Fractal Analysis of Effective Permeability for Meter Fluid

2013 ◽  
Vol 331 ◽  
pp. 181-183
Author(s):  
Mei Juan Yun
Keyword(s):  
Fractal Dimension ◽  
Fluid Flow ◽  
Effective Permeability ◽  
Structural Parameters ◽  
Empirical Constant ◽  
Clear Physical Meaning ◽  
Fractal Models ◽  
Fractal Properties ◽  
Analytical Expressions ◽  
Physical Principles

The Meter fluid is the representative fluid which may be reduced to the Reiner-Philippoff, Ellis and Newtonian fluids in appropriate conditions. Fractal models for flow rate, velocity and effective permeability for Meter fluid in a capillary are proposed based on the fractal properties of tortuous capillary. There are no empirical constant and all parameters in the proposed expressions have clear physical meaning. The proposed models are expressed as functions of relate the properties of Meter fluid to the structural parameters of fractal capillary. It is shown that the effective permeability increases with the increase of pressure gradient and decreases with the increase of tortuosity fractal dimension. The analytical expressions help to reveal the physical principles for Meter and other non-Newtonian fluid flow.

Fractal Study on Rabinowitch Fluid Flow in a Capillary

2013 ◽  
Vol 331 ◽  
pp. 141-143
Author(s):  
Mei Juan Yun
Keyword(s):  
Effective Permeability ◽  
Fluid Transport ◽  
Structural Parameters ◽  
Characteristic Parameters ◽  
Empirical Constant ◽  
Clear Physical Meaning ◽  
Fractal Models ◽  
Fractal Properties ◽  
Analytical Expressions ◽  
Physical Principles

Fractal models for flow rate, velocity and effective permeability of Rabinowitch fluid in a capillary are proposed based on the fractal properties of tortuous capillary. There is no empirical constant and each parameter in the proposed expressions has clear physical meaning. The effective permeability is expressed as a function of radius of capillary, straight distance of capillary, tortuosity fractal dimension, fluid characteristic parameters and pressure difference, and it relate the properties of Rabinowitch fluid with the structural parameters of fractal capillary. The presented analytical expressions reveal and improve the understanding of the physical principles of Rabinowitch fluid transport through a capillary.

scholarly journals Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Meijuan Yun
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Quantitative Description ◽  
Flow In Porous Media ◽  
Power Law Fluid ◽  
Related Data ◽  
Fractal Models ◽  
Fractal Properties ◽  
Seepage Characteristics ◽  
Analytical Expressions

We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.

scholarly journals Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

2021 ◽  
Author(s):  
Amirsaman Rezaeyan ◽  
Vitaliy Pipich ◽  
Jingsheng Ma ◽  
Leon Leu ◽  
Timo Seemann ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fluid Flow ◽  
Pore Size ◽  
Transport Properties ◽  
Transport Phenomena ◽  
Slip Flow ◽  
Pore Sizes ◽  
Size Dependent ◽  
Fractal Models ◽  
Continuum Flow

AbstractIn geoenergy applications, mudrocks prevent fluids to leak from temporary (H2, CH4) or permanent (CO2, radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

STRUCTURAL PARAMETERS OF AQUEOUS COLLOIDAL DISPERSIONS OF FULLERENE C60

2019 ◽  
pp. 31-37
Author(s):  
V.Yu. Fokina ◽  
E.А. Kizima ◽  
I.V. Miheev ◽  
A.I. Ivankov ◽  
V.M. Garamus
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Structural Parameters ◽  
Colloidal Dispersions ◽  
Fullerene C60 ◽  
Solvent Exchange ◽  
X Ray ◽  
Dense Nucleus ◽  
Exchange Technique

Two types of fullerene C60 water dispersions were investigated by a small-angle X-ray and neutron scattering. As a result, structural parameters of fullerene aggregates were obtained. The water dispersions were obtained by the solvent-exchange technique and by huge dilution of initial C60/Nmethylpyrrolidone solution. The structure organization of water dispersions is considered in respect to their technique preparation. It was shown that fullerene aggregates were characterized by highly polydispersity in size for all dispersions. In the case of son/nC60 dispersion it was found that fullerenes formed aggregates with a dense nucleus (namely a surface fractal) with a radius of 58 ± 1 nm and a fractal dimension of 2.3. In turn, the nmp/nC60 system was characterized by the branched aggregates with fractal dimension 1.5 and bimodal particle size distribution.

scholarly journals DEVELOPMENT OF THE BASIC CAPACITIVE ACCELEROMETERS MODELS BASED ON THE VHDL-AMS LANGUAGE FOR THE CIRCUIT LEVEL OF COMPUTER-AIDED DESIGN

2020 ◽  
Vol 2 (1) ◽  
pp. 15-20
Author(s):  
V. M. Teslyuk ◽  
◽  
P. Yu. Denysyuk ◽  
T. V. Teslyuk ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Computer Aided Design ◽  
Structural Parameters ◽  
Software Systems ◽  
Mems Devices ◽  
Electric Circuits ◽  
Capacitive Accelerometer ◽  
Level Of Automation ◽  
Electric Parameters ◽  
Physical Principles

In the article, the basic VHDL-AMS models of MEMS-based capacitive accelerometers were developed. The models were designed for two basic types of capacitive accelerometers, namely lamellar and counter-pivotal. The developed models allow us to determine the source of electrical capacitive accelerometers depending on the incoming mechanical and structural parameters and were constructed for MEMS CAD at the circuit level. The circuit level of MEMS development requires an analysis of the total integrated device electric circuits. For this purpose, all the MEMS components should be written in the specific software systems, which would be understandable for the software system. Taking into account that MEMS devices operate on different physical principles, certain difficulties may arise during the electrical analysis, that is, the work of mechanical or other devices need to be described with the help of electric parameters. In the general case, the method for building the VHDL-AMS model of the MEMS-based capacitive accelerometer is needed construction of the simplified mechanical model, and then a simplified electrical model. On the basis of the simplified models, the VHDL-AMS model of electromechanical MEMS devices has been developed. In the article, the method of automated synthesis and mathematical models using the VHDL-AMS language, which is based on the method of electrical analogies were described. They use systems of ordinary differential equations and partial differential equations to determine the relationships between input and output parameters. The sequence and quantity of used differential equations are determined by the physical principles of operation of the MEMS element and the number of energy transformations, which allows increasing the level of automation of synthesis operations compared to existing methods. The results of the basic lamellar and counter-pivotal capacitive accelerometers are also shown. This enables to conduct research and analysis of its parameters and investigate the output electric parameters dependence on the input mechanical ones.

Fractal Properties of Financial Assets and Forcasting Financial Crisis

2018 ◽  
pp. 23-41 ◽  
Author(s):  
Inna Nekrasova ◽  
Oxana Karnaukhova ◽  
Oleg Sviridov
Keyword(s):  
Fractal Dimension ◽  
Financial Markets ◽  
Future Development ◽  
Small Time ◽  
Practical Significance ◽  
Financial Assets ◽  
Time Intervals ◽  
Price Fluctuations ◽  
Fractal Properties ◽  
Fractal Index

The chapter is aimed at identification of criteria to select financial assets for investment; observing price fluctuations at small time intervals (up to one week) as possible predictors of the future of a significant increase in the price fluctuations amplitude; determining a fractal dimension of the financial markets on the basis of R/S-analysis; constructing a fractal index indicator to identify a bifurcation point, which gives birth to a possibility of crisis phenomena in economy. Therefore, the practical significance of the chapter lies in the idea of equipping academics and practitioners with new methods and tools for analysis and forecasting future development and dynamics of the financial markets.

Analysis and Research on Fractal Model of Normal Contact Stiffness of Joint Interfaces

2011 ◽  
Vol 328-330 ◽  
pp. 336-345
Author(s):  
Guo Sheng Lan ◽  
Xue Liang Zhang ◽  
Hong Qin Ding ◽  
Shu Hua Wen ◽  
Zhong Yang Zhang
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Normal Load ◽  
Contact Stiffness ◽  
Fractal Model ◽  
Normal Contact ◽  
Fractal Models ◽  
Normal Contact Stiffness

Through the analysis and research on three fractal models of normal contact stiffness of joint interfaces, the differences between them can be found. Furthermore, numerical simulation was carried out to obtain the complicated nonlinear relations between normal contact stiffness and the normal load. The results show that the normal contact stiffness increases with the normal load, decreases with G but complicatedly varies with D. According to different fractal dimension, we can chose an appropriate one among the three fractal models of normal contact stiffness of joint interfaces when describing normal contact stiffness of joint interfaces.

Spatial Distribution and Fractal Properties of Aggregating Magnetic and Non-Magnetic Particles

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 219-230 ◽  
Author(s):  
A. Provata ◽  
K. N. Trohidou
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Magnetic Particles ◽  
Composite System ◽  
System Size ◽  
Real Space ◽  
Magnetic Clusters ◽  
Self Similarity ◽  
Fractal Properties ◽  
Simple Connectivity

We study the spatial distribution in aggregating systems of mixtures of magnetic and non-magnetic particles using Monte-Carlo simulations together with scaling arguments. In particular, we show that (a) as the system size grows, the fractal dimension of the composite system is dominated by the smaller fractal dimension, (b) the system is realized as a back-bone consisting of magnetic particles (lower fractal dimension) with denser regions of non-magnetic particles attached to it at random positions. Using simple connectivity features observed in pure magnetic and non-magnetic clusters and self-similarity arguments we predict, via Real-Space-Renormalization, fractal exponents Dm = 1.25 ± 0.05 for the magnetic clusters and Dnm = 1.4 ± 0.1 for the non-magnetic clusters.

scholarly journals Applications of fractal analysis to physiology

1991 ◽  
Vol 70 (6) ◽  
pp. 2351-2367 ◽  
Author(s):  
R. W. Glenny ◽  
H. T. Robertson ◽  
S. Yamashiro ◽  
J. B. Bassingthwaighte
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Temporal Correlation ◽  
Physiological Data ◽  
Fractal Properties ◽  
Fractal Analyses ◽  
Intact Organism ◽  
Physiological Systems

This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism.

scholarly journals FRACTAL DIMENSIONS FOR UNSATURATED POROUS MEDIA

Fractals ◽  
2004 ◽  
Vol 12 (01) ◽  
pp. 17-22 ◽  
Author(s):  
BOMING YU ◽  
JIANHUA LI
Keyword(s):  
Porous Media ◽  
Transport Properties ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Thermal Dispersion ◽  
Unsaturated Porous Media ◽  
Empirical Constant ◽  
Pore Sizes ◽  
Analytical Expressions

The analytical expressions of the fractal dimensions for wetting and non-wetting phases for unsaturated porous media are derived and are found to be a function of porosity, maximum and minimum pore sizes as well as saturation. There is no empirical constant in the proposed fractal dimensions. It is also found that the fractal dimensions increase with porosity of a medium and are meaningful only in a certain range of saturation Sw, i.e. Sw>S min for wetting phase and Sw<S max for non-wetting phase at a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified to be consistent with the existing experimental observations and it makes possible to analyze the transport properties such as permeability, thermal dispersion in unsaturated porous media by fractal theory and technique.

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