Fractal Characteristics Of Pore Structure Research Articles

Micro-morphology and fractal characteristics of pore structure of aeolian sand concrete under long-term semi-immersion with chloride solution

To investigate the influence of chloride exposure on hydraulic concrete, we investigated the microstructural changes and pore evolution of aeolian sand concrete (ASC) during prolonged semi-immersion in chloride solution. Our analysis included examining the mass loss rate, relative dynamic elastic modulus, and maximum depth of chloride erosion. Utilizing scanning electron microscopy (SEM), X-ray diffraction (XRD), and nuclear magnetic resonance (NMR), we assessed the microscopic morphology and pore structure evolution. Additionally, we employed fractal theory to evaluate pore structure heterogeneity in ASC before and after exposure to chloride erosion. After 450 days of chloride erosion, ASC displayed minimal changes in mass loss rate and relative dynamic elastic modulus, with a maximum erosion depth of 9.8 mm. Chlorides adhered to the immersed end at the concrete's base and migrated from the surface to the exposed top end during erosion. The erosion depth at the top end ranged from 23.9 % to 25.9 % of that at the bottom end. Within ASC, hydration products reacted with chlorides, resulting in the formation of Friedel's salt, a characteristic corrosion crystal. Following erosion, the total porosity of ASC increased, accompanied by shifts in pore size distribution. The internal structure of ASC underwent distinctive evolution, transitioning from small to large pores. ASC consistently exhibited fractal properties both before and after erosion. The fractal dimension D1 demonstrated an inverse relationship with pores of radius (r) less than 0.01 μm, while D2 was directly proportional to pores with r ≤ 0.01 μm and 0.01 <r ≤ 0.1 μm, and inversely proportional to pores with 1 <r ≤ 10 μm and r > 10 μm. This study significantly contributes to the theoretical understanding of ASC's endurance mechanisms in chloride environments.

A Novel Porous Diffusion Model during Gas Desorption in Coal Based on Fractal Characteristics of Pore Structure

A Novel Porous Diffusion Model during Gas Desorption in Coal Based on Fractal Characteristics of Pore Structure

Fractal Characteristics of Pore Structure of Gas Shale: A Case Study of Lower Silurian Longmaxi Formation

Fractal Characteristics of Pore Structure of Gas Shale: A Case Study of Lower Silurian Longmaxi Formation

Multifractal estimation of NMR T2 cut-off value in low-permeability rocks considering spectrum kurtosis: SMOTE-based oversampling integrated with machine learning

The transverse relaxation time (T2) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T2 spectra and T2 cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T2 cut-off values, ranging from 7 to 50 ms. Additionally, the T2 spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T2 spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T2 cut-off value were separately developed based on the classified T2 spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T2 spectral shift. However, the T2 spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T2 spectrum and pore types, as well as to predict the T2 cut-off value of low-permeability rocks using machine learning and data augmentation techniques.

Relationship between fractal characteristics of pore-structure and thermal properties of FA-based AAM under different curing conditions

The microstructure of hardened alkali-activated materials (AAM) plays an essential role in determining the mechanical properties at elevated temperatures, particularly the pore structure. Mercury Intrusion Porosimeter (MIP) was employed to study the fractal characteristics of the pore structure of samples under standard and sealed curing conditions, which includes pore size distribution, shape, surface area, and tortuosity of AAM pastes after exposure to high temperatures. Additionally, the compressive strength of AAMs at elevated temperatures was determined. Comparing the samples under standard curing conditions, sealed curing conditions significantly improved the 28-day compressive strength (43.6 MPa) and residual compressive strength (achieving 60.2% of the 28-day strength) when exposed to 1000 °C. Based on research, the fractal characteristics of pore structures have a significant effect on the thermal properties of samples at high temperatures. Differences in thermal properties may be attributable to resistance caused by pore structures with heterogeneity and complexity, as well as the shape of the pores, which have small pore throats and large pore capacities. Under standard curing conditions, the samples exhibited a pore structure characterized by a reduced neck diameter, larger cavity size, a coarser pore surface, and decreased connectivity. As a result, the 28-day samples under standard curing conditions experienced significantly elevated pore pressure.

Study on permeability performance of cemented tailings backfill based on fractal characteristics of pore structure

The permeability of the backfill has a significant impact on the leaching and transport ability of pollutants to groundwater through the backfill area, and the way of pollutants enter the backfill mainly depends on the pore structure inside the backfill. Therefore, permeability is also a reflection of pore structure characteristics. The test used mine tailings as aggregate, Portland cement (PC 32.5) as cementing material, and added different additives (lime, fly ash, and anionic polyacrylamide (APAM)) to make backfill samples with a mass concentration of 74% and a cement-sand ratio of 1:4 and 1:6, respectively. Four groups of backfill samples with curing ages of 3d, 7d, and 28d were tested by nuclear magnetic resonance (NMR) and centrifugal testing machines, and the T2 spectrum distribution characteristics of the samples before and after centrifugation were obtained. According to the test results and fractal theory, it is found that the four groups of backfill have double fractal characteristics. With the increase of curing age or cement-sand ratio, the fractal dimension of small aperture distribution (Dmin) of backfill pore structure generally increases, while the fractal dimension of large aperture distribution (Dmax) and permeability gradually decrease. Dmax represents the number of large pores and has a high correlation with porosity, indicating that it has a great influence on porosity. The high degree of correlation between permeability and Dmin indicates that the formation of water passage in backfill is related to fine pores. Meanwhile, the permeability prediction results using the correlation between the fractal bound water saturation model and the Coates model show that the measured and predicted values of the bound water saturation, and the predicted permeability values and the calculated values of the Coates model all fit well, which verifies the feasibility of this method.

Quantitative characterization of the pore volume fractal dimensions for three kinds of liquid nitrogen frozen coal and its enlightenment to coalbed methane exploitation

Liquid nitrogen fracturing technology is an important means to improve the permeability of coal seams and realize unconventional natural gas extraction. In order to study the fractal characteristics of pore structure of coal frozen by liquid nitrogen, the pores of both nonfrozen and frozen samples of lignite, bituminous coal, and anthracite were measured with a high-pressure adsorption meter, a mercury porosimeter, and a low-field nuclear magnetic resonance (NMR). The test results showed that after freezing in liquid nitrogen, the pores of coal were effectively expanded. Among them, Nitrogen adsorption of lignite, bituminous coal and anthracite increased by 20.82%, 6.54% and 20.39%. The conversion rates from adsorption pore to seepage pore were 2.16%, 0.78% and 3.57%. The research results of pore fractal dimension showed that the multifractal characteristics of macropores were higher than that of mesopores and micropores. After liquid nitrogen freezing, the pore fractal dimension of lignite, bituminous coal and anthracite decreased by 0.031, 0.009 and 0.003, and the pore structure tends to be smooth. It showed the liquid nitrogen freezing coal enhances the migration and drainage of coalbed methane, which has reference significance for the further research of liquid nitrogen fracturing technology.

Pore structure analysis and permeability prediction of shale oil reservoirs with HPMI and NMR: A case study of the Permian Lucaogou Formation in the Jimsar Sag, Junggar Basin, NW China

The pore structure characteristics and formation permeability are important reservoir information for the development of shale oil. The pore structures of the shale oil formation in the Lucaogou Formation in the Jimsar Sag are characterized with high-pressure mercury injection (HPMI), nuclear magnetic resonance (NMR), and fractal theory. The capillary bundle model, geometric model, and wetting phase model are used to obtain the fractal dimension of the capillary pressure curve. Among them, Df1 from the capillary bundle model is between 2.1937 and 3.4131, Df2 from the geometric model is within a range of 1.0414–3.575, and Df3 from the wetting phase model is from 0.5691 to 2.7047. For NMR spectra, the pore space is divided into micropores, mesopores, and macropores based on the peak value of the NMR T2 spectra, and the fractal dimension of different pore types is calculated, where Dfmi is from 1.564 to 2.301, Dfme is in a range from 2.082 to 2.941, and Dfma is between 2.831 and 2.991. The relationships between the fractal dimension and petrophysical parameters are analyzed, and the results indicate that among the three types of models, the fractal dimension of the capillary bundle model has the highest correlation with the core petrophysical parameters. Therefore, it is recommended to use the capillary bundle model to evaluate the fractal characteristics of pore structures. In particular, the fractal dimension is positively correlated with the throat coefficient and negatively correlated with the size of the pore throat. In contrast, the fractal dimension of NMR has a poor correlation with core petrophysical parameters. There is no obvious correlation between the fractal dimension of micropores and petrophysical parameters, while the fractal dimension of mesopores and macropores is only correlated with the throat-sorting coefficient, and the correlation coefficient is less than 0.15. Thus, the fractal dimension from NMR data is not suitable for studying the fractal characteristics of shale oil cores in the Lucaogou Formation. In addition, we predicted the permeability of shale cores using the Swanson model, Pittman model, and Winland model. The permeability prediction results show that the Swanson model has the greatest accuracy, followed by the Winland model. Among them, the accuracy index (ACI) of the Swanson model is 0.901, and the ACI of the Winland model is between 0.483 and 0.897. The permeability prediction by the Pittman model is poorest among these three models.

Research on Strength Prediction Model and Microscopic Analysis of Mechanical Characteristics of Cemented Tailings Backfill under Fractal Theory

In order to further study the internal relationship between the microscopic pore characteristics and macroscopic mechanical properties of cemented tailings backfill (CTB), in this study, mine tailings and ordinary Portland cement (PC32.5) were selected as aggregate and cementing materials, respectively, and different additives (anionic polyacrylamide (APAM), lime and fly ash) were added to backfill samples with mass concentration of 74% and cement–sand ratios of 1:4, 1:6 and 1:8. After 28 days of curing, based on the uniaxial compressive strength test, nuclear magnetic resonance (NMR) porosity test and the fractal characteristics of pore structure, the relationships of the compressive strength with the proportion and fractal dimension of pores with different radii were analyzed. The uniaxial compressive strength prediction model of the CTB with the proportion of harmless pores and the fractal dimension of harmful pores as independent variables was established. The results show that the internal pores of the material are mainly the harmless and less harmful pores, and the sum of the average proportions of the two reaches 73.45%. Some characterization parameters of pore structure have a high correlation with the compressive strength. Among them, the correlation coefficients of compressive strength with the proportion of harmless pores and fractal dimension of harmful pores are 0.9219 and 0.9049, respectively. The regression results of the strength prediction model are significant, and the correlation coefficient is 0.9524. The predicted strength value is close to the actual strength value, and the predicted results are accurate and reliable.

Fractal characteristics of pore structure of hardened cement paste prepared by pressurized compact molding

The microstructure of hardened cement paste is directly related to its macroscopic properties. Pressurized compact molding can effectively improve the microstructure of hardened cement paste. In order to study the characteristics of pore structure of hardened cement paste and the mechanism of microstructure regulation and defect reduction after pressure compaction, Mercury Intrusion Porosimetry (MIP) and X-Ray Diffraction (XRD) was used to characterize the microstructure of hardened cement paste and the mass fraction of the main phase. Results indicate that the pressurized compact molding significantly reduced the total porosity and critical pore diameter of hardened cement paste, and the pore size was micro-nano. The pore surface fractal dimension (SFD) of the paste was multi-segmental fractal and scale dependent after compaction, and the irregular drift behavior in the transition region was not obvious. A new understanding of the pore volume distribution characteristics of hardened cement paste was proposed based on the change of main phase mass fraction.

Fractal characteristics of pore structure of hybrid Basalt–Polypropylene fibre-reinforced concrete

The pore characteristics of hybrid basalt–polypropylene fibre-reinforced concrete (HBPRC) are investigated using mercury intrusion porosimetry. The research results indicate that the cumulative pore volume of concrete increases with fibre addition. The pore surface fractal dimension (DS) of HBPRC in gel, capillary, and large pore regions decreases sequentially although it has no physical characteristics in a transition pore region. The incorporation of fibres has an insignificant effect on DS in gel and capillary pore regions; however, it has a reducing effect on DS in the large pore region. Furthermore, the greater the concrete strength, the larger DS becomes and the greater the reducing effect of fibres on DS in the large pore region. Through microscopic and mesoscopic analyses, it has been suggested that bubbles introduced by fibres and the weak dispersion of such fibres are the main reasons for the deterioration of the large pore structure of HBPRC.

Comparison of fractal models using NMR and CT analysis in low permeability sandstones

Fractal geometry provides an effective method for characterization of the complex and irregular pore structure of Eocene Shahejie low permeability sandstones in the Raoyang Sag, the Bohai Bay Basin, China. Laboratory measurements including porosity, permeability, scanning electron microscope (SEM), thin sections, nuclear magnetic resonance measurements (NMR) and X-ray computed tomography (CT) technology are used to provide insights into the fractal characteristics of pore structure in sandstones of Eocene Shahejie Formation in the Bohai Bay Basin, China. Quantitative CT analysis reveals the pore radius is not always linear to T2 (transverse relaxation time) value obtained from the NMR tests, but instead power function of T2. Fractal analysis was performed on the T2 distribution using various fractal models, and the related fractal dimensions are calculated. The fractal dimensions calculated using various fractal models are correlated with NMR parameters and permeability. The fractal curves break into two segments at the T2cutoff (T2 separating the immovable and movable fluids) value or smaller when using fractal model Ⅰ and fractal model Ⅱ, and only the large-scale pore networks can be described by the fractal geometry. Mostly the entire pore size distributions (micro-pores to large-scale pore networks) can be described by the fractal model Ⅲ, and the calculated fractal dimensions are in accordance with the CT scanning and thin section data, and are strongly correlated with the T2gm (geometric mean of T2), permeability and BVI (bulk volume of immovable fluids). The fractal behaviors of pore size distributions from NMR analysis have implications for pore structure evaluation in low permeability sandstones with similar geological settings.

Fractal characteristics of pore structure of compacted bentonite studied by ESEM and MIP methods

In this paper, we aim to clarify microstructure of bentonite from Cerny vrch deposit in the Czech Republic. We adopt results of ESEM and MIP experiments performed at various suctions along wetting and drying paths on bentonite samples compacted from powder to two different initial dry densities. The data were used for quantification of fractal dimension characteristics of pores of different sizes. Two different methods of calculating fractal dimension were used for MIP data, and one method was used for evaluation of ESEM images. Fractal dimensions obtained from MIP data, combined with the measured pore size density functions, allowed us to identify two different pore families: micropores and macropores. Macropores can be further subdivided into fine macropores and coarse macropores based on fractal analysis. The pore systems were further distinguished by different responses to suction changes and to compaction effort. In general, we observed slight increase in fractal dimension with increasing suction and with increasing dry density.

Full‐Sized Pore Structure and Fractal Characteristics of Marine‐Continental Transitional Shale: A Case Study in Qinshui Basin, North China

Based on 10 shale samples collected from 4 wells in Qinshui Basin, we investigate the full‐sized pore structure and fractal characteristics of Marine‐Continental transitional shale by performing organic geochemistry, mineralogical composition, Nitrogen gas adsorption (N2 adsorption) and Nuclear Magnetic Resonance (NMR) measurements and fractal analysis. Results show that the TOC content of the shale samples is relatively high, with an average value of 2.44wt%, and the thermal evolution is during the mature‐over mature stage. The NMR T2 spectrum can be used to characterize the full‐sized pore structure characteristics of shale. By combining N2 adsorption pore structure parameters and NMR T2 spectrums, the surface relaxivity of samples are calculated to be between 1.7877 um/s and 5.2272 um/s. On this basis, the T2 spectrums are converted to full‐sized pore volume and surface area distribution curves. The statistics show that the pore volume is mainly provided by mesopore, followed by micropore, and the average percentages are 65.04% and 30.83% respectively; the surface area is mainly provided by micropore, followed by mesopore, and the average percentages are 60.8004% and 39.137% respectively; macropore contributes little to pore volume and surface area. The pore structure characteristics of shale have no relationship with TOC, but strong relationships with clay minerals content. NMR fractal dimensions Dmicro and Dmeso have strong positive relationships with the N2 adsorption fractal dimensions D1 and D2 respectively, indicating that Dmicro can be used to characterize the fractal characteristics of pore surface, and Dmeso can be used to characterize the fractal characteristics of pore structure. The shale surface relaxivity is controlled by multiple factors. The increasing of clay mineral content, pore surface area, pore surface fractal dimension and the decreasing of average pore size, will all lead to the decreasing of shale surface relaxivity.

Compressibility and fractal dimension analysis in the bituminous coal specimens

Coal is the typical multi-pore media. Numerous experiments have been done to investigate the pore structure of coal. Mercury intrusion porosimetry is still a popular way to analyze the pore characteristics. Compressibility effect on the mercury intrusion porosimetry data cannot be ignored. So N2 adsorption (NA) and mercury intrusion porosimetry (MIP) were applied to analyze the pore structure of coal. In this paper, the mercury intrusion process was divided into three stages including interpore filling, large intrapore filling, and small intrapore filling. The fractal analysis is an important mathematical method, which is widely used to evaluate heterogeneity in the size-dependent distribution of porosity. The fractal characteristics of pore structures in four coal samples with the same rank were also investigated. Three pore fractal dimensions corresponding to the three stages of mercury intrusion, D1C, D2C, and D3C were calculated with the Brooks–Corey capillary pressure model. Df calculated with Farin model is used to estimate an overall fractal dimension. The correlation between the pore fractal dimension and the pore size distribution (PSD) characteristics was further discussed.

Damage Effects and Fractal Characteristics of Coal Pore Structure during Liquid CO2 Injection into a Coal Bed for E-CBM

Pore structure has a significant influence on coal-bed methane (CBM) enhancement. Injecting liquid CO2 into coal seams is an effective way to increase CBM recovery. However, there has been insufficient research regarding the damage effects and fractal characteristics of pore structure at low temperature induced by injecting liquid CO2 into coal samples. Therefore, the methods of low-pressure nitrogen adsorption-desorption (LP-N2-Ad) and mercury intrusion porosimetry (MIP) were used to investigate the damage effects and fractal characteristics of pore structure with full aperture as the specimens were frozen by liquid CO2. The adsorption isotherms revealed that the tested coal samples belonged to type B, indicating that they contained many bottle and narrow-slit shaped pores. The average pore diameter (APD; average growth rate of 18.20%), specific surface area (SSA; average growth rate of 7.38%), and total pore volume (TPV; average growth rate of 18.26%) increased after the specimens were infiltrated by liquid CO2, which indicated the generation of new pores and the transformation of original pores. Fractal dimensions D1 (average of 2.58) and D2 (average of 2.90) of treated coal samples were both larger the raw coal (D1, average of 2.55 and D2, average of 2.87), which indicated that the treated specimens had more rough pore surfaces and complex internal pore structures than the raw coal samples. The seepage capacity was increased because D4 (average of 2.91) of the treated specimens was also higher than the raw specimens (D4, average of 2.86). The grey relational coefficient between the fractal dimension and pore structure parameters demonstrated that the SSA, APD, and porosity positively influenced the fractal features of the coal samples, whereas the TPV and permeability exerted negative influences.

Fractal Characteristics of Pore Structures in GGBFS-based Cement Pastes

Abstract The present study evaluated pore surface fractal characteristics of high-strength cement pastes with different ground granulated blast-furnace slag (GGBFS) replacement ratios. Using the results of mercury intrusion porosimetry measurements, the surface fractal dimension in various pore-size ranges was calculated. Experimental results show that the fractal characteristics appeared in mesopores in range of 6–10 nm and 10–25 nm and larger capillary pores with sizes of more than 100 nm. In larger capillary pores, as the GGBFS replacement ratio increased up to 65%, the surface fractal dimension and pore volume decreased, and they increased when the GGBFS replacement ratio increased from 65% to 80%. In contrast, higher GGBFS replacement ratios in mesopore regions resulted in an increased surface fractal dimension and pore volume. Furthermore, in the regions where fractal characteristics appeared, pore volume and the surface fractal dimension exhibited a proportional relationship. The ratio of the surface fractal dimension to the volume of larger capillary pores was strongly correlated with the compressive strength of the specimens.

Fractal characterization of pores in shales using NMR: A case study from the Lower Cambrian Niutitang Formation in the Middle Yangtze Platform, Southwest China

The fractal dimensions of the Lower Cambrian Niutitang Formation shales in the Middle Yangtze Platform, Southwest China were investigated for pore structure and fractal characteristics using low-field nuclear magnetic resonance (NMR) and N2 adsorption. The field emission scanning electron microscopy (FE-SEM), N2 and CO2 adsorption, NMR, porosity and permeability analysis were performed on six shale samples collected from outcrops. The NMR T2 distributions are consistent with the combination of pore size distributions from N2 and CO2 adsorption. The discrepancy of fractal dimensions between NMR and N2 adsorption resulting from the pore size distribution indicates that NMR fractal dimensions provide more accurate insight into the fractal characteristics of pore structure in shales than N2 adsorption fractal dimensions. The results show that the min(DNMR), with respect to the shorter relaxation times, reflects the roughness of the micropore surface area and the max(DNMR), with respect to the longer relaxation times, reflects pore volume for larger pores. The surface fractal dimension min(DNMR) has a positive correlation with TOC contents and thermal maturity, attributable to the conversion of kerogen and occurrence of organic matter pores. Min(DNMR) increases with increasing quartz content, while max(DNMR) increases with increasing clay content. The porosity from helium gas injection ranges from 2.8% to 6.7%, and permeability is between 3.55 and 6.62 × 10−2 mD. The min(DNMR) has a positive correlation with permeability, and the max(DNMR) exhibits a positive correlation with porosity, indicating that the volume fractal dimension max(DNMR) and surface fractal dimension min(DNMR) provide new indicators to measure porosity and permeability, respectively.

Fractal characteristics of pore structures in 13 coal specimens: Relationship among fractal dimension, pore structure parameter, and slurry ability of coal

The fractal characteristics of pore structures in 13 different coal specimens were investigated. Insights into the relationship among fractal dimension, pore structure parameter, and slurry ability of coal were provided. N2 adsorption/desorption at 77K was applied to analyze the pore structure of coal. Two fractal dimensions, D1 and D2, at relative pressures of 0 to 0.45 and 0.45 to 1, respectively, were calculated with the fractal Frenkel–Halsey–Hill model. Results reveal that the value of D1 is mainly affected by the influence of meso- and macro-pores with an average pore size range of 10nm to 220nm on the specific surface area; therefore, D1 can be utilized to quantitatively describe the surface roughness of these meso- and macro-pores in coal. Meanwhile, the value of D2 is mainly related to the effects of fine mesopores with an average pore size range of 2nm to 10nm on the total pore volume; therefore, D2 can be utilized to quantitatively describe the volumetric roughness of these mesopores in coal. D1 has no apparent linear correlation with the pore structure parameters and maximum solid loading of coal, and D2 has a positive linear correlation with the specific surface area and total pore volume of coal. The increase in specific surface area, total pore volume, and D2 has negative effects on the slurry ability of coal. High-rank coals with high ash content and low volatile matter relatively have higher D1 and lower D2. Meanwhile, with increasing coal rank, D2 has a decreased trend. The fine mesopores with an average pore size range of 2nm to 10nm in coal have direct effects on the pore structure parameters and D2 of coal; thus, the slurry ability of coal may be improved if the number of these mesopores in coal is reduced by modification processes, such as microwave irradiation, hydrothermal treatment and so on.

Determination of the Box-Counting Fractal Dimension of Pore Distribution in Eggshell Based on Scanning Electron Microscopy Image Analysis

The fractal characteristics of pore structures were investigated using duck eggshells as an object of study. The images of the sharp end, the equator and the blunt end of the eggshells were acquired by using scanning electronic microscope. The image processing operations were conducted for the preprocessing and the image converted into binary image. Then we developed programs based on the principle of changing megascopic degree and applied them to plot the lgN(δ)~lg(δ).The relationship between lgN(δ)and lg(δ)maintained linearity over a range [2,64] pixels. Therefore, the fractal dimensions of pore distributions were obtained from the negative slope by regression analysis. The experimental results showed that the fractal feature of the pore in eggshells was remarkable. The analysis confirmed that the blunt end of the eggshell in the pore distributions was more obvious than the sharp end and the equator.