Characteristics of Pore Structure and Fractal Dimension of Isometamorphic Anthracite

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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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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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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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 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.

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Characteristics of pore structure and fractal dimension of low-rank coal: A case study of Lower Jurassic Xishanyao coal in the southern Junggar Basin, NW China

Fuel ◽

10.1016/j.fuel.2016.11.069 ◽

2017 ◽

Vol 193 ◽

pp. 254-264 ◽

Cited By ~ 113

Author(s):

Haijiao Fu ◽

Dazhen Tang ◽

Ting Xu ◽

Hao Xu ◽

Shu Tao ◽

...

Keyword(s):

Fractal Dimension ◽

Pore Structure ◽

Junggar Basin ◽

Lower Jurassic ◽

Low Rank ◽

Low Rank Coal ◽

Nw China

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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.

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Effect of Nanosilica on Impermeability of Cement-Fly Ash System

Advances in Civil Engineering ◽

10.1155/2020/1243074 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Huaqing Liu ◽

Yan Zhang ◽

Ruiming Tong ◽

Zhaoqing Zhu ◽

Yang Lv

Keyword(s):

Fractal Dimension ◽

Fly Ash ◽

Bond Strength ◽

Pore Structure ◽

Calcium Hydroxide ◽

Cement Hydration ◽

Pozzolanic Reaction ◽

Surface Protection ◽

Durability Of Concrete

Surface protection has been accepted as an effective way to improve the durability of concrete. In this study, nanosilica (NS) was used to improve the impermeability of cement-fly ash system and this kind of material was expected to be applied as surface protection material (SPM) for concrete. Binders composed of 70% cement and 30% fly ash (FA) were designed and nanosilica (NS, 0–4% of the binder) was added. Pore structure of the paste samples was evaluated by MIP and the fractal dimension of the pore structure was also discussed. Hydrates were investigated by XRD, SEM, and TG; the microstructure of hydrates was analyzed with SEM-EDS. The results showed that in the C-FA-NS system, NS accelerated the whole hydration of the cement-FA system. Cement hydration was accelerated by adding NS, and probably, the pozzolanic reaction of FA was slightly hastened because NS not only consumed calcium hydroxide by the pozzolanic reaction to induce the cement hydration but also acted as nucleation seed to induce the formation of C-S-H gel. NS obviously refined the pore structure, increased the complexity of the pore structure, and improved the microstructure, thereby significantly improving the impermeability of the cement-FA system. This kind of materials would be expected to be used as SPM; the interface performance between SPM and matrix, such as shrinkage and bond strength, and how to cast it onto the surface of matrix should be carefully considered.

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