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.

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.

A FRACTAL MODEL FOR RELATIVE PERMEABILITY OF UNSATURATED POROUS MEDIA WITH CAPILLARY PRESSURE EFFECT

Fractals ◽  
2007 ◽  
Vol 15 (03) ◽  
pp. 217-222 ◽  
Author(s):  
YANJUN LIU ◽  
BOMING YU
Keyword(s):  
Experimental Data ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Pressure Difference ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Permeability Model ◽  
Empirical Constant ◽  
Proposed Model ◽  
Fluid Properties

A fractal relative permeability model is derived which takes into account the capillary pressure difference effect. The proposed model is expressed as a function of saturation, fractal dimensions, fluid properties and capillary pressure difference, and there is no empirical constant introduced in the proposed model. The effect of the capillary pressure difference on the relative permeability is analyzed, and the results indicate that the capillary pressure difference has the significant influence on the relative permeability at low saturation. The predicted relative permeabilities are compared with the available experimental data. Good agreement is found between the present model predictions and the available experimental data.

Fractal Model for Thermal Contact Conductance

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
Mingqing Zou ◽  
Boming Yu ◽  
Jianchao Cai ◽  
Peng Xu
Keyword(s):  
Random Number ◽  
Rough Surfaces ◽  
Thermal Contact ◽  
Fractal Model ◽  
Thermal Contact Conductance ◽  
Bulk Resistance ◽  
Contact Conductance ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Good Agreement

A random number model based on fractal geometry theory is developed to calculate the thermal contact conductance (TCC) of two rough surfaces in contact. This study is carried out by geometrical and mechanical investigations. The present study reveals that the fractal parameters D and G have important effects on TCC. The predictions by the proposed model are compared with existing experimental data, and good agreement is observed by fitting parameters D and G. The results show that the effect of the bulk resistance on TCC, which is often neglected in existing models, should not be neglected for the relatively larger G and D. The main advantage of this model is the randomization of roughness distributions on rough surfaces. The present results also show a better agreement with the practical situation than the results of other models. The proposed technique may have the potential in prediction of other phenomena such as friction, radiation, wear and lubrication on rough surfaces.

scholarly journals Examination of the fractal model for streaming potential coefficient in porous media

2019 ◽  
Vol 35 (1) ◽  
Author(s):  
Luong Duy Thanh
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Zeta Potential ◽  
Streaming Potential ◽  
Fractal Model ◽  
Potential Coefficient ◽  
Proposed Model ◽  
Alternative Approach ◽  
High Fluid ◽  
Good Agreement

In this work, the fractal model for the streaming potential coefficient in porous media recently published has been examined by calculating the zeta potential from the measured streaming potential coefficient. Obtained values of the zeta potential are then compared with experimental data. Additionally, the variation of the streaming potential coefficient with fluid electrical conductivity is predicted from the model. The results show that the model predictions are in good agreement with the experimental data available in literature. The comparison between the proposed model and the Helmholtz-Smoluchowski (HS) equation is also carried out. It is seen that that the prediction from the proposed model is quite close to what is expected from the HS equation, in particularly at the high fluid conductivity or large grain diameters. Therefore, the model can be an alternative approach to obtain the zeta potential from the streaming potential measurements.

scholarly journals STRESS SENSITIVITY ANALYSIS OF FRACTAL POROUS MEDIA BASED ON THE ELASTO-PLASTIC THICK-WALLED CYLINDER MODEL

Fractals ◽  
2021 ◽  
Vol 29 (03) ◽  
pp. 2150162
Author(s):  
ZHAOQIN HUANG ◽  
XIN SU ◽  
YANCHAO LI ◽  
KAI ZHANG ◽  
JUN YAO
Keyword(s):  
Porous Media ◽  
Fractal Theory ◽  
Fractal Model ◽  
Stress Sensitivity ◽  
Proposed Model ◽  
Cylinder Model ◽  
Stress Cycles ◽  
Dependent Flow ◽  
Stress Dependent ◽  
Walled Cylinder

The stress-dependent flow and transport behaviors of porous media are ubiquitous in various scientific and engineering applications. It has been shown that the change of effective stress has important effects on the permeability and porosity of porous media. In this paper, a new stress sensitivity model for porous media is developed based on the fractal theory and the elasto-plastic thick-walled cylinder model. The proposed model is able to predict the elasto-plastic deformation of the fractal porous media under loading–unloading stress cycles, which plays a crucial role on the permanent variations of the permeability and porosity. It is found that the permeability of stress-sensitivity porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, minimum and maximum capillary diameters, Young’s modulus and Poisson’s ratio of capillary. Each parameter has a clear physical meaning. The validity of the developed fractal model is verified by comparing the model predictions with the available experimental data.

scholarly journals A NOVEL FRACTAL MODEL FOR ESTIMATING PERMEABILITY IN LOW-PERMEABLE SANDSTONE RESERVOIRS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040005
Author(s):  
SHUNING DONG ◽  
LULU XU ◽  
ZHENXUE DAI ◽  
BIN XU ◽  
QINGYANG YU ◽  
...  
Keyword(s):  
Predictive Model ◽  
Water Inrush ◽  
Image Data ◽  
Theoretical Models ◽  
Underground Water ◽  
Fractal Model ◽  
Sem Images ◽  
Permeability Model ◽  
Microstructural Parameters ◽  
Sandstone Reservoirs

Permeability is one of the most important parameters for accurately predicting water flow in reservoirs and quantifying underground water inrush into coal mines. This study developed a predictive permeability model by considering the microstructural parameters and tortuosity effects of low-permeability sandstone. The model incorporates the fractal geometry theory, Darcy’s law, and Poiseuille equation into a multistep inversion framework for systematic interpretation of sandstone scanning electron microscopy (SEM) images. A threshold segmentation algorithm is applied to transform SEM images into binary images. Then, we used an improved statistical algorithm with binary image data to estimate the geometric parameters of each pore, such as the perimeter and area. The fractal parameters of pore microstructure were determined by fitting the data of pore perimeters and areas. Finally, the effects of tortuosity on microscopic percolation were considered, and a conventional model was modified for quantifying the relationship between microscopic pore structures parameters and macroscopic permeability. Eight groups of sandstone samples from the Xingdong coal mine in North China were collected for estimating permeability by the developed inversion framework. A direct permeability measurement was also conducted on each sample with an AP-608 automatic measuring instrument. The measured permeability values were compared with results from theoretical models, and we found that the accuracy of the newly developed predictive model is better than that of a conventional permeability model. The predictive model developed in this study provides a useful tool for estimating permeability in low-permeable sandstone reservoirs.

FRACTAL ANALYSIS OF STRESS SENSITIVITY OF PERMEABILITY IN POROUS MEDIA

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550001 ◽  
Author(s):  
XIAO-HUA TAN ◽  
XIAO-PING LI ◽  
JIAN-YI LIU ◽  
LIE-HUI ZHANG ◽  
JIANCHAO CAI
Keyword(s):  
Porous Media ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Permeability Model ◽  
Minimum Diameter ◽  
Mechanics Of Materials ◽  
Proposed Model ◽  
Fractal Characteristics ◽  
Experimental Expression ◽  
Good Agreement

A permeability model for porous media considering the stress sensitivity is derived based on mechanics of materials and the fractal characteristics of solid cluster size distribution. The permeability of porous media considering the stress sensitivity is related to solid cluster fractal dimension, solid cluster fractal tortuosity dimension, solid cluster minimum diameter and solid cluster maximum diameter, Young's modulus, Poisson's ratio, as well as power index. Every parameter has clear physical meaning without the use of empirical constants. The model predictions of permeability show good agreement with those obtained by the available experimental expression. The proposed model may be conducible to a better understanding of the mechanism for flow in elastic porous media.

scholarly journals Compact Modelling of Electrical, Optical and Thermal Properties of Multi-Colour Power LEDs Operating on a Common PCB

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1286
Author(s):  
Krzysztof Górecki ◽  
Przemysław Ptak
Keyword(s):  
Integrated Circuits ◽  
Optical Model ◽  
Printed Circuit Board ◽  
Circuit Board ◽  
Junction Temperature ◽  
Optical Parameters ◽  
Spice Simulation ◽  
Light Emitting ◽  
Proposed Model ◽  
Good Agreement

This paper concerns the problem of modelling electrical, thermal and optical properties of multi-colour power light-emitting diodes (LEDs) situated on a common PCB (Printed Circuit Board). A new form of electro-thermo-optical model of such power LEDs is proposed in the form of a subcircuit for SPICE (Simulation Program with Integrated Circuits Emphasis). With the use of this model, the currents and voltages of the considered devices, their junction temperature and selected radiometric parameters can be calculated, taking into account self-heating phenomena in each LED and mutual thermal couplings between each pair of the considered devices. The form of the formulated model is described, and a manner of parameter estimation is also proposed. The correctness and usefulness of the proposed model are verified experimentally for six power LEDs emitting light of different colours and mounted on an experimental PCB prepared by the producer of the investigated devices. Verification was performed for the investigated diodes operating alone and together. Good agreement between the results of measurements and computations was obtained. It was also proved that the main thermal and optical parameters of the investigated LEDs depend on a dominant wavelength of the emitted light.

Static and Dynamic Structure of Molecular Monomers and Dimers of the Rare-earth Fluorides

2001 ◽  
Vol 56 (5) ◽  
pp. 381-385
Author(s):  
Z. Akdeniz ◽  
M . Gaune-Escard ◽  
M. P. Tosi
Keyword(s):  
Rare Earth ◽  
Bond Length ◽  
Geometrical Structure ◽  
Vibrational Mode ◽  
Dynamic Structure ◽  
Molecular Shape ◽  
Proposed Model ◽  
Infrared Studies ◽  
Charged Clusters ◽  
Good Agreement

Abstract We determine a model of the ionic interactions in RF3 compounds, where R is a rare-earth element in the series from La to Lu, by an analysis of data on the bond length and the vibrational mode frequencies of the PrF3, GdF3 and HoF3 molecular monomers. All RF3 monomers are predicted to have a pyramidal shape, displaying a progressive flattening of the molecular shape in parallel with the lanthanide contraction of the bond length. The vibrational frequencies of all monomers are calculated, the results being in good agreement with the data from infrared studies of matrix-isolated molecules. We also evaluate the geometrical structure and the vibrational spectrum of the La2F6 and Ce2F6 dimers, as a further test of the proposed model. -PACS 36.40.Wa (Charged clusters)

Reloading Stress Relaxation Behavior Analysis Based on a Creep Model for High Temperature Bolting Steel

2013 ◽  
Vol 328 ◽  
pp. 950-954
Author(s):  
Wei Wei Zhang ◽  
Hong Xu ◽  
Hong Yuan Li
Keyword(s):  
High Temperature ◽  
Stress Relaxation ◽  
Steady State Creep ◽  
Relaxation Behavior ◽  
Creep Model ◽  
National Research Institute ◽  
Time Intervals ◽  
Stress Relaxation Behavior ◽  
Proposed Model ◽  
Good Agreement

An analytical method based on a creep model is being developed to investigate the effect of retightening on stress relaxation behavior for high-temperature turbine and valve studs/bolts. In order to validate the approach, the calculated results are compared to the results of uniaxial reloading stress relaxation testing, which were performed by the National Research Institute for Metals of Japan (NRIM) for 12Cr-1Mo-1W-1/4V stainless steel bolting material at 550°C. It was shown that the proposed model based on Altenbach-Gorash-Naumenko creep model for the primary and steady state creep could be applied for the present data. The calculated residual stresses versus time curves were in good agreement with the measured for initial stress level of 273.6MPa at 550°C and for specific reloading time intervals of 24, 72, 240, and 720 hours.

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