Research Article Comprehensive Fractal Description of Porosity of Coal of Different Ranks

e Scientific World Journal, Article ID 498, 7 pages http://dx.doi.org/.55/4/498 Research Article Comprehensive Fractal Description of Porosity of Coal of Different Ranks Jiangang Ren, Guocheng Zhang,, Zhimin Song,, Gaofeng Liu,, andbingli, College of Resources and Environment, Henan Polytechnic University, Jiaozuo, Henan 454, China State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Henan Polytechnic University, Jiaozuo, Henan 454, China College of Resources and Environment, Henan Institute of Engineering, Zhengzhou, Henan 459, China Correspondence should be addressed to Zhimin Song; songzhimin96@6.com Received 5 March 4; Accepted 4 April 4; Published May 4 Academic Editor: Guojie Zhang Copyright 4 Jiangang Ren et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between. nm and 6.4 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of nm and nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure.. Introduction A coal reservoir is a kind of double pore strata, being composed of a matrix pore and a fracture. The aperture structureofcoalservesasthebasisforresearchonthe occurrence of coal bed methane, the physical and chemical action between the gas-water medium, and the coal matrix block, as well as desorption, diffusion, and seepage of coal bed methane [ 5]. Coal is characterized by the heterogeneity of its surface and structure, mainly embodied in the unevenness of the surface of the coal as well as in the pores of different sizes and shapes in the coal structure. This kind of heterogeneity plays a decisive role in the adsorption process [6]. When conducting research on the pore structure of coal, characterization must beconductedonmultipleaspects,includingthespecific surface area, aperture distribution, and coal heterogeneity. The research shows that the pore distribution and surface morphology of coal have heterogeneity and statistical fractal characteristics; thus, it is difficult to describe them with Euclideangeometry,whiletheuseoffractalgeometryismuch more suitable for their description [7 ]. When using the fractal dimensions of coal to conduct characterization for its heterogeneity, usually we employ the mercury intrusion method and liquid nitrogen adsorption method to test and calculate the fractal dimensions of the coal [, ]. In most cases, the fractal dimensions calculated by these two methods are overlapped in the aperture range between 5.5 nm and 5 nm. Since these two methods are based on different principles, the results obtained are different. Therefore, we must seek a reasonable method to obtain the fractal dimensions for full apertures of coal pores, realize the unity of the data, and calculate the comprehensive fractal dimension. With the purpose of solving the problems mentioned above, we used the mercury intrusion method and lowtemperatureliquidnitrogenadsorptionmethodtoanalyze theporestructureandporeshapeofcoal;accordingto

The Scientific World Journal Table:Coalqualityanalysisforcoalsample. Sample number M ad (%) A ad (%) V daf (%) R o,max (%) Porosity (%) Number.69 6.45 6..8 7.5 Number.5 8.5 4.57.86 5. Number.6.4 8.59.6.4 Number 4.6 6. 7.7.49 4.6 Note: the M ad ismoisture,the A ad isash,andthe V daf is volatile matter of proximate analysis in coal. The R o,max isthemaximumreflectanceofvitrinite. Table : Experimental results of pore volume for coal samples obtained using mercury intrusion method. Sample number Pore volume (ml/g) Pore volume ratio (%) V V V V 4 V t V /V t V /V t V /V t V 4 /V t Number.4.66..9. 7.9.78 9.9.6 Number.67.7.98.86..8.5.4 6.7 Number..7.6.95.7.85. 4.96 5.9 Number 4.7..84.86.87.74 5.5 44.9 45.99 Note: the subscript t is total pore, is macropore (Φ > nm), is mesopore ( nm Φ> nm), is transition pore ( nm Φ> nm), and 4 is micropore ( nm Φ>5.5 nm). the data obtained from the mercury intrusion experiment and low-temperature liquid nitrogen adsorption experiment, we calculated the fractal dimensions of different aperture segments of coal, defined and calculated the comprehensive fractal dimensions of the coal pore, and conducted characterization for coal pore distribution heterogeneity.. Coal Sample and Experiment The coal samples used in this experiment included the following: lignite from the Shandong, Longkou Beizao Mine (Number ); gas coal from the Shandong, Weishan, Caiyuan Mine (Number ); coking coal from the Shanxi, Gujiao, Xiqu Mine (Number ); and anthracite from the Henan, Jiaozuo, GuhanshanMine(Number4).Samplepreparationswerein accordance with GB/T 7-999. The analytical results for thecoalqualityareshownintable. The AutoPore IV 955 automatic mercury intrusion instrument and the ASAPM automatic specific surface analyzerproducedbytheamericanmicromeriticsinstrument Company were, respectively, used in the mercury intrusion experiment and liquid nitrogen adsorption experiment. The former can test pores from the coal samples with a diameter greater than 5.5 nm, and the latter can test pores with a diameter range between nm and 6 nm. The sizes of coal samples in the mercury intrusion experiment were 6 mm. The granularity of coal samples in liquid nitrogen adsorption experiment were.7.5mm. The two experiments were carried out at the Engineering Center of the Coal Mine Disaster Prevention and Disaster Relief Education Department at Henan Polytechnic University.. Experimental Results and Discussion.. Experimental Results. Decimal classification of XO:OT (96) was used [4],andthetestresultsareshowninTables,, 4,and5...FractalDimensionsofCoalPoresCalculatedUsingMercury Intrusion Method. In accordance with the principle of calculating fractal dimensions of coal pores using the mercury intrusion method [], we obtained the following formula: log [ dv p(r) dp (r) ] (4 D ) log r (D 4)log p (r). () We drew diagrams with log[dv p(r) /dp(r)] and log p(r) and obtained the slope K and then D 4=K;namely, D =4+K, () where dv p(r) is the total pore volume under given pressure (equal to the volume of the mercury injected into the pore); D isthefractaldimensionofporevolume(mercury intrusion method); p(r) is the applied pressure, MPa; and r is the pore diameter of coal sample, nm. The diagrams of the statistical relationship between log[dv p(r) /dp(r)] and log[p(r)] of the four coal samples were drawn according to the original data from the mercury intrusion experiment (see Figure ). From Figure, wecancalculatethefractaldimensionof coal sample pore distribution using the mercury intrusion method (Table 6). The results show that, when the aperture of lignite (Number ), gas coal (Number ), and coking coal (Number )isgreaterthanorequaltonm,thecorrelationbetween log[dv p(r) /dp(r)] and log[p(r)] is significant; the correlation coefficientsareallgreaterthan8%,andthecoalporesin the pore segment have obvious fractal characteristics. When the aperture is less than nm, the correlation between log[dv p(r) /dp(r)] and log[p(r)] is not significant; the correlation coefficients are all smaller than 5%, and the coal pores in the pore segment do not have fractal characteristics. Whentheapertureofanthracite(Number4)isgreaterthan or equal to nm, the correlation between log[dv p(r) /dp(r)]

The Scientific World Journal Table : Experimental results of specific surface areas of coal samples obtained by mercury intrusion methods. Sample number Specific surface area of pore (m /g) Specific surface area ratio of pore (%) S S S S 4 S t S /S t S /S t S /S t S 4 /S t Number.4.95.74 4.986 7.59.6. 8.97 69.65 Number.9.8.75 4.65 6.49.4.5 6.97 7.64 Number.5.9. 5.4 7.7.7.54 8.9 7.47 Number 4..7.68 4.6 6.77..7 5.94 7.78 Note: the aperture structure classification is the same as that of Table. Table 4: Experimental results of pore volume of coal samples obtained by liquid nitrogen adsorption method. Sample number Pore volume (ml/g) Pore volume ratio (%) V V V 4 V t V /V t V /V t V 4 /V t Number.57.4.64.78 6. 47.67 6. Number.4.9.679.69 4.7 48.5.8 Number.68.56.75.476 4. 4.97 5. Number 4..5.77.7487 6.9.4 5.9 Note:thesubscript 4 istheporevolumeofmicropore(nm Φ>nm)andothersare sameastable. Table 5: Experimental results of specific surface area of coal samples obtained by liquid nitrogen adsorption method. Sample number Specific surface area of pore (m /g) Specific surface area ratio of pore (%) S S S 4 S t S /S t S /S t S 4 /S t Number.66.449.77.89.49.7 7.78 Number.6.76.7.46 5.4.8 6.95 Number.58.77.457.87.5 6.84 9.65 Number 4..4 5.69 5.6.57 7. 9. Note: the aperture structure classification is the same as that of Table 4. Table 6: Calculation results of fractal dimension of coal sample pore distribution obtained using mercury intrusion method. Sample number Aperture range (nm) Linear fitting equations of different aperture segments R K D < r 5757. y =.8x.46.9696.8.869 Number r y =.6854x +.9.844.6854.46 r y =.4755x.78.95.4755.545 r< y 4 =.798x.97.688 / / < r 5757. y =.775x +.88.959.775.95 Number r y =.49x +.844.96.49.588 r y =.89x.467.84.89.67 r< y 4 =.885x.6979.6 / / < r 5757. y =.5x.45.9694.5.7748 Number r y =.7697x.6.89.7697. r y =.46x.57.89.46.7584 r< y 4 =.49x.65.44 / / < r 5757. y =.69x.585.9676.69.76 Number 4 r y =.6457x.447.746.54.54 r y =.7x.8.86 / / r< y 4 =.569x.776.76 / / Note: the R iscoefficientofcorrelation,the K isslope,andthe D is fractal dimension of pore volume (mercury intrusion method).

4 The Scientific World Journal log[dvp(r)/dp(r)] 4 4 y # y log[p(r)] y y4 log[dvp(r)/dp(r)] 4 4 y # y log[p(r)] y y4 Aperture range: < r 5757. nm Aperture range: r nm Aperture range: r nm Aperture range: r<nm Aperture range: < r 5757. nm Aperture range: r nm Aperture range: r nm Aperture range: r<nm (a) Number coal sample (b) Number coal sample log[dvp(r)/dp(r)] 4 4 y # log[p(r)] y y y 4 log[dvp(r)/dp(r)] 4 4 y 4# log[p(r)] y y y 4 Aperture range: < r 5757. nm Aperture range: r nm Aperture range: r nm Aperture range: r<nm Aperture range: < r 5757. nm Aperture range: r nm Aperture range: r nm Aperture range: r<nm (c) Number coal sample (d) Number 4 coal sample Figure : Statistical relationship between log[dv p(r) /dp(r)] and log[p(r)]. and log[p(r)] is significant; the correlation coefficients are all greaterthan74%,andthecoalporesintheporesegmenthave obviousfractalcharacteristics.whentheapertureissmaller than nm, the correlation between log[dv p(r) /dp(r)] and log[p(r)] is not significant; the correlation coefficients are all smallerthan5%,andthecoalporesintheporesegmentdo not have fractal characteristics... Fractal Dimension of Coal Pore Calculated Using Liquid Nitrogen Adsorption Method. From the principle of the calculation of fractal dimensions of coal pores using the liquid nitrogen adsorption method [5, 6], we can obtain the following formula: Ln ( V )=C+(D V )[Ln [Ln ( P )]], () m P where V is the total pore volume under given pressure (equal to the adsorption volume); V m is the adsorption capacity; D is the fractal dimension of pore volume (liquid nitrogen adsorption method); P is the adsorption pressure, MPa; P is the maximum adsorption pressure, MPa; and C is the constant. The diagram of the statistical relationship between Ln V and Ln[Ln(P /P)] of the four coal samples can be drawn according to the original data from the liquid nitrogen adsorption experiment (see Figure ). According to Figure, we can calculate the fractal dimension of coal sample pore distribution using the liquid nitrogen adsorption method (Table 7).The results show that,when theaperturerangeisbetween.nmand6.4nm,the correlation between Ln V and Ln[Ln(P /P)] is significant; the correlation coefficients of the four coal samples are all greaterthan96%,andthecoalporeshaveobviousfractal characteristics. However, when bounded by apertures of nm and nm, the calculated fractal dimensions are different..4. Comprehensive Fractal Dimensions of Coal Pores. Coal is a kind of porous solid, and its surface is inhomogeneous. Quantitative description and characterization can be conducted for the complex structure of a porous solid surface and energy inhomogeneity by introducing fractal dimensions to the research of porous materials. Almost all the solids with highly specific surface area have a fractal dimension between and. The closer to the fractal dimension is, the smoother

The Scientific World Journal 5 ln V ln V. #.5. y.5 y..5 6 5 4 y ln[ln(p /P)] Aperture range: d 6.6 nm Aperture range: d nm Aperture range:. d < nm (a) Number coal sample. #.9 y.8 y.7.6 y.5 6 5 4 ln[ln(p /P)] Aperture range: d 48. nm Aperture range: d < nm Aperture range:.5 d < nm (c) Number coal sample ln V ln V. #.5. y.5. y y.5 y. 6 5 4 ln[ln(p /P)] Aperture range: d 6.4 nm Aperture range: d < nm Aperture range:. d < nm (b) Number coal sample. 4#.5. y.5 y. 6 5 4 ln[ln(p /P)] Aperture range: d 8.64 nm Aperture range: d nm Aperture range:. d < nm (d) Number 4 coal sample Figure : Statistical relationship between Ln V and Ln[Ln(P /P)]. thesurfaceis;whiletheclosertothefractaldimensionis,the rougher the surface is [7 ]. The above-mentioned analyses show that the fractal dimension of coal has important links with its complex pore structure and nonuniform surface area. Hereby,weusedaweightedaverageinaccordancewith a specific surface area ratio for the corresponding fractal dimensions of different aperture distribution segments of coal, calling it the comprehensive fractal dimension of coal, and denoted it by D Z. Its calculation formula is as follows: D Z = D i b i, (4) where D Z is the comprehensive fractal dimension of coal; D i is the corresponding fractal dimension of ith aperture distribution segment; b i is the specific surface area ratio of the corresponding pore of ith aperture distribution segment; and i is the ith aperture distribution segment, being the positive integer. The pore parameters of macropores, mesopores, and transition pores in the coal can be measured by the mercury intrusion method, while the pore parameters of partial mesopores, all transition pores, and micropores in the coal can be measuredbytheliquidnitrogenadsorptionmethod[, ]. By comparing the data in Tables 6 and 7,whenwecalculated the fractal dimensions of transition pores, the precision of the liquid nitrogen adsorption method was higher than that of the mercury intrusion method (the correlation coefficients of the former are all greater than those of the latter). Therefore, when the aperture d was greater than nm, we used the mercury intrusion method to calculate the fractal dimension; when the aperture d was greater than nm and less than orequaltonm,weusedtheliquidnitrogenadsorption methodtocalculatefractaldimension;finally,weuseda weighted average for the fractal dimensions obtained so as to arrive at the comprehensive fractal dimension. The results are shown in Table 8. 4. Conclusions () The results of calculating the fractal dimension of coal using the mercury intrusion method show the following: when the aperture of lignite, gas coal, and coking coal is greater than or equal to nm, the coal pores in the pore segment have obvious fractal characteristics;whentheapertureissmallerthan nm, the coal pores in the pore segment do not have fractal characteristics; when the aperture of anthracite isgreaterthanorequaltonm,thecoalporesin the pore segment have obvious fractal characteristics; and when the aperture is smaller than nm, the

6 The Scientific World Journal Table 7: Calculation results of fractal dimension of coal sample pore distribution obtained by liquid nitrogen adsorption method. Sample number Aperture range (nm) Linear fitting equations of different aperture segments R K D d 6.6 y =.5x.77.9878.5.7499 Number d < y =.98x.987.9994.98.66. d < y =.6x.59.9977.6.668 d 6.4 y =.548x.596.9969.548.745 Number d < y =.447x.85.9997.447.557. d < y =.65x.4884.996.65.685 d 48. y =.8x +.589.957.8.978 Number d < y =.77x +.579.998.77.98.5 d < y =.757x +.57.997.757.94 d 8.64 y =.45x +.44.9.45.5785 Number 4 d < y =.8x +.656.9956.8.887. d < y =.48x +.8.9999.48.858 Note: the R iscoefficientofcorrelation,the K isslope,andthe D is fractal dimension of pore volume (liquid nitrogen adsorption method). Table 8: Calculation results of comprehensive fractal dimension of pore distribution of coal. Sample number Aperture range (nm) D i Specific surface area (m /g) Specific surface area ratio (%) D z d >.869.4. Number r.46.95 4.94 r.668.449..655. d <.66.77 7.5 d >.95.9.77 Number r.588.8 6.89 r.685.76.97.58. d <.557.7 6.7 d >.7748.5.4 Number r..9.5 r.94.77 6.85.99. d <.98.457 9.76 d >.76.. Number 4 r.54.7. r.858.4 7.4.8. d <.887 5.69 9.4 Note: the D i is corresponding fractal dimension of ith aperture distribution segment and the D z is comprehensive fractal dimension of coal. coal pores in the pore segment do not have fractal characteristics. () The results of calculating the fractal dimension of coal using the liquid nitrogen adsorption method show that, when the aperture range is between. nm and 6.4 nm, the coal pores have obvious fractal characteristics. However, when bounded by apertures of nm and nm, the calculated fractal dimensions are different. () We defined and calculated the comprehensive fractal dimensions of coal pores, introduced them to the research field of the nonuniformity of coal, achieved theeffectiveunityofthefractaldimensionsforfull apertures of coal pores, and perfected the fractal research of coal pores, thereby facilitating the characterization for the nonuniformity of coal. Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper. Acknowledgments This study is funded by the National Natural Science Foundations of China (no. 46), the Project of Henan Provincial Science and Technology Program (no. 44 and no. 4);andtheOpenProjectofStateKeyLaboratory Cultivation Base for Gas Geology and Gas control (no. WSB8).

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