scholarly journals Thermo Electric Sensitivity Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2019 ◽  
Vol 2 (3) ◽  
Keyword(s):  
Fractal Dimension ◽  
Capillary Pressure ◽  
Functional Relationship ◽  
Fractal Dimensions ◽  
Thermo Electric ◽  
Sensitivity Maximum ◽  
Phase Saturation ◽  
Second Procedure ◽  
The Relationship ◽  
Electric Sensitivity

The quality and assessment of a reservoir can be documented in details by the application of thermo electric sensitivity. This research aims to calculate fractal dimension from the relationship among thermo electric sensitivity, maximum thermo electric sensitivity and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among capillary pressure and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, thermo electric sensitivity, maximum Thermo electric sensitivity 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 thermo electric sensitivity and maximum thermo electric sensitivity versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined 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.

scholarly journals Seismo Radial Grain Velocity Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2020 ◽  
Vol 4 (1) ◽  
Keyword(s):  
Saudi Arabia ◽  
Fractal Dimension ◽  
Capillary Pressure ◽  
Functional Relationship ◽  
Fractal Dimensions ◽  
Velocity Versus ◽  
Phase Saturation ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of seismo radial grain velocity. This research aims to calculate fractal dimension from the relationship among seismo radial grain velocity, maximum seismo radial grain velocity and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among capillary pressure and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismo radial grain velocity, maximum seismo radial grain velocity 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 seismo radial grain velocity and maximum seismo radial grain velocity versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined 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.

scholarly journals On Similarity of Seismo Magnetic Power Density and Pressure Head Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2020 ◽  
pp. 1-8
Author(s):  
Khalid Elyas Mohamed Elameen Alkhidir ◽  
Keyword(s):  
Fractal Dimension ◽  
Power Density ◽  
Functional Relationship ◽  
Fractal Dimensions ◽  
Pressure Head ◽  
Density Maximum ◽  
Phase Saturation ◽  
Head Pressure ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of seismo magnetic power density. This research aims to calculate fractal dimension from the relationship among seismo magnetic power density, maximum seismo magnetic power density and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among inverse pressure head * pressure head and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismo magnetic power density, maximum seismo magnetic power density and fractal dimension. The second equation implies to the wetting phase saturation as a function of pressure head 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 seismo magnetic power density and maximum seismo magnetic power density versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm (inverse of pressure head and pressure head) 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

scholarly journals Seismo Electric Transfer Function Fractal Dimension for Characterizing Shajara Reservoirs Of The Permo-Carboniferous Shajara Formation, Saudi Arabia

2018 ◽  
Vol 1 (1) ◽  
Keyword(s):  
Fractal Dimension ◽  
Transfer Function ◽  
Capillary Pressure ◽  
Fractal Dimensions ◽  
Pressure Profile ◽  
Wide Range ◽  
Phase Saturation ◽  
Second Procedure ◽  
Bottom To Top ◽  
The Relationship

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). 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 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.

scholarly journals On Similarity of Seismo Magentic Field and Pressure Head Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2020 ◽  
Vol 4 (1) ◽  
Keyword(s):  
Magnetic Field ◽  
Fractal Dimension ◽  
Functional Relationship ◽  
Fractal Dimensions ◽  
Pressure Head ◽  
Field Versus ◽  
Phase Saturation ◽  
Head Pressure ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of seismo magnetic field. This research aims to calculate fractal dimension from the relationship among seismo magnetic field, maximum seismo magnetic field and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among inverse pressure head * pressure head and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismo magnetic field, maximum seismo magnetic field and fractal dimension. The second equation implies to the wetting phase saturation as a function of pressure head 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 seismo magnetic field and maximum seismo magnetic field versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm (inverse of pressure head and pressure head) 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.

scholarly journals On Similarity of Seismo Magentic Field and Pressure Head Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2020 ◽  
Vol 3 (1) ◽  
Keyword(s):  
Magnetic Field ◽  
Fractal Dimension ◽  
Functional Relationship ◽  
Fractal Dimensions ◽  
Pressure Head ◽  
Field Versus ◽  
Phase Saturation ◽  
Head Pressure ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of seismo magnetic field. This research aims to calculate fractal dimension from the relationship among seismo magnetic field, maximum seismo magnetic field and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among inverse pressure head * pressure head and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismo magnetic field, maximum seismo magnetic field and fractal dimension. The second equation implies to the wetting phase saturation as a function of pressure head 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 seismo magnetic field and maximum seismo magnetic field versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm (inverse of pressure head and pressure head) 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.

scholarly journals Diffusion coefficient fractal dimension for characterizing Shajara reservoirs of the Permo – carboniferous Shajara formation, Saudi Arabia

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Khalid Elyas Mohamed Elameen Alkhidir
Keyword(s):  
Diffusion Coefficient ◽  
Fractal Dimension ◽  
Capillary Pressure ◽  
Fractal Dimensions ◽  
Pressure Profile ◽  
Phase Saturation ◽  
Coefficient Versus ◽  
Second Procedure ◽  
Bottom To Top ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of diffusion coefficient. This research aims to calculate fractal dimension from the relationship among diffusion coefficient, maximum diffusion coefficient and wetting phase saturation and to approve 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, diffusion coefficient, maximum diffusion coefficient 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 diffusion coefficient and maximum diffusion 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 determined 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 obtained units from bottom to top are: Lower, Middle and Upper Shajara Diffusion Coefficient Fractal Dimension Units. It was found that fractal dimension increases with increasing grain size and permeability.

scholarly journals Seismic Shear Wave Velocity Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2019 ◽  
Vol 2 (3) ◽  
Keyword(s):  
Fractal Dimension ◽  
Capillary Pressure ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Velocity Versus ◽  
Seismic Shear ◽  
Phase Saturation ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of seismic shear wave. This research aims to calculate fractal dimension from the relationship among seismic shear wave velocity, maximum seismic shear wave velocity and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among capillary pressure and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismic shear wave velocity and maximum seismic shear wave velocity 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 seismic shear wave velocity and maximum seismic shear wave velocity versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined 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.

scholarly journals Transverse Relaxation Time Fractal Dimension of Nuclear Magnetic Resonance for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2019 ◽  
Vol 2 (2) ◽  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Fractal Dimension ◽  
Relaxation Time ◽  
Magnetic Resonance ◽  
Capillary Pressure ◽  
Transverse Relaxation Time ◽  
Transverse Relaxation ◽  
Phase Saturation ◽  
Second Procedure ◽  
Nuclear Magnetic

The quality of a reservoir can be described in details by the application of transverse relaxation time of nuclear magnetic resonance fractal dimension. The objective of this research is to calculate fractal dimension from the relationship among transverse relaxation time of nuclear magnetic resonance, maximum transverse relaxation time of nuclear magnetic resonance 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, transverse relaxation time of nuclear magnetic resonance, maximum transverse relaxation time of nuclear magnetic resonance 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 transverse relaxation time of nuclear magnetic resonance and maximum transverse relaxation time of nuclear magnetic resonance versus logarithm wetting phase saturation. The slope of the first procedure = 3-Df (fractal dimension). The second procedure for obtaining the fractal dimension was completed by plotting logarithm of capillary pressure versus the logarithm of wetting phase saturation. The slope of the second procedure = Df -3. The results show similarities between transverse relaxation time of nuclear magnetic resonance and capillary pressure fractal dimension.

Pore size fractal dimension for characterizing Au/TiO2 catalyst

2018 ◽  
Vol 32 (33) ◽  
pp. 1850415
Author(s):  
Asif Mahmood
Keyword(s):  
Fractal Dimension ◽  
Pore Size ◽  
Surface Area ◽  
Pore Volume ◽  
Bet Surface Area ◽  
Negative Slope ◽  
Phase Saturation ◽  
Maximum Pore Size ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a catalyst can be documented in detail by the application of pore size. This research aims to calculate fractal dimension from the relationship among pore size, maximum pore size and wetting phase saturation and to confirm it by the fractal dimension derived from the relationship among the ratio between surface area per unit pore volume, entry surface area per unit pore volume and wetting phase saturation. In this research, pore size was measured on Au/TiO2 using Brunauer–Emmett–Teller (BET) surface area. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, pore size, maximum pore size and fractal dimension. The second equation implies to the wetting phase saturation as a function of surface area per unit pore volume, entry surface area per unit pore volume 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 pore size and maximum pore size versus logarithm wetting phase saturation. The positive slope of the first procedure = 3 − Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm of the ratio between surface area per unit pore volume, entry surface area per unit pore volume versus the logarithm of wetting phase saturation. The negative slope of the second procedure = Df − 3. It was found that the plasma + thermally treated Au/TiO2 has the highest fractal dimension value owing to possibility of having holes and channels. The results also show similarity between pore size fractal dimension and surface area per unit pore volume fractal dimension. In our case, as conclusions, the higher the fractal dimension, the better the catalytic activity.

THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 217-229 ◽  
Author(s):  
FRANK B. TATOM
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractional Calculus ◽  
Fractal Dimensions ◽  
Linear Functions ◽  
Fractal Curve ◽  
Random Fractal ◽  
Fractal Functions ◽  
Decay Exponent ◽  
The Relationship

The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-differentiation are developed. Based on an understanding of fractional calculus applied to random fractal functions, consideration is given to an analogous application to deterministic or nonrandom fractals. The concept of expressing each coordinate of a deterministic fractal curve as a “pseudo-time” series is investigated. Fractional integro-differentiation of such series is numerically carried out for the case of quadric Koch curves. The resulting time series produces self-similar patterns with fractal dimensions which are linear functions of the order of the fractional integro-differentiation. These curves are assigned the name, fractional Koch curves. The general conclusion is reached that fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates which can be expressed as functions of one independent variable, which is typically time (or pseudo-time).

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