Fractal Approach on Quantitative Analysis of Micro Pore Structure of Isotropic Consolidated Clay

2011 ◽  
Vol 250-253 ◽  
pp. 1846-1851
Author(s):  
Xiao Xuan Liu ◽  
Ji Ru Zhang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Soil Consolidation ◽  
Koch Curve ◽  
Sem Images ◽  
Fractal Approach ◽  
Consolidation Pressure ◽  
Size Number ◽  
Isotropic Consolidation

The micro pore structure of isotropic consolidated clay was studied by using a scanning electron microscope (SEM). A digital imaging technique was applied to analyze the evolution of size, number of pores and their distributions in the process of isotropic consolidation according to the SEM images. Based on the fractal concepts of Koch curve and Sierpinski carpet, the Koch fractal dimension Dk and the Sierpinski fractal dimensionDsof soil pores are obtained from the measured data. The variations of bothDkandDsfollowing the change of micro pore parameters and mechanical properties of clay are investigated. The results show that the porosity and pore size decreases as the consolidation pressure increases, and the range of pore size becomes narrower.Dkreflects the degree of irregularity of the pore-solid interface in soil, and the larger theDkthe more irregular the soil pore profile. The distribution of Dkwas found in agreement with a total normal distribution in soil pore. The magnitude ofDsreflects the variation of porosity of clay under isotropic consolidation. Large fractal corresponds to large consolidation pressure and small porosity.Dsdisplays a significant linear regression relationship with porosity, consolidation pressure, consolidation deformation of clay and an exponential growth relationship with permeability coefficient of clay. Both Dk andDsis sensitive to isotropic consolidation of soil and they may be cited as useful indicators for soil consolidation.

scholarly journals Effect of Grain Size on Microscopic Pore Structure and Fractal Characteristics of Carbonate-Based Sand and Silicate-Based Sand

2021 ◽  
Vol 5 (4) ◽  
pp. 152
Author(s):  
Shao-Heng He ◽  
Zhi Ding ◽  
Hai-Bo Hu ◽  
Min Gao
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Quartz Sand ◽  
Glass Bead ◽  
Fractal Theory ◽  
Calcareous Sand ◽  
Wide Range ◽  
Fractal Characteristics

In this study, a series of nuclear magnetic resonance (NMR) tests was conducted on calcareous sand, quartz sand, and glass bead with a wide range of grain sizes, to understand the effect of grain size on the micro-pore structure and fractal characteristics of the carbonate-based sand and silicate-based sand. The pore size distribution (PSD) of the tested materials were obtained from the NMR T2 spectra, and fractal theory was introduced to describe the fractal properties of PSD. Results demonstrate that grain size has a significant effect on the PSD of carbonate-based sand and silicate-based sand. As grain size increases, the PSD of sands evolves from a binary structure with two peaks to a ternary structure with three peaks. The increase in the grain size can cause a remarkable increase in the maximum pore size. It is also found that the more irregular the particle shape, the better the continuity between the large and medium pores. In addition, grain size has a considerable effect on the fractal dimension of the micro-pore structure. The increase of grain size can lead to a significant increase in the heterogeneity and fractal dimension in PSD for calcareous sand, quartz sand and glass bead.

scholarly journals The Impacts of Matrix Compositions on Nanopore Structure and Fractal Characteristics of Lacustrine Shales from the Changling Fault Depression, Songliao Basin, China

Minerals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 127 ◽  
Author(s):  
Zhuo Li ◽  
Zhikai Liang ◽  
Zhenxue Jiang ◽  
Fenglin Gao ◽  
Yinghan Zhang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Dimensions ◽  
Organic Medium ◽  
Songliao Basin ◽  
Sem Images ◽  
Fractal Characteristics ◽  
Inorganic Mineral ◽  
Nanopore Structure ◽  
High Fractal Dimension

The Lower Cretaceous Shahezi shales are the targets for lacustrine shale gas exploration in Changling Fault Depression (CFD), Southern Songliao Basin. In this study, the Shahezi shales were investigated to further understand the impacts of rock compositions, including organic matters and minerals on pore structure and fractal characteristics. An integrated experiment procedure, including total organic carbon (TOC) content, X-ray diffraction (XRD), field emission-scanning electron microscope (FE-SEM), low pressure nitrogen physisorption (LPNP), and mercury intrusion capillary pressure (MICP), was conducted. Seven lithofacies can be identified according to on a mineralogy-based classification scheme for shales. Inorganic mineral hosted pores are the most abundant pore type, while relatively few organic matter (OM) pores are observed in FE-SEM images of the Shahezi shales. Multimodal pore size distribution characteristics were shown in pore width ranges of 0.5–0.9 nm, 3–6 nm, and 10–40 nm. The primary controlling factors for pore structure in Shahezi shales are clay minerals rather than OM. Organic-medium mixed shale (OMMS) has the highest total pore volumes (0.0353 mL/g), followed by organic-rich mixed shale (ORMS) (0.02369 mL/g), while the organic-poor shale (OPS) has the lowest pore volumes of 0.0122 mL/g. Fractal dimensions D1 and D2 (at relative pressures of 0–0.5 and 0.5–1 of LPNP isotherms) were obtained using the Frenkel–Halsey–Hill (FHH) method, with D1 ranging from 2.0336 to 2.5957, and D2 between 2.5779 and 2.8821. Fractal dimensions are associated with specific lithofacies, because each lithofacies has a distinctive composition. Organic-medium argillaceous shale (OMAS), rich in clay, have comparatively high fractal dimension D1. In addition, organic-medium argillaceous shale (ORAS), rich in TOC, have comparatively high fractal dimension D2. OPS shale contains more siliceous and less TOC, with the lowest D1 and D2. Factor analysis indicates that clay contents is the most significant factor controlling the fractal dimensions of the lacustrine Shahezi shale.

PORE STRUCTURE CHARACTERIZATION FOR A CONTINENTAL LACUSTRINE SHALE PARASEQUENCE BASED ON FRACTAL THEORY

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940006 ◽  
Author(s):  
LEI ZHANG ◽  
XUEJUAN ZHANG ◽  
HAO CHAI ◽  
YAOCAI LI ◽  
YONGJIE ZHOU
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Clay Mineral ◽  
Mineral Content ◽  
Fractal Theory ◽  
Average Pore Size ◽  
Structure Characterization ◽  
Imaging Method ◽  
Average Pore

Fractal dimension is an important parameter in the evaluation of tight reservoirs. For an outcrop section of the Nenjiang formation in the Songliao Basin, China, the pore structure and pore fractal characteristics of shale parasequences were investigated using fractal theory. In addition, factors causing pore structure changes were analyzed using the results of low-temperature nitrogen adsorption and scanning electron microscope (SEM) experiments. Conducive to gas migration and secondary pores development such as dissolution, results showed that nanoscale pores dominated by fracture-like morphology and consequent good internal connectivity were observed in each pore size section within the target layer. Each parasequence is characterized by a sequential upward decrease of average pore size and an upward increase of total pore volume, with an increasing number of pores from 2[Formula: see text]nm to 50[Formula: see text]nm. Pores are isolated from each other, with poor connectivity and relatively complex composition of brittle minerals and clay minerals. Main components of the brittle minerals, quartz and feldspar, occur in 20–50% and higher clay mineral content ranging from 50% to 70%. In the parasequence cycle, clay mineral gradually decreases while the brittle mineral content increases. Fractal dimension is negatively correlated with clay mineral content and positively correlated with brittle mineral (quartz and feldspar) content. The fractal dimension calculated by the imaging method and the FHH method shows an upward increasing tendency in each of the parasequence cycles. This is as a result of different phenomena, varied sediment hydrodynamic forces leading to particle size differences and increased brittle minerals resulting in microcracks, therefore, the fractal dimension of the large pores (imaging method) increases upward in the parasequence. Simultaneously, with increased content and accompanied dissolution of brittle minerals causing an increase of small pores from base to top of the parasequence, the fractal dimension of the small pores (FHH method) grows.

scholarly journals Fractal analysis of pore structures in graphene oxide-carbon nanotube based cementitious pastes under different ultrasonication

2019 ◽  
Vol 8 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Yuan Gao ◽  
Hongwen Jing ◽  
Zefu Zhou
Keyword(s):  
Graphene Oxide ◽  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Size Range ◽  
Fractal Dimensions ◽  
Pore Characteristics ◽  
Pore Structures ◽  
Cement Additive ◽  
Multi Walled Carbon Nanotubes

Abstract Nano cement additive using a hybrid of graphene oxide (GO) and multi-walled carbon nanotubes (MWCNTs) combines the excellent affinity of GO and the superior mechanical properties of MWCNTs. Ultrasonication is the key process to disperse the GO/MWCNTs and further optimizes the pore structures of cement-based pastes. Fractal dimension can effectively and quantitatively characterize the pore structures of cementitious composites. The present study investigates the fractal dimensions of pore structures of GO/MWCNT-OPC pastes under power- and time-controlled ultrasonication based on the mercury intrusion porosimetry (MIP) tests data. The finding of this study shows that comparing to calculating the fractal dimension of the overall pore size range, assessing the variations of fractal dimension of individual pore size range is more effective in evaluating the pore characteristic. The fractal dimension of larger capillary pores $$\left( {{D}_{>{{10}^{4}}nm}} \right)$$can be use to describe the change of pore structure of GO/MWCNT-OPC pastes under ultrasonication treatment with sufficient accuracy as higher value of $${{D}_{>{{10}^{4}}nm}}$$indicates better pore characteristics. The fractal dimension change trend of mesopores is always opposite to that of bigger capillary pores. Modest increment in both power- and time-controlled ultrasonication seems to result in the increase of the fractal dimension of capillary pores and lead to better reinforcement effects. Prolongation of ultrasonication time slightly influences the pore structure of the specimens, while nano cement additives exposed to excess ultrasonication power fail to afford adequate reinforcing effect and finally cause the deterioration of the pore structures. The findings of this study can provide helpful information of GO/MWCNT-OPC pastes and ultrasonication treatment in the future.

Pore Size Distribution and Fractal Characteristics of the Nanopore Structure in Organic-Rich Shales Using the Neimark-Kiselev Fractal Approach

2021 ◽  
Vol 21 (1) ◽  
pp. 646-658
Author(s):  
Mingming Wei ◽  
Li Zhang ◽  
Yongqiang Xiong ◽  
Ping’an Peng ◽  
Yiwen Ju
Keyword(s):  
Pore Structure ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Shale Gas ◽  
Fractal Dimensions ◽  
Clay Content ◽  
Scientific Basis ◽  
Fractal Approach ◽  
Fractal Characteristics

Shale gas has been playing an increasingly important role in meeting global energy demands. The heterogeneity of the pore structure in organic-rich shales greatly affects the adsorption, desorption, diffusion and flow of gas. The pore size distribution (PSD) is a key parameter of the heterogeneity of the shale pore structure. In this study, the Neimark-Kiselev (N-K) fractal approach was applied to investigate the heterogeneity in the PSD of the lower Silurian organic-rich shales in South China using low-pressure N2 adsorption, total organic carbon (TOC) content, maturity analysis, X-ray diffraction (XRD) and field emission scanning electron microscopy (FE-SEM) measurements. The results show that (1) the fractal dimension DN-K obtained by N-K theory better represents the heterogeneity of the PSD in shale at an approximately 1–100 nm scale. The DN-K values range from 2.3801 to 2.9915, with a mean of 2.753. The stronger the PSD heterogeneity is, the higher the DN-K value in shale is. (2) The clay-rich samples display multimodal patterns at pore sizes greater than 20 nm, which strongly effect the PSD heterogeneity. Quartz-rich samples display major peaks at less than or equal to a 10 nm pore size, with a smaller effect on the PSD heterogeneity in most cases. In other brittle mineral-rich samples, there are no obvious major peaks, and a weak heterogeneity of the PSDs is displayed. (3) A greater TOC content, maturity, clay content and pore size can cause stronger heterogeneity of the PSD and higher fractal dimensions in the shale samples. This study helps to understand and compare the PSD and fractal characteristics from different samples and provides important theoretical guidance and a scientific basis for the exploration and development of shale gas resources.

Fractal Characteristics of the Middle-Upper Ordovician Marine Shale Nano-Scale Porous Structure from the Ordos Basin, Northeast China

2021 ◽  
Vol 21 (1) ◽  
pp. 274-283
Author(s):  
Liang Liu ◽  
Wuling Mo ◽  
Min Wang ◽  
Nengwu Zhou ◽  
Yu Yan ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Ordos Basin ◽  
Fractal Dimensions ◽  
Upper Ordovician ◽  
Average Pore ◽  
Marine Shale ◽  
Fractal Characteristics ◽  
The Relationship

The fractal characteristics of marine shale from the Middle-Upper Ordovician Wulalike Formation (O2w) in the southwest margin of the Ordos Basin are studied. Based on low-temperature nitrogen adsorption experiments, the FHH (Frenkel-Halsey-Hill) model was employed to investigate the relationship between the marine shale composition, such as TOC, mineral content and shale gas content, and pore structure parameters, such as BET specific surface area, average pore diameter, porosity and fractal dimension. The results show that the pore size distribution curve of shale slowly decreased after the pore size was greater than 50 nm, the pore size distribution showed multiple peaks, and the peak value was mainly in the range of 2–10 nm. Most pores are nanopores, although the pore type and shape are different. Two different fractal dimensions D1 and D2 are obtained from the two segments with relative pressures of 0–0.5 and 0.5–1.0, respectively: the D1 range is 2.77–2.82, and the D2 range is 2.63–2.66. As D1 is larger than D2, the pore structure of small pores is more uniform than that of large pores in the shale samples. The relationship between the fractal dimensions D1 and D2 and the total organic carbon (TOC) content is a convex curve. Fractal dimension D reaches its maximum when TOC is 0.53 wt.%. Fractal dimension D decreases with increasing specific surface area, porosity and average pore size. The fractal dimension has a different influence on the gas storage and migration in shale; the larger the fractal dimension is, the stronger the heterogeneity and the more complex the pore structure, and this outcome is conducive to the storage of gas in shale but not beneficial to the permeability and production of gas.

scholarly journals The Correlation between Pore Structure and Macro Durability Performance of Road Concrete under Loading and Freeze-Thaw and Drying-Wetting Cycles

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Sheng-bo Zhou ◽  
Jun-lin Liang ◽  
Wei-an Xuan ◽  
Ye Qiu
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Negative Correlation ◽  
Concrete Strength ◽  
Linear Equations ◽  
Structure Parameters ◽  
Positive Correlation ◽  
Freeze Thaw ◽  
Loading Level

The grey correlation theory and multiple regression method are used to reveal macro performance degradation rules of road concrete under loading and freeze-thaw and drying-wetting cycles; then the correlation between mesoscopic pore structure and residual strength and antifreezing index of concrete is analyzed. Under the freeze-thaw and drying-wetting cycles with 50% loading level, the pore structure parameters that influence concrete strength show the following sequence: fractal dimension > most probable pore size > porosity > less harmful pore. The correlation between strength and pore parameters can be represented with multiple nonlinear equations. A negative correlation is shown between strength and fractal dimension and most probable pore size. Conversely, a positive correlation is shown between strength, porosity, and less harmful pore. Under the freeze-thaw and drying-wetting cycles with 80% loading level, the pore structure parameters that influence concrete strength show another sequence: fractal dimension > porosity > less harmful pore > most probable pore size. The correlation between antifreezing index and pore parameters should be described with multiple linear equations. The relative dynamic elastic modulus shows a positive correlation to most probable pore size, pore surface area, and porosity but a negative correlation to less harmful pore and pore spacing coefficient.

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.

scholarly journals Fractal Dimension of Basalt Fiber Reinforced Concrete (BFRC) and Its Correlations to Pore Structure, Strength and Shrinkage

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3238
Author(s):  
Yue Li ◽  
Aiqin Shen ◽  
Hua Wu
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Pore Diameter ◽  
Size Range ◽  
Basalt Fiber ◽  
Shrinkage Strain ◽  
Fiber Reinforced Concrete ◽  
Average Pore ◽  
Fractal Characteristics

In this study, we focused on exploring the correlations between the pore surface fractal dimensions and the pore structure parameters, strength and shrinkage properties of basalt fiber-reinforced concrete (BFRC). The pore structure of BFRCs with various fiber contents and fiber lengths was investigated using mercury intrusion porosimetry (MIP) measurements. Through Zhang’s model, the fractal characteristics of BFRCs in the whole pore size range and in different pore size ranges were calculated from the MIP test data. The results showed that the addition of BF increased the total porosity, total pore volume and pore area but decreased the average pore diameter, indicating that BFs refined the pore structure of the concrete. BFRC presented obvious fractal characteristics in the entire pore-size range and individual pore-size ranges; generally, the fractal dimension increased with increasing fiber content. Moreover, correlation analysis suggested that the fractal dimension of BFRC in the whole pore-size range (FD) was closely related to the fractal dimension in the macropore region (Dm) and average pore diameter (APD). The influence of pore structure factors on mechanical strength and shrinkage was studied by grey correlation theory, and the results showed that Dm showed positive correlations with strength and fracture energy, with increasing Dm tending to strengthen and toughen the concrete. An increase in fiber content and length was detrimental to reducing the drying shrinkage strain. In the transition pore region, the fractal dimension (Dt) at diameters ranging from 20 to 50 nm and shrinkage strain exhibited a highly linear relation. These results merit careful consideration in macro-property evaluation by using the pore surface fractal dimension in a specific region instead of the whole region. Finally, grey target theory was applied to evaluate the rank of the mechanical strength and shrinkage of concrete, and the results showed that the overall properties of concrete with a BF length of 18 mm and a BF content of 0.06% ranked the best.

Correlation of Pore Structure and Permeability by SEM-Image Analysis

1990 ◽  
Vol 48 (1) ◽  
pp. 428-429
Author(s):  
C. A. Callender ◽  
Wm. C. Dawson ◽  
J. J. Funk
Keyword(s):  
Image Analysis ◽  
Pore Structure ◽  
Imaging System ◽  
Pore Space ◽  
Simulation Models ◽  
Image Analyzer ◽  
Imaging Data ◽  
Sem Images ◽  
Thin Sections ◽  
Rock Types

The geometric structure of pore space in some carbonate rocks can be correlated with petrophysical measurements by quantitatively analyzing binaries generated from SEM images. Reservoirs with similar porosities can have markedly different permeabilities. Image analysis identifies which characteristics of a rock are responsible for the permeability differences. Imaging data can explain unusual fluid flow patterns which, in turn, can improve production simulation models.Analytical SchemeOur sample suite consists of 30 Middle East carbonates having porosities ranging from 21 to 28% and permeabilities from 92 to 2153 md. Engineering tests reveal the lack of a consistent (predictable) relationship between porosity and permeability (Fig. 1). Finely polished thin sections were studied petrographically to determine rock texture. The studied thin sections represent four petrographically distinct carbonate rock types ranging from compacted, poorly-sorted, dolomitized, intraclastic grainstones to well-sorted, foraminiferal,ooid, peloidal grainstones. The samples were analyzed for pore structure by a Tracor Northern 5500 IPP 5B/80 image analyzer and a 80386 microprocessor-based imaging system. Between 30 and 50 SEM-generated backscattered electron images (frames) were collected per thin section. Binaries were created from the gray level that represents the pore space. Calculated values were averaged and the data analyzed to determine which geological pore structure characteristics actually affect permeability.

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