Fractal classification and natural classification of coal pore structure based on migration of coal

ARTICLESJu. Y, Wang. G, Jiang. B, Microcosmic analysis of ductile shear- Chinese Science Bulletin 2005 Vol.50 Supp66-71ing zones of coal seams of brittle deformation domain in superfi- Fractal classification andcial lithosphere, Science in China, Ser. D, 2003, 34(5): 393-413. Zhang. H. Wang. X, Microstructures of coal and their reservoir natural classification of coalproperty, Coal Geology and Exploration (in Chinese), 1998, 27(10):43-46pore structure based on14. Li,H, Major and minor structural features of a beding shear migration of coal bed methanezone along a coal seam and related gas outburst, Pingdingshancoalfield, northerm China, Intermational Journal of Coal Geology, FU Xuehai, QIN Yong, ZHANG Wanhong2001,47(2:101-113WEI Chongtao& ZHOU Rongfu15. Zhou, J, Wang, G, Shao, Z, High temperature and high pressure College of Mineral Resource and Earth science, China University ofexperimental studies of coals, Journal of China Coal Society(inMining and Technology, Xuzhou 221008, ChinaCorrespondence should be addressed to Fu Xuehai(email: fuxuehai@Chinese),1994,19(3):324-33216. Jiang, B, Qin, Y, Jin. F, Coal deformation test under high tem- Abstract According to the data of 146 coal samplesperature and confining, Journal of China Coal Society(in Chinese), measured by mercury penetration, coal pores are classified1997,22(1):80-84.into two levels of <65 nm diffusion pore and >65 nm seeppore by fractal method based on the characteristics of diffuJin,F, Qin,Y, Coal deformation test under high temperature and sion, seepage of coal bed methane( CBM) and on the researchconfining pressure, Coal Geology and Exploration (in Chinese), results of specific pore volume and pore structure. The diffu1999,27(1):13-16sion pores are further divided into three categories: <8 nimicropore,8-20 nm transitional pore, and 20-65 nm mini-18. Tullis, J, Yund, R. A, Transition from cataclastic flow to dislocpore based on the relationship between increment of specifiction creep of feldspar: mechanisms and microstructures, 1987, surface area and diameter of pores, while seepage pores arGeol,15(7):606-609further divided into three categories: 65--325 nm mesopore,325-1000 nm transitional pore, and >1000 nm macropore19.Urai,J. L, Means, W.D., Lister, GS, Dynamic recrysallization based on the abrupt change in the increment of specific poreof minerals, Minearl and rock Deformation: Laboratory Studies: volume.The Paterson Volume, Geophysical Monograph, 1986, 36: Keywords: coal pore structure, fractal classification, coal bed meth20. Liu J. Walter, J, Weber, K, Fluid-enhanced low temperature plas-DoI:10.1360/98zk0009ticity of calcite rocks: microstructures and mechanisms, Geology,Coal is an anisotropic porous medium; its pore-struc2002,30(9):7787-790.re is closely related to the absorbability and flowability21. Passchier, C. W, Trouw, R. A. J, Microtectonics, Berlin: of coal bed methane(CBM). The distribution of poreSpringer-Verlag, 1965, 1-283diameters of coal is the foundation for the study of CBM22. Poirier, J.P, Creep of Crystals, Cambridge: Cambridge Univer- including its occurrence, mutual interaction among gas,sity Press, 1995, 1-260water and coal matrix, and desorption, diffusion, and23. Wong, T F, David, C, Zhu, W. L. The transition from brittle seepagePores are found in coals from nm grade to mm gradefaulting to cataclastic flow in porous sandstones: mechanical de. We cannot describe quantitatively the special characterisformation,JGR,1997,102(B2:30093025tic even by electron microscopy, densimetry, mercury24. Lloyd, G.E., Knipe, RJ., Deformation mechanisms accommodat- penetration method, and adsorption method distributioning faulting of quartzite under crustal conditions, Journal of But the introduction of fractal mathematics has offeredStructural Geology, 1992, 14(1): 127-143chance for solving such a problem25. Zhu, Z, Structural Geology (in Chinese), Beijing: GeologicalAiming at different purposes and based on differentaccuracies. scholars both at home and abroad have carriedPublishing House, 2003, 1-262out a large amount of researches on classification of poreWang,G,Zhu,Y, On flow of coal bed, Journal of China Univer- diameters of coal. In China, the most widely used classisity of Mining and Technology(in Chinese), 1988. (3): 16-25D. Deformation某化二中国煤ccimal system classificamorphism of bituminous and anthracite coals from China, Interna- PoCNMH Gational Theory and Ap-tional Journal of Coal Geology, 2000, 43(1-4): 227-242.plicssoclauonare commonly seen in someReceived Mach 15, 2005; accepted June 16, 2005) In addition, Qin et al made some research on the naturalChinese Science Bulletin Vol 50 Supp. December 2005ARTICLESclassification about pore structure of high rankto crystal, have a fractal characteristic3. The spongehe diameters distribution of coal has a wide range structure idea put forward by Menger can be used fwith more than 6 grades. Considering that the above-men- simulating the characteristics of pores in coal 4l. Let ationed classification is full of artificial factors, this paper cube with a side length of r be the initial element andwill discuss the fractal classification and natural classifi- partition it into m small cubes with the same size. Takesome of the small cubes out according to a certain rule1 Flowing characteristics of CBMThen the number of the left small cubes is Nbl. By repeat-ing this operation, the size of the left cubes becomesYang et al. thought that the flow of CBM in coal obeys smaller and smaller while their number becomes largerthe Fick diffusion law. With the help of digital solution of and larger. After K times of repeated operation, the sideCBM for coal fragment and proposed a concept of limit length of the left cube is n=R/m, and the sum is N=N,theat-conduction equation, they set up a diffusion model ofsize in diffusion process.. Zhou et al. pointed out that orthe flow of CBM in coal basically obeys the Darcylaw'9-.According to the Darcy law and with the help ofsimilarity theory, they advanced a seeping model of CBMand thought that it was feasible to use Darcy law inThe overall volume istudying the flow mechanism of CBM. However, recentlysome scholars have found that, in many cases, the flow ofCBM does not abide by this law. They noticed that=Npermeability coefficient of CBM in its flowing processchanges with the diameters of the pore. This means that In formula (1), D= log(Nb1)log(m)is called the num-the diffusion and seeping of CBM is a continuous process ber of volumnal fractal dimension of poreswhere there exists a combined action-multi-level diffuFrom formula(2)we have the volume of coal poression and multi-level seeping. It is this combined action Voc ri. Thenthat determines the flow velocity of CBMWhen the pore diameter is larger than the average freepath of methane molecule, the seeping of methane willtake place in pores. With an increase in diameter, the stable laminar flow. violent laminar flow. and turbulent flow 2.2 Samples and mercury penetrationmay occur. When the diameter is smaller than the average Samples were collected from 146 coal mines in Chinafree path of methane molecule, the methane will be dif- they are mainly the C-P coals and a few Jurassic ones. Thefused in pores. With a decrease in diameter, the Knudsenvitrinite reflectance Ro.max is between 0.43% and 8.61%.diffusion, surface diffusion, and solid diffusion may oc- Coal ranks are from lignite to anthracite, and genetic typcur2( Fig. 1)is humic coal. Theury penetration device of 93102 Fractal classification of pore radiusype made by micromeritics Instrument Co (USA)was2.1 Theoretical basisused, whose highest measurable pressure is 206 MPa andthe lower limit of measurable diameter is 7.2 nmSince the fractal concept was put forward by mandelIn order to eliminate the influence of micropores, min-bort in 1975, the fractal geometry has been used to study eral lingot pores, and corrosion pores on the test result, wesome objects possessing similarity but no characteristic concentrate on pores of 7 2-5000 nm, which are mainlylength, and has become a powerful tool for describing the pores evolved from maceral, such as retained strucirregular objects. Many researches show that both pore ture pores of plants, intercrystalline pores, intergranulargeometry and particle geometry of materials, from atomic pores, gas pores, and so on中国煤化工10000Solid diffuSurface diffusion Kundsen Diffusionilent flowore diameter/nmCNMHGFig. 1. Flowing characteristic of methane in coal poresChinese Science Bulletin Vol 50 Supp. December 2005ARTICLES2.3 Fractal calculationSubstituting(6)into(3), we haveIn the test process, the mercury can only be pressed intodVP(r)/dP(r)o[r/P(r)]r2-Dhe micro-fractures. Only under a high pressure, can themercury be pressed into pores in coal. In order to over- substituting(5)into(7), we havecome the internal surface tension between mercuryavery/dP(r)∝solid, a pressure P(r) must be applied before the(with a diameter r) is filled by mercury. For a cylin-via a logarithm operation to the two sides of formula(8),der-shaped pore, the relation between P(r)and r meet the we havewell-known Washburn equationP(r)=(-28cs6)/r,log[dVp(ydP(r)]oc(4-Db)logro(Db-4)logP(r).(9)where P(r) is the pressure applied, MPa; r is the radius ofBased on graphical construction according to log[dVp)/pores, nm; is the surface tension of mercury, N/cm eis dP(n)l and logp(r)(dvpo is the volume increment ofthe contact angle of mercury with the solid surface(0= pores corresponding to the increment of pressure dP(r))140°we can get the slope k(]ig. 2), which is Db-4 =k, and soSolving formula(4), we havethe voluminal fractal dimension isP(r)xr=7500orP(r)=7500.(10In the experiment, the overall volume of pores under a 2.4 Fractal classificationgiven pressure equals the volume of mercury injected into Inthe pores, expressed as dvk=dvp).logP(r) in the interval of 0.9-1.3(corresponding to theDifferentiating both sides of formula(5), we haveradius of pores of 54--85 nm), which means the radius inP(r)dr+rdP(r=0this interval has discontinuity points. These discontinuitypoints are distributed in stages(Fig. 3). They are 54, 66,Dr=-r/P(r)]dP(r)(6)accordance with the result by Zhao et al. pch is in goodand 85 nm or so, averaged by 65 nm, why=1.2164x+0.0952y-1.1148x+0.1203-121840%R=2.87%1.52logI P(r)MPalog[P(r)/MPa-12948x00106=-1.0649-2.285产099要,Rm165%Rm0.50%2.51.5-0.50.51.52.5中国煤化工25gP(r)/MPaCNMHGFig. 2. Relations between log[dVpin /dP(r)] and log P(r)Chinese Science Bulletin Vol 50 Supp. December 2005ARTICLESCBM. So, the diffusion pores can be classified into micro-pore(<8 nm), transitional pore(8-20 nm), and mini-pore。:(20-65 nm). The micro-pores are dominated by surfacediffusion, while the mini-pores are mainly by Knudsenrt3.2 Seeping poresThe average special pore volume of >65 nm poresounts for 97.02% of the total, while their special surfacearea accounts for only 13.9%(Table 2). These pores are0005101.5202.5303.5404.550one of the main channels for the seepage of CBM. In theR。m、(%)research on diameter distribution of pores, the correlationFig 3. Relations between discontinuity points and ro maxbetween diameter and inrement of special pore volumeshould be investigated. The analysis shows that the specialpore volume increment(dv or dv/dD)of all samples deCoincidently, the radius of coal pores leading to fractal creases periodically with the increasing radius, indicatingiscontinuity points are approximately in accordance with that the radius structure of pores is distributed periodicallythe average free path of molecules of CBM (Table 1). Generally, the relation of dS/dD and D of most samplesBased on the characteristics of diffusion and seepage as has two abrupt points and there exists certain differencewell as average path of molecules of CBM, the pores anbetween different ranks of coal (Table 3). All the samplesdivided into seeping pore(>65 nm) and diffusion pore have one thing in common; that is, the special pore vol-(<65nm)ume of pores, whose radii are 325 nm and 1000 nm, has abench-like decrease(Fig. 5). Because 325 and 1000 nmTable I The diameter and average free path of molecules of CBM are respectively 5 and 18 times of the average free path of(20℃,0.101325MPa)CBM, the seeping pores can be divided into mesoporeGas molecules(65-325 nm), transitional pore(325-1000 nm),and033Average free path/nm83.974.6macro-pore(>1000 nm)and the flowing of CBM can bedivided correspondingly into stable laminar flow, violentlaminar flow. and turbulent flow3 Natural classification of coal pores3.1 Diffusion pores3.3 Classification of radius structureBased on the above-mentioned fractal characteristicsa the average special pore volume of pores whose radius the regularity of pore radius leading to abrupt points ofsmaller than <65 nm accounts for only 2.98 of the special surface increment of diffusion pores and specialtotal volume of tested pores. However, their special sur-face area accounts for 86.2%(Table 2). In the research on pore volume increment of seeping pores, and the relationdistribution of pore diameter, the relation between incre-between radius and diffusion and seepage of CBM, thecoal pores are divided into two levels and 6 categoriesment of special surface area and pore diameters should beinvestigated. The result shows that the ratio(ds or dS/dD)of increment of special surface area and diameter of allTable 4 shows that, for those micro-pores(<8 nm),samples increases periodically with the decrease in poreCBM is characterized by surface diffusion, for the transidiameter, indicating that the diameter structure of pores istional pores(8-20 nm) it is characterized by mixed dif-distributed periodically. Generally, the relation of dS/dDfusion(surface diffusion and Kundsen diffusion), and forand D of most samples has two abrupt points and there the minl-pores(20-65), it is dominated by Kundsen difexists a certain difference between different ranks of coal fusion. In addition, for those mesopores(65-325 nm)(Table 3). All the samples have one thing in common; that the flowing of CBM obeys the Darcy law and hence itis, the special surface area decreases for those pores whose appears as a stable laminar flow, for those transitionalradius is 8 and 20 nm(Fig. 4).8 and 20 nm one seventh pores (325-1000 nm), it appears as a violent laminarand one third, respectively, of the average free path of flow, and for the macro-pores(>1000 nm), it appears as aTable 2 Percentages of specific volume(V), specific surface area(S)of different pore radiDiffusion pores20-65nm中国煤化工>1000nmCNMHG0.465123Chinese Science Bulletin Vol 50 Supp. December 2005ARTICLES10000Am38%R。mx=2.29%iEsxS310000Rm=159%0.65%1000100D/nmFig 4. Increment distribution curves of specific surface area of diffusion pores.1000010000R0m=423%R0m=213%10000100100001000000D/nmD/nm10000R0=、=187%co100010100010000中国煤化工1000CNMHGFig. 5. Distribution curves of special pore volume increment of seeping poresChinese Science Bulletin Vol 50 Supp. December 2005ARTICLESTable 3 Average radius of abrupt points of different ranks of coal_ReferencesAverage radius ofR(%6) Sample abrupt rAverage radius of1. Meyers, R. A, Coal Structure, New York: Academic Press, 1982,ecific surfaceabrupt points forarea/nmspecific volume/nm2. Rodrigues, C. F, Lenos, M. J, The measurement of coal porosity20-3.534with different gases, Intermational Journal of Coal Geology, 2002,1.0-2.03217<1.077897848(3-4):245-2813. Hodot, B. B, Outburst of Coal and Gas( Chinese Translation)Table 4 Classification of coal pores based on migration characteristicsLevel Classification Radius/nm Flow characteristic4. Gan, H, Nandi, S. P, Walker, P. Nature of the porosity inMicro-poreSurface diffusionAmerican coals, Fuel, 1972, 51(6): 272-277diffusion Transitional pore 8-20Kundsen diffusion5. Walker, P. L, Densities, porosities and surface area of coal macer-65~ble laminar fowals as measured by their interaction with gases, vapours and liq-seepage Transitional pore 325-1000 Violent laminar flowuids.Fuel,l988,67(10:815-823Macro-pore>100Turbulent flow6. Qin Yong, Xu Zhiwei, Zhang Jing, Natural classification of thehigh-rank coal pore structure and its application, Journal of Chinaturbulent flowCoal Society,1995,203):266-271.4 Conclusion7. Yang Qiluan, Wang Youan, Diffusion theory of gas in coal bed andThe mercury penetration can only measure those poreswhose diameters are greater than 7. 2 nm. The mm-levelits application, Journal of China Coal Society, 1986, 11(3): 87pores measured under a low pressure include most micro-fractures. If these fractures are simplified into cylin8. Yang Qiluan, Testing research on gas diffusion rule of coal scraps,drical pores and then calculated by Washburn equation, itwill lead to a big error. Pores smaller than 7. 2 nm occupyf China Coal Mine Security, 1987, (2): 9-16.a large percentage, forming a adsorption space for CBMShining, Sun Jizheng, Flow theory of gas in coal beds anThe diameter distribution of these pores has a certainits application, Journal of China Coal Society, 1965, 2(1): 24-3regularity(especially the molecule structured pores). Sopores smaller than 7. 2 nm do not possess the fractal fea-10. Zhou Shining, Application of computer in research of gas flowture, indicating the existence of a lower limit of observaons, Journal of China Coal Society, 1983, (2): 29-35tion measurement in fractal researches11. Zhou Shining, Flow mechanism of gas in coal beds, Joumal ofBased on the fractal study of pores from 7. 2 to 5000 nnChina Coal Society, 1990, 15(1): 15-24and on the diffusion and seeping characteristic of CBMthe pores are divided by 65 nm into diffusion pores(65 12. He Xueqiu, Liu Minju, Fracture Electro-magnetic Dynamics ofnm) and seeping pores(65 nm), of which the <65 nmCoal or Rock Containing Gas, Xuzhou: China University of Minpores form the adsorption and diffusion field of CBMing Technology Press, 1995, 147-151while the >65nm pores form seeping passages of CBM. Inaddition, based on the relation of special surface area in13. Xie Heping, Fractal-Guide of Rock Mechanics, Beijing, Sciencecrement and each pore radius, the diffusion pores are di-Press,1996,93-123.vided into micro-pore(<8 nm), transitional pore(8-20 14. Friesen, w 1. Mikule, R J. fractal dimensions of Coal Partinm), and mini-pore (20 nm). Based on the relation ofcles, Journal of Colloid and Interface Science, 1987, 20(1): 263pecial pore volume increment and each pore radius, theseeping pores are divided into mesopore(65-325 nm),transitional pore( 325-1000 nm), and macro-pore(>1000 15. Zhao Aihong, Liao Yi, Tang Xiuyi, Quantitative analysis of coalnm)structure by fractal analysis, Journal of China Coal Society. 1998Jun, Fu Jianqiu, Chen Xinhua, Xiao Weiguo, Yao Pu, Zhao Muhua, andWu Di. at China University of Mining afor their中国煤化工 mics(I)( Chinese transpation in the research. This work wasthe nationPress,1984.9-1lBasic Developing Project of China(200and theHCNMHGNatural Science Foundation of China( Grant No. 40372074)(Received March 15, 2005; accepted June 16, 2005)Chinese Science Bulletin Vol 50 Supp. Dr2005