micropore structure and fractal characteristics of low...

Research ArticleMicropore Structure and Fractal Characteristics ofLow-Permeability Coal Seams

Guang-zhe Deng 12 and Rui Zheng 12

1College of Energy Science and Engineering Xirsquoan University of Science and Technology Xirsquoan 710054 China2Key Laboratory of Western Mine Exploitation and Hazard Prevention Ministry of Education Xirsquoan 710054 China

Correspondence should be addressed to Rui Zheng zhengruiyz163com

Received 17 May 2018 Revised 2 September 2018 Accepted 10 September 2018 Published 16 October 2018

Academic Editor Guoqiang Xie

Copyright copy 2018 Guang-zhe Deng and Rui Zheng -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

With the raw coal from a typical low-permeability coal seam in the coalfield of South Junger Basin in Xinjiang as the researchobject this paper examined six kinds of coal samples with different permeabilities using a scanning electron microscope anda low-temperature nitrogen adsorption test that employed a JSM-6460LV high-resolution scanning electron microscope andan ASAP2020 automatic specific surface area micropore analyzer to measure all characteristic micropore structural pa-rameters According to fractal geometry theory four fractal dimension calculation models of coal and rock were establishedafter which the pore structure characteristic parameters were used to calculate the fractal dimensions of the different coalseams -e results show that (1) the low-permeability coal seam in the coalfield of South Junger Basin in Xinjiang belongs tomesoporous medium with a certain number of large pores and no micropores -e varying adsorption capacities of thedifferent coal seams were positively correlated with pore volume surface area and the mesoporous surface area proportionsfrom which it was concluded that mesopores were the main contributors to pore adsorption in low-permeability coal seams(2) -e raw coal pore fractal dimension had a negative linear relationship to average pore size a positive linear relationshipwith total pore volume total surface area and adsorption capacity and a positive correlation with the mesoporous surfacearea proportion that is the higher the fractal dimension the larger the pore volume and surface area of the raw coal (3) -epermeability of the low-permeability coal seam had a phase correlation with the micropore development degree that is thepermeability had a phase negative correlation with the pore distribution fractal dimension and there was a positive cor-relation between permeability and porosity -ese results are of theoretical significance for the clean exploitation of low-permeability coal seam resources

1 Introduction

Coal is a complex porous medium with its macroscopicphysical properties (porosity permeability and adsorb-ability) and its physical and mechanical properties beingclosely related to its microscopic pore structure character-istics It is important to study the pore structure charac-teristics of the coal seam for understanding and interpretingcoal reservoir [1]

Close research attention has been paid to the relation-ships between micropore structures and the macroscopicphysical properties of coal and rock mass While it is knownthat the pore structures of coal and rock mass are complex

and have obvious heterogeneity it has been difficult todescribe and characterize these pore structures using tra-ditional methods However fractal theory has been found tobe an effective method for characterizing complex porousmedia for example it can be used for pore structureidentification diffusion coefficient permeability coefficientmeasurement and so on [2ndash5] -e fractal dimension isa quantitative descriptive parameter for specific fractalcharacteristics -erefore based on fractal theory the porestructures of sandstone were analyzed from which a newmethod for simultaneously measuring porosity and poresurface fractal dimensions was proposed which allowedfor the relationships between the fractal dimensions and

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 4186280 15 pageshttpsdoiorg10115520184186280

residual water saturation to be identified [6ndash8] A study offour bituminous coals and oxidized bituminous coal samplesat 270degC was able to determine the fractal dimensions andfractal distribution sensitivities to oxidation treatments [9]Based on the creep fracture damage model of a jointed rockmass the results show that the greater the number of rockjoints the larger the fractal dimensions the more thefracture energy absorbs material [10ndash13] Coal pore struc-ture has been analyzed using mercury injection experimentswhich allowed for the fractal dimensions of the pore coalbody surface to be calculated and the pore structure char-acteristics to be quantitatively characterized [14 15] -erelationships between the adsorption characteristics of coalsamples and the fractal dimension of low-temperature poresurfaces have been established using nitrogen adsorptiontests [16ndash21] and using digital core technology the re-lationships between the fractal dimension of pore diameterand permeability have been established [22 23] Fractaltheory has also been employed to determine the relation-ships between pore fractal dimensions and permeability[24ndash26] from which it was found that the compressibilityhardness and porosity of coal bodies were related to thefractal dimensions [27ndash29] A study on the influence ofconfined pressure and pore water pressure on the coalsample structure and percolation characteristics establisheda quantitative relationship between pore structure fractalsand coal sample permeability [30 31] According to thepore structure characteristics of low-permeability coalseams a 3D pore model for low-permeability coal wasconstructed and the influence of porosity on mechanicalproperties of coal was discussed [32]

Although there has been significant research on thephysical properties of coal seams there has been littleresearch focused on the microscopic pore structures of low-permeability coal seams and the effect of these on themacroscopic exploitation and utilization of the coal seams-erefore to further explore the relationships between themicrostructure characteristics and the macroscopic phys-ical properties of low-permeability coal seams this paperused the low-permeability coal seam in the coalfield ofSouth Junger Basin in Xinjiang to systematically analyzethe coalrsquos physical characteristics and pore structure usingan MTS-815 servo test system a scanning electron mi-croscope and a surface microporous fractal instrumentwhich allowed for all kinds of fractal models used to studyand explain the micropore structure of the coal seam -efractal characteristics of pore structure in low-permeabilitycoal seams and the relationships between the pore structureand the macroscopic physical parameters are also dis-cussed -ese results can greatly assist in the interpretationand prediction of the macroscopic properties in coal seams

2 Fractal Description of Coal and RockPore Structures

In fractal geometry the fractal dimension is the objectivetool used to measure the degree of ldquoirregularityrdquo andldquocomplexityrdquo in two fractal sets -e fractal dimensiondefinition has the following relations [33]

ϕ λmin

λmax1113888 1113889

DeminusDf

(1)

where ϕ is porosity De is the Euclidean space di-mension and Df is the fractal dimension In two-dimensional space De 2 1langDflang2 In three dimen-sions De 3 2langDflang3 λminλmax are the minimum andmaximum pore diameters

21 FractalDimensionPoreDistributionModel To assess thefractal dimension pore distribution which reflects the in-homogeneity of the pores the fractal box dimension methodhas been a widely used fractal measurement method therationale for which is as follows

When the fractal figure covers the fractal curve imagewith a square lattice of a certain scale some of the meshmay contain part of the curve while other parts of the meshremain empty with the number of nonempty mesh in-creasing as the mesh side length gradually reduces If theside length of a square mesh is r and the number ofnonempty mesh is N(r) then the fractal box dimension is[34]

D minus limr⟶0

lnN(r)

ln r (2)

-e corresponding N(r) value is calculated for differentgrid side lengths r the logarithmic coordinate curves of r

and N(ge r) are given and the relation is obtained throughfitting [35]

ln(N(ge r)) cminusD ln(r) (3)

-e slope k of Equation (3) is used to fit the straight linewith the box dimension D minusk and having a value between1 and 2 In this paper DD is the fractal dimension of poredistribution

22 FractalDimension PoreVolumeModel From the fractaldefinition the density function of the pore radius distri-bution in porous media has the following relationships[36]

f(r) crminusDminus1

(4)

where r is the pore radius D is the pore fractal dimensionand c is a constant

If the pore gap is a sphere the cumulative pore volume isthe integral of the radius distribution density function to theradius therefore the cumulative pore volume V(le r) witha pore radius less than r can be obtained as follows

V(le r) 1113946r

rmin

f(r)ar3dr

ac

3minusDr3minusD minus r

3minusDmin1113872 1113873 (5)

-e cumulative total pore volume is V

V ac

3minusDr3minusDmax minus r

3minusDmin1113872 1113873 (6)

2 Advances in Materials Science and Engineering

Putting Equations (5) and (6) into the following formulathe expression for the cumulative pore volume fraction NVwith a pore radius of no more than r can be obtained

NV V(le r)

V

r3minusD minus r3minusDminr3minusDmax minus r3minusDmin

(7)

Due to the strong heterogeneity in coal and rock mediathe maximumminimum pore size varies greatly that isrmax≫ rmin therefore Equation (7) can be simplified to

NV r

rmax1113888 1113889

3minusD

(8)

Equation (9) is then obtained from the logarithm ofEquation (8)

ln NV( 1113857 (3minusD)ln(r) + C1 (9)

where C1 (Dminus 3)ln(rmax) is a constant -e fractal di-mension of the cumulative pore volume is D 3minus k withthe value being between 2 and 3 In this paper DV is thefractal dimension of pore volume

23 Fractal Dimension Pore Area Model If the pore isa sphere a cumulative pore area S(ge r) with a pore diameterof not less than r can be obtained

S(ge r) 1113946rmax

rf(r)ar

2dr

ac


2minusD1113872 1113873 (10)

-e cumulative total pore area is S

S ac


2minusDmin1113872 1113873 (11)

Putting Equations (10) and (11) into the following for-mula the expression for the cumulative pore area fractionNS with a pore radius of not less than r can be obtained

NS S(ge r)

S

r2minusDmax minus r2minusD

r2minusDmax minus r2minusDmin (12)

As rmax≫ rmin Equation (12) can be simplified to

NS 1minusr

rmax1113888 1113889

2minusD

(13)


ln 1minusNS( 1113857 (2minusD)ln(r) + C2 (14)

where C2 (Dminus 2)ln(rmax) is a constant -e fractal di-mension of the cumulative pore area is D 2minus k with itsvalue being between 1 and 2 In this paper DA is the fractaldimension of pore area

24 Fractal Dimension Pore Surface Model Fractal theorystates that the surface fractal dimension does not theo-retically depend on the size of the pores or the surfacerather it is an intrinsic characteristic of the surface itself asit is a measure of surface roughness -e FrenkelndashHalseyndashHill (FHH) model is an important method for

obtaining the specific surface fractal dimension of complexfractal porous media [37] the equation for which is [38]

lnV minusf(D)ln lnP0

P1113874 1113875 + C (15)

where V represents the adsorption volume at the equi-librium pressure P P0 is the vapor saturation pressure C isthe constant P0P is the relative pressure and f(D) is thefractal dimension D expression

-e fractal dimension D was introduced into the ad-sorption isotherm equation for microporous solid surfaces[39ndash41] f(D) 3minusD therefore the fractal FHH equationcan be written as [42 43]

lnV (Dminus 3)ln lnP0

P1113874 1113875 + C (16)

When the low-temperature nitrogen adsorption datalnV and ln(ln(P0P)) were plotted the fitting line slopewas k and the fractal pore surface dimension was calcu-lated as D k + 3 with its value being between 2 and 3 Inthis paper DS is the fractal dimension of pore surface

3 Fractal Characteristics of the Outer Pores inLow-Permeability Coal Seams

31 Coal Sampling In this paper the typical low-permeability coal seam coal samples B1 + 2 and B3+6were taken as the research objects -e coal sample perme-ability was measured using an MTS-815 servo test systemwhich showed that the coal test samples belonged to the low-permeability coal seam with the permeability coal seam re-lationships being B-3ltB-4ltB-1ltB-5ltB-2ltB-6 (Table 1)

32 Electron Microscope Scanning Experiment A coalsample is usually broken apart to obtain a natural sectionafter which the sample is scanned to ensure that thescanned image is closer to the true shape of the pore -epore and fissure structural characteristics observed fromcoal sample 16 were found to be accurate and stable [44] Inthis paper the coal sample was first cut into 16 sectionsusing small grinding wheels after which the coal samplesections were broken to form a natural section To ensureimage clarity so as to be able to count the scanning data thenatural sections needed to be smooth

A high-resolution scanning electron microscope testsystem (Figure 1) was used to scan the natural coal samplesections from 6 different coal seams and obtain the SEMimages (Figure 2)

-e pore structure was analyzed at 1000 times mag-nification to be able to analyze the low-permeability coalseam surface pore structure characteristics -e B-1 coalsamples were found to have mainly intergranular poresmore mineral crystal particles and developing cracks andmicrocracks -e B-2 coal sample was denser witha smaller quantity of intergranular minerals a large crackcutting surface or even holes more regular flat cracksa stacked fracture and strong toughness -e B-3 coalsample had a large amount of distributed residual tissue

Advances in Materials Science and Engineering 3

plant pores from the precipitation of the granular min-erals it is possible to see the xylem retained by thestructural silk body and the phloem cell cavity thereforethe pore level was stronger and more developed and there

were more micropores-e B-4 coal samples were relativelydense mainly intergranular pores that had a larger poresize and a different pore shape -ere were also a smallquantity of intergranular pores that had been caused by

Table 1 Permeability of different coal samples

Coal sample Porosity () Permeability (md) Appraise ClassifyB-1 82 375

Permeability range Ultralow-permeability reservoirB-2 77 977B-3 70 029B-4 50 043B-5 63 532B-6 68 132 Poor permeability Low-permeability reservoir

(a) (b)

Figure 1 SEM test system and raw coal sample

(a) (b) (c)

(d) (e) (f )

Figure 2 Raw coal sample SEM images (times1000) (a) B-1 coal sample (b) B-2 coal sample (c) B-3 coal sample (d) B-4 coal (e) B-5 coalsample (f ) B-6 coal sample


mineral crystallization layered cracks and a small distri-bution of a number of mineral particles -e B-5 coalsample was compact with minerals in the intergranularinclusions a large crack cutting surface more regularcracks laminated fractures and a stronger toughness andstronger crack than the B-2 coal sample -e B-6 coalsample and the B-3 coal sample were similar as they bothhad a large distribution of plant residual tissue poresa precipitation of granular minerals a structural silk bodywith retained xylem and various cellular lumen tissuephloem Larger more-developed micropores could also beseen at certain magnification rates

33 Fractal Dimension Calculation and Analysis Usingan Ostu threshold binarization processing method andMATLAB programming the SEM images for each coalsample at different magnification rates were processed andthe corresponding binary images were obtained (Figure 3) inwhich the black area are the macropores and the white area isthe coal skeleton (including the filling mineral composition)

-e fractal dimension of pore distribution for the binarysample images was calculated using the ldquobox-countingrdquoalgorithm in Fractal Fox 20 software from which it wasfound that the fractal dimension of pore distribution wasbetween 1 and 2 -e software calculation interface andresults are shown in Figure 4 and Table 2

Table 2 shows that the average fractal dimensionof pore distribution in the coal samples was B-5 gt B-4 gtB-3 gt B-1 gt B-6 gt B-2 -e maximum fractal dimension ofpore distribution was observed in the B-5 coal sample andthe minimum mean fractal dimension was observed in theB-2 coal sample -e average fractal dimensions of theB-1 B-3 B-4 and B-6 coal samples were in the middlewith no significant differences Fractal theory states thatthe larger the fractal dimension of coal pore distributionthe more developed the pores and the more uneven thedistribution -erefore the B-5 coal seam was found tohave the most developed pores and the most unevendistribution with the most undeveloped pores beingfound in the B-2 coal seam which was basically consistentwith the analysis in Figure 2

4 FractalCharacteristicsof theInternalPores inLow-Permeability Coal Seams

41 Low-Temperature Liquid Nitrogen AdsorptionExperiment To further study the internal pore structurecharacteristics of the low-permeability coal seam a corre-lation analysis experiment of the specific surface area thepore diameter and the pore volume of a raw coal sample wasconducted using an ASAP2020 specific surface microporeanalyzer -e experimental system and experimental resultsare shown in Figures 5 and 6 and Table 3

-e analysis in Figure 6 shows that the adsorption ca-pacity of the different coal seams differed when the relativepressure was the same -e adsorption capacity of the B-3coal seam was the largest followed by the B-6 coal seam

with the adsorption capacities of the remaining coal seamsbeing small that is B-4gtB-2gtB-5gtB-1

-e average pore diameter of the B-1 to B-6 coal seamswas 1033ndash327 nm the mesoporous volume proportionwas more than 51 and the large pore volume ratio wasbetween 1759 and 4855 -e specific mesoporoussurface area was more than 50 and the macroporousspecific surface area was 592 to 5014 (Table 3)-erefore it was concluded that the low-permeability coalseam in the South Junger Basin coalfield in Xinjiang be-longs to mesoporous material its pore distribution wasmore complex the mesoporous was dominant there werea certain number of large pores and there were no mi-cropores -e pore volume and specific surface area of theB-3 coal seam was the largest followed by the B-6 coalseam with the relationship between the pore volumes andspecific surface areas of the other coal seams being B-4 gt B-2 gt B-5 gt B-1 -e results showed that there was a positivecorrelation between the adsorption capacities the porevolumes and the specific surface areas of the different coalseams

42 Fractal Dimension Calculation and Analysis From theliquid nitrogen at low-temperature isothermal adsorptionexperimental data for the B-1 to B-6 coal seam samples thepore radius r the corresponding volume NV(le r) and thearea NS(ge r) of each coal sample were obtained FromFormulas (9) and (14) a linear relationship between lnNVln(1minusNS) and ln r was observed-e fractal dimensions DVfor the volume and the fractal dimensions DA for the surfacearea of the different coal samples were calculated using linearfitting in the double logarithmic coordinate system usingorigin software (-e results are shown in Figures 7ndash9 andTable 4)

-e fitting correlation coefficients are all above 072 theresults show that the fitting correlation is good

-e volume fractal dimension relationship for the coalseams was B-3gtB-6gtB-4gtB-1gtB-2gtB-5 and the surfacearea fractal dimension relationship for the coal seams wasB-3gtB-4gtB-1gtB-6gtB-5gtB-2 -e volume fractal di-mension and the surface area fractal dimension for B-1 B-4and B-6 were similar and the general variation trends werethe same which indicated that these two methods were ableto identify the pore radius distribution characteristics ofthe coal samples (Figure 9) -e analysis showed that thefractal dimension of the B-3 coal sample was the largest thatis it had irregular and small pore sizes with the average poresize measured by the low-temperature adsorption experi-ment being 1033 nm the number of mesoporous being thelargest and the pore structure being the most complex -efractal dimensions of the B-1 B-4 and B-6 coal sampleswere almost the same which corresponded to the numberof macropores -e fractal dimensions of the B-2 and B-5coal samples were the smallest which was consistent withthe largest number of macropores and the simplest porestructure According to the analysis of Table 4 and Figure 9the maximumminimum pore size ratio has an effect on thecorrelation coefficient of the fractal dimension of coal


(a)

(b)

Figure 4 Calculation of the interface and pore distribution fractal dimension fitting curve using Fractal Fox 20 Software

(a) (b)

Figure 3 (a) SEM diagram and (b) binary diagram for the B-1 coal sample magnified 500-fold


sample surface area but it has no effect on the trend ofquantitative characterization of pore structure

-e fractal dimension of coal pore surface is a measure ofirregular roughness of the pore surface which reflects thecomprehensive index of pore distribution pore diameterand pore volume of coal Based on the low-temperaturenitrogen adsorption isotherm experimental data on thecoal samples the pore surface fractal dimensions were

calculated using Formula (16) (the results are shown inFigure 10)

-e results show that the fitting correlation coefficientwas above 093 and the correlation was good

-e pore surface fractal dimension order was B-3 gt B-6 gt B-4 gt B-2 gt B-1 gt B-5 (Figure 10) -e pore surfacefractal dimension of the B-3 coal sample was the largestwhich was consistent with its complex pore structure -epore surface fractal dimension of the B-5 coal sample wasthe smallest as the pore boundary was smoother com-pared with the other coal samples -e pore surface fractaldimensions of B-1 B-2 and B-4 coal samples were in themiddle with similar sizes which indicated that the poresurfaces were generally rough -e pore surface fractaldimension of B-6 was greater than that of B-4 indicatingthat the pore roughness of the B-6 coal sample was greaterthan the pore roughness of B-4

5 Relationship between Pore FractalDimension and Macrophysical Properties inLow-Permeability Coal Seams

-e relationships between the pore structures and the fractaldimensions were determined using origin software theexperimental data and the fractal dimension calculationresults (Figure 11)

-e fractal dimension of pores in different coal seamsshows a negative linear relationship with the average poresize and a positive linear relationship with total surface areaand total pore volume-e results showed that the larger theaverage pore radius fractal dimension the larger the porevolume and surface area -e linear relationships betweenthe volume fractal dimension the surface area fractal di-mension and the mesoporous surface area ratio werepositively correlated -e surface fractal dimension hasa positive exponential relationship with the mesoporous

Table 2 Fractal dimensions of pore distribution of raw coalsamples

Coalsample Magnification Fractal

dimension R2 Mean fractaldimension DD

B-1

500 19031 094326

174681000 17569 0979571000+ 16339 0935672000 17815 0964582000+ 16586 094362

B-2

500 17058 095124

1457161000 13135 0969591000+ 15879 0974512000 11818 0934622000+ 14968 096786

B-3

500 19612 097896

1793881000 14917 0963231000+ 18141 0934172000 18078 0974892000+ 18946 096587

B-4

500 18544 099452

179891000 16664 097641000+ 19731 0963122000 16586 0947542000+ 1842 096851

B-5

500 19859 098394

183711000 17858 0971531000+ 18875 0967282000 17415 0975552000+ 17848 096173

B-6

500 18909 094283

1691841000 16697 0964281000+ 18521 0957842000 14124 0923752000+ 16341 097618

Figure 5 ASAP2020 specific surface microanalyzer

00 02 04 06 08 10ndash05

00

05

10

15

20

25

30

B-1B-2B-3

B-4B-5B-6

Ads

orba

nce (

cm3 g

)

Relative pressure (PP0)

Figure 6 Adsorption isotherms of nitrogen for the raw coalsamples


Table 3 Specific surface area pore volume and pore size of raw coal samples

Coal sample Averagepore diameter (nm)

Cumulativepore volume (cm3middotgminus1)

Cumulative specificsurface area (m2middotgminus1)

Pore volumespecific surface area ratioof different pore size segments ()

Macropore (gt50) Mesopore (2sim50)B-1 292002 0000589 00807 38713822 61296178B-2 317096 0000938 01183 34125014 65884986B-3 103268 0008605 33331 2422592 75789408B-4 267596 0001153 01724 403451 606549B-5 327034 000083 01015 48554703 51455297B-6 216436 0003718 06871 17592012 82417988

15 20 25 30 35 40 45 50 55 60 65ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash459562+07529xR2=099872

DV=3ndashk=22481

lnN

V

lnr

B-1

(a)

20 25 30 35 40 45 50 55 60ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash454385+0786xR2=099987

lnN

V

lnr

DV=3ndashk=2214

B-2

(b)

05 10 15 20 25 30 35 40 45 50 55 60 65

ndash04

ndash03

ndash02

ndash01

00

y=ndash05164+008798xR2=099895

DV=3ndashk=2912

lnN

V

lnr

B-3

(c)

05 10 15 20 25 30 35 40 45 50 55 60 65ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash427295+071867xR2=099909

DV=3ndashk=2281

lnN

V

lnr

B-4

(d)

Figure 7 Continued


10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )

Figure 7 Calculation of pore volume fractal dimensions for the B-1 to B-6 coal samples

15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued


surface area ratio In general the higher the fractal di-mensions of the pores in the different coal seams the largerthe mesoporous proportion

-e results showed that coal seam permeability is re-lated to the porosity development degree outside the coal

seam -e permeability of B-3 and B-4 was basicallyconsistent and the corresponding fractal dimensions werebasically the same however as the permeability of B-2 andB-6 was larger the corresponding fractal dimensions werethe smallest -ere was a stage negative correlation found

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )

Figure 8 Calculation of pore surface area fractal dimensions for the B-1 to B-6 coal samples

12

14

16

18

20

22

24

26

28

30

Volume fractal dimension DVSurface area fractal dimension DA

Frac

tal d

imen

sion D

Coal sample numberB-2B-1 B-6B-5B-4B-3

Figure 9 Fractal dimension of pore structure in different coal seams

Table 4 Maximum and minimum pore radius and volumearea fractal dimension for the B-1 to B-6 coal samples

Coalsample

Maximumminimum porediameter (nm)

Maximumminimumpore ratio

Volume fractaldimension DV

R2 Area fractaldimension DA

R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505


between permeability and the pore distribution fractaldimension and a positive correlation found between per-meability and porosity (Figure 12) -erefore these resultswere consistent with the conclusion that porous media

permeability decreases with an increase in the fractal di-mension and pore structure complexity [45] -e fractaldimension of pore distribution in different coal seams wasB-5 gtB-4 gtB-3 gtB-1 gtB-6 gtB-2 which indicated that the

ndash55 ndash50 ndash45 ndash40 ndash35 ndash30 ndash25 ndash20 ndash15 ndash10ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

y=ndash54742ndash08776xR2=099597

lnV

ln(ln(P0P))

DS=2122

B-1

(a)

ndash45 ndash40 ndash35 ndash30 ndash25 ndash20 ndash15 ndash10

ndash50

ndash45

ndash40

ndash35

ndash30

ndash25

y=ndash60186ndash08456x

R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)

ndash45 ndash40 ndash35 ndash30 ndash25 ndash20 ndash15 ndash10ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )

Figure 10 Calculation of pore surface fractal dimension for the B-1 to B-6 coal samples


10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094

Volume fractal dimension DVArea fractal dimension DASurface fractal dimension DS

Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

Total surface area (cm2middotgndash1)

R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092

Total pore volume (10ndash4 cm3middotgndash1)

(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092

Mesoporous surface area ratio ()

Volume fractal dimension DV

Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27

Surface fractal dimension DS

ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067


Area fractal dimension DA

Linear fit of DA

(f )

Figure 11 Relationship between the pore fractal dimension and the pore structure parameters for the B-1 to B-6 coal samples


distribution of the B-5 pores was the most uneven in theplane images as shown in Figure 2

-e results showed that the adsorption capacity of thedifferent coal seams was consistent with the change trend ofmesoporous surface area and mesopore is the main part ofpore adsorption in low-permeability coal seams (Figure 13)With the increase of mesoporous surface area the surfaceroughness increases and the adsorption ability of the coalmesoporous surface increases

-e surface fractal dimension measures the pore surfacecharacteristics and reflects the adsorption ability of the coalseam-e adsorption capacity of raw coal in low-permeabilitycoal seams has a positive linear relationship with the surfacefractal dimension (Figure 14) with the relationship beingy 776942xminus 1617684 2le xle 3 R2 093

6 Conclusions

-is article took the raw coal from a typical low-permeabilitycoal seam in the coalfield of South Junger Basin in Xinjiangas the research object to examine the microscopic porestructures and fractal characteristics of low-permeabilitycoal seams using a high-resolution scanning electron mi-croscope (SEM) fractal software (Fractal fox20) anda specific surface microporous analyzer (ASAP2020) -emain conclusions were as follows

(1) From the principles of fractal geometry a fractaldimension calculation model for the volumesurface area surface and pore distribution for thecoal micropore structures was established -evalidity of the fractal model was verified bya scanning electron microscope and a nitrogenadsorption test at low temperature

(2) -e low-temperature nitrogen adsorption testfound that the typical low-permeability coal seam inthe coalfield of South Junger Basin in Xinjiang

belongs to the mesoporous medium which ismainly mesoporous with a certain amount of largepores no micropores and a more complex poredistribution Under the same pressure conditionsa positive correlation was found between the ad-sorption capacity the pore volume and the specificsurface area of the coal seam

(3) -e pore fractal dimensions and the pore structuralparameters were fitted using origin software fromwhich it was found that the pore fractal dimension inlow-permeability coal seams has a negative linearrelationship with average pore size a positive linearrelationship with total surface area and total porevolume and a positive correlation with the meso-porous surface area ratio that is the higher the

145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion

Pore distribution fractal dimension DDPorosityPermeability

Different coal seams

45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)

Figure 12 Fractal dimension porosity and permeability for the B-1 to B-6 coal samples

0

2

4

Adsorption capacityMesoporous surface area ratio

B-6B-5B-4B-3B-2B-1Different coal seam

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (

)Figure 13 Adsorption capacity and mesoporous surface area forthe B-1 to B-6 coal samples


fractal dimension the larger the pore volume sur-face area and mesoporous surface area

(4) -e permeability of low-permeability coal seams hasa phase correlation with the micropore developmentdegree Permeability was found to have a phasenegative correlation with the pore distribution fractaldimension and a positive correlation with perme-ability and porosity which indicated that the mi-cropore has an important influence on thepermeability of low-permeability coal seams

(5) -e study on the relationships between pore ad-sorption capacity mesoporous surface area andsurface fractal dimensions in low-permeability coalseams showed that coal seam adsorption capacitywas positively related to mesoporous surface areabecause of the mesopores and had a positive linearrelationship with the surface fractal dimensionwhich can quantitatively characterize the adsorptioncapacity of the coal seam -ese results could be ofsignificant value when assessing the adsorptioncharacteristics for coal bed methane exploration

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was supported by Major Scientific and Tech-nological Projects of ldquo13115rdquo Science and Technology

Innovation Project in Shaanxi (2009ZDKG57) Scienceand Technology to Support Major Projects in Xinjiang(2014AB025) and the Major Projects of the Natural Scienceand Education in Shaanxi (2015JS060)

References

[1] C H Guo X Wu C W Zhang C Wangang and Z HaoldquoCharacterization of micro-structure in coalbed methanereservoir to appraise reservoir qualityrdquo Journal of Nanoscienceand Nanotechnology vol 17 no 9 pp 6859ndash6866 2017

[2] Y F Xu and P Dong ldquoFractal approach to hydraulicproperties in unsaturated porous mediardquo Chaos Solitons ampFractals vol 19 no 2 pp 327ndash337 2004

[3] M Mahamud O Lopez J J Pis and J A Pajares ldquoTexturalcharacterization of coals using fractal analysisrdquo Fuel Pro-cessing Technology vol 81 no 2 pp 127ndash142 2003

[4] M R Othman Z Helwani and Martunus ldquoSimulated fractalpermeability for porous membranesrdquo Applied MathematicalModelling vol 34 no 9 pp 2452ndash2464 2010

[5] S Talu Micro and Nanoscale Characterization of ree Di-mensional Surfaces Basics and Applications Napoca StarPublishing House Cluj-Napoca Romania 2015

[6] B Meng ldquoDetermination and interpretation of fractalproperties of the sandstone pore systemrdquo Materials andStructures vol 29 no 4 pp 195ndash205 1996

[7] S G Qin H L Wu M B Tian J C Wu and S L YaoldquoFractal characteristics of the pore structure of low perme-ability sandstonerdquo Applied Mechanics and Materials vol 190-191 pp 482ndash486 2012

[8] G Lesniak and P Such ldquoFractal approach analysis of imagesand diagenesis in pore space evaluationrdquo Natural ResourcesResearch vol 14 no 4 pp 317ndash324 2005

[9] M M Mahamud and M F Novo ldquo-e use of fractal analysisin the textural characterization of coalsrdquo Fuel vol 87 no 2pp 222ndash231 2008

[10] G Z Deng and Y K Zhang ldquoAn analysis model of themechanics of jointed rock massrdquo Journal of Coal Science ampEngineering vol 6 no 1 pp 30ndash36 2000

[11] K W Li and R N Horne ldquoExperimental study and fractalanalysis of heterogeneity in naturally fractured rocksrdquoTransport in Porous Media vol 78 no 2 pp 217ndash231 2009

[12] S Erdem and M A Blankson ldquoFractalndashfracture analysis andcharacterization of impact-fractured surfaces in differenttypes of concrete using digital image analysis and 3Dnanomap laser profilometeryrdquo Construction and BuildingMaterials vol 40 pp 70ndash76 2013

[13] Y X Zhao S Gong C G Zhang Z Zhang and Y JiangldquoFractal characteristics of crack propagation in coal underimpact loadingrdquo Fractals vol 26 no 2 article 1840014 2018

[14] Y H Li G Q Lu and V Rudolph ldquoCompressibility andfractal dimension of fine coal particles in relation to porestructure characterization using mercury porosimetryrdquo Par-ticle amp Particle Systems Characterization vol 16 no 1pp 25ndash31 1999

[15] N Hao Y L Wang L T Mao and Q Liu ldquo-e fractalcharacteristic analysis of coal pore structure based on themercury intrusion porosimetryrdquo Applied Mechanics andMaterials vol 353-356 pp 1191ndash1195 2013

[16] K J Li F G Zeng J C Cai G Sheng P Xia and K ZhangldquoFractal characteristics of pores in Taiyuan formation shalefrom Hedong coal field Chinardquo Fractals vol 26 no 2 article1840006 2018

20 21 22 23 24 25 26 27

0

1

2

3

4

5

Adsorption capacity Linear fit of adsorption

Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

Figure 14 Relationship between adsorption quantity and poresurface fractal dimension


[17] B S Nie X F Liu L L Yang J Meng and X Li ldquoPorestructure characterization of different rank coals using gasadsorption and scanning electron microscopyrdquo Fuel vol 158pp 908ndash917 2015

[18] D Gao M Li B Wang B Hu and J Liu ldquoCharacteristics ofpore structure and fractal dimension of isometamorphicanthraciterdquo Energies vol 10 no 11 pp 1881ndash1892 2017

[19] S Hou X Wang X Wang Y Yuan S Pan and X WangldquoPore structure characterization of low volatile bituminouscoals with different particle size and tectonic deformationusing low pressure gas adsorptionrdquo International Journal ofCoal Geology vol 183 pp 1ndash13 2017

[20] C Peng C C Zou Y Q Yang G Zhang and W WangldquoFractal analysis of high rank coal from southeast Qinshuibasin by using gas adsorption and mercury porosimetryrdquoJournal of Petroleum Science and Engineering vol 156pp 235ndash249 2017

[21] J Z Liu Z Y Zhang S K Choi and Y Lu ldquoSurfaceproperties and pore structure of anthracite bituminous coaland ligniterdquo Energies vol 11 no 6 pp 1502ndash1515 2018

[22] B M Yu ldquoAnalysis of flow in fractal porous mediardquo AppliedMechanics Reviews vol 61 no 5 article 050801 2008

[23] M Zhao and B M Yu ldquo-e fractal characterization of porestructure for some numerical rocks and prediction of per-meabilitiesrdquo Journal of Chongqing University vol 34 no 4pp 88ndash94 2011 in Chinese

[24] Y B Yao DM Liu D Z Tang et al ldquoFractal characterizationof seepage-pores of coals from China an investigation onpermeability of coalsrdquo Computers amp Geosciences vol 35no 6 pp 1159ndash1166 2009

[25] Y D Cai D M Liu Z J Pan Y Che and Z Liu ldquoIn-vestigating the effects of seepage-pores and fractures on coalpermeability by fractal analysisrdquo Transport in Porous Mediavol 111 no 2 pp 479ndash497 2016

[26] X M Yu Z S Lu and H Q Rao ldquoResearch on permeabilityof porous graphite based on fractal theoryrdquo Chinese Journalof Mechanical Engineering vol 42 pp 74ndash77 2006 inChinese

[27] B B Gao H G Li L Li et al ldquoStudy of acoustic emission andfractal characteristics of soft and hard coal samples with samegrouprdquo Chinese Journal of Rock Mechanics and Engineeringvol 33 pp 3498ndash3504 2014

[28] J Li and X Wu ldquoResearch of coal pores and integrity eval-uation method based on fractal theoryrdquo Applied Mechanicsand Materials vol 670-671 pp 258ndash262 2014

[29] B Zhang J Zhu F He and Y Jiang ldquoCompressibility andfractal dimension analysis in the bituminous coal specimensrdquoAIP Advances vol 8 no 7 article 075118 2018

[30] X Y Zhang C F Wu and S X Liu ldquoCharacteristic analysisand fractal model of the gas-water relative permeability of coalunder different confining pressuresrdquo Journal of PetroleumScience and Engineering vol 159 pp 488ndash496 2017

[31] Z Liu H Yang W Y Wang W Cheng and L Xin ldquoEx-perimental study on the pore structure fractals and seepagecharacteristics of a coal sample around a borehole in coal seamwater infusionrdquo Transport in Porous Media vol 125 no 2pp 289ndash309 2018

[32] G Z Deng and R Zheng ldquoReconstruction of 3D micro porestructure of coal and simulation of its mechanical propertiesrdquoAdvances in Materials Science and Engineering vol 2017Article ID 5658742 9 pages 2017

[33] B M Yu and J H Li ldquoSome fractal characters of porousmediardquo Fractals vol 9 no 3 pp 365ndash372 2001

[34] B B Mandelbrot e Fractal Geometry of Nature W HFreeman and Company New York NY USA 1982

[35] K Falconer Fractal Geometry Mathematical Foundationsand Applications John Wiley amp Sons Hoboken NJ USA2003

[36] C Z He and M Q Hua ldquoFractal geometry description ofreservoir pore structurerdquo Oil amp Gas Geology vol 19 no 1pp 15ndash23 1998

[37] S H Zhang S H Tang D Z Tang W Huang and Z PanldquoDetermining fractal dimensions of coal pores by FHHmodelproblems and effectsrdquo Journal of Natural Gas Science andEngineering vol 21 pp 929ndash939 2014

[38] P Pfeifer Y J Wu M W Cole and J Krim ldquoMultilayeradsorption on a fractally rough surfacerdquo Physical ReviewLetters vol 62 no 17 pp 1997ndash2000 1989

[39] D Avnir and M Jaroniec ldquoAn isotherm equation for ad-sorption on fractal surfaces of heterogeneous porous mate-rialsrdquo Langmuir vol 5 no 6 pp 1431ndash1433 1989

[40] Y B Yin ldquoAdsorption isotherm on fractally porous mate-rialsrdquo Langmuir vol 7 no 2 pp 216-217 1991

[41] M Jaroniec ldquoEvaluation of the fractal dimension from a singleadsorption isothermrdquo Langmuir vol 11 no 6 pp 2316-23171995

[42] Y B Yao D M Liu D Tang S H Tang and W HuangldquoFractal characterization of adsorption-pores of coals fromNorth China an investigation on CH4 adsorption capacity ofcoalsrdquo International Journal of Coal Geology vol 73 no 1pp 27ndash42 2008

[43] J C Cai F S J Martinez M A Martin and E Perfect ldquoAnintroduction to flow and transport in fractal models of porousmedia part Irdquo Fractals-Complex Geometry Patterns andScaling in Nature and Society vol 22 no 3 article 14020012014

[44] J Xu L Wang S J Peng et al ldquoAnalysis of pore charac-teristics on the surface of raw coal under different sizesrdquoDisaster Advances vol 3 no 4 pp 510ndash516 2010

[45] J L Liu C A Tian Y W Zeng et al ldquoFractal dimensionalitydependence of microstructural parameters and permeabilityin fractal porous mediardquo Advances in Water Science vol 17no 6 pp 812ndash817 2006 in Chinese


CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

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BioMed Research InternationalMaterials

Journal of


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nom

ate

ria

ls


Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

residual water saturation to be identified [6ndash8] A study offour bituminous coals and oxidized bituminous coal samplesat 270degC was able to determine the fractal dimensions andfractal distribution sensitivities to oxidation treatments [9]Based on the creep fracture damage model of a jointed rockmass the results show that the greater the number of rockjoints the larger the fractal dimensions the more thefracture energy absorbs material [10ndash13] Coal pore struc-ture has been analyzed using mercury injection experimentswhich allowed for the fractal dimensions of the pore coalbody surface to be calculated and the pore structure char-acteristics to be quantitatively characterized [14 15] -erelationships between the adsorption characteristics of coalsamples and the fractal dimension of low-temperature poresurfaces have been established using nitrogen adsorptiontests [16ndash21] and using digital core technology the re-lationships between the fractal dimension of pore diameterand permeability have been established [22 23] Fractaltheory has also been employed to determine the relation-ships between pore fractal dimensions and permeability[24ndash26] from which it was found that the compressibilityhardness and porosity of coal bodies were related to thefractal dimensions [27ndash29] A study on the influence ofconfined pressure and pore water pressure on the coalsample structure and percolation characteristics establisheda quantitative relationship between pore structure fractalsand coal sample permeability [30 31] According to thepore structure characteristics of low-permeability coalseams a 3D pore model for low-permeability coal wasconstructed and the influence of porosity on mechanicalproperties of coal was discussed [32]

Although there has been significant research on thephysical properties of coal seams there has been littleresearch focused on the microscopic pore structures of low-permeability coal seams and the effect of these on themacroscopic exploitation and utilization of the coal seams-erefore to further explore the relationships between themicrostructure characteristics and the macroscopic phys-ical properties of low-permeability coal seams this paperused the low-permeability coal seam in the coalfield ofSouth Junger Basin in Xinjiang to systematically analyzethe coalrsquos physical characteristics and pore structure usingan MTS-815 servo test system a scanning electron mi-croscope and a surface microporous fractal instrumentwhich allowed for all kinds of fractal models used to studyand explain the micropore structure of the coal seam -efractal characteristics of pore structure in low-permeabilitycoal seams and the relationships between the pore structureand the macroscopic physical parameters are also dis-cussed -ese results can greatly assist in the interpretationand prediction of the macroscopic properties in coal seams

2 Fractal Description of Coal and RockPore Structures

In fractal geometry the fractal dimension is the objectivetool used to measure the degree of ldquoirregularityrdquo andldquocomplexityrdquo in two fractal sets -e fractal dimensiondefinition has the following relations [33]

ϕ λmin

λmax1113888 1113889

DeminusDf

(1)

where ϕ is porosity De is the Euclidean space di-mension and Df is the fractal dimension In two-dimensional space De 2 1langDflang2 In three dimen-sions De 3 2langDflang3 λminλmax are the minimum andmaximum pore diameters

21 FractalDimensionPoreDistributionModel To assess thefractal dimension pore distribution which reflects the in-homogeneity of the pores the fractal box dimension methodhas been a widely used fractal measurement method therationale for which is as follows

When the fractal figure covers the fractal curve imagewith a square lattice of a certain scale some of the meshmay contain part of the curve while other parts of the meshremain empty with the number of nonempty mesh in-creasing as the mesh side length gradually reduces If theside length of a square mesh is r and the number ofnonempty mesh is N(r) then the fractal box dimension is[34]

D minus limr⟶0

lnN(r)

ln r (2)

-e corresponding N(r) value is calculated for differentgrid side lengths r the logarithmic coordinate curves of r

and N(ge r) are given and the relation is obtained throughfitting [35]

ln(N(ge r)) cminusD ln(r) (3)

-e slope k of Equation (3) is used to fit the straight linewith the box dimension D minusk and having a value between1 and 2 In this paper DD is the fractal dimension of poredistribution

22 FractalDimension PoreVolumeModel From the fractaldefinition the density function of the pore radius distri-bution in porous media has the following relationships[36]

f(r) crminusDminus1

(4)

where r is the pore radius D is the pore fractal dimensionand c is a constant

If the pore gap is a sphere the cumulative pore volume isthe integral of the radius distribution density function to theradius therefore the cumulative pore volume V(le r) witha pore radius less than r can be obtained as follows

V(le r) 1113946r

rmin

f(r)ar3dr

ac

3minusDr3minusD minus r

3minusDmin1113872 1113873 (5)

-e cumulative total pore volume is V

V ac


3minusDmin1113872 1113873 (6)



NV V(le r)

V


(7)


NV r

rmax1113888 1113889

3minusD

(8)


ln NV( 1113857 (3minusD)ln(r) + C1 (9)



S(ge r) 1113946rmax

rf(r)ar

2dr

ac


2minusD1113872 1113873 (10)


S ac


2minusDmin1113872 1113873 (11)


NS S(ge r)

S




NS 1minusr

rmax1113888 1113889

2minusD

(13)







P1113874 1113875 + C (15)




P1113874 1113875 + C (16)













(a) (b)


(a) (b) (c)

(d) (e) (f )
















(a)

(b)


(a) (b)














B-1

500 19031 094326

174681000 17569 0979571000+ 16339 0935672000 17815 0964582000+ 16586 094362

B-2

500 17058 095124

1457161000 13135 0969591000+ 15879 0974512000 11818 0934622000+ 14968 096786

B-3

500 19612 097896

1793881000 14917 0963231000+ 18141 0934172000 18078 0974892000+ 18946 096587

B-4

500 18544 099452

179891000 16664 097641000+ 19731 0963122000 16586 0947542000+ 1842 096851

B-5

500 19859 098394

183711000 17858 0971531000+ 18875 0967282000 17415 0975552000+ 17848 096173

B-6

500 18909 094283

1691841000 16697 0964281000+ 18521 0957842000 14124 0923752000+ 16341 097618


00 02 04 06 08 10ndash05

00

05

10

15

20

25

30

B-1B-2B-3

B-4B-5B-6

Ads

orba

nce (

cm3 g

)










15 20 25 30 35 40 45 50 55 60 65ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash459562+07529xR2=099872

DV=3ndashk=22481

lnN

V

lnr

B-1

(a)

20 25 30 35 40 45 50 55 60ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash454385+0786xR2=099987

lnN

V

lnr

DV=3ndashk=2214

B-2

(b)

05 10 15 20 25 30 35 40 45 50 55 60 65

ndash04

ndash03

ndash02

ndash01

00

y=ndash05164+008798xR2=099895

DV=3ndashk=2912

lnN

V

lnr

B-3

(c)

05 10 15 20 25 30 35 40 45 50 55 60 65ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash427295+071867xR2=099909

DV=3ndashk=2281

lnN

V

lnr

B-4

(d)

Figure 7 Continued


10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )


15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued





ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





NV V(le r)

V


(7)


NV r

rmax1113888 1113889

3minusD

(8)


ln NV( 1113857 (3minusD)ln(r) + C1 (9)



S(ge r) 1113946rmax

rf(r)ar

2dr

ac


2minusD1113872 1113873 (10)


S ac


2minusDmin1113872 1113873 (11)


NS S(ge r)

S




NS 1minusr

rmax1113888 1113889

2minusD

(13)







P1113874 1113875 + C (15)




P1113874 1113875 + C (16)













(a) (b)


(a) (b) (c)

(d) (e) (f )
















(a)

(b)


(a) (b)














B-1

500 19031 094326

174681000 17569 0979571000+ 16339 0935672000 17815 0964582000+ 16586 094362

B-2

500 17058 095124

1457161000 13135 0969591000+ 15879 0974512000 11818 0934622000+ 14968 096786

B-3

500 19612 097896

1793881000 14917 0963231000+ 18141 0934172000 18078 0974892000+ 18946 096587

B-4

500 18544 099452

179891000 16664 097641000+ 19731 0963122000 16586 0947542000+ 1842 096851

B-5

500 19859 098394

183711000 17858 0971531000+ 18875 0967282000 17415 0975552000+ 17848 096173

B-6

500 18909 094283

1691841000 16697 0964281000+ 18521 0957842000 14124 0923752000+ 16341 097618


00 02 04 06 08 10ndash05

00

05

10

15

20

25

30

B-1B-2B-3

B-4B-5B-6

Ads

orba

nce (

cm3 g

)










15 20 25 30 35 40 45 50 55 60 65ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash459562+07529xR2=099872

DV=3ndashk=22481

lnN

V

lnr

B-1

(a)

20 25 30 35 40 45 50 55 60ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash454385+0786xR2=099987

lnN

V

lnr

DV=3ndashk=2214

B-2

(b)

05 10 15 20 25 30 35 40 45 50 55 60 65

ndash04

ndash03

ndash02

ndash01

00

y=ndash05164+008798xR2=099895

DV=3ndashk=2912

lnN

V

lnr

B-3

(c)

05 10 15 20 25 30 35 40 45 50 55 60 65ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash427295+071867xR2=099909

DV=3ndashk=2281

lnN

V

lnr

B-4

(d)

Figure 7 Continued


10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )


15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued





ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









(a) (b)


(a) (b) (c)

(d) (e) (f )
















(a)

(b)


(a) (b)














B-1

500 19031 094326

174681000 17569 0979571000+ 16339 0935672000 17815 0964582000+ 16586 094362

B-2

500 17058 095124

1457161000 13135 0969591000+ 15879 0974512000 11818 0934622000+ 14968 096786

B-3

500 19612 097896

1793881000 14917 0963231000+ 18141 0934172000 18078 0974892000+ 18946 096587

B-4

500 18544 099452

179891000 16664 097641000+ 19731 0963122000 16586 0947542000+ 1842 096851

B-5

500 19859 098394

183711000 17858 0971531000+ 18875 0967282000 17415 0975552000+ 17848 096173

B-6

500 18909 094283

1691841000 16697 0964281000+ 18521 0957842000 14124 0923752000+ 16341 097618


00 02 04 06 08 10ndash05

00

05

10

15

20

25

30

B-1B-2B-3

B-4B-5B-6

Ads

orba

nce (

cm3 g

)










15 20 25 30 35 40 45 50 55 60 65ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash459562+07529xR2=099872

DV=3ndashk=22481

lnN

V

lnr

B-1

(a)

20 25 30 35 40 45 50 55 60ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash454385+0786xR2=099987

lnN

V

lnr

DV=3ndashk=2214

B-2

(b)

05 10 15 20 25 30 35 40 45 50 55 60 65

ndash04

ndash03

ndash02

ndash01

00

y=ndash05164+008798xR2=099895

DV=3ndashk=2912

lnN

V

lnr

B-3

(c)

05 10 15 20 25 30 35 40 45 50 55 60 65ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash427295+071867xR2=099909

DV=3ndashk=2281

lnN

V

lnr

B-4

(d)

Figure 7 Continued


10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )


15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued





ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls

















(a)

(b)


(a) (b)














B-1

500 19031 094326

174681000 17569 0979571000+ 16339 0935672000 17815 0964582000+ 16586 094362

B-2

500 17058 095124

1457161000 13135 0969591000+ 15879 0974512000 11818 0934622000+ 14968 096786

B-3

500 19612 097896

1793881000 14917 0963231000+ 18141 0934172000 18078 0974892000+ 18946 096587

B-4

500 18544 099452

179891000 16664 097641000+ 19731 0963122000 16586 0947542000+ 1842 096851

B-5

500 19859 098394

183711000 17858 0971531000+ 18875 0967282000 17415 0975552000+ 17848 096173

B-6

500 18909 094283

1691841000 16697 0964281000+ 18521 0957842000 14124 0923752000+ 16341 097618


00 02 04 06 08 10ndash05

00

05

10

15

20

25

30

B-1B-2B-3

B-4B-5B-6

Ads

orba

nce (

cm3 g

)










15 20 25 30 35 40 45 50 55 60 65ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash459562+07529xR2=099872

DV=3ndashk=22481

lnN

V

lnr

B-1

(a)

20 25 30 35 40 45 50 55 60ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash454385+0786xR2=099987

lnN

V

lnr

DV=3ndashk=2214

B-2

(b)

05 10 15 20 25 30 35 40 45 50 55 60 65

ndash04

ndash03

ndash02

ndash01

00

y=ndash05164+008798xR2=099895

DV=3ndashk=2912

lnN

V

lnr

B-3

(c)

05 10 15 20 25 30 35 40 45 50 55 60 65ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash427295+071867xR2=099909

DV=3ndashk=2281

lnN

V

lnr

B-4

(d)

Figure 7 Continued


10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )


15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued





ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls















B-1

500 19031 094326

174681000 17569 0979571000+ 16339 0935672000 17815 0964582000+ 16586 094362

B-2

500 17058 095124

1457161000 13135 0969591000+ 15879 0974512000 11818 0934622000+ 14968 096786

B-3

500 19612 097896

1793881000 14917 0963231000+ 18141 0934172000 18078 0974892000+ 18946 096587

B-4

500 18544 099452

179891000 16664 097641000+ 19731 0963122000 16586 0947542000+ 1842 096851

B-5

500 19859 098394

183711000 17858 0971531000+ 18875 0967282000 17415 0975552000+ 17848 096173

B-6

500 18909 094283

1691841000 16697 0964281000+ 18521 0957842000 14124 0923752000+ 16341 097618


00 02 04 06 08 10ndash05

00

05

10

15

20

25

30

B-1B-2B-3

B-4B-5B-6

Ads

orba

nce (

cm3 g

)










15 20 25 30 35 40 45 50 55 60 65ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash459562+07529xR2=099872

DV=3ndashk=22481

lnN

V

lnr

B-1

(a)

20 25 30 35 40 45 50 55 60ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash454385+0786xR2=099987

lnN

V

lnr

DV=3ndashk=2214

B-2

(b)

05 10 15 20 25 30 35 40 45 50 55 60 65

ndash04

ndash03

ndash02

ndash01

00

y=ndash05164+008798xR2=099895

DV=3ndashk=2912

lnN

V

lnr

B-3

(c)

05 10 15 20 25 30 35 40 45 50 55 60 65ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash427295+071867xR2=099909

DV=3ndashk=2281

lnN

V

lnr

B-4

(d)

Figure 7 Continued


10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )


15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued





ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










15 20 25 30 35 40 45 50 55 60 65ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash459562+07529xR2=099872

DV=3ndashk=22481

lnN

V

lnr

B-1

(a)

20 25 30 35 40 45 50 55 60ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash454385+0786xR2=099987

lnN

V

lnr

DV=3ndashk=2214

B-2

(b)

05 10 15 20 25 30 35 40 45 50 55 60 65

ndash04

ndash03

ndash02

ndash01

00

y=ndash05164+008798xR2=099895

DV=3ndashk=2912

lnN

V

lnr

B-3

(c)

05 10 15 20 25 30 35 40 45 50 55 60 65ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash427295+071867xR2=099909

DV=3ndashk=2281

lnN

V

lnr

B-4

(d)

Figure 7 Continued


10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )


15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued





ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




10 15 20 25 30 35 40 45 50 55 60 65ndash45

ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

y=ndash537638+092049xR2=09994

DV=3ndashk=2079

lnN

V

lnr

B-5

(e)

10 15 20 25 30 35 40 45 50 55 60 65

ndash20

ndash15

ndash10

ndash05

00

y=ndash25337+043018xR2=099976

DV=2569

lnN

V

lnr

B-6

(f )


15 20 25 30 35 40 45 50 55 60 65 70ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=146218

B-1

y=053782xndash301365R2=072425

ln(1

ndashNS)

lnr

(a)

20 25 30 35 40 45 50 55 60ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=122009

B-2

y=077991xndash431912R2=075084

ln(1

ndashNS)

lnr

(b)

ln(1

ndashNS)

lnr10 15 20 25 30 35 40 45 50 55 60

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

DA=17939

B-3

y=02061xndash092596R2=059082

(c)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

DA=154446

B-4

y=045554xndash245825R2=077354

(d)

Figure 8 Continued





ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=129707

B-5

y=070293xndash376537R2=075619

(e)

ln(1

ndashNS)

lnr15 20 25 30 35 40 45 50 55 60

ndash25

ndash20

ndash15

ndash10

ndash05

00

05

DA=14118

B-6

y=05882xndash275763R2=072505

(f )


12

14

16

18

20

22

24

26

28

30


Frac

tal d

imen

sion D




Coalsample





R2

B-1 1933137 5224595 225 099872 146 072425B-2 17956886 2026637 221 099987 122 075084B-3 9771325 3006461 291 099895 179 059082B-4 13319301 4424917 228 099909 155 077354B-5 15266264 5782576 208 09994 1297 075619B-6 11149356 3131742 257 099976 141 072505





ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

DS=2122

B-1

(a)


ndash50

ndash45

ndash40

ndash35

ndash30

ndash25


R2=09962

lnV

ln(ln(P0P))

DS=2154

B-2

(b)


04

06

08

10

12

14

16


lnV

ln(ln(P0P))

DS=2633

B-3

(c)


ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-4

DS=2186

(d)


ndash40

ndash35

ndash30

ndash25

ndash20

ndash15

ndash10

ndash05


lnV

ln(ln(P0P))

B-5

DS=2077

(e)


ndash15

ndash10

ndash05

00

05


lnV

ln(ln(P0P))

B-6

DS=2257

(f )



10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30

R2=070

R2=097

R2=094


Frac

tal d

imen

sion

Aperture (nm)

(a)


Frac

tal d

imen

sion

00 05 10 15 20 25 30 35

12

14

16

18

20

22

24

26

28

30


R2=081

R2=096

R2=058

(b)


Frac

tal d

imen

sion

0 20 40 60 80 100

12

14

16

18

20

22

24

26

28

30

R2=052

R2=096

R2=092


(c)

Frac

tal d

imen

sion

50 60 70 80 90 100

21

22

23

24

25

26

27

28

29

30

R2=092



Linear fit of DV

(d)

Frac

tal d

imen

sion

50 60 70 80 90 10020

21

22

23

24

25

26

27


ExpGro2 fit of DS

R2=09


(e)

Frac

tal d

imen

sion

50 60 70 80 90 100

12

13

14

15

16

17

18

R2=067



Linear fit of DA

(f )






6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







6 Conclusions






145

150

155

160

165

170

175

180

185

B-6B-5B-4B-3B-2B-1

Frac

tal d

imen

sion



45

50

55

60

65

70

75

80

85

Poro

sity

()

0

2

4

6

8

10

12

14

Perm

eabi

lity

(md)


0

2

4



Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)

50

60

70

80

90

100

Mes

opor

ous s

urfa

ce ar

ea ra

tio (






Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







Data Availability




Acknowledgments



References

















20 21 22 23 24 25 26 27

0

1

2

3

4

5


Fractal dimension

y=776942xndash1617684R2=093

Ads

orpt

ion

capa

city

(cm

3 middotgndash1

)



































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




micropore structure and fractal characteristics of low...

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