FRACTAL CHARACTERISTICS OF NANOSCALE PORES IN SHALE AND ITS IMPLICATIONS ON METHANE ADSORPTION CAPACITY

Pore structure in shale controls the gas storage mechanism and gas transport behaviors. Since nanoscale pores in shale matrix have fractal characteristics, fractal theory can be used to study its structure. In addition, fractal method has its own advantages to investigate nanopores in shale, especially for the heterogeneity and irregularity of nanopores in shale. In this work, fractal features of nanoscale pores and the implication on methane adsorption capacity of shale were investigated by employing low pressure nitrogen adsorption, scanning electron microscopy (SEM), and methane adsorption experiments. Frenkel–Halsey–Hill (FHH) model was also used to calculate the fractal parameters of nanoscale pores in shale. The results showed that nanoscale pores in 12 shale samples have obvious fractal features. All the fractal curves of these shale samples can be divided into two segments, which are cut off by [Formula: see text], and the fractal dimensions of these two segments vary from 2.48 to 2.92 [Formula: see text] and 2.42 to 2.80 [Formula: see text], respectively. Based on SEM images, it is found that self-similarity of organic pore systems in shales refers to two aspects. One is that relatively large-scale and small-scale pores have similar formation properties and types, which are of elliptical shape with rough surface. The other is that some small-scale pores are formed by rough surface of relatively large pores. The results also demonstrate that methane adsorption capacity of shale samples increase with increasing total organic carbon (TOC) contents. This is mainly because organic matter is rich in pores and has relatively large fractal dimension values. Larger fractal dimensions indicate rougher pore surfaces and could form more small-scale organic pores. These organic pores would provide more space for methane adsorption.

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FRACTAL CHARACTERISTICS OF PORES IN TAIYUAN FORMATION SHALE FROM HEDONG COAL FIELD, CHINA

Fractals ◽

10.1142/s0218348x18400066 ◽

2018 ◽

Vol 26 (02) ◽

pp. 1840006 ◽

Cited By ~ 12

Author(s):

KUNJIE LI ◽

FANGUI ZENG ◽

JIANCHAO CAI ◽

GUANGLONG SHENG ◽

PENG XIA ◽

...

Keyword(s):

Adsorption Capacity ◽

Clay Minerals ◽

Fractal Dimensions ◽

Methane Adsorption ◽

Relative Pressure ◽

Coal Field ◽

Adsorption Sites ◽

Taiyuan Formation ◽

Pore Size Distributions ◽

Fractal Characteristics

For the purpose of investigating the fractal characteristics of pores in Taiyuan formation shale, a series of qualitative and quantitative experiments were conducted on 17 shale samples from well HD-1 in Hedong coal field of North China. The results of geochemical experiments show that Total organic carbon (TOC) varies from 0.67% to 5.32% and the organic matters are in the high mature or over mature stage. The shale samples consist mainly of clay minerals and quartz with minor pyrite and carbonates. The FE-SEM images indicate that three types of pores, organic-related pores, inorganic-related pores and micro-fractures related pores, are developed well, and a certain number of intragranular pores are found inside quartz and carbonates formed by acid liquid corrosion. The pore size distributions (PSDs) broadly range from several to hundreds nanometers, but most pores are smaller than 10[Formula: see text]nm. As the result of different adsorption features at relative pressure (0–0.5) and (0.5–1) on the N2 adsorption isotherm, two fractal dimensions [Formula: see text] and [Formula: see text] were obtained with the Frenkel–Halsey–Hill (FHH) model. [Formula: see text] and [Formula: see text] vary from 2.4227 to 2.6219 and from 2.6049 to 2.7877, respectively. Both TOC and brittle minerals have positive effect on [Formula: see text] and [Formula: see text], whereas clay minerals, have a negative influence on them. The fractal dimensions are also influenced by the pore structure parameters, such as the specific surface area, BJH pore volume, etc. Shale samples with higher [Formula: see text] could provide more adsorption sites leading to a greater methane adsorption capacity, whereas shale samples with higher [Formula: see text] have little influence on methane adsorption capacity.

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Simulation of methane adsorption in diverse organic pores in shale reservoirs with multi-period geological evolution

International Journal of Coal Science & Technology ◽

10.1007/s40789-021-00431-7 ◽

2021 ◽

Author(s):

Shangbin Chen ◽

Chu Zhang ◽

Xueyuan Li ◽

Yingkun Zhang ◽

Xiaoqi Wang

Keyword(s):

Organic Matter ◽

Pore Size ◽

Adsorption Capacity ◽

Thermal Evolution ◽

Methane Adsorption ◽

Storage Site ◽

Pressure Sensitivity ◽

Adsorption Characteristics ◽

Shale Reservoirs ◽

Organic Pores

AbstractIn shale reservoirs, the organic pores with various structures formed during the thermal evolution of organic matter are the main storage site for adsorbed methane. However, in the process of thermal evolution, the adsorption characteristics of methane in multi type and multi-scale organic matter pores have not been sufficiently studied. In this study, the molecular simulation method was used to study the adsorption characteristics of methane based on the geological conditions of Longmaxi Formation shale reservoir in Sichuan Basin, China. The results show that the characteristics of pore structure will affect the methane adsorption characteristics. The adsorption capacity of slit-pores for methane is much higher than that of cylindrical pores. The groove space inside the pore will change the density distribution of methane molecules in the pore, greatly improve the adsorption capacity of the pore, and increase the pressure sensitivity of the adsorption process. Although the variation of methane adsorption characteristics of different shapes is not consistent with pore size, all pores have the strongest methane adsorption capacity when the pore size is about 2 nm. In addition, the changes of temperature and pressure during the thermal evolution are also important factors to control the methane adsorption characteristics. The pore adsorption capacity first increases and then decreases with the increase of pressure, and increases with the increase of temperature. In the early stage of thermal evolution, pore adsorption capacity is strong and pressure sensitivity is weak; while in the late stage, it is on the contrary.

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Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

MATEC Web of Conferences ◽

10.1051/matecconf/201815901006 ◽

2018 ◽

Vol 159 ◽

pp. 01006

Author(s):

Bagus Hario Setiadji ◽

Supriyono ◽

Djoko Purwanto

Keyword(s):

Fractal Dimension ◽

Fractal Theory ◽

Asphalt Mixture ◽

Fractal Dimensions ◽

Calculation Model ◽

Careful Consideration ◽

Upper And Lower Bounds ◽

Aggregate Gradation ◽

Fractal Characteristic ◽

Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

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Application of Fractal Theory in Aggregate Gradation Research

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.204-208.1923 ◽

2012 ◽

Vol 204-208 ◽

pp. 1923-1928

Author(s):

Bo Tan ◽

Rui Hua Yang ◽

Yan Ting Lai

Keyword(s):

Fractal Dimension ◽

Fractal Theory ◽

Asphalt Mixture ◽

Fractal Dimensions ◽

Aggregate Gradation ◽

Structure Characteristics ◽

Aggregate Distribution ◽

Dimension Formula ◽

Mass Fractal ◽

Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

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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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A MODIFIED TWO-SCALE MICROWAVE SCATTERING MODEL FOR A GAUSSIAN-DISTRIBUTED CONDUCTING ROUGH SURFACE

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-3-2141-2018 ◽

2018 ◽

Vol XLII-3 ◽

pp. 2141-2146

Author(s):

F. Yu ◽

H. Wang ◽

Z. Y. Chen

Keyword(s):

Surface Roughness ◽

Rough Surface ◽

Large Scale ◽

Incident Angle ◽

Wavelet Packet ◽

Small Scale ◽

Backscattering Coefficient ◽

Microwave Scattering ◽

Scattering Model ◽

Scale Roughness

A modified two-scale microwave scattering model (MTSM) was presented to describe the scattering coefficient of natural rough surface in this paper. In the model, the surface roughness was assumed to be Gaussian so that the surface height z(x, y) can be split into large-scale and small-scale components relative to the electromagnetic wavelength by the wavelet packet transform. Then, the Kirchhoff Model (KM) and Small Perturbation Method (SPM) were used to estimate the backscattering coefficient of the large-scale and small-scale roughness respectively. Moreover, the ‘tilting effect’ caused by the slope of large-scale roughness should be corrected when we calculated the backscattering contribution of the small-scale roughness. Backscattering coefficient of the MTSM was the sum of backscattering contribution of both scale roughness surface. The MTSM was tested and validated by the advanced integral equation model (AIEM) for dielectric randomly rough surface, the results indicated that, the MTSM accuracy were in good agreement with AIEM when incident angle was less than 30&deg; (&theta;i&thinsp;&lt;30&deg;) and the surface roughness was small (ks&thinsp;=&thinsp;0.354).

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INVESTIGATION OF FRACTAL CHARACTERISTICS AND METHANE ADSORPTION CAPACITY OF THE UPPER TRIASSIC LACUSTRINE SHALE IN THE SICHUAN BASIN, SOUTHWEST CHINA

Fractals ◽

10.1142/s0218348x19400115 ◽

2019 ◽

Vol 27 (01) ◽

pp. 1940011 ◽

Cited By ~ 2

Author(s):

LEI CHEN ◽

ZHENXUE JIANG ◽

KEYU LIU ◽

WEI YANG ◽

SHU JIANG ◽

...

Keyword(s):

Pore Structure ◽

Adsorption Capacity ◽

Sichuan Basin ◽

Southwest China ◽

Upper Triassic ◽

Methane Adsorption ◽

Relative Pressure ◽

Pore Surface ◽

Fractal Characteristics ◽

The Sichuan Basin

To better understand the nanopore characteristics and their effects on methane adsorption capacity of shales, we performed fractal analysis of nine shale samples collected from the fifth member of Upper Triassic Xujiahe Formation in the Sichuan Basin, southwest China. [Formula: see text] adsorption results show that shales have different adsorption characteristics at relative pressure of 0–0.5 and 0.5–1. Two fractal dimensions [Formula: see text] and [Formula: see text] were calculated using the Frenkel–Halsey–Hill (FHH) equation. Results show that the methane adsorption capacity increases with the increase of [Formula: see text] and [Formula: see text], of which [Formula: see text] has a more significant influence on adsorption capacity than [Formula: see text]. Further studies indicate that [Formula: see text] represents the pore surface fractal characteristics caused by the irregularity of shale surface, whereas [Formula: see text] represents the pore structure fractal characteristics, which is mainly affected by shale components (e.g. TOC, clay minerals) and pore parameters (e.g. average pore diameter, micropores content). A higher [Formula: see text] corresponds to a more irregular pore surface, which provides more space for methane adsorption. While a higher [Formula: see text] indicates a more complex pore structure and a stronger capillary condensation action on the pore surface, which in turn enhances the methane adsorption capacity.

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Pore Structure and Fractal Characteristics of Different Shale Lithofacies in the Dalong Formation in the Western Area of the Lower Yangtze Platform

Minerals ◽

10.3390/min10010072 ◽

2020 ◽

Vol 10 (1) ◽

pp. 72 ◽

Cited By ~ 3

Author(s):

Longfei Xu ◽

Jinchuan Zhang ◽

Jianghui Ding ◽

Tong Liu ◽

Gang Shi ◽

...

Keyword(s):

Pore Structure ◽

Fractal Dimensions ◽

Upper Permian ◽

Hydrocarbon Generation ◽

Yangtze Platform ◽

Dalong Formation ◽

Fractal Characteristics ◽

Lower Yangtze ◽

Siliceous Shale ◽

Organic Pores

The purpose of this article was to quantitatively investigate the pore structure and fractal characteristics of different lithofacies in the upper Permian Dalong Formation marine shale. Shale samples in this study were collected from well GD1 in the Lower Yangtze region for mineral composition, X-ray diffraction (XRD), and nitrogen adsorption–desorption analysis, as well as broad-ion beam scanning electron microscopy (BIB-SEM) observation. Experimental results showed that the TOC (total organic carbon) content and vitrinite reflectance (Ro) of the investigated shale samples were in the ranges 1.18–6.45% and 1.15–1.29%, respectively, showing that the Dalong Formation shale was in the mature stage. XRD results showed that the Dalong Formation shale was dominated by quartz ranging from 38.4% to 54.3%, followed by clay minerals in the range 31.7–37.5%, along with carbonate minerals (calcite and dolomite), with an average value of 9.6%. Based on the mineral compositions of the studied samples, the Dalong Formation shale can be divided into two types of lithofacies, namely siliceous shale facies and clay–siliceous mixed shale facies. In siliceous shale facies, which were mainly composed of organic pores, the surface area (SA) and pore volume (PV) were in the range of 5.20–10.91 m2/g and 0.035–0.046 cm3/g, respectively. Meanwhile, the pore size distribution (PSD) and fractal dimensions were in the range 14.2–26.1 nm and 2.511–2.609, respectively. I/S (illite-smectite mixed clay) was positively correlated with SA, PV, and fractal dimensions, while illite had a negative relationship with SA, PV, and fractal dimensions. I/S had a strong catalytic effect on organic matter for hydrocarbon generation, which was beneficial to the development of organic micropores, so I/S was conducive to pore structure complexity and the increase in SA and PV, while illite easily filled organic pores, which was not beneficial to the improvement of pore space. In clay–siliceous mixed shale facies, which mainly develop inorganic pores such as intergranular pores, SA and PV were in the range of 6.71–11.38 m2/g and 0.030–0.041 cm3/g, respectively. Meanwhile, PSD and fractal dimensions were in the range of 14.3–18.9 nm and 2.563–2.619, respectively. Quartz and I/S showed weak positive correlations with SA, PV, and fractal dimensions. The various compact modes between quartz particles and the disorder of I/S were conducive to the complexity of pore structure and the improvement of SA and PV. The research findings can provide a reference for the optimization and evaluation of shale gas favorable area of the Lower Yangtze Platform.

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Quantitative Analysis for Micro Geometrical Characteristic of Rough Surface Profile Based on Fractal Theory

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.154-155.19 ◽

2010 ◽

Vol 154-155 ◽

pp. 19-22

Author(s):

Xiu Juan Yang ◽

Zhi Qian Xu ◽

Xiang Zhen Yan

Keyword(s):

Surface Roughness ◽

Fractal Dimension ◽

Quantitative Analysis ◽

Rough Surface ◽

Vertical Section ◽

Fractal Theory ◽

Surface Profile ◽

Fractal Dimensions ◽

Geometrical Characteristic ◽

Accuracy Requirement

In this paper, a quantitative analysis for the micro geometrical characteristic of rough surface profile is researched with the fractal theory. Firstly, the fractal dimensions of profile curves under different surface roughness are obtained by using the vertical section method, and then the theoretical relationship between the surface roughness and the fractal dimension is built. Secondly, according to the surface profile curve composed of many triangle peaks, the angles and heights of them are calculated to study the micro geometrical size. Through their variation laws changing with the fractal parameters, the calculation formulas of their average values related to fractal dimension are obtained by using mathematics regression tools. Finally, combing three theoretical relationships built above, the geometrical characteristic of the rough surface profile can be calculated with the surface roughness and accuracy requirement known.

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Fractal Characteristics of Motion Trace Curve of Landslide Monitoring Points

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.90-93.1285 ◽

2011 ◽

Vol 90-93 ◽

pp. 1285-1290 ◽

Cited By ~ 2

Author(s):

Xian Ming Hu ◽

E Chuan Yan ◽

Kun Lv ◽

Ting Ting Zhang

Keyword(s):

Fractal Theory ◽

Fractal Dimensions ◽

Monitoring Data ◽

Movement Direction ◽

Landslide Monitoring ◽

Box Dimension ◽

Monitoring Point ◽

Fractal Characteristics ◽

Landslide Development ◽

Effective Use

According to the analysis of the landslide monitoring data, it is revealed that the amount of the cumulative displacement of the landslide depends on the monitoring cycle. And the trajectory curve of monitoring point has the fractal characteristics. The fractal dimension of the landslide internal points’ movement direction is various with the landslide development, which is decreased from the generation to the deformation and then to the damage. Meanwhile, based on the fractal boxing counting theorem, the program in Matlab is created to calculate the box dimension of the curve. Take a reviving landslide in Three-Gorge as an example, the fractal dimensions of the surface GPS monitoring points’ trajectory curves from 2007 to 2009 are obtained, and the dimension of each point is close to 1. The result indicates that this landslide is in the plastic deformation stage. It is the same with the landslide actual deformation. Therefore, the fractal theory has a great significance in the effective use of the monitoring data, the reorganization of the evolving stage and the prediction of the deformation trend for the landslide.

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