniferous shajara formation, saudi arabia
1. 1 Volume 2018 , Issue 01
Arch Petro Chem Eng.
Advances in Petroleum and Chemical Engineering
Research Article Alkhidir KEME. Arch Petro Chem Eng: JPCE-101.
Electric potential gradient fractal dimension for characterizing Shajara
Reservoirs of the Permo-carboniferous Shajara formation, Saudi Arabia
Khalid Elyas Mohamed Elameen Alkhidir*
Department of Petroleum and Natural Gas Engineering, college of Engineering, King Saud University, Riyadh, Saudi arabia.
*
Corresponding author: Khalid Elyas Mohamed Elameen Alkhidir, Department of Petroleum and Natural Gas Engineering,
college of Engineering, King Saud University, Riyadh, Saudi arabia. Tel: +966114679118; Email:
kalkhidir@ksu.edu.sa
Citation: Alkhidir KEME (2018) Electric potential gradient fractal dimension for characterizing Shajara Reservoirs of the Permo-
carboniferous Shajara formation, Saudi Arabia. Arch Petro Chem Eng: JPCE-101.
Received Date: 25 May, 2018; Accepted Date: 28 May, 2018; Published Date: 06 June, 2018
Abstract
The quality and assessment of a reservoir can be documented in details by the application of electric potential gradient. This
research aims to calculate fractal dimension from the relationship among electric potential gradient, maximum electric potential
gradient 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 potential gradient, maximum electric potential
gradient 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 potential gradient and maximum electric potential gradient versus
logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). 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 Potential Gradient Fractal
Dimension Unit, Middle Shajara Electric Potential Gradient Fractal dimension Unit, and Upper Shajara Electric Potential
Gradient Fractal Dimension Unit. The results show similarity between electrical potential gradient 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.
Keywords: Capillary pressure fractal dimension; Electric potential gradient fractal dimension; Shajara Formation; Shajara
Reservoirs.
Intruduction
The wetting phase saturation can be described as function of
capillary pressure and fractal dimension was demonstrated by
[1]. The Purcell model was found to be the best fit to the
experimental data of the wetting phase relative permeability
for the cases as long as the measured capillary pressure curve
had the same residual saturation as the relative permeability
curve was described by [2]. A theoretical model to correlate
capillary pressure and resistivity index based on the fractal
scaling theory was reported by [3]. The fractal dimension
2. 2 Volume 2018 , Issue 01
Arch Petro Chem Eng.
Citation: Alkhidir KEME (2018) Electric potential gradient fractal dimension for characterizing Shajara Reservoirs of the Permo-
carboniferous Shajara formation, Saudi Arabia. Arch Petro Chem Eng: JPCE-101.
resulting from longer transverse NMR relaxation times and
lower capillary pressure reflects the volume dimension of
larger pores was described by [4]. The fractal dimension
derived from the short NMR relaxation times is similar to the
fractal dimension of the internal surface was described by [4].
The fractal dimensions can be used to represent the
complexity degree and heterogeneity of pore structure, and the
coexistence of dissolution pores and large intergranular pores
of Donghetang sandstones contributes to a heterogeneous pore
throat distribution and a high value of fractal dimension was
reported by [5].The relationship among capillary pressure
(PC), nuclear magnetic transverse relaxation time (T2) and
resistivity index (I) was studied by [6]. An increase of bubble
pressure fractal dimension and pressure head fractal
dimension and decreasing pore size distribution index and
fitting parameters m*n due to possibility of having
interconnected channels was confirmed by[7]. An increase of
fractal dimension with increasing arithmetic, geometric
relaxation time of induced polarization, permeability and
grain size was investigated by[8,9,10]. An increase of seismo
electric and resistivity fractal dimensions with increasing
permeability and grain size was described by [11,12].
Materials and Methods
Sandstone samples were collected from the surface type
section of the Permo-Carboniferous Shajara Formation,
latitude 2652 17.4, longitude 43 36 18. (Figure1). Porosity
was measured on collected samples using mercury intrusion
Porosimetry and permeability was derived from capillary
pressure data. The purpose of this paper is to obtain electric
potential gradient fractal dimension and to confirm it by
capillary pressure fractal dimension. The fractal dimension of
the first procedure is determined from the positive slope of the
plot of logarithm of the ratio of electric potential gradient to
maximum electric potential gradient (log(II0.5/IIImax0.5)
versus log wetting phase saturation (logI). Whereas the fractal
dimension of the second procedure is determined from the
negative slope of the plot of logarithm of log capillary
pressure (log (IX) versus logarithm of wetting phase
saturation (log I). The electric potential gradient can be scaled
as
𝐈 = [
[𝐈𝐈] 𝟎.𝟓
[𝐈𝐈𝐈] 𝐦𝐚𝐱
𝟎.𝟓
]
𝟑−𝐃𝐟
(𝟏)
Where I the water saturation, II the electric potential gradient
(volt/meter), [III]max the maximum electric potential gradient
(volt/meter), and Df the fractal dimension.
Equation 1 can be proofed from
𝐈𝐕 = [[
𝐕
𝐕𝐈 𝐦𝐚𝐱
]
𝟐
∗ 𝐕𝐈𝐈 ∗ 𝐈𝐈] (𝟐)
Where IV the electric current density in ampre/square meter,
V the pore radius in meter, VImax the maximum pore radius in
meter, VII the electric conductivity in Siemens per meter, and
II the electric potential gradient in volt per meter.
Multiply both sides of equation 2 byVI2
max
𝐈𝐕 ∗ 𝐕𝐈 𝐦𝐚𝐱
𝟐
= [𝐕 𝟐
∗ 𝐕𝐈𝐈 ∗ 𝐈𝐈] (𝟑)
Take the square root of equation 3
√𝐈𝐕 ∗ 𝐕𝐈 𝐦𝐚𝐱
𝟐 = √[𝐕 𝟐 ∗ 𝐕𝐈𝐈 ∗ 𝐈𝐈] (𝟒)
𝐈𝐕 𝟎.𝟓
∗ 𝐕𝐈 𝐦𝐚𝐱 = 𝐕 ∗ 𝐕𝐈𝐈 𝟎.𝟓
∗ 𝐈𝐈 𝟎.𝟓
( 𝟓)
Rearrange equation 5
𝐕 =
𝐈𝐕 𝟎.𝟓
∗ 𝐕𝐈 𝐦𝐚𝐱
𝐕𝐈𝐈 𝟎.𝟓 ∗ 𝐈𝐈 𝟎.𝟓
( 𝟔)
The maximum electric current density (VIIImax) can be scaled
as
𝐕𝐈 𝐦𝐚𝐱=
𝐕𝐈𝐈𝐈 𝐦𝐚𝐱
𝟎.𝟓
∗ 𝐕𝐈 𝐦𝐚𝐱
𝐕𝐈𝐈 𝟎.𝟓 ∗ 𝐈𝐈 𝟎.𝟓
(𝟕)
Divide equation 6 by equation 7
𝐕
𝐕𝐈 𝐦𝐚𝐱
=
𝐈𝐕 𝟎.𝟓∗𝐕𝐈 𝐦𝐚𝐱
𝐕𝐈𝐈 𝟎.𝟓∗𝐈𝐈 𝟎.𝟓
𝐕𝐈𝐈𝐈 𝐦𝐚𝐱
𝟎.𝟓 ∗𝐕𝐈 𝐦𝐚𝐱
𝐕𝐈𝐈 𝟎.𝟓∗𝐈𝐈 𝟎.𝟓
( 𝟖)
Equation 8 after simplification will become
𝐕
𝐕𝐈 𝐦𝐚𝐱
=
𝐈𝐕 𝟎.𝟓
𝐕𝐈𝐈𝐈 𝐦𝐚𝐱
𝟎.𝟓
( 𝟗)
Take the logarithm of equation 9
𝐥𝐨𝐠[
𝐕
𝐕𝐈 𝐦𝐚𝐱
] = 𝐥𝐨𝐠[
𝐈𝐕 𝟎.𝟓
𝐕𝐈𝐈𝐈 𝐦𝐚𝐱
𝟎.𝟓
] (𝟏𝟎)
𝐁𝐮𝐭; 𝐥𝐨𝐠[
𝐕
𝐕𝐈 𝐦𝐚𝐱
] =
𝐥𝐨𝐠 𝐈
𝟑 − 𝐃𝐟
(𝟏𝟏)
Insert equation 11 into equation 10
𝐥𝐨𝐠 𝐈
𝟑 − 𝐃𝐟
= 𝐥𝐨𝐠[
𝐈𝐕 𝟎.𝟓
𝐕𝐈𝐈𝐈 𝐦𝐚𝐱
𝟎.𝟓
] ( 𝟏𝟐)
Equation 12 after log removal will become
𝐈 = [
𝐈𝐕 𝟎.𝟓
𝐕𝐈𝐈𝐈 𝐦𝐚𝐱
𝟎.𝟓
]
𝟑−𝐃𝐟
(𝟏𝟑)
Equation 13 relates water saturation I; electric current density
IV ; maximum electric current density VIIImax; and the fractal
dimension Df
Insert equation 13 into equation 1
𝐈 = [
𝐈𝐕 𝟎.𝟓
𝐕𝐈𝐈𝐈 𝐦𝐚𝐱
𝟎.𝟓
]
𝟑−𝐃𝐟
= [
[𝐈𝐈] 𝟎.𝟓
[𝐈𝐈𝐈] 𝐦𝐚𝐱
𝟎.𝟓
]
[𝟑−𝐃𝐟]
(𝟏𝟒)
3. 3 Volume 2018 , Issue 01
Arch Petro Chem Eng.
Citation: Alkhidir KEME (2018) Electric potential gradient fractal dimension for characterizing Shajara Reservoirs of the Permo-
carboniferous Shajara formation, Saudi Arabia. Arch Petro Chem Eng: JPCE-101.
Equation 14 the proof of equation 1 which relates the water
saturation I, the electric potential gradient II, the maximum
electric potential (III)max gradient, and the fractal dimension
Df.
The capillary can be scaled as
𝐥𝐨𝐠 𝐈 = [𝐃𝐟 − 𝟑] ∗ 𝐥𝐨𝐠 𝐈𝐗 + 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 (𝟏𝟓)
Where I, the water saturation, IX, the capillary pressure and
Df the fractal dimension.
Result and Discussion
Based on field observation the Shajara Reservoirs of the
Shajara Formation of the Permo-Carboniferous Unayzah
Group were divided here into three units as described in
Figure1.These units from bottom to top are: Lower Shajara
Reservoir, Middle Shajara reservoir, and Upper Shajara
Reservoir.
Their acquired results of the electric potential gradient fractal
dimension and capillary pressure fractal dimension are
displayed in Table 1. Based on the attained results it was
found that the electric potential gradient fractal dimension is
equal to the capillary pressure fractal dimension. The
maximum value of the fractal dimension was found to be
2.7872 assigned to sample SJ13 from the Upper Shajara
Reservoir as verified in Table 1. Whereas the minimum value
of the fractal dimension 2.4379 was reported from sample SJ3
from the Lower Shajara reservoir as displayed in Table1. The
electric potential gradient fractal dimension and capillary
pressure fractal dimension were observed to increase with
increasing permeability as proofed in Table1 owing to the
possibility of having interconnected channels.
The Lower Shajara reservoir was denoted by six sandstone
samples (Figure 1), four of which label as SJ1, SJ2, SJ3 and
SJ4 were selected for capillary pressure measurement as
confirmed in Table1. Their positive slopes of the first
procedure ( log of the ratio of electric potential gradient to
maximum electric potential gradient versus log wetting phase
saturation) and negative slopes of the second procedure (log
capillary pressure versus log wetting phase saturation (I) are
delineated in Figure 2, Figure 3, Figure 4, and Figure 5. Their
electric potential gradient fractal dimension and capillary
pressure fractal dimension values are shown in Table 1. As we
proceed from sample SJ2 to SJ3 a pronounced reduction in
permeability due to compaction was reported from 1955 md to
56 md which reflects decrease in electric potential gradient
fractal dimension from 2.7748 to 2.4379 as specified in table
1. Again, an increase in grain size and permeability was
verified from sample SJ4 whose electric potential gradient
fractal dimension and capillary pressure fractal dimension was
found to be 2.6843 as described in table 1.
In contrast, the Middle Shajara reservoir which is separated
from the Lower Shajara reservoir by an unconformity surface
as shown in Figure 1. It was designated by four samples
(Figure 1), three of which named as SJ7, SJ8, and SJ9 as
illustrated in Table1 were selected for capillary measurements
as described in Table 1. Their positive slopes of the first
procedure and negative slopes of the second procedure are
shown in Figure 6, Figure 7 and Figure 8. Additionally, their
electrical potential gradient fractal dimensions and capillary
pressure fractal dimensions show similarities as delineated in
Table 1.Their fractal dimensions are higher than those of
samples SJ3 and SJ4 from the Lower Shajara Reservoir due to
an increase in their permeability as explained in table 1.
On the other hand, the Upper Shajara reservoiris separated
from the Middle Shajara reservoir by yellow green mudstone
as revealed in Figure 1. It is defined by three samples so
called SJ11, SJ12, SJ13 as explained in Table 1. Their positive
slopes of the first procedure and negative slopes of the second
procedure are displayed in Figure 9, Figure 10 and Figure 11.
Moreover, their electric potential gradient fractal dimension
and capillary pressure fractal dimension are also higher
thanthose of sample SJ3 and SJ4 from the Lower Shajara
Reservoir due to an increase in their permeability as clarified
in table 1.
Overall a plot of electric potential gradient fractal dimension
versus capillary pressure fractal dimension as shown in Figure
12 reveals three permeable zones of varying Petrophysical
properties. Such variation in fractal dimension can account for
heterogeneity which is a key parameter in reservoir quality
assessment. This reservoir heterogeneity was also confirmed
by plotting positive slope of the first procedure versus
negative slope of the second procedure as described in Figure
13.
Figure 1: Stratigraphic column of the surface type section of
the Permo-carboniferous Shajara Formation, latitude 2652
17.4, longitude 4336 18.
4. 4 Volume 2018 , Issue 01
Arch Petro Chem Eng.
Citation: Alkhidir KEME (2018) Electric potential gradient fractal dimension for characterizing Shajara Reservoirs of the Permo-
carboniferous Shajara formation, Saudi Arabia. Arch Petro Chem Eng: JPCE-101.
Figure 2: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ1.
Figure 3: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ2.
Figure 4: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ3.
Figure 5: Log (II0.5
/IIImax
0.5
) versus log I (blue color) & Log
IX versus log I (red color) for sample SJ4.
Figure 6: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ7.
Figure 7: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ8.
Figure 8: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ9.
Figure 9: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ11.
5. 5 Volume 2018 , Issue 01
Arch Petro Chem Eng.
Citation: Alkhidir KEME (2018) Electric potential gradient fractal dimension for characterizing Shajara Reservoirs of the Permo-
carboniferous Shajara formation, Saudi Arabia. Arch Petro Chem Eng: JPCE-101.
Figure 10: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ12.
Figure 11: Log (II0.5
/IIImax
0.5
) versus log I (blue color)& Log
IX versus log I (red color) for sample SJ13.
Figure 12: Electric potential gradient fractal dimension versus
capillary pressure fractal dimension
Figure 13: Positive slope of the first procedure versus
negative slope of the second procedure
Formation Reservoir Sample
Porosity
%
k
(md)
Positive
slope of the
first
procedure
Slope=3-Df
Negative
slope of the
second
procedure
Slope=Df-3
Electric
potential
gradient
fractal
dimension
Capillary
pressure
fractal
dimension
Permo-CarboniferousShajara
Formation
Upper
Shajara
Reservoir
SJ13 25 973 0.2128 -0.2128 2.7872 2.7872
SJ12 28 1440 0.2141 -0.2141 2.7859 2.7859
SJ11 36 1197 0.2414 -0.2414 2.7586 2.7586
Middle
Shajara
Reservoir
SJ9 31 1394 0.2214 -0.2214 2.7786 2.7786
SJ8 32 1344 0.2248 -0.2248 2.7752 2.7752
SJ7 35 1472 0.2317 -0.2317 2.7683 2.7683
Lower
Shajara
Reservoir
SJ4 30 176 0.3157 -0.3157 2.6843 2.6843
SJ3 34 56 0.5621 -0.5621 2.4379 2.4379
SJ2 35 1955 0.2252 -0.2252 2.7748 2.7748
SJ1 29 1680 0.2141 -0.2141 2.7859 2.7859
Table 1: Petrophysical model showing the three Shajara Reservoir Units with their corresponding values of electric potential
gradient fractal dimension and capillary pressure fractal dimension.
6. 6 Volume 2018 , Issue 01
Arch Petro Chem Eng.
Citation: Alkhidir KEME (2018) Electric potential gradient fractal dimension for characterizing Shajara Reservoirs of the Permo-
carboniferous Shajara formation, Saudi Arabia. Arch Petro Chem Eng: JPCE-101.
Conclision
The sandstones of the Shajara Reservoirs of the Shajara
formation permo-Carboniferous were divided here into
three units based on electric potential gradient fractal
dimension
The Units from base to top are: Lower Shajara electric
potential gradient Fractal dimension Unit, Middle
Shajara Electric Potential Gradient Fractal Dimension
Unit, and Upper Shajara Electric Potential Gradient
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.
Acknowledgement
The author would to thanks King Saud University, college
of Engineering, Department of Petroleum and natural gas
engineering, Department of Chemical Engineering,
Research Centre at College of Engineering, and King
Abdullah Institute for research and consulting Studies for
their supports.
References
1. Toledo GT, Navy RA, Davis HT, Scriven LE (1994)
Capillary pressure, water relative permeability,
electrical conductivity and capillary dispersion
coefficient of fractal porous media at low wetting phase
saturation. SPE advanced technology Series 2: 136-141.
2. Li K, Horne RN (2002) Experimental verification of
methods to calculate relative permeability using
capillary pressure data. SPE 76757, Proceedings of the
2002 SPE Western Region Meeting/AAPG Pacific
Section Joint Meeting held in Anchorage, Alaska.
3. Li K, Willams W (2007) Determination of capillary
Pressure function from resistivity data. Transp. Porous
Media 67: 1-15.
4. Zhang Z, Weller A (2014) Fractal Dimension of Pore-
Space Geometry of Eocene sandstone formation.
Geophysics 79: D377-D387.
5. Wang Z, Pan M, Shi Y, Liu L, Xiong F, Qin Z (2018)
Fractal analysis of Donghetangs and stones using NMR
measurements. Energy & Fuels 32: 2973-2982.
6. Guo Y-h, Pan B-z, Zhang L-h, Fang C-h (2018)
Research and application of the relationship between
transverse relaxation time and resistivity index in tight
sandstone reservoir. J Petrol Sci Eng 160: 597-604.
7. AlKhidir KEME (2017) Pressure head fractal
dimension for characterizing Shajara Reservoirs of the
Shajara Formation of the Permo-Carboniferous
Unayzah Group, Saudi Arabia. Arch Pet Environ
Biotechnol: 1-7.
8. Alkhidir KEME (2018) Arithmetic relaxation time of
induced polarization fractal dimension for
characterizing Shajara Reservoirs of the Shajara
Formation. Nanosci Nanotechnol 1:1-8
9. Alkhidir KEME (2018) Geometric relaxation time of
induced polarization fractal dimensionfor characterizing
Shajara Reservoirs of the Shajara formation of the
Permo-Carboniferous Unayzah Group-Permo. Int J Pet
Res 2: 105-108.
10. Alkhidir KEME (2018) Geometric relaxation time of
induced polarization fractal dimensionfor characterizing
Shajara Reservoirs of The Shajara Formation of the
Permo-Carboniferous Unayzah Group, Saudi Arabia.
SF J Petroleum 2: 1-6.
11. AlKhidir KEME (2018) Seismo Electric field fractal
dimension for characterizing Shajara Reservoirs of the
Permo-Carboniferous Shajara Formation, Saudi Arabia.
Pet Petro Chem Eng J 2: 1-8.
12. Alkhidir KEME (2018) Resistivity Fractal Dimension
for Characterizing Shajara Reservoirs of the Permo
Carboniferous Shajara Formation Saudi Arabia. Recent
Adv. Petrochem Sci 5: 1-6.