FRACTAL PORE STRUCTURE MODEL AND MULTILAYER FRACTAL ADSORPTION IN SHALE

Fractals ◽  
2014 ◽  
Vol 22 (03) ◽  
pp. 1440010 ◽  
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.

FRACTAL MODELS FOR GAS–WATER TRANSPORT IN SHALE POROUS MEDIA CONSIDERING WETTING CHARACTERISTICS

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050138
Author(s):  
QI ZHANG ◽  
XINYUE WU ◽  
QINGBANG MENG ◽  
YAN WANG ◽  
JIANCHAO CAI
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Pressure ◽  
Surface Diffusion ◽  
Water Transport ◽  
Relative Permeability ◽  
Fluid Transport ◽  
Water Saturation ◽  
Fractal Theory ◽  
Gas Slippage

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.

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.

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

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050072 ◽  
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.

FRACTAL-BASED ANALYSIS OF THE RELATION BETWEEN TOOL WEAR AND MACHINE VIBRATION IN MILLING OPERATION

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050101
Author(s):  
MUHAMMAD OWAIS QADRI ◽  
HAMIDREZA NAMAZI
Keyword(s):  
Fractal Dimension ◽  
Tool Wear ◽  
Fractal Theory ◽  
Complex Structure ◽  
Vibration Signal ◽  
Depth Of Cut ◽  
Machining Parameters ◽  
Machine Vibration ◽  
Milling Operation ◽  
Machining Operations

Tool wear is one of the unwanted phenomena in machining operations where tool has direct contact with the workpiece. Tool wear is an important issue in milling operation that is caused due to different parameters such as machine vibration. Tool wear shows complex structure, and machine vibration is a chaotic signal that also is complex. In this research, we analyze the correlation between tool wear and machine vibration using fractal theory. We run the experiments in which machining parameters, namely depth of cut, feed rate and spindle speed change, and accordingly analyze the variations of fractal dimension of tool wear versus the fractal dimension of machine vibration signal. Based on the obtained results, variations of complexity of tool wear are reversely correlated with the variations of complexity of vibration signal. Fractal analysis could potentially be applied to other machining operations in order to investigate the relation between tool wear and machine vibration.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
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.

Fractal Study on the Complexity of Limestone Surface Pore Structure

2012 ◽  
Vol 548 ◽  
pp. 275-280
Author(s):  
Xin Wu ◽  
Si Long ◽  
Guo Hui Li
Keyword(s):  
Fractal Dimension ◽  
Rock Mass ◽  
Pore Structure ◽  
Fractal Geometry ◽  
Fractal Theory ◽  
Microscopic Images ◽  
Simple Rules ◽  
Complex Phenomena ◽  
Mathematics And Physics

Complex characteristics of pore structure of rock mass, such as limestone, are difficult to describe by means of general mathematics and physics. While, the fractal geometry can describe some simple rules behind complex phenomena; and these simple rules can describe the complex phenomena. Therefore in this paper, the fractal theory is applied to study the complexity of the limestone pore structure. Through calculating the fractal dimension of the limestone pore microscopic images of different zoom scales, the scale-independence is proved to be possessed by complexity of pore, which indicates that the limestone is a good fractal body, and its complexity can be studied by means of fractal dimension.

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

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.

scholarly journals Characteristics of micro- and nano-pores in shale oil reservoirs

2020 ◽  
Author(s):  
Debin Xia ◽  
Zhengming Yang ◽  
Tiening Gao ◽  
Haibo Li ◽  
Wei Lin
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Oil And Gas ◽  
Fractal Theory ◽  
Oil Reservoirs ◽  
Practical Significance ◽  
Oil Reservoir ◽  
Shale Oil ◽  
Structure Characteristics ◽  
Shale Oil Reservoirs

Abstract Porosity is the most common form of reservoirs, and its size, shape, and connectivity directly affect the capacity of oil and gas storage and production. To study the micro–nano-pore structure characteristics of shale oil reservoirs and quantitatively characterize its heterogeneity, this work uses high-precision high-pressure mercury intrusion (HPMI) experimental techniques to study the micro–nano-pore structure characteristics of shale oil, and based on the experimental data, fractal theory is used to quantitatively characterize its heterogeneity. The results of the study show that the micro–nano-pores in the shale oil reservoir are concentrated and continuous, and the pore radius is mainly distributed among the range of 30–500 nm, nanoscale pores are an important part of the pores of the shale oil reservoir. The fractal dimension of the shale oil reservoir is larger than the fractal dimension of typical tight oil reservoirs, indicating that the heterogeneity of shale oil reservoir is stronger. The research results have some theoretical and practical significance for the production of inter-salt shale oil reservoirs.

Research on the Pore Structure of Alkali-Slag Cement Stone Activated with Water Glass

2011 ◽  
Vol 194-196 ◽  
pp. 899-903 ◽  
Author(s):  
Juan He ◽  
Chang Hui Yang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Water Glass ◽  
Fractal Theory ◽  
Cement Stone ◽  
Pore Surface ◽  
Slag Cement ◽  
Adsorption Method ◽  
Surface Fractal Dimension ◽  
Surface Fractal

In view of the phenomena that alkali-slag cement has high mechanical strength and good impermeability and they are closely related with the pore structure of cement stone,water glass was selected as the alkali activater, nitrogen adsorption method was adopted to study the pore structure of alkali-slag cement stone, while the pore surface fractal dimension was determined by fractal theory. The results show that the pore structure of alkali-slag cement stone posesses obvious fractal characters and that fits the Frenkel-Halsey-Hill(FHH) model quite well.So the pore surface fractal dimension can be used to synthetically evaluate the superior or inferior of the pore structure of cement stone.

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