scholarly journals Pore Structure of Grain-Size Fractal Granular Material

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2053 ◽  
Author(s):  
Yifei Liu ◽  
Dong-Sheng Jeng
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Granular Material ◽  
Pore Structure ◽  
Granular Materials ◽  
General Function ◽  
Fractal Structures ◽  
Experimental Database ◽  
Box Counting Dimension ◽  
Menger Sponge

Numerous studies have proven that natural particle-packed granular materials, such as soil and rock, are consistent with the grain-size fractal rule. The majority of existing studies have regarded these materials as ideal fractal structures, while few have viewed them as particle-packed materials to study the pore structure. In this study, theoretical analysis, the discrete element method, and digital image processing were used to explore the general rules of the pore structures of grain-size fractal granular materials. The relationship between the porosity and grain-size fractal dimension was determined based on bi-dispersed packing and the geometric packing theory. The pore structure of the grain-size fractal granular material was proven to differ from the ideal fractal structure, such as the Menger sponge. The empirical relationships among the box-counting dimension, lacunarity, succolarity, grain-size fractal dimension, and porosity were provided. A new segmentation method for the pore structure was proposed. Moreover, a general function of the pore size distribution was developed based on the segmentation results, which was verified by the soil-water characteristic curves from the experimental database.

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.

A continuous, laboratory-size density separator for granular materials

1965 ◽  
Vol 35 (271) ◽  
pp. 536-541 ◽  
Author(s):  
M. P. Jones
Keyword(s):  
Grain Size ◽  
Granular Material ◽  
Granular Materials ◽  
Standard Laboratory ◽  
Continuous Density

SummaryDetails are given for the construction of a continuous, density separator from standard laboratory glassware and equipment. The separator can treat up to 5 g/min of granular material from 150 to 2000 µ in grain size, and the liquid used is continually recirculated by a simple airlift.

Nano-Pore Structure and Fractal Characteristics of Shale Gas Reservoirs: A Case Study of Longmaxi Formation in Southeastern Chongqing, China

2021 ◽  
Vol 21 (1) ◽  
pp. 343-353
Author(s):  
Wei-Dong Xie ◽  
Meng Wang ◽  
Xiao-Qi Wang ◽  
Yan-Di Wang ◽  
Chang-Qing Hu
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Shale Gas ◽  
Fractal Dimensions ◽  
Gas Reservoirs ◽  
Longmaxi Formation ◽  
Shale Gas Reservoirs ◽  
Fractal Characteristics ◽  
Temperature Liquid ◽  
Menger Sponge

Pore structure and fractal dimensions can characterize the adsorption, desorption and seepage characteristics of shale gas reservoirs. In this study, pore structure, fractal characteristics and influencing factors were studied of the Longmaxi formation shale gas reservoir in southeastern Chongqing, China. Scanning electron microscopy was used to describe the characteristics of various reservoirs. High pressure mercury intrusion and low temperature liquid N2 and CO2 adsorption experiments were used to obtain pore structure parameters. V–S model, FHH model and Menger sponge model were selected to calculate the micropore, mesopore and macropore fractal dimensions, respectively. The results show that organic matter pores, inter-granular pores, intra-granular pores and micro-fractures are developed within the shale, and the pore morphology is mostly ink pores and parallel plate pores with aperture essentially in the 1–2 nm and 2–50 nm ranges. Moreover, macropores are the most complex in these samples, with mesopores being less complex than macropores, and the micropores being the simplest. D1 (micropore fractal dimension) ranges from 2.31 to 2.50, D2 (mesopore fractal dimension) ranges from 2.74 to 2.83, D3 (macropore fractal dimension) ranges from 2.87 to 2.95, and Dt (comprehensive fractal dimension) ranges from 2.69 to 2.83 of fractal characteristics. D1 and D2 are mainly controlled by TOC content, while D3 and Dt are mainly controlled by brittle and clay mineral content. These results may be helpful for exploration and the development of shale gas in southeastern Chongqing, China.

scholarly journals The variation of grain size distribution in rock granular material in seepage process considering the mechanical–hydrological–chemical coupling effect: an experimental research

2020 ◽  
Vol 7 (1) ◽  
pp. 190590 ◽  
Author(s):  
Hailing Kong ◽  
Luzhen Wang ◽  
Hualei Zhang
Keyword(s):  
Grain Size ◽  
Granular Material ◽  
Size Distribution ◽  
Granular Materials ◽  
Grain Size Distribution ◽  
Coupling Effect ◽  
Water Pressure ◽  
Geotechnical Engineering ◽  
Material Structure ◽  
Filling Material

As a common solid waste in geotechnical engineering, rock granular material should be properly treated and recycled. Rock granular material often coexists with water when it is used as the filling material in geotechnical engineering. Water flowing in rock granular materials is a complex progress with the mechanical–hydrological–chemical (MHC) coupling effect, i.e. the water scours in the gaps and spaces in the rock granular material structure, produces chemical reactions with rock grains, rock grains squeeze each other under the water pressure and compression leading to re-breakage and producing secondary rock grains, and the fine rock grains are migrated with water and rushed out. In this process, rock grain size distribution (GSD) changes, it affects the physical and mechanical characteristics of the rock granular materials, and even influences the seepage stability of the rock granular materials. To study the variation of GSD in the rock granular material considering the MHC coupling effect after the seepage process, seepage experiments of rock grain samples are carried out and analysed in this paper. The result is expected to have a positive impact on further studies of the properties of the rock granular material.

Fractal Research of Pore-Structure in Porous Titanium Fibers

2014 ◽  
Vol 804 ◽  
pp. 259-262 ◽  
Author(s):  
Shi Feng Liu ◽  
Hui Ping Tang ◽  
Xin Yang ◽  
Zhao Hui Zhang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Geometry ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Porous Titanium ◽  
Spatial Network ◽  
Vacuum Sintering ◽  
Box Counting ◽  
Box Counting Dimension

This paper adopted the vacuum sintering technology to prepare titanium fiber porous material with a three-dimensional spatial network fiber backbone and connectivity pore structure. With the help of fractal geometry theory and scanning and digitizing the image, the fractal research of pore-structure in porous titanium fibers is executed and we studied the influence of adopting the box-counting dimension method to calculate the fractal dimension. Additionally, we determined the quantitative relationship between fractal dimension and the porosity of the porous in titanium fiber, while described the physical meaning of the fractal dimension.

scholarly journals A frictional Cosserat model for the slow shearing of granular materials

2002 ◽  
Vol 457 ◽  
pp. 377-409 ◽  
Author(s):  
L. SRINIVASA MOHAN ◽  
K. KESAVA RAO ◽  
PRABHU R. NOTT
Keyword(s):  
Angular Velocity ◽  
Granular Material ◽  
Shear Layer ◽  
Granular Materials ◽  
Layer Thickness ◽  
Couette Flow ◽  
Velocity Fields ◽  
Cosserat Continuum ◽  
Cosserat Model ◽  
Cylindrical Couette Flow

A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.

Experimental determination of fragmentation efficiency for Plinian and Pelean eruptions of Mt. Pelée, Martinique

2021 ◽  
Author(s):  
Mila Huebsch ◽  
Ulrich Kueppers ◽  
Guillaume Carazzo ◽  
Anne-Marie Lejeune ◽  
Audrey Michaud-Dubuy ◽  
...  
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Open Porosity ◽  
High Speed ◽  
Model Development ◽  
Active Volcano ◽  
Petrophysical Properties ◽  
Density Currents ◽  
Fragmentation Efficiency ◽  
Plinian Eruptions

<p>Mt. Pelée is a historically active volcano, situated on the island of Martinique (Lesser Antilles), that has shown a variety of explosive styles in the recent past, ranging from dome-forming (Pelean) to open-vent (Plinian) eruptions.  The 1902-1905 eruption is infamous for the pyroclastic density currents (PDCs) that destroyed the towns of St. Pierre and Morne Rouge, killing 30 000 residents.  Since the last eruption (dome-forming) in 1929-1932, Mt. Pelée was quiet and considered dormant until recently.  In late 2020, the local Volcanological Observatory (OVSM) raised the alert level following a noticeable increase in seismicity, bringing into effect a reinforcement of monitoring resources.  As St. Pierre is long since re-established, along with several other towns along the volcano’s flanks, it is of utmost importance to understand the possible range of eruptive activity to improve the preparedness strategies of local communities.</p><p>The precise controls on eruption dynamics vary across volcanic systems and cannot be constrained via direct observation. However, crucial inferences can be made based on petrophysical properties and mechanical behaviours of erupted materials.  For this study, we collected samples from PDC deposits of Mt. Pelée, from the two historic Pelean (1902-1905, and 1929-1932) and three pre-Columbian Plinian eruptions (1300 CE P1, 280 CE P2, and 79 CE P3). We measured petrophysical properties (density, porosity, permeability) of cylindrical samples drilled from bomb-sized clasts and investigated their fragmentation behaviour via grain size and high-speed video analysis. These results are used in comparison with field data of grain-size distribution (GSD) of individual outcrops and calculated total GSD data.  We investigated the effects of transport-related sorting or fining.</p><p>The “Pelean” samples are found to be denser (32-47% open porosity) than the pumiceous “Plinian” samples (55-66% open porosity).  Moreover, these two classes are distinctly different in their crystallinity as samples underwent different ascent conditions.  In our experiments, distinct fragmentation behaviour and resulting GSDs are observed for samples from each eruption style, regardless of experimental pressure conditions (5-20 MPa). Our results show the paramount importance of open porosity on fragmentation efficiency in pumiceous samples, alongside a strong influence of crystallinity.  The fractal dimension of fragmentation calculated from weight fractions, independent of grain shape, shows clear differences in fragmentation efficiency as a function of sample properties and experimental starting conditions.</p><p>Our results suggest that (i) the variability in porosity and permeability is too low to cause the increased explosivity exhibited during the 1902 eruption compared to the 1929 event, (ii) open porosity has a major control on fragmentation efficiency in pumiceous samples, (iii) fragmentation efficiency can be effectively evaluated by calculating the fractal dimension of the cumulative weight fractions of experimental products.</p><p>The influence of crystallinity and pore textures on fragmentation efficiency must be further investigated to aid hazard model development for future eruptions of Mt. Pelée. Future work will constrain these textural parameters of naturally and experimentally fragmented materials from Mt. Pelée, to further elucidate the controls on eruptive dynamics at this hazardous volcano.</p>

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

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.

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