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

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.

Download Full-text

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

Journal of Nanoscience and Nanotechnology ◽

10.1166/jnn.2021.18885 ◽

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.

Download Full-text

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

Materials ◽

10.3390/ma13143238 ◽

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.

Download Full-text

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

Fractal and Fractional ◽

10.3390/fractalfract5040152 ◽

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.

Download Full-text

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.250-253.1846 ◽

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.

Download Full-text

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

Minerals ◽

10.3390/min9020127 ◽

2019 ◽

Vol 9 (2) ◽

pp. 127 ◽

Cited By ~ 6

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.

Download Full-text

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

Fractals ◽

10.1142/s0218348x19400061 ◽

2019 ◽

Vol 27 (01) ◽

pp. 1940006 ◽

Cited By ~ 3

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.

Download Full-text

Experimental Study on Pore Characteristics and Fractal Dimension Calculation of Pore Structure of Aerated Concrete Block

Advances in Civil Engineering ◽

10.1155/2019/8043248 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11 ◽

Cited By ~ 6

Author(s):

Jun Fu ◽

Yue Yu

Keyword(s):

Fractal Dimension ◽

Pore Structure ◽

Fractal Theory ◽

Concrete Block ◽

Average Diameter ◽

Pore Characteristics ◽

Average Pore ◽

X Ray ◽

Matlab Program ◽

Aerated Concrete

It is important to control and predict the macroscopic properties through pore structure parameters of cement-based materials. Microscopic pore structure of concrete has many characteristics, such as sizes and disordered distribution. It is necessary to use fractal theory to describe the pore structure of concrete. In order to establish the relationship between the pore structure characteristics of aerated concrete and porosity, shape factor, pore superficial area, average pore diameter, and average diameter, the fractal dimension of the pore structure was used to evaluate the pore structure characteristics of aerated concrete. The X-ray computed tomography (CT) images of the aerated concrete block pore structure were obtained by using the XTH320 series X-ray three-dimensional microscope. The pore characteristics of aerated concrete block were studied according to Image-Pro Plus (IPP). Based on the research of the fractal dimension measurement methods, the proposed MATLAB program automatically determined the fractal dimension of the aerated concrete block pore structure images. The research results indicated that the small pores (20 μm∼60 μm) of aerated concrete block account for a large percentage compared with the large pores (60 μm∼400 μm or more) from pore diameter distribution and the pore structure of aerated concrete block has obvious fractal features and the fractal dimension of aerated concrete block pore structure images were calculated to be in the range of 1.775–1.805. The pore fractal dimension has a strong correlation with the pore fractal characteristics of aerated concrete blocks. The fractal dimension of the pore structure linearly increases with porosity, shape factor, and pore surface area. The fractal dimension of the pore structure decreases with the average pore size and average diameter. Thus, the fractal dimension of the pore structure that is calculated by the MATLAB program based on fractal theory can be assumed as the integrative evaluation index for evaluating the pore structure characteristic of aerated concrete block.

Download Full-text

Nano/Micro Pore Structure and Fractal Characteristics of Baliancheng Coalfield in Hunchun Basin

Journal of Nanoscience and Nanotechnology ◽

10.1166/jnn.2021.18729 ◽

2021 ◽

Vol 21 (1) ◽

pp. 682-692

Author(s):

Youzhi Wang ◽

Cui Mao

Keyword(s):

Fractal Dimension ◽

Specific Surface ◽

Pore Structure ◽

Surface Area ◽

Specific Surface Area ◽

Pore Diameter ◽

Fractal Dimensions ◽

Nitrogen Adsorption ◽

Average Pore ◽

Coal Reservoir

The pore structure characteristic is an important index to measure and evaluate the storage capacity and fracturing coal reservoir. The coal of Baliancheng coalfield in Hunchun Basin was selected for experiments including low temperature nitrogen adsorption method, Argon Ion milling Scanning Electron Microscopy (Ar-SEM), Nuclear Magnetic Resonance (NMR), X-ray diffraction method, quantitative mineral clay analysis method. The pore structure of coal was quantitatively characterized by means of fractal theory. Meanwhile, the influences of pores fractal dimension were discussed with experiment data. The results show that the organic pores in Baliancheng coalfield are mainly plant tissue pores, interparticle pores and gas pores, and the mineral pores are corrosion pores and clay mineral pores. There are mainly slit pore and wedge-shaped pore in curve I of Low temperature nitrogen adsorption. There are ink pores in curve II with characteristics of a large specific surface area and average pore diameter. The two peaks of NMR T2 spectrum indicate that the adsorption pores are relatively developed and their connectivity is poor. The three peaks show the seepage pores and cracks well developed, which are beneficial to improve the porosity and permeability of coal reservoir. When the pore diameter is 2–100 nm, the fractal dimensions D1 and D2 obtained by nitrogen adsorption experiment. there are positive correlations between water content and specific surface area and surface fractal dimension D1, The fractal dimension D2 was positively and negatively correlated with ash content and average pore diameters respectively. The fractal dimensions DN1 and DN2 were obtained by using the NMR in the range of 0.1 μm˜10 μm. DN1 are positively correlated with specific surface area of adsorption pores. DN2 are positively correlated volume of seepage pores. The fractal dimension DM and dissolution hole fractal dimension Dc were calculated by SEM image method, respectively controlled by clay mineral and feldspar content. There is a remarkable positive correlation between D1 and DN1 and Langmuir volume of coal, so fractal dimension can effectively quantify the adsorption capacity of coal.

Download Full-text

Quantitative Characterization of Heterogeneity in Different Reservoir Spaces of Low-Permeability Sandstone Reservoirs and Its Influence on Physical Properties

Advances in Civil Engineering ◽

10.1155/2021/2399016 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Fengjuan Dong ◽

Na Liu ◽

Zhen Sun ◽

Xiaolong Wei ◽

Haonan Wang ◽

...

Keyword(s):

Fractal Dimension ◽

Pore Structure ◽

Fractal Theory ◽

Fractal Dimensions ◽

Low Permeability ◽

Quantitative Characterization ◽

Average Value ◽

Porosity And Permeability ◽

Sandstone Reservoirs

The complex pore structure of low-permeability sandstone reservoir makes it difficult to characterize the heterogeneity of pore throat. Taking the reservoir of Sanjianfang formation in QL oilfield as an example, the fractal dimension of different storage spaces is calculated by using fractal theory based on casting thin section, scanning electron microscope, and high-pressure mercury injection, and the correlation between porosity, permeability, and contribution of different storage space permeabilities is analyzed. The results show that the reservoir of Sanjianfang formation in QL oilfield mainly develops small pores, fine pores, and micropores, and the fractal dimension of micropore structure is between 2.6044 and 2.9982, with an average value of 2.8316. The more complex the pore structure is, the stronger the microheterogeneity is. The higher the fractal dimension, the more complex the pore structure and the smaller the porosity and permeability. The fractal dimensions of small pores, fine pores, and micropores increase successively with the decrease in pore radius, and the microstructure heterogeneity of large pores is weaker than that of small pores. It provides a theoretical basis for the exploration and development of low-permeability sandstone reservoirs.

Download Full-text

Fractal Characteristics of Pores in the Longtan Shales of Guizhou, Southwest China

Geofluids ◽

10.1155/2020/8834758 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16

Author(s):

Yuqi Huang ◽

Peng Zhang ◽

Jinchuan Zhang ◽

Xuan Tang ◽

Chengwei Liu ◽

...

Keyword(s):

Organic Matter ◽

Fractal Dimension ◽

Pore Structure ◽

Shale Gas ◽

Storage Capacity ◽

Evaluation Criteria ◽

Fractal Dimensions ◽

Gas Absorption ◽

Relative Pressure ◽

And Storage

The pore structure of marine-continental transitional shales from the Longtan Formation in Guizhou, China, was investigated using fractal dimensions calculated by the FHH (Frenkel-Halsey-Hill) model based on low-temperature N2 adsorption data. Results show that the overall D 1 (fractal dimension under low relative pressure, P / P 0 ≤ 0.5 ) and D 2 (fractal dimension under high relative pressure, P / P 0 > 0.5 ) values of Longtan shales were relatively large, with average values of 2.7426 and 2.7838, respectively, indicating a strong adsorption and storage capacity and complex pore structure. The correlation analysis of fractal dimensions with specific surface area, average pore size, and maximum gas absorption volume indicates that D 1 can comprehensively characterize the adsorption and storage capacity of shales, while D 2 can effectively characterize the pore structure complexity. Further correlation among pore fractal dimension, shale organic geochemical parameters, and mineral composition parameters shows that there is a significant positive correlation between fractal dimensions and organic matter abundance as well as a complex correlation between fractal dimension and organic matter maturity. Fractal dimensions increase with an increase in clay mineral content and pyrite content but decrease with an increase in quartz content. Considering the actual geological evaluation and shale gas exploitation characteristics, a lower limit for D 1 and upper limit for D 2 should be set as evaluation criteria for favorable reservoirs. Combined with the shale gas-bearing property test results of Longtan shales in Guizhou, the favorable reservoir evaluation criteria are set as D 1 ≥ 2.60 and D 2 ≤ 2.85 . When D 1 is less than 2.60, the storage capacity of the shales is insufficient. When D 2 is greater than 2.85, the shale pore structure is too complicated, resulting in poor permeability and difficult exploitation.

Download Full-text