A NUMERICAL STUDY OF EQUIVALENT PERMEABILITY OF 2D FRACTAL ROCK FRACTURE NETWORKS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050014
Author(s):  
XIAOSHAN WANG ◽  
YUJING JIANG ◽  
RICHENG LIU ◽  
BO LI ◽  
ZAIQUAN WANG
Keyword(s):  
Numerical Study ◽  
Fractured Rock ◽  
Rock Fracture ◽  
Least Square Method ◽  
Site Investigation ◽  
Fracture Network ◽  
Least Square ◽  
Fracture Density ◽  
Equivalent Permeability ◽  
Dfn Model

This paper presents a numerical study on the equivalent permeability of a fractured rock. A series of two-dimensional discrete fracture network (DFN) models for the calculation of equivalent permeability are generated based on discrete element method (DEM). A sufficient large “parent” DFN model is generated based on the data obtained from a site investigation result of Three Gorges Project in China. Smaller DFN models are extracted from the large “parent” DFN model to calculate the equivalent permeability with an interval of rotation angle of [Formula: see text]. Fluid flow through fractures in both horizontal and vertical directions is simulated. The results show that when the side length of DFN models are larger than 40[Formula: see text]m, the equivalent permeability of both [Formula: see text] and [Formula: see text] become stable, indicating that a DFN model size of 40[Formula: see text]m can be approximated as a representative elementary volume (REV) for those studied rocks. Penetration ellipses are fitted using the least square method on the basis of the calculated equivalent permeability tensor and the main seepage directions of this fractured rock were determined as 63–67[Formula: see text]. Fractal characteristics of DFN models are analyzed with box-counting method by changing the fracture trace length and fracture density, and the results show that equivalent permeability exhibits a logarithmic increasing trend with the increment of fractal dimension.

scholarly journals Correlations between Geometric Properties and Permeability of 2D Fracture Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiaolin Wang ◽  
Liyuan Yu ◽  
Hanqing Yang
Keyword(s):  
Fractured Rock ◽  
Rock Fracture ◽  
Fractal Dimensions ◽  
Fracture Network ◽  
Network Structures ◽  
Rock Masses ◽  
Fracture Networks ◽  
Geometric Properties ◽  
Equivalent Permeability ◽  
Fractured Rock Masses

The equivalent permeability of fractured rock masses plays an important role in understanding the fluid flow and solute transport properties in underground engineering, yet the effective predictive models have not been proposed. This study established mathematical expressions to link permeability of 2D fracture networks to the geometric properties of fractured rock masses, including number density of fracture lines, total length of fractures per square meter, and fractal dimensions of fracture network structures and intersections. The results show that the equivalent permeability has power law relationships with the geometric properties of fracture networks. The fractal dimensions that can be easily obtained from an engineering site can be used to predict the permeability of a rock fracture network. When the fractal dimensions of fracture network structures and intersections exceed the critical values, the effect of randomness of fracture locations is negligible. The equivalent permeability of a fracture network increases with the increment of fracture density and/or fractal dimensions proportionally.

scholarly journals Developing a new algorithm for numerical modeling of discrete fracture network (DFN) for anisotropic rock and percolation properties

2021 ◽  
Vol 11 (2) ◽  
pp. 839-856
Author(s):  
Erfan Hosseini ◽  
Mohammad Sarmadivaleh ◽  
Zhongwei Chen
Keyword(s):  
Fractured Rock ◽  
Fracture Network ◽  
Connected Components ◽  
Threshold Condition ◽  
Fracture Density ◽  
Anisotropic Rock ◽  
Fracture Properties ◽  
Fracture Length ◽  
Discrete Fracture ◽  
Dfn Model

AbstractThe role of natural fractures in future reservoir performance is prominent. The fractured porous media is composed of an interconnected network of fractures and blocks of the porous medium where fractures occur in various scales and have a strong influence either when most of the flow is concentrated and them or when they act as barriers. A general numerical model for discrete fracture networks (DFN) is usually employed to handle the observed wide variety of fracture properties and the lack of direct fracture visualization. These models generally use fracture properties’ stochastic distribution based on sparse and seismic data without any physical model constraint. Alternatively, a DFN model includes usual numerical geomechanical approaches like boundary element and finite element. But here, a geostatistical methodology has been used to generate a DFN model. In this paper, an alternative modeling technique is employed to create the realization of an anisotropic fractured rock using simulated annealing (SA) optimization algorithm. There is a notable positive correlation between fracture length and position. There are three principal subjects in a study of fractured rocks. Firstly, the network’s connectivity, secondly, fluid flows through the system, and thirdly, dispersion. Here, connectivity of generated networks is considered. Continuum percolation is the mathematical model to study the geometry of connected components in a random subset of space. Different random realizations from the S.A. algorithm in four different sizes of L = 100, 150, 200, 250 at post-threshold condition are used as disordered media in percolation theory to compute percolation properties using Monte Carlo simulation. The percolation threshold (critical fracture density) and two crucial scaling exponents (β and υ) that dictate the model’s connectivity behavior are estimated to over 200 realizations.

scholarly journals Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

2021 ◽  
Vol 5 (4) ◽  
pp. 167
Author(s):  
Tamour Zubair ◽  
Muhammad Usman ◽  
Umar Nazir ◽  
Poom Kumam ◽  
Muhammad Sohail
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Comparison Study ◽  
Nano Fluid ◽  
Complicated Geometry ◽  
Maple Code

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

scholarly journals A new theoretical model for guiding the gas extraction in coal mines

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 293-300 ◽  
Author(s):  
Jing Xie ◽  
Zetian Zhang ◽  
Mingzhong Gao ◽  
Ru Zhang ◽  
Man Wang ◽  
...  
Keyword(s):  
Coal Mines ◽  
Network Models ◽  
Major Axis ◽  
Fracture Network ◽  
Gas Extraction ◽  
Fracture Density ◽  
Equivalent Permeability ◽  
Discrete Fracture ◽  
The Mean ◽  
First Time

Based on the fractal-percolation properties, the equivalent permeability analysis of 3-D discrete fracture network models are investigated and analyzed for the first time. The 3-D fractal dimension was calculated with the 3-D fracture density, the mean major axis of fracture and the aspect ratio of major to minor axis. The reconstructed mining-induced fracture network model was used to validate that the correlation between the predicted and actual results is very strong in a sense. The equivalent permeability results can be adopted to guide the gas extraction in coal mines.

INVESTIGATIONS ON REPRESENTATIVE ELEMENTARY VOLUME AND DIRECTIONAL PERMEABILITY OF FRACTAL-BASED FRACTURE NETWORKS USING POLYGON SUB-MODELS

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050085
Author(s):  
JING ZHANG ◽  
RICHENG LIU ◽  
LIYUAN YU ◽  
HONGWEN JING ◽  
QIAN YIN
Keyword(s):  
Preferential Flow ◽  
Numerical Study ◽  
Length Distribution ◽  
Fracture Network ◽  
Representative Elementary Volume ◽  
Polar Coordinate System ◽  
Elementary Volume ◽  
Fracture Length ◽  
Directional Permeability ◽  
Dfn Model

Since the directional permeability of fractured rock masses is significantly dependent on the geometric properties of fractures, in this work, a numerical study was performed to analyze the relationships between them, in which fracture length follows a fractal distribution. A method to estimate the representative elementary volume (REV) size and directional permeability ([Formula: see text] by extracting regular polygon sub-models with different orientation angles ([Formula: see text] and side lengths ([Formula: see text] from an original discrete fracture network (DFN) model was developed. The results show that the fracture number has a power law relationship with the fracture length and the evolution of the exponent agrees well with that reported in previous studies, which confirms the reliability of the proposed fractal length distribution and stochastically generated DFN models. The [Formula: see text] varies significantly due to the influence of random numbers utilized to generate fracture location, orientation and length when [Formula: see text] is small. When [Formula: see text] exceeds some certain values, [Formula: see text] holds a constant value despite of [Formula: see text], in which the model scale is regarded as the REV size and the corresponding area of DFN model is represented by [Formula: see text] (in 2D). The directional permeability contours for DFN models plotted in the polar coordinate system approximate to circles when the model size is greater than the REV size. The [Formula: see text] decreases with the increment of fractal dimension of fracture length distribution ([Formula: see text]. However, the decreasing rate of [Formula: see text] (79.5%) when [Formula: see text] increases from 1.4 to 1.5 changes more significantly than that (34.8%) when [Formula: see text] increases from 1.5 to 1.6 for regular hexagon sub-models. This indicates that the small non-persistent fractures dominate the preferential flow paths; thereafter, the flow rate distribution becomes more homogeneous when [Formula: see text] exceeds a certain value (i.e. 1.5). A larger [Formula: see text] results in a denser fracture network and a stronger conductivity.

scholarly journals Analyzing the correlation between stochastic fracture networks geometrical properties and stress variability: a rock and fracture parameters study

2021 ◽  
Vol 11 (2) ◽  
pp. 685-702
Author(s):  
Meysam Khodaei ◽  
Ebrahim Biniaz Delijani ◽  
Mastaneh Hajipour ◽  
Kasra Karroubi ◽  
Ali Naghi Dehghan
Keyword(s):  
Stress Distribution ◽  
Fractured Rock ◽  
Stochastic Approach ◽  
Fracture Network ◽  
Tectonic Stress ◽  
Fracture Density ◽  
Fracture Networks ◽  
Normal Stiffness ◽  
Geometrical Properties ◽  
Stress Variability

AbstractIn this study, the correlation between geometric properties of the fracture network and stress variability in a fractured rock was studied. Initially, discrete fracture networks were generated using a stochastic approach, then, considering the tensorial nature of stress, the stress field under various tectonic stress conditions was determined using finite-difference method. Ultimately, stress data were analyzed using tensor-based mathematical relations. Subsequently, the effects of four parameters including rock tensile strength, rock cohesion, fracture normal stiffness and fracture dilation angle on the stress perturbation distribution were evaluated. The obtained results indicated that stress perturbation and dispersion are directly related to fracture density, which is expressed as the number of fractures per unit area utilizing the window sampling approach. It was also demonstrated that they are inversely related to power-law length exponent which represents the length of fracture. It was observed that stress distribution, among the evaluated parameters, is more sensitive to the fracture normal stiffness and the effects of rock parameters on stress distribution are negligible. It was concluded that the highest stress distribution is created when the fracture network is dense with fractures having high length and low normal stiffness value.

Parallel Computing for Analysis on Intersections between Fractures in Rock Masses

2014 ◽  
Vol 955-959 ◽  
pp. 3001-3005
Author(s):  
Zhi Yu Li ◽  
Ming Yu Wang ◽  
Jian Hui Zhao
Keyword(s):  
Parallel Computing ◽  
Large Scale ◽  
Numerical Study ◽  
Fractured Rock ◽  
Fracture Network ◽  
Mine Safety ◽  
Main Concern ◽  
Rock Masses ◽  
Geothermal Resources ◽  
Intersection Analysis

Fractures dominate the path for fluid flow in fractured rock masses, which is a main concern in groundwater protection, coal mine safety and energy exploitation, e.g., petroleum and geothermal resources. Intersection analysis is one crucial procedure for discrete fracture network modeling as it can provide necessary information for evaluating the connectivity of fractures. This paper is proposed to improve the performance of intersection analysis by means of parallel computing. The algorithm is designed in view of both the computational efficiency and the smooth connection with other procedures in modeling. Numerical study indicates that the proposed parallel algorithm is practical and can significantly reduce the calculation time of intersection analysis under large scale simulations.

Direct Assessment of Effective Renal Plasma Flow from Renoscintigraphy with a Gamma Camera and an On-Line Computer

1981 ◽  
Vol 20 (06) ◽  
pp. 274-278
Author(s):  
J. Liniecki ◽  
J. Bialobrzeski ◽  
Ewa Mlodkowska ◽  
M. J. Surma
Keyword(s):  
Count Rate ◽  
Renal Plasma Flow ◽  
Early Period ◽  
Least Square Method ◽  
Least Square ◽  
Uptake Coefficient ◽  
Positive Linear Correlation ◽  
On Line ◽  
Best Fit ◽  
Plasma Activity

A concept of a kidney uptake coefficient (UC) of 131I-o-hippurate was developed by analogy from the corresponding kidney clearance of blood plasma in the early period after injection of the hippurate. The UC for each kidney was defined as the count-rate over its ROI at a time shorter than the peak in the renoscintigraphic curve divided by the integral of the count-rate curve over the "blood"-ROI. A procedure for normalization of both curves against each other was also developed. The total kidney clearance of the hippurate was determined from the function of plasma activity concentration vs. time after a single injection; the determinations were made at 5, 10, 15, 20, 30, 45, 60, 75 and 90 min after intravenous administration of 131I-o-hippurate and the best-fit curve was obtained by means of the least-square method. When the UC was related to the absolute value of the clearance a positive linear correlation was found (r = 0.922, ρ > 0.99). Using this regression equation the clearance could be estimated in reverse from the uptake coefficient calculated solely on the basis of the renoscintigraphic curves without blood sampling. The errors of the estimate are compatible with the requirement of a fast appraisal of renal function for purposes of clinical diagknosis.

PENGARUH KNOWLEDGE MANAGEMENT, KOMPETENSI, MOTIVASI TERHADAP KINERJA KARYAWAN

2015 ◽  
Vol 5 (2) ◽  
pp. 1
Author(s):  
Miftahol Arifin
Keyword(s):  
Knowledge Management ◽  
Linear Regression ◽  
Significant Influence ◽  
Employee Performance ◽  
Least Square Method ◽  
Least Square ◽  
Analysis Tool ◽  
Ordinary Least Square ◽  
Competence Motivation ◽  
Performance Analyze

The purpose of this research is to analyze the influence of knowledge management on employee performance, analyze the effect of competence on employee performance, analyze the influence of motivation on employee performance). In this study, samples taken are structural employees PT.centris Kingdom Taxi Yogyakarta. The analysis tool in this study using multiple linear regression with Ordinary Least Square method (OLS). The conclusion of this study showed that the variables of knowledge management has a significant influence on employee performance, competence variables have an influence on employee performance, motivation variables have an influence on employee performance, The analysis showed that the variables of knowledge management, competence, motivation on employee performance.Keywords: knowledge management, competence, motivation, employee performance.

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