Multi-Angle Investigation of the Fractal Characteristics of Nanoscale Pores in the Lower Cambrian Niutitang Shale and Their Implications for CH4 Adsorption

2021 ◽  
Vol 21 (1) ◽  
pp. 156-167
Author(s):  
Yang Wang ◽  
Caifang Wu ◽  
Yong Qin ◽  
Shimin Liu ◽  
Rui Zhang
Keyword(s):  
Fractal Dimension ◽  
Clay Minerals ◽  
Lower Cambrian ◽  
Fractal Dimensions ◽  
Methane Adsorption ◽  
Bet Surface Area ◽  
Commercial Development ◽  
Pore Structures ◽  
Nanoscale Pore ◽  
Pore Types

Shale gas has received widespread interest due to its successful commercial development in China. Pore structures in shale can directly control its gas storage and migration properties. In this study, field emission scanning electron microscopy (FE-SEM), low-pressure N2/CO2 adsorption and highpressure methane adsorption were used to investigate the nanoscale pore structures of the Lower Cambrian Niutitang Formation in the southeastern Upper Yangtze platform. The fractal parameters of the pore structures were also calculated using the Frenkel–Halsey–Hill (FHH) model. The relationships between the fractal dimensions and TOC content, mineral composition and pore structure parameters were also discussed. The results show that organic matter and clay minerals are primary factors affecting the nanoscale pore development. Slit-shaped pores and ink-bottle-shaped pores are the predominant pore types in the Niutitang shale. The Brunauer-Emmett-Teller (BET) surface areas vary from 4.91 m2/g to 34.33 m2/g, and the pore volumes range from 0.689 m3/100 g to 2.964 m3/100 g. Two fractal dimensions (D1 and D2) of the Niutitang shale were obtained using the FHH model, with D1 ranging from 2.605 to 2.684, and D2 ranging from 2.681 to 2.865. D1 adequately characterizes the surface roughness of the pore structures, while D2 represents the complexity of the pore types. Inter-particle (InterP) pores commonly have greater shape complexities than OM pores and intra-particle (IntraP) pores, based on analyses using Image-Pro Plus software. In addition, the TOC content and clay minerals have great effects on the fractal dimension D1. Meanwhile, the fractal dimension D1 increases with increasing BET surface area, but there is no definite relationship between the fractal dimensions and pore volumes. Both the fractal dimensions D1 and D2 are negatively correlated with pore sizes. Further investigation indicates that the fractal dimension D1 exhibits a strong positive relationship with the methane adsorption capacity indicating that Niutitang shales with greater values of the fractal dimension D1 have higher methane adsorption capacities.

scholarly journals Pore Structure and Fractal Characteristics of Organic-Rich Lacustrine Shales of the Kongdian Formation, Cangdong Sag, Bohai Bay Basin

2021 ◽  
Vol 9 ◽  
Author(s):  
Shouxu Pan ◽  
Ming Zha ◽  
Changhai Gao ◽  
Jiangxiu Qu ◽  
Xiujian Ding
Keyword(s):  
Organic Matter ◽  
Specific Surface ◽  
Pore Structure ◽  
Surface Area ◽  
Clay Minerals ◽  
Mineral Composition ◽  
Fractal Dimensions ◽  
Nitrogen Adsorption ◽  
Thermal Maturity ◽  
Pore Types

In order to examine the pore structure and reveal the fractal geometric nature of shales, a series of laboratory experiments were conducted on lacustrine shale samples cored from the Kongdian Formation. Based on the low temperature nitrogen adsorption, fluorescent thin section and field emission scanning electronic microscope, a comprehensive pore structure classification and evaluation were conducted on shale samples. Fractal dimensions D1 and D2 (with relative pressure of 0–0.45 and 0.45–1.00, respectively) were obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH) method. With additional means of X-ray diffraction analysis, total organic carbon content analysis and thermal maturity analysis, the relationships between pore structure parameters, fractal dimensions, TOC content and mineral composition are presented and discussed in this paper. The results show that interparticle pores and microfractures are predominant, whereas organic matter pores are rarely found. The pore morphology is primarily featured with wide-open ends and slit-shaped structures. In terms of pore scale, mesopores and macropores are predominant. The value of fractal dimension D1 representing small pores ranges from 2.0173 to 2.4642 with an average of 2.1735. The value of D2 which represents large pores ranges from 2.3616 to 2.5981 with an average of 2.4960. These low numbers are an indication of few pore types and relatively low heterogeneity. In addition, smaller D1 values reveal that large pores have more complicated spatial structures than smaller ones. The results of correlation analysis show that: 1) D2 is correlated positively with specific surface area but negatively with average pore diameter; 2) D1 and D2 literally show no obvious relationship with mineral composition, TOC content or vitrinite reflectance (Ro); 3) both total Barrett-Joyner-Halenda (BJH) volume and specific surface area show a positive relationship with dolomite content and a negative relationship with felsic minerals content. These results demonstrate that the pore types are relatively few and dominated by mesopores, and the content of brittle minerals such as dolomite and felsic minerals control the pore structure development whilst organic matter and clay minerals have less influence due to low thermal maturity and abundance of clay minerals.

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

2019 ◽  
Vol 8 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Yuan Gao ◽  
Hongwen Jing ◽  
Zefu Zhou
Keyword(s):  
Graphene Oxide ◽  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Size Range ◽  
Fractal Dimensions ◽  
Pore Characteristics ◽  
Pore Structures ◽  
Cement Additive ◽  
Multi Walled Carbon Nanotubes

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.

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

Fractals ◽  
2018 ◽  
Vol 26 (02) ◽  
pp. 1840006 ◽  
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.

scholarly journals Full‐Scale Pore Structure and Fractal Dimension of the Longmaxi Shale from the Southern Sichuan Basin: Investigations Using FE‐SEM, Gas Adsorption and Mercury Intrusion Porosimetry

Minerals ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 543 ◽  
Author(s):  
Wang ◽  
Jiang ◽  
Jiang ◽  
Chang ◽  
Zhu ◽  
...  
Keyword(s):  
Organic Matter ◽  
Fractal Dimension ◽  
Pore Structure ◽  
Clay Minerals ◽  
Sichuan Basin ◽  
Mercury Intrusion Porosimetry ◽  
Fractal Dimensions ◽  
Full Scale ◽  
Mercury Intrusion ◽  
Longmaxi Shale

Pore structure determines the gas occurrence and storage properties of gas shale and is a vital element for reservoir evaluation and shale gas resources assessment. Field emission scanning electron microscopy (FE‐SEM), high‐pressure mercury intrusion porosimetry (HMIP), and low‐pressure N2/CO2 adsorption were used to qualitatively and quantitatively characterize full‐scale pore structure of Longmaxi (LM) shale from the southern Sichuan Basin. Fractal dimension and its controlling factors were also discussed in our study. Longmaxi shale mainly developed organic matter (OM) pores, interparticle pores, intraparticle pores, and microfracture, of which the OM pores dominated the pore system. The pore diameters are mainly distributed in the ranges of 0.4–0.7 nm, 2–20 nm and 40–200 μm. Micro‐, meso‐ and macropores contribute 24%, 57% and 19% of the total pore volume (PV), respectively, and 64.5%, 34.6%, and 0.9% of the total specific surface area (SSA). Organic matter and clay minerals have a positive contribution to pore development. While high brittle mineral content can inhibit shale pore development. The fractal dimensions D1 and D2 which represents the roughness of the shale surface and irregularity of the space structure, respectively, are calculated based on N2 desorption data. The value of D1 is in the range of 2.6480–2.7334 (average of 2.6857), D2 is in the range of 2.8924–2.9439 (average of 2.9229), which indicates that Longmaxi shales have a rather irregular pore morphology as well as complex pore structure. Both PV and SSA positively correlated with fractal dimensions D1 and D2. The fractal dimension D1 decreases with increasing average pore diameter, while D2 is on the contrary. These results suggest that the small pores have a higher roughness surface, while the larger pores have a more complex spatial structure. The fractal dimensions of shale are jointly controlled by OM, clays and brittle minerals. The TOC content is the key factor which has a positive correlation with the fractal dimension. Clay minerals have a negative influence on fractal dimension D1, and positive influence D2, while brittle minerals show an opposite effect compared with clay minerals.

Nanoscale Pore Fractal Characteristics of Permian Shale and Its Impact on Methane-Bearing Capacity: A Case Study from Southern North China Basin, Central China

2021 ◽  
Vol 21 (1) ◽  
pp. 139-155
Author(s):  
Xiaoliang Wei ◽  
Qian Chen ◽  
Jinchuan Zhang ◽  
Haikuan Nie ◽  
Wei Dang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Water Saturation ◽  
Fractal Dimensions ◽  
Micropore Volume ◽  
Central China ◽  
Gas Content ◽  
Structure Parameters ◽  
Relative Pressure ◽  
Nanoscale Pore

Fractal dimension is closely related to the nanoscale pore structure of shale, and it also has an important influence on the gas content of shale. To investigate the correlation between the fractal dimension and the methane (CH4) bearing features of shale, seven Permian shale samples were analyzed with field emission scanning electron microscopy (FE-SEM), low temperature nitrogen (N2), carbon dioxide (CO2) and CH4 adsorption and on-site gas desorption experiments. Based on the N2 adsorption and desorption data, we proposed a new method to better determine the gas adsorption stage at different relative pressure (P/P0) points in the multilayer adsorption or capillary condensation stage. On this basis, two fractal dimensions, D1 (representing the surface roughness) and D2 (representing pore irregularity), were obtained. By correlating the fractal dimensions and nanoscale pore structure parameters, we found that D1 does not correlate with the pore structure parameters except for the micropore volume. Influenced by the aggregation of porous and nonporous materials, D2 has a positive linear relationship with the specific surface area (SSA) and micropore volume but has a negative linear correlation with the average diameter of pores. D1 is negatively correlated with water saturation and positively correlated with free CH4 content. The CH4 adsorption content is positively correlated with D2. By fitting the on-site desorption data, the positive correlation between the total desorbed CH4 content and the desorbed CH4 content in stage 2 and D2 was also confirmed. D2 better reflects the CH4 adsorption capacity of organic-rich shale than D1. However, D1 can be used to reflect the influence of shale surface properties on water saturation and to indirectly reflect the free CH4 content in shale. The fractal dimension (D1 and D2) is a clear indicator of the total free and adsorbed CH4 content, but cannot indicate the desorbed CH4 content at different stages.

Pore structure and adsorption hysteresis of the middle Jurassic Xishanyao shale formation in the Southern Junggar Basin, northwest China

2021 ◽  
pp. 014459872098513
Author(s):  
Bo Liu ◽  
Yifei Gao ◽  
Kouqi Liu ◽  
Jinzhong Liu ◽  
Mehdi Ostadhassan ◽  
...  
Keyword(s):  
Pore Structure ◽  
Clay Minerals ◽  
Pore Volume ◽  
Middle Jurassic ◽  
Fractal Dimensions ◽  
Junggar Basin ◽  
Northwest China ◽  
Mean Value ◽  
Pore Structures ◽  
Single Well

In order to understand the pore structures of the Middle Jurassic Xishanyao Formation in the Junggar Basin, 11 shale samples from a single well were picked and were subjected to several analyses including mineralogy, (programmed) Rock-Eval pyrolysis for geochemical and N2 adsorption for pore structure analysis. The results showed that the mean value of total organic carbon (TOC) content of these samples is around 1.54% while Tmax varies between 429 to 443°C, indicating they are in the oil window. Mineral assemblages of the samples is mainly quartz and clay (illite, chlorite and kaolinite). Moreover, negative correlations between the K-feldspar/plagioclase and micro-mesopore volume was found, depicting that few of such pore sizes exist in these two abundant minerals. In contrast, micro, meso and macro pores all were detected in clay minerals. Particularly, the pores with radii of around 5.35 nm were abundant in clay minerals and there was not a robust relationship between the organic matter, surface area and pore volume. Finally, fractal analysis was performed to better delineate heterogenous characteristics of pore structures which showed that D2 (representing the larger pores) is greater than D1 (smaller pores). In addition, the differences between the fractal dimensions of the adsorption and desorption (D2d–D2a) branches to better interpret the hysteresis, was defined. The positive correlation between the (D2d–D2a) and the meso-macro pore volume, pointed out that the meso-macro condensation is the main reason for hysteresis that was observed in N2 adsorption experiments in the Xishanyao Shale samples.

scholarly journals Characterization of Pore Structures and Implications for Flow Transport Property of Tight Reservoirs: A Case Study of the Lucaogou Formation, Jimsar Sag, Junggar Basin, Northwestern China

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1251
Author(s):  
Yang Su ◽  
Ming Zha ◽  
Keyu Liu ◽  
Xiujian Ding ◽  
Jiangxiu Qu ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Pore Network ◽  
X Ray ◽  
Pore Structures ◽  
Lucaogou Formation ◽  
Tight Reservoirs ◽  
Jimsar Sag

Quantitate characterization of pore structures is fundamental to elucidate fluid flow in the porous media. Pore structures of the Lucaogou Formation in the Jimsar Sag were investigated using petrography, mercury intrusion capillary porosimetry (MICP) and X-ray computed tomography (X-ray μ-CT). MICP analyses demonstrate that the pore topological structure is characterized by segmented fractal dimensions. Fractal dimension of small pores (r < Rapex) ranges from 2.05 to 2.37, whereas fractal dimension of large pores (r > Rapex) varies from 2.91 to 5.44, indicating that fractal theory is inappropriate for the topological characterization of large pores using MICP. Pore volume of tight reservoirs ranges over nine orders of magnitude (10−1–108 μm3), which follows a power-law distribution. Fractal dimensions of pores larger than a lower bound vary from 1.66 to 2.32. Their consistence with MICP results suggests that it is an appropriate indicator for the complex and heterogeneous pore network. Larger connected pores are primary conductive pathways regardless of lithologies. The storage capacity depends largely on pore complexity and heterogeneity, which is negatively correlated with fractal dimension of pore network. The less heterogeneous the pore network is, the higher storage capability it would have; however, the effect of pore network heterogeneity on the transport capability is much more complicated.

FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

2003 ◽  
Vol 06 (02) ◽  
pp. 241-249
Author(s):  
JOSEPH L. PE
Keyword(s):  
Number Theory ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Distinguishing Characteristic ◽  
Local Behavior ◽  
Remarkable Similarity ◽  
Recursive Procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

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