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.

SEEPAGE PROPERTIES OF ROCK FRACTURES WITH POWER LAW LENGTH DISTRIBUTIONS

Fractals ◽  
2019 ◽  
Vol 27 (04) ◽  
pp. 1950057 ◽  
Author(s):  
TONGJUN MIAO ◽  
SUJUN CHENG ◽  
AIMIN CHEN ◽  
YAN XU ◽  
GUANG YANG ◽  
...  
Keyword(s):  
Power Law ◽  
Structural Parameters ◽  
Length Distribution ◽  
Fracture Network ◽  
Analytical Models ◽  
Fracture Density ◽  
Fracture Networks ◽  
Permeability Model ◽  
Fracture Length ◽  
Power Law Exponent

Fractures with power law length distributions abound in nature such as carbonate oil and gas reservoirs, sandstone, hot dry rocks, etc. The fluid transport properties and morphology characterization of fracture networks have fascinated numerous researchers to investigate for several decades. In this work, the analytical models for fracture density and permeability are extended from fractal fracture network to general fracture network with power law length distributions. It is found that the fracture density is related to the power law exponents [Formula: see text] and the area porosity [Formula: see text] of fracture network. Then, a permeability model for the fracture length distribution with general power law exponent [Formula: see text] and the power law exponent [Formula: see text] for fracture length versus aperture is proposed based on the well-known cubic law in individual fracture. The analytical expression for permeability of fractured networks is found to be a function of power law exponents [Formula: see text], area porosity [Formula: see text] of fracture network, and the micro-structural parameters (maximum fracture length [Formula: see text], fracture azimuth [Formula: see text] and fracture dip angle [Formula: see text]). The present model may shed light on the mechanism of seepage in fracture networks with power law length distributions.

Dispersion in Metal Foam: A Pore Scale Numerical Study

2012 ◽  
Vol 326-328 ◽  
pp. 410-415
Author(s):  
Jean Michel Hugo ◽  
Frédéric Topin
Keyword(s):  
Metal Foam ◽  
Numerical Study ◽  
Fluid Phase ◽  
Numerical Approach ◽  
Representative Elementary Volume ◽  
Pore Scale ◽  
Elementary Volume ◽  
Foam Sample ◽  
Mass Fluxes ◽  
Phase Conductivity

We determine thermal dispersion in metal foams using a pore scale numerical approach. Samples are contained in a channel crossed by a steady fully established fluid flow. The size of the foam sample is chosen according to a Representative Elementary Volume (REV).Two configurations are tested with several foam structures, pore size and pore shape. In the first configuration, heat and mass fluxes are in the same direction, in the second one, fluxes are perpendicular such as in heat exchanger. Results obtained on apparent fluid phase conductivity are discussed along with pressure drop data and compared to available literature data.

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.

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 Determination of Fractured Rock’s Representative Elementary Volume by a Numerical Simulation Method

2019 ◽  
Vol 9 (4) ◽  
pp. 4448-4451
Author(s):  
H. Gasmi ◽  
M. Touahmia ◽  
A. Torchani ◽  
E. Hamdi ◽  
A. Boudjemline
Keyword(s):  
Wave Propagation ◽  
Simulation Method ◽  
Fracture Network ◽  
Homogenization Method ◽  
Representative Elementary Volume ◽  
Elementary Volume ◽  
Fractured Network ◽  
Numerical Program

The present study aims at developing a numerical program called DISSIM which can analyze the homogenization of rock massifs using a new subroutine which calculates Representative Elementary Volume (REV). The DISSIM methodology consists of two steps. The first step involves the modeling of the fractured network in order to provide a surface simulation that represents the real fracture of the examined front. The second step is to numerically model the wave propagation through the simulated fracture network while characterizing the attenuation of vibrations due to the effect of discontinuities. This part allows us to determine in particular the wave propagation velocity through the fractured mass, from which we can determine the homogenized Young's modulus. However, after extensive bibliographic research, it was realized that a third step appeared to be necessary. In fact, it is necessary to look for a representative elementary volume on which we apply the proposed homogenization method. Two types of the representative elementary volume are proposed in this article, the geometric REV and the mechanical REV. The presentation of these two types of REV and the DISSIM methodology are detailed in this paper. Then, this methodology was applied to the study of a real case. The present research provides a method allowing the calculation of both types of REV for fissured rocks. The case study yielded comparable results between the mechanical REV and the geometric REV, which is compatible with previous research studies.

scholarly journals New insights on homogenization for hexagonal-shaped composites as Cosserat continua

Meccanica ◽  
2021 ◽  
Author(s):  
Marco Colatosti ◽  
Nicholas Fantuzzi ◽  
Patrizia Trovalusci ◽  
Renato Masiani
Keyword(s):  
Continuum Theory ◽  
Representative Elementary Volume ◽  
Elementary Volume ◽  
Displacement Fields ◽  
Micropolar Continuum ◽  
Rigid Particles ◽  
Hexagonal Shape ◽  
Classical Models ◽  
Elastic Interfaces ◽  
Cosserat Continua

AbstractIn this work, particle composite materials with different kind of microstructures are analyzed. Such materials are described as made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry is described by a limited set of parameters. Three different textures are analyzed and static analyses are performed for a comparison among the solutions of discrete, micropolar (Cosserat) and classical models. In particular, the displacements of the discrete model are compared to the displacement fields of equivalent micropolar and classical continua realized through a homogenization technique, starting from the representative elementary volume detected with a numeric approach. The performed analyses show the effectiveness of adopting the micropolar continuum theory for describing such materials.

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