99/00198 Study of the relationship between fractal dimension and viscosity ratio for viscous fingering with a modified DLA model

1999 ◽  
Vol 40 (1) ◽  
pp. 20
Keyword(s):  
Fractal Dimension ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
The Relationship ◽  
Dla Model

Study of Fingering Dynamics of Two Immiscible Fluids in a Homogeneous Porous Medium with Considering Wettability Effects Using a Pore-Scale Multicomponent Lattice Boltzmann Model

2021 ◽  
Author(s):  
Eslam Ezzatneshan ◽  
Reza Goharimehr
Keyword(s):  
Porous Medium ◽  
Dynamic Viscosity ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Immiscible Fluids ◽  
Pore Scale ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.

An analysis of fractal dimension and tortuosity based on 2D numerical reconstruction model of reservoir rocks

2019 ◽  
Vol 7 (4) ◽  
pp. SJ1-SJ6 ◽  
Author(s):  
Liang Luo ◽  
Jiahong Jin ◽  
Wei Wei ◽  
Jianchao Cai
Keyword(s):  
Fractal Dimension ◽  
Oil And Gas ◽  
Universal Method ◽  
Structure Generation ◽  
Reservoir Rocks ◽  
Numerical Reconstruction ◽  
The Monte Carlo Method ◽  
Microstructure Parameters ◽  
Rock Model ◽  
The Relationship

The microstructure of reservoir rocks plays an important role in oil and gas accumulation and production. We examine a universal method to evaluate these properties of rocks, such as pore tortuosity, matrix porosity, and connectivity, and we respectively construct a 2D numerical reconstruction rock model with different microstructure parameters by the Monte Carlo method and the quartet structure generation set method. We further study the heterogeneity (characterized by fractal dimension and tortuosity) of the constructed image for reservoir rocks by the numerical and theoretical analysis and obtain the formulas for fractal dimension and tortuosity versus porosity. The simulation results show that the logarithmic relation is between the pore fractal dimension and porosity, and the relationship between tortuosity and porosity has the form of power. This process provided an important method to advance 2D reconstruction technology of reservoir rocks and effectively determine the relationship between microstructure and porosity.

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 Shape matters: morphological metrics of glioblastoma imaging abnormalities as biomarkers of prognosis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lee Curtin ◽  
Paula Whitmire ◽  
Haylye White ◽  
Kamila M. Bond ◽  
Maciej M. Mrugala ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Tumor Location ◽  
Primary Brain Tumor ◽  
Resonance Imaging ◽  
Significant Relationships ◽  
Biological Phenomena ◽  
Microenvironmental Factors ◽  
Magnetic Resonance Imaging Mri ◽  
The Relationship ◽  
Standard Magnetic Resonance Imaging

AbstractLacunarity, a quantitative morphological measure of how shapes fill space, and fractal dimension, a morphological measure of the complexity of pixel arrangement, have shown relationships with outcome across a variety of cancers. However, the application of these metrics to glioblastoma (GBM), a very aggressive primary brain tumor, has not been fully explored. In this project, we computed lacunarity and fractal dimension values for GBM-induced abnormalities on clinically standard magnetic resonance imaging (MRI). In our patient cohort (n = 402), we connect these morphological metrics calculated on pretreatment MRI with the survival of patients with GBM. We calculated lacunarity and fractal dimension on necrotic regions (n = 390), all abnormalities present on T1Gd MRI (n = 402), and abnormalities present on T2/FLAIR MRI (n = 257). We also explored the relationship between these metrics and age at diagnosis, as well as abnormality volume. We found statistically significant relationships to outcome for all three imaging regions that we tested, with the shape of T2/FLAIR abnormalities that are typically associated with edema showing the strongest relationship with overall survival. This link between morphological and survival metrics could be driven by underlying biological phenomena, tumor location or microenvironmental factors that should be further explored.

Microstructure of Agglomerates of Nanometer Particles

1995 ◽  
Vol 380 ◽  
Author(s):  
Alfred P. Weber ◽  
James D. Thorne ◽  
Sheldon K. Friedlander
Keyword(s):  
Fractal Dimension ◽  
Laser Ablation ◽  
Coordination Number ◽  
Computer Simulations ◽  
Large Fraction ◽  
Low Density ◽  
Nanometer Particles ◽  
The Relationship

ABSTRACTThe microstructure of an agglomerate can be characterized by the coordination number. The relationship between the fractal dimension and the coordination number of agglomerates of nanometer particles was investigated in experiments and computer simulations. The results for silver agglomerates formed by laser ablation agreed well with the simulations. The coordination number is low for low density fractals because of the large fraction of surface particles which have fewer bonds. The sensitivity of the coordination number to the fractal dimension increases with increasing fractal dimension.

A Numerical Study for the Relationship between Natural Manganese Dendrites and DLA Patterns

2016 ◽  
Vol 71 (3) ◽  
pp. 225-234
Author(s):  
Tugba Ozbey ◽  
Mehmet Bayirli
Keyword(s):  
Critical Exponent ◽  
Numerical Study ◽  
Formation Mechanisms ◽  
Diffusion Limited Aggregation ◽  
Density Correlation ◽  
Diffusion Limited ◽  
Crystalline Anisotropy ◽  
The Relationship ◽  
Good Agreement ◽  
Dla Model

AbstractThe formation mechanisms and the origin of manganese dendrites on the magnesite ore have been under discussion. The growth process of the manganese dendrites is statistically studied by comparing them to aggregations obtained according to the diffusion limited aggregation (DLA) model via Monte Carlo simulations. In this case, ten manganese dendrite patterns changing from the least dense to the densest aggregations on the surface are separately selected to determine the relationship between real and simulated patterns. The sticking parameter is ranged from 0.05≤t≤1. The density–density correlation functions C(r) (their critical exponent A), fractal dimension Df, critical exponent α, and critical exponent β pertaining to the root mean square (rms) thickness have been computed for both the ten manganese dendrites and the simulated aggregations representing them. The results indicate that manganese dendrites may be determined with the general DLA model. Analyses of manganese dendrites, both scaling and simulations, suggest the growth mechanism for the macroscopic expression of crystalline anisotropy for the dendritic patterns. These results are in good agreement with the values in other literature and can be helpful in comparing natural and simulated aggregations (both dendritic and compact deposits).

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