A FRACTAL PERMEABILITY MODEL FOR POROUS–FRACTURE MEDIA WITH THE TRANSFER OF FLUIDS FROM POROUS MATRIX TO FRACTURE

Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950121 ◽  
Author(s):  
TONGJUN MIAO ◽  
AIMIN CHEN ◽  
YAN XU ◽  
SUJUN CHENG ◽  
BOMING YU
Keyword(s):  
Fractal Dimension ◽  
Geothermal Energy ◽  
Theoretical Foundation ◽  
Flow Behavior ◽  
Porous Matrix ◽  
Fracture Aperture ◽  
Permeability Model ◽  
Microstructural Parameters ◽  
Dimension Formula ◽  
Proposed Model

The transfer of fluids from porous matrix to fracture is a key issue to accurately predict the fluid flow behavior in porous–fracture media. In this work, to take into account the transfer of fluids, the analytical model of dimensionless permeability is proposed based on the fractal geometry theory for porous media. The proposed model is expressed as a function of microstructural parameters of the porous matrix and fracture, such as the pore area fractal dimension [Formula: see text], fractal dimension [Formula: see text] for tortuosity of tortuous capillaries, the ratio [Formula: see text] of the maximum pore size in porous matrix to fracture aperture, as well as the ratio [Formula: see text] of the pressure difference along the fracture to that along the porous matrix layers. The model reveals that the ratios [Formula: see text] and [Formula: see text] have significant influences on the permeability contribution from the porous matrix to the seepage behavior of the fracture. While the contribution of porosity of leak-wall porous surface of the fracture to the permeability is less than 10%. The present results may provide an important theoretical foundation for exploration of petroleum, gas and geothermal energy extraction systems.

PERMEABILITY MODELS FOR TWO-PHASE FLOW IN FRACTAL POROUS-FRACTURE MEDIA WITH THE TRANSFER OF FLUIDS FROM POROUS MATRIX TO FRACTURE

Fractals ◽  
2021 ◽  
Vol 29 (06) ◽  
pp. 2150148
Author(s):  
TONGJUN MIAO ◽  
AIMIN CHEN ◽  
YAN XU ◽  
SUJUN CHENG ◽  
LIWEI ZHANG ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Two Phase Flow ◽  
Structural Parameters ◽  
Porous Matrix ◽  
Fracture Aperture ◽  
Phase Flow ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Dimension Formula ◽  
Phase Saturation

Study of transport mechanism of two-phase flow through porous-fracture media is of considerable importance to deeply understand geologic behaviors. In this work, to consider the transfer of fluids, the analytical models of dimensionless relative permeabilities for the wetting and non-wetting phases flow are proposed based on the fractal geometry theory for porous media. The proposed models are expressed as functions of micro-structural parameters of the porous matrix and fracture, such as the fractal dimension ([Formula: see text] for pore area, the fractal dimensions [Formula: see text] for wetting phase and for non-wetting phase, porosity ([Formula: see text], the total saturations ([Formula: see text], the porous matrix saturation ([Formula: see text] of the wetting and non-wetting phases, fractal dimension ([Formula: see text] for tortuosity of tortuous capillaries, as well as the ratio ([Formula: see text] of the maximum pore size in porous matrix to fracture aperture. The ratio ([Formula: see text] has a significant impact on the relative permeabilities and total saturations of wetting phases. The results reveal that the flow contribution of wetting phase from the porous matrix to both the seepage behavior of the fracture and total wetting phase saturation can be neglected as [Formula: see text]. The models may shed light on the fundamental mechanisms of the wetting and non-wetting phase flow in porous-fracture media with fluid transfer.

scholarly journals Semianalytical Model for Flow Behavior Analysis of Unconventional Reservoirs with Complex Fracture Distribution

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dayou Shi ◽  
Zhengyuan Lu
Keyword(s):  
Fractal Dimension ◽  
Flow Rate ◽  
Flow Behavior ◽  
Great Influence ◽  
Fracture Aperture ◽  
Secondary Fracture ◽  
Stimulated Reservoir Volume ◽  
Fracture Spacing ◽  
Reservoir Volume ◽  
Aperture Distribution

The secondary fracture spacing/aperture has a great influence on flow behavior of multifractured horizontal wells. In this paper, the effects of secondary fracture spacing/aperture distribution on porosity/permeability of the stimulated reservoir volume are described. A new fractal composite flow model was proposed, which can comprehensively characterize the secondary fracture spacing/aperture heterogeneity in the stimulated reservoir volume. Results showed that the larger the fractal dimension of the secondary fracture aperture is, the greater the dimensionless flow rate will be. The smaller the fractal dimension of the secondary fracture spacing is, the smaller the dimensionless flow rate will be. The secondary fracture spacing distribution had a greater influence on flow behavior than the secondary fracture aperture distribution. If the heterogeneity of the secondary fracture spacing or aperture is not considered, the bottomhole pressure and production curve will change greatly. At last, the proposed model was applied to match the production data of two actual fields.

PERMEABILITY PREDICTION IN ROUGHENED FRACTURES UNDER STRESS CONDITION USING FRACTAL MODEL

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950030 ◽  
Author(s):  
GANG LEI ◽  
NAI CAO ◽  
QINGZHI WEN
Keyword(s):  
Stress Condition ◽  
Fractal Model ◽  
Coupled Flow ◽  
Permeability Model ◽  
Microstructural Parameters ◽  
Rough Fracture ◽  
Proposed Model ◽  
Stress Dependent ◽  
Rock Lithology ◽  
Good Agreement

The prediction of permeability in rough fracture under stress condition presents ever more of a challenge in various scientific and engineering fields. However, up to now, the essential controls on stress-dependent permeability of rough fracture are not determined. In order to find a relationship between the microstructure and the permeability of rough fracture, an analytical method for the permeability of roughened fracture under stress condition is proposed based on the fractal model. The validity of the proposed model is obtained by the good agreement between the simulated results and the experimental data. Compared with the previous models, our model takes into account more factors, including the influence of the microstructural parameters of rough fracture and rock lithology. This paper presents that (1) the rock with soft lithology can yield smaller normalized permeability, (2) normalized permeability decreases with the increases of percent of smaller rough elements. The fractal permeability model can reveal more mechanisms that affect the coupled flow deformation behavior in the fractured porous media.

EVOLUTION OF FRACTAL DIMENSIONS AND GAS TRANSPORT MODELS DURING THE GAS RECOVERY PROCESS FROM A FRACTURED SHALE RESERVOIR

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950129 ◽  
Author(s):  
BOWEN HU ◽  
J. G. WANG ◽  
ZHONGQIAN LI ◽  
HUIMIN WANG
Keyword(s):  
Fractal Dimension ◽  
Surface Diffusion ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Fractal Dimensions ◽  
Gas Extraction ◽  
Multilayer Adsorption ◽  
Permeability Model ◽  
Dimension Formula ◽  
Shale Reservoir

Previous studies ignore the evolutions of pore microstructure parameters (pore diameter fractal dimension [Formula: see text] and tortuosity fractal dimension [Formula: see text]) but these evolutions may significantly impact the gas transport during gas extraction. In order to investigate these evolutions of fractal dimension properties during gas extraction, following four aspects are studied. Firstly, surface diffusion in adsorbed multilayer is modeled for fractal shale matrix. Our new matrix permeability model considers the slip flow, Knudsen diffusion and surface diffusion. This model is verified by experimental data. Secondly, a new fracture permeability model is proposed based on fractal theory and the coupling of viscous flow and Knudsen diffusion. Thirdly, the multilayer adsorption and these permeability models are introduced into the equations of gas flow and reservoir deformation. Finally, sensitivity analysis is performed to determine the key factors on fractal dimension evolution. The results show that the multilayer adsorption can accurately describe the adsorption properties of real shale reservoir. Shale reservoir deformation and gas desorption govern the evolutions of fractal dimensions. The multilayer adsorption and adsorbed gas porosity [Formula: see text] play an important role in the evolutions of fractal dimensions during gas extraction. The monolayer saturated adsorption volume [Formula: see text] is the most sensitive parameter affecting the evolution of fractal dimensions. Therefore, the effects of gas adsorption on the evolution of fractal dimensions cannot be neglected in shale reservoirs.

A PERMEABILITY MODEL FOR WATER–GAS PHASE FLOW IN FRACTAL FRACTURE NETWORKS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850087 ◽  
Author(s):  
TONGJUN MIAO ◽  
AIMIN CHEN ◽  
YAN XU ◽  
SUJUN CHENG ◽  
KEDONG WANG
Keyword(s):  
Gas Phase ◽  
Flow Behavior ◽  
Fractal Theory ◽  
Nonlinear Function ◽  
Phase Flow ◽  
Fracture Networks ◽  
Permeability Model ◽  
Empirical Parameter ◽  
Proposed Model ◽  
Water Gas

Flow mechanism of water–gas phase is of significant importance to accurately understand and predict the fluid flow behavior in many fields, such as water and oil exploration, hot dry rock development and optimization of fuel cells. In this work, a novel relative permeability (RP) model for two-phase flow in fracture networks is proposed based on the fractal theory. The proposed model is expressed as a nonlinear function of saturation of water and gas with no empirical parameter. A stronger interference between water and gas phases than that of the X-model is found. The proposed model may provide a better understanding of the fundamental mechanism of water–gas phase flow in fracture network.

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1429-1451 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Fractal Dimension ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Local Maximum ◽  
Fractal Dimensions ◽  
Dimension Formula ◽  
Phonon Spectra ◽  
Wide Range ◽  
Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

The Constitutive Model for High Temperature Flow Behavior of SiC/6168Al Composite

2015 ◽  
Vol 1089 ◽  
pp. 37-41
Author(s):  
Jiang Wang ◽  
Sheng Li Guo ◽  
Sheng Pu Liu ◽  
Cheng Liu ◽  
Qi Fei Zheng
Keyword(s):  
Constitutive Model ◽  
Hot Deformation ◽  
Flow Behavior ◽  
Type Equation ◽  
Strain Rate Range ◽  
Compression Tests ◽  
Stress Strain ◽  
Hollomon Parameter ◽  
Proposed Model ◽  
Relationship Of

The hot deformation behavior of SiC/6168Al composite was studied by means of hot compression tests in the temperature range of 300-450 °C and strain rate range of 0.01-10 s-1. The constitutive model was developed to predict the stress-strain curves of this composite during hot deformation. This model was established by considering the effect of the strain on material constants calculated by using the Zenter-Hollomon parameter in the hyperbolic Arrhenius-type equation. It was found that the relationship of n, α, Q, lnA and ε could be expressed by a five-order polynomial. The stress-strain curves obtained by this model showed a good agreement with experimental results. The proposed model can accurately describe the hot flow behavior of SiC/6168Al composite, and can be used to numerically analyze the hot forming processes.

scholarly journals Squeezing Force of the Magnetorheological Fluid Isolating Damper for Centrifugal Fan in Nuclear Power Plant

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Jin Huang ◽  
Ping Wang ◽  
Guochao Wang
Keyword(s):  
Nuclear Power ◽  
Theoretical Foundation ◽  
Fluid Dynamic ◽  
Flow Behavior ◽  
Magnetorheological Fluid ◽  
Centrifugal Fan ◽  
Parallel Channel ◽  
Mr Fluid ◽  
Mr Fluids ◽  
Control Devices

Magnetorheological (MR) disk-type isolating dampers are the semi-active control devices that use MR fluids to produce controllable squeezing force. In this paper, the analytical endeavor into the fluid dynamic modeling of an MR isolating damper is reported. The velocity and pressure distribution of an MR fluid operating in an axisymmetric squeeze model are analytically solved using a biviscosity constitutive model. Analytical solutions for the flow behavior of MR fluid flowing through the parallel channel are obtained. The equation for the squeezing force is derived to provide the theoretical foundation for the design of the isolating damper. The result shows that with the increase of the applied magnetic field strength, the squeezing force is increased.

Prediction of High Viscosity Liquid/Gas Two-Phase Slug Length in Horizontal and Slightly Inclined Pipelines

2021 ◽  
Author(s):  
Omar Shaaban ◽  
Eissa Al-Safran
Keyword(s):  
Numerical Optimization ◽  
Flow Behavior ◽  
Mechanistic Model ◽  
High Viscosity ◽  
Oil Well ◽  
Liquid Slug ◽  
Two Phase ◽  
Proposed Model ◽  
Wide Range ◽  
Flow Closure

Abstract The production and transportation of high viscosity liquid/gas two-phase along petroleum production system is a challenging operation due to the lack of understanding the flow behavior and characteristics. In particular, accurate prediction of two-phase slug length in pipes is crucial to efficiently operate and safely design oil well and separation facilities. The objective of this study is to develop a mechanistic model to predict high viscosity liquid slug length in pipelines and to optimize the proper set of closure relationships required to ensure high accuracy prediction. A large high viscosity liquid slug length database is collected and presented in this study, against which the proposed model is validated and compared with other models. A mechanistic slug length model is derived based on the first principles of mass and momentum balances over a two-phase slug unit, which requires a set of closure relationships of other slug characteristics. To select the proper set of closure relationships, a numerical optimization is carried out using a large slug length dataset to minimize the prediction error. Thousands of combinations of various slug flow closure relationships were evaluated to identify the most appropriate relationships for the proposed slug length model under high viscosity slug length condition. Results show that the proposed slug length mechanistic model is applicable for a wide range of liquid viscosities and is sensitive to the selected closure relationships. Results revealed that the optimum closure relationships combination is Archibong-Eso et al. (2018) for slug frequency, Malnes (1983) for slug liquid holdup, Jeyachandra et al. (2012) for drift velocity, and Nicklin et al. (1962) for the distribution coefficient. Using the above set of closure relationships, model validation yields 37.8% absolute average percent error, outperforming all existing slug length models.

scholarly journals Thermos-Solid-Gas Coupling Dynamic Model and Numerical Simulation of Coal Containing Gas

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiao Fukun ◽  
Meng Xin ◽  
Li Lianchong ◽  
Liu Jianfeng ◽  
Liu Gang ◽  
...  
Keyword(s):  
Principal Stress ◽  
Dynamic Model ◽  
Gas Flow ◽  
Flow Behavior ◽  
Coupling Model ◽  
Gas Pressure ◽  
Permeability Model ◽  
Gas Seepage ◽  
Coupling Dynamic ◽  
Coupling Dynamic Model

Based on gas seepage characteristics and the basic thermo-solid-gas coupling theory, the porosity model and the dynamic permeability model of coal body containing gas were derived. Based on the relationship between gas pressure, principal stress and temperature, and gas seepage, the thermo-solid-gas coupling dynamic model was established. Initial values and boundary conditions for the model were determined. Numerical simulations using this model were done to predict the gas flow behavior of a gassy coal sample. By using the thermo-solid-gas coupling model, the gas pressure, temperature, and principal stress influence, the change law of the pressure field, displacement field, stress field, temperature field, and permeability were numerically simulated. Research results show the following: (1) Gas pressure and displacement from the top to the end of the model gradually reduce, and stress from the top to the end gradually increases. The average permeability of the Y Z section of the model tends to decrease with the rise of the gas pressure, and the decrease amplitude slows down from the top of the model to the bottom. (2) When the principal stress and temperature are constant, the permeability decreases first and then flattens with the gas pressure. The permeability increases with the decrease of temperature while the gas pressure and principal stress remain unchanged.

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