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.

scholarly journals A Dual Fractal Poroelastic Model for Characterizing Fluid Flow in Fractured Coal Masses

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Guannan Liu ◽  
Dayu Ye ◽  
Feng Gao ◽  
Jishan Liu
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Coalbed Methane ◽  
Coupling Effect ◽  
In Situ Stress ◽  
Permeability Model ◽  
Fracture Length ◽  
Coal Deformation ◽  
Throat Diameter

In the process of coalbed methane exploitation, the fracture and pore structure is the key problem that affects the permeability of coalbed. At present, the coupling effect of fracture and pore structure and in situ stress is seldom considered in the study of coal seam permeability. In this paper, the fractal seepage model is coupled with coal deformation, and the adsorption expansion effect is considered. A multifield coupling model considering the influence of matrix and fracture structure is established. Then, the influence of pore structure parameters of main fracture on macropermeability is analyzed, including (1) fractal dimension of fracture length, (2) maximum fracture length, (3) fractal dimension of throat diameter, and (4) fractal dimension of throat bending. At the same time, the simulation results are compared with the results of Darcy’s uniform permeability model. The results show that the permeability calculated by the proposed model is significantly different from that calculated by the traditional cubic model. Under the action of in situ stress, when the porosity and other parameters remain unchanged, the macropermeability of coal is in direct proportion to the fractal dimension of coal fracture length, the fractal dimension of throat diameter, and the maximum fracture length and in inverse proportion to the fractal dimension of coal throat curvature.

A STUDY ON GAS DRAINAGE CONSIDERING COUPLING PROCESS OF FRACTURE-PORE MICROSTRUCTURE AND COAL DEFORMATION

Fractals ◽  
2021 ◽  
Vol 29 (02) ◽  
pp. 2150065
Author(s):  
LIU GUANNAN ◽  
YE DAYU ◽  
YU BOMING ◽  
GAO FENG ◽  
CHEN PEIJIAN
Keyword(s):  
Fractal Dimension ◽  
Coal Seam ◽  
Fractal Theory ◽  
Coupling Model ◽  
Coal Bed ◽  
Gas Migration ◽  
Gas Drainage ◽  
Field Coupling ◽  
Distribution Rule ◽  
Coal Deformation

Coal seam contains a large number of fractures, whose shape and structure of fissures are complicated, and they are the main channels for gas migration. Therefore, the quantitative analysis of the internal relationship between the microstructure and the macroscopic permeability is the key issue to increase the drainage volume. Some investigators discussed the permeability of coal seams based on the fractal theory, but the mechanisms of gas migration under the influence of fissure microstructures and coal deformation are still unclear. Moreover, most of the multi-process coupling analysis in the stage of Coal Bed Methane (CBM) mining was not taken into account. In this paper, the effects of fissure structures on the coal gas drainage rate in multi-field coupling are studied. Aiming at the mechanisms of gas drainage under the joint action of fracture structure, in-situ stress and adsorption deformation, we propose a two-scale multi-field coupling model, which takes into account the influences of micro fracture and pore structure. On this basis, we obtained the pressure evolution rule of coal seam pore system and fissure system and the distribution rule of coal seam displacement with drilling positions. Meanwhile, the effects of coal seam maximum fracture length, maximum pore diameter, the fractal dimension for fractures and fractal dimension for pores on coal seam extraction are discussed.

A MULTI-FIELD COUPLED SEEPAGE MODEL FOR COAL SEAM WITH FRACTURES OF POWER LAW LENGTH DISTRIBUTIONS

Fractals ◽  
2021 ◽  
pp. 2150140
Author(s):  
GUANNAN LIU ◽  
YUHAO HU ◽  
BOMING YU ◽  
FENG GAO ◽  
FENGTIAN YUE ◽  
...  
Keyword(s):  
Coal Seam ◽  
Power Law ◽  
Fractal Theory ◽  
Length Distribution ◽  
Volume Strain ◽  
Adsorption Effect ◽  
Fracture Length ◽  
Matrix Deformation ◽  
Power Law Exponent ◽  
Fracture Distribution

In the process of gas mining, the fracture distribution with power law length and the pore structure with adsorption effect have an important influence on the coal seam permeability. In recent years, the research on the internal structure of coal seam and the fluid flow mechanism has attracted a large number of researchers. In this paper, by considering the coal matrix deformation caused by adsorption, a pore-fracture model coupled with the multi-field effects and with power law length distribution of fractures in coal seam is established based on the fractal theory for porous media. In this work, we study the influences of the power law exponent [Formula: see text] of fracture length and the ratio [Formula: see text] of the minimum to maximum fracture lengths on the permeability of coal seam and the evolution mechanism of permeability with the structural and mechanical parameters of coal seam. It is found that the permeability of coal seam is inversely proportional to [Formula: see text], directly proportional to [Formula: see text], and to Langmuir volume constant and Langmuir volume strain constant. Compared with other factors, the power law component [Formula: see text] of fractures has the most significant effect on the coal seam permeability.

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.

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.

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.

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 Effect of peat mire evolution on pore structure characteristics in thick coal seam: Examples from Xishanyao Formation (Middle Jurassic), Yili Basin, China

2020 ◽  
Vol 38 (5) ◽  
pp. 1484-1514 ◽  
Author(s):  
Rongfang Qin ◽  
Anmin Wang ◽  
Daiyong Cao ◽  
Yingchun Wei ◽  
Liqi Ding ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Coal Seam ◽  
Specific Surface ◽  
Pore Structure ◽  
Surface Area ◽  
Specific Surface Area ◽  
Pore Volume ◽  
Thick Coal Seam ◽  
Structure Characteristics ◽  
Cyclic Changes

The physical properties of thick coal seams show strong vertical heterogeneity; thus, an accurate characterization of their pore structure is essential for coalbed methane (CBM) exploration and production. A total of 18 coal samples, collected from a thick coal seam in the Yili Basin of NW China, were tested by a series of laboratory experiments to investigate the peat mire evolution and pore structure characteristics. The results show that the No. 4 coal seam has undergone multiple stages of evolution in the peatification stage, and was divided into four water-transgression/water-regression cycles according to the regular cyclic changes of the vitrinite/inertinite ratio, structure preservation index, gelification index, vegetation index, trace element ratios, and stable carbon isotopes of organic matter. The changes of pore structure characteristics with the changes of coal deposition cycles are also analyzed. It is concluded that pore structure characteristics of the four cycles are quite different. In each water-transgression cycle, the vitrinite gradually increased and the inertinite gradually decreased, resulting in a decrease of the porosity, pore volume, specific surface area, and fractal dimension. While in each water-regression cycle, the vitrinite gradually decreased and the inertinite gradually increased, leading to an increase of the porosity, pore volume, specific surface area, and fractal dimension. A strong relationship exists between the porosity, pore volume, specific surface area, fractal dimension, and submacerals, with fusinite and semifusinite which contained more pores having a positive correlation, desmocollinite and corpovitrinite which contained few pores having a negative correlation.

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.

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