Fractal dimension of concrete incorporating silica fume and its correlations to pore structure, strength and permeability

Complicated gas–water transport behaviors in nanoporous shale media are known to be influenced by multiple transport mechanisms and pore structure characteristics. More accurate characterization of the fluid transport in shale reservoirs is essential to macroscale modeling for production prediction. This paper develops the analytical relative permeability models for gas–water two-phase in both organic and inorganic matter (OM and IM) of nanoporous shale using the fractal theory. Heterogeneous pore size distribution (PSD) of the shale media is considered instead of the tortuous capillaries with uniform diameters. The gas–water transport models for OM and IM are established, incorporating gas slippage described by second-order slip condition, water film thickness in IM, surface diffusion in OM, and the total organic carbon. Then, the presented model is validated by experimental results. After that, sensitivity analysis of gas–water transport behaviors based on pore structure properties of the shale sample is conducted, and the influence factors of fluid transport behaviors are discussed. The results show that the gas relative permeability is larger than 1 at the low pore pressure and water saturation. The larger pore pressure causes slight effect of gas slippage and surface diffusion on the gas relative permeability. The larger PSD fractal dimension of IM results in larger gas relative permeability and smaller water relative permeability. Besides, the large tortuosity fractal dimension will decrease the gas flux at the same water saturation, and the surface diffusion decreases with the increase of tortuosity fractal dimension of OM and pore pressure. The proposed models can provide an approach for macroscale modeling of the development of shale gas reservoirs.

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Characteristics of Pore Structure and Fractal Dimension of Isometamorphic Anthracite

Energies ◽

10.3390/en10111881 ◽

2017 ◽

Vol 10 (11) ◽

pp. 1881 ◽

Cited By ~ 5

Author(s):

Di Gao ◽

Meng Li ◽

Baoyu Wang ◽

Bin Hu ◽

Jianguo Liu

Keyword(s):

Fractal Dimension ◽

Pore Structure

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FRACTAL PORE STRUCTURE MODEL AND MULTILAYER FRACTAL ADSORPTION IN SHALE

Fractals ◽

10.1142/s0218348x14400106 ◽

2014 ◽

Vol 22 (03) ◽

pp. 1440010 ◽

Cited By ~ 21

Author(s):

LIEHUI ZHANG ◽

JIANCHAO LI ◽

HONGMING TANG ◽

JINGJING GUO

Keyword(s):

Fractal Dimension ◽

Pore Structure ◽

Saturated Vapor ◽

Adsorption Property ◽

Fractal Theory ◽

Complex Structure ◽

Structure Model ◽

Adsorption Model ◽

Adsorption Volume ◽

Isothermal Adsorption

The complex structure and surface property of porous media have significant impact on its accumulation and adsorption capacity. Based on the fractal theory, this paper presents a fractal pore structure model for shales. The effect of different pore structures on fractal dimension is discussed, and the influence of fractal dimension and pore size distribution on porosity is also analyzed. It is shown that the fractal dimension D decreases with the increase of structure parameter q/m for a certain pore diameter ratio, and porosity has positive relationship with fractal dimension. This paper also presents a multilayer fractal adsorption model which takes into account the roughness of adsorption surface by using fractal theory. With the introduction of pseudo-saturated vapor pressure in the supercritical temperature condition, the proposed adsorption model can be applied into a wider range of temperature. Based on the low-pressure nitrogen adsorption and methane isothermal adsorption experiments, the effect of fractal dimension on the adsorption behavior of shales is discussed. Fractal dimension has significant impact on the surface adsorption property and adsorption layer number n. The monolayer saturated adsorption volume Vm increases with the increase of D, while parameter C has the opposite variation trend. Finally, the optimal combination of fractal parameters for describing pore structure of shale samples is selected.

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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.

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Influence of Silica Fume on the Pore Structure of Mortar when Measured by Water Vapour Sorption Isotherms

The Modelling of Microstructure and its Potential for Studying Transport Properties and Durability ◽

10.1007/978-94-015-8646-7_12 ◽

1996 ◽

pp. 257-270 ◽

Cited By ~ 2

Author(s):

E. Helsing Atlassi

Keyword(s):

Pore Structure ◽

Water Vapour ◽

Silica Fume ◽

Sorption Isotherms ◽

Water Vapour Sorption ◽

Vapour Sorption

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STUDY ON EVOLUTION OF FRACTAL DIMENSION FOR FRACTURED COAL SEAM UNDER MULTI-FIELD COUPLING

Fractals ◽

10.1142/s0218348x20500723 ◽

2020 ◽

Vol 28 (04) ◽

pp. 2050072 ◽

Cited By ~ 3

Author(s):

GUANNAN LIU ◽

BOMING YU ◽

DAYU YE ◽

FENG GAO ◽

JISHAN LIU

Keyword(s):

Fractal Dimension ◽

Coal Seam ◽

Pore Structure ◽

Fractal Theory ◽

In Situ Stress ◽

Volume Strain ◽

Fracture Length ◽

Field Coupling ◽

Pore Evolution ◽

Fractured Coal

In the process of gas extraction, fracture-pore structure significantly influences the macroscopic permeability of coal seam. However, under the multi-field coupling, the mechanism of coal seam fracture-pore evolution remains to be clarified. In this paper, considering the effect of adsorption expansion, the fractal theory for porous media coupled with the multi-field model for coal seam is considered, and a multi-field coupling mechanical model is constructed by considering the influence of fracture-pore structure. Furthermore, the evolution mechanism of fractal dimension with physical and mechanical parameters of coal seam is studied. It is found that the fractal dimension for coal seam is inversely proportional to mining time and in situ stress, proportional to elastic modulus, Langmuir volume constant and Langmuir volume strain constant, and inversely proportional to Langmuir pressure constant. Compared with other factors, Langmuir pressure constant and Langmuir volume strain constant have the significance influence on the fractal dimension for the fracture length.

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Rheological Behavior and Microstructure Characteristics of SCC Incorporating Metakaolin and Silica Fume

Materials ◽

10.3390/ma11122576 ◽

2018 ◽

Vol 11 (12) ◽

pp. 2576 ◽

Cited By ~ 7

Author(s):

Gang Ling ◽

Zhonghe Shui ◽

Tao Sun ◽

Xu Gao ◽

Yunyao Wang ◽

...

Keyword(s):

Pore Structure ◽

Silica Fume ◽

Mechanical Performance ◽

Free Water ◽

Hydration Product ◽

Replacement Ratio ◽

Microstructure Characteristics ◽

Beneficial Effects ◽

Slump Flow ◽

Strength And Durability

This study explores the effects of metakaolin (MK) and silica fume (SF) on rheological behaviors and microstructure of self-compacting concrete (SCC). The rheology, slump flow, V-funnel, segregation degree (SA), and compressive strength of SCC are investigated. Microstructure characteristics, including hydration product and pore structure, are also studied. The results show that adding MK and SF instead of 4%, 6% and 8% fly ash (FA) reduces flowability of SCC; this is due to the fact that the specific surface area of MK and SF is larger than FA, and the total water demand increases as a result. However, the flowability increases when replacement ratio is 2%, as the small MK and SF particles will fill in the interstitial space of mixture and more free water is released. The fluidity, slump flow, and SA decrease linearly with the increase of yield stress. The total amount of SF and MK should be no more than 6% to meet the requirement of self-compacting. Adding MK or SF to SCC results in more hydration products, less Ca(OH)2 and refinement of pore structure, leading to obvious strength and durability improvements. When the total dosage of MK and SF admixture is 6%, these beneficial effects on workability, mechanical performance, and microstructure are more significant when SF and MK are applied together.

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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.

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The Contribution of the Transition Zone to the Strength of High Quality Silica Fume Concretes

MRS Proceedings ◽

10.1557/proc-114-97 ◽

1987 ◽

Vol 114 ◽

Cited By ~ 12

Author(s):

A. Bentur ◽

A. Goldman ◽

M. D. Cohen

Keyword(s):

Pore Structure ◽

Transition Zone ◽

Silica Fume ◽

Fresh Concrete ◽

High Strength ◽

High Quality ◽

The One

ABSTRACTThe strength of high strength silica fume concretes is usually attributed to the reduction in w/c ratio and the refinement of the pore structure. A study of concretes and pastes, with and without silica fume, suggests that the contribution of the silica fume to strength is also the result of the densification of the transition zone. It is argued here that this influence is as important as the one due to the reduction in w/c ratio. It is suggested that the densification of the transition zone is the result of the effect of the silica fume on the nature of the fresh concrete.

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