A NEW METHOD FOR CALCULATING FRACTAL DIMENSIONS OF POROUS MEDIA BASED ON PORE SIZE DISTRIBUTION

Fractals ◽  
2018 ◽  
Vol 26 (01) ◽  
pp. 1850006 ◽  
Author(s):  
YUXUAN XIA ◽  
JIANCHAO CAI ◽  
WEI WEI ◽  
XIANGYUN HU ◽  
XIN WANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Pore Space ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
New Method ◽  
Distribution Data

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

Depth and composition dependent nanopore structures of Indian shale gas reservoirs: An implication on storage potential

2021 ◽  
Author(s):  
Abinash Bal ◽  
Santanu Misra ◽  
Manab Mukherjee
Keyword(s):  
Fractal Dimension ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Negative Correlation ◽  
Fractal Dimensions ◽  
Clay Content ◽  
Pore Network Model ◽  
Cambay Basin ◽  
Gas Reservoirs

<p>We investigated the nanopore structures of shale samples obtained from Cambay and Krishna-Godavari (KG) basins in India using low-pressure N<sub>2</sub> sorption method. The samples occurred at variable depths (1403-2574m and 2599-2987m for Cambay and KG basins, respectively) and have wide ranges of clay contents (56-90%) both in volume and mineralogy. The results of this study indicate the specific surface area (SSA) and pore diameters of the samples share a non-linear negative correlation. The SSA is a strong function of the clay content over the samples’ depth. The specific micropore volumes of the KG basin have relatively higher (8.29-24.4%) than the Cambay basin (0.1-3.6%), which leads to higher SSA in the KG basin. From different statistical thickness equations, the Harkins Jura equation was found to be most suitable for the computation of BJH pore size distribution and t-plot inversion in shale. Shale samples from Cambay basin show unimodal pore size distribution, with a modal diameter of 4-5nm, while in the KG basin, show bi-modal to multimodal pore size distribution, mostly ranges from 3-12 nm. In the fractal FHH method, fractal exponent D<sub>f</sub>-3 provides a better realistic result than fractal dimensions calculated from (D<sub>f</sub>-3)/3. In our samples, pore surface fractal dimension (D<sub>f1</sub>) show a positive correlation with SSA and a negative correlation with pore diameter, and pore structure fractal dimension (D<sub>f2</sub>) shows a negative correlation both with clay(%) and depth. The experimental data obtained in this study are instrumental in developing the pore-network model to assess the hydrocarbon reserve and recovery in shale.</p>

Fractal analysis of permeability near the wall in porous media

2014 ◽  
Vol 25 (07) ◽  
pp. 1450021 ◽  
Author(s):  
Mingchao Liang ◽  
Boming Yu ◽  
Li Li ◽  
Shanshan Yang ◽  
Mingqing Zou
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Pore Space ◽  
Fractal Theory ◽  
Particle Diameter ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Proposed Model ◽  
Medium Porosity ◽  
The Relationship

In this paper, a fractal model for permeability of porous media is proposed based on Tamayol and Bahrami's method and the fractal theory for porous media. The proposed model is expressed as a function of the mean particle diameter, the length along the macroscopic pressure drop in the medium, porosity, fractal dimensions for pore space and tortuous capillaries, and the ratio of the minimum pore size to the maximum pore size. The relationship between the permeability near the wall and the dimensionless distance from the wall under different conditions is discussed in detail. The predictions by the present fractal model are in good agreement with available experimental data. The present results indicate that the present model may have the potential in comprehensively understanding the mechanisms of flow near the wall in porous media.

A FRACTAL PERMEABILITY MODEL FOR SHALE MATRIX WITH MULTI-SCALE POROUS STRUCTURE

Fractals ◽  
2016 ◽  
Vol 24 (01) ◽  
pp. 1650002 ◽  
Author(s):  
MAO SHENG ◽  
GENSHENG LI ◽  
SHOUCENG TIAN ◽  
ZHONGWEI HUANG ◽  
LIQIANG CHEN
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Shale Gas ◽  
Gas Permeability ◽  
Pore Space ◽  
Fractal Theory ◽  
Permeability Model ◽  
Multi Scale ◽  
Nanopore Structure

Nanopore structure and its multiscale feature significantly affect the shale-gas permeability. This paper employs fractal theory to build a shale-gas permeability model, particularly considering the effects of multiscale flow within a multiscale pore space. Contrary to previous studies which assume a bundle of capillary tubes with equal size, in this research, this model reflects various flow regimes that occur in multiscale pores and takes the measured pore-size distribution into account. The flow regime within different scales is individually determined by the Knudsen number. The gas permeability is an integral value of individual permeabilities contributed from pores of different scales. Through comparing the results of five shale samples, it is confirmed that the gas permeability varies with the pore-size distribution of the samples, even though their intrinsic permeabilities are the same. Due to consideration of multiscale flow, the change of gas permeability with pore pressure becomes more complex. Consequently, it is necessary to cover the effects of multiscale flow while determining shale-gas permeability.

Correlation Between Fractal Dimension of Matrix and Extraction Behavior of Plant Materials

2010 ◽  
Author(s):  
Junhong Yang ◽  
Qianqian Di ◽  
Jun Zhao ◽  
Liqiu Wang
Keyword(s):  
Fractal Dimension ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Fractal Dimensions ◽  
Sem Images ◽  
Plant Materials ◽  
Matrix Microstructure ◽  
Extraction Behavior ◽  
Mercury Injection

This paper studies the correlation between fractal dimension of matrix microstructure of plant materials and extraction behavior using Astragalus root slices as examples. This work compared the yield of extracts on the conventional solvent soaking extraction of samples irradiated 3min by microwave 600W and 900W, respectively. Regarding to microwave treated samples, the area fractal dimensions (DL) of aperture in shape were estimated by using the slit island method on the basis of SEM images analysis, the volume fractal dimensions (DV) of pore size distribution inside matrix were also determined by the mercury injection method on the basis of measured results (6nm–40×105nm) by automatic mercury injection apparatus. Our findings are that, 900W treated sample behaves higher yield of extracts than 600W. The values of DL and DV both increase with increasing of microwave power. The higher values of DL correspond to the much irregular and deformed shape of aperture, which seems un-benefit for the extraction of component inside matrix. However, the higher values of DV correspond to the less concentration of pore size distribution, implying better connectivity of pore or channel at multi-scale (including trachea 20μm–50μm, aperture 0.1μm–1μm and plasmodesma 1nm–10nm in size) and permeability inside matrix during extraction, higher yield of extracts. It demonstrates that combining the two fractal dimensions can present much more information for better understanding of mass transfer behavior and the knowledge of material properties.

NANOSCALE PORE SIZE DISTRIBUTION EFFECTS ON GAS PRODUCTION FROM FRACTAL SHALE ROCKS

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950142
Author(s):  
JINZE XU ◽  
KELIU WU ◽  
RAN LI ◽  
ZANDONG LI ◽  
JING LI ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Gas Transport ◽  
Gas Production ◽  
Lower Sensitivity ◽  
Apparent Permeability ◽  
Transport Efficiency ◽  
Nanoscale Pore

Effect of nanoscale pore size distribution (PSD) on shale gas production is one of the challenges to be addressed by the industry. An improved approach to study multi-scale real gas transport in fractal shale rocks is proposed to bridge nanoscale PSD and gas filed production. This approach is well validated with field tests. Results indicate the gas production is underestimated without considering a nanoscale PSD. A PSD with a larger fractal dimension in pore size and variance yields a higher fraction of large pores; this leads to a better gas transport capacity; this is owing to a higher free gas transport ratio. A PSD with a smaller fractal dimension yields a lower cumulative gas production; this is because a smaller fractal dimension results in the reduction of gas transport efficiency. With an increase in the fractal dimension in pore size and variance, an apparent permeability-shifting effect is less obvious, and the sensitivity of this effect to a nanoscale PSD is also impaired. Higher fractal dimensions and variances result in higher cumulative gas production and a lower sensitivity of gas production to a nanoscale PSD, which is due to a better gas transport efficiency. The shale apparent permeability-shifting effect to nanoscale is more sensitive to a nanoscale PSD under a higher initial reservoir pressure, which makes gas production more sensitive to a nanoscale PSD. The findings of this study can help to better understand the influence of a nanoscale PSD on gas flow capacity and gas production.

Positronium Thermalization Process in Nanoporous Materials and its Influence on the Shape of PALS Spectrum

2008 ◽  
Vol 607 ◽  
pp. 39-41
Author(s):  
Jerzy Kansy ◽  
Radosław Zaleski
Keyword(s):  
Mesoporous Silica ◽  
Pore Size Distribution ◽  
Porous Materials ◽  
Pore Size ◽  
Size Distribution ◽  
Nanoporous Materials ◽  
New Method ◽  
New Model ◽  
Conventional Models ◽  
Mcm 41

A new method of analysis of PALS spectra of porous materials is proposed. The model considers both the thermalization process of positronium inside the pores and the pore size distribution. The new model is fitted to spectra of mesoporous silica MCM-41 and MSF. The resulting parameters are compared with parameters obtained from fitting the “conventional” models, i.e. a sum of exponential components with discrete or/and distributed lifetimes.

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